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= 2 again occupy regions of higher Θ∼ values than those of Eθ/Er |
= 0.5 do, and the sizes of instability regions for Eθ/Er |
= 2 are smaller. In addition, (a)–(f) again reveal that the primary instability regions are all larger than the secondary instability regions, another tendency consistent with results displayed in The widths of the primary and secondary instability regions ΔΘ∼ versus rotational speeds Ω∼ are plotted in , where the instability regions are calculated while Ko and Kt are kept unchanged and Ω∼ ranges from 0 to 10. Due to the contributions of the geometry stiffness induced by rotation, the width ΔΘ∼ decreases as the rotational speed Ω∼ increases. In addition, it is observed that the plate with the higher orthotropic ratio Eθ/Er has smaller ΔΘ∼, i.e., the plate of a higher orthotropic ratio Eθ/Er is more stable as revealed in where results obtained for Ω∼=0, 1, and 2 are displayed.The width of the primary instability region ΔΘ∼ versus the inner radius ξ˜ is plotted in , where the outer radius is kept constant and Ω∼=0, 1, and 2. It is observed that ΔΘ∼ increases as the inner radius ξ˜ becomes larger, but ΔΘ∼ decreases as rotational speed Ω∼ increases. In addition, reveals that curves of a higher Eθ/Er value appear steeper, i.e., effects by changes in ξ˜ are more significant for the plate of higher Eθ/Er value. Since increasing ξ˜ reduces the value of b˜ making the plate stiffer, it is expected that increasing ξ˜ makes the plate less stable, which is consistent with the above observation that ΔΘ∼ increases with ξ˜.The width of the primary instability regions ΔΘ∼ versus the core layer thickness h˜2 are shown in , where Ω∼=0, 1, and 2, and Eθ/Er |
= 0.5 and 2. It is observed that increasing thickness of the viscoelastic core layer results in a wider instability region, i.e., a larger value of ΔΘ∼. In addition, a lower modulus ratio also results in a wider instability region. Besides, it is also observed that a higher rotational speed makes the instability region narrower. Increasing h˜2 makes the plate stiffer. Therefore, increasing h˜2 is expected to result in a less stable plate, which is consistent with the above observation that ΔΘ∼ increases with h˜2.The width of the primary instability region ΔΘ∼ versus the non-dimensional modulus of the viscoelastic core E∼2 is shown in , where Ω∼=0, 1, and 2, and Eθ/Er |
= 0.5 and 2. It is observed that increasing E∼2 first reduces the instability region which reaches a minimum before it increases, i.e., the value of ΔΘ∼ decreases to a minimum before it increases. It is known that increasing E∼2 increases both stiffness and shear effects. When the value of E∼2 is small, the effects of stiffness increase is obscured by the increase of shear effects. As a consequence, the plate becomes more stable by increasing E∼2 when it is small. As the value of E∼2 increases, the influence of increase in shear effects becomes more and more saturated until the effects of stiffness increase becomes relevant. Therefore, as the value of E∼2 increases, stability of the plate increases first and reaches a maximum before the stability reduces. The same phenomenon was also reported by Wang and Chen The parametric resonance of a rotating axisymmetric polar orthotropic sandwich annular plates with damping viscoelastic core layer has been studied. A discrete layer annular finite element and Bolotin’s method were employed in the present analysis. The following conclusions are drawn from numerical results reported in the previous section.The effects of the dynamic in-plane loading Kt and static in-plane loading Ko on the dynamic instability are more apparent for lower modulus ratio Eθ/Er.The higher the orthotropic ratio Eθ/Er is, the smaller the instability regions. The damping effects increase as thicknesses b˜ and/or orthotropic ratio Eθ/Er increase.Raising the orthotropic ratio Eθ/Er increases the static critical buckling load of the plate. In addition, increasing the plate rotational speed results in an increased static buckling load, and the width of instability region decreases when the rotational speed increases.A larger inner radius ξ˜ of the annular plate results in a wider instability region.The width of instability region is significantly affected by the core thickness.Increasing the value of E∼2 first reduces the instability region. Keep on increasing the value of E∼2 makes the instability region reaches a minimum. Then, the system becomes less stable if the value of E∼2 is further increased.Optimization of intrinsic and extrinsic tendon healing through controllable water-soluble mitomycin-C release from electrospun fibers by mediating adhesion-related gene expressionTo balance intrinsic and extrinsic healing during tendon repair is challenging in tendon surgery. We hypothesized that by mediating apoptotic gene and collagen synthesis of exogenous fibroblasts, the adhesion formation induced by extrinsic healing could be inhibited. With the maintenance of intrinsic healing, the tendon could be healed with proper function with no adhesion. In this study, we loaded hydrophilic mitomycin-C (MMC) into hyaluronan (HA) hydrosols, which were then encapsulated in poly(L-lactic acid) (PLLA) fibers by micro-sol electrospinning. This strategy successfully provided a controlled release of MMC to inhibit adhesion formations with no detrimental effect on intrinsic healing. We found that micro-sol electrospinning was an effective and facile approach to incorporate and control hydrophilic drug release from hydrophobic polyester fibers. MMC exhibited an initially rapid, and gradually steadier release during 40 days, and the release rates could be tuned by its concentration. In vitro studies revealed that low concentrations of MMC could inhibit fibroblast adhesion and proliferation. When lacerate tendons were healed using the MMC-HA loaded PLLA fibers in vivo, they exhibited comparable mechanical strength to the naturally healed tendons but with no significant presence of adhesion formation. We further identified the up-regulation of apoptotic protein Bax expression and down-regulation of proteins Bcl2, collage I, collagen III and α-SMA during the healing process associated with minimum adhesion formations. This approach presented here leverages new advances in drug delivery and nanotechnology and offers a promising strategy to balance intrinsic and extrinsic tendon healing through modulating genes associated with fibroblast apoptosis and collagen synthesis.Adhesion formation during tendon healing may cause difficult joint movement and is a major clinical complication. With improvements in surgical techniques and post-operative mobilization, tendon adhesions after tendon repair have been decreased, but the problem has not been solved completely. Many different approaches have been tried to prevent adhesion formation. Physical barriers with biochemical drugs are the main approaches to reduce adhesions To prevent the adhesion formation successfully, we first need to understand the mechanism of tendon healing and adhesion formation. As reported, there are two types of tendon healing: intrinsic and extrinsic. Intrinsic healing is developed by the proliferation and migration of tenocytes from the epitenon and endotenon into the injury site whereas extrinsic healing is achieved by invasion of cells from the surrounding sheath and synovium Mitomycin-C (MMC), an anti-tumor agent, has demonstrated its capability to prevent post-operative adhesion formation by inhibiting fibroblast proliferation and inducing fibroblast apoptosis The use of MMC is, however, complicated with much acute and chronic toxicity. For example, significant local tissue damage may occur when it is used in local injections at high concentration, leading to increased scar tissue formation and even failure of wound healing Electrospinning offers great flexibility for drug delivery applications -lactic acid) (PLLA) is a well-known biodegradable and biocompatible polymer. By varying its molecular weight, its degradation time in vivo can be tuned from weeks to months. However, due to the hydrophilic nature of MMC, it cannot be directly dissolved in organic solvents such as dichloromethane (DCM), leading to low drug encapsulation efficiency in the PLLA nano/microparticles. Hydrosol nanoparticles, where water is the dispersed phase and possesses high dispersion stability, may be obtained by ultrasonic dispersion and have been used as efficient drug carriers The aim of this project was therefore to develop a new and efficient micro-sol electrospinning technique to fabricate core–shell polymer fibers for controllable loading and release of hydrophilic MMC to achieve prevention of tendon adhesion formation with no detrimental effect on tendon healing (). In present study, the morphology, diameter, wettability and mechanical strength of the resultant electrospun fibers were first characterized. Release of MMC from the electrospun fibers was subsequently examined. In vitro fibroblast behaviors including viability, adhesion, proliferation and apoptosis on the MMC-loaded PLLA fibrous membranes were further evaluated and the in vivo tendon healing and formation of adhesion tissue were further investigated using rat Achilles and rabbit flexor digitorum profundus (FDP) tendon models. To understand the mechanism and to control the adhesion formation, expression of adhesion associated Bcl-2, Bax, collagen I, collagen Ⅲ and α-SMA in the adhesion tissues were finally determined.Fermentation-derived hyaluronan (HA, sodium salt, Mw = 0.5 MDa) without further purification was purchased from Yuancheng Technology Co. (Wuhan, China). PLLA (Mw = 100 kDa, Mw/Mn = 2.16) was obtained from Jinan Daigang Co. (Jinan, China). All other chemical reagents, unless otherwise stated, were purchased from GuoYao Regents Company (Shanghai, China). All tissue culture plastics (TCPs) were purchased from Nunc (Roskilde, Denmark). Dulbecco's modified Eagle's medium (DMEM), fetal bovine serum (FBS), trypsin and penicillin/streptomycin were purchased from Gibco (Gibco, Grand Island, NY). Collagen I was from Biorbyt, Cambridge, UK. Collagen III was from Abbiotec, San Diego, CA, USA. α-SMA, Bcl-2 and Bax were from Protein Tech Group, Wuhan, China. β-actin was from Abcam, Cambridge, MA, USA.First, 10 mg HA was dissolved in 990 mg distilled water to make 1 wt % HA hydrosols. Then, 10 mg and 40 mg MMC (Kyowa Hakko Kirin, China) were separately mixed into HA hydrosol. Afterwards, a solvent mixture containing 4 g DCM and 1% Span-80 (with respect to PLLA) was mixed with the drug-loaded HA hydrosol, and the mixture was stirred for 20 min to obtain uniform water-in-oil (W/O) emulsions containing micro-sol particles. At last, 2.0 g N, N-dimethylformamide (DMF) and 1.0 g PLLA were dissolved in the emulsion to obtain micro-sol electrospinning solution. The control PLLA solution was obtained by mixing and stirring 1.0 g PLLA, 4.0 g DCM and 2.0 g DMF.A 0.7 mm diameter needle was fitted to a 2.0 ml glass syringe and a syringe pump. The solutions with 1%, 4% (10 mg, 40 mg) MMC or without MMC were drawn into the syringe to prepare PLLA-MMC1, PLLA-MMC2 and PLLA membranes, respectively. The concentrations of 1 and 4% were optimized to achieve significant difference in the cell inhibition effect with no substantial cytotoxicity (cell viability <50%). A high-voltage power supply provided a 15–20 kV voltage difference between the needle tip and a collector (grounded aluminum foil). The electrostatic force drew the polymer solution from the needle tip to reach the collector that was placed 20 cm from the needle tip. The flow rate of the polymer solution was controlled at 0.06 ml/min. The fabricated fibrous membranes were dried overnight in a vacuum oven before further study.The size of HA micro-sol particles in the prepared emulsion was measured using dynamic light scattering (DLS, Zetasizer, Malvern, Nano-ZS90). The morphology of the membranes was observed by scanning electron microscopy (SEM, FEI Quanta 200, Eindhoven, Netherlands). Individual fiber's inner structure was examined by transmission electron microscopy (TEM, Hitachi HT7700) at 120 kV. The mean diameter was calculated by measuring at least 200 random fibers from 20 images with Photoshop 8.0. The wettability of different surfaces was determined using a sessile drop contact angle system with a goniometer (Krüss GmbH DSA 100 Mk 2). The water contact angles (WCAs) were measured after 10 s at 25 °C and calculated by image processing of sessile drop profiles with DSA 1.8 software. For mechanical tests, the test strips (15.0 × 3.0 × 0.2 mm3) of dry and wet (after immersion in water for 24 h) conditions were measured using a rheometer (Instron 5567, Norwood, MA). Load-deformation data was recorded at a stretching speed of 5 mm/min. The ultimate tensile strength was obtained from the stress–strain curves (n = 5).Loading efficiency of MMC into the PLLA-MMC membranes was measured by extracting the drug from the fiber samples. At first, a known weight of fibers (total mass = 20 mg) was completely dissolved in 1 ml of DCM. Then 4.0 ml phosphate-buffered saline (PBS, pH = 7.4) was added into the mixture to extract the supernatant. After many repeated extraction processes, all of the drugs in fibers were completely extracted. A known amount of MMC was added into a polymer solution of the same concentration and extracted as above, then, the extraction efficiency was measured by comparing the two results.50 mg of PLLA-MMC1 (1% MMC) and PLLA-MMC2 (4% MMC) fibrous membranes were immersed in 20 ml PBS. The suspensions placed in 50 ml centrifugal tubes were maintained in a thermostated shaker (Thermo, USA) at room temperature with 100 cycles/min. 5.0 ml release buffer was removed from the centrifugal tube and replaced with 5.0 ml fresh PBS at different time points. The quantity of released MMC from the PLLA-MMC fibrous membranes in the release buffer was measured by ultraviolet–visible spectrophotometry (UV-2550, Shimadzu, Japan) at 364 nm. To determine the concentration of the drug released, a standard calibration curve of MMC in the range of 0–350 μg/ml was used. Based on the initial weight of MMC incorporated into the electrospun fibrous membrane, the percentage of released drug from the membranes was calculated.NIH/3T3 fibroblasts were used to evaluate viability, adhesion, proliferation and apoptosis on PLLA and PLLA-MMC fibrous membranes. The cells were incubated in DMEM supplemented with 10% FBS, 100 U/ml penicillin and 100 U/ml streptomycin at 37 °C in a humidified atmosphere with 5% CO2. The culture medium was changed every 3 days. Cells were harvested with 0.25% trypsin when reaching 70% confluence. The electrospun membrane discs of 15 mm diameter and 200 μm thickness were placed into a 24-well plate and sterilized using 75% ethanol for 1.5 h. After repeated washes with PBS, cell suspensions were seeded onto the fibrous membrane surfaces at a density of 4 × 104 cells/cm2 and incubated in an incubator containing 5% CO2 at 37 °C for different time. TCPs were used as control.100 μl cell suspension (1 × 105 cells/ml) was seeded into each well and incubated for 1, 3 or 5 days. At different time points, Cell Counting Kit-8 (CCK-8, Dojindo, Japan) was mixed with culture medium at 10% of the volume and incubated with cells for 4 h. 200 μl of the solution was then transferred into a 96-well plate. Absorbance at 450 nm was measured using a spectrophotometer (Synergy 2, BioTek). Number of cells was calculated according to the standard number–absorbance curve of CCK-8 specification.Live/dead staining was used to determine the viability of cells on different surfaces by a Live/dead stain kit (Invitrogen, Eugene, OR). Cells were seeded onto the samples at a density of 4 × 104 cells/cm2 in each well of a 24-well plate. After 24 h of culture, cells were washed twice in PBS and stained with 2 μM calcein AM and 10 μM EthD-1 for 30 min in an incubator. Stained cells were observed under a confocal laser scanning microscope (Leica TCSSP2, Heidelberg, Germany). The live cells on the surface of the specimens were stained bright green with calcein AM, and the dead cells were stained red with EthD-1. Dead/live cell ratio on each surface was calculated as the number of dead cells divided by the number of live cells.Cells were seeded onto the samples at a density of 2 × 104 cells/cm2 in each well of a 24-well plate. After 24 h of culture, the cytoskeletal arrangements on fibrous membranes and TCPs were determined by actin staining. Firstly, samples with cells were washed three times with PBS and then fixed in 4% paraformaldehyde for 10 min. Secondly, they were washed repeatedly with PBS after removing the fixative, and permeabilized with 0.1% Triton X-100 (Sigma, USA) for 10 min. Then, samples were stained with 20 μg/ml of phalloidin (Cytoskeleton, U.S.) for 30 min and with 1 μg/ml DAPI (Sigma, USA) for 5 min at room temperature before imaging using a confocal laser scanning microscope. The average cell area on different surfaces was calculated as the total cell area divided by the number of cells measured using NIH image J software.A fluorescence-based TUNEL assay was used to detect DNA fragmentation and apoptosis of cells on different surfaces with in situ cell death detection kit (TUNEL, Roche Applied Science, Mannheim, Germany). Cell seeding was performed at density of 4 × 104 cells/cm2 in a 24-well plate. Following 24 h of culture, cells were washed twice in PBS and fixed for 30 min at 37 °C in 4% paraformaldehyde. PBS washing was conducted again followed by addition of 0.1% Trition X-100 on ice for 2-min permeabilization. After another PBS wash, cell staining was performed with TUNEL reaction mixture for 1 h. Cells were then counter-stained by 1 μmg/ml DAPI for 5 min at 37 °C before visualization using fluorescent microscope (Leica). TUNEL-stained fibroblast nuclei with fragmented DNA displayed bright green color whereas DAPI-stained nuclei exhibited blue color. The ratio of number of TUNEL-stained cells to number of DAPI-stained cells was calculated as the percentage of TUNEL-stained cells.All protocols of the animal study were approved by the institutional review committee of Shanghai Jiao Tong University, School of Medicine and the National Institutes of Health.By general anesthesia with intravenous injections of pentobarbital sodium (30 mg/kg body weight), the hind limbs of 72 male Sprague–Dawley rats (weighing 200–250 g) were sterilized for aseptic surgery. A 1.5 cm lateral incision was made and the distance between the transverse transection site of the Achilles tendon and the calcaneal bone was about 5 mm. This was followed by repair using modified Kessler technique with 6-0 prolene suture (Ethicon Ltd., Edinburgh, UK). Each animal was randomly placed in either the control group or one of the two experimental groups (n = 24 per group). The control group received no membrane around the repair site, while a 1 cm × 2 cm × 200 μm piece of PLLA or PLLA-MMC2 membrane was wrapped around the repair site for each of the experimental group. The operated leg was immobilized in a cast to control the movement of the talocrural joint after skin closure. The rats were sacrificed 21 days after the surgery.The rabbit FDP tendon model was chosen as the length of the tendon was appropriate for biomechanical analysis. By general anesthesia with intravenous injections of pentobarbital sodium (30 mg/kg body weight), the middle digit FDP tendons of 54 adult New Zealand white rabbits (weight range, 2.0–3.0 kg) were exposed on the lateral aspect of zone II after sterile skin preparation. The flexor tendon sheath and the flexor digitorum superficialis (FDS) tendon were removed. The FDP was subject to transverse incision followed by repair using modified Kessler technique using 6-0 prolene suture. Each animal was randomly placed in either the control group or one of the two experimental groups (n = 18 per group). For each group, the repair site of the tendon was treated as rat Achilles tendon model. The operated leg was immobilized in a cast after skin closure. The rabbits were sacrificed 21 days after the surgery.Before sacrificing the animals, any sign of inflammation or ulcer of the repaired site was examined. The long toe or hind limb was longitudinally incised through its whole length to expose the tendon. Based on the surgical findings, a score between 1 and 5 was assigned to each particular area in order to assess the severity of peritendinous adhesions To evaluate peritendinous adhesions and tendon healing, the work of flexion and maximal tensile strength, respectively, were determined using a rheometer (Instron 5548). The work of flexion represents the work necessary to overcome the resisting forces from the tendon sheath in rabbit FDP tendon model. A force gauge was used to fix the proximal end of the rabbit FDP tendon and a self-made device with its stainless steel rods-fixed distal interdigital joint was attached to the proximal phalanx of the toe. Tendon was pulled by the actuator at 10 mm/min until the range of proximal interdigital joint reached 40°. Mathematical integration was then conducted to calculate work of flexion. Then, for both animal models, nonslip clamps attached to the rheometer were used to fix both ends of the tendon. The tendon was again pulled at 10 mm/min by actuator, until the tendon achieved terminal rupture. In this case, the rheometer recorded the maximal tensile force.Adhesion tissues around the repair site of rat Achilles tendons in different groups were collected and homogenized in 200 μl of ice-cold RIPA (Bio-Rad, Hercules, USA) supplemented with 1 μl of 200 mM PMSF (Kang Chen Corp., Shanghai, China), respectively. The mixture was incubated on ice for 60 min and then centrifuged at 12,000 rpm for 10 min. The supernatant was collected and the protein concentrations of the supernatant were measured by the BCA protein assay kit (Thermo, Rockford, USA). The samples were electrophoresed through a 10% SDS-PAGE gel, and then transferred onto PVDF membrane (Millipore, Bedford, MA). After blocking with 5% non-fat milk, the membranes were incubated with antibodies against collagen I, collagen III, α-SMA, Bcl-2, Bax and β-actin overnight at 4 °C. After washing with PBS, the membranes were incubated with the secondary antibodies (Cell Signaling, Beverly, MA) for 1 h. The membranes were washed with PBS three times and scanned with an imaging system (Image Quant LAS 4000 mini, GE). The densitometry of bands was analyzed using Image Pro-plus 6.0 (Media Cybernetics, USA).All data were presented as mean ± standard deviation (SD). One-way ANOVA was performed to assess statistical difference using SPSS 10.0 software. Statistical significance was declared when p < 0.05.The DLS measurement indicated the size distribution of HA-micro-sol particles in DCM. It was found that the diameter of the particles was about 500 nm and the polydispersity index (PDI) was 0.314, indicating the uniformity of micro-sol particles. In addition, the particle size distribution remained unchanged within 2 h. Electrospun PLLA fibers and micro-sol electrospun PLLA-MMC fibers were successfully fabricated through the electrospinning method. SEM micrographs of PLLA and PLLA-MMC fibers (A) showed that the electrospun fibers of each membrane were bead-free, round and continuous. As shown in B, a core–shell structure with MMC-hydrosol inside and PLLA outside could be found in the PLLA-MMC fibers. The diameters of all samples showed uniform distributions (C). The diameters of PLLA, PLLA-MMC1 and PLLA-MMC2 fibers were 2.24 ± 0.35, 1.51 ± 0.51 and 1.78 ± 0.62 μm, respectively. In addition, the interior diameter of MMC-hydrosol in PLLA-MMC fibers increased with the increased MMC concentration from 0.46 to 0.59 μm.To determine the wettability of different membrane surfaces, the WCAs were observed as 132.4 ± 3.4, 129.6 ± 2.5 and 127.3 ± 3.1 degrees for PLLA, PLLA-MMC1 and PLLA-MMC2 fibers, respectively, and statistical analysis indicated no significant difference between the PLLA and PLLA-MMC fibrous membranes (p > 0.05).To determine the mechanical properties of different membranes, the strain-stress response was examined (see example in A). The results showed that the tensile strengths of the dry electrospun PLLA, PLLA-MMC1 and PLLA-MMC2 fibrous membranes were 3.92 ± 0.26, 3.52 ± 0.29 and 3.46 ± 0.21 MPa, respectively. Compared with PLLA membranes, there was a decrease of the maximum mechanical tensile strength on the PLLA-MMC fibrous membrane possibly due to the presence of HA cores. In addition, statistical analysis indicated no significant difference between the PLLA-MMC1 and PLLA-MMC2 fibrous membranes, suggesting that the addition of MMC had no significant effect on the mechanical properties of the PLLA-MMC fibrous membranes. Additionally, for the plain PLLA membrane, there was no significant difference in the mechanical properties before and after water immersion, possibly due to the hydrophobicity of the PLLA fibrous membrane as indicated by the results of water contact angles. The PLLA membranes with MMC had slightly reduced tensile strength (2.52 ± 0.51 MPa) after immersion in water possibly due to the water sorption in the presence of HA.MMC in the electrospun fibers before/after electrospinning and after release was shown to have the same absorbance peak at 364 nm, suggesting that the MMC before and after electrospinning and after release was not chemically modified. The loading efficiencies of MMC were 84.7% and 79.3% for PLLA-MMC1 and PLLA-MMC2, respectively. The cumulative release of MMC from the core–shell structured fibers of different PLLA-MMC membranes was shown in C. It was found that the MMC released from both PLLA-MMC fibers undertook a typical biphasic pattern: initial burst release, followed by a steadier and slower release. Percentages of MMC release from PLLA-MMC1 and PLLA-MMC2 membranes were 26% and 31% for the first two days (burst release), 45% and 65% for the subsequent 6 days (constant fast release) and almost complete for 40 days (reduced release), respectively. The initial burst release might be due to the diffusion from the core through the fibers. The MMC concentration gradient between the fiber core and the surface decreased along with MMC release, thus reducing the MMC release rates. As diffusion dominated the drug release, when the MMC content increased, the rate of drug release increased. Daily quantity of MMC released in vitro from the PLLA-MMC electrospun fibers was illustrated in D. The cumulative release of MMC from the PLLA-MMC membrane was calculated based on the daily release. Approximately 5.3 ± 0.3 μg and 23.6 ± 3.2 μg MMC were released in 20 days for PLLA-MMC1 and PLLA-MMC2, respectively. These data were used as references for in vivo investigations.In this report, in vitro biological evaluation of the drug-containing PLLA membranes was measured by cell viability, adhesion, proliferation and apoptosis. The cell viability assay indicated that cells could survive on all surfaces after 24 h of culture, with lowest survival rate on the surfaces of the PLLA-MMC2 membranes (A and C). Fewer live cells were found on the PLLA-MMC fibers compared to those on the naked fibers or TCPs (A). Furthermore, the number of dead cells on the PLLA-MMC fibers significantly increased with the increasing concentration of MMC (A and C). The ratio of dead/live cells on the different surfaces after 24 h of culture was shown in The cell filament staining observations showed that cells had normal cytoskeletal arrangement and largest cell area on TCPs compared with other surfaces, while cytoplasmic shrinkage and reduced cell area were observed on the PLLA and PLLA-MMC membranes, due to the hydrophobic nature of PLLA The proliferation of NIH/3T3 fibroblasts on the surface of PLLA fibers (with or without MMC) was compared after 1, 3, and 5 days of culture (E). The results showed that cells grew best on TCPs, while the number of cells was slightly less on the PLLA and least on the PLLA-MMC membranes, especially on the PLLA-MMC2 membranes. These results have suggested that the PLLA-MMC membranes could inhibit fibroblast proliferation effectively.Cellular apoptosis was detected on different surfaces by the TUNEL assay after 24 h of culture (). Apoptotic cells were stained by TUNEL in green while cell nuclei were stain by DAPI in blue. Few apoptotic cells were observed on TCPs, but increased number of apoptotic cells on the PLLA membranes was seen with the increase of MMC concentration (A). The percentage of apoptosis was the highest for cells on the PLLA-MMC2 membranes, and the amount of apoptotic cells out of the total number of cells was approximately 20% (To conclude, the in vitro cell behavior investigations indicated that the PLLA-MMC fibers inhibited the survival, adhesion and proliferation of fibroblasts and induced cell apoptosis as the MMC concentration increased. Based on the overall consideration of the physical and biological properties of the PLLA-MMC fibrous membranes, PLLA-MMC2 with higher MMC concentrations was chosen for the following animal study due to its enhanced fibroblast inhibition capability.Representative histological sections of the tendons in each group of both animal models were shown in C. In most specimens of the control group, there were severe fibrous tissue formations between the tendon and the surrounding granulation tissue. The repair sites of the PLLA-treated tendons were filled with loose bundles of fibrous tissue around the repaired tendon. It is worth noticing that, in the PLLA-MMC2 fibrous membrane group, fewest peritendinous adhesions were seen. Moreover, the PLLA-MMC2 group exhibited the optimal repair of the broken tendons. The control group showed adhesion tissues expanded into the broken ends with disorganized fiber alignment, which may hinder the tendon healing. In the PLLA group, fibers were moderately aligned, and the repaired tendon at the laceration site appeared tightly connected. In the PLLA-MMC group, the collagen fibers in the repaired tendon at the laceration site were aligned with a high degree of orientation although tiny cracks still existed (Adhesion scores of the PLLA-MMC2 group were significantly lower than those of the control group and the PLLA group (D). Similarly, the grades for the histological tendon adhesions were significantly lower in the PLLA-MMC2 fibrous membrane group than in the other two groups (The mechanical evaluation results have shown that the maximal tensile strength representing tendon healing was not significantly different among the three groups in both models (F). The work of flexion representing peritendinous adhesions in the rabbit FDP tendon model was significantly lower in the PLLA –MMC2 group than that in the control group and the PLLA group, but there was no significant difference in work of flexion between the control group and PLLA group (To evaluate the effect of PLLA-MMC2 membrane on cell apoptosis and collagen suppression in vivo, western blot assays were performed. The expression of collagen I, collagen III, Bcl-2, Bax, α-SMA in adhesion tissues around the repaired tendon after 3 weeks were examined in rat Achilles tendon model, with β-actin as protein loading control (B and C, Bax expression was significantly higher in the PLLA-MMC2 group than in the untreated control group or the PLLA membrane group. On the contrary, Bcl-2 expression was the lowest in the PLLA-MMC group. In addition, there was no significant difference in the Bax and Bcl-2 expressions between the untreated control group and the PLLA membrane group. Similarly, collagen I and collagen III expressions were significantly lower in the PLLA-MMC membrane group than in the other two groups (p < 0.05), but there was no significant difference between the untreated control group and the PLLA group (D and E). The PLLA-MMC2 membrane also effectively suppressed α-SMA expression while the PLLA membrane did not show effective down-regulation of α-SMA expression (F). The above results have suggested that the PLLA-MMC2 membrane significantly inhibited the expression of tissue adhesion-related proteins.In this study, we developed a simple and efficient micro-sol electrospinning technology to incorporate water-soluble drug MMC into PLLA fibrous membranes with sustained release properties. The developed PLLA-MMC membranes were able to inhibit fibroblast adhesion and proliferation. Moreover, the PLLA-MMC membranes could act as a physical barrier to successfully inhibit adhesion formation with no detrimental effect on tendon healing, possibly by mediating apoptotic gene expression as well as syntheses of adhesion-associated collagen and α-SMA. These results have demonstrated that fine-tuned release of MMC is a promising strategy for balancing intrinsic and extrinsic tendon healing by tuning the release of MMC to regulate the apoptotic gene expression, adhesion-associated collagen and α-SMA synthesis, thus to control the formation of adhesion tissues (extrinsic healing) without impairing the natural tendon healing process (intrinsic healing). Leakage of MMC to neighboring tissues may be of concern as it may damage neighboring tenocytes and thus delay the intrinsic healing. However, as the amount of MMC in HA micro-sols can be finely tuned and only a small dose of MMC was used, significant inhibition of intrinsic healing was not observed in present study. Moreover, fibroblast proliferation was significantly inhibited, preventing peritendinous adhesion formation.In this study, we fabricated core–shell structured fibers with the HA-sol particles as the core phase and PLLA as the shell layer. To achieve this structure, we first dispersed a stable micro-sol particle solution in an organic phase using ultrasonic emulsification method. The micro-sol could act as a protective layer to prevent the water-soluble MMC from contacting the organic solvent to avoid potential damage of drug activities. In addition, most of the soft particles were smaller than 1 μm in diameter and remained stable in the solution for at least 2 h without apparent aggregation. Due to the faster evaporation of the organic solvent than water, the viscosity of the outer PLLA layer increased much faster than that of the inner micro-sol particles, directing the HA micro-sol to settle into the fiber interior instead of the surface, resulting in the movement and stretch of the inner HA micro-sol Interestingly, HA-sols exhibited relatively slow burst release of MMC on the early stage and long-term sustained release of MMC for about 40 days, compared with other entrapment carriers, possibly due to the high dispersion stability of HA-sols in the core of the PLLA fibers MMC, as a potent apoptosis-inducing drug As we know, intrinsic healing, which dominates at the middle and late stage of tendon repair, results in superior biomechanics and fewer complications. However, it has limited healing capacity due to the lack of sufficient nutrients such as growth factors at the repair site The Bcl-2 family of proteins, located on the mitochondrial membrane, promote (Bax, Bak, Bad) or inhibit apoptosis (Bcl-2, Bcl-XL) through regulating release of cytochrome C from the mitochondria into the cytoplasm As previously mentioned, the possible mechanisms for this adhesion resistance without poor healing by the PLLA-MMC fibrous membranes were as follows. First, PLLA-MMC fibrous membrane, as a physical barrier with very small pores, blocked invasion of extrinsic fibroblastic cells for the peritendinous adhesions partly but allowed passage of cytokines, growth factors and synovial fluid for the tendon healing. Second, controlled release of MMC stimulated the apoptosis of exogenous fibroblasts by mediating apoptotic gene expression as well as syntheses of adhesion-associated collagen and α-SMA. As the dose of MMC used was low, the intrinsic healing was not damaged. Third, the HA hydrosol, released from the PLLA fibers, may promote tendon healing and lubricate tendon gliding. Through synergistic effect of the respective function of different substances, the inhibition of formation of tendon adhesions was achieved.The application of MMC-loaded PLLA micro-sol electrospun fibrous membranes avoided repeat local injection of MMC In this study, we obtained excellent MMC-loaded PLLA micro-sol electrospun fibrous membranes, which could achieve controlled release of water-soluble MMC. The membrane could inhibit fibroblast adhesion and proliferation and induce cell apoptosis in vitro. In addition, it could prevent tissue adhesion surrounding tendon without detrimental effect for the healing process of injured tendon by mediating fibroblast apoptosis as well as syntheses of collagen and α-SMA in vivo. Thus, it has potential clinical values as anti-adhesion materials for tendon healing.The authors confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome.The thermal expansion behaviour of SiCp/Al–20Si composites solidified under high pressuresAl–20Si matrix composites reinforced with SiC particles have been fabricated by high pressure solidification and the effects of solidification pressure and SiC volume fraction on the thermal expansion behaviour have been systematically investigated. A peak of the coefficient of thermal expansion (CTE) is observed during the first heating process due to the precipitation of Si from the supersaturated Al(Si) solid solution, whereas the CTE increases monotonically during the second heating process. The Al–20Si alloy solidified at 3 GPa shows the lowest CTE value during the second heating as a result of the modification of the eutectic silicon and of the small size and high volume fraction of the precipitated Si particles. The CTE of the composite decreases with increasing the SiC content in both heating processes. The theoretical model agrees well with the experimental results and our study indicates that high pressure solidification is a promising route for the development of SiCp/Al–Si composites for packaging applications.Electronic packaging materials are used to protect the electronic components from external damage, mechanical forces, and atmospheric or chemical contamination As an important physical property of electronic packaging materials, the thermal expansion behaviour is determined by several factors, including type, morphology and volume fraction of the reinforcements Among the previous studies on the thermal expansion of SiC particles reinforced Al-based MMCs, very little attention has been paid to the effect of solidification pressure. Alloys or composites solidified under high pressures can effectively change the distribution of second phases and the homogeneity of the composites, and may also lead to non-equilibrium microstructures Due to the mismatch of coefficients of thermal expansion (CTEs) between SiC and the metallic matrix, thermal residual stress (TRS) is introduced during cooling, in which the matrix will be in tension and the reinforcement in compression Therefore, it is theoretically and experimentally important to clarify the effects of solidification pressure, SiC volume fraction and thermal residual stress on the variations of CTEs of the composites. Accordingly, in the present work, the CTEs of Al–20Si alloy and different SiC particle reinforced Al–20Si composites are investigated under different solidification pressures in order to explore the viability to reduce the CTEs of the metal matrix composites.Samples consisting of an Al–20Si (wt.%) matrix reinforced with different volume fractions (0, 35, 40 and 45 vol.%) of SiC particles (size 5–15 μm) have been prepared by solidification at different pressures (1–3 GPa). For comparison, the same Al–20Si alloys solidified under atmospheric pressure were also investigated.The microstructure of the composites was characterized by optical microscopy (OM) using an Olympus optical microscope and by transmission electron microscopy (TEM) using a Philips CM12 microscope. In addition, the densities of the samples were determined using the Archimedes principle.The CTEs of the samples were measured between room temperature and 723 K using a NETZSCH DIL 402C dilatometer at heating and cooling rates of 5 K/min under argon atmosphere in two consecutive cycles. To eliminate systematic errors, the dilatometer was calibrated by measuring a silica sample under the same experimental conditions. Each result presented here is an average of three distinct experiments. The measured samples were cylinders of 6 mm diameter and 18 mm length. The top and the bottom of the specimens were polished to guarantee plane-parallel surfaces. shows the optical micrographs of the unreinforced Al–20Si matrix and of the composites containing different volume fractions of SiC solidified at 3 GPa. The OM images show that the composites have no appreciable porosity and that the reinforcement is homogeneously distributed throughout the matrix. shows a typical TEM image of the SiC/Al interface of the composite with 35 vol.% SiC processed under a solidification pressure of 3 GPa. The TEM image reveals a clean interface free of interfacial reaction products, suggesting that a homogeneous and well bonded matrix–reinforcement interface can be obtained by the high pressure solidification process.The relative density of the composites () increases with increasing solidification pressure and it decreases with increasing the SiC volume fraction. The Al–20Si alloy solidified at atmospheric pressure reveals the lowest density owing to its higher degree of porosity.The CTE is expressed as the change in the dimensions of the material as a function of temperature . At low temperatures (region 1), the CTE of the Al–20Si matrix fabricated at atmospheric pressure is slightly larger than those of the material obtained under high pressures. In this temperature range, the CTE decreases with increasing the solidification pressure and the alloy solidified at 3 GPa exhibits the lowest CTE in region 1. On the other hand, the CTE of the sample fabricated at atmospheric pressure is found to be much lower in region 2 with respect to the alloys obtained under high pressures, which display a similar behaviour characterized by a distinct CTE peak. The CTE peaks always occur in the temperature range between 408 and 596 K, which corresponds well to the DSC peak due to the precipitation of Si from the supersaturated α-Al matrix reported in our previous study From the atomic perspective, thermal expansion is reflected by the increase of the average distance between the atoms Moreover, the alloy prepared at atmospheric pressure is not dense due to residual porosity (94.3% relative density; ), which allows for the ease expansion and the contraction of the matrix during heating shows the CTE curves of the alloys during the second heating. The CTEs of all the alloys monotonically increase with increased temperature and no peaks corresponding to Si precipitation are visible. The CTEs of the samples solidified under high pressures show lower values compared with the one solidified at atmospheric pressure. The CTE decreases with increasing solidification pressures and exhibits the lowest value for the solidification at 3 GPa. This can be attributed to the modification of the microstructure and the supersaturated Si precipitates from α-Al as free Si. Fine eutectic silicon and precipitated Si particles have larger total specific surface area than that of the coarse silicon in Al–Si matrix, leading to a more effective restriction on the thermal expansion of Al in the matrix Moreover, the CTE curves display a sluggish increase at higher temperatures. As it is known, the CTE is determined by both the expansion caused by the rise of temperature and the expansion caused by solid solubility. As given by Hahn et al. where 1a0·da0dT is the intrinsic lattice expansivity, and 1a0ΔaΔCAe-ΔH/RTΔHRT2 stands for the contribution due to the variation in solute concentration. The values of ΔaΔC, A and ΔH are −1.73 × 10−3 (A/at.%), 994 and 45,500 J/mol, respectively shows the CTE curves of the composites reinforced with different SiC contents during the first and second heating stages. The curves show similar tendency as already observed for the unreinforced Al–20Si matrix, including the peaks corresponding to the Si precipitates.The CTEs of the composites show smaller expansion than the unreinforced Al–20Si during both the heating steps. Also, it can be found that the addition of SiC decreases the CTE effectively. The CTEs of the specimens with 35% SiC are found to be about 20% and 19.6% lower than that of the unreinforced matrix during the first and second heating processes. The lowest value is obtained for the 45% SiC/Al–20Si composite.The thermal expansion of the composite is determined by the expansion of the Al–20Si matrix and the contraction of SiC through interfaces. A larger content of SiC increases the contraction leading to an overall reduction of the CTE of the composites. On the other hand, the residual stress also has an influence on the composite The CTE of composites is rather difficult to be predicted precisely because it is influenced by several factors, including matrix plasticity and the internal structure of the composite where a is the coefficient of linear thermal expansion, V is volume fraction, while the subscripts c, m and p refer to composite, matrix and particle, respectively.The Kerner model assumes that the reinforcement is discontinuous, spherical and wetted by a uniform layer of matrix; thus, the CTE of a composite is considered as identical to that of a volume element composed of a spherical reinforcement particle surrounded by a shell of matrix; here, both the normal and shear stress are taken into account. This model gives the composite CTE as αc=αmVm+αpVp+VpVm(αp-αm)×Kp-KmVmKm+VpKp+3KmKp4Gmwhere Gm is the shear modulus of the matrix.Schapery’s model is based on Kerner’s model, which assumes that the particles are spherical in shape and wetted by a uniform, isotropic, homogenous matrix layer where Kc is the bulk modulus of the composite and is obtained from Hashin’s bounds where Gm and Gp are the shear modulus of the matrix and the particle, respectively. It is noteworthy that for the upper bound, the CTE given by Schapery coincides with the CTE value determined from the Kerner’s model due to their assumptions shows the calculated CTEs for the unreinforced matrix processed at different solidification pressures. The calculated CTE values decrease with increasing solidification pressure, and under the solidification pressure of 3 GPa, the alloy exhibits the lowest CTE values in all the models, in agreement with the experimental results (). According to the models, the most important factors are the CTE of the matrix, the reinforcement, and their volume fractions. As demonstrated in our previous study shows the comparison between theoretical and experimental CTEs for the unreinforced Al–20Si alloy. It is found that the experimental CTEs is below the Turner model at T |
< 373 K and T |
> 573 K. Due to the low temperature and the instability of the alloy, the CTE shows lower values at T |
< 373 K, and as a result of the increased solid solubility of Si in Al, the CTE values decrease at T |
> 573 K. Between 373 K and 573 K, the experimental CTEs lie between the Turner model and the lower bound of the Schapery model, which indicates that the experimental CTEs agree well with the theoretical models and that the elastic interactions are dominant in their CTEs during this temperature range. displays the calculated CTEs of the SiC/Al–20Si composites solidified at 3 GPa. As it can be observed, all the four models show similar trends, the CTE values decrease with increasing the volume fraction of the SiC and the Turner model shows the lowest value.The comparison between theoretical calculations and experimental results for the composites produced at 3 GPa are shown in . The experimental CTEs are below both Schapery models up to 344 K, and fall between lower and upper Schapery bound for temperatures between 344 and 723 K. The Schapery models cover most the experimental data and it is suggested that Schapery models can be used for the CTEs of the composites. Previous work Based on the results mentioned above, the following conclusions can be drawn: (1) SiC particles are distributed uniformly in the matrix, and the interface is clean from reaction products; (2) a CTE peak is observed in the temperature range between 408 and 596 K in both the unreinforced matrix and the composites produced under high pressure during the first heating process, which can be ascribed to the precipitation of Si from the supersaturated Al(Si) solid solution. The CTEs of the matrix alloy and composites after the second heating increase monotonically and no CTE peak can be observed; (3) the modification of the eutectic silicon combined with the precipitated Si particles with small size result in the decrease of the CTEs during the second heating process. The Al–20Si alloy obtained under 3 GPa exhibit a lower CTE compared with ones obtained under 1 GPa and 2 GPa; (4) the CTE decreases with increasing SiC content in both heating processes; and (5) the experimental CTE values of the matrix alloy lie in Turner model and lower bound of Schapery between 373 and 573 K. Schapery models cover most the experimental data for the composites.Therefore, it can be expected that high pressure solidification technique would be helpful to develop the SiCp/Al–Si matrix composite as a packaging material. Further, systematic microstructural characterization and optimization of these composites are required to satisfy the requirements of advanced electronic packaging application.Experimental study and theoretical analysis on axial compressive behavior of concrete columns reinforced with GFRP bars and PVA fibersThere have been some studies on the axial compressive behavior of concrete columns reinforced with fiber-reinforced polymer (FRP) bars. But most studies focused on normal concrete without fibers. In this paper, 10 concrete columns reinforced with glass fiber-reinforced polymer (GFRP) bars and polyvinyl alcohol (PVA) fibers were designed to investigate the influence of reinforcement type, longitudinal reinforcement ratio, spacing and size of GFRP ties on the axial compressive behavior of the specimens. Analytical and numerical studies were explored in this paper. The test results indicated that the concrete column reinforced with GFRP bars and PVA fibers (GFRP PVA-FRC column) and the concrete column reinforced with steel bars and PVA fibers (steel PVA-FRC column) had the similar failure processes and failure modes. The axial bearing capacity and brittleness of the GFRP PVA-FRC columns increased with the increasing longitudinal reinforcement ratio. When the volumetric ratio was constant, the confinement efficiency and ductility of the specimens using GFRP ties with smaller diameter and closer spacing were higher than that using GFRP ties with larger diameter and larger spacing. A new stress-strain constitutive model for PVA fiber reinforced concrete confined by GFRP bars was proposed. The numerical results showed that the concrete in the columns reinforced with GFRP longitudinal bars and GFRP ties could give full play to its strength. The conclusions could be references for the engineering application.When the steel reinforced concrete components were used in erosion environments such as bridges, ports or chemical plants, the structural performance deteriorated due to the corrosion of steel reinforcements. And the failure of the critical steel reinforcement concrete components could cause the collapse of the whole structure In recent years, various researchers had investigated the behavior of flexural and shear members of FRP reinforced concrete FRP bars were linear elastic materials, without yielding stage before failure. The tensile strength of FRP bars was higher than the yield strength of steel bars. The axial compressive behavior of concrete columns reinforced with FRP bars (FRP RC columns) was different from that reinforced with steel bars. The experimental results on concrete columns reinforced with steel bars (steel RC columns) could not be directly applied to FRP RC columns. So this paper would investigate the axial compressive behavior of the FRP RC columns.There were four types of FRP bars containing glass fiber reinforced polymer (GFRP) bar, carbon fiber reinforced polymer (CFRP) bar, basalt fiber reinforced polymer (BFRP) bar and aramid fiber reinforced polymer (AFRP) bar. GFRP bars were widely used in constructions because of their high cost effective performance Some previous studies on concrete columns reinforced with steel bars and fibers under axial compression indicated that the fibers delayed the concrete cover spalling and increased the bearing capacity and ductility of the columns As the reinforcements in the compressive concrete component, GFRP bars had a great influence on the behavior of the whole component. There has been some research on the compressive properties of GFRP bars, but the test results were diversity for the anisotropic and nonhomogeneous nature, different components, diameter, manufacturing process and test method of the FRP bars Some researchers have investigated the behavior of concrete columns reinforced with FRP bars, but the concrete used was focused on normal concrete without fibers. Pantelides tested 10 concrete columns confined by GFRP spirals or steel spirals under axial load. The longitudinal reinforcements were steel bars or GFRP bars. The all steel reinforced and hybrid columns were subjected to accelerated corrosion. The test results indicated that the hybrid specimens had a higher corrosion resistance A few researchers proposed the confinement models for concrete confined by FRP bars. Afifi et al proposed a confinement model for concrete confined by CFRP bars To date, little research had been done on concrete columns reinforced with fibers and FRP bars and no constitutive models for fiber reinforced concrete confined by GFRP bars had been proposed. This paper investigated the axial compressive behavior of GFRP PVA-FRC columns and proposed a confinement constitutive model. The test results could be references for the theoretical research and engineering application.This paper reported the test results of GFRP PVA-FRC columns under axial compression. The first objective was to investigate the effect of the reinforcement type, longitudinal reinforcement ratio, spacing and size of GFRP ties on the axial compressive behavior, axial compressive bearing capacity, confinement efficiency and ductility of the GFRP PVA-FRC columns. The second objective was to develop the calculation formula of axial compressive bearing capacity of the GFRP PVA-FRC columns. The third objective was to propose a stress-strain constitutive model for the PVA fiber reinforced concrete confined by GFRP bars.10 square fiber reinforced concrete columns were constructed and tested to investigate the effect of the reinforcement type, longitudinal reinforcement ratio, spacing and size of GFRP ties on the axial compressive behavior of the columns. Among the 10 columns, a column with no reinforcement and a column with steel reinforcements were introduced as reference specimens, and the other 8 PVA-FRC columns were reinforced with GFRP bars. The width and the height of each specimen were 350 mm and 1200 mm. The concrete cover was 25 mm.The details of the test specimens were listed in . Each specimen with reinforcements was identified with letters and numbers. The letters G and S stood for the longitudinal reinforcement type and the transverse reinforcement type respectively. V stood for the longitudinal reinforcement. H stood for the transverse reinforcement. The first number, second number, third number and fourth number stood for the quantity and the diameter of the longitudinal reinforcement, the diameter and spacing of the transverse reinforcement. P identified the specimen with no reinforcement.All the GFRP assembled cages were shown in , and the tie layouts had 2 configurations, shown in . The column end regions of 250 mm were strengthened with tie spacing at 30 mm to prevent premature failure there. The specimens were cast vertically. Nature curing lasted 28d.In this experiment, the concrete grade was C50. C50 meant the standard value of compressive strength of 150 mm cubes were 50 MPa at the age of 28 days. The cement used was Portland 42.5R. Gravels were crashed and had a continuous gradation. The fine fineness modulus of medium sands was 2.3. The water reducing ratio of the water reducing agent was 30%. The diameter and length of the PVA fibers were 20 μm and 10 mm. The tensile strength of the PVA fibers was 1600Mpa. The mixture properties of the fiber reinforce concrete was shown in Six 150 mm × 150 mm×300 mm concrete blocks were poured at the same time when each concrete batch was casting. The compressive strength fcp and elastic modulus Ec of the concrete were determined according to GB/T 50081-2002 . The average compressive strength fcp and elastic modulus Ec of the concrete were reported in , fcp was average compressive strength of the concrete blocks(MPa); Pmax was the peak load(kN); εtransverse,εbar,εch and εcc were tie strain (με), longitudinal reinforcement strain (με), concrete transverse strain (με) and concrete axial strain (με) according to fcc; fcc was axial compressive strength of confined concrete (MPa), fco was axial compressive strength of unconfined concrete (MPa).For the steel PVA-FRC column, HRB400 steel bars and HPB300 steel bars were used as longitudinal reinforcements and transverse reinforcements respectively. For the GFRP PVA-FRC columns, GFRP bars were used as longitudinal reinforcements and transverse reinforcements. The GFRP bars were made of E-glass fibers impregnated in thermosetting vinyl ester resin, additives, and fillers with a fiber content of 80% (by volume). The properties of the steel bars and GFRP bars were reported in Before casting, the middle of the longitudinal reinforcements, the middle and the corner of the transverse reinforcements were instrumented with electrical strain gauges. Before testing, the surface of the concrete was instrumented with four longitudinal and four transversal electrical strain gauges at midheight of each side. The axial displacement of each specimen was recorded using two displacement gauges with a range of 100 mm. The two displacement gauges were located symmetrically at midheight of the specimens.The experiments were carried out on the 20000 kN electro-hydraulic servo pressure testing machine. Prior to testing, all the specimens were capped on both ends with a thin layer of quartz sand for leveling and to ensure uniform distribution of the applied load across the cross section. The specimens were loaded to 300 kN and in the loading process, numerical readings were observed. If the difference between any reading of the strain gauge and the average reading was less than 5% of the average reading, the specimens could be formally loaded, otherwise re-leveling and re-centering.The specimens were tested under load control at a rate of 2.5 kN/s until the load reached to 80% of the predicted peak load. Thereafter, displacement control was used at a rate of 0.002 mm/s. When the resistance of the tested specimen dropped to 60% of the peak load or the axial displacement reached a value of 30 mm, the specimen was considered to have been damaged, and the test stopped.Take specimen G8V16-G8H60 as an example, the cracking appearances in the test region at different loading stages were shown in . The failure modes of all the specimens were shown in The specimen with no reinforcement initially behaved in an elastic manner, and the axial strain and the transverse strain were low. When the load reached about 85% of the peak load, the slightly sound of concrete cracking was heard, and at the same time, the first vertical crack appeared in the upper corner of the specimen. The specimen reached its peak load rapidly after the first crack appeared. Thereafter, the cracks widened suddenly and the axial compressive bearing capacity dropped rapidly. The failure process was short. The damaged specimen had few cracks, but the cracks were wide.The GFRP PVA-FRC columns and the PVA-FRC column with no reinforcement behaved in a similar elastic manner in the initial loading process. At this load level, the axial strain and the transverse strain of the concrete were low, and confinement provided by the ties was not activated. When the load reached about 80% of the peak load, the slightly sound of concrete cracking was heard, and at the same time, the first vertical crack appeared in the upper corner of the specimen. As the load increased, the number and the width of cracks increased, and short cracks propagated to long cracks. After the peak load, the rate of the cracks propagating increased. As a result, the axial strain and the transverse strain of the concrete increased progressively. At this point, the concrete core dilated and the concrete cover swelled activating the confinement of the ties. When the axial compressive bearing capacity dropped to about 65% of the peak load, the micro cracks propagated to a 45°main crack. The specimens exhibited slower failure process and better ductility comparing with the specimen with no reinforcement.The steel PVA-FRC column and the GFRP PVA-FRC columns showed a similar failure process and exhibited a similar failure mode. In the failure process of the steel RC column and the GFRP PVA-FRC columns, the sound of the rupture of GFRP bars was heard, but there was no sound of the rupture of steel bars.For all the specimens, there was no serious spalling of the concrete cover after failure. The superior integrity of the specimens reflected bridging effect of the fibers.The equation of concrete axial stress was given as follows:where σ was the concrete axial stress (MPa); P was the load carried by the columns in the testing process (kN); Pbar was the load carried by the longitudinal reinforcements in the testing process (kN); Pbar = εbEbAb, εb was the longitudinal reinforcement strain (με), Eb was elastic modulus of the longitudinal reinforcement (MPa), Ab was the area of the longitudinal reinforcement (mm2); A was the area of the concrete that carried axial load (mm2)., if A took the gross sectional area of concrete, the axial stress-axial strain response was the curve OABC as shown in . If A took the area of concrete core, the axial stress-axial strain response was the curve ODEF as shown in In the loading process, before the concrete cover cracked (The cracking load was about 80% of the peak load), the area of the concrete that carried load was the gross concrete area, and the axial stress-axial strain response was the curve OA; After the concrete cover spalled, the area of the concrete that carried load was the confined concrete core, and the axial stress-axial strain response was the curve EF; The transition between point A and point E was smooth. Three curves of OA, AE and EF were combined to form the actual axial stress-axial strain response.The concrete axial stress of each specimen was normalized by its corresponding value of fco to eliminate the effect of the differences of unconfined concrete compressive strength of different batchs. The axial normalized stress-axial strain curves were shown in , in the initial stage of loading process, the curves of all the specimens had nearly linear slope which indicated the behavior of all the specimens at this time were mainly related to the concrete. When the load of the specimen reached about 80% of its peak load, the specimen cracked and the axial stiffness began to decrease, and the increase rate of axial deformation of the specimens accelerated.The axial strain at peak stress of the specimen P was 1884 με. showed that the post peak curve of the specimen P dropped rapidly, and post peak curve was limited in extent. The failure of the specimen P was brittle. The GFRP PVA-FRC columns reached the peak stress at a strain value ranging from 2200 με ∼ 3029 με, with an average value of 2478 με, which was 31.53% higher than that of the specimen P. The steel PVA-FRC column reached the peak stress at a strain value of 3938 με, which was 109.02% higher than that of the specimen P. The post peak curves of the GFRP PVA-FRC columns and the steel PVA-FRC column dropped gradually. The GFRP PVA-FRC columns and the steel PVA-FRC columns failed in a ductile manner with larger axial strain.The specimens G8V16-G10H60 and S8V16-S10H60 were designed to investigate the effect of reinforcement type on the axial compressive behavior of the specimens. They were reinforced with GFRP and steel bars, respectively, with the same reinforcement ratio and tie configuration. The GFRP PVA-FRC specimen and the steel PVA-FRC specimen had their peak loads equal to 5357 kN and 7727 kN, fcc/fco equal to 1.60 and 1.81, ductility equal to 1.83 and 1.70. These results indicated that the peak load and the confinement efficiency of the GFRP PVA-FRC column were lower than that of the steel PVA-FRC column. The GFRP PVA-FRC column and the steel PVA-FRC column had the nearly same ductility.At concrete axial peak stress, the axial strains of GFRP and steel longitudinal bars were 1922 με and 2989 με, and the strains of GFRP and steel ties were 1398 με and 1967 με. showed that the post peak curves of specimen G8V16-G10H60 and S8V16-S10H60 were quite different. The post peak curve of the specimen G8V16-G10H60 did not exhibit a horizontal stage, for the GFRP bars were linear elastic material without yielding stage. The post peak curve of the specimen S8V16-S10H60 exhibited a horizontal stage at a tie strain value equal to 2400 με which was closed to the steel yield strain.The concrete cover was peeled off after the specimens had failed. showed the close-up rupture of GFRP longitudinal reinforcements and the buckling of steel longitudinal and transverse reinforcements in the failed zones.The specimens G12V16-G10H90 and G12V18-G10H90 had the GFRP ties of same diameters and spacing. The two specimens with different longitudinal reinforcement ratios (2.09% and 2.64%) were designed to investigate the effect of longitudinal GFRP reinforcement ratio on the axial compressive behavior of the specimens. The specimens G12V16-G10H90 and G12V18-G10H90 had their peak loads equal to 4500 kN and 4972 kN, fcc/fco equal to 1.48 and 1.50, ductility equal to 3.67 and 2.14.The axial bearing capacity, confinement efficiency and ductility of specimen G12V16-G10H90 were 90.51%, 98.67% and 171.50% of that of the specimen G12V18-G10H90. These results indicated that as the longitudinal reinforcement ratio increased, the axial bearing capacity increased significantly, the confinement efficiency almost unchanged and the ductility of the specimens decreased obviously.The specimens G8V16-G8H60 and G8V16-G8H38 had the same longitudinal reinforcements. They were designed with same tie diameters of 8 mm and different tie spacing of 60 and 38 mm to investigate the effect of tie spacing on the axial compressive behavior of the specimens. An increase of 17.24% in confinement efficiency and an increase of 14.80% in ductility were obtained as the tie spacing decreased from 60 mm to 38 mm.The specimens G8V16-G10H90 and G8V16-G10H60 had the same longitudinal reinforcements. They were designed with the same tie diameters of 10 mm and different tie spacing of 90 and 60 mm. An increase of 15.11% in confinement efficiency and a decrease of 3.68% in ductility were obtained as the tie spacing decreased from 90 mm to 60 mm.The specimens G8V16-G12H130 and G8V16-G12H90 had the same longitudinal reinforcements. They were designed with the same tie diameter of 12 mm and different tie spacing of 130 and 90 mm. An increase of 11.94% in confinement efficiency and an increase of 25.33% in ductility were obtained as the tie spacing decreased from 130 mm to 90 mm. showed the comparison of concrete axial normalized stress-axial strain curves for the specimens with the same tie diameters and different tie spacing. It was concluded that when the tie diameters of the specimens were the same, the confinement efficiency increased as the tie spacing decreased. The post-peak branch of the specimen G8V16-G12H130 was limited in extent compared to the other GFRP PVA-FRC specimens. The ultimate axial strain and the ductility of specimen G8V16-G12H130 were lower. As the tie spacing increased, confinement for concrete core offered by transverse reinforcements decreased, and the bracing length of the longitudinal reinforcements increased which reduced the stability of longitudinal reinforcements against local buckling at maximum axial stress. So in order to ensure the higher strength of the confined concrete and the higher deformation capacity of the GFRP PVA-FRC specimens, the tie spacing should not be larger than 130 mm in practical engineering.The specimens G8V16-G8H60 and G8V16-G10H60 had the same longitudinal reinforcements. They were designed with the same tie spacing of 60 mm and different tie diameters of 8 and 10 mm to investigate the effect of tie diameter on the axial compressive behavior of the GFRP PVA-FRC specimens. As the tie diameter increased from 8 mm to 10 mm, an increase of 10.34% in confinement efficiency and a decrease of 26.80% in ductility were obtained.The specimens G8V16-G10H90 and G8V16-G12H90 had the same longitudinal reinforcements. They were designed with the same tie spacing of 90 mm and different tie diameters of 10 and 12 mm to investigate the effect of tie diameter on the axial compressive behavior of the GFRP PVA-FRC specimens. As the tie diameter increased from 10 mm to 12 mm, an increase of 7.91% in confinement efficiency and nearly the same ductility were obtained.Comparing the confinement efficiency of the specimen G8V16-G8H60 with that of the specimens G8V16-G8H38 and G8V16-G10H60 which had the same volumetric ratio of 2.70%, it was concluded that when the volumetric ratio was unchanged, the effect of tie spacing on confinement efficiency was greater than the effect of tie diameter on confinement efficiency. Comparing the confinement efficiency of the specimen G8V16-G10H90 with that of G8V16-G10H60 and G8V16-G12H90, the same conclusion was obtained. showed the comparison of concrete axial normalized stress-axial strain curves for the specimens with the same tie spacing and different tie diameters. It was concluded that when the tie spacing of the specimens was unchanged, as the tie diameter increased, the confinement efficiency increased but the ductility was not improved.The specimens G8V16-G8H60, G8V16-G10H90 and G8V16-G12H130 had the same volumetric ratio of 1.80%. The specimens used three different tie diameters (8 mm, 10 mm and 12 mm) and three different tie pacing (60 mm, 90 mm and 120 mm). Their confinement efficiencies were 1.45, 1.39 and 1.34, ductility were 2.50, 1.90 and 1.50. The specimens G8V16-G8H38、G8V16-G10H60 and G8V16-G12H90 had the same volumetric ratio of 2.70%. The specimens used three different tie diameters (8 mm, 10 mm and 12 mm) and three different tie pacing (38 mm, 60 mm and 90 mm). Their confinement efficiencies were 1.70, 1.60 and 1.50, ductility were 2.87, 1.83 and 1.88. The test results indicated that when the volumetric ratio was constant, the confinement efficiency decreased as the tie diameter increased. Except the specimen G8V16-G12H90, the ductility of the other specimens decreased as the tie diameter increased when the volumetric ratio was constant. showed the comparison of concrete axial normalized stress-axial strain curves of the specimens with the same volumetric ratio, but different tie diameters and tie spacing. As shown in , when the volumetric ratio was constant, confinement efficiency decreased as the tie diameter and tie spacing increased. The post peak curve of the specimen with larger tie spacing dropped rapidly, indicating that even if the volumetric ratio was high, the tie spacing of the specimen should not be larger than 130 mm. The enhancement of confined concrete strength due to increasing tie diameter could not make up the reduction of confined concrete strength due to increasing tie spacing.Our research team had experimented on the axial compressive behavior of circular GFRP-FRC columns. The tested circular columns were 300 mm in diameter and 1300 mm in height. The gross sectional area of the circular columns was closed to that of the square columns in this experiment. The circular specimens G6V16-G10H50 and G6V16-G12H73 with the same volumetric ratio of 1.90% had the confinement efficiency of 1.55 and 1.66. The square specimens G8V16-G8H60 and G8V16-G10H90 with the same volumetric ratio of 1.80% had the confinement efficiency of 1.45 and 1.39. It was concluded that the confinement for the concrete core of square ties were lower than that of circular ties.The circular specimen G12V16-G10H50 and the square specimen G12V16-G10H90 had the volumetric ratios of 1.90% and 2.49%, and the confinement efficiencies of 1.62 and 1.48. The test results indicated that the specimen with higher volumetric ratio might not have higher confinement efficiency. According to the calculation method proposed by Mander (1988) The square ties had lower confinement effectiveness coefficient than that of the circular ties, and there was stress concentration in the corner of the square ties, so the confinement provided by the GFRP square ties was lower. But the fabrication of circular GFRP ties was complex, and the circular GFRP ties were inconvenient to be used in composite sections (T-shaped, I-shaped). The joints of circular section members were difficult to be constructed. Thus the square columns with GFRP reinforcements were still widely used in the projects.Mander found that lateral pressure of transverse GFRP reinforcement on concrete core in square columns was not uniform. The confining lateral pressure was greatest at the intersection of each limb, and smallest in the middle of each limb. In order to simplify the calculation, the confining lateral pressure was assumed to be uniform along transverse reinforcement where fl was the confining lateral pressure of GFRP ties; Af was the area of GFRP transverse reinforcement; ffv was the stress of GFRP tie at concrete axial peak stress; s was tie spacing; dc was dimension of the concrete core delimited by outer tie centerlines.There was arching action when the concrete core was confined by the square ties as shown in . Mander proposed a confinement effectiveness coefficient ke to calculate the effective lateral pressure of the square ties where fle was the effective lateral pressure; ke was the confinement effectiveness coefficient; wi′ was the clear distance between adjacent longitudinal reinforcements. s′ was the clear tie spacing; ρs% was longitudinal reinforcement ratio.where fbend was the bend strength of the GFRP transverse reinforcement; Ef was the elastic modulus of GFRP transverse reinforcement; ff was the tensile strength of the straight GFRP transverse reinforcement; rv was the bending radius of the GFRP transverse reinforcement at corner; dv was the diameter of the GFRP transverse reinforcement;In this experiment, rv/dv=4, substitute it into Eq. The test results showed that the stress of GFRP ties was low at concrete axial peak stress and did not reached its bend strength. The lateral pressure of the ties would be overestimated if its bend strength was taken as its stress corresponding to the concrete axial peak stress.Shi et al. found that the stress of transverse reinforcement at axial peak stress of the concrete was related to the tie configuration, unconfined concrete strength and volumetric ratio where ke was the confinement effectiveness coefficient; ρst% was volumetric ratio; fco was the unconfined concrete strength.Based on the test data, the peak stress of confined concrete was shown in The Ottosen failure criteria was expressed as follows:In the GFRP PVA-FRC columns, σ1 = σ2 = −fle, σ3 = −fcc. Substituting σ1, σ2 and σ3 into Eq. Based on the test data, the peak stress of confined concrete was shown in fccfco=1.13+4.13×10-3+10.65flefco+flefcoThe following calculation of strain corresponding to the peak stress of confined concrete was determined based on regression analysis of the test results (See The axial stress-axial strain relationship of confined concrete was the basis of design and nonlinear analysis of the structure. It had a great significance to study the mechanical properties of the columns such as axial compressive bearing capacity and ductility. A reasonable constitutive model could improve the accuracy of the calculation results. In the past, various researchers investigated the axial compressive behavior of concrete columns reinforced with steel bars or FRP tube and proposed constitutive models for the confined concrete respectively. Nonetheless, there was little investigation on the constitutive models for concrete confined by FRP bars The steel bars undergone a yield stage before their failure, while the GFRP bars always maintained their liner elastic property before their failure; The confining lateral pressure of FRP tube was uniform in the longitudinal direction, while the confining lateral pressure of GFRP bars were maximum at each transverse reinforcements (shown in ). Therefore, the models of normal concrete confined by steel bars or GFRP tube could not be directly applied to the fiber reinforced concrete confined by GFRP bars.Based on the experiment results and existing constitutive models where Ec was elastic modulus of the concrete (MPa); E1, A, B were parameters calculated from Eqs. E1=1.67×10-2(fco)-2.81(εcc/εco)0.14(fle/fco)-0.33 showed a comparison between the experimental and theoretical axial stress-axial strain relationships of the specimens. The comparison showed satisfactory correlation between the theoretical and experimental results.A non-linear finite element method using the software ABAQUS was presented. The numerical model was developed to investigate the effect of the type of longitudinal reinforcement or transverse reinforcement on the axial behavior of the concrete columns.The concrete damaged plasticity (CDP) model from the ABAQUS user’s manual ABAQUS/Explicit was used to model the reinforced concrete columns. The load was applied on a rigid body using the displacement controlled mode for better convergence. The mesh size of the model was 30 mm. The concrete was modeled as C3D8R elements. The steel bars and GFRP bars were modeled as T3D2 elements. showed a comparison between the numerical and experimental results of load-axial strain curves. It showed that the experimental axial compressive bearing capacity was lower than that of the numerical model. This was due to the initial imperfection existed in the concrete and a small amount of eccentricity produced in the specimen when the specimen was loaded. Though there was discrepancy between the experimental results and the numerical results, the model captured the overall behavior well. The finite element model was validated.A parametric study was carried out to investigate the axial compressive behavior. The parameters were the type of longitudinal reinforcement or transverse reinforcement. The compressive strength and the tensile strength of the concrete in the model were 43 MPa and 2.9 MPa which were the average value of the concrete in the experimental research. The yield strength of the steel longitudinal reinforcement and the steel transverse reinforcement were 400 MPa and 300 MPa in the model. The compressive strength and the tensile strength of the GFRP bar were 840 MPa and 575 MPa in the model.The axial load-axial strain curves of models S12V16-S10H90 and G12V16-S10H90 were shown in . N and NC stood for the total load and the load carried by the concrete. The axial compressive capacity of model S12V16-S10H90 was 5764 kN which was 11.57% higher than that of G12V16-S10H90.The curves of the total axial load-axial strain and the axial load carried by the concrete-axial strain of models S12V16-S10H90 and G12V16-S10H90 nearly overlapped up to 80% of the peak load. It showed that the type of longitudinal reinforcement had little influence on the axial compressive behavior when the axial deformation was low.After the peak load, the gap of the axial load between models S12V16-S10H90 and G12V16-S10H90 decreased with the increase of the axial deformation. The axial load carried by the steel longitudinal reinforcements in model S12V16-S10H90 kept unchanged after the steel yielded. The axial load carried by the GFRP longitudinal reinforcements increased until the GFRP ruptured which decreased the attenuation rate of the total axial bearing capacity.The axial load-axial strain curves of models S12V16-S10H90 and S12V16-G10H90 were shown in . The axial compressive capacity of model S12V16-S10H90 was 6.05% higher than that of model S12V16-G10H90.In the initial stage of the post peak section, the attenuation rate of the total axial bearing capacity of model S12V16-G10H90 was higher than that of S12V16-S10H90. With the increase of axial deformation, the attenuation rate of the total axial load of model S12V16-G10H90 slowed down and finally became lower than that of S12V16-S10H90. This was attributed to the increasing confinement of the GFRP ties with the increasing transverse deformation of the model.The axial stress-strain curves and the compressive damage-axial strain curves of the concrete in the middle height of the columns were shown in . It could be concluded that the concrete axial stress was greatly affected by the transverse reinforcement and little affected by the longitudinal reinforcement. The axial peak stress of the concrete confined by the steel ties were higher than that confined by the GFRP ties. But the attenuation rate of the axial stress of the concrete confined by steel ties was higher than that confined by GFRP ties in the latter section of the post peak stage. When the models reached their limit state, the compressive damage of the concrete confined by GFRP ties was higher than that confined by steel ties. showed the damage quantification of the models. Follow the sequence of the models S12V16-S10H90, G12V16-S10H90, S12V16-G10H90 and G12V16-G10H90, the quantity of the failure elements in every model increased and the transverse deformation decreased. The concrete in model G12V16-G10H90 could give full play to its strength when the model reached limit state, so the concrete had better cost-effective. The elastic modulus of the GFRP bar was lower than that of steel bar, and was closer to that of the concrete. Therefore, the combination of the GFRP reinforcement and the concrete could be more coordinated when subjected to load.In the past theoretical research and engineering design, the calculation of axial bearing capacity took no account of the effect of the FRP ties on the concrete core. The widely used equations to predict the axial bearing capacity of normal concrete reinforced with FRP bars were proposed by Kobayashi and Fujisaki, Tobbi and Farghaly where f′c was axial compressive strength of concrete cylinder; 0.85 was a reduction factor for the difference attributed to the size effect, shape, and concrete casting practice between columns and concrete cylinders; Ag was gross cross-sectional area of the column; Afrp was cross-sectional area of FRP longitudinal reinforcement; ffrp was ultimate FRP tensile strength; εcc was axial strain at axial peak stress of the concrete; Efrp was elasticity modulus of FRP bars; 0.35 was a reduction factor accounting for the reduction in the compressive strength of the FRP bars. In this experiment, 0.85 f′c was replaced by fco.The test results indicated that the axial bearing capacity would be underestimated if the confinement for the concrete core of the GFRP ties was ignored. The following equation was proposed to predict the axial compressive bearing capacity.where fcc was axial peak stress of confined concrete calculated from Eq. ; Acor was core area of the confined concrete; εcc was concrete axial strain at concrete axial peak stress of fcc calculated from Eq. presented the ratios of the experimental peak load to the predicted maximum load. It was concluded that Eq. provided the most accurate value of the axial peak load, and the results could be applied in the engineering structural design.The GFRP PVA-FRC column and the steel PVA-FRC column had similar failure processes and similar failure modes. The former failed due to the fracture of longitudinal reinforcements, and the latter failed due to the bucking of steel bars. The confinement efficiency and ductility of GFRP PVA-FRC column were 88.39% and 107.65% of that of the steel PVA-FRC column.As the longitudinal reinforcement ratio of the GFRP PVA-FRC specimens increased from 2.09% to 2.64%, the peak load increased by 10.49%, the confinement efficiency increased by 1.35%, and the ductility decreased by 41.69%. Therefore, it was necessary to define a reasonable longitudinal reinforcement ratio, which not only provided sufficient axial compressive bearing capacity, but also ensured that the GFRP PVA-FRC columns had sufficient ductility.The GFRP ties could provide good confinement for concrete core. The effect of tie spacing on the confinement efficiency was greater than that of tie diameter on confinement efficiency. The GFRP PVA-FRC columns with smaller tie diameter and smaller tie spacing had better axial compressive performance, when the volume ratio was constant. To provide enough ductility of the GFRP PVA-FRC columns, the tie spacing should not be larger than 130 mm.In the latter section of the post peak stage, using the GFRP longitudinal reinforcements or the GFRP ties could reduce the attenuation rate of the axial load. GFRP bars played a favorable role in the adequate exertion of concrete strength.The test results provided some basis for theoretical research and engineering application of GFRP PVA-FRC columns. The proposed calculation of the peak load had a high accuracy. The proposed constitutive model agreed well with the experimental results.We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.In situ polymerization of isotactic polypropylene sepiolite nanocomposites and its copolymers by metallocene catalysisIsotactic Polypropylene (iPP)-sepiolite nanocomposites were prepared by in situ polymerization using nanoclays as support of the catalytic system. This study proposes a method of immobilization that considers the use of the density of the polar groups present on sepiolite surface, to fix the co-catalyst. In addition, the resulting polymerization process defines the reaction time as a variable which will provide a mechanism for controlling the productivity of the reaction, making possible the obtaining of a masterbatch which may be useful in increasing the PP-clay compatibility in melt blending processes. The results of the proposed method have allowed not only the additivation of polypropylene during the synthesis, but also the structure control in terms of stereo-specificity and molecular weight, improving its final properties. Furthermore, in an effort to improve the impact properties of the iPP matrix, iPP copolymers were synthesized with 1-olefins of different chain lengths as co-monomers. The influence of the amount of co-monomer, amount of filler and type of branching obtained on the final properties of iPP nanocomposites were studied.It is known that the commercial use of polypropylene started with the rise of the catalyzed reactions leading to the possibility of control the specific conformation of the substituent group of its structure (CH3) and therefore the final properties of this thermoplastic. The isotactic conformation of this material was discovered by Ziegler and Natta (Z-N) in the 1960s Over time, polypropylenes produced under metallocene catalysis have had many advantages compared to their contra part synthesized with Z-N type catalysts In spite of their advantages, metallocene catalysts as homogeneous systems have presented problems in industrial applications, mainly because of the particle sizes of the polymers they produce and the oxide residues that damage the polymerization reactors. In addition, there is a major impediment in its marketing due to the high cost of the co-catalyst (MAO) used. One way of solving these problems has been the immobilization of the catalytic system through a chemical or physical support on the surface of a solid particle The literature on support of metallocene systems is very broad and is essentially based on the study of the type of material used as support and the method by which the catalyst system is anchored, in all cases seeking stability of the catalytically active species. Nowadays publications in this area are of special interest as the immobilization of metallocene catalysts has increased the complexity of these, adding new study variables From the beginning of the use of the technology of immobilization until now, the supports have been of micrometric size (metal oxides Today the advances in the synthesis of polyolefin are almost exclusively based on the most efficient use of the metallocene catalysts through their immobilization, but in this case, paying particular attention to avoid the loss of regularity in the structure of the PP synthesized, because, as already mentioned, its properties depend almost exclusively on it. Thus, this study is based on maximizing the benefits of metallocene catalysis through immobilization or support in high surface nanometric particles such as sepiolite The combination of the isotactic polypropylene synthesis with supported metallocene catalysts and the obtaining of a reinforced matrix with nanometric loads are the objective of this study, since the support will have dual functionality: to maximize the efficiency of the catalyst in terms of stereoregularity of the polymer structure and be an active reinforcement, without competing with each other. In the work of Zrkrzewska et al. The polymerization gas used was propene (supplied by Air Liquide). This gas is polymerization grade, with less than 0.06 ppm of oxygen and 0.4 ppm of nitrogen.The following compounds were part of the catalyst system employed: dimethylsilylbisbenzyl zirconium (IV)-dichloride (Me2Si(Ind)2ZrCl2, Aldrich), which was used as catalys. Methylaluminoxane (MAO, 17 wt% solution in toluene, AzkoNobel). Triisobutylaluminum (TIBA, 25 wt% solution in toluene, Sigma-Aldrich). All were used without any treatment.The solvents and monomers used were previously distilled. Toluene (Fisher Scientific, Spain) was refluxed on a desiccant system based on metal sodium and benzophenone (both supplied by Sigma-Aldrich, Spain).All materials sensitive to air, water and impurities were handled in an inert atmosphere under a flow of Nitrogen (99% purity, Air Liquide) within a glovebox or inside the polymerization reactor, respectively.The nanoclay used for the preparation of the PP nanocomposites and like co-catalyst support was a sepiolite (SEP): [Si12O30Mg8(OH)4(H2O)4⋅H2O] without superficial treatment (Pangel HV, supplied by TOLSA). These fillers were dried under vacuum at 80 °C for 24 h before treatment.Once the nanocomposites had been obtained, two thermal stabilizers for polyolefins were used during extrusion process of the specimens (Irganox 1010 and Irgafos 168 supplied by Ciba, Spain).A commercial iPP matrix (Moplen 501L from LyondellBasell), a polyolefin with maleic anhydride grafts (PP-f-AM, Polybond 3200 from Chemtura), using as functionalizing agent and the aforementioned sepiolite was used for obtaining nanocomposites by dilution of masterbach.The sepiolite used was subjected to a drying process at 80 °C for 24 h, then it was stored in the glovebox. A certain amount of clay was placed with a solution of MAO under the clay: MAO ratio of 2:1 for 90 min OH) from sepiolite surface, which acts as a Brønsted acid Al bond (1015 cm−1) present in the treated sepiolites was identified by FTIR as proof of the effective covalent binding between the MAO and the Silanol groups on the surface of the sepiolite.Polymerization of isotactic propene (iPP) was carried out following a rigorous cleaning process of the reactor. The polymerization temperature was set at 20 °C, once achieved, 0.05 M solution of TIBA in toluene was transferred to the reactor and kept under propene atmosphere stirring for 5 min at 600 rpm.In a second step, the reactor was fed with 3.0 × 10−6 mols of a stereo-specific catalyst (Me2Si(Ind)2ZrCl2) in 100 ml of toluene and the amount of MAO solution suitable to have an Al/Zr ratio of 1200. The reaction started with the propene injection at 5 bars and held for one hour.The catalytic activity was stopped by hydrolyzing the MAO with the addition of 100 ml of a mixture of ethanol and 10%v. of hydrochloric acid. The polymer was precipitated in 800 ml of water and kept under stirring for 12 h. It was finally filtered and dried at 80 °C under vacuum for another 12 h approximately.The same polymerization conditions of the iPP, without load, was employed for iPP nanocomposites polymerization with different amounts of modified sepiolite under the treatment described above. The clay was incorporated in the first stage of the polymerization with the TIBA solution. The samples obtained were identified as N0.25iPP_2:1, N0.5iPP_2:1, N1iPP_2:1, N1.5iPP_2:1 and N2iPP_2:1 with 0.25, 0.5, 1, 1.5 and 2 g of clay fed to the reactor, respectively.A second battery test (polymerized with 2 g of initial sepiolite) but with different polymerization times: 5, 10, 20, 30 and 40 min) was obtained, which were named according to the reaction time: N2iPP_t5, N2iPP_t10, N2iPP_t20, N2iPP_t30 and N2iPP_t40. These samples were obtained to determine the variation of the final load content and the polypropylene structure, modifying this experimental parameter.The iPP masterbach was polymerized with 10 g of modified clay under the 2:1 treatment and a polymerization time similar to that of the iPP homo-polymer (1h), but using 5L reactor. This material was called Master_iPP which presented approximately 30 wt% of final load. The masterbach was diluted in a commercial iPP matrix through melt blending to three different concentrations (2.5%, 4.5% and 7.5 wt%) in an internal mixer at 80 rpm, 5 min and 190 °C. The obtained mixtures were denominated: NiPPM_A, NiPPM_B and NiPPM_C respectively. In addition, nanocomposites were obtained by melt extrusion using a functionalizing agent (PP-f-AM) and the modified clay. The obtained samples were labelled as NiPPF_A, NiPPF_B, NiPPF_C and NiPPF_D with 4.5%, 10%, 17.5% and 26.5 wt% of effective filler respectively.The iPP co-polymers and its nanocomposites were synthesized in two stages: in the first battery of reactions, the amount of co-monomer in the reaction medium was varied, maintaining constant the amount of added modified clay and in the second stage, the amount of clay was varied and the molar concentration of co-monomer remained constant during the polymerization. In this way, it has been possible to study the influence of these experimental variables on the incorporation of the branches in the nanocomposite.The composition of the obtained iPP nanocomposites are presented in . All of them were polymerized with their corresponding co-polymers without load under identical synthesis conditions.Finally, the nanocomposite N1CoO0.10iPP and N1CoD0.10iPP corresponding to an iPP polymerized in the presence of octene (C-8) and decene (C-10) as co-monomer were obtained. In this way, the influence of the chain length of the co-monomers on the final properties has been studied.All the synthesized materials were molded in a Schwabenthan hot plate press, heating at 200 °C, for 5 min without pressure and the second step was applied 10 MPa with an additional 10 min. Finally, the plates were stamped with the specific dimensions for each characterization test.Differential Scanning Calorimetry is a technique that allows quantifying the transition energy that the polymer undergoes when it is submitted to a heating protocol. Through the measurement of the heat flow, the crystallization temperature (Tc), crystallinity percentage (%X) and enthalpy (ΔHm) were determined in a Mettler Toledo calorimeter model DSC821e coupled to a computer with STARe Software (Mettler Toledo STARe Thermal Analysis System). The tests were run in an inert atmosphere under a nitrogen flow of 200 ml/min and using a heating rate of 20 °C/min over a temperature range of 25–200 °C. This heating cycle was repeated twice and only the results of the second sweep were reported to avoid the influence of the thermal and mechanical history of the sample. For the metallocene PP a melting enthalpy of 190 J/g was used The Self-nucleation and successive annealing technique allows obtaining qualitative results on the distribution of chains branching, since it is possible to characterize co-polymers whose crystallization occurs in a wide range of temperatures The thermogravimetric analysis allows the study of mass changes associated with physical and chemical changes of the sample when it is subjected to a heating protocol. The thermogravimetric analysis was carried out on a Mettler Toledo 851e equipped with an automatic control system and a data acquisition and processing terminal. The weight percent of clay measurements were taken after a temperature sweep from 50 °C to 950 °C under inert atmosphere and at a rate of 20 °C/min.This technique allows to identify the molecular vibrations produced by the absorption of infrared radiation on a sample. This technique has allowed the qualitative identification of the species present through the characteristic bands in the vibrational spectra of the samples. For these measurements, a Bomen Hartman and Braun FTIR spectrometer, model MB-155 and a total attenuated reflectance accessory (ATR) were used.The FTIR spectra have also been useful for making a semi-quantitative analysis of the co-monomer content in the co-polymers and the degree of isotacticity in the PP samples. These measurements were confirmed in the most representative samples by 13C NMR tests.13C NMR assays are used to determine the amount and distribution of the co-monomers and the isotacticity of the synthesized iPP, through the identification of the couplings and molecular vibrations of the samples. 13C NMR assays were performed on a 500 MHz NMR Spectrometer (BRUKER AVANCE III 500, 11.74 Teslas).Transmission electron microscopy has been used to evaluate the dispersion achieved by sepiolite in the synthesized nanocomposites. The microphotographs have been made with a transmission electron microscope Jeol JM 2000FX with a voltage of 200 kV.The mechanical properties were performed on specimens in the form of dumbbell type 1A, according to the standard, on an INSTRON 5500R60025 universal test machine, at room temperature, according to the procedure specified by the standard. Ten specimens were used for each experiment. The modulus of elasticity was determined with the strain gauge coupling and at a speed of 1 mm/min, whereas for the strain deformation test a velocity of 50 mm/min was applied for all nanocomposites.The determination of the melt flow behaviour of the materials was carried out on a Ceast model 7026 at 190 °C and 2.16 kg of load. This test was carried out under the standard UNE-EN ISO 1133.The density determination was done in order to study the variations in weight of the synthesized nanocomposites, by the effect of the addition of the clay and the co-monomers. These measurements were made using an analytical balance Mettler Toledo, model AX205 DR, under the standard ISO 1183-1. The analysis was determined on five samples of each material.Gel permeation chromatography is a separation technique for quantitatively obtaining the molecular weight distribution of a polymer. The technique consists of passing the dissolved polymer through molecular sieves of different sizes. The equipment used was a Waters GPCV2000 chromatograph (D04180221P) and the solvent used for all polyolefins was 1,2,4-trichlorobenzene at a temperature of 145 °C. A 2 L Gel column 10 μM Mixed B and a PL Gel 10 μm 1 × 106 were used.The thermal characterization of the iPP nanocomposites synthesized have shown that whether the amount of sepiolite increases, an increase in the crystallization and in the melting temperatures of the material is achieved. Furthermore, a progressive increase in the crystallinity percentage is also observed in This is a consequence of nucleating action of the nanoparticles on the matrix. (a) shows how the melting endotherms move to higher temperatures, as a sign of the thickening of the crystals formed; therefore, this effect is accompanied by an increase in the area under the curve because the crystalline sections have also grown in number when the sepiolite increases in the reaction medium. However, above a certain percentage of load this effect is attenuated, as a consequence of the loss of productivity (impurities) and the steric hindrance provokes the increase of the concentration of the nanoparticles in the reaction medium The increase of crystallinity of iPP at low clay concentrations are not only due to the presence of sepiolite in the medium, but also to the highly hierarchical order of the matrix. It is known, that nanoparticles are good nucleating agents on PP matrix with less stereo-defects preventing that chains form part of the crystal The nanocomposite shows a slight increase of molecular weight in number and weight as compared to its unloading analogue. This confirms that the selected experimental conditions (low temperature with the stereo-specific metallocene catalyst used) promote a slow and coordinated reaction that itself (without the presence of clay), promotes the formation of a material with 91.7% iso-tactics and a polydispersity equal to 2, that is, an ideal homogeneous catalysis of a single active site.This confirms that the supported catalysts (in this case at a nanometric load) facilitate the propagation reactions before the termination reactions Although it could be thought that the presence of clay in the synthesis of iPP nanocomposites could represent a steric hindrance to the rotation and the controlled insertion of the monomer in the growing chain, at low load concentrations the coordinated activity of the catalyst is not affected. On the contrary, the stereo-regularity of the synthesized iPP increases up to 96%. This is due to the stability provided by the immobilization of the catalyst in a solid particle.The synthesis procedure used has not only demonstrated a high hierarchy of the synthesized structure, but also an excellent dispersion and distribution of the nanoclay in the polymer matrix (see ). The non-oriented (compression) molding process allowed the observation of clay fibers in both longitudinal and transversal directions.Additionally, the polymerization powders obtained showed a macrostructural morphology in the form of threads, as a consequence of the replication phenomenon (growth of the polymer from the surface of the fibrillar load) ). The starting material (homo-polymer without load) has a specific modulus above 1700 MPa, a direct consequence, as mentioned above, of the type of catalyst and the experimental conditions of synthesis. With the presence of the clay there is a progressive increase of the Young's modulus due to the stiffening that promotes the reinforcement and to the nucleating effect of the nanoparticles on the synthesized matrix.It is well known that the nanofillers improve the rigidity on the nanocomposites at the expense of reducing the elongation at break. When the amount of filler is increased, the mobility of the amorphous sections is conditioned which results in a progressive loss of the elongation at break (When the properties of nanocomposites with the greatest amount of filler were evaluated, a very low productivity was obtained, as expected, as a result of the increase on the density of the OH groups. This causes, as a direct consequence, the exponential increase of the amount of clay in the final materials, with the additional aggravating factor that the synthesized matrix had a totally atactic conformation. Thus, when fed with more than 2 g of sepiolite to the reactor, the material that was obtained was impossible to characterize because of its low melt stability (low melting temperature and high fluidity, proper behaviour of aPP) and due to form a kind of clay agglomerate that was not stable in the synthesized matrix.One way to achieve higher-load iPP nanocomposites, without affecting the stereo-specificity of the matrix, is to control the productivity of the reaction over time. Li et al. presents the thermal and structural properties of these materials. The consequent increase in productivity can be observed when the polymerization times are increased. In it is observed that there is a polymerization time in which the amount of polymer synthesized is stabilized, that is to say, by a process of deactivation or consumption of the catalysts. If time is higher cannot be further diluted the load, because the process of synthesis has stopped. This demonstrates that under these specific experimental conditions, nanocomposites with less than 4.2 wt% of load cannot be obtained unless any experimental variable (T, P, [Zr], etc.) will be manipulated. This is associated with the increase of productivity, but bearing in mind that in that case the molecular weight and stereoconformation of the final polymer could also undergo some important variations. Finally, this demonstrates that all synthesis processes of nanocomposites have to be designed taking into account how each experimental variable determines the properties of the final nanocomposite.It should be expected that these materials, which have been synthesized under identical conditions (same clay concentration and active centers for the polymerization) should have the same microstructure, because the polymerization time only determines the amount of material produced. This is demonstrated when measuring iso-tacticity index (with FTIR measures) they remain invariant (between 96% and 97%), and that is, everything produced has the same structural conformation, independently of the amount of synthesized material.In addition, for a deeper study of the microstructure of these materials, a controlled annealing was applied to samples through a SSA test. The results, which are reflected in the endotherms of , reveal that all materials, regardless of polymerization time, have the same crystalline sections. These sections need a higher melting temperature as the amount of synthesized material is increased as a consequence, in turn, of the increase of crystalline populations and lamellar thicknesses which leads to an increase of the molecular weight with the polymerization times. This is also reflected in the data of The materials with the highest amount of load, which could not be mechanically characterized by the lack of synthesized material, have been useful to produce a masterbatch that can be subsequently dissolved in a commercial matrix of PP. This may be possible because a material with enough thermal and structural stability has been grown on the surface of sepiolite and should be compatible with an iPP in a subsequent dilution process.For this study, the necessary considerations to achieve a high percentage of iso-tacticity on the filler were taken into account. Therefore, the results of the previous study were used, where it was stated that decreasing the reaction times, whose experimental parameters control iso-tacticity, it is possible to obtain iso-tactical materials with a high percentage of final filler. presents the results of the nanocomposites with the same final clay content (4.2 wt%) obtained by different methods. In this case, other properties have been measured, such as the heat deflection temperature (HDT), to determine its maximum temperature of use and the maximum penetration energy in a high-speed impact test (Puncture), in addition to the modulus in tension and the elongation at break. shows that the nanocomposites obtained by in situ polymerization present the best values for Young’s modulus. The use of the polymerization process increased the isotacticity allowing to rise 51% of the Young's modulus comparing with its unload counterpart. On the contrary, in the melt blending nanocomposite, where the matrix has been nucleated by the presence of clay but does not undergo changes on its stereo-regularity, the increase in modulus and loss of ductility are smaller. The dilution method, through the using of a masterbatch, lead to a balance of the properties, i.e., a moderate increase in stiffness without such a dramatic loss of ductility.Another evidence of the improvement of the properties of the PP when it is mixed with a concentrate of load by both melt extrusion and mixer chamber, is the increase in a 5% of its maximum temperature of use, which opens many possibilities to find applications of these materials. shows a comparison of Young's modulus for the three studied methods. The stiffness improvements are related to the slope of the curves. In this sense, nanocomposites obtained by in situ polymerization presented highest values of Young's modulus for the same amount of nanoclay. However, in situ polymerization cannot be used for nanocomposites with a high content of sepiolite. In order to obtain highly loaded nanocomposites, melt blending and master dilution may be used.Iso-tactical polypropylenes with high stereo-regularity and high percentages of crystallinity are not useful for all applications where PP is required. Especially in applications at low temperatures, or when translucency is required because they are very rigid and opaque due to their high crystallinity. For this reason, many researchers have focused on the production of PP copolymers. In this sense the use of small olefins grafts Our work consisted of synthesizing iPP copolymers and its nanocomposites with 1-olefins of different lengths (hexene, octene and decene). To understand the influence of the variables such as the amount of co-monomer and the amount of clay over the structure-properties relationship, three concentrations of hexene with different quantity of sepiolite were used.The properties measured of these materials are presented in The iPP copolymers synthesized presented a dependence between the experimental conditions, their structure and their final properties. Thus, whenever an α-olefin is added to the polymerization medium it acts as a transfer and termination agent which interrupts the propagation process of the growing chain. This produced a drop in molecular weight, crystallinity and melting temperatures and thus, consequently a significant improvement in the flowability that favors its processing (see SSA curves of hexene-based iPP nanocomposites are shown in . It is observed that the nanocomposite copolymer (N1CoH0.05iPP) presented mainly one crystalline section, contrary to the copolymer CoH0.05iPP. This phenomenon is caused by the presence of sepiolite, which is able to cluster the different crystalline sections into one. On the other hand, the rise of the co-monomer in the final structure produced an increase in the number of crystalline sections., the influence of amount of co-monomer (hexene), amount of clay and length of co-monomer on the structure of the iPP nanocomposites was represented in . In this way, the structure-properties relationship of the synthesized copolymers can be better understood.As it is was expected, the increase of hexene co-monomer leads to raise its content in the final material. Comparing the samples CoiPP and NCoiPP can be observed how the presence of sepiolite increases the final content of the co-monomer (see (1b, 1c and 1d) the inverse correlation between the amount of co-monomer and the iso-tacticity, melt temperature and crystallinity can be observed. This is because the incorporation of branches to the PP chain, not only means a defect for the crystal, which will subsequently decrease the crystallization capacity of the synthesized chains, but also limits the stereo-specific activity of the catalyst to continue producing isotactic sections. In all cases the corresponding nanocomposites exhibited better values for each property. This phenomenon is promoted by the decrease in the number of crystalline sections and the nucleating effect produced by the sepiolite.To explain the influence on the properties of the amount of clay added, (2a, 2b, 2c, 2d, 2e) is studied. In 2a and 2b, it was possible to observe that when the amount of clay is increased (for a fixed percentage of co-monomer), the incorporation of the co-monomer was more effective and made more orderly. This is because the presence of the sepiolite promotes a greater insertion of the branches to the structure of the nanocomposite. Additionally, the nanocomposites presented a rise of melt temperature and crystallinity (see (2c and 2d)) due to the nucleating effect of the sepiolite. As shown in the graph 9 (2e), high concentrations of co-monomer [0.15 M] increased the amount of clay present in the final nanocomposite due to the lack of synthesized matrix.The effect of type of branching is plotted in (3a, 3b, 3c, 3d and 3e). An important observation of figure (3a) is that the productivity of the grafted co-monomer depends more on the presence of clay than of the length of ramification included in the chain. However, the length of the grafted co-monomer caused a significant drop in stereo-regularity (see (3b)). This is because the steric hindrance over the catalyst activity is greater when longer co-monomers are grafted (3c and 3d) were observed that the highest fusion temperature and crystallinity was achieved when the length of the ramifications was six carbons. The most important observation is that in both cases, the nanocomposites showed best properties that the unload copolymer owing to the nucleating effect of the sepiolite. (3e) reflected that percentage of the final clay in the nanocomposites increased when the co-monomer length was higher. This is due to the steric hindrance is increased over the activity of the catalyst when longer comonomers are grafted. The copolymerization reactions with co-monomers of great length limits not only the stereo-specificity of the reaction but also its productivity. That is reflect in the percentage final of load in the nanocomposites, which is greater when the length of the graft monomer is longer because a smaller amount of polymer is synthesized.To conclude, the summary of the mechanical properties is presented in the graphs of . It was observed the significant drop of the Young's Modulus presented by the copolymers, due to the dramatic loss of iso-tacticity and crystallinity that these materials suffered when they incorporated ramifications. Only the nanofilled materials were able to compensate the fall of Young's Modulus by the nucleating effect of the sepiolite and by the improvement of the stereo-regularity of the synthesized chains (see (2a, 2b and 2c) the materials with clay showed the best properties in elongation at break, not only because they incorporated more amount of co-monomer to the structure, but also because it has been in a more orderly way (narrower polydispersities between 4.20 and 3.90, while the uncharged copolymers had IP close to 5).The most important conclusion to be drawn from this study is the need to understand the importance of stereo-regularity in coordination polymers in order to apply the in situ polymerization technique, since the proposed polymerization mechanisms considerably affect the structure of the polymer formed.In iso-tactical polypropylenes it is important to point out that their in situ nano-reinforcement depends, almost exclusively, on the success of the stereo-specific activity of the catalyst used in the presence of the clay and co-monomers concentration in the reaction medium.Finally, it is necessary to validate the alternative method of dilution of the masterbatch for the production of polyolefin nanocomposites. This method exploits the advantages of obtaining in situ nanocomposites in a more productive and economical way, taking into accounts that for this, a balance is made between the properties that are obtained in each method and the cost of production.Mechanical properties of corrugated composites for candidate materials of flexible wing structuresCorrugated-form composites are expected to be very flexible in the corrugation direction and stiff in the direction perpendicular to the corrugation. In this study, the corrugated composites manufactured from carbon fiber plain woven fabrics draw attention as a candidate material for flexible structural components, e.g. morphing wings. In-plane stiffness and strength of the original corrugated composites are evaluated through the tensile and bending tests in both in-plane longitudinal and transverse directions. A simple analytical model for the initial stiffness of the corrugated composites is developed, and the predictions are compared with the experimental results. Moreover, some improvements, installing of stiff rod and flexible rubber, are attempted for the creation of smooth aerodynamic surface and the improvement of stiffness. Mechanical properties of the modified corrugated composites are also evaluated and compared with those of the original corrugated composites. The applicability of the corrugated composites to the flexible wing structures are discussed based on the specific stiffness, longitudinal-to-transverse stiffness ratio, etc.Recent development of smart technologies, including sensors and actuators, provides the potential to increase aircraft system safety, affordability, and environmental compatibility One solution to this cumbersome problem is to adopt anisotropic materials that act flexible in the chord direction and stiff in the span direction. In usual flight profiles, aerodynamically induced bending loads in the span direction dominantly operates in the wing structures, while chord-wise morphing influences the aerodynamic characteristics significantly. One might imagine fiber-reinforced rubber/elastomer has anisotropic characteristic that shows stiffness in the fiber direction and flexibility in the transverse direction. However, fiber-reinforced rubber/elastomer has low resistance against compressive instability in the fiber direction, and thus, low bending strength. Therefore, the authors propose corrugated-form composites as a candidate for morphing wing structures.Corrugated structures are widely used as the cores of the sandwich structures (e.g. sandwich composites and card board) shows the corrugated-form composites that are flexible in the corrugation direction and stiff in the transverse direction to the corrugation. The corrugated composites may be applicable to morphing wing structures in the manner that the corrugation direction aligns to the chord direction as shown in . Morphing wings manufactured from the corrugated composites are expected to withstand the bending loads in the span direction and change shape easily in the chord direction.In this article, feasibility study on the application of corrugated composites to wing structures is carried out by investigation of the ultra-anisotropic mechanical properties of corrugated composites. Experimental results of the tensile and bending properties of the corrugated composites are presented in conjunction with the simple analytical prediction. In addition, some modifications are attempted to the corrugated composites for the creation of smooth aerodynamic surface and the improvement of stiffness. Mechanical properties of the modified corrugated composites are evaluated and compared with those of the original corrugated composites. Discussions on the applicability of the corrugated composites to the flexible wing structures are provided.The material used in this study was T300-1K/RS11, carbon fiber plain woven fabrics prepreg system. The corrugated composites were manufactured at 130 °C for 2 h under proprietary process (Ultracor Inc.). The nominal wave height (hc) and spacing (wc) were set as 3 mm (see ). In this study, the corrugation direction (flexible direction) and the direction perpendicular to the corrugation direction (stiff direction) are referred to as “transverse” and “longitudinal” directions, respectively. The longitudinal and transverse modulus and strength of the corrugated composites are evaluated by tension and bending tests in reference to Japanese Industrial Standards (JIS) K7073 and K7074. For the transverse flexural modulus, deflection of one-sided fixed cantilever due to its own weight was measured. The flexural stiffness per width, D, can be expressed aswhere δe, ρ, g, and L means the measured deflection at the free end, density of corrugated composites, gravity acceleration, and cantilever length, respectively. Although corrugated composites have non-uniform density, we assume corrugated composites as homogeneous materials with ρ. Note that ρ is defined as the weight divided by the apparent volume (L |
× |
hc |
× width). The density of corrugated composites used in this study was 163 kg/m3.Longitudinal tensile specimens were 200 mm long with 40 mm rectangular aluminum end-tabs, leaving a 120 mm gauge section. Transverse tensile specimens were 150 mm long with 35 mm aluminum end-tabs. The aluminum tabs were bonded to the specimens using epoxy adhesives. Tension test apparatus is shown in . An extensometer (Instron Corp.) was attached to the specimen in order to measure the strain in the longitudinal tensile test, while the strain was measured by the crosshead displacement in the transverse tensile test. In the longitudinal bending test, four-point bending load was applied to the specimens using 3 mm diameter load noses. The width of the specimen and span length were 15 mm and 120 mm, respectively. The cantilever length in the transverse flexural test was set to be 60 mm. A laser deflection sensor (LK-080, Keyence Corp.) was used for measurement of the central deflection of the longitudinal bending specimens and the free end deflection of the transverse bending specimens. The specimen configurations are summarized in Stress–strain relationships of the tensile tests in longitudinal and transverse directions are shown in . The stress of corrugated composites is defined as the loads divided by effective cross-sectional areas (width × thickness), where thickness is equal to the measured hc, and the strain is nominal strain. Almost linear behaviors can be observed in both directions, although some increase and decrease of tangential modulus are identified in the longitudinal and transverse direction, respectively. The increase of tangential modulus in the longitudinal direction is due to the geometric change of the woven fabrics (i.e. decrease of undulation), which is commonly observed in the fabric composites. During the transverse loading, microscopic damages induced in the curved regions of the corrugated composites cause the decrease of transverse tangential modulus. The failure strains are about 1% in the longitudinal direction and 45% in the transverse direction. Corrugated composites turned out to have the capacity to extend flexibly in the transverse direction.The load–deflection curves of the longitudinal bending tests are presented in . Specimens were fractured in the vicinities of the upper load noses, which resulted in jaggy shapes of the load curves. The bending strength was calculated from the maximum load (Pmax) based on the beam theory, as it is assumed that corrugated composites are treated as homogeneous beams.Tensile and flexural properties (averaged values and standard deviations) are summarized in . Young’s moduli of the corrugated composites were almost same as those of plastics in longitudinal direction and rubber/elastomer in the transverse direction. Longitudinal-to-transverse ratios of tensile and flexural moduli were about 4600 and 6800, respectively. Therefore, it was confirmed that corrugated composites have the ultra-anisotropic characteristics. The above-mentioned unique property of the corrugated composites stems from the fact that membrane and bending stiffnesses of the fabrics are related to the loadings in the longitudinal and transverse direction, respectively. This relationship can be checked in the stiffness analysis as described later.The obtained flexural strength and the tensile strength in longitudinal direction were comparable because the former reached more than 80% of the latter as shown in . It can be concluded that corrugated composites have enough resistance against bending loads in the longitudinal direction., there are slight differences between the stress–strain curves and the load–deflection curves corresponding to individual specimens. Although the measured strengths and nonlinear behaviors at high strain levels vary among specimens, initial moduli provide the satisfactory reproducibility (see ). The variation in the strength can be observed in the common fabric composites. In the case of corrugated composites, corrugation geometries (i.e. wave spacing, wave height, corrugation radius, etc.) vary locally, which results in variation of mechanical behaviors at high strain levels. However, initial mechanical properties can be obtained without large dispersion when using specimens with enough length.Corrugated composites can be designed depending on the corrugated appearance (e.g. wave height, wave spacing) as well as the material to be used. A simple analytical model is developed to predict longitudinal and transverse stiffnesses of the corrugated composites. The cross-sectional micrograph of the corrugated composites is shown in (a), and the analytical area is defined in (b). In this study, plain woven fabric composite is treated as a homogeneous material, which has corrugated appearance, instead of modeling of the corrugated plain woven fabrics directly. The two-step modeling consists ofevaluation of effective stiffness of the plain woven fabrics,modeling of corrugated “effective” composites.In the step (i), one-dimensional mosaic model The relationship between the parameters in where rc is the curvature radius of the curved section and lc (⩾0) is half length of the straight section.The effective properties of the corrugated composites are formulated using the effective properties of fabrics and geometric parameters. In the longitudinal direction, the effective extensional and flexural properties of the corrugated composites can be evaluated by considering the volume fraction and the moment of inertia of the fabrics in the analytical area, respectively. Transverse effective properties can be predicted based on Castigliano’s theorem using a curved Bernoulli–Euler beam as shown in . Note that plain woven fabrics have equal biaxial stiffnesses (i.e. A11 |
= |
A22 and D11 |
= |
D22), and this behavior is implicit in the following formulations. Material anisotropy should be incorporated into the analytical model when treating the corrugated composites manufactured from other fabrics.The longitudinal Young’s modulus of the corrugated composites, ELeff, can be predicted from considering the volume fraction of the fabrics or homogeneous material.For the estimation of the longitudinal flexural modulus of the corrugated composites, it is assumed that plain woven fabrics are homogeneous and have Young’s modulus of A11/t (because woven fabrics generally have small Poisson’s ratios). By calculating the moment of inertia of cross-sectional area, we can express the effective longitudinal flexural modulus per width of the corrugated composites, DLeff, asDLeff=A1116lc3+24πlc2rc+3πrc4rc2+t2+8lc12rc2+t248rcIn order to predict the transverse modulus of the corrugated composites, a curved Bernoulli–Euler beam is considered as shown in . Calculation of the deflection or rotation angle at the point A leads to formulation of the transverse modulus based on Castigliano’s theorem. The deflection of the point A due to transverse load P, δ, can be described asTherefore, the effective transverse Young’s modulus of the corrugated composites, ETeff, is expressed asIn the same way, the rotation angle at the point A due to moment M, ψ, isThe effective transverse flexural modulus per width of the corrugated composites, DTeff, can be expressed asThe longitudinal and transverse stiffnesses are explicitly related to extensional stiffness of the fabrics, A11, and flexural stiffness, D11, respectively. These correlations cause the unique property of the corrugated composites.It is worth noting that an interesting analytical approach is presented for corrugated beam structures using the asymptotic expansion method by Potier-Ferry and Siad , coincides with the analytical result of Ref. In this study, the equivalent extensional and flexural stiffnesses of plain woven fabrics were determined using the one-dimensional crimp model (estimated using fiber and matrix properties), normalized undulation length of 0.8, and ply thickness of 0.15 mm; A11 |
= 4.96 × 106 (N/m) and D11 |
= 0.0056 (N/m). Using these effective properties of plain woven fabrics, the tensile and flexural stiffnesses of the corrugated composites were calculated using Eqs. . Comparison between predicted and experimental results is shown in , in which slight differences are observed between the two. As the reproducibility of the experimental stiffness measurements was satisfactory (see ), the conceivable reason of this discrepancy is due to analytical simplicity. In this study, the effective fabric properties are applied to the estimation of the effective stiffnesses of the corrugated composites (i.e. two-step modeling). Therefore, effects of local undulation of the fabrics and local geometric variations on the mechanical behavior of the periodic cells of corrugated composites are not included in the present simple model. Although there are slight differences between predicted and experimental values, mechanical properties of corrugated composites can be simply estimated using the present analytical model.Mechanical properties of the corrugated composites depend on the corrugated appearance or shape parameters (wc and hc). In , predicted longitudinal/transverse tensile and flexural stiffness is plotted as functions of wave spacing and height using geometrical and material properties described above. We can design the stiffness of the corrugated composites by choosing the appropriate shape parameters, however, there should be some limitation of shape parameters in manufacturing (e.g. too small spacing is not realistic). Under the situations of wing application, higher stiffness out of the designable range may be necessary in the longitudinal direction. Moreover, corrugated composites have wavy surface, which may have adverse effect on the aerodynamic characteristics. Therefore, two issues are considered to be solved in the application of corrugated composite to wing structures. One is the lack of stiffness in the longitudinal direction, and the other is wavy surface. In the following section, some improvements are attempted to the corrugated composites for these problems.Two improvements were attempted to the corrugated composites; (1) installation of stiff rod (e.g. unidirectional CFRP rod) in the valley sections, and (2) one-sided filling of flexible rubber. The former is implemented in order to improve the stiffness in the longitudinal direction of the corrugated composites, while the latter leads to the creation of smooth aerodynamic surface. Three modified specimens were prepared (see ); rod-stiffened corrugated composites (CC1), corrugated composites with one-sided filling of rubber (CC2), and rod-stiffened corrugated composites with one-sided filling of rubber (CC3). Mechanical properties of the modified corrugated composites are measured and compared with those of the original corrugated composites (CC0). In this experiment, the emphasis is placed on; (1) improvement of longitudinal stiffness, (2) whether the flexibility in the transverse direction remains or not, and (3) specific stiffness.Unidirectional CFRP rods with diameter of 1 mm (Mitsui Kagaku Sanshi Co. Ltd.) are utilized as the stiff rods, and RTV rubber (KE45, Shin-Etsu Chemical Co. Ltd.) is filled in the one side of the valley section of the corrugated composites. In order to prepare CC1 and CC3 specimens, CFRP rods were bonded to the valley sections of the corrugated composites using epoxy adhesives. The measured Young’s moduli of CFRP rod and RTV rubber were 92 GPa and 1.3 MPa, respectively.Tensile and flexural tests of the three modified composites were carried out under the condition that is same as those described in the experimental procedure of the original corrugated composites. In this study, it is assumed that longitudinal moduli of CC2 are nearly equal to those of CC0 because the modulus of filled rubber is very small compared to the longitudinal stiffness of the corrugated composites (CC0). The longitudinal moduli of CC3 are also assumed to be same as those of CC1. Thus, longitudinal and transverse tests were conducted for CC1, while only transverse tests were performed for CC2 and CC3.Summary of the test results (tensile/flexural stiffness and strength) is provided in . It can be concluded that the longitudinal stiffness increases due to the installation of CFRP rods without loss of flexibility in the transverse direction. The longitudinal-to-transverse stiffness ratios and specific stiffness are summarized in . Specific stiffness based on the flexural modulus is calculated according to the following equation:The modified corrugated composites were found to have excellent mechanical properties for morphing wing structures (anisotropic characteristics) as well as light weight structures (specific stiffness). One-sided filling of rubber, which was attempted in order to create smooth aerodynamic surface, resulted in the decrease of specific stiffness. Specific stiffness will increase when thin film is attached to the corrugated composites instead of filling rubber. It is concluded that installation of stiff rods in the valley section of corrugated composites is effective method in order to improve the mechanical properties in the longitudinal direction without loss of flexibility in the transverse direction.Corrugated composites were proposed as candidate materials for flexible wing structures in relation to the morphing aircraft technology. Mechanical properties of the corrugated composites in the longitudinal and transverse directions were evaluated through tensile and flexural tests. It was confirmed that the corrugated composites have ultra-anisotropic characteristics (i.e. stiff in the longitudinal direction and flexible in the transverse direction), and the capacity to extend and deform flexibly in the transverse direction. A simple analytical model of the stiffness of the corrugated composites was developed, and validated by comparing with the experimental results.Modifications for the improvement of stiffness and the creation of smooth aerodynamic surface were attempted to the corrugated composites; (1) installation of CFRP rod in the valley regions, and (2) one-sided filling of flexible rubber. Mechanical properties of the modified corrugated composites were evaluated and compared with those of the original corrugated composites. It was concluded that longitudinal stiffness increases due to the installation of CFRP rods without loss of flexibility in the transverse direction. The modified corrugated composites turned out to have excellent mechanical properties for morphing wing components as well as light weight structures.Molecular statics and molecular dynamics simulations of the critical stress for motion of a/3 〈112¯0〉 screw dislocations in α-Ti at low temperatures using a modified embedded atom method potentialMolecular statics and molecular dynamics, and constant temperature, constant volume (NVT) simulations, were performed to determine the core structure and critical stress for motion of a/3〈112¯0〉 screw dislocations in α-Ti at temperatures ranging from 0 to 50 K using a modified embedded atom method (MEAM) potential. Five different core structures were obtained for the a/3〈112¯0〉 screw dislocations in α-Ti, one completely spread on the prism plane, three others partially spread on the prism plane and partially spread on the pyramidal and basal planes, and one with predominantly Shockley partial splitting on the basal plane. The core completely spread on the prism plane is found to be the lowest energy structure. The Peierls stress for the minimum energy structure completely spread on the prism plane at 0 K is found to be a high value of 6.875 × 10−3 |
μ, where μ is the shear modulus and is independent of the orientation of the applied stress. It is shown that this high Peierls stress at 0 K is a consequence of the angular interactions in the MEAM potential. The kink-pair formation energy at zero applied stress is found to be low and equal to 0.16 eV. NVT molecular dynamics simulations show that the minimum stress required to move the screw dislocations by kink-pair formation at temperatures ranging from 5 to 50 K is significantly lower than the 0 K Peierls stress value. A classical phenomenological kink-pair model is fitted to the molecular dynamics data and used to correct for the significantly lower strain rate of deformation present in experiments as compared to molecular dynamics simulations. The corrected simulation data are in reasonable agreement with low-temperature experimental observations of yield stress in single-crystal α-Ti oriented for a/3〈112¯0〉 prism slip. The developed kink-pair model for prism slip in α-Ti will be useful in higher length scale crystal plasticity models for the deformation behavior of α-Ti.Ti alloys, because of their light weight and high strength, are preferred over steels for energy-absorbing applications Previously, there have been calculations of the core structure of a/3〈112¯0〉 screw dislocations in α-Ti using first principles techniques The rest of the manuscript is organized as follows: Section describes the simulation methodology, potentials and the technique used to depict the core structures. Section describes and discusses the results from 2-D molecular statics simulations of the core structure and Peierls stress at 0 K of a/3〈112¯0〉 screw dislocations in α-Ti; 3-D molecular statics simulations determining kink-pair formation energy on the prism plane for a/3〈112¯0〉 screw dislocations in α-Ti using the MEAM potential; and 3-D molecular dynamics simulations of the critical stress required to move a/3〈112¯0〉 screw dislocations on the prism plane by kink-pair formation at temperatures ranging from 5 to 50 K using the MEAM potential. Section For the 2-D molecular statics simulations of the core structure and the Peierls stress at 0 K of a/3〈112¯0〉 screw dislocations in α-Ti, a single periodic unit cell along the x or dislocation line direction [21¯1¯0] was chosen. The simulation cell was 300 Å in size along the other two perpendicular directions, [011¯0] and [0 0 0 1]. There were 16,027 atoms in the simulation cell. Note that the size of the simulation cell chosen is much larger than was previously used for similar simulations using first principles or the MEAM potential The technique used to determine the kink-pair formation energy of a/3〈112¯0〉 screw dislocations on the prism plane in α-Ti was very similar to that used to determine constriction energies in face-centered cubic Ni The initial conditions for the 3-D molecular dynamics simulations was a 100 periodic unit long length screw dislocation simulation cell relaxed using the conjugate gradient technique at a particular applied pure shear stress on the (011¯0) prism plane. Periodic boundary conditions were applied along the dislocation line direction. Free surface boundary conditions were applied along the other two directions. The number of atoms in the simulation cell was 1,602,700. Additional forces were applied on atoms in a thin layer (twice the range of the interatomic interactions in the MEAM potential) at both boundaries along the y direction For most of the simulations, we used the MEAM potential developed for α-Ti by Hennig and co-workers where θijk is the angle between atoms j, i and k centered on atom i. In Eq. (2), the second term represents three-body or angular interactions. In the classical central force EAM formalism, this term is absent.The MEAM potential describes the structural, elastic and defect properties of the α, β and ω phases of Ti fairly accurately To determine the effect of angular interactions in the MEAM potential on the core structure and Peierls stress at 0 K of a/3〈112¯0〉 screw dislocations in α-Ti, 2-D simulations were performed using the highly optimized central force EAM potential developed for α-Ti by Zope and Mishin compares the stacking fault energies on the prism, pyramidal and basal planes obtained using the EAM and MEAM potentials with first-principles calculation results Five distinct core structures were obtained for the a/3〈112¯0〉 screw dislocation in α-Ti using the MEAM potential, and the differential displacement plots of the screw component for the five different core structures are shown in . The first three distinct core structures were obtained by varying the origin of the anisotropic displacement field by which the screw dislocation was initially introduced into the 2-D simulation cell. Thirty different elastic centers were attempted for the initial anisotropic displacement field and in all cases the screw dislocation core relaxed to one of the three structures shown in corresponds to the global minimum energy structure, where the core is planar and predominantly spread on the (011¯0) prism plane. In the higher energy structures corresponding to , the core is partially spread on the prism plane and partially on the pyramidal and basal planes. Core 2 is ∼0.006 eV/b and core 3 is ∼0.004 eV/b higher in energy compared to the minimum energy structure predominantly spread on the prism plane, core 1. The last two core structures, cores 4 and 5, were obtained when the screw dislocation was initially inserted as two a/6[21¯1¯0] partials separated by 5 and 15 Å, respectively, on the (0 0 0 1) basal plane. Core 4 shows a non-planar structure with significant spreading on the prism, basal and pyramidal planes, and is ∼0.012 eV/b higher in energy compared to core 1. Core 5 is planar, with predominantly a Shockley partial-type splitting on the basal plane, and is ∼0.13 eV/b higher in energy compared to the minimum energy structure, core 1. The difference in energies between cores 1 and 5 are in fairly good agreement with first principles calculation results shows the relative energies of various core structures obtained for the a/3〈112¯0〉 screw dislocations in α-Ti using the MEAM potential. Similar core structures for the a/3〈112¯0〉 screw dislocation in α-Ti were obtained previously (cores 1 and 4) from first-principles calculations, as well as calculations using the MEAM potential using much smaller simulation cells The global minimum energy core completely spread on the prism plane () was subjected to pure compressive stresses close to the [314¯0], [628¯3] and [448¯3] directions. The screw dislocation overcame the Peierl’s barrier between applied stresses of 494 and 543 MPa along approximately the [314¯0] direction. The Schmid factor for this direction of applied stress is 0.5. Therefore, the resolved shear stress at which the screw dislocation moves lies between 247 and 272 MPa. In terms of the shear modulus μ, which is 39.5 GPa for this potential, this corresponds to a Peierls stress of ∼0.0066 μ. gives the differential displacement plot of the equilibrated core at an applied stress of 494 MPa along approximately the [314¯0] direction. For the applied stress direction close to [448¯3], the screw dislocation overcame the Peierls barrier between stresses of 632 and 711 MPa. For this direction of applied stress, the Schmid factor is 0.375. Therefore, the resolved shear stress at which the screw dislocation overcomes the Peierls barrier for approximately the [448¯3] applied stress direction lies between 237 and 266 MPa, which is ∼0.0064 μ. Similar behavior was observed for the [628¯3] direction of applied stress. These results suggest very little orientation dependence for the Peierls barrier of a/3〈112¯0〉 screw dislocations in α-Ti. This can be understood in terms of very little non-planarity and minimal edge components in the screw dislocation core of and is consistent with the fact that, experimentally, hcp crystals obey Schmid law. Also experimentally, the 0.2% critical resolved shear stress for prismatic slip in high-purity α-Ti at 4.2 K is ∼70–120 MPa, which is 0.0018–0.003 μ A highly optimized central body EAM potential was subjected to compressive stresses close to the [314¯0] direction, the screw dislocation overcame the Peierls barrier at very low stresses of ∼10 MPa, significantly different from the results obtained with the MEAM potential, discussed previously. These results suggest that the three-body interactions present in the MEAM potential lead to the high Peierls barrier for prism slip in α-Ti.Non-planar cores 2 and 3, obtained with the MEAM potential for the a/3〈112¯0〉 screw dislocations in α-Ti, were also subjected to pure compressive stresses along the [314¯0] direction. Core 2, transformed under an applied stress to core 1 (), and overcame the Peierls barrier at a resolved shear stress of ∼0.0066 μ, very similar to core 1. Core 3, however, was stable and did not overcome the Peierls barrier even at applied resolved shear stresses of ∼0.02 μ (One half of the single kink simulation cell consisted of a 100 periodic unit cell with the screw dislocation core spread on the (011¯0) prism plane, obtained from molecular statics conjugate gradient minimization, with periodic boundary conditions along the dislocation line direction and fixed boundary conditions along the other two directions. The other half was a similar core but displaced with respect to the original half by the kink vector, 1/6[202¯3], on the prism plane. The two halves are connected together at the center of the simulation cell and conjugate gradient minimization was applied on these initial atomic positions with fixed boundary conditions along all three directions. By reversing the position of the displaced core (right or left), the structure of the two different single kinks (right or left kink) could be obtained. Kink energies were determined by summing up the difference between energies of corresponding atoms in the relaxed region between the kink simulation cell and the long-length dislocation simulation cells. The single kink formation energies determined in this fashion for a/3〈112¯0〉 screw dislocations on the prism plane using the MEAM potential were fairly low, 0.07 and 0.09 eV. The kink energies were confined to a thin layer (yz prismatic shell) at the center of the simulation cell, ±25 Å along the x or dislocation line direction. The kink-pair formation energy at zero applied stress is then 0.16 eV, which is significantly lower than the calculated and experimentally determined kink-pair formation energies for a/2[1 1 1] screw dislocations in bcc metals shows the molecular dynamics simulation critical stress data as a function of temperature for a/3〈112¯0〉 screw dislocations on the prism plane in α-Ti. The critical stress is normalized with respect to the Peierls stress at 0 K obtained from the 2-D molecular statics simulations. Several (four or five) molecular dynamics simulations for each temperature and stress were run for a total of 100 ps. The minimum stress at which the screw dislocation moves at least one periodic unit on the prism plane by kink-pair formation in 100 ps was taken to be the critical stress. Also shown in are the kink-pair model results for a/3〈112¯0〉 screw dislocations in α-Ti obtained by fitting to the molecular dynamics simulation data using the Kocks–Ashby phenomenological kink-pair model For constant strain rate, ln[(dε0/dt)/(dε/dt)] is equal to ΔH/kT and is a constant. p and q are also constants, and are obtained from the fit to the simulation data as 0.5 and 2, respectively. Therefore,σ=σp{1.0-{kTln[(dε0/dt)/(dε/dt)]/ΔH0}0.5}2orσp(1.0-CT0.5)2From the fit to the simulation data, C is obtained as 0.09 K−1/2 for a/3〈112¯0〉 screw dislocations in α-Ti using the MEAM potential. Also, ΔH/kT is ∼15, with ΔH0 |
= 0.16 eV, obtained from 3-D molecular statics simulations. Now, the minimum velocity detected in the simulations is ∼1 m s−1. For this velocity, from Orowan’s expression, dε/dt |
= ρbv, where ρ is the mobile dislocation density and b is the Burgers vector of the dislocation, one obtains dε/dt in the simulations as ∼100 s−1 for a mobile dislocation density of 1012 |
m−2. The experimental strain rates are in the range 10−4–10−6 |
s−1. For the experimental strain rates, C for α-Ti becomes 0.134 K−1/2 (Eq. (6)). The model strain rate – experimental strain rate in corresponds to σ/σp |
= (1.0 − |
CT0.5)2 with C |
= 0.134 K−1/2, and represents kink-pair model data corrected for the much lower strain rate present in experiments. Also, ΔH/kT in experiments is calculated to be ∼34 which is very close to the experimentally determined value of ∼36 are the experimental critical resolved shear stress data for a/3〈112¯0〉 screw dislocations on the prism plane in α-Ti Two-dimensional molecular statics simulations using the MEAM potential reveal five different core structures for a/3〈112¯0〉 screw dislocations in α-Ti. These core structures are in reasonable agreement with previous first-principles calculations Relation of hardness and oxygen flow of Al2O3 coatings deposited by reactive bipolar pulsed magnetron sputteringAluminum oxide thin films are widely used because of their excellent properties, especially in terms of chemical, thermal, abrasive and corrosive resistance. But many properties of alumina films are significantly deposition parameters dependent. Since different applications and environments demand different kind of properties in thin films, it is important to determine the influence of the deposition parameters on the alumina film properties. In this work, different alumina structures were deposited by means of reactive, bipolar, pulsed, magnetron sputtering. In order to find the appropriate parameter combination to synthesize crystalline alumina (for this investigation γ-Al2O3), substrate temperature, power density at the target and oxygen flow were varied. The γ-Al2O3 films were synthesized at 650 °C, 0.2 Pa, 800 W, 1:4 duty cycle, 19.2 kHz, and 11–12% oxygen flow. The structure and morphology of the deposited Al2O3 films were characterized by X-ray diffractometry (XRD) and scanning electron microscopy (SEM). Since the coating hardness is a decisive factor for many applications, the aim of this paper was to investigate the influence of the oxygen flow on the alumina hardness. It was observed that the hardness and the structure of the PVD-deposited alumina coatings are significantly oxygen flow dependent. The hardness of the alumina films was determined by nanoindentation. It varied between 1 and 25.8 GPa. The hardness increased by increasing oxygen flow until the target reached the poisoned state, where a hardness reduction was clearly observed.Amorphous and crystalline alumina thin films are widely used. Particularly, the synthesis of crystalline alumina coatings by means of PVD technology has aroused a keen interest of the scientist in the last years In this work, different alumina structures were deposited by means of reactive bipolar pulsed magnetron sputtering. In order to find the appropriate parameter combination to synthesize crystalline alumina (for this investigation γ-Al2O3), substrate temperature, power density at the target and oxygen flow were varied. Since the coating hardness is a decisive factor for many applications, the aim of this paper was to investigate the influence of the oxygen flow on the alumina hardness.Tungsten carbide cutting inserts THM-11 were used as substrates. The samples were mirror polished (Ra |
< 0.01 μm) with a 6-μm diamond suspension and cleaned in a multi-stage ultrasonic cleaning bath with alkaline solutions of different concentrations and finally rinsed with de-ionized water and dried with nitrogen.The Al2O3 films were deposited in a laboratory-sputtering device (Z400, Leybold-Heraeus) equipped with a bipolar pulser (SPIK™ 2000A, Melec). The pulser was used to increase the target power density without drastically affecting the substrate temperature. A 99.9 at.% aluminum target with a diameter of 75 mm was used as material source. TiAlN was deposited in some experiments as bonding layer. Oxygen was used as a reactive gas. All alumina coatings were deposited at 0.2 Pa in an Ar–O2 atmosphere. shows a schematic drawing of the used setup. Vacuum quality prior to deposition was 7.8 · 10− 3 Pa. The samples are heated up to 480 °C and ion etched during 30 min at an argon pressure of 1 Pa and 100 W RF. After etching, the reactive gas is introduced into the deposition chamber at a total pressure of 0.2 Pa. This low pressure was chosen to achieve a big mean free path and thereby a higher particle energy during deposition. In order to find the appropriate parameter combination to synthesize γ-Al2O3, substrate temperature, power density at the target and oxygen flow were varied as displayed in . Three different experiment series were performed. In the first experiment series, the oxygen flow was varied between 2% and 16% while the substrate temperature and the power at the target stayed constant at 550 °C and 600 W. In the second experiment series, the oxygen flow was varied between 3% and 16% while the substrate temperature and the power at the target stayed constant at 650 °C and 600 W. In the third experiment series, the oxygen flow was varied between 3% and 16% while the substrate temperature and the power at the target stayed constant at 650 °C and 800 W. For each experiment series, the hysteresis effect was previously analyzed, with this intention cathode voltage was recorded as a function of the oxygen flow.To deposit oxide coatings by sputtering of metallic targets, the formation of an insulating film at the target surface (target poisoning) must be avoided. For this reason, the phenomenon target poisoning and its effect on the plasma composition was examined by means of OES techniques. In order to determine the influence of the oxygen concentration within the plasma during the reactive pulsed sputtering process, aluminum lines (see OES spectrum in ) were monitored by means of an OES device (TRIAX 180, HORIBA Jobin Yvon). This device allows capturing the spectra emitted by atoms and ions during optical transitions in the wavelength range from 300 nm to 800 nm.For all coated samples, thickness, coating's adhesion, hardness and Young's modulus were determined.Coating thickness was determined by calo test (calo tester, CemeCon). A scratch-testing equipment (scratch tester, LSRH) was used to evaluate the coating's adhesion. In this device, a diamond tip is drawn along the sample surface with a predefined normal load. The applied load was increased in steps of 10 N until a maximal load of 90 N.An X-ray device (XRD 3000, Seifert) was operated by X-ray of the CuKα-line (40 kW, 30 mA) in grazing-incidence mode in order to determine the existence of crystalline phases in the deposited films and to analyze the film structures. The measurements were carried out with a step width of 0.05°, duration of 5 s and a fixed omega axis at 2°.Fractured cross-section areas of the coated samples were examined by scanning electron microscopy (SEM) to analyze the coating's morphology.Further, coating hardness and Young's modulus were measured by nanoindentation (MTS Nano Indenter). Before nanoindentation, all specimens were polished and ultrasonically cleaned in isopropanol. In this mechanical testing method, a triangular pyramidal Berkovich indenter penetrated the coated surface perpendicular with a defined load. The indentation cycle was carried out with the maximum load of 10 mN. In order to reduce the influence of the substrate, a penetration depth of 1/10 of the coating's thickness was not exceeded.All deposited coatings exhibited thickness in between 1 and 2 μm. Critical scratch loads of the alumina coatings without TiAlN were in between 75 and 85 N. Using TiAlN as a bonding layer, scratch critical loads were superior to 90 N (see The intensity of the aluminum lines (λ |
= 395.6 nm) measured by OES and the cathode voltage as function of the percentage of oxygen flow during the reactive sputtering process are presented in . By increasing the oxygen flow, a constant decrease of the aluminum lines intensity and of the cathode voltage was observed.No γ-Al2O3 peaks were detected by XRD examinations of the alumina coatings deposited at 550 °C and 600 W (see experiment series I in ). By increasing temperature up to 650 °C at the same power at the target (see experiment series II in ) also no γ-Al2O3 peaks could be detected. Nevertheless, the SEM micrographs in showed some differences between the cross-section morphology of these alumina coatings.By increasing the target power up to 800 W at a constant substrate temperature of 650 °C (see experiment series III in ), it was possible to synthesize crystalline alumina at oxygen flows of 11% and 12% (see X-ray examinations in ). The cross-section morphology of a γ-Al2O3 coating deposited at 12% oxygen flow is shown in To facilitate the analysis of the oxygen flow influence on the alumina hardness, only the alumina coatings corresponding to the experiment series III were investigated., four different deposition zones were identified when the deposition rate decreased by increasing of the oxygen flow in the experiment series III. X-ray examinations of the films deposited by each one of the four zones confirmed the deposition of different structures in each zone. In zone 1, the films were metallic, in zone 2 amorphous (see b and c) and the structures observed in zone 4 were once more amorphous.The hardness of these coatings is displayed in At low oxygen flow, almost no influence of the cathode voltage and/or intensity of the aluminum lines in the OES spectrum could be detected in (metallic mode). In this “metallic mode”, all oxygen atoms react with the sputtered aluminum atoms and condense as alumina at the substrate surface and at the chamber walls. After a certain oxygen flow, the oxidation process at the target surface begins. In this mode, the sputter yield is lower than the formation rate of alumina at the target surface At parameter combinations I and II, it was not possible to synthesize γ-Al2O3 in spite of the wide range in oxygen flow (see ). Only at a substrate temperature of 650 °C and a power rate of 800 W by a duty cycle of 1:4, it was possible to form γ-phase.To understand these results, it is necessary to analyze the synthesis of Al2O3. The particles that will constitute the coating, normally try to achieve a stable state, which is characterized by the minimum possible free energy. In order to form crystal lattices, a sufficient diffusion length is needed, which is deposition rate and surface particles mobility dependent. This dependency is described by the following equations x: diffusion section of the deposited particles [nm]; Ds: surface diffusion coefficient [nm2/s]; a: lattice spacing [nm]; d˙s: deposition rate [nm/s]D0: constant [cm2/s]; Q: diffusion activation energy [J]; R: Boltzmann constant 1.38 · 10− 23 J/K; Tsu: substrate temperature [K], typical values of the Al2O3 surface diffusion coefficient at room temperature is virtually zero ). The diffusion length of the particles at an Al2O3 deposition rate of 1 nm s− 1 is about 2 · 10− 34 nm. Then, the diffusion length values are far below the order of magnitude of the lattice spacing (a |
= 0.780 nm) On the other hand, the adjusted low pressure (0.2 Pa) can help to increase the mean free path of sputtered particles, hence increasing their average kinetic energy , four zones corresponding to four different ranges are differentiated. According to XRD and SEM examinations, as well as nanoindentations, coatings deposited in different zones exhibited different crystallographic structures and mechanical properties. In the first zone, the oxygen flow was not enough to produce a completely oxidized film. Consequently, metallic aluminum peaks in X-ray examinations were detected. The second zone is characterized by high deposition rates and formation of completely oxidized amorphous films (see , a high deposition rate causes a reduction of the diffusion length of the condensed particles at the substrate surface and favors the formation of amorphous structures. In the third zone, lower deposition rates compared with these in zones 1 and 2 were observed. It is likely to be caused by obtaining a diffusion length that exceeded the lattice spacing (a |
= 0.780 nm), which allows the formation of arranged crystalline structures. Therefore, γ-Al2O3 peaks can be seen in the XRD examinations (see b and c). The fourth zone is a poisoned target zone, where the target is almost completely oxidized. From the target only few metallic atoms are still sputtered and supposable most of them are sputtered by AlOx molecules. This phenomenon could produce at least the following two disadvantages, which result in amorphous films. First, the reduced mobility because of the larger molecule dimensions and masses make difficult the necessary rearranging processes at the substrate surface. Second, the important energy fraction produced during the exothermic reaction 4Al + 3O2 |
= 2Al2O3 in process is reduced because fewer Al atoms are available to react.A big influence of the oxygen flow on the coating hardness is clearly observed in , which can be associated to the coating structures. Metallic films deposited in zone 1 exhibited a maximal hardness of 1.2 GPa. The hardness of the amorphous films in zone 2 varied between 7.5 and 10.2 GPa. The hardness of the coatings deposited in zone 3 was clearly higher due to the formation of the crystalline phases. The hardness variation of the alumina films deposited in zone 3 is likely to be caused by a variation of the γ-phase fraction in coating and also can depend on the grain size of the crystalline structure. The metastable crystalline γ-Al2O3 film deposited at an oxygen flow of 12% exhibited the highest hardness (25.8 GPa). At about 14% oxygen flow, a hardness reduction was clearly observed although the hardness did not descend below 10 GPa. It is likely to be caused by the change to the poisoned sputtering mode (see , developing of the cathode voltage and deposition rate in zone 4), which implies the formation of amorphous structures These results demonstrated that the hardness of the deposited PVD alumina coatings is significantly oxygen flow dependent.By increasing oxygen flow at 650 °C, 0.2 Pa, 800 W, 1:4 duty cycle and 19.2 kHz, four different deposition zones were observed. Each zone is characterized by different deposition rates and coating structures. In the third zone, O2-flow (approximately between 8.5% and 12.5%) was possible to synthesize γ-Al2O3 coatings. It is likely to be caused by obtaining a diffusion length that exceeded the lattice spacing (a |
= 0.780 nm), which allows the formation of arranged crystalline structures. The significant influence of the oxygen flow on the PVD-alumina hardness was verified in this investigation. Alumina hardness increased by increasing oxygen flow until crystalline alumina structures (γ-Al2O3) were synthesized. The γ-Al2O3 coatings that were deposited at different oxygen flows exhibited also different hardness. It is likely to be caused by the synthesis of alumina coatings with different content of γ-phase and/or different grain size. This will be analyzed in future works. The γ-alumina coatings deposited at an oxygen flow of 12% exhibited the highest hardness (25.8 GPa). At about 14% oxygen flow, a hardness reduction was clearly observed and also the formation of amorphous structures. It is likely to be caused by the change to the poisoned sputtering mode.Tensile properties and failure behavior of chopped and continuous carbon fiber composites produced by additive manufacturingThe use of additive manufacturing (AM) is rapidly expanding in many industries mostly because of the flexibility to manufacture complex geometries. Recently, a family of technologies that produce fiber reinforced components has been introduced, widening the options available to designers. AM fiber reinforced composites are characterized by the fact that process related parameters such as the amount of reinforcement fiber, or printing architecture, significantly affect the tensile properties of final parts. To find optimal structures using new AM technologies, guidelines for the design of 3D printed composite parts are needed. This paper presents an evaluation of the effects that different geometric parameters have on the tensile properties of 3D printed composites manufactured by fused filament fabrication (FFF) out of continuous and chopped carbon fiber reinforcement. Parameters such as infill density and infill patterns of chopped composite material, as well as fiber volume fraction and printing architecture of continuous fiber reinforcement (CFR) composites are varied. The effect of the location of the initial deposit point of reinforcement fibers on the tensile properties of the test specimens is studied. Also, the effect that the fiber deposition pattern has on tensile performance is quantified. Considering the geometric parameters that were studied, a variation of the Rule of Mixtures (ROM) that provides a way to estimate the elastic modulus of a 3D printed composite is proposed. Findings may be used by designers to define the best construction parameters for 3D printed composite parts.Rapid prototyping was introduced in the decade of 1980. Since then, various additive manufacturing processes have been developed. In the early years, these technologies focused on prototyping. However, during the last 20 years, they have evolved into the additive manufacturing technologies known today, that are oriented to the production of functional parts.Among all the AM process, the most widely used 3D printing methods for processing polymer composites are selective laser sintering (SLS) and fused deposition modeling (FDM), also known as fused filament fabrication (FFF). In comparison to SLS, the FFF process has the advantages of low input energy and material cost, minimum waste, and consistent prototype accuracy []. Additionally, FFF has other advantages such as no need for chemical post-processing, and less expensive machines and materials, which result in a cost-effective process []. On the other hand, FFF parts have limited mechanical properties. To overcome these limitations new approaches to produce 3D printed composites are being proposed, for example, different techniques of particle reinforced composites, short-fiber reinforced composites and nano-composites were summarized in [] that produces continuous fiber reinforced (CFR) components was introduced. In this process, reinforced fibers of different types are combined with conventional polymers to produce reinforced parts. The method uses independent nozzles to process reinforced materials such as carbon fiber, fiberglass, or Kevlar, with a conventional polymer that serves as a matrix. Parts produced by this process have shown properties that are comparable to aluminum, which has raised much interest for their potential use in engineering applications [In addition to the process parameters, composite parts manufactured by AM technologies are affected by how the fibers are incorporated into the polymer matrix, geometric parameters (such as infill density and infill patterns), and the amount and arrangement of the fibers. While there is a vast amount of knowledge and experience for the design of parts made out of composite materials using conventional production methods [], designers of parts that use the new AM technologies need guidelines that are compatible with the new processes, and that facilitate the introduction of AM parts in engineering applications. As a consequence, there is a growing interest in establishing process parameters (speed, temperatures, etc.) that improve part properties, and reduce the fabrication time as well as the cost of FFF parts.Most of the commercial AM machines and their software limit the changes that users can make to process parameters such as deposition speed or material temperature. In contrast, non-commercial slicing software used to convert the CAD designs into printing layers offer several geometric parameter control options, such as infill density, infill pattern, layers thickness, etc. Characterizing and understanding the effects that the printing parameters have on the final properties of the 3D printed composites parts can play an important role in the capacity of this type of parts to be used in engineering applications.] there are several different possibilities for fiber integration into the part. In particular for FFF composites, and considering the time and location of the fiber incorporating process, there are three methods of fiber implementation that seem more viable:Type 1, incorporation of the fiber before the printing process, that is, the filament itself is a composite (Type 2, incorporating it in the print head, meaning, two materials are combined when they pass through the extruder (Type 3, incorporating it on the component, thus requiring two or more independent extruders, each one with an independent nozzle (This classification is relevant because the properties of the part depend not only on the amount, often measured in terms of the volume fraction of the reinforcing fiber, but also on the manner in which the fibers are integrated into the matrix material.Currently, equipment for Type 1 and Type 3 methods is commercially available. In contrast, Type 2 method equipment is still at the development stage. In particular, the head mechanism that incorporates the fiber into the polymer matrix must be designed and tested for each application, depending on the fiber and matrix polymer characteristics.In this work, a machine that is capable of Type 1 and Type 3 processes is used to explore the relationship of process conditions with part properties. The first part of this study focuses on the evaluation of the mechanical performance of Type 1 FFF composites. The effects of Infill Density and Infill Patterns in Onyx samples were compared with Nylon samples with the same geometric parameters. In this context, Infill Patterns refers to the geometric shapes repeated on the inside of the part, while the Infill Density is the amount of polymer material (Onyx or Nylon) deposited inside the part. Other geometric variables, such as the number of roof / floor layers, and width of walls (refered to as shell) were kept constant for all the tests.The second part of this work analyzes the influence of fiber volume fraction (VF) and fiber placement arrangement on the mechanical performance of Type 3 FFF parts. Analysis of the results from these tests suggested that the initial point of application of the reinforcement fiber affects the tensile properties of the specimen. For this reason, an exploratory study about the effect that the point of initial application of the reinforcing fiber has on part properties was also conducted.The article is organized as follows. Section presents a state of the art review for fiber reinforced AM technologies. Section presents the characteristics of the materials tested, the geometric parameters evaluated, and the fabrication and characterization equipment. Section shows the results and discussion for volume fraction calculations. The tensile properties results, as well as mesostructure and fatigue mechanism analysis for specimens produced by Type 1 and Type 3 processes are presented in Section proposes a complementary method based on the Rule of Mixtures to predict the elastic modulus of the CFR specimens, while in Section the effect of the start point of reinforcement on mechanical properties for CFR composites is analyzed. Finally, Section presents some implications for part design, and Section summarizes the conclusions and future work.] reported the fabrication of Type 1 CFR specimens using an FDM machine (Creatr, Leapfrog Co.) and a composite filament (FilaBot Co.) with a diameter of 1.75 mm which contained 5% (weight percentage) chopped carbon fiber and acrylonitrile-butadiene-styrene (ABS) thermoplastic matrix. In their work, they evaluated the mechanical properties for different values of four process parameters: nozzle temperature, infill speed, raster angle and layer thickness. Their goal was to find the best parameters to improve the tensile strength of the parts. Stratasys recently introduced FDM Nylon 12CF, a carbon fiber-filled thermoplastic, which contains 35% chopped carbon fiber by weight, characterized by a high flexural strength and stiffness-to-weight ratio [Examples of parts produced by a Type 2 machine were reported by Yang et al. []. They presented a 3D printing equipment with a novel composite extrusion head that can process continuous carbon fiber with ABS and PLA respectively. Also, a novel technique called continuous lattice fabrication (CLF) was proposed by Eichenhofer et al. []. The CLF head is comprised of a two-stage, pultrusion-extrusion system. They reported an increase in tensile properties for carbon fiber-reinforced PA12 composites, that can reach tensile strength of 560 MPa and elastic moduli of 83 GPa along the fiber direction. The technique include a softening cycle procedure [] that attempts to maximize the mechanical properties of the printed composites by minimizing the residual void content.Examples of Type 1 and Type 3 machines are presented by Wang et al. [] in a review for 3D printing polymer composites. Baumann et al. [] reported that Type 3 machines produce a considerable increase in tensile strength and elastic modulus for different cases of continuous carbon fibers reinforced polymers. This study showed the potential that these processes have to produce functional parts for engineering applications. Other examples of Type 3 processes are presented by Dickson et al. [], who reported the fabrication of continuous carbon, fiberglass and Kevlar fiber reinforced polymer composites on a Markforged Markone 3D printer. In particular, they evaluated the tensile and flexural properties of test specimens with carbon fiber reinforcement and concluded that these materials could reach tensile strengths of up to 368 MPa, which exceeds the strength of some conventional structural materials, such as Aluminum 6061-T6. They also analyzed the effect of the increase of volume fraction of fiberglass on tensile properties of the material. Melenka et al. [] presented an evaluation of the tensile properties of 3D printed structures reinforced with Kevlar and propose a method to predict the elastic modulus using compliances matrices. Van der Klift et al. [] presented an evaluation of tensile properties for two carbon fiber 3D printed specimens and present a prediction of the elastic modulus by the rule of mixtures of composites. Additional investigations for fiber reinforcement during 3D printing have been conducted for medical applications, like those reported by Christ et al. [] presented a novel manufacturing process to fabricate highly integrated lightweight structures. Other works analyzed the effect of process parameters on final mechanical properties, such as the case of Yang et al. [A significant effort has been made to correlate process parameters of new AM technologies with part properties. On the other hand, there are few studies of the effect of fiber geometric patterns on design aspects. Fernandez et al. [] present an evaluation of infill patterns or infill density in tensile mechanical behavior of ABS parts. Courter et al. [] conducted a material characterization of ABS specimens to obtain as-built properties including the bead aspect ratio, void ratio, void shape and bonding between beads that were used in finite element (FE) simulation of the FFF process. Their results show that FE simulations capture the interaction between tool path and their impact on the final state of the printed part. Klahn et al. [] presented some cases for SLS and SLM that showed how the re-design of the part geometry for AM contributed to the success of the product, improving its technological and economic viability.From the previous discussion, process parameters as well as geometric variables such as infill patterns, infill density, and part shape (void ratio, void shape and bonding between beads) affect the final mechanical properties of 3D printed composites. Much work is still needed to develop product design guideliens that match finished part properties, with materials properties of the feedstock and AM process capabilities, in a way to build Design for Additive Manufacturing capabilities. In particular, this work focused on the evaluation of the effects that fiber arrangement and part geometry have on tensile properties of 3D printed composites, in an effort to help designers produce viable AM applications.In this work, three different types of specimens are fabricated and tested.Nylon samples printed with PA6 (Polyamide 6), a copolymer filament produced in the form of a wireSamples printed with Onyx, a nylon filament that is strengthened with chopped carbon fibers, andCFR composites: nylon filament used as matrix, reinforced with continuous carbon fibers processed using the Type 3 methodNylon and Onyx filaments are supplied with a diameter of 1.75 mm, while the reinforcing carbon fiber filament is supplied with a diameter of 0.35 mm []. The reinforcement material is a filament that may contain up to 1000 individual carbon fibers infused with a sizing agent, as reported in []. Fiberglass and Kevlar are also available as reinforcement fibers. shows the different types of specimens printed.Test specimens were fabricated in accordance with ASTM D638 Standard Test Method for Tensile Properties of Plastic. Section 6.1.3 of this standard recommends that reinforced composites, including highly orthotropic laminates, shall conform to the dimensions of the Type I specimen (1). This geometry was also chosen because it has a larger cross section area. The larger cross-section allows to have more reinforcing material.A Markforged Marktwo commercial 3D printer machine was used to print all the specimens. The printer has a dual extrusion head that allows the manufacture of CFR composites parts (Type 3 in ) with different types of fibers: Carbon Fiber, Kevlar, Fiberglass, High-Strength High-Temperature Fiberglass. In this case, the printing process consists of two stages, each of which is performed by a separate print unit in the dual printer head. For this reason the width of nylon matrix strands (Wwall) is different from the reinforcing fiber strands (Wfiber). The Nylon matrix is printed first, and the reinforcing fiber is deposited in a second stage within the same layer.The printer can deposit the fiber in a “concentric” pattern that forms annular rings or in a unidirectional pattern called “isotropic” by the manufacturer, that creates continuous reinforced lines in the entire layer. The schematics of the different fiber reinforced patterns is shown in ], Nylon is printed with a hot end temperature of 263◦C onto a non-heated print. The fiber reinforced composite filament is heated in a transverse pressure zone to a temperature higher than the melting temperature of the matrix material. As a result, the matrix material is melted interstitially within the filament. The head applies an ironing force to the melted matrix material.This AM machine can also process Type 1 filaments []. For Nylon and Onyx, the printing process is similar to a conventional FDM. The dual printing head uses only the plastic nozzle (a). The filament is fed through the nozzle which melts, extrudes and deposits the material, layer by layer, in the desired shape, while the moving platform is lowered after each layer is deposited. Three sets of experiments were conducted, and they are referred to as “Setup” in . Five specimens for each test of the three different experimental setups were manufactured. The test geometry was created using a computer-aided design (CAD) software package (SolidWorks 2016). The CAD geometry of the specimens was exported as a stereolithography file (STL) and loaded into a cloud slicing software (Eiger). In this software, different parameters were modified for each test of the different experimental setups.In experimental Setup 1, the matrix materials, the infill patterns, and density parameters were modified to build a full 23 factorial experiment with two levels. The following three factors were used:Infill Patterns: Rectangular (filaments at 45° with respect to load direction) and Triangular (filaments at 0° or 60° with respect to load direction)For the continuous carbon fiber reinforcement samples in Setup 2, a “concentric” fiber pattern was selected. For the geometry selected the total number of printing layers is 26. However, the maximum number of reinforced layers is 18, while the maximum number of reinforced concentric rings is 5. The number of concentric rings (R) and the number of layers (L) that contain carbon fiber reinforcement were varied, creating different “printing architectures”. In Setup 2, two “printing architectures” with the same fiber content were manufactured. Specimens with only one concentric ring, referred to as 1R in the discussion that follows, and samples with 3 concentric rings referred to as 3R, were printed. The overall printing parameters used to manufacture the test specimens in the different experimental setups are summarized in For all the specimens in Setups 1 and 2, the starting point for fiber deposition was fixed outside of the tensile area of the specimens. In Setup 3, additional samples for 1R-12 L test were manufactured, moving the initial point of the reinforcement fibers to the middle, and uniformly distributed over the tensile area of the specimens. The ASTM D638 Standard does not require the use of tabs in its specimens. However, to reduce the effect of the clamping forces on the specimen, the tabbing guide for composite test specimens [] was used to attach tab strips in the samples. Tab strips were added using 3 M Scotch-Weld DP810 as adhesive and glass fabric / epoxy laminated circuit board as tabbing material.Tensile tests were performed utilizing three different machines: an Instron 5 K N 3365, a SHIMADZU 100 K N and an MTS 810 250 K N tension machines. To test 1R-18 L and 3R-6 L specimens, shown in , the SHIMADZU machine was used, while 3R-18 L and 5R-18 L samples were performed on the MTS testing machine due to the high load capacity required to produce a fracture in the specimens. After the tensile tests, the fractured specimens were examined using a Stereo ZEISS optical microscopy for Onyx samples, and SEM EVO MA25 ZEISS microscopy for continuous reinforced samples.The Elastic modulus (E) in MPa was calculated from the slope of the stress-strain curve with the stresses σ1 and σ2 that are measured at strains ε1=0.05% and ε2=0.25% respectively. Similar to other works [], the specimens were held in place using wedge clamps and tested at a crosshead speed of 5 mm/minute as per ASTM D638 standard.For Nylon and Onyx samples, the tensile strength at yield (in MPa) was estimated. The criteria used was to identify the stress where the parallel line to the elastic modulus line, at 0.02 strain. intersects with the stress-strain curve. For CFR samples the tensile strength at break was used. This was considered to be the maximum stress during the tensile test.A schematic of the internal structure of the continuous fiber-reinforced 3D printed specimen is shown in . Four distinct regions can be distinguished in the test samples: walls region, roof and floor layers, infill layers and reinforced layers. Each region has a different mechanical performance due to the printing toolpath. In the roof and floor layers region the head follows a path in a range of ±45° from the longitudinal axis, while for walls and reinforcement layers the printer toolpath is parallel to the longitudinal axis. Finally, the infill orientation depends on the pattern, Rectangular or Triangular, and the density selected.In composites analysis studies, the amount of fiber has been directly correlated with the mechanical properties of the composite, through the fiber volume fraction (FVF), and has been used for stiffness predictions. Methods that can be used to calculate the volume fraction in traditional composite analysis, include the burn-out process [] which require the destruction of the specimens by eliminating the matrix material. However, in this study, the fiber volume fraction was calculated using a geometric approach following the procedure reported by Melenka et al. [According to Melenka, the volume of each region of the test specimen can be determined from the geometry of the sample following Eqs. . The overall composite volume can be calculated using Eq. the volume fraction of reinforcement fiber can be determined, where φfiber is the volume fraction of fiber, Vi denotes the volumes of the different regions in the composite, Vcomposite is the overall volume of the specimen, and I is the infill density. Also, N is the total number of layers, while Nwalls,andNfloor/Nroof are the number walls and floor / roof layers selected in the shell of the specimen. Finally, Nfiber and Rfiber defined the number of layers and concentric rings reinforced with fiber.Vroofandfloor=W-2*Nwall*Wwall*H*Tlayer*(Nfloor+Nroof)Vinfill=W-2*Nwall*Wwall*H*I*Tlayer*(N-Nfloor-Nroof-Nfiber)In this study, the width of fiber strands (Wfiber) and nylon strands (Wwall) were determined with a Stereo ZEISS optical microscope. For calculations, a tensile volume of W = 57 mm H = 13 mm T = 3.2 mm was considered. The infill density (I) was selected to be 0.1 (10%) and the Layer thickness (Tlayer) was fixed at 0.125 mm in Eiger. summarizes the parameters used in the calculations. An excel template was used to calculate the four region volumes for each printing architecture following Eqs. , and finally, the fiber volume fraction φfiber is calculated using Eq. summarizes the FVF found for all the eight cases in Setup 2. These values were also used for prediction of elastic modulus (Section show a comparison of the effects of infill density and infill pattern for the two types of raw materials, Onyx and Nylon, on the tensile properties of the specimens, for Experimental Setup 1.Regarding the elastic modulus, tests with Nylon specimens with 10% of infill density and rectangular pattern reported a value of 311.6 MPa (see Appendix ). Onyx samples with the same parameters displayed an elastic modulus of 581.6 MPa. Same for 70% Rectangular, 10% Triangular and 70% Triangular specimens where the Onyx samples show an increase of 128% (627.3 MPa vs 490.7 MPa), 297% (1064.9 MPa vs 358.4 MPa), and 216% (1293.9 MPa vs 598.9 MPa), respectively, compared to Nylon samples (The data obtained in Experimental Setup 1 was analyzed in Minitab 17 through an Analysis of Variance (ANOVA). Results suggest that the differences between the means of the different materials are statistically significant for the elastic modulus and tensile strength in the three factors analyzed. The ANOVA study was conducted with a confidence level of 95% and a significance level of α = 0.05. The significance (p-values less than 0.05) of raw material (Onyx vs. Nylon), infill density (10% and 70%) and infill patterns (Rectangular and Triangular) were proved in all cases. presents the Pareto charts of the standardized effects for Experimental Setup 1, in support of the previous statements. Similarly, Appendix shows the summary of results from ANOVA analysis.The results from ANOVA analysis indicate that the elastic modulus for the two materials are definitely different (Factor A). For both materials on the Elastic Modulus, the analysis shows that infill pattern (Factor C) had a more important effect than infill density (Factor B). Regarding the tensile strength, the materials again have different values (Factor A). However, the study shows that the infill density (Factor B) has a higher effect than the infill pattern on strength. For the interaction between factors, raw material-infill pattern (AC) and infill density-infill pattern (BC) affect elastic modulus, while only raw material-infill pattern (AC) is statistically significant for tensile strength.The Analysis of Variance is consistent with the values of tensile properties presented in , where the infill pattern has a considerable effect on the mechanical properties. In particular, the Onyx specimens with a triangular pattern show an increment of ˜80-105% for elastic modulus, and ˜20–25% more for tensile strength compared with the rectangular pattern samples; while the Nylon specimens with a triangular pattern show an increment of 15–22% for elastic modulus, and ˜9–24% more for tensile strength compared with the rectangular pattern samples.The values obtained in Setup 1 are lower than the values found in Markforged datasheets []. This is likely due to the fact that the specimens in Setup 1 have much less infill than Markforged samples, and a different geometry (ASTM D638 Type IV) was tested for datasheet. As a verification experiment, a Nylon specimen with 100% of infill density and Triangular pattern was fabricated and tested. The specimen shows an elastic modulus of 945.9 MPa similar to Markforged datasheet (940 MPa) and reach a tensile stress at break of 34 MPa. show the effects of printing architecture and volume fraction on the tensile properties of the specimen for continuous carbon fiber reinforcement samples.The tensile properties obtained for continuous carbon fiber reinforced composites proved to be significantly better than the rest of the specimens in Setup 1. The increase in the elastic modulus can go up to 25 times Enylon (Nylon 100% Triangular) reaching 23.7 GPa for 5R-18 L test, which is close to E for commercial Fiber-glass (25 GPa) or Kevlar (25 GPa) composites; although it is only one third of the E reported for standard Carbon Fiber composites (70 GPa) []. The tensile strength of 5R-18 L samples reached 304.28 MPa, which is close to TS = 310 MPa reported for Aluminum 6061-T6. []. Similar performance was reported by Dickson et al. [], who presented composite specimens with yield strengths of up to 368 MPa with volume fraction of 35% carbon fiber. present the Pareto charts of the standardized effects for Experimental Setup 2. Appendix shows the summary of results from ANOVA analysis.The data in Setup 2 was also analyzed in Minitab 17 through an ANOVA. Results suggest that the differences between the means are statistically significant (p-values less than 0.05) for the two factors: Fiber Volume Fraction and Printing Architecture. A comparison of the two printing architectures (3R compared with 3 times of 1R) with the same volume fraction, suggests that the arrangement of fibers affects tensile properties, with a better performance for wider arrangement (3R). FDM is a layer by layer process. When 3R samples are manufactured, the fiber rings are printed in the same pass. a shows a magnified image of a 3R sample. On the other hand, 1R rings are printed in different layers. b shows magnified images of a 1R sample. In c non-uniform wetting of the fibers bundles by the matrix can be observed. Differences in thermal patterns or pressure of deposition of these proceses may have an effect on the properites of the samples. A definite explanation for this behavior requires further study, however.Specimens were 3D printed with Onyx and their fabrication was stopped at the middle (Layer 13). These samples were observed with a Stereo ZEIS optical microscope to have a better understanding of how the infill patterns are constructed. Two infill patterns (Rectangular and Triangular) and two infill densities (10% and 70%) were analyzed and their angles were measured. Good correspondence with the theoretical orientation angles of 45° for a rectangular shape and 0°/60° for triangular shape was found. However, the “density” of strands between the two patterns types shows significant differences, as seen in . The rectangular shape appears to have a higher infill density. This is because the strands are printed alternately at + /- 45° with respect to the tension axis. Under these conditions, the contact area between the strands is reduced, while in the triangular shape all the strands are stacked in the same orientation.For all the tests in Experimental Setup 1, Nylon and Onyx specimens, the Triangular shape (T 0°/60°) has a better tensile performance because there are more strands that are oriented at 0° (in the direction of the load). The better contact and the orientation of the stacked strands provides a better mechanical performance. shows the arrangement of strands in triangular and rectangular patterns.For CFR composites, the mechanical properties increased considerably by increasing volume fraction of the reinforcement fiber. Individual diameters of the reinforcement fiber of a broken sample were measured using an SEM EVO MA25 ZEISS microscope. The software reported the following fiber diameters: 6.98 μm, 8.816 μm, 7.939 μm and 7.254 μm. These values are in the low end of the advertised data (10 ± 2 μm), and some fall out if this range. The broken carbon fibers are shown in . Again, it can be seen that the individual fibers do not appear to be wetted well by the matrix.], the integrity and mechanical properties of AM parts are directly related to the mesostructure of fused filament fabricated parts, i.e. the void geometry and the bonding between individual polymer strands. Since infill density is below 100% in all samples, mechanical properties are determined predominantly by the individual strands.When the fracture mechanisms of the Nylon and Onyx samples are compared, it can be seen that the Nylon samples fail in a macroscopically ductile manner, while Onyx displays a macroscopically more brittle failure. Nylon samples show an initial visco-elastic behavior up to a macroscopic engineering strain of ±0.15 (see ), i.e. the yield point. As one of the strands exceeds this yield point, it exhibits microscopically plastic strain localization and does not contribute any more to the overall force the sample can endure. As a consequence, the effective area is reduced, and neighboring strands also reach their yield stress, until the whole sample exhibits macroscopically plastic strain flow. This is manifested by a stress that stays almost constant (up to an engineering strain of ±0.25). The material then starts to strain harden and, as a consequence, the stress is increasing again. In this region, the sample rapidly starts to elongate until macroscopic final failure, when the maximum tensile stress is reached across the whole sample cross-section. This failure mechanism is shown in a, where elongated strands can be detected and a deformed shape of the initially rectangular geometry can be seen.The Onyx failure mechanism is somewhat different. Due to the chopped carbon fibers which are supported by a Nylon matrix, the material has an increased elastic modulus and breaks right after reaching the macroscopic ultimate stress, which coincides with the yield point at a macroscopic engineering strain of ±0.10 (see ). The failure mechanism starts when one of the strands reaches locally its ultimate stress value. However, in this case, the strand immediately breaks, as that stress is above the ultimate tensile stress of the Nylon matrix. This causes a sudden increased stress concentration in the neighboring strands and their subsequent failure. An overall macroscopic brittle failure is the result, as is shown in b shows this brittle failure mechanism in a surface layer of an Onyx sample, where no extended Nylon ligaments can be detected.The failure mechanism of the CFR samples is rather similar to the Onyx samples, also showing macroscopically brittle failure. The continuous bundles of carbon fibers are responsible for withstanding the forces applied to the samples, with a high elastic modulus and a limited maximum elongation (see ). At the moment these fiber bundles reach their maximum stress, they break and cause a sudden increase in the stress of the neighboring Nylon strands, far above the stresses these Nylon strands can withstand. These then exhibit a very limited local plastic strain flow, resulting in a macroscopically brittle failure behavior, as shown by the stress-strain curve. An image of a broken carbon fiber bundle and its neighboring Nylon strand with limited plastic strain flow, i.e. elongated Nylon ligaments, is shown in For the prediction of elastic modulus of for CFR composites, Melenka et al. [] proposed a Volume Average Stiffness (VAS) Method. The VAS involves three main steps. First, micromechanical models are used to determine the elastic constants for each of the four regions (shown in Section ). Once the micromechanical properties of the roof / floor, infill and walls regions are determined, the compliance matrices for a transversely isotropic material can be populated. Third, the stiffness averaging is performed by establishing the volume fraction of each section within the test specimen in order to determine the contribution of each section to the overall mechanical properties. Finally, to determine the effective mechanical properties of the fiber reinforced 3D printed parts the global stiffness matrix is inverted, and the effective elastic constants can be obtained.Following the method by Melenka, a simplified approach to predict the elastic modulus based on the Rule of Mixtures (ROM) is presented here. The contribution of the roof / floor, infill and walls regions is calculated by Equation , that calculates the volume fraction of the matrix (φmatrix). For the presented approach the elastic modulus of the composite can be obtained from Equation , by reducing the compliance matrix to only one constant, assuming the specimen behaves in an isotropic manner.φmatrix=Vroofandfloor+Vwall+VinfillVcompositeRuleofmixturescomposites:Epredicted=φmatrixEmatrix+φfiberEfiberPredicted values of elastic moduli were calculated using the values described in and the elastic modulus of raw materials values of Ematrix=940MPa and Ecf=50GPa obtained from Markforged materials datasheet []. Predicted values were compared to experimental data. Results are summarized in A good agreement between measured and predicted values was found for the tests with volume fraction lower than 11%. However, for the fractions higher than 11% the rule of mixture was less accurate. This behavior is consistent with the values reported by Van Der Klift et al. [] who also found that at higher volume fractions this kind of composite does not behave according to the rule of mixtures. In contrast, Melenka´s method shows good correlation for larger amount of fiber reinforcement. However, for lower fiber reinforced contents, the method fails to predict the elastic modulus.The difference of the approach presented here with respect to Melenka´s method is that the micro-mechanics model does not consider the anisotropic nature of the fiber. The compliance matrix is reduced to a single constant E. The proposed method provides a simple way to estimate the expected mechanical performance of CFR composites with lower fiber contents, where the mechanical behavior of the composite is dominated by the matrix (Nylon). For a larger amount of fiber, the composite must be treated as a transversely isotropic material and Melenka´s method is more effective to predict the elastic constants. This behavior should be expected for CFR printed parts, because the integrity of the fiber / matrix interface may affect the efficiency of load transfer. As can be seen in c, voids may be found between Nylon strands and fiber bundles.In Experimental Setup 2, most of the specimens fractured in the same area close to the inflection point in the dog bone. Previous studies by Dickson et al. [] suggested that the crack initiation coincides with this region due to shear forces experienced by the change in fiber alignment, and through FEM simulation demonstrated the locations of the highest third major stresses (regions of highest compression) in these points. In contrast, Melenka et al. [] argued that the break occurs at the starting point of fiber reinforcement.As explained before, a third experimental setup was conducted to analyze the effect of moving the initial point of reinforcement deposit. The goal was to analyze the phenomena that produce the failure in the CFR samples. shows the printed samples and the differences in the start point of fiber reinforcement. a shows the configuration used for all the previous tests, with a start point outside the tensile area. For most applications, it is not always possible to keep the starting point of reinforcement outside the load area. The effects of the location of the initial point of reinforcement inside the tensile area were evaluated with two tests: Middle ( summarizes the values for elastic modulus and the tensile strength of the Middle and Distributed tests and compared with the regular test (Outside). shows the stress-strain curves for the different specimens tested.The middle samples of 1R 12 L compared with the Outside test exhibit a decrease of 16.9% in the elastic modulus and 16.5% in the tensile strength. To overcome this limitation, the test with distributed start points over the tensile area was proposed. The Distributed test shows good tensile results. The samples exhibit an increase of 8.4% in the elastic modulus and 11.3% in the tensile strength compared to Outside test. This is probably due to the distribution of the start points, which releases some compression stresses in the inflection area, preventing the crack initiation in the first fracture mechanism (), while the stacked distribution creates only small defects that are not critical for the second mechanism (A SEM inspection of the 1R-12 L samples in experimental Setup 3 suggests that fracture is different for the samples where the starting point of deposition of the fiber reinforcement is outside the tensile area (in the regular test, refered to as “Outside” in previous sections), compared with samples where the starting point is in the middle of the tensile area (denominated “Middle”) or distributed over different points within the tensile area (denominated “Distributed”). These different starting points influence the mechanical properties, such as the elastic modulus and ultimate tensile strength. Therefore, the fiber reinforcement starting point should be considered as a critical design parameter. shows details about the fracture mechanism when the start of reinforcement is outside the tensile area. a shows a cross-section zone where both carbon fibers and Nylon strands are present and visible. It can be seen that fracture has started at the fiber bundles, with brittle fiber bundle failure and a certain amount of fiber pull-out. In b, some of the carbon fibers affected by fiber pull-out are shown, with a brittle failure surface. c shows an image of a cross-section zone with only Nylon strands, also demonstrating a brittle failure surface and very limited local plastic strain flow i.e. in the form of elongated Nylon ligaments. shows images of a specimen where the starting point of the fiber reinforcement is in the middle of the tensile area. Failure occurs at the cross-section where the starting point of the deposit of reinforced fibers is present, see d. In that particular cross-section, there is a small zone with no fiber bundles present (see d, side of start point). Since there are less fiber bundles present to withstand the tensile force, this results in a lower macroscopic ultimate tensile stress. From a, a right-hand microscope view of the break surface area on the side of the start point, it can be seen that the carbon fiber bundles on this side of the tensile sample do not contribute to the ultimate tensile force, as no fiber failure nor fiber pull-out is detected. At the side of the starting point, in the zone of the cross-section where only Nylon strands are present, the Nylon strands can undergo more pronounced local plastic strain flow, as can be seen in b where some extended Nylon ligaments can be detected. Once the ultimate tensile force of the fiber bundles is reached, the cross-section fails in a similar manner as for the previous “Outside” case, i.e. brittle fiber bundle failure and a certain amount of fiber pull-out; compare Based on the previous results, and to make better use of the capabilities of the process for 3D printed composites, designers should consider the following recommendations:Use the triangular infill pattern, especially for chopped composites.The infill density (the amount of matrix material deposited inside the part) has a minor role in the tensile properties. Reducing the infill density results in lower printing costs and should be seen as an option, if conditions allow. For example, Onyx Rectangular samples with 70% of infill density take 69 min to print, while 10% samples take 48 min. Thus, strength is reduced by 7.4% while cycle time is reduced by 30.4%.Use a wider arrangement of the fiber reinforced strands, instead of stacked strands of fiber reinforcement.The designer must consider the fracture mechanisms discussed in Section . Avoid placing all the initial points of fiber in a single place. Fixing the initial points of fiber in a distributed manner helps improve overall part strength.Clearly, these recommendations are based on the study of standard specimens. The effect on real parts needs to be assessed in future studies.In this work, 3D printed composites with continuous carbon fiber reinforcement and chopped carbon fiber (Onyx) composites were manufactured and tested. Onyx samples show small improvements with respect to Nylon. Results showed that factors such as infill density and infill patterns in 3D printed chopped composites affect part strength. As discussed, the Triangular shape has a better tensile performance and should be used whenever possible.The influence of fiber volume fraction (VF) and fiber placement arrangement on continuous carbon fiber reinforcement composites were measured. As expected, the tensile properties for CFR composites have much better performance when the amount of fiber is increased. From the comparison of the two printing architectures (1R vs 3R) with the same volume fraction, it was shown that the arrangement of fibers has an effect on tensile properties with a slightly better performance for the wider arrangement. The effects of moving the initial point of reinforcement deposit on the fracture mechanisms, elastic moduli and tensile strength were also studied.A variation of the ROM method to predict elastic modulus for CFR composites with lower fiber content that considers different geometric characteristics was proposed. Good correspondence between predicted and experimental data was found for volume fractions smaller than 11%.Findings may help the designer to define the best parameters for the print part, and should also be helpful for the design of 3D printed composites.There are three directions for future work. First, as explained in Section , the behavior of the 3R vs 1R requires further study. The AM machine will be supplied with instrumentation to measure changes in thermal patterns in the specimens during processing. Second, Computer Tomography (CT) will be used to observe fiber behavior of 3D printed carbon fiber and fiberglass composites under uniaxial tension. The goal would be to measure and observe irregularities, such as first fiber strands broken, void areas or non-uniform distribution of the thickness strands. Of particular interest is to determine the “load elastic limit”, when the first critical defects appear in this kind of composite specimens. Finally, the effect of the use of design recommendations on real parts needs to be assessed in test cases.The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.ASTM D368 Standard Test Method for Tensile Properties of Plastics, Active Standard ASTM D638-14.Dwell and penetration of tungsten heavy alloy long-rod penetrators impacting unconfined finite-thickness silicon carbide ceramic targetsImpact experiments with a tungsten heavy alloy long rod projectile against silicon carbide tiles were performed to study the transition from dwell to penetration and to compare against earlier investigations which focused either on small scale semi-infinite set-ups or on finite thickness set-ups with confinement. A depth-of-penetration configuration consisting of a ceramic tile and an extended steel backing was used to assess the impact response of the unconfined finite-thickness ceramic. The ceramic tile was either bare or had a cover plate attached to the front. The cover plate thickness has been varied and gives best results for a thickness of about half the projectile diameter used in the experiments. For the bare ceramic, a long dwell phase can be maintained up to impact velocities of around 900 m/s. For the buffered ceramic, partial dwell can be achieved up to around 1700 m/s. The results corroborate those of earlier investigations mentioned above. More importantly, the present results show that it is possible to substantially erode a heavy alloy long-rod penetrator at the surface of a finite thickness ceramic element without lateral confinement in direct impact experiments even at high impact velocities.For the regime of long-rod penetrators impacting at velocities of about 1000 to 2000 m/s onto high-strength targets, the interaction behavior is strongly determined by material properties like strength and hardness Ceramics also exhibit a mechanism of defeating a projectile known as dwell effect or interface defeat: a high-velocity projectile erodes at the ceramic surface and flows out radially with no significant penetration (). Dependent on material and target set-up, the duration of the dwell effect can vary from a fraction of the projectile interaction time up to a complete erosion of the projectile at the target surface. For the latter case, the term “interface defeat” is frequently used.The dwell effect for rod penetrators has been investigated in complicated target arrangements about 15–25 years ago, e.g. Refs. , although the first observation of the basic effect in light armor studies dates back much earlier, e.g. Ref. , many different target layerings with light and heavy confinements were analyzed using direct-impact tests and also small-scale reverse impact tests. Nonetheless, due to the complexity inherent to the target design the key interaction mechanisms were still masked by the overall ballistic response of the setup. Therefore, a natural step was to consider bare and semi-infinite ceramics, in order to focus on the behavior of the ceramic material. This more academic approach also used small-scale reverse impact experiments and allowed for fundamental characterization of the ceramic material upon high-velocity impact of a long rod In the present paper, we address the transferability of the results of the above work to direct impacts of tungsten heavy alloy (WHA) rod penetrators onto single ceramic tiles of limited thickness, only supported by a backing. This implies a significant increase in scale by a factor of 6 for key geometries like rod diameter compared to experiments done in, e.g., Refs. , and at the same time a reduction of the thickness of the ceramics to less than 5 times the projectile diameter, i.e. we aim at extending prior work, e.g. Refs. The W-Ni-Fe based generic tungsten-heavy-alloy (WHA) penetrator used in the experiments has a diameter D of 6 mm and a length L of 90 mm. The 9 mm long nose section is conical with a 3.6 mm blunt tip (see ). The penetrator material is Kennametal E-922Y. The ceramic targets are quadratic tiles of dimensions 100 mm × 100 mm, 25 mm thick, made of commercial grade, pressureless sintered silicon carbide (SiC). The specific material is designated as SiC-F and is manufactured by 3M (formerly EKasic-F from ESK). A target consists of one SiC tile glued to a rolled homogenous armor (RHA) steel plate of 40 mm thickness. Depending on the impact velocity, additional RHA plates are placed behind the target, in order to ensure a semi-infinite RHA target for penetration measurement. shows the key mechanical properties for the different materials.The sabot-guided projectile was accelerated with a powder gun into a stationary observation tank. The impact was monitored with a multiple anode X-ray tube and a high-speed video camera. The impact velocity was varied between 400 and 1800 m/s. Experiments were carried out for the bare ceramic and for a buffered version, where a small copper disc was glued to the ceramic surface (see ). The purpose of the copper buffer is to attenuate the impact shock and to increase the dwell-to-penetration transition velocity compared to a bare surface. The basic effect of such buffers is well-known as, e.g., discussed in Refs. . The buffer thickness was optimized at a constant impact velocity followed by a variation of the velocity for the optimal buffer thickness. Contrary to prior work , the buffer is not combined with lateral confinement. shows the results for the bare ceramic targets (9 experiments). Total yaw angle, impact velocity vP and residual penetration depth PR into the supporting RHA plates were measured. The area density of the penetrated material for the complete target arrangement calculates asfrom the densities ρSiC and ρRHA of ceramic and backing, respectively, the thickness of the ceramic lSiC and the residual penetration in the backing PR. The standard velocity measurement procedure yields an error of about 1 %. The error for the depth measurement is about ± 0.1 mm.Results for the buffered target configurations are given in (8 experiments). In addition to the data of the buffer thicknesses lCu is incorporated. Accordingly, the area density of the penetrated material for the buffered target arrangement calculates with the density ρCu of the buffer as:In case of the buffered target, the copper buffer (3 mm thickness) shows a bulging during the impact process with slightly different shapes for the different impact velocities (around 1000 m/s for Test 14 and around 1700 m/s for Test 15). The copper shields the X-ray radiation, thus no penetrator fragments are visible. The bulging suggests that there is material expanding radially below the buffer plate, similar to the material flow clearly visible in case of the bare ceramics in test 2. shows the corresponding crater images of the cross-sectioned RHA plates for the tests of . For the bare targets of Tests 2 (dwell) and 8 (penetration), the difference in penetration depth is significant and reflects the 850 m/s difference in vP. For the buffered targets of Tests 14 and 15, the penetration depth is smaller than in test 8. Apparently, the penetrator dwells at a vP of around 1700 m/s for a substantial time (Test 15). At a significantly reduced vP of around 1000 m/s (Test 14), the penetration depth is only slightly smaller as for Test 15. It seems that the dwell effect is less distinct at the lower velocity.For the tests with buffer, the bulging of the copper plate visible in the X-ray images is also seen in the optical images.In addition, the development of cracks is visible for the ceramic target. As the interaction time of the penetrator with the ceramic is longer at lower impact velocities, the images at t4 show a later point in time and thus more developed cracks for Tests 2 and 14 than for Tests 8 and 15, respectively. However, comparing images for each case taken at nearly 300 µs after impact, when the penetrator either is consumed or has penetrated the steel backing, it becomes evident that for the lower impact velocities, overall damage of the ceramic is substantially lower than for the higher velocities ( shows the area density of the penetrated material ρA versus impact velocity vP for the various experiments. Additionally, the penetration into semi-infinite RHA is shown according to the Walker–Anderson model for penetration . The strength parameter of RHA had to be increased in the model (to 1.3 GPa) to match data for the semi-infinite reference penetration of the penetrator into RHA of representative quality (diamond symbols) (see also ). Note, however, that the target strength in the Walker–Anderson model represents an effective flow stress, which is typically larger than given by quasi-static measurements For the bare ceramic targets (square red data points) up to vP = 900 m/s the total penetration is almost constant. This corresponds to a fragmentation of the ceramic layer without more than superficial penetration into the RHA backing as well as to the indications of the dwell effect that are visible in the X-ray images obtained for those experiments. However, as the steel backing nonetheless shows small indentions for all of those experiments, it is evident that the penetrator dwells only partially and does not completely erode at the surface and during the subsequent penetration of the ceramic. For vP above 900 m/s the total penetration increases linear with impact velocity.For the buffered targets, the first step was a variation in buffer thickness from 100% down to 25% of the projectile diameter at a constant vP of about 1200 m/s to see the effects on overall target performance (triangular symbols). While the 4, 3 and 1.5 mm buffer configurations perform similar and exhibit a lower ρA than the bare target configuration, the 6 mm buffer configuration achieves only about the same ρA as the bare target (). This is an indication that a thick buffer may inhibit the dwell potential of the ceramic. As the 3 mm buffer shows the lowest ρA values of all tested buffer configurations, it was chosen for all subsequent tests where vP was varied.Considering in the following the tests with the 3 mm buffer only ( – round symbols), the penetrated area density remains in the range of 150 kg/m2 up to 270 kg/m2 and thus a substantial erosion of the heavy alloy long rod penetrator by partial dwell occurs when compared to the penetration values for the bare target. The difference in ρA between buffered and bare target increases with impact velocities of up to 1700 m/s.At around 1800 m/s though, the difference in ρA between buffered and the linear extrapolation for the bare target becomes very small. Here, vP is well above the transition velocity from dwell to penetration for a similar material combination investigated in Ref. . Therefore, penetration is expected to start right away with no dwell phase.Overall, the results correspond well to findings in the literature Experiments with buffered finite thickness SiC targets at different scales presented in The total mass efficiency EM of the ceramic target is defined as ρA (penetrated area density) of the semi-infinite RHA divided by ρA of the respective complete target arrangement consisting of ceramics, backing, and optional buffer. shows that for impact velocities vP above 900 m/s, there is a linear increase of the total penetration with impact velocity for RHA and the bare ceramic target. To a lesser extent, a linear increase can also be assumed for the buffered ceramic target up to a vP of around 1600 m/s. Interestingly, the three linear curves of different slopes intersect at around vP = 900 m/s, i.e. at that velocity the mass efficiency of ceramics (bare and buffered) with RHA backing is about 1 in relation to RHA. At higher impact velocities – i.e. in between 900 m/s and 1600 m/s – the mass efficiency increases by a nonlinear function determined by the different slopes of the linear curves for ρA and their common offset of about 100 kg/m2 at around vP = 900 m/s. shows the total mass efficiency EM in relation to RHA for the bare and buffered ceramic targets as a function of vP. In the considered velocity range of 900 m/s to 1600 m/s, EM for the bare target increases only slightly from 1 up to 1.3. However, EM for the buffered target arrangement increases significantly from 1 up to 2.5. So the buffer not only increases the transition velocity from dwell to penetration but has also a positive effect on the mass efficiency of the target.To extend and verify findings in material behavior with respect to the dwell effect on ceramics – so far derived mainly from experiments with semi-infinite or confined ceramic samples – direct impact experiments with long WHA rods against unconfined, finite thickness SiC tiles supported by a steel backing were performed at impact velocities ranging from 500 m/s to 1800 m/s. The simple test set-up with significantly increased dimensions compared to earlier work focuses on the dwell potential of the finite-thickness ceramic and thus avoids considering the complicated interplay of a ceramic element with its confinement and the applied pre-stresses in set-ups that are commonly found in literature.The new experiments show that at least a partial dwell effect for heavy alloy long-rod penetrators at laboratory-scale can be achieved without a complicated target set-up for finite-thickness ceramics, even without lateral confinement. A buffer material in front of the ceramic that attenuates the impact shock can increase the transition velocity as well as the mass efficiency of the target. The variation in buffer layer thickness showed that the best protective properties are achieved for a layer thickness of about half of the thickness of the laboratory penetrator diameter.The results show that it is possible to substantially erode a heavy alloy long-rod penetrator at the surface of a finite thickness ceramic element even without lateral confinement. This has been proven by direct impact experiments at impact velocities up to 1700 m/s.Compatibilization and property enhancement of poly(lactic acid)/polycarbonate blends through triacetin-mediated interchange reactions in the meltTetrabutylammonium tetraphenylborate (TBATPB) and triacetin were added during extrusion to melt blends of polylactic acid (PLA) and polycarbonate bisphenol A (PC) through a reactive compatibilization approach in order to enhance the materials' mechanical properties and thermal resistance. Dynamic mechanical thermal analysis revealed a new peak attributable to the glass transition temperature (Tg) of the PLA-PC copolymer at a temperature lower than the Tg typical of PC and higher than the Tg of PLA. The results of tensile tests, thermogravimetric analysis, differential scanning calorimetry, scanning electron microscopy, transmission electron microscopy, size exclusion chromatography, and NMR analysis for the compatibilized and uncompatibilized blends were, on the whole, in agreement with the formation of the PLA-PC copolymer due to the action of the TBATPB and triacetin during the short extrusion time. The mechanical behaviour, morphology, and thermal properties of the PLA/PC compatibilized blends were investigated as a function of composition, with the intention of broadening the utility of these biobased-blends. Finally, a general scheme for the reactions that occur during extrusion was proposed based on the experimental results.The development of new materials derived from renewable sources is a goal of high technological and environmental priority. In this context, polymers derived from agricultural sources, such as the corn starch-derived polylactic acid (PLA) and its copolymers, are of great importance today In principle, PLA-based materials that are able to maintain their mechanical properties in temperatures above the Tg and below their melting temperatures can be obtained a) by an annealing step allowing crystallization, either by reheating after moulding or through the use of nucleating and accelerating agents, or b) by physical mixing with a second PLA-immiscible polymer component which is characterized by a glass phase having a high TgAnnealing after moulding or increasing the crystallization rate by nucleation In the physical mixing approach, the blending of PLA with polycarbonate bisphenol A (PC), with its high Tg (above 150 °C), can be a successful strategy. In the patent literature, blends of PLA with PC Extensive scientific work on the blending of PLA with different polymers has been performed, and the effects on characteristics such as biocompatibility or ductility have been studied. To improve the compatibility between two immiscible components, a third component is added as a compatibilizer or catalyst in most cases. The compatibilizer can be either premade or formed in situ during melt blending. One successful application of this type of reactive blending was the addition of peroxides to several PLA blends On the other hand, the blending of PC with polyamides or polyesters can result in improved phase adhesion when a coupling agent Several studies have investigated the blending of PLA and PC (Tg ≈ 160 °C) to enhance thermal resistance From the preceding literature survey, it is evident that new compatibilized biodegradable materials based on PLA and aromatic polycarbonates would be useful, especially if they exhibit thermomechanical properties suitable for the production of materials for different industrial sectors and can be prepared through rapid processes that are compatible with industrial extrusion.In this work, PLA/PC compatibilized blends were prepared by a process of reactive extrusion in the molten state in the presence of triacetin (TA) and tetrabutylammonium tetraphenylborate (TBATBP). The extrusion conditions such as temperature and time were selected to promote the occurrence of interchange reactions between the polymers. The procedure afforded compatibilized blends which were assessed with respect to their mechanical properties, morphology, and thermal and biodegradation behaviours as a function of composition. Compatibilized and uncompatibilized blends were compared to understand structure–property relationships and develop a general reaction mechanism on the basis of molecular weight and spectroscopic evidence. Such bio-based polymers and composites would broaden the potential utility of these renewable materials.-lactic) acid was purchased from NatureWorks LLC, having a nominal average molecular weight Mw = 199,590 Da (Ingeo™ 2003D Extrusion Grade) and a density of 1.24 g/cm3. The polycarbonate of bisphenol A (Iupilon S3000) with a density of 1.20 g/cm3 and average molecular weight Mw = 20 kDa was purchased from Mitsubishi Engineering Plastics. Triacetin (TA, also known as glycerin triacetate or 1,2,3-triacetoxypropane) and tetrabutylammonium tetraphenylborate (TBATPB, CAS #15522-59-5) were purchased from Aldrich Chemicals. The chemical structures of these raw materials are presented in After the starting polymers (PLA and PC) were dried at 60 °C and 133 Pa for 4 days, they were mechanically mixed at room temperature for about 10 min in different ratios with a high speed mixer. Then, the triacetin and TBATPB were added and mixing was continued for another 10 min using the same equipment. The resulting mixtures were processed with a MiniLab II Haake™ Rheomex CTW 5 conical twin-screw extruder (Thermo Scientific Haake GmbH, Karlsruhe, Germany). Mixing was conducted at 210 °C and 230 °C with a screw speed of 100 rpm for a recirculating time of 1 min. After extrusion, the molten materials were transferred through a preheated cylinder to the Haake™ MiniJet II mini injection moulder (Thermo Scientific), to obtain Haake type-III specimens that were used for measurements and analysis. The specimens were placed in plastic bags and vacuum sealed to prevent moisture absorption.Tensile tests were performed at room temperature, at a crosshead speed of 10 mm/min, by means of an Instron 4302 universal testing machine (Canton MA, USA) equipped with a 10 kN load cell and interfaced with a computer running the TestWorks 4.0 software (MTS Systems Corporation, Eden Prairie, MN, USA).Differential scanning calorimetry (DSC) measurements were carried out to investigate the thermal behaviour of the materials with a TA Q200 instrument (TA Instruments, Newcastle, DE, USA) with nitrogen as the carrier gas and indium used for calibration. The samples were first heated from −100 °C to 250 °C at 10 °C/min, and then cooled to −100 °C at 20 °C/min. Then, the second heating was investigated using the same conditions as the first heating.Size exclusion chromatography (SEC) analysis was performed with a Jasco PLUS system consisting of a PU-2029 pump, CO-2063 column oven set at 80 °C, RI-2031 differential refractometer, and UV-2077 UV detector, fitted with two PL-Gel Mixed D columns. Column calibration was performed with narrow distribution poly(styrene) standards. A 4 mg/mL solution of the polymer in THF (0.1% w/V) was filtered through a 0.2 mm membrane syringe filter, and 20 μL solution was injected using a 1 mL/min flow rate.13C NMR spectra were acquired on a Bruker DRX400 spectrometer in deuterated chloroform. The excitation pulse for 13C was calibrated at 30 °C, and the repetition time was 1.5 s. Proton irradiation was applied before each scan to enhance the nuclear Overhauser effect (NOE) and during the 1 s FID acquisition for heteronuclear decoupling.Thermogravimetric analysis (TGA) was performed under a flow of nitrogen gas at a scan speed of 10 °C/min, from room temperature to 1000 °C, using a TGA 1000 instrument (Rheometric Scientific Inc., USA).DMTA was carried out on a Gabo Eplexor® 100N (Gabo Qualimeter GmbH, Ahlden, Germany). Test bars were cut from the tensile bar specimens (size: 20 × 5 × 1.5 mm) and mounted in a tensile geometry. The temperature used in the experiment was varied from −100 °C to 170 °C at a heating rate of 2 °C/min and frequency of 1 Hz.The morphology of the composites was studied by scanning electron microscopy (SEM) using a JEOL JSM-5600LV (Tokyo, Japan), by analysing cryofractured sample surfaces, previously sputtered with gold.The transmission electron microscopy (TEM) study was performed with a JEOL 1210 operating at 120 kV. The samples were trimmed with a Leica ULTRACUT E ultramicrotome room using a diamond-trimming knife and then ultra-thin sectioned with the same ultramicrotome using a diamond knife. The section thickness was nominally 70 nm (setting). TEM micrographs were obtained in representative areas of the samples at 3000× magnification.Aerobic biodegradability tests were carried out under controlled composting conditions according to ISO 14855. The test materials were examined in the form of granulates. The composting inoculum was derived from an organic fraction of municipal solid waste that was aerated and stabilized under pilot-scale composting conditions over a period of more than 20 wk. The compost was sieved to remove particles over 5 mm in size, and the fine fraction was then used as the inoculum. Control reactors contained only this inoculum without test material. The reactors were placed in an incubator without light at 58 ± 2 °C and continuously aerated. During biodegradation, microorganisms present in the inoculum converted carbon in the reference or test material into CO2. The gas leaving each individual reactor was analysed at regular intervals for CO2 and O2 content, and the gas flow rate was measured. The biodegradation percentage was determined as the percentage of the carbon in the starting reference or test material that was converted into CO2. Continuation of the biodegradation test was possible since sufficient O2 supply was present in the reactor headspace. The tests were fully complete after 150 d.Preliminary studies to assess the effect of the TA/TBATPB addition on the reactive extrusion of PLA and PC blends were carried out on a PLA40/PC60 composition. The different blend compositions and conditions are listed in The extrusions were conducted at 210 °C and 230 °C at a 100 rpm screw speed, for a recirculating time of 1 min. The material was then injection moulded: the mould temperature was 50 °C, the injection time was 20 s, and the injection pressure was 790 mm Hg. Afterwards, the moulded samples were annealed at 80 °C and 1 mm Hg for 48 h. The samples were tested by DMTA and tensile tests.Blend 1, obtained without the addition of TBATPB catalyst or TA, exhibited a tensile strength of 54.6 MPa and an elongation at break of 5.1% after extrusion at 210 °C. The analogous mixture, Blend 5, extruded at 230 °C, afforded a higher elongation at break (96%). This means that the higher extrusion temperature resulted in transformations that led to improved compatibility. Blend 2, in which TA was used, displayed very ductile behaviour; its elongation at break of 98.7% indicates its plasticization. Blend 3, with only TBATPB, was even more brittle than Blend 1, with an elongation at break of 2.3% (). This means that TBATPB is not active as a catalyst at this temperature (210 °C), probably as a consequence of the short extrusion time. Blend 4, which contained both TBATPB and TA, showed significantly improved mechanical properties over Blend 3, with a tensile strength of 65.5 MPa (corresponding to a 20.0% increase over the simple mechanical blend), while maintaining an excellent value for elongation at break (46.5%), attesting to the synergism of the TBATPB and TA.The trend was confirmed by comparing the stress–strain curves of the blends prepared at 230 °C (). As mentioned above, Blend 5, the simple mechanical mixture, shows a rather ductile behaviour, with a tensile strength of 62 MPa and an elongation at break of 96.4%; but both Blends 6 and 7 show increased yield strengths of 65.1 and 63.9 MPa as well as elongations at break of 100.7 and 46.9%, respectively. This indicates that both TBATPB and TA are chemically active in the system at this temperature. The best mechanical performance is shown by Blend 8, wherein both TA and TBATPB were added during the extrusion, showing a tensile strength of 68.6 MPa (an increase of 12.1% with respect to the mechanical mixture), while maintaining a very good elongation at break of 35.3%. Thus, the synergistic action of the TBATPB and TA in promoting the compatibility of the PLA/PC system is thus confirmed.Dynamic mechanical thermal analysis was carried out in the temperature range −100 to 250 °C at a heating rate of 2 °C/min and a frequency of 1 Hz. From the point of view of dynamic mechanical properties, the traces obtained by plotting tan δ versus temperature revealed a new peak that did not appear in the case of the simple physical mixture of the two homopolymers. This new peak appeared at a Tg lower than that of PC, and may be related to the presence of PC-blocks in a copolymer. In , for blends extruded at 210 °C, the new peaks can be seen for Blend 2 (TA only) and Blend 4 (TBATPB/TA) at 123.5 and 113.5 °C, respectively, whereas it was not present for Blend 1 (mechanical mixture) or Blend 3 (TBATPB only)., a similar superimposition is shown for the blends prepared at 230 °C. Blend 6 (containing TA only) and Blend 7 (containing TBATPB/TA) show the new peak at 128 °C, whereas the mechanical blend (Blend 5) exhibits a peak associated with the Tg of the PC phase at 160 °C. Blend 7, in which only TBATPB was used, reveals a peak at a slightly lower temperature, 155 °C, which can be probably be explained by the occurrence of interchange reactions leading to PC blocks with lengths shorter than in the mechanical blend. The DMTA data are consistent with the fact that PLA and PC are immiscible. In addition, the PLA-rich phase exhibits both amorphous and crystalline phases. The Tg values of both PLA (50–70 °C) and PC (155−160 °C) are not, in general, much different from typical values of the two polymers, but a new peak appears at intermediate temperatures (110−130 °C) for the copolymer, in agreement with the results of Liu et al. , we compare non-annealed samples of pure PLA, Blend 1, and Blend 4, to show that both blends have a much higher storage modulus across and beyond the Tg of PLA. Also, the modulus of PLA tends to increase starting from about 80 °C to 120 °C, where it reaches a new maximum. This is associated with the partial crystallization of the PLA phase. A similar phenomenon is observed for Blend 1, although in a limited way, whereas it is not visible for Blend 4. This can be explained by the presence of the PC-PLA copolymer in this material. The PLA blocks that are probably present in the copolymer are shorter than in pure PLA or in the mechanical mixture with PC. Moreover, they are surrounded by rigid PC blocks that strongly limit molecular mobility and hinder the crystallization process. As proof of this statement, we can observe an increase in the modulus of Blend 4 above 160 °C, which corresponds to the Tg of the PC blocks, up to 200 °C, where the Young's modulus of the blend reaches a new maximum. This can be explained by considering that the PC-blocks are beyond their Tg, and hence, the PLA blocks recover their mobility and are able to crystallize.The TGA and derivative thermogravimetric (DTG) curves of PLA40/PC60 (Blends 1−4) with and without catalyst at 210 °C are reported in a and b, respectively, and the corresponding data are reported in The degradation of pure PLA occurs in a single step starting at 280 °C through a final temperature of 427 °C, with a DTG peak temperature (Tmax) at 356 °C. The Tmax is the temperature at the maximum rate of weight loss, that is, the decomposition temperature. Song et al. PLA40/PC60 blends with and without different catalysts processed at 210 °C exhibited two stages of degradation, attributable first to PLA and then to PC. The onset of degradation in the blend began at the temperature typical of PLA and finished at 547 °C, before the typical end-point temperature for PC. This thermal behaviour is quite similar to those of the blends that were processed at 230 °C, as shown in a and b. Although the Tmax of PLA in both cases did not change in the presence of TA/TBATPB, that of PC changed from 509 °C in the pure polymer to 455 °C in the blends. This phenomenon might possibly be explained by the fact that the degradation product of PLA could have facilitated the thermal degradation of PC. At both processing temperatures, the DTG peaks for PLA degradation in the blends are broader than in pure PLA, meaning that the thermal resistance of the materials increases in the presence of the polycarbonate. More specifically, Blends 2, 4, 6, and 8, all containing TA, appeared to have a slight peak from 120 to 220 °C, with a Tmax of 180 °C. This peak was far from the boiling and degradation temperatures of TA, 260 and 312 °C, respectively , the temperatures for obtaining 10% and 50% degradation (T10%, T50%) of all the blends at 230 °C are quite similar. Beyond that, the decomposition temperatures of the blends at 70% degradation (T70%) are much affected by the presence of TBATPB, as can be seen clearly in the expansion in a. The slightly increased thermal resistance of the blend obtained at 230 °C with TA and TBATPB, as evidenced in the expansion in a, with respect to mechanical blend, may indicate that some specific interactions or chemical reactions have occurred between PLA and PC, as observed in the case of poly(vinyl chloride)/ethylene-vinyl acetate blends On the basis of these mechanical and thermal results, a processing temperature of 230 °C was selected for further studies in which mechanical, thermal, morphological, and biodegradation properties were investigated as a function of polymeric composition in the presence and absence of TA/TBATPB.The tensile properties of the PLA/PC blends as a function of composition are reported in . For comparison, the tensile strength, Young's modulus, and elongation at break of pristine PC are 57.2 MPa, 2.25 GPa, and 84.4%, respectively (As the amount of PLA increases, the Young's modulus of the blends increases up to 3.54 GPa, i.e. the Young's modulus of pure PLA. The tensile strengths of the blends did not change, as the tensile strengths of pure PLA and PC are quite similar. Conversely, the elongations at break of the blends decreased from 126% for the PLA40/PC60 blend to 3.3% for the PLA60/PC40 blend (near the value of 4.1% for pure PLA). This change can be explained by a phase inversion, occurring at a composition of ∼50/50 PLA/PC, from a phase morphology in which PC is the matrix and PLA the dispersed phase, to the opposite condition in which PLA is the continuous phase and PC is the discontinuous phase. It was worth noting that the elongation at break for the PLA40/PC60 blend reaches 126%, which is significantly higher than that of pure PC (84%), evidencing the strong toughening effect by the PLA domains in these blends. presents the Young's modulus values for blends with different PLA/PC compositions that were processed in the presence of TA and TBATPB (indicated with the suffix CAT) or as physical blends. The experimental data appear to fit well with Barentsen's model ) at the two extremes of the compositional range. In the middle range, the Young's modulus of the blends is substantially higher than what is predicted by Barentsen's model. A better fit can be obtained with the model proposed by Veenstra and co-workers ). The big difference in the elongation at break between PLA40/PC60 and PLA60/PC40 indicates that a phase inversion occurs between these two compositions. Above this critical composition, the elastic modulus follows the trend predicted for a rigid PLA-rich matrix phase with dispersed PC domains; that is why the experimental data are fitted again with Barentsen's model, and the elongation at break rapidly decreases to the values characteristic of pristine PLA., for the droplet/matrix morphologies, equation ) was used for as high as 20 wt% PLA when PLA (the stiff component) was the matrix, whereas from 80 to 100 wt%, where the stiff PLA component is the minor phase, equation was applied. In the case of co-continuous morphologies, when the stiff PLA component dominated (∼50–60 wt% PLA), equation was used, whereas in the range 20–50 wt% PLA, equation was applicable. With these calculations, the experimental data and the theoretical models fit in a quite satisfactory way.The Young's modulus values of the PLA/PC binary blends were well fitted by Veenstra's model . Nevertheless, at all compositions, the Young's modulus of the blends prepared in the presence of catalyst is always higher than the elastic modulus for the corresponding physical blends, as can be noted by comparing the data in . The Young's modulus of the blends decreases for PC contents ranging from 0 to 30 wt%, and then does not change much from 30 to 40 wt%, suggesting that the materials start to reach a co-continuous phase morphology, which is similar to the behaviour observed for physical blends.It is interesting to observe that the experimental data for the Young's modulus of the blends prepared with TA/TBATPB exceed the theoretical predictions. Also, the compositional range for full co-continuity seems to be widened, from 20 to 60 wt% PLA for the physical blends to 20−80 wt% PLA for the blends obtained in presence of the catalysts. This can be explained by the decrease in PLA molecular weight, resulting in reduced melt elasticity The thermal behaviours of the materials were investigated by DSC. shows the thermograms of the second scans at a heating rate of 10 °C/min.The crystallinity of the materials was calculated using the formula Xc=(ΔHm/ϕPLA/ΔHm0)∗100%, where ΔHm0 is the theoretical melting heat of 100% crystalline PLA (93 J/g) The Tgs of pure PLA and the PLA in the blends did not differ and remained near 59.1 °C, even in different compositions. It decreased to 48.8 °C in the presence of TA/TBATPB in blends containing 20 and 60 wt% PC. These results indicate that TA is not only involved in melt reactions, but also plays the role of a plasticizer in the PLA More specifically, the Xc of PLA in PLA80/PC20-CAT is slightly higher than the crystallinity percentage of pure PLA, but it is significantly increased with respect to the Xc of the corresponding physical blend, in accordance with the important role of the TA/TBATPB in favouring PLA crystallization. However, at high PC content, the crystallization of PLA is quite low, as shown in the thermograms of the PLA40/PC60 blends. Melting peaks are not evident, so the materials can retain their mechanical properties at higher temperatures.The data from the DMTA of the blends without a catalyst are shown in , after annealing at 80 °C for 24 h. The first peak on the tan δ curve is the relaxation of pure PLA at 69 °C. The tan δ curve usually indicates the relaxation processes of a polymer. The major relaxation process in PLA is associated with the TgAbove the Tg of PLA, the storage modulus of the blends increases with increasing PC content. The blends obtained without additives showed two peaks at 69 and 160 °C, corresponding to the Tgs of PLA and PC, respectively. This indicates the presence of separated PLA and PC phases, in agreement with the SEM, TEM, and mechanical properties results. Furthermore, the height of the tan δ peak is associated with the mobility of the amorphous regions in the polymer ), the blends exhibit Tg = 60 °C for PLA, with a reduction similar to that observed by DSC analysis. Additionally, a new peak occurs between the Tg values of PLA and PC. Similarly to the explanations given above, this result is the most important evidence for the formation of a PLA-PC copolymer. In the crystalline condition, the middle peak on the tan δ curve does not change significantly as the amount of PC varies. These results are different with respect to those shown in , in which the blends were not annealed at 80 °C for 24 h before testing. This dissimilarity can be explained by the consequence of the presence of an increased crystalline fraction of PLA in the former blends, reducing the mobility of the polymer chains, and thus affecting the relaxation of the new copolymer. In fact, the lowest peak is associated with one of the PLA80-PC20 blend, showing high crystallinity.A, the DMTA results for pure PLA are shown. Above the Tg, the storage modulus shows a minimum at about 80 °C and then modulus increases, reaching a maximum at 120 °C. This implies that the crystallization of the PLA phase proceeded during the DMTA run (low scan rate). The decreasing storage modulus of PLA in the blends starts and ends at lower temperatures than in the original PLA due to TA plasticization.B shows that, in the case of the PLA40.PC60-CAT and PLA30.PC70-CAT blends, the storage modulus does not decrease in the temperature zone typical of PLA crystallization, which is completely different from the PLA40/PC60 physical blends. This is evidence to confirm that the TA/TBATPB addition results in the formation of chemical links between PLA and PC, so the chain mobility of PLA becomes limited and crystallization does not occur. This is a significant point for the application of PLA, because the material can maintain its mechanical properties up to 100 °C.Moreover, the temperatures of the middle peaks or Tgs attributable to the PLA-PC copolymer change as a function of PC content in the non-annealed samples (), in agreement with the predictive models of Tgs for polymer blends suggested by Gordon Taylor Tg=φ1Tg,1+kKw(1−φ1)Tg,2φ1+kKw(1−φ1)+qφ1(1−φ1)Tg=φ1Tg,1+(1−φ1)Tg,2+φ1(1−φ1)[a0+a1(2φ1−1)+a2(2φ1−1)]where φ1 is the volume fraction of component 1, Tg,1 and Tg,2 are the glass transition temperatures of component 1 and 2 respectively and kGT, kKw, q, a0, a1, and a2 are empirical parameters of equations By increasing the amount of PC, the Tg of the PLA-PC copolymers decreases slightly and does not change from 40 to 60 wt% PC; above this value, it increases. Therefore, this complex behaviour of Tg does not fit the model of Gordon–Taylor when applied to a binary polymer with a simple interaction in the amorphous state. In that equation, Tg versus the weight fraction follows a linear or hyperbolic function. In addition, the crystallization temperature of PLA is quite similar to the Tg of the PLA-PC copolymer. Thus, the crystallization process will affect the transition temperature of the PLA-PC copolymer. Concerning this peculiar phenomenon, Kalogeras explains that, in terms of microstructure, such intriguing variations may be partly attributed to the different types of segregation in the copolymer and their relative contributions to the overall structure. In fact, different kinds of segregation may occur: (a) inter-lamellar segregation (the amorphous new copolymer resides in the inter-lamellar region within the lamellar stack); (b) inter-fibrillar segregation (the amorphous chains are placed outside the lamellar stacks of the PLA crystalline component(s), but are still located within the spherulite); and/or (c) inter-spherulitic segregation (the amorphous phase is expelled from the lamellar stacks and resides at the inter-spherulitic region of the PLA component) An investigation about the macromolecular weights of the PLA/PC blends was carried out by SEC, using both refractive index (RI) and ultraviolet (UV) detectors. A superimposition of the chromatograms obtained by the RI detector is shown in . The chromatographic curves obtained by RI detection consisted of a peak at a long elution time (i.e. at lower molecular weight) due to the PC, with a shoulder at a shorter time due to the PLA. In , the PLA shoulder intensity is clearly much lower than that for the PC, even in the PLA-based blends. This observation suggests that the PLA chain length was significantly reduced in the presence of TA and TBATBP.The use of the UV detector at 254 nm should provide evidence for the linkage of PLA to PC. In fact only PC is detectable by this detector, and the presence of linked PLA chains having the molecular weight of pure PLA should result in the presence of a shoulder at a lower retention time. However, a shoulder could not be discerned, thus indicating the likelihood that only short PLA chains are linked to PC. On the basis of chromatograms examination, the molecular weight of PC is not significantly influenced by the processing, and that the amount of formed copolymer would be low and have a molecular weight similar to PC.The molecular weight data referred to polystyrene standards are reported in . PC-PLA copolymer formation was anyway demonstrated by the data obtained with the UV detector. In fact, although the Mn of PC was similar or slightly decreased with respect to the pure PC, the Mw values slightly but significantly increased, and the dispersity index Id also increased in all the blends obtained with the TA/TBATPB additives. In particular, the Mw of PLA60/PC40-CAT was 68300 (Id = 2.22), whereas the corresponding value for PLA60/PC40 was 53,800 (Id = 1.75). In the latter blend, only a very slight decrease in the molecular weight of PC was observed with respect to pure PC due to chain scission. In contrast, in the presence of TA/PBATPB, as was evidenced in PLA/PBAT blends obtained in the presence of a transesterification catalyst To investigate PLA chain scission in the blends, the theoretical Mn (Mnth) was calculated by considering the Mn values of pure PLA and PC as obtained from the analysis via RI detection. The calculated values are significantly higher than the experimental ones obtained via RI detection. The difference between the theoretical and the experimental values, ΔMn, was also calculated, and it was found to increase as the PLA content in the blend increased. These data are in good agreement with the observations from the chromatograms: the molecular weight of PLA is significantly reduced during processing and to a greater extent than that of PC. The data set for the blend obtained without TA/TBATPB showed that the occurrence of PLA chain scission cannot be exclusively ascribed to the action of the catalyst, as it occurred to a slight minor extent in the absence of the TBATPB and TA. Moreover, after simplifying by neglecting the effect of copolymer formation on the molecular weight, the molecular weight of the PLA in all the blends was calculated by considering equation where MnRI is the number average weight determined by RI detection, MnUV is the number average molecular weight determined by UV detection (considered the Mn of PC), and xPC and xPLA are the mole fractions of PC and PLA, respectively. The calculated values are reported in the last column of . The results confirm the occurrence of chain scission in PLA, especially in blends with a higher PLA content.The 13C NMR spectra of the two pure polymers are rather simple (a). Although small impurity peaks are present, the signal assignments are quite straightforward and account for the repeating units of PLA (a) and PC (b).b, 13C NMR data for the physical blend (c) are reported as well as for a PLA80/PC20 blend of the two polymers obtained in the presence of TA/TBATPB (d). Upon examination, no particular differences between the two samples can be noted. The signal marked with the asterisk (*) in spectrum (d) is due to residual acetone. At this stage, no evidence of copolymerization is apparent in spectrum (d). The main signals from the starting polymers are all present and their intensity is in fair agreement with the weight ratios in both spectra (c) and (d). Other smaller signals are visible, but they are also present in spectra (a) and (b) of the starting polymers. Because of the many similar functional groups, the detection of processing products by 13C NMR could be difficult because of the overlapping of signals.The spectral differences observed between the spectra of the pure polymers and blends obtained with catalysts were almost negligible. On the other hand, the copolymer would be a minor component in the presence of the predominant pure polymers, and would show identical spectral signals. Although a similar comparison was carried out by examining 1H NMR spectra, they could not provide further evidence of copolymer formation for the same reasons.An NMR investigation was carried out by Liu et al. Mechanistically, the PLA chains in this process are broken down in the presence of TA/TBATPB, and then react with PC. This is in good agreement with prediction made on the basis of the work of Penco et al. TA, which is the main blend component based on molar fraction and the most mobile chemical species in the system, reacts with the OH groups in PLA and PC under the melting conditions of extrusion and the catalytic influence of TBATBP to produce molecules with 1, 2, or 3 hydroxyl groups (glycerol in the latter case). The chain scission of PLA occurs through the involvement of these activated molecules derived from TA. PLA having a linear or branched structure and a lower molecular weight is thus formed. PLA degradation also occurs during processing at high temperature in the presence of residual humidity, and results in the increased concentration of both hydroxyl and terminal carboxylic groups. These can react with TA, resulting in the evolution of acetic acid, in agreement with the TGA results.The interchange reaction of modified PLA with PC can produce block copolymers with variable-length PLA blocks and branching points. The occurrence of branching creates an irregular structure which is probably responsible for the peculiar thermal properties of the blends. The presence of TA is fundamental as it facilitates the rapid formation of the PLA-PC copolymer, thus favouring the occurrence of compatibilization under laboratory extrusion conditions (60 s).The morphologies of the blends were investigated by SEM. displays two micrographs obtained for the PLA80/PC20 blend in the presence (A) or absence (B) of TA/TBATPB. In the former, phase separation is evident and the PC domains in the PLA matrix can be observed. The large spaces noticed at the edges of domains between the PC and PLA are attributable to low adhesion. The dimensions of the PC domains were variable, in the range 1–3 μm.. This phenomenon can be explained by a decrease in the surface tension of the PC due to the formation of the PLA-PC copolymer.The ratio between the viscosity of the dispersed phase and that of the matrix, ηD/ηM, in the PLA/PC 80/20 blend is higher than 1, as the PC (i.e. the dispersed phase) is highly viscous in the melt at 230 °C (a lower temperature than usually employed for processing). The occurrence of chain scission in the PLA when TA and TBATPB are added results in an increase in the viscosity ratio, inducing an increase in the dispersed-phase diameter, in good agreement with Wu's theory c for PLA60/PC40. This fact was applied to model the mechanical properties of the blend. Furthermore, there seem to be some small sub-inclusions inside the PC domains due to the rare coalescence of PLA particles inside the highly viscous PC phase. In the presence of TA/TBATPB in the PLA60/PC40 blend, the chain scission leads to an increase in the viscosity ratio and the collapse of the dispersed particles in the continuous PC phase, because the percolation threshold is overcome. In fact, the viscosity ratio affects the co-continuity range width, which usually becomes narrower for a viscosity ratio closer to 1 The average biodegradation (%) of PLA, PC, and physical blend granulates are shown in a. Although pure PC is not biodegradable, pure PLA starts to degrade after 18 days, and proceeds to 50 wt% after 55 d and 100 wt% after 80 d. After 150 d, the degradation was 138 wt%. Biodegradation percentages above 100% are explained by a synergistic effect known as priming, which occurs if the compost inoculum in the test reactor produces more CO2 than the compost inoculum in the control reactors. This results in a net CO2 production that is not produced exclusively from the test item and, in the case of readily degradable products, in a measured biodegradation percentage exceeding 100%.In the physical blends, the final percentage of degradation is similar to the percentage of PLA in the blend. Depending on the PC content, the onset of degradation was delayed and the final biodegradation percentage reduced. Interestingly, bi-sigmoidal curves were observed for all the PLA/PC physical blends. The times at which the inflection points in the curves occur are increased as the amount of PC in the blends increases.The PLA/PC blends containing TA/TBATPB (b) did not show bi-sigmoidal trends and the start of degradation was anticipated. The former observation can be the consequence of interchange reactions between PLA and PC and the latter observation can be attributed to the lower molecular weight of PLA due to chain scission, which would favour biodegradation. As a result, the presence of TA and TBATPB could initially increase the speed of degradation, but decrease the final biodegradation percentage. The formation of linkages between the PLA and PC blocks due to interchange reactions and the presence of the branching points introduced by TA insertion The preparation of PLA and PC blends obtained by extrusion with and without TA/TBATPB was investigated. The addition of both TA and TBATPB at 230 °C resulted in improved compatibility through the formation of a PLA-PC copolymer. In fact, a tan δ trend with a new peak was obtained by DMTA analysis. The new peak was situated between the Tg values of PLA and PC. The Tg of the copolymer as a function of blend composition was consistent with the models of Kwei The tensile characterization of physical PLA/PC blends showed that the Young's modulus was improved as the PLA content was increased. The maximum elongation at break was obtained as the content of PC reached the percolation threshold, allowing the achievement of a co-continuous phase morphology. More specifically, the data fit well with two different predictive models. As the catalyst was added, the Young's modulus of the materials increased as a result of both the improvement of compatibility and chain scission in the PLA phase, enabling the achievement of a co-continuous phase morphology for lower PC contents.DSC and DMTA confirmed that, as the content of PC increased, the crystalline fraction of the materials was reduced. More specifically, in the PLA40/PC60–CAT blend, the typical decrease in storage modulus due to the overcoming of Tg followed by the increase due to crystallization was not observed, suggesting the maintenance of mechanical stability at temperatures higher than the Tg of PLA and the disabling of the crystallization process. The effect is probably attributable to the links formed between PLA and PC, which reduce PLA mobility. These advantageous properties broaden the temperature range for applications of current materials based on PLA.Investigations of the reactions occurring in the melt through SEC and NMR analysis were consistent with the evident PLA chain scission on one hand and the formation of a low amount of PLA-PC multiblock copolymer, probably partially branched, on the other. The presence of TA was fundamental as it allowed the rapid formation of the PLA-PC copolymer, thus favouring the compatibilization under laboratory extrusion conditions (60 s).In addition, the SEM and TEM analyses confirmed the effects of TA/TBATPB on the morphology of the blends. The interaction between the domains and the matrix was improved as the adhesion between the PC and PLA phase increased, whereas the sizes of the dispersed domains increased in agreement with the improved tendency toward co-continuity because of PLA chain scission.Chain scission was also responsible for the anticipated onset of biodegradation in the blends obtained with TA and TBATPB in contrast to the physical blends. Nevertheless, the final biodegradation percentage was lowered mainly by the addition of PC and slightly by the presence of TA/TBATPB. The biodegradation behaviour was in good agreement with the reactivity and phase morphology deductions. In general, the final percentage of biodegradation in all the blends is quite similar to the percentage of PLA in the blend. Therefore, the presence of PC does not appear to be detrimental to PLA biodegradation.The Young's modulus of binary blends will change as the amount of polymers varies due to the different effects on the mechanical properties of constituent polymers and the phase behaviour of blends. In the literature, there are several studies that attempt to predict the mechanical properties of binary polymer blends where E1 and E2 are the elastic moduli of the two components and ϕ1 and ϕ2 are the volume fractions.Another model to describe droplet/matrix blends, was proposed by Barentsen The elastic modulus of polymer blends with a droplet/matrix morphology when the dispersed particles are evenly distributed in the matrix can be estimated with the Barentsen’s model which considers a series model of parallel parts (Ea) or parallel model of serial linked parts (Eb):The modulus of the blend (Ea or Eb) is expressed as a function of a volume fraction (ϕd = 1−ϕm = λ3), the modulus of the dispersed phase (Ed), and the modulus of the matrix (Em).Nevertheless in polymer blends, the morphology of the materials will be different as the proportions of each component vary. The morphology of the blends, which can show a changing phase behavior from phase-separation, to the formation of co-continuous phases and even phase inversion, will have a significant effect on the final properties and makes the prediction of such models, which do not consider the type of phase morphology, not fully reliable. In fact, both the Davies's and Barentsen's models, based only on the properties of the individual separated phases, do not fit well with the experimental data for co-continuous blends.In a co-continuous blend, the dispersed phase does not consist of separate particles in the matrix phase, but it is interconnected and forms elongated domains, which extend throughout the matrix. To visualize co-continuity, Veenstra and co-workers proposed that the dispersed phases consist of three orthogonal bars of polymer 1 embedded in a unit cube where the remaining volume is occupied by component 2. Repeating this unit cube in 3D shows that component 2 has the same framework as component 1, i.e. both the components are interconnected. In a manner similar to Barentsen, modulus relations for a series model of parallel parts (Ec) and for a parallel model of serial-linked parts (Ed) can be derived Ec=(a4+2a3b)E12+2(a3b+3a2b2+ab3)E1E2+(2ab3+b4)E22(a3+a2b+2ab2)E1+(2a2b+ab2+b3)E2where a is related to the volume fraction of component 1 by 3a2−2a3 = ϕ1 and b is related to the volume fraction of component 2 by b = 1−a. will be applied when the stiff component dominates and equation as the stiff component is the minor phase. The same arguments can be used for the parallel model of serial-linked parts (Eq. ) and the series model of parallel-linked parts (Eq. ) that were derived for co-continuous blends.The mechanical properties of nanostructured materials have been measured by an indentation technique that utilizes special tips Previous quantum mechanical calculations of the ground electronic state of ThT showed that the potential minimum of the dihedral angle between the benzothiazole and dimethylaniline moieties lies at 37° because of a compromise between coplanarization tendency and steric hindrance To investigate the mechanical properties of polymer nanostructures, ThT was embedded in poly(ethylene oxide) (PEO) and poly(acrylic acid) (PAA), both of which are water-soluble and biocompatible polymers. Films and nanofibers of the polymers containing ThT were prepared by spin-coating and electrospinning, respectively. The morphology of the sample was characterized by scanning electron microscopy (SEM). The fluorescence properties of the films were characterized by time-correlated single photon counting (TCSPC) and the excited-state dynamics of ThT in nanofibers were investigated by fluorescence lifetime imaging microscopy (FLIM). We described our observations in terms of the mechanical properties of the polymers and showed that ThT can be used as an excellent fluorescence dye that can probe matrix rigidity.ThT, poly(ethylene glycol) (MW 200 000), and poly(acrylic acid) (MW 240 000) were purchased from Sigma–Aldrich. ThT was purified before use, as-received ThT was recrystallized in the 3:1 mixture of acetonitrile and ethanol, filtered, and washed with ethanol.Polymer films containing ThT were made onto a cover glass by spin coating of 1.0 × 10−7 mole of ThT and polymer in 5.0 mL of distilled water at the spin rate of 2000 rpm for 10 s. The processed polymer film was dried at 60 °C for 30 min.Electrospun polymer nanofibers were prepared with 2.5 × 10−6 mole of ThT and polymer in 5.0 mL of the 1:1 mixture of distilled water and ethanol. After stirring the ThT/polymer solution for 24 h, the solution was injected into a syringe which was attached to a needle tip. The flow rate of the solution on the needle tip was operated at 2 μL/min. The distance between the end of a needle tip and the cover glass of a grounded aluminum plate was 12 cm via an electrospinning system (NanoNC ESR200R2). The syringe needle was connected to a high voltage power source at the applied voltage of 6.8 kV. The collected electrospun fibers were dried at 60 °C for 30 min. The diameters of the electrospun fibers were controlled through a combination of several experimental conditions such as the jet size, the applied electrical voltage, the polymer concentration and the solution viscosity. If those parameters are larger, a larger fiber diameter is usually produced.The light source was a picosecond diode laser operating at wavelength of 442 nm (Picoquant LDH-P-C-440M & PDL800-B) at 20 MHz. A platform for sample excitation and fluorescence detection was an inverted confocal microscope (Nikon, TE2000-S) with an oil immersion objective lens (NA 1.4, ×60). A long pass cut-off filter (Semrock BLP01-473R) was placed in front of the detector and the total fluorescence signal parallel to the excitation polarization was detected by a microchannel plate photomultiplier tube (Hamamatsu R3809U-51) and processed by a fast board (Becker–Hickl, SPC-830). The instrument response function (IRF) was about 90 ps. The measured decay curves were analyzed by using the FluoFit software (Picoquant). The fluorescence lifetimes were extracted from the measured decay curves by a nonlinear least square fit with deconvoluting IRF. FLIM of polymer nanofibers was obtained by sample scanning and the data was imported into SPCImage (Becker and Hickl) to fit the fluorescence decay curves contained in the 512 × 512 pixels.The fluorescence decay curves are fitted to sum-of-exponentials:where αi and τi indicate the amplitude and lifetime of the ith-component of the exponential decays, respectively. Then, the amplitude-averaged fluorescence lifetime is given by:The thicknesses of the ThT-embedded PEO and PAA films measured through an AFM tip-scratch method , the decay profiles of ThT in polymer films are far from linear when displayed on a semilogarithmic scale. Such a complex decay process may arise from two factors: One is that the excited-state potential surface of ThT is barrierless, which leads to the nonexponential population decay The experimentally measured fluorescence decay curve is a convolution of IRF with the true decay law. To obtain the fluorescence decay parameters through curve fitting, the IRF and the functional form must be known. The IRF was obtained from the scattering from a cover glass and a triple exponential form was used to obtain the average lifetime. The fit was satisfactory with an acceptable χ2, and the obtained parameters are given in . The average lifetimes obtained for ThT in PEO and PAA are 0.13 and 1.29 ns, respectively. The average lifetime difference between the two polymers can be explained by the degree of rigidity. The Young’s moduli of PEO (MW 200 000) and PAA (MW 240 000) were 0.21 and 4.5 GPa, respectively When the internal twisting motion is much faster than other nonradiative decay pathways, the isomerization rate constant, kiso, is calculated throughwhere kr is the radiative rate constant. Using the equation, the photoisomerization rate constants of ThT in PEO and PAA were calculated as 7.4 × 109 and 0.44 × 109 |
s−1, respectively. Previously, the average lifetimes of DCVJ and DASPI were measured in PAA (MW 240,000) as 1.67 and 1.95 ns. When the kr values of 2.8 × 108 |
s−1 for DCVJ Electrospinning is an effective technique to synthesize various polymer fibers , nanofibers were successfully formed without beads or pores and had a size distribution range of 200–400 nm. The apparent structure of the PAA fibers is relatively more linear than that of PEO, implying that PAA has a higher mechanical strength than does PEO.FLIM possesses two important advantages over intensity imaging shows the FLIM images of ThT-doped PEO and PAA nanofibers. The colors represent the average lifetimes of ThT from 10 ps to 1.2 ns. The figure clearly distinguishes PEO and PAA nanofibers by the different lifetimes (yellow and green), and this differentiation was not realized with SEM data. The spatial resolution of a confocal microscope is diffraction-limited to approximately 200 nm, which is comparable to the diameter of the fabricated nanofibers. shows the distribution of the amplitude-weighted lifetimes of ThT embedded in PEO and PAA nanofibers that obtained from the FLIM image. The bars indicate the average lifetimes of ThT in the polymer films (0.13 ns for PEO and 1.29 ns for PAA). The fluorescence lifetimes of the PEO nanofibers are distributed from 50 to 200 ps: the lifetimes of PAA nanofibers are distributed from 600 to 900 ps, and these lifetimes have the mean value of 100 and 710 ps, respectively. The broad lifetime distribution arises from insufficient photon counts, matrix heterogeneity, and interfacial effects ThT is a salt in which the cationic chromophore is charge-balanced with the chloride as a counter anion. Using polarized emission microscopy, Krebs et al. investigated the binding mode of ThT to the amyloid fibril PEO and PAA are neutral, hydrophilic polymers without any aromatic rings. Thus, when ThT is embedded into the polymers, any specific hydrophobic and electrostatic interactions between ThT and the polymer matrices are not expected. However, it may be possible that ThT interacts with the hydroxyl group of PEO or the carboxyl group of PAA. Conclusively, it is not certain to specify any binding mode of ThT to the polymer structures. This letter does not intend to unveil the binding mode of ThT to polymer, but to access the possibility of using ThT as a rigidity sensor. It may require further detailed study on the rigidity-dependent dynamics of ThT to estimate quantitatively the mechanical property of amyloid fibrils.ThT is one of photoisomerizing dyes that can be used to probe the mechanical property of solid media. We have investigated the excited-state dynamics of ThT in PEO and PAA polymer films and nanofibers by TCSPC and FLIM. The TCSPC data showed that the fluorescence lifetime of ThT in PAA was significantly longer than that in PEO. The FLIM data showed that the time-resolved images can easily distinguish the PEO and PAA nanofiber structures, which were not discernable by SEM. Therefore, ThT belongs to a series of fluorescence sensors that probe the rigidity of polymer nanostructures. Since such a photophysical behavior of ThT is a general phenomenon, the use of ThT is not restricted to probe amyloid fibrils but reserves wider applications.Rate effect on mechanical properties of hydraulic concrete flexural-tensile specimens under low loading rates using acoustic emission technique► We study rate effect on hydraulic concrete specimens under very low loading rates. ► AE hits and its peak rate decrease with the increase of loading rate. ► Under a higher loading rate AE sources distribute in a relatively diffuser manner. ► The capacity of AET capturing microcracking localization is verified.Acoustic emission (AE) waveform is generated by dislocation, microcracking and other irreversible changes in a concrete material. Based on the AE technique (AET), this paper focuses on strain rate effect on physical mechanisms of hydraulic concrete specimens during the entire fracture process of three point bending (TPB) flexural tests at quasi-static levels. More emphasis is placed on the influence of strain rate on AE hit rate and AE source location around peak stress. Under low strain rates, namely 0.77 × 10−7 |
s−1, 1 × 10−7 |
s−1 to 1 × 10−6 |
s−1 respectively, the results show that the tensile strength increases as the strain rate increases while the peak AE hit rate decreases. Meanwhile, the specimen under a relatively higher strain rate shows a relatively wider intrinsic process zone in a more diffuser manner, lots of distributed microcracks relatively decrease stress intensity, thus delay both microcracking localization and macrocrack propagation. These phenomena can be attributed to Stéfan effect. In addition, further tests, namely the combination of AE monitoring and strain measuring systems was designed to understand the correlation between AE event activity and microfracture (i.e., microcracking and microcracking localization). The relative variation trend of cumulative AE events accords well with that of the load–deformation curve.Hydraulic concrete, namely concrete in hydraulic structures, requires a smooth and well-graded particle size distribution curve for the combined aggregates (commonly three or four-graded). A maximum size aggregate (MSA) of 75–100 mm is considered the optimum. Pozzolans and other selected admixtures (e.g. air-entraining agents and antifreeze) are second constitutes employed in mass concrete for hydraulic structures, and their amounts depend on the location of the concrete mass Acoustic emission (AE) has been used to monitor the microseismic activity associated with damage and localization by earlier researches Thus in this work, the effect of very low strain rate (i.e., strain rate <10−6 |
s−1) on quasi-static flexural-tensile properties of hydraulic concrete was investigated using AET. Cumulative AE events, cumulative AE hits, AE hit rates obtained through TPB tests on hydraulic concrete specimens under low loading rates were used to identify the stage characteristic of the fracture process. More emphasis was placed on strain rate effect on mechanical behavior. Both three dimensional AE source location methods and linear location methods were employed to investigate the physical mechanism of fracture (i.e., intrinsic process zone) of specimens under various loading rates. To verify the reliability of the AET identifying the microcracking localization under low strain rates, notched TPB tests measured by both AE and conventional strain systems were designed to compare the deformation variation trend of local zones close to the midspan of specimens with the AE development process.The mix proportion of hydraulic concrete, adopted by one actual concrete dam as listed in in detail, was used in this testing. TPB flexural tests were carried out on three-graded concrete beam specimens. The aggregate sizes (large, medium and small) of the test specimens in diameter were respectively 40–80 mm, 20–40 mm and 5–20 cm, and the aggregate gradation of these aggregates was 4:3:3. 52.5 # moderate heat cement was employed. Generally, physical properties should be determined by tests of the full graded of sufficient size to accommodate the MSA used. However due to the practical difficulties (e.g. relatively small specimens and size of experimental apparatus) in performing a full graded test, the wet sieved method, in which the aggregates larger than 40-mm are removed through 40-mm sieve after concrete mixing, is commonly employed in tests. The wet sieved concrete was used in this work to cast test specimens, and all specimens were compacted using a needle vibrator during specimen preparation. Three series of concrete beams were prepared (shown in ): (1) five relatively smaller beam specimens of 100 mm × 100 mm × 400 mm (thickness × depth × span) with a smooth boundary (i.e., no notch) (labeled with WQI-1–WQI-5); (2) five relatively larger specimens of 150 mm × 150 mm × 550 mm with no notch (labeled with WQII-1–WQII-5); (3) two specimens of 150 mm × 150 mm × 550 mm (labeled with WQIII-1–WQIII-2) with predefined 60-mm notch. That is to say, a total number of 12 concrete specimens were tested. The specimens were demolded 2 days after casting and then were cured by water with covering wet straws for 7 days; afterwards they were naturally cured in the laboratory. For beams with notch, they were taken out for single edge notch cutting according to the requirements of the experiments before 2 days of testing. The specimen was loaded at the mid-span by a concentrated load and was supported as shown in . The specimens of all sizes were cast in the same manner from the same batch of concrete.In previous studies to investigate the loading rate effect on flexural-tensile properties of hydraulic concrete, strain gauge type connectors were commonly used. A few attempts to use AET to understand rate effect on the mechanical properties of concrete. For example, Ranjith et al. ). Besides these, the experimental setup consisted of an electronic universal testing machine (CSS4410), a triaxial compressive testing machine, a clip-on gage (Model 3541), a dial indicator and a 10t force sensor.Two series of tests were conducted for different emphases, namely TPB flexural tests under various low loading rates (strain rates) on ten un-notched specimens at quasi-static levels with a smooth boundary and TPB flexural tests under a very low strain rate (about 10−7 |
s−1) on two specimens with a notch respectively. For the former, the CSS4410 universal testing machine, manufactured by Changchun Research Institute for Mechanical Science (CRIMS), was used. This machine adopts EDC 100 digital control system (manufactured by DOLI, Germany), which provides two kinds of increment controlling modes namely load and displacement, as controller. Beam specimens were tested at three low loading rates under load increment control (listed in ) to investigate rate effect. The corresponding average strain rates were 0.77 × 10−7 |
s−1, 10−7 |
s−1 and 10−6 |
s−1, respectively. TPB flexural tests on notched specimens were conducted using the triaxial compressive testing machine with a maximum capacity of 5000 kN by CRIMS. These tests took about 0.5–0.7 h due to low loading rates.The SAMOSTM AE system manufactured by the Physical Acoustic Corporation (PAC) was used for the AE measurements. AE transducers of R6α (PAC) with a resonant frequency of approximately 60 kHz, which can be used in most AE applications, were coupled onto the two opposite surfaces of the specimens to monitor the AE activities (shown in a–c). In order to reduce loss of signal energy, medical adhesives which have low impedance were used to couple the AE sensors, meanwhile elastic bands were used to help these sensors stationary (a–c). The three dimensional AE localization problem can be exactly determined with a minimum of four sensors to calculate the three coordinates. A fifth sensor is sometimes needed to remove ambiguities when the sensors are poorly arrayed. The use of more sensors results in the location problem being over-determined and improves the localization accuracy respectively. Through preliminary tests, the AE signals were amplified with a gain of 40 dB in a preamplifier considering the noise level of the loading apparatus. The threshold value of 40 dB was selected to ensure a high signal to noise ratio The strain signals were measured by DH-3817 dynamic strain measuring system (Donghuatest Corporation, China) with eight channels. To record strain as well as load and crack mouth opening displacement (CMOD) simultaneously, two DH-3817 systems were connected in series. The CMOD of predefined notch was measured using Model 3541-012M-004-ST with 12 mm gauge length (Epsilon Technology Corporation), placed at the preexisting notch tip.To study the effect of strain rate on flexural-tensile properties of hydraulic concrete, TPB tests on un-notched specimens (i.e., WQI-1–WQI-5, WQII-1–WQII-5) under three different strain rates were conducted (listed in ). Based on AE signals such as AE events, AE hits and peak AE hit rates, strain rate effect on flexural-tensile properties was analyzed combining the AE source location technique, strain rate theory AE waveform is generated by dislocations, microcracking and other irreversible changes in a stressed quasi-brittle material. AE activity is approximately proportional to the area under the AE waveform . During the initial loading stage, the inherent defects propagate and new microcracks form in the zones of paste-aggregate bond or cement paste in a diffuse manner. As the loading increases, microcracks propagate to form one or more macrocracks keep energy balance, but they stop propagating when encountering local resistance (i.e., aggregate). This is the phenomenon of microcracking localization in particular zones of the specimen. As damage increases and peak stress reaches, one of macrocracks created during the previous stage propagates through coarse aggregates, leading to failure of the specimen.Although AE characteristics during the entire process of TPB tests on concrete beams were already obtained by earlier researchers An AE hit, namely one waveform, is the signal that exceeds the employed threshold and causes the AE system channel to accumulate data. AE hit is frequently used to show the AE activity with counted number for a period (i.e., hit rate) or accumulated numbers. Therefore, it will be appropriate to employ AE hit and its rate as well as AE event to represent the AE developing process (or study damage process of specimen). Under various strain rates, curves of cumulative AE events recorded corresponding to stress levels were plotted in a and b). The stress level (normalized value, %) was defined at the percentage of the strength provides detailed information about the experimental results, such as ultimate loads, peak AE hit rates, cumulative AE hits and AE events. It was also observed that the variation trend of WQII-2 does not accord well with others. This can be attributed to randomness, which can be avoided absolutely, during the cast of the specimens and the experiments. When a specimen contains relative more microcracks (defects during casting), active AE generation is expected even under relative low compressive stress due to crack propagation from existing defects or microcracks a and b shows the AE activities vary during the entire loading process under loading control.a and b, on the whole, AE activities show the similar variation trend during entire loading process for two series of beams under various strain rates: AE events was not active in the loading stage until the stress level reach 90%, and then sharply active.Following Labuz and Zietlow, the so-called intrinsic process zone was taken as the criteria for defining the structural behavior especially microstructural phenomena in terms of localized microcracking. As mentioned above, size effect and material effect on this zone were extensively studied by earlier researchers: this zone was found to be depended on material types significantly but likely independent on size in a relative sense Multiple AE channels are synchronized for the three-dimensional location algorithm. The location algorithm was based on nonlinear regression methods. To improve location, four hits per AE event were used (i.e., over-determined method) for exceptional accuracy. Although the macrocrack developed through the thickness of the concrete beam and AE locations are three dimensional, they are only shown in the plane of beam allowing easy outstanding the intrinsic process zone.a–j compares the AE locations around peak stress of these specimens. In a–j, X-axis represents distance from left along the span and Y-axis represents the depth of the beam. In addition, to display the AE source distribution more visually, linear location method was also employed. a–j compares the distributions of the AE events along the beam span. In a–j, thin cylinders represent the number of AE events release by the corresponding cross section perpendicular to the span. Clearly, there were distinct differences in the distributions for the different strain rates.a and b shows the AE developing processes under the strain rates during the entire process have obvious stage characteristics: (1) during the initial loading stage, there were little AE activities; (2) as the stress level reached around peak value (about 90%), the AE activities became significantly intense and increased sharply. The corresponding cracking processes of concrete under a flexural-tensile force were stable microcracking, microcracking propagation and localization shows that the tensile strength is dependent on strain rate. It was clear that the specimens under relatively larger strain rate had higher tensile strength. This matches closely the law in the physical mechanisms summarized in b, it could be seen that as strain rate increased the cumulative AE events, the cumulative AE hits, and the AE hit rate around peak stress decreased correspondingly for the same sizes of specimens (i.e., WQII-1–WQII-5). This is because the damage of a specimen under a relatively lower strain rates develops more fully. In addition, it could also be found that AE hit was more sensitivity to strain rate than that of AE event. When the strain rate decreased in one order of magnitude, the AE hits increased about two times. The cumulative AE hits correlated well with the cumulative fracture process , there are some interesting differences between the source location results of the specimens under different strain rates. At peak stress, the specimen under a relatively higher strain rate showed a wider intrinsic process zone (), which was defined above. The zone of localized damage of Specimen WQI-2 (b) was approximately 60-mm wide, but that of Specimen WQII-4 (i) was approximately 90-mm wide. This can also be further approved by a–j. Upon comparing AE event distributions along the span of these specimens, it could be observed that the intrinsic process zone was affected by strain rate to some extent as expected. Narrower band of damage was likely to cause much higher stress intensity, making it easier for failure. This law means that failure mechanisms of specimens under various low strain rates (<10−6 |
s−1) vary more or less: (1) under relatively lower strain rates, microcracking localizes in a narrower band close to the midspan, and failure of a specimen in this condition can be attributed to propagation of one of a few main macrocracks created by microcracking localization close to the midspan; (2) but under relatively higher strain rates, microcracks distributes in a relatively diffuse manner but not directly connected to (or considered as surround the main macrocrack), this is just the reason why the strength increases overall with increase of the strain rate, lots of distributed microcracking counters both microcracking localization and macrocrack propagation, namely Stéfan effect As discussed above, failure of a specimen under low strain rates is mainly controlled by a few main macrocracks in a narrower band close to the midspan. The macroscopic deformation of a brittle material is decomposed into response of the material matrix, dislocations, and deformation due to the fracture of microcracks To investigate the correlation between microcracking and AE of a TPB flexural specimen under low strain rates, further tests were designed. DH-3817 dynamic strain measuring system was used to record deformation of the notched specimens (WQIII-1–WQIII-2) to assess the deformation behaviors (macromechanical property) then to understand microcracking localization (micromechanical phenomena). Localizations of microcracking of TPB flexural specimens under low strain rate first appear in the tensile zones close to the bottom of the midspan, and then gradually propagate to the compression zones close to the top. To this end, nine strain gauges were glued onto the surfaces around the midspan and the middle between AE sensors and the midspan. The strain gauge array is shown in c. The surfaces where strain gauges were attached onto were smoothed with sand papers and deoiled with solvents. Among these gauges, the original lengths of the bilateral gauges were uniformly 20-mm; those of the gauges at the midspan were 20-mm, 40-mm and 60-mm from top to bottom respectively (denoted as SI, SII and SIII as shown in c). Based on the AE signals and strain records, the correlation between microcracking and AE was analyzed to verify the reliability of AET identifying the physical mechanism during the fracture process of hydraulic concrete.As expected, the measured strains of bilateral gauges were too small to be considered herein. a and b shows all the plots of measured deformation versus time. It was observed that the deformation–time plots showed the same developing trend except the curve around peak stress of SII glued on WQIII-1. This was because the macrocrack that caused the fracture surface of WQIII-1 bypassed SII (b shows the photo of the failure mode of WQIII-2. The typical records for the deformation–time (recorded by SIII) and the corresponding AE events release with respect to time during the process stress reaches the peak value are shown in a and b shows the typical records for the load–time and the AE events release with respect to time.a and b shows the plots of measured deformation versus load. a and b shows the plots of variation of deformation and cumulative AE events. Also, it was observed that the cases of the deformation–load curve and the cumulative AE events–deformation plot of SII on WQIII-1 (shown in ) did not accord with others for the above mentioned reason. The results that follow thus focus primarily on the other strain gauges. Nevertheless these plots can typically give the AE characteristic of events in relation to micro and macrocrack propagation and coalescence. The typical records for the deformation–load and the AE characteristic (also recorded by SIII) are shown in a, the variation trend of the deformation–time plot accorded well with that of the AE event–time plot. In a, both of the two plots can be divided into three stages, i.e., 0–900 s, 900–1600 s and 1600–1760 s. It was observed that during the first stage, there was very less AE events release and very small deformation taking place. During the second stage, the AE event rate began to rise, and the deformation became relatively large. During the third stage, the AE events release increased steeply and the corresponding deformation suddenly jumped. In b, the cumulative AE events release showed the same stage characteristic as in a, but the stage characteristic of the deformation versus time was not obvious as that of the cumulative AE events. This can be partly attributed to the insensitive performance of strain gauges on the surface to the interior deformation of specimens. However, on the whole, the results of were similar to the previous studies on the cement-based materials by Landis a and b, it was found that the deformation for a certain time (corresponding to a certain number of cumulative AE events), the deformation recorded by SIII was the largest, SI was the smallest (negative in the initial stage for compression). a and b presents the typical microresponse of TPB tests on concrete specimens; microcracking localization occurred first in the tensile zones close to the bottom then to the compression zones in the top. From a and b, it was observed that the AE events release during the fracture process had a good correlation with the load versus the deformation curve, especially for WQIII-1 (a). Both the load–deformation curve and the variation of the cumulative AE events could be divided into three stages during the whole loading process: (1) Stage I (0 < deformation < 0.008 mm), stable microcracking stage: the elastic stage of proportional increase of the deformation with the load; (2) Stage II (0.008 < deformation < 0.018 mm), localization of microcracking: there was a turning point in both the load–deformation curve and the curve of cumulative AE events; (2) Stage III (deformation > 0.018 mm), propagation of one of macrocracks: the load–deformation curve descended, while AE events still increased. indicate that the correlation between cumulative AE events and load–deformation accords with the previous studies . Hence, it can be concluded that AET can characterize microcracking and track the evolution of damage in concrete, and the results of the TPB flexural tests using AET to investigate rate effect under low strain rates were reliable.The AET was used to investigate strain rate effect on the evolution of fracture of TPB flexural tests on hydraulic concrete beam specimens under different very low strain rates, namely 0.77 × 10−7 |
s−1, 1 × 10−7 |
s−1 to 1 × 10−6 |
s−1 respectively. Further tests, namely the combination measurement of AE and local deformation of TPB flexural tests on notched specimens, were also conducted to verify the correlation between AE events and microcracking localization. As a result of the study, the following conclusions can be drawn.In the very low strain rate range, physical mechanisms of TPB flexural concrete specimens are also sensitive to strain rate to some extent. Specimens under relatively larger strain rates have higher tensile strengths. This can be attributed to Stéfan effect, which counters both microcracking localization and macrocrack propagation.As the strain rate increases, all the cumulative AE events, the cumulative AE hits, and the AE hit rate around peak stress decrease correspondingly for the same sizes of specimens. This is because the damage of specimens under lower strain rates develops more fully.At peak stress, the specimen under a higher strain rate showed a wider intrinsic process zone in a more diffuser manner, microcracking surround but not directly connected to the main macrocrack. Wider band of damage is likely to relatively decrease stress intensity. Lots of distributed microcracking delays both microcracking localization and macrocrack propagation. This is also the reason why the strength increases with the increase of the strain rate.The correlation between microcracking and AE events was verified by the combination measurement of AE and local deformation of notched TPB specimens under a flexural tensile force. Similar to variations of AE characteristic, curves of deformation–time and deformation–load of local zones close to the midspan shows the stage characteristic. The AET can track dynamic microbehaviors such as microcracking and microcracking localization in concrete.The working conditions in this paper are suitable for many practical applications for dam safety reassessment, and the preliminary results of low strain rate on physical mechanism of hydraulic concrete using AET described in this paper can guide further studies.Effect of DC bias and RF self-bias on the structure and properties of chromium oxide coatings prepared by vacuum cathodic arc depositionCr2O3 coatings were prepared by vacuum cathodic arc deposition (VCAD) on cemented carbide YT15 at different voltages of both direct current (DC) and radio frequency (RF) bias. The structure and properties of the coatings were investigated by scanning electron microscope, X-ray diffraction, and nanoindentation. With both DC and RF bias, coatings deposited at zero and low bias voltage exhibit a columnar structure and a preferred orientation (PO) of (104). As the bias voltage increases, the columnar structure starts to disappear and PO gradually becomes (006). Besides, the crystallite size of the coatings declines as the bias voltage increases. Comparing to DC bias, the RF bias leads to smaller crystallite size by virtue of higher energy and density of ion bombardment. The electrical resistivity of the coatings and saturation ion current density during deposition were measured to explain this effect. The hardness of the coatings was significantly enhanced by the bias voltage, particularly by the RF bias. A nano-hardness of 44.7 GPa was found in the coating deposited under −100 V RF bias, which has not been previously reported.Cr2O3 has long been considered to be the hardest oxide []. It also exhibits many other desirable properties such as low friction coefficient, electrical insulating, chemical inertness, and high-temperature stability. Previous studies have demonstrated the usage of Cr2O3 in many existing and potential applications in, e.g., read–write heads in digital magnetic recording units [], and many other wear resistant applications []. Also, α-Cr2O3 has recently been studied as a template layer for the growth of α-Al2O3 coatings, an important component in wear-resistant coatings and diffusion barrier coatings []. Cr2O3 coatings could be deposited by a variety of techniques including magnetron sputtering (MS) [], vacuum cathodic arc deposition (VCAD) []. Among those deposition methods, VCAD has become a promising one because of its high ionization rate and process stability.For most techniques used to deposit Cr2O3 coatings, the bias voltage applied at the substrate is one of the most important processing parameters. It has been found that substrate bias has strong impacts on the texture of Cr2O3 coatings due to crystallite refinement and re-crystallization induced by ion-bombardment []. However, few studies have considered the influence of high electrical resistivity of Cr2O3 coatings on incident energy of ions. To our knowledge, the different effect of RF bias, which is insensitive to electrical resistance of the depositing film, comparing to DC bias has never been reported. Moreover, the influence of bias on the preferred orientation of Cr2O3 crystallites has been investigated, but previous studies reported different or even opposite results []. Bias is also commonly known to have strong influences on hardness of the coatings [, Cr2O3 coatings prepared in most studies exhibit hardness around 30 GPa. Although a super high hardness of 45 GPa was reported by Gautier and Machet [], in their study both O2 and N2 were introduced during the deposition and the coating was a mixture of Cr2O3 and "a non-identified phase". Further analysis gives rise of a trend that coatings deposited by methods that promote ionization, such as AIP and RF magnetron sputtering, exhibit a relatively high hardness. However, more research is needed for a better understanding of the hardening mechanism.In this work, we deposited a series of Cr2O3 coatings by vacuum cathodic arc deposition (VCAD) with both DC bias and RF self-bias, with the purpose to further clarify the influence of bias on micro-structure, preferred orientation, and properties of Cr2O3 coatings.Cr2O3 coatings were deposited using an arc ion plating system, the schematic of which is shown in . The arc cathode was a rectangular Cr target (568 mm × 118 mm, 99.95 at% purity) mounted on the vertical wall of the chamber. Cemented carbide substrates were polished and cleaned in an ultrasonic cleaner before being fixed on a substrate holder, which was 160 mm away from the target and connected to the bias power supply. When the pressure reached less than 5 × 10−3 Pa, a heater started to work to preheat the substrate to 250 °C. The temperature was then kept around 250 °C until the end of deposition. After the temperature became stable and the background pressure reached below 5 × 10−4 Pa, pure Ar was introduced and a −1000 V bias was applied to the substrate which kept a glow discharge at a pressure of 2 Pa for 20 min to remove the oxide layer of the substrates. To further improve the adhesion, the substrate was cleaned by Cr ions which were accelerated by −300 V bias. After that a Cr interlayer about 80 nm thick was deposited in pure Ar atmosphere at a pressure of 1.6 Pa. During the subsequent deposition of Cr2O3, flow rate of Ar and O2 were kept at 200 sccm and 100 sccm respectively, and the working pressure was kept at 1.4 Pa. The deposition time of Cr2O3 were 15 min. All the coatings were deposited using the same process condition except for the substrate bias used for Cr2O3 layer deposition. Substrate bias were applied using two different modes: one was direct current (DC) and the other was radio frequency (RF), which was also referred to as self-bias voltage []. For both DC and RF modes, three deferent bias voltages were applied: −50, −75, −100 V.The RF power supply was capacitively coupled to the substrate holder while the chamber was grounded for both DC and RF bias processes. For −100 V RF bias, an additional sample was deposited with twice the thickness to enhance the signal obtained from X-ray Diffraction (XRD) measurements. A control sample was also deposited without bias (the substrate was floated) and with a slightly longer deposition time of 18 min. The samples and main deposition parameters are listed in The cross-section morphologies were acquired by a ZEISS SUPRA55 SEM with accelerating voltage at 5 kV and working distance of 5 mm. Grazing incidence X-ray diffraction (GIXRD) were carried out on D/max 2500 using Cu anode at an incident angle of 2° to identify the texture and crystal structure. To investigate the preferred orientation, X-ray diffraction (XRD) θ–2θ measurements were carried out for samples 0#, 50DC, 75DC, 100DC and 100RF-2. The hardness and Young's modulus of the coatings was evaluated by continuous stiffness measurement (CSM) using a nano-indenter (MTS XP) and finally determined by the average values at indentation depth between 100 nm and 120 nm. The data at lower and higher depth were exclude to avoid the influence of indentation size effects and the softer substrate []. The internal stress of the coatings was determined by X-ray diffraction using the sin2ψ method [The electrical resistivities of the coatings were measured using the following method. First, we applied conductive silver paint on several isolated spots on surface of coatings and wait until it dried. The area of each spot was controlled to be less than 1 square millimeter. Then we measured the resistance (R) between each spot and the substrate. The area, A, of each spot was calculated from micrographs taken with an optical microscope. The resistivity, ρ, was the average value of ρ′ calculated by ρ' = RA/T, where T was the thickness of the coating.A home-made Langmuir probe was used to evaluate the plasma density at different biases. The probe was mounted at a similar position of the substrate and was about 5 cm from the substrate holder (see ). The saturation ion currents were measured when −50, −100 V DC and RF bias were applied. Due to the rapid motion of the arc point during deposition, the inflection point of electron current was difficult to be measured. Instead, we use the saturation ion current, which was relatively stable, to evaluate the effect of plasma density.The micrographs of the cross section are shown in . Measured from those micrographs, the thicknesses of deposited coatings are in a range of 1.0–1.4 μm (a) exhibits columnar grains with a strong orientation perpendicular to the surface. Most of the columnar grains grow from near the Cr interlayer to the surface, through almost the whole Cr2O3 layer. There appears to be some space between columnar grains, suggesting a loose structure of the coating. By contrast, coatings deposited with bias (b–g) exhibit denser structures. The samples 50DC and 50RF also exhibit some columnar grains, but the grains appear shorter than those in the 0# sample. As the bias voltage increases, the columnar structure starts to disappear. There might be some vertical texture in 75DC, but the grains have become indistinguishable. In coatings deposited with 100 V bias, i.e. 100DC and 100RF, no columnar crystal is visible.Based on the results obtained from grazing incidence X-ray measurement present in , all the coatings are identified to be single phase of α-Cr2O3. The peaks, except two WC peaks from the substrate, can match the peaks of corundum structured Cr2O3 [ICSD data file card #70–3765], although there are some slight shifts in the peak induced by residual stress. The shapes and intensities of the peaks vary significantly as the bias voltage increases. 0# sample shows sharp peaks and high intensity. It also consists of many small peaks which are weaker or even indiscernible in other samples. These results indicate a well crystallized structure in the 0#sample. The peak intensity of coatings deposited with both DC and RF bias is lower, and the full width at half maximum (FWHM) is higher than that without bias. As the bias voltage increases, the peak intensity drops and FWHM rises, indicating a decrease of crystallite size. The average crystallite size is evaluated by the Debye-Scherrer formula and the results are listed in , which shows a decline as the bias increases. The peak intensity () of coatings deposited with RF self-bias is much lower than that of the DC bias samples, which may suggest a low crystallinity of coatings deposited with RF self-bias.The decrease of columnar structure, and crystallite size as bias voltage increase is commonly observed in other reports. At low voltage bias or without bias, the columnar structure is formed as a consequence of competitive growth of differently oriented neighboring crystals. At higher bias voltage, as the energy of impinging ions increases, more defects on the surface will be created. The dense defects will result in more nucleation sites and finally a decrease of crystallite size. Re-nucleation also takes place as the coating grows and destroys the columnar structure []. As a result, RF bias is more effective in decreasing the crystallite size.To further understand the difference between DC and RF bias, it is necessary to consider the electrical resistance of Cr2O3 coatings, which may cause a decrease of the sheath voltage around the substrates in DC bias situation but has little effect on RF bias. Besides, the ionization rate may also be influenced by bias and affects the bombardment on the coatings.The average resistivities of the DC-bias coatings are shown in . It is similar for sample 50DC and 0# sample. As the voltage increases, the resistivities of DC bias coatings drop a lot. The resistivities of the RF-bias coatings (1.6 × 108, 3.6 × 108, 1.6 × 108 Ω m for 50RF, 75RF, 100RF respectively) are not presented in the graph. The saturation ion current densities (SICD) are 0.016, 0.016, 0.015, 0.07, 0.062 mA∙mm−2 without bias and with DC-50 V, DC-100 V, RF-50 V, RF-100 V bias respectively. With RF bias, SICD is much higher than those without bias and with DC bias. This means the amount of ions attracted by RF bias was about 4 times of that by DC bias. It is quite straightforward since the RF bias increased the ionization rate.Then we consider both resistance and saturation current in DC bias situation. Because of the high resistivity, the bias current density is limited to be less than U/ρT, where T is the thickness, ρ is the electronic resistivity, and U is the voltage applied on the coatings. We assume all the voltage were applied on the coatings to evaluate the upper limit of bias currents density. For 50 V DC bias, when the thickness is about 1 μm, the bias current density is limited to be less than 2.8 × 10−5 mA∙mm−2, which is much lower than the saturation current density. This leads to accumulation of positive charges on surface which will reduce the amount of incoming ions but attract more electrons to neutralize the positive charge until a balance is reached. As a result, the effective bias voltage should be much lower than 50 V. As for the case of 100 V DC bias, the bias current density limitation is about 3.4 × 10−3 mA∙mm−2 which is also lower than the saturation current density. Although at the beginning of deposition, the resistance is relatively low, the effective bias voltage will decrease as the coatings grow. As a result of the coating resistivity and saturation ion current density, the energy and density of ion bombardment at DC bias were lower than those at RF bias.X-ray diffraction (XRD) θ–2θ measurement was taken out to investigate the preferred orientation in out-of-plane direction of 0#, 50DC, 75DC, 100DC, 100RF-2 samples. The results are shown in . Diffraction peaks of the substrate also appeared in the pattern because the coatings were relatively thin. There are 4 major possible peaks of Cr2O3: (012), (104), (006) and (116) orientations. The (012) peak is neglected because it is quite weak and just appear in 0# sample; The peak at around 39° might be confusing because it may be (200) orientation of Cr (39.113°) or (006) orientation of Cr2O3 (39.784°). It is attributed to (006) orientation of Cr2O3 for two reasons. First, the peek exhibits more and more shifts towards lower 2θ as bias voltage increases just like (104) of Cr2O3. But no shift should be expected for (200) of Cr because Cr interlayer was deposited at constant bias; Second, the intensity of this peek of 100RF-2 is much higher than that of other samples, which is impossible if we attribute it to Cr interlayer. Based on these reasons, (104), (006) and (116) are taken as the three main peaks to analyze the crystallite orientation.The intensity fraction of (104) peak is calculated by Ir104 = I104/(I104+I006+I116) and so are (006) and (116) peaks. The results are shown in . It is clearly shown that (104) peak is dominating for 0# and 50DC samples. As the bias voltage increases, (006) peak becomes stronger while (104) and (116) become weaker. For 75DC and 100DC samples, (006) is the predominant peak of Cr2O3. For sample 100RF-2 which is 2 μm thick, (006) is quite strong and takes a higher percentage of Cr2O3 peaks.The (104) preferred orientation at low and zero bias voltage is due to the evolutionary selection during grain coarsening, which is the most common process leading to selection of preferred orientation during film growth []. A layer with random texture can be seen between Cr interlayer and columnar-structured Cr2O3 from the morphology of the cross section of sample 0# (a), in which the crystallites with preferred orientation grow more rapidly than others. This layer is also presented in Cr2O3 coating prepared by Pedersen et al. [] with magnetron sputtering (MS) without bias. However, Pedersen et al. found the coating exhibit a PO of (006) without bias. In other reports, Ji et al. [] deposited Cr2O3 with AIP and the preferred orientation was similar to the results found in this work.The discrepancy could be attributed to the different deposition temperatures. It is likely that the temperature affects the evolutionary selection by changing the surface diffusion modes of atoms. According to the theory of Kajikawa et al. [], when surface diffusion is limited among planes within the same grain, the high-energy planes become PO. When surface diffusion becomes more rapid and surface diffusion among grains occurs, the low-energy planes become PO. For Cr2O3 coatings with corundum structure, (006) is a closely packed plane of oxygen, which makes it a low-energy plane. In comparison, (104) is not a low-energy plane []. In this work, the coatings were deposited at a relatively low temperature (250 °C), lower than 450 °C reported in the work of Pedersen et al. []. Estimated by Arrhenius equation D = D0∙exp{-Q/RT}, where R is the ideal gas constant, and the estimated activation energy, Q, which are 247.5 × 103–309.2 × 103 J/mol for Cr3+ and 212.9 × 103–351.6 × 103 J/mol for O2−, based on the result of Lebreau et al. [], the diffusion coefficient D at 450 °C is approximately 6 orders of magnitude higher than that at 250 °C. Because of that, with the low diffusion coefficient found in this work, atoms tend to diffuse from surface of (006), the low energy plane, to (104), the high energy plane, within the same grain, which leads to PO of (104). In contrast, under the high diffusion coefficient situation, the grains with (006) orientation have high probability to receive atoms diffusing from surrounding grains. As a result, grains with (006) orientation will expand during the deposition, eventually leading to PO of (006).On the other hand, the change of PO from (104) to (006) at high bias voltage can be explained by an enhancement of diffusion coefficient induced by the bias voltage. Although the measured temperature is the same for different bias, the temperature at the very surface of the substrate is expected to be higher at high bias voltage, due to ion bombardment. According to Ljungcrantz et al. [], in which arc-evaporated TiN films were deposited with a substrate-to-target distance of 20 cm, when −100 V bias was applied, the substrate temperature was about 70 °C higher than that without bias. In addition, the incident ions carry energy at the level of tens of electron volts [], which was transferred to the surrounding atoms within a small area. Thus, the mobility of the surrounding atoms will be greatly increased. As a result, adatoms get enough energy to diffuse among grains, which eventually led to the change of PO.The Cr2O3 coatings deposited in this work exhibit different nano-hardness with different biases as shown in . The coating deposited without bias exhibits a plain hardness around 20.1 GPa. With DC bias, the hardness increases remarkably to 34.3, 34.5, 37.2 GPa for 50, 75, 100 V respectively. This result is similar to the work of Ji et al. []. With RF bias, the hardness reaches 36.4, 40.6, 44.7 GPa for 50, 75, 100 V respectively. It is worth noting that the hardness of the sample deposited with 100 V RF bias, 44.7 GPa, is much higher than those reported in previous studies.It is clearly shown that the bias has remarkable influence on the hardness. The possible hardening mechanism is, in general, the bias enhances the ion bombardment which leads to the development of compressive stress inside the coatings [] and the refinement of the crystal structure.It is expected that the compressive stress promotes the hardness of coatings [, except a small tensile internal stress in the coating deposited without bias, compressive internal stresses do exist in coatings deposited with bias. As the bias voltage increases, the compressive stress becomes higher, which is in accordance with the raise of hardness. In addition to XRD test, the elastic modulus (), which is usually correlated with the residual stress [], shows a quite similar trend to hardness. The decrease of grain size may also plays an important role in the increase of nano-hardness. According to the Hall-Petch relation [], the decreased grain size leads to higher hardness. As it has been shown above, the grain size becomes smaller as the bias voltage increases. The extraordinary hardness of coatings deposited with RF bias can be explained as a more effective ion bombardment. As we have discussed, the effective bias voltage and saturation ion current in RF bias situation is higher than that of DC bias, which suggests that the ion energy and ion density are higher during the deposition with RF bias.Cr2O3 coatings are deposited on YT15 by vacuum cathodic arc deposition at both DC and RF bias. The bias has great influences on the structure, grain size, preferred orientation and nano-hardness of the coatings. The main points are as follows:No bias and low voltage bias result in columnar structure; high voltage bias can destroy the columnar structure and lead to small grain size;The resistance of coatings reduces the effective bias voltage in DC bias setup, resulting in lower ion energy than that with RF bias. The saturation ion current of RF bias is much higher than DC bias, resulting in the bombardment of ions with higher density. Higher ion energy and denser bombardment of RF bias result in smaller grain size than DC bias;The preferred orientation of Cr2O3 coatings are affected by bias. The (104) orientation is dominant in coatings deposited without bias and with low voltage bias due to evolutionary selection. With the increase of bias voltage, the preferred orientation gradually changes from (104) to (006), due to enhanced surface diffusion.Both DC and RF bias result in the improvement of hardness of Cr2O3 coatings. RF bias is more effective than DC bias at increasing the hardness. Cr2O3 coatings could reach a nano-hardness of 44.7 GPa with −100 V RF bias applied.Fracture of beams with random field properties: Fractal and Hurst effectsThe classical problem of peeling a beam off a substrate is studied through a re-examination of Griffith's fracture criterion in the presence of multiscale random properties. Four types of wide-sense homogeneous Gaussian random fields of the vector {Young's modulus E, surface energy density γ}, parametrized by the beam axis, are considered: Ornstein–Uhlenbeck, Matérn, Cauchy, and Dagum. The latter two are multiscale and allow decoupling of the fractal dimension and Hurst effects. Also calculated is the variance of the crack driving force G with any given type of random field in terms of the covariances of E and γ, under either fixed-grip or dead-load conditions. This investigation is complemented by a study of the stochastic crack stability which involves a stochastic competition between potential and surface energies. Overall, we find that, for Cauchy and Dagum models, the introduction of fractal-and-Hurst effects strongly influences the fracture mechanics results. Notably, while the Cauchy and Dagum models represent a more realistic scenario of random fields, given the same covariance on input, the response on output is strongest for Matérn, then Ornstein–Uhlenbeck, then Cauchy and, finally, Dagum model.The linear elastic fracture mechanics involves two material properties: the material stiffness tensor C and the surface energy γ. A paradigm of that theory is offered by the experiment carried out by Obreimoff on the cleavage of mica off a rigid substrate (. In this one-dimensional (1d) situation, one deals with the beam bending, so that C is represented by Young's modulus E, while γ pertains to the beam-substrate interface.The theoretical method relies on the Griffith fracture criterion for crack growth (where G is the strain energy release rate, W is the work performed by the applied loads, U is the elastic strain energy, A is the crack surface area formed, and γ is the energy required to form a unit of the new material surface. Two special cases – the so-called “dead-load” and “fixed-grips” conditions – are usually encountered in practice. In the dead-load case, with reference to Clapeyron's theorem, the work performed by the constantly applied loads is twice the increase of elastic strain energy (∂W/∂A = 2∂U/∂A). Thus, In the fixed-grips case, the surface of the continuum on which the loads are applied is assumed to remain stationary during crack growth. If the work of the body forces is ignored, the work performed by the applied loads vanishes and ), both E and γ are taken to be constant, but, given the presence of a randomly multiscale-heterogeneous material structure, E and γ should, more realistically, be taken as random fields (RFs) along the beam's span x. The beam is then described by a vector RF {E, γ}. The Obreimoff experiment was treated in that stochastic setting (), albeit without the consideration of the correlation structure of the RF involved. In the present study, we investigate the latter aspect.One way to classify RFs (equivalently, random processes) is to distinguish between those that do versus those do not possess fractal-and-Hurst properties. Models that do not allow such characteristics are those with white noise, exponential, and Matérn correlations. The need to actually include such characteristics is motivated by the richness of temporal and spatial phenomena in the real world: geophysics, atmosphere, biology, and economy (). In particular, fracture mechanics theory provides stepping-stone models to studies of many critical phenomena in geomechanics (), where long cracks like fault lines in geologically unstable areas are relevant in geotechnical and foundation engineering. In this paper, we focus on fracture of beams described by two classes of wide-sense homogeneous RFs with fractal-and-Hurst characteristics: Cauchy (). The correlation functions of these two types allow a decoupling (i.e., independent choice) of the fractal dimension D and the Hurst exponent H. Typically, i.e. for self-affine RFs (and random processes), the latter two are linked by the relation H = 2 − D. With motivations coming from both harmonic analysis (complete monotonicity) and probability theory (fractal dimensions and Hurst effect), the Dagum RF was first proposed in As general background, a fractal is a roughness measure of a statistically self-similar profile (i.e., a realization on the real line) or surface of Rn (n = 2 or 3), whereas Hurst reflects a long distance dependence, or, equivalently, a long memory dependence in a time series. While the fractal dimension measures the strength of a fractal, the key Hurst parameter is the exponent H. In general, 0 < H < 0.5 indicates a time series with negative autocorrelation (e.g., a decrease between values will likely be followed by an increase), whereas 0.5 < H < 1 indicates a time series with positive autocorrelation (an increase between values followed by another increase). The case H = 0.5 indicates a true random walk, where there is no preference for a decrease or increase following any particular value.Random fields and processes with fractal and Hurst effects have been studied in a series of 1d mechanics models: first- and second-order dynamical systems (), and elastostatics of rods and beams (of shear or Bernoulli-Euler type) (). While the problems involving Cauchy RFs could be tackled through explicit formulas, Dagum RFs typically demanded numerical integrations. Moving to 2d problems, one has to carry out direct (Monte Carlo type) simulations (There also exists a range of studies on fracture in fractal materials relying on other techniques than random fields, some of which provide insight into the fractal-and-Hurst effects from a different perspective than ours, e.g. (The objective of the present study is to examine how the strain energy U and the strain energy release rate G are affected by Gaussian RFs E and γ, taken as either Ornstein-Uhlenbeck, Matérn, Cauchy, or Dagum. gives the background on the underlying RF models. In we explore in what ways, under dead-load and fixed-grips conditions, U and G are sensitive to one or both of these fields for specific classes of covariance functions. investigates the crack stability in these settings.In this paper, a real-valued Gaussian RF F defined over a probability space (Ω, A, P) is used, where P here denotes a Gaussian measure, and with realizations on X⊂R. F is taken to be zero-mean and wide-sense homogeneous so that it is completely specified by second-order moments, in particular by the associated covariance function C(·,·):R×R→R defines as:In view of the wide-sense homogeneous assumption, there exists a mapping CF:R+∪{0}→R, such thatThis framework allows us to identify two important properties of RFs we want to study:The fractal dimension D reflects the local properties; it is a roughness measure with a range [n, n + 1); since the focus is on beams, n = 1 is used.The long memory in time series (or spatial data) is associated with power-law correlations and often referred to as the Hurst effect, characterized by the H parameter (These properties relate to those of the associated correlation function. Next, it is important to assess the local regularity properties of the sample paths of a Gaussian process. To this end, it has been established that, if, in the weakly homogeneous case, for some α ∈ (0, 1), there holdswhere r = x2 − x1. Then, with probability one, the fractal dimension of F(•) satisfieswhere, as before, CF = covariance function of F. In , GrF=graph(F)={(x,F(x)),x∈[−1,1]}⊂R2 so that the parameter α determines the fractal dimension D.The scaling laws describe how rather elementary measurements vary with the resolution, a subject that along with the relation between index-α and D is discussed at length in (). Besides to the index-α related to the fractal dimension D, for Gaussian RFs, it is also possible to distinguish an index-β related to H [see () for an exposition of Gaussian index-β RF, where β = α/2]. Here, if for some β ∈ (0, 1)Then the field is said to have a long memory, with H = β/2. For H ∈ (1/2, 1) or H ∈ (0, 1/2) the correlation is said to be, respectively, persistent or anti-persistent (). The same properties can be studied through the Fourier transform of the covariance function (i.e., the spectral density) under the conditions stated in Tauberian-type and Abelian-type theorems (), with the parameters α and β interpreted in the opposite way. Basically, α is associated with the velocity of decay of the spectral density, while β with the local behavior of the spectral density around near-zero frequencies.We shall consider these four types of RFs:where μ is a positive scaling parameter which in the limit μ → ∞ becomes white noise.where ν = a parameter that determines the smoothness at the origin of CM, and thus the mean square differentiability of F. Here, Kν = a modified Bessel function of order ν. Note three special cases:CM(r,1/2) = e-r which (as is well known) coincides with the covariance function of the Ornstein–Uhlenbeck type;which is positive definite for η > 0 and 0 < θ < 2. Special cases of this class will also be of interest. In particular, CC(•; 2; γ) is the characteristic function of the symmetric Bessel distribution, CC(•; α; α) is the characteristic function of the Linnik distribution, and CC(•; 1; γ) is the symmetric generalized Linnik characteristic function.which is positive definite for 0 < ε < δ and 0 < θ < 2. shows some sample realizations of the Gaussian Ornstein–Uhlenbeck (which in the limit becomes a white noise), Matérn, Cauchy, and Dagum RFs, for distinct parameter settings, all on 1d (one-dimensional domains, i.e. the beam axis). The plots illustrate the trends in linking the local and global properties of RFs with their associated correlation functions. In particular, in relation to , respectively, the realizations of the RFs have D = n + 1 − α/2, with probability 1, while the RF has a long memory with H = 1 − β/2. Thus, the parameter α is associated with the fractal dimension and the parameter β allows one to evaluate the Hurst effect.Furthermore, the sub-plots (a)-(d) clearly show that the white noise, Matérn, and Ornstein–Uhlenbeck RFs have no Hurst effects. As is well known, the smoothing parameter ν can be interpreted as the parameter α for the estimation of the fractal dimension (). In particular, for the Matérn model, the fractal dimension of a sample path in Rn equals the maximum of n and n + 1 − ν . For a differentiable field with smoothness parameter ν > 1, the fractal dimension of a sample path equals its topological dimension, n. Generally, the larger the ν, the smoother the process. So, with the Matérn model we can take into account the fractal characteristics, albeit with light tails, in fact, in the sub-plots (c)-(d) show a fractal dimension D = 1. Moreover, about the Ornstein–Uhlenbeck model, keeping in mind that this model is a special case of the Matérn model when ν = 0.5, for the sub-plot (b), D = 1.5. It is worth underlining that, in , μ is only a scalar parameter not linked to the fractal dimension, so for this model the fractal dimension is constant.In contradistinction to the Ornstein–Uhlenbeck and Matérn models, the Cauchy and Dagum models are capable of generating RFs with independently given fractal dimension and Hurst parameter. One can easily verify that the Cauchy model behaves like , β = η = (0, 1). If we focus on the sub-plots (e) and (f), the interpretation is twofold: a smoother profile is associated to a low value of D, as in sub-plot (e), (θ = 1.6 corresponding D = 1.2), instead of a rougher profile associated with a high D, as in sub-plot (f), (θ = 0.2 corresponding D = 1.9). If the long-memory parameter is large, similar values occur in lengthy patches or clusters, and the realization stays at approximately the same level for quite some length without noticeable jumps in value, as in sub-plot (e), (η = 0.2 corresponding H = 0.9), whereas if the long-memory parameter is low, the profile does not persist at any given level and fluctuates rather quickly between two extremes with significant jumps in value, as in sub-plot (f), (η = 1.6 correspond H = 0.2).Although the Dagum model inverts the relation, as it behaves respectively like for α = ε = (0, 2] and β = δ = (0, 1), we observe the same behavior for Dagum RFs as for Cauchy RFs. The sub-plot (g), (ε = 0.8 correspond D = 1.6), show quite smoother profiles than the sub-plot (h), (ε = 0.2 correspond D = 1.9). Similarly, in the sub-plot (g), (δ = 0.2 corresponds H = 0.9), we can see less noticeable jumps than the sub-plot (h), (δ = 0.8 corresponds H = 0.6).The force is deterministic, but the kinematic variable is random (), implying that only the second term in remains, and, assuming a Euler-Bernoulli beam, the strain energy is:Here a is the crack length, M is bending moment, I is beam's moment of inertia, and E is elastic modulus. Henceforth, we simply work with a = A/B, where B is the constant beam (and crack) width, so that, on account of Clapeyron's theorem, the strain energy release rate isNow, the beam's elastic modulus E is taken as a sum of a constant mean E and a zero-mean Gaussian WSS random field E′(ω, x)where Ω is the sample space of elementary events. The random material is thus defined as an ensemble B = {B(ω); ω ∈ Ω} = {E(ω, x); ω ∈ Ω, x ∈ [0, a]}. Hereinafter, we explicitly show the dependence on Ω, whenever we wish to indicate the random nature of a given quantity prior to ensemble averaging. that U is a random integral, such that, for each and every realization ω ∈ Ω, we should considerThe variance of the strain energy U(a) is determined as follows. First, by applying the expectation operation to 〈U(a)〉=〈∫0aM(x)22IE(ω,x)dx〉=∫0aM(x)22I〈1E〉dx.Next, given two points x1 and x2, we have two random variables E(x1) and E(x2), so that the variance of U is found asVar[U(a)]:=〈(U(a,E(x1))−〈U(a)〉)(U(a,E(x2))−〈U(a)〉)〉=∫0a∫0aM(x1)2M(x2)24I2CE−1(x1,x2)dx1dx2,in which we have used the covariance of the reciprocal Young's modulus E−1(•): =1/E(•):CE−1(x1,x2)=〈(1E(x1)−〈1E〉)(1E(x2)−〈1E〉)〉=〈(E−1(x1)−〈E−1〉)(E−1(x2)−〈E−1〉)〉.At this point, the probability transformation method (PTM) () is applied to relate the covariance CE(x1,x2) with CE−1(x1,x2). The PTM gives the direct one-to-one relationship between the joint probability density functions (pdf's) of two random vectors related with each other by the deterministic law corresponding to the assigned space transformation, see . Hence, given the joint pdf pE(E(x1),E(x2)), it is easy to prove thatpE−1(E1−1,E2−1)=1(E1−1)21(E2−1)2pE(E1−1,E2−1),where E1−1=E−1(x1)=1/E(x1) and E2−1=E−1(x2)=1/E(x2). Then, the covariance CE−1(x1,x2) is found asCE−1(x1,x2)=∫−∞∞∫−∞∞E1−1E2−1pE−1(E1−1,E2−1)dE1−1dE2−1=∫−∞∞∫−∞∞1E1−11E2−1pE(E1−1,E2−1)dE1−1dE2−1., the strain energy release rate G(a) becomesIt follows that a similar procedure to the one used to determine the variance of the strain energy U(a) can be employed in order to obtain the variance of the strain energy relate rate G(a). The mean and the variance function of the strain energy release rate are, respectively,Var[G(a)]:=〈(G(a,E(x1))−〈G(a)〉)(G(a,E(x2))−〈G(a)〉)〉=∂2Var[U(a)]B2∂a2.Now, noting the variance Var[U(a)] of strain energy U(a), it is possible to obtain the variance Var[G(a)] of the strain energy relate rate G(a). The expressions of these two quantities are not derivable in explicit forms but, using numerical computation of , have been determined for all the cases of CE(x1,x2) in . The results presented aim to investigate the influence of the fractal-and-Hurst effects in the problem under examination. To this aim, several combinations of the parameters that describe these effects are taken into account, . Mainly the parameters have been set so as to have RFs with Hurst parameter (H) between 0.5 to 0.8 and fractal dimension (D) between 1.2 and 1.7.Overall, we observe that, while the Cauchy and Dagum models represent more realistic scenarios of RFs, the variance on the output is strongest for the Matérn model. Then, for Ornstein–Uhlenbeck and Cauchy models, the variance on output is between those of Matérn and Dagum models; in fact, the latter one is the model with the weakest variance on output.In order to evaluate the dependence on a of the pdf of the strain energy U(a), an approach based on the direct evaluation of the response probability density function (pdf) () is applied. The crack axis has been discretized by intervals of constant amplitude da, i.e. a generic crack length ai = ida is considered. Corresponding to ai, the strain energy U(ai) can be defined as a Riemann sum approximating the integral (U(ai)=∫0aiM(xi)22IE(xi)dxi≈∑iM(xi)22IE(xi)Δxi=∑iM(xi)22IΔxi1E(xi)=∑iM(xi)22IΔxiE−1(xi),where Δxi = iΔxi = ida. Using the above relationship, U(ai) can now be written asThis implies that, in the interval of the length crack (a0 , ai), the value at the generic crack length up to ai of the strain energy U(ai) is given by the following linear algebraic equation system: establishes a linear algebraic relationship between the strain energy U(ai), evaluated at various crack lengths up to ai, and the stochastic vector Ei−1, evaluated at from crack lengths up to ai . in order to evaluate pU(ai)(U(ai)). Using numerical computation, we obtain the pdf and plot it in , wherein the crack axis is discretized by intervals of constant amplitude da = 0.2. It is gleaned from that the pdf of the strain energy, evaluated for several cases of D and H, shows a strongly nonlinear character of the relationship between the input and the output. The fractal-and-Hurst effects appear to be more or less in line with the previous trends observed on the variance of output.In this case, the displacement is constant (i.e., non-random), while the load is random. Now, only the first term in (b), implies P(a, ω) = 3uIE(ω, x)/a3, so that gives a direct relationship between G(a, ω) and E(ω, x) from which we first obtain the mean and variance functions of the strain energy release rateVar[G(a,r)]:=〈(G(a,E(x1))−〈G(a)〉)(G(a,E(x2))−〈G(a)〉)〉=(9u2I2Ba4)2CE(r).Thus, it is possible to obtain the variance of the strain energy relate rate G(a, r), at a fixed value of r or for a fixed value of a. We employ the same method as before in order to determine the effect of the covariance function CE(r). show the variances Var[G(a)] for a fixed value of the crack length (a = 1) and a fixed value of r (r = x2 − x1 = 0.1). Although in this case a linear relationship appears between the input and output, the previous qualitative conclusions for these two cases carry through as supported by several different cases of D and H.Crack stability in any particular realization of a random beam, in a general loading situation, is governed by a condition of the same form as that in deterministic fracture mechanics (∂2(Π(ω)+Γ(ω))∂a2{<0:unstableequilibrium,=0:neutralequilibrium,>0:stableequilibrium.Here both, the total potential energy Π(ω) and the surface energy Γ(ω) are random. Two example problems will now be considered with respect to crack stability.The first concerns a line crack in an infinite plate subjected to a uniform stress perpendicular to the crack axis. The potential energy of the system is given byThe terms Π, Γ, and (Π + Γ) are plotted in for E and γ constant. This figure shows that the total potential energy of the system (Π + Γ) at the critical crack length ac presents a maximum, which corresponds to an unstable equilibrium.Taking into account that beam's material is random, the mean and variance of the potential energy Π(ω) are, respectively,Var[Π(a,r)]:=〈(Π(a,E(x1))−〈Π(a)〉)(Π(a,E(x2))−〈Π(a)〉)〉=(−σ2πa2)2CE−1(r),Next, if we take the surface energy density as an RF made up of a constant mean γ and a zero-mean fluctuation γ′(ω, x)The mean and the variance function of the variance of the surface energy Γ(ω) are, respectivelyVar[Γ(a,r)]:=〈(Γ(a,γ(x1))−〈Γ(a)〉)(Γ(a,γ(x2))−〈Γ(a)〉)〉=(4a)2Cγ(r).Finally, the variance of the sum (Π(ω) + Γ(ω)) isVar[Π(ω)+Γ(ω)]:=Var[Π(ω)]+Var[Γ(ω)]+2Cov[Π(ω),Γ(ω)],and taking, as in our earlier study, the two-component RFs to be uncorrelated, gives when we fix r = x2 − x1 = 0.1. In this case, the beam is described by a vector RF {E, γ}. Nevertheless, by inspection of , the qualitative trend is similar to the trends depicted in , with the scatter of response being weaker than under the Dagum, Cauchy, Ornstein–Uhlenbeck, and Matérn inputs.The second problem concerns the experiment carried out by Obreimoff on the cleavage of mica (while the surface energy Γ(ω) is given byIn this second problem, the total energy of the system (U(ω) + Γ(ω)) at the critical crack length ac is minimum, which corresponds to a stable equilibrium. From the fracture criterion, the equilibrium crack length ac is obtained as plots Π = U, Γ and (U + Γ) when E and γ are constant. This gives the reference deterministic case.Now, we take the surface energy density and the beam's stiffness as two RFs: γ (ω, x), E (ω, x). The mean and variance of the elastic and surface energies are, respectively,Supposing these two RFs to be uncorrelated (i.e., Cov[U(ω), Γ(ω)] → 0), we findNumerical results for several parameter cases are shown in , where we set r = x2 − x1 = 0.1. Clearly, for the experiment of Obreimoff similar trends to those already observed in for the first example problem are obtained, and similar conclusions can be drawn.Considering the critical crack length, ac, taking into account the relation , it is possible to obtain the relative pdf by applying the PTM. With the aim to investigate the influence on the response output by the four RFs on input, it seems reasonable to compare the pdf of the critical crack length for the following cases. Since in the stochastic crack stability problem the beam is described by the vector RF {E, γ}, in each sub-plot of γ is fixed as Cauchy (a), Matérn (b), Ornstein–Uhlenbeck (c) or Dagum (d), and then E varies for these four cases of RFs. Hence, the same tendency is observed: the pdf of ac is the most dispersed for Matérn, then Ornstein–Uhlenbeck, Cauchy, and Dagum models, respectively. Therefore, we observe the same ordering as before.This work employs the classical Obreimoff's experiment to examine the fractal-and-Hurst effects of the RF material properties on elastic brittle fracture. Two RF models–Cauchy and Dagum–enable such an investigation and, in order to elucidate the fractal-and-Hurst effects, Ornstein–Uhlenbeck (which, in the limiting case, becomes white noise) and Matérn RFs are also considered. All the RFs are assumed to be truncated Gaussian so as to ensure positive values of the elastic modulus and surface energy density along the beam axis.The variance function of the strain energy U(a) and of the strain energy release rate G(a), both for dead-load and fixed-grip conditions, are found in explicit forms. For dead-load condition there is an inverse relationship between U(a) or G(a), with the Young modulus E(ω, x). In fact, our 2004 study found that, in the case of dead-load conditions, U(a) and/or G(a) computed by straightforward averaging of the spatially random elastic modulus E(ω) is lower than that obtained by correct ensemble averaging of the stored elastic energy. Thus, in the present study, in order to evaluate the exact covariance function of energy and its release rate, a recently established probability transformation method (PTM), has been applied. However, there is a direct relationship between G(a) and E(ω, x) for fixed-grip condition and, in fact, G(a) is to be computed by a direct ensemble averaging of E(ω). We find that, under these conditions, the variance function depends on a and r. Moreover, an approach based on the direct evaluation of the response probability density function by PTM is applied and the pdf of the strain energy U(a) is obtained.In general, we find that, given the same variance on input, the variance on output is more pronounced for the Matérn RF. Moreover, by assuming different values of the fractal dimension and Hurst parameters on the input, we obtain strong differences in the response on the output. Also, the response is stronger for the Cauchy model than for the Dagum model.Furthermore, a study of the stochastic crack stability is conducted: it involves a stochastic competition between potential and surface energies. Then, also in this last case, the fractal and the Hurst effects are taken into consideration through Gaussian Cauchy and Dagum RFs. In particular, it is possible to evaluate the pdf of the critical crack length, pac(ac), from analysis of Obreimoff's experiment. Again, the Matérn model leads to a stronger dispersion of the data than Cauchy and Dagum. However, both the presence of inverse relationships and the introduction of the Cauchy and Dagum models complicate the evaluation of explicit analytical forms, so that one has to resort to numerics. Overall, due to the lack of analytical forms, this mathematical problem remains open: Do the Cauchy and Dagum RF inputs lead, respectively, to Cauchy and Dagum responses?Given the fact that fractal-and-Hurst effects are multiscale properties of materials seen primarily in nature, the present study should provide an indication as to the fracture phenomena in geomechanical/geophysical settings.Rossella Laudani: Methodology, Data curation, Writing - review & editing. Martin Ostoja-Starzewski: Conceptualization, Supervision, Writing - review & editing.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.The PTM is based on a probabilistic approach to space transformation laws of random vectors. In particular, it gives a direct deterministic relationship between the joint pdfs of two random vectors related to each other by a deterministic law corresponding to the assigned space transformation. Consider an n-dimensional random vector x, whose joint pdf px(x) is known, and let g(•) be n-dimensional invertible application, with g−1(•) Then, it is possible to obtain the joint pdf of the random vector z, pz(z), through the following relationship (where Jg(z) is the Jacobian matrix associated with the transformation given in Eq. (A.1a), that is:∇xT being the n-th order row-vector operator collecting all the partial derivatives with respect to the components xi of x and the symbol ⊗ indicating the Kronecker product. Expression (A.2) gives a direct deterministic relationship between the joint PDFs of the random vector z and that of the random vector x. In other words, the pdf of the output variables pz(z), can be computed once the pdf of the input variables px(x) is known and the transformation law is defined.Let zj be the single component of the output random vector z defined by the scalar transformation zj = hj(x). In () it was shown that the pdf of zj, by using the properties of the Dirac delta function, can be reduced as follows:pzj(zj)=∫−∞+∞…∫−∞+∞px(y)δ(zj−hj(y))dy1…dyn.The computational effort related to the evaluation of the multiple integrals appearing in the previous equation can be sensibly reduced if the calculus is conducted in terms of the characteristic functions (cf). For example, starting from Eq. (A.4), the application of the Fourier transform to both its members gives:Mzj(zj)=12π∫−∞+∞…∫−∞+∞px(y)exp(−iωjhj(y))dy=12πE[(−iωjhj(y))],where Mzj(·) is the characteristic function of the random variable zj, E[ • ] is the stochastic mean of the random variable inside the brackets and where the fundamental properties of the Dirac delta function δ(zj − hj(y)) have been taken into account. From the cf of the system response, the pdf of the displacements can be easily obtained by applying the inverse Fourier transform to Eqs. (A.5).Examination of hydrogen embrittlement in FeAl by means of in situ electrochemical micropillar compression and nanoindentation techniquesThe effect of the electrochemical potential on the indent load-displacement curve and pillar stress strain curve, especially the unstable elastic-plastic transition (pop-in), was studied in detail. The observations showed a reduction in the pop-in load for both experiments due to in situ hydrogen charging. Clear evidence is provided that hydrogen atoms facilitate homogenous dislocation nucleation.Iron aluminides are of considerable interest for low to moderate temperature structural applications in which low cost, low density and good corrosion or oxidation resistance are required.In spite of all these inherent advantages, the ordered FeAl alloys exhibit poor ductility due to their susceptibility to hydrogen embrittlement Although the qualitative effects of hydrogen on dislocations were observed from conventional mechanical experiments, the results are difficult to interpret quantitatively. This is mainly due to difficulties in exploring the details of plastic deformation locally. On the other hand, in situ environmental TEM experiments on thin films are also difficult to interpret, since the electron beam produces high hydrogen fugacities and local heating The instrumented indentation technique either in the form of a nanoindenter combined with atomic force microscope, NI-AFM, or nano-compression machine for focused ion beam (FIB) cut micropillars The experiments were all performed on electropolished Fe-40 at.% Al single crystal provided by Oak Ridge national laboratory. Detailed descriptions of the hardware and procedures we use to perform indentations in solution (Borate buffer with a pH of 8.4) under electrochemical control are provided elsewhere Micropillars were cut in the electropolished Fe-40 at.% Al single crystal using a Strata™ dual beam focused ion beam (FIB) system from FEI. These pillars, 3μm in diameter, were compressed in the same Hysitron® TriboIndenter™ nanoindentation system used for in situ electrochemical nanoindentation tests shows typical load-displacement curves for indentation tests performed under anodic conditions. shows the resulting curves at a cathodic polarization of −1100 mV. The observed changes in pop-in behavior at different electrochemical potentials are summarized in , where the mean values of the pop-in loads at alternating electrochemical potentials with standard deviation error bars are presented. shows reproducible pop-in behavior for hydrogen free and hydrogen charged conditions. The surface topography of the sample was imaged at the different potentials and no change in the surface roughness due to the electrochemical polarization was observed The complexity of the stress field below the nanoindenter motivated us to perform micropillar compression test on FeAl inside solution under electrochemical control. The uniaxial stress condition in micropillar compression test makes the analysis of load-displacement data easier. shows typical scanning electron images (SEM) of pillars before and after compression. Examination of the stress strain curves () showed that the general shape of the stress-strain curves for pillars tested in air is identical to that of standard nanoindents performed on FeAl. SEM examination of these pillars (b) after compression testing also showed no visible deformation of the pillar itself. The pillar had actually “indented” its base. We see a pop-in like strain burst, typical for standard nanoindentation of FeAl, and after that ideal plastic deformation. Only in the case of hydrogen charged pillars at cathodic potentials (−1100 mV) do we see deformation of the pillar itself (The above results clearly indicate that the pop-in load in the hydrogen charged condition is distinctly lower than that of the hydrogen free condition. As a first assumption, this reduction in pop-in load can be interpreted as HELP. The initial elastic loading begins as soon as the tip makes contact with the surface of the material, and continues until dislocation motion or nucleation occurs. Typical dislocation densities in an annealed metal are in the range 106–108 |
cm−2; this implies a dislocation spacing of 1 to 10 μm. A typical indentation test in the elastic regime probes a maximum lateral region of two hundred nanometers up to the point at which the pop-in occurs. This suggests that the volume of material sampled by the indentation test at pop-in is smaller than the average dislocation spacing, so that an indent placed randomly on the surface will have a significant chance of sampling a region that contains no pre-existing dislocations.Numerous experimental studies lend credibility to the assumption that the indenter tip initially makes contact with a volume of material small enough to be dislocation free if the sample is well-annealed and electropolished where P is the applied load, R is the radius of the tip curvature, and Er is the reduced modulus, given bywhere E is the elastic modulus of the material, ν is the Poisson's ratio, and the subscripts 1 and 2 indicate the tip and the sample, respectively. For FeAl (E |
= 244 GPa gives Er |
= 217 GPa. If we insert the 0.7 μm tip radius into Eq. , we obtain a maximum shear stress for each pop-in load. This maximum shear stress is responsible for the homogenous dislocation nucleation at zτ(max).The predominant slip system in FeAl is 〈111〉 {110} at room temperature where W is the line energy of the dislocation loop, b is the Burgers vector and τ is the external shear stress acting on the loop. The first term on the right-hand side of Eq. describes the energy required to create a dislocation loop in a defect-free lattice and is equal to the increase in lattice energy due to the formation of a dislocation loop. The second term gives the work done by the applied stress τ as a result of the Burgers vector displacement and indicates the work done on the system to expand the dislocation. The line energy W for a circular loop, which results from the lattice strain in the vicinity of the dislocation for r>ρ, is given by where μ is the shear modulus and ρ is the dislocation core radius. Using Eq. ΔG=2−ν1−νμb2r4(ln4rρ−2)−πr2b[0.31(6Er2π3R2P)1/3] relates the material properties and experimentally observed pop-in load to free energy of dislocation nucleation. The nucleation of a loop is similar to the nucleation of a sphere of a new phase, where the corresponding function ΔG contains terms of second and third power of r. In both cases ΔG has a maximum (nucleation barrier) at a critical radius rc above which the system gains energy by increasing r. According to Eq. this maximum energy is decreased with increasing load P and a pop-in, i.e. homogeneous formation of circular dislocation loop, becomes possible without thermal energy at ΔG |
= 0. This condition and dΔG/dr |
= 0 for a maximum are fulfilled, ifThe corresponding critical load Pc for a pop-in is obtained from Eq. according to this criterion and by using the constants given in . The reduction of the pop-in load by about a factor of 3.5 corresponds to a decrease of W by 40%. According to Eq. this reduction can be attributed to changes in μ, and/or ρ. The effects of hydrogen on the other parameters involved in Eq. are either negligible or inapplicable. Considering no change in the dislocation core radius the dissolved hydrogen results in the reduction of shear modulus from 94 GPa to 57 GPa. Let us therefore consider which fundamental properties of a material determine its elastic constants. The bulk modulus B is given by the second derivative of the crystal energy Uc with dilatation. Rose et al. where U is the cohesive energy, U∗(d∗) is an approximately universal function which describes the shape of the binding energy curve for metals, d* is a scaled length, l is a scaling length and rws is the Wigner-Seitz radius has a simple physical meaning: the reduction in the shear modulus is equal to the reduction of the strength of the interatomic bonds, as assumed in the HEDE model.On the other hand, if we consider the other extreme of no reduction of the shear modulus, an increase of the dislocation core radius is responsible for the reduction in pop-in load. According to classic dislocation theory an increase in the dislocation core radius means a reduction of the dislocation line energy where cA is the chemical potential of solute atom A dissolved in a material of B atoms with a constant number nB. The dislocation lengthlD, temperature T and volume V are maintained constant. According to Eq. the line energy of a dislocation decreases with increasing solute chemical potential if the excess is positive, i.e. solute atoms segregate to the dislocation core. Hence, an increase in the core radius is direct evidence for a decrease in dislocation line energy resulting from hydrogen segregation to the dislocation line The in situ electrochemical micro-compression tests are also in very good agreement with the nanoindentation results. The small size of the pillars resulted in dislocation source starvation The fine scale mechanical probing capabilities of NI-AFM were used to examine the effect of hydrogen on dislocation nucleation in FeAl. It has been demonstrated that hydrogen reduces the pop-in load or enhances the micropillar plasticity which can be interpreted as the HELP mechanism. Classical dislocation theory was used to model homogenous dislocation nucleation and it was shown that hydrogen reduces the required activation energy. The activation energy for homogenous dislocation nucleation is related to the material specific parameters; μ and ρ. These material properties can be influenced by hydrogen resulting in a reduction of the activation energy required for dislocation nucleation. The universality of cohesion in bulk metals relates the reduction of the shear modulus to the reduction of the cohesion, implying the HEDE mechanism. The increase in the core radius of a dislocation due to hydrogen is direct evidence for a decrease in dislocation line energy and hydrogen segregation to the dislocation line.Thus, HELP and HEDE are the two sides of the same coin and are acting together to cause hydrogen embrittlement. However, depending on the experimental approach utilized to probe the hydrogen effect, either HELP or HEDE can be observed. In this study, by utilizing a proper experimental approach, it was possible to resolve the ambiguous nature of the hydrogen embrittlement in FeAl intermetallic alloy. Electrochemical NI-AFM gives us new insights into the fundamentals of hydrogen embrittlement and allows us to find a proper solution for increasing the resistance of FeAl intermetallic alloys against hydrogen embrittlement.Comparison of laboratory rolling–sliding wear tests with in-service wear of nodular cast iron rollers against wire ropesThe present work describes the wear behaviour of nodular cast iron in rolling–sliding contact with steel wire ropes and steel wires in laboratory and in-service conditions. In each of the studied examples, the wear had proceeded through a surface fatigue process, in which inter-nodular crack propagation and simultaneous deformation in a thin sub-surface zone had resulted in the formation of ferrous scales consisting of material from the metal matrix of the cast iron. The scale layers of the wear surface were oriented towards the direction of the sliding component of the motion, and the spalling of the scales was identified as the dominating mechanism for material removal from the wear surface. The initiation behaviour of the inter-nodular cracks was analysed by crack measurements and statistical analysis of the depths and initiation angles of the cracks in relation to the wear surface. The initiation depths of the cracks increased with increasing contact pressure. Roller samples from in-service and from the component wear tests showed closely similar distributions of the crack depths and crack initiation angles. The sample from the twin-disc test showed aspects of cracking behaviour that were typical of both the rolling and the sliding direction of the roller samples.Wire rope drives are all around us, in lifting equipment, cable cars, cable railways, funiculars, just to mention some of the applications. A rope drive comprises a wire rope and one or several rollers, over which the wire rope is bent during operation. The wire rope is built up from a large number of steel wires wound together to a complex structure, which carries loads in the length direction while being laterally flexible. The most widely used wire material in rope drives is a high-strength non-alloyed carbon steel with a pearlitic microstructure The wire rope is traditionally the most critical component in a wire rope drive, because the breakage of the wire rope usually is an issue of both economical and safety-related relevance. Cable breakages can occur for instance due to fretting wear and fatigue at poorly lubricated wires of a cable, or due to abrasive wear Recent studies on the wear of rollers of wire rope drives are mainly limited to steel and polymer roller materials In this study, the wear behaviour of nodular cast iron components in contact with steel wire ropes and wires in different conditions was characterized by microscopy and statistically analysed in terms of cracks caused during the wear processes. Grooved rollers made from nodular cast iron had operated in contact with steel wire ropes under bi-directional rolling motion in the running direction of the rope and sliding motion in a direction perpendicular to the rolling motion. An in-service roller sample, two component wear test roller samples, and an unused roller sample with an as-machined groove were characterized. A twin-disc test was performed with unidirectional rolling–sliding motion against a steel-wire-coated disc. The statistical analysis of the fatigue wear cracks can be utilised in the validation of the similarity of the wear behaviour of in-service samples and wear test samples, and in the adjustment of wear test parameters.The grooved rollers and the cast iron disc sample for the twin-disc test had been produced from nodular cast iron EN-GJS-700-2, which comprises of spherical graphite precipitations in an almost fully pearlitic iron matrix. The minimum standard tensile strength was 700 MPa and the minimum standard elongation 2%. presents the median hardness of the cast iron samples. The wire rope grooves in the roller samples had been produced by turning with form-cutting tools.The rollers had operated against wire ropes with a diameter of 8 mm and a tensile strength grade of 2160 N/mm2. The wire rope construction consisted of 8×19 regular left lay Seale outer strands and a steel wire rope core. The wires of the wire ropes, as well as the wire used in twin-disc tests, had been drawn from unalloyed pearlitic steel with a carbon content of about 0.6%, according to the manufacturers. The wire used in the twin-disc tests had an ultimate tensile strength of 1700 N/mm2 and a hardness of 456 HV5 with a standard deviation of ±6 HV5, as determined by a median obtained from ten indentations on each of three longitudinal cross-sections.The grooved rollers had operated under contact with wire ropes under specific rope forces and bi-directional rolling motion. illustrates the contact geometry of the wire rope in the roller groove. The contact between the roller and the wire rope consists of numerous small contact areas. As the wear of the wire rope proceeds, the contact points evolve into lens-like ovals.Two of the roller samples had operated in two tests in component test equipment used for life-time testing of wire ropes. illustrates the test set up. The wire rope was run by the drive roller in a regularly changing bi-directional running motion with a running distance of approximately 1.0 m per full cycle, or 0.5 m per running direction. The wire rope ran over three freely rotating invert rollers. The middle invert roller was the one chosen for characterization in the present work. To prevent sliding, the wire rope had been secured to the drive roller, and the ends of the wire rope had been attached to each other with rope wedge sockets. In the wear tests, the applied loads, and consequently the rope forces, were kept constant. The fleet angle, i.e., the deflection angle between the radial plane of the roller and the axis of the wire rope exiting or entering the groove, was 0° in the present wear tests.The two wear-test roller samples had operated in five life-time tests with similar wire ropes. Before each test, the wire rope had been lubricated with an additive-free paraffinic vaseline (petrolatum) with a kinematic viscosity of 80 mm2/s when heated to a temperature of 100 °C. One of the roller samples had been tested with a rope force of 10 kN for a duration of 639,198 running cycles, and the other one with 15 kN and 309,969 running cycles. In addition, an unused as-machined roller sample was characterized for comparison.The in-service roller sample had operated as one of two invert rollers in a hoist system consisting of a rope drum, two load-carrying invert rollers, and an equalizing roller between the invert rollers. Both ends of the wire rope had been fastened in the rope drum. The invert roller sample had operated under a variable load, an intermittently changing running direction, and a varying fleet angle, for approximately 400–500 h. The wire rope of the in-service machinery had been lubricated with paraffinic vaseline before commissioning, but most likely not during the service life.Due to the free rotation of the roller and the almost equally large rope forces on both sides of the roller, the sliding between the roller and the wire rope in the running direction had been negligible both during the in-service operation and in the component wear tests.The twin-disc test was carried out with a cast iron disc in rolling–sliding contact with a steel wire of 1.4 mm in diameter wrapped as a spiral around a grooved steel disc. presents a schematic of the contact in the initial stage of the test. The cast iron disc had an initial diameter of 50 mm and a radius of curvature of 100 mm in the axial direction. The steel-wire-coated disc had an initial circumference of 50 mm. In the twin-disc test, the normal force was 500 N and the initial circumferential velocities were 3.0 m/s for the cast iron disc and 2.94 m/s for the steel-wire-coated disc, corresponding to a slip-ratio of 0.2% in the contact. Initially, due to the curvature of the cast iron disc in the direction of its axis, contacts between the steel wire and the cast iron discs occurred on only two points. The number of contacts increased as the wear process proceeded. Due to diameter changes caused by wear, the circumferential velocities and the sliding ratio changed during the test. The duration of the test was 48 h, during which the tribosystem was lubricated automatically with a total of 1.0 g of paraffinic vaseline (petrolatum) with a drop point of approximately 80 °C and a kinematic viscosity of 20 mm2/s when heated to a temperature of 100 °C.The samples were characterized both qualitatively and quantitatively. Qualitative characterization of the microstructure and wear behaviour was performed by inspecting the worn surfaces and cross-sections of the samples using an optical microscope and a Philips XL30 scanning electron microscope (SEM). The characterized cross-sectional planes of the roller components are presented in . The sectional samples were prepared so that the sample planes were closely parallel to the tangent of the wear surface. The sectional samples of the roller components in the plane parallel to the rolling direction were prepared so that the cross-section in the rolling direction was located at the groove bottom. The cross-sectional twin-disc samples were produced so that the sample plane was at the midpoint of the disc axis.Quantitative characterization of the worn surfaces of the nodular cast iron samples was conducted by measurement of the depths and initiation angles of wear cracks in relation to the surface of the component. The measurements were performed by computer assisted optical microscopy of the cross-sectional samples, on 171 µm long and 128 µm wide image fields, using a magnification factor of 103. illustrates the measurement procedure for single cracks. The crack depth h was determined as the distance between the general surface line in the image area and the probable initiation point of the crack.The initiation angle α of a crack was defined as the angle between the general surface line and a straight line that begun from the probable initiation point of the crack and followed the crack line for as long as the crack was linear. Cracks extending towards the wear surface were given positive values and, consequently, cracks oriented inwards obtained negative values. In the case of the unused roller sample and the twin-disc sample, the cracks oriented towards the direction of the motion of the contact, i.e., the direction of the sliding motion of the machining tool or the steel wire disc on the surface of the nodular cast iron component, were given angles −90°…0°…90°. In the case of the roller components, the rolling motion had a changing direction, and one of the rolling directions was arbitrarily chosen to have the initiation angle values −90°…0°…90°. The angles −90°…±180°…90° then represented the cracks oriented towards the other rolling direction. The measurement uncertainty of the angles caused by the microscope system was ±1°.The measurement of the crack initiation angles was slightly inaccurate, because most of the cracks were somewhat curved. This was caused by the nonlinear crack propagation paths and by curvedness caused by the plastic deformation of the wear surface.The crack depths and initiation angles in the roller samples were measured in both the inspected planes, i.e., in the plane parallel to the rolling direction at the groove bottom and in the plane perpendicular to the rolling motion. The measurements of the twin-disc sample were performed in the plane parallel to the rolling–sliding motion, in the middle parts of the disc axis, where the contact pressure had been at its highest. The number of analysed cracks for each sample and cross-section plane in the statistical analysis are given in The measurement data of the depths and initiation angles of the cracks were analysed statistically. Cumulative histograms were defined for the crack depths of each sample, using bins, i.e., discrete interval groups, of 5 µm with relative frequencies. Depths of less than 2 µm were disregarded.To analyse the initiation angles of the crack, they were presented in circular histograms with relative frequencies having bins of, for example, −4° to +5°, +6° to +15 °, etc. The bins have been labelled ±0°, +10° and so on, for a more convenient presentation of the results.The as-machined wire-rope groove of the unused roller had a rough surface with bare graphite nodules visible under the microscope. b presents a cross-section in the plane parallel to the machining direction, revealing a shallow sub-surface zone, in which the metal matrix has been plastically deformed towards the motion direction of the cutting tool. In the deformed zone, cracks have initiated at the interface of the graphite nodules and the matrix metal. Most of the cracks had an initiation angle that was oriented diagonally towards the surface. In the immediate vicinity of the groove surface, the cracks were curved as following the surface. In addition to the cutting of the material, delamination of the metal matrix above the cracks had played a role in the material removal process.The in-service roller showed a rather different damage type than did the unused roller. a presents the wear surface at the groove bottom of the in-service roller sample, showing metallic scales and a pit and, in addition, scratches perpendicular to the rolling direction. Small hard particles were present in the surface of the in-service roller sample, as embedded in the metal matrix of the worn surface. The scales were caused by cracks extending to the surface, and had a rather uniform orientation perpendicular to the rolling directions.b presents a cross-section of the in-service roller in the plane parallel to the rolling directions. The image reveals deformed graphite nodules and cracks in the metal matrix that originate from the interface between the graphite nodules and the metal matrix. The cracks appeared deeper than those in the unused roller component, and, contrary to those in the unused sample, they did not have a uniform orientation but appeared to be distributed quite evenly between the two rolling directions. Networks of inter-nodular cracks had formed at depths of approximately 20 µm or less from the surface. At higher depths from the surface, most of the cracks had not yet interconnected between the graphite nodules.c shows a cross-section perpendicular to the rolling direction at the groove bottom of the in-service roller, revealing strong deformation of the matrix metal and the graphite nodules with uniform orientation. The cross-sections also revealed cracks originating from the interfaces between the graphite nodules and the matrix metal. In the plane perpendicular to the rolling directions, the cracks were mostly oriented diagonally towards the wear surface, parallel to the deformation, or deeper into the material in the opposite orientation. presents a surface area of the in-service roller with a loosely attached, delaminated fragment of the metal matrix, which, if detached, would have resulted in a surface pit similar to the one shown in a. Deformation tongues had been formed at the loose edge of the delaminated fragment, and the final crack had been propagating at the opposite edge of the delaminated fragment, as shown by the arrow in . A smaller spall had cracked off from the area indicated by the dashed line. In the rightmost part of the pit inside the dash-lined area, a depression formed by the deformation tongue of the smaller spall can be seen. The leftmost part of the pit consists of intact fracture surface. Pits caused by the removal of large spalls were rather rare in the roller samples. Small, hard particles embedded in the metal matrix are also visible in . EDS analyses showed that the particles consisted of tungsten, carbon and cobalt. The scratches visible in a were most probably caused by hard particles sliding against the groove surface.The component wear test results showed, that the increase in the rope force from 10 kN to 15 kN had halved the average life-time of the wire ropes and doubled the average volumetric wear rate of the roller. In this context, the wear rate is equal to the wear volume divided by the force acting on the contact and the distance of motion. At the end of the test sequences comprising the five wire ropes, the wear volumes of the rollers were nearly equal.The roller sample tested at the 10 kN rope force had a rather smooth wear surface covered by metallic scales oriented uniformly perpendicular to the rolling directions, as presented in a. The wear surface showed scarce pits caused by the removal of scales, but no scratches or embedded hard particles were observed. The cross-sections showed rather similar behaviour to that of the in-service roller sample. b presents a cross-section perpendicular to the direction of rolling revealing cracks, which had a uniform orientation diagonally towards the surface, and similarly oriented strong deformation. In the plane parallel to the rolling direction, the deformation had been weaker, and neither the deformation nor the cracks had a uniform orientation. At depths close to the surface, the internodular cracks had joined and formed networks.The roller tested with the 15 kN rope force revealed macroscopic imprints at the groove bottom that were corrugated as the result of repeated contacts with the surface wires of the wire rope. Corrugations are formed when the diameter of the groove is such that the contact between the strands and the roller occur repeatedly at the same point, i.e., the circumference of the groove bottom is close to a multiple of the lay length of the wire rope. On the two other worn roller samples, such conditions had not occurred, or at least not towards the end of the operational life-time, and no corrugation imprints had been formed. In addition to the momentary circumference length of groove bottom of the roller, the corrugation may be promoted by increased load, by increasing the contact pressure and by elongating the wire rope, thus affecting the lay length. The corrugated wear surface contained valleys at the spots where the strands and wires had repeatedly contacted the groove, and peaks between the valleys. a shows a rough wear surface at a corrugation valley. Similarly to those of the other two worn roller samples, the deformation tongues of the roller tested at the 15 kN rope force had a uniform orientation perpendicular to rolling. However, the surface was rougher than those of the other two worn roller samples. b presents a cross-section perpendicular to the direction of rolling. The cross-sectional sample revealed deformation and crack propagation at the corrugation valleys similar to that in the other two roller samples. However, at the corrugation peaks, the deformation was oriented from both directions towards the centre of the peak. The peaks were formed by material pushed away from the contact areas. Scratches or hard particles were not observed in the sample.The twin-disc test sample made from cast iron showed traces of a wear behaviour that was somewhat different from that of the roller samples. a presents a wear surface on the twin-disc test disc sample, which was covered by matrix-related metal scales oriented in parallel to the direction of motion, as well as numerous pits. b shows deformation that is oriented towards the sliding direction and cracks along a plane parallel to the rolling–sliding direction of the twin-disc test disc sample. The deformation was clearly oriented towards the sliding direction. In the vicinity of the surface, the inter-nodular cracks had intersected and formed long networks. The networks of cracks had a general orientation diagonally towards the surface. The networks of cracks appeared to slightly favour the orientation towards the sliding direction. However, the orientation was not as evident as in the case of the worn roller samples in the plane perpendicular to the direction of rolling. The cracked sub-surface zone in the twin-disc sample reached deeper than the corresponding zones in the roller samples, and the deepest cracks appeared to be unaffected by the deformation. A plane perpendicular to the rolling–sliding direction of the twin-disc sample revealed low deformation of the sub-surface zone and long networks of cracks, oriented in parallel to the surface.The surface crack depths were characterized for all the present samples. shows the cumulative frequencies of the surface crack depths as measured from the present samples. The crack depths of the roller samples in the histogram were measured from the groove bottom parallel to the rolling directions. shows that the three worn rollers have very similar distributions of the crack depths. The unused roller sample shows a narrow distribution of the crack depths, with the deepest crack initiating at a depth of 19 μm. The in-service roller and the wear-test roller from the test with the 15 kN rope force have a slightly higher maximum crack depth (approximately 60 µm) than the sample tested with the 10 kN rope force (approx. 50 µm). The twin-disc sample had a somewhat wider crack depth distribution, having the deepest crack initiating at a depth of 77 μm. shows the relative frequencies of the crack initiation angles for all four rollers in the plane parallel to the rolling direction, and for those of the twin-disc sample in the plane parallel to the direction of motion. The 0° angle represents the contact motion direction of the twin-disc sample and the cutting tool motion direction in the as-machined roller sample. In the case of the worn roller sample, the angles 0° and ±180° represent the two running directions of the wire-rope. The negative angles represent cracks extending deeper into the sub-surface material from the graphite nodules, and positive angles correspondingly those extending towards the wear surface. The peak in the curve of the as-machined roller sample are extended to 20% in the angle bins of +20° and +30°. shows that the unused roller sample had an evident preference of crack initiation orientation towards the machining direction. Approximately one-half of the machining cracks had initial angles of 10°…30° in relation to the cutting tool motion direction. A smaller peak in the crack distribution occurred at almost opposite angles (−170°…−160°), which represented the cracks oriented deeper into the material from graphite nodules, which were already part of the machining surface and were partially cut.Each of the worn roller samples had an approximately symmetrical distribution of crack initiation angles in relation to the two rolling directions. indicates that the cracks initiating towards both rolling direction have clear peaks at angles of +10°…+20° and +170°…+160°. These orientations represent +10°…+20° angles in relation to the surface line in the two opposite rolling directions. Furthermore, the cracks with negative angles, i.e., those that were oriented deeper into the material, had quite symmetrical distributions when considering the two rolling directions.The twin-disc sample showed a somewhat similar distribution of crack initiation angles as did the worn rollers. Similarly to the roller samples, the twin-disc sample had high distributions at +10°…+20° and +170° angle bins. However, it also had a high distribution at −170°…±180° angle, which is not present in the roller samples. represents the initiation angles of the cracks in the surface zones of the worn roller samples, in the plane perpendicular to the rolling direction. The curve of the twin-disc sample is the same as in , i.e., in the plane parallel to the contact motion. Each worn roller sample showed a distribution peak at the angles of +20°…+30° in relation to the surface in the direction of the deformation, and another peak at the angle bin of −170°, representing cracks that extended deeper into the material in the direction opposite to the deformation.Again, the distribution of the twin-disc sample in the plane parallel to the motion shows rather similar behaviour to that of the roller samples, having high distribution at the angles of +20° and −170°. However, the roller samples did not have a peak at +170° in the plane perpendicular to rolling.The wear behaviour appeared similar in each of the worn roller samples. The roller samples showed deformation tongues oriented perpendicularly to the direction of rolling. However, the roller sample tested with the 15 kN rope force had experienced corrugation and had consequently a rougher surface than had the other roller samples.The wear process of the nodular cast iron samples had proceeded mainly through rolling contact fatigue under rolling–sliding conditions. Cracks had initiated at the interfaces of the graphite nodules and propagated inter-nodularly through the metal phase of the cast iron material. On the other hand, the sliding motion had induced plastic deformation of the material in the sub-surface region. The cracks extending to the surface enabled strong deformation, which resulted in the formation of scale-like deformation tongues on the wear surface.The material removal proceeded by spalling of the metallic surface scales, as described in the context of . At the initial stage of the formation of the spall, one or multiple cracks had emerged on the surface in the direction of sliding and the two orientations parallel to the rolling direction. The scale formed by these multidirectional cracks was then removed through crack growth between the graphite nodules and the surface in the final undamaged neck of the metal fragment.In the twin-disc sample, the cracking scales and the deformation tongues were formed in the direction of motion at the contact point, because the direction of motion was uniform. On the other hand, in each of the three worn roller samples, the deformation and the deformation tongues were uniformly oriented in one of the directions perpendicular to the rolling. It can be concluded that the deformation in this direction had to be caused by torsional and bending stresses in the wire ropes, arising in the surface strands and particularly individual surface wires in contact with the roller with respect to transfer of contact stresses. The subsequent surface deformation state due to the locality of the contact is two-dimensional, because slip is prevalent in the direction perpendicular to the direction of rolling. The torsional and bending stresses in the wire rope have caused shear stresses in the sub-surface of the roller and, as a result, contact surface sliding in the direction perpendicular to the direction of rolling when the wire rope deforms and accommodates against the higher stiffness roller surface. Despite the lack of significant roller scale wire rope slip, sliding can result from the high contact pressures that subsequently deform the wire rope and particularly the surface strands and wires, thus promoting surface shear and finite sliding. The scratches caused by the hard particles in the in-service roller sample support the assumption that the stress state has caused sliding between the wire rope and the roller. The sliding rate between the groove and the wire rope could not be determined.The amount of surface fatigue pits was substantially higher in the twin-disc sample than in the rollers. The high wear rate was caused by the high applied contact pressure, which accelerated the wear process. Moreover, the radial stiffness of the twin-disc arrangement exceeded that of the roller tests, hence the radial forces in the twin-disc test contained larger dynamic components than did the forces in the roller tests and promoted pitting-type surface damage and caused more extensive sub-surface damage due to the deeper penetrating contact stress fields.Quite similar wear behaviour was observed by Oksanen et al. The statistical analysis of the three worn roller samples showed a consistent wear behaviour. Both the crack depths and the crack initiation angles had closely similar distributions both in the in-service sample and the component wear test samples. The crack orientations were comparable to the surface shear and normal stress–strain states expectable under such surface loading conditions. It can be concluded that the test set up produced realistic wear behaviour of the roller components. The machining damage in the unused roller showed similar elements of surface deformation and cracks initiating from the graphite nodules. Some material removal had occurred by delamination of the material above the cracks initiating from the graphite nodules, which was somewhat similar to the surface fatigue in the worn rollers. However, the material removal in the unused roller occurred mostly by cutting of the matrix metal, and the cracks in the damaged sub-surface were evidently shallower than those in the worn rollers. In other words, the fatigue wear process was more severe than the machining, and the quality of the machining surface did not significantly affect the wear process after the removal of the outermost surface layer by surface fatigue.The twin-disc test disc sample made from cast iron showed notably higher maximum crack depths than did the roller samples. This was most likely caused by the higher contact pressure level. The distribution of the crack initiation angles of the disc sample in the plane parallel to the rolling–sliding motion showed a complex behaviour that has elements from both sliding and unidirectional rolling. In addition to the partial sliding, the unidirectional contact motion affected the distribution of the initial crack orientations in the twin-disc test sample. However, the wear behaviour of the twin-disc test disc appears to imitate that of the roller samples under the bi-axial contact motion quite well. By decreasing the contact pressure and increasing the sliding ratio, it might be possible to further optimise the wear behaviour simulation ability of the twin-disc test.In order to obtain a comprehensive understanding of the relation between the behaviour in the twin-disc tests and in the component operation, a complex modelling approach would be required. The model should be capable of describing both the deformation and wear responses of the twin-disc and wire rope arrangements, using a representative contact model accounting for sliding and frictional responses. Especially the resolution of the wire-rope-affiliated contacts with the required precision is a challenging task. Due to the inherent complexities of the problem, numerical solution would most probably be the best approach. If such an approach can be demonstrated, the models can be utilised to reproduce comparable contact conditions in the wire-rope-operation and in the twin-disc test.It was not clear if the cracks extending from the graphite nodules deeper into the material had actually initiated with a negative crack initiation angle, or if they had propagated purely from the graphite nodules that were deeper in the material towards those closer to the surface. It was found probable and even highly likely, that the cracks could propagate simultaneously from two nodules and merge in the metal matrix.The present analysis of the wear behaviour of nodular cast iron in contact with steel wire ropes and wires resulted in the following findings:The contact fatigue wear proceeds through surface deformation oriented towards the sliding direction and through internodular crack growth. The cracks propagate between the graphite nodules in the orientations are diagonal to the wear surface, towards both the rolling direction and the sliding direction. The propagation of the cracks to the surface, as well as the surface deformation, result in the formation of metallic deformation tongues oriented towards the sliding direction.In the roller samples, the sliding direction and consequently the deformation tongues are oriented perpendicular to the rolling directions due to the stress state caused by the torsional and bending stresses in the wire rope.Material removal proceeds through the spalling of the deformation tongues by crack growth between the graphite nodules and the surface.The distributions of the crack depths and the crack initiation angles are quite similar in the in-service roller and the two wear test rollers. In addition, the wear surfaces are similar particularly on the in-service roller and on the roller from the wear tested performed with 10 kN rope force. Therefore, the test set up employed for the present component wear testing simulates well the in-service conditions.The unidirectional sliding–rolling contact in the twin-disc test results in a distribution of the crack initiation angles that has combined aspects of the behaviour in the rolling and sliding directions of the roller samples.Increased contact pressure and radial stiffness increase the maximum crack initiation depth and promote pitting-type surface fatigue.By adjusting the contact pressure and the sliding ratio in the twin-disc test, the wear behaviour can be optimised to better simulate the contact between a roller and a wire rope.In situ mechanical properties of the chondrocyte cytoplasm and nucleusThe way in which the nucleus experiences mechanical forces has important implications for understanding mechanotransduction. Knowledge of nuclear material properties and, specifically, their relationship to the properties of the bulk cell can help determine if the nucleus directly experiences mechanical loads, or if it is a signal transduction mechanism secondary to cell membrane deformation that leads to altered gene expression. Prior work measuring nuclear material properties using micropipette aspiration suggests that the nucleus is substantially stiffer than the bulk cell [Guilak, F., Tedrow, J.R., Burgkart, R., 2000. Viscoelastic properties of the cell nucleus. Biochem. Biophys. Res. Commun. 269, 781–786], whereas recent work with unconfined compression of single chondrocytes showed a nearly one-to-one correlation between cellular and nuclear strains [Leipzig, N.D., Athanasiou, K.A., 2008. Static compression of single chondrocytes catabolically modifies single-cell gene expression. Biophys. J. 94, 2412–2422]. In this study, a linearly elastic finite element model of the cell with a nuclear inclusion was used to simulate the unconfined compression data. Cytoplasmic and nuclear stiffnesses were varied from 1 to 7 kPa for several combinations of cytoplasmic and nuclear Poisson's ratios. It was found that the experimental data were best fit when the ratio of cytoplasmic to nuclear stiffness was 1.4, and both cytoplasm and nucleus were modeled as incompressible. The cytoplasmic to nuclear stiffness ratio is significantly lower than prior reports for isolated nuclei. These results suggest that the nucleus may behave mechanically different in situ than when isolated.How mechanical forces are experienced by the nucleus has important consequences for understanding mechanotransduction (). Mechanotransduction is the process by which mechanical loads induce changes in the gene expression profile of a cell, which can ultimately alter cellular physiology and homeostasis. It has also been shown that alterations in the physical dimensions of the nucleus, resulting from an applied load on the tissue (), correlate with changes in gene regulation. Previous investigation into the mechanical characteristics of isolated nuclei suggest that they behave like a viscoelastic material and are significantly stiffer than the cell as a whole (). However, these results are possibly influenced by the fact that the nuclei were removed from their in situ environment. The nuclear lamina, the framework for nuclear structure, is intimately linked to intermediate filaments positioned throughout the cytoplasm (). Thus, mechanical properties of the nucleus may change when these connections are disrupted and the nucleus undergoes structural reorganization.In this study, a finite element modeling approach was employed to obtain cytoplasmic and nuclear stiffness values which best match previously reported cellular and nuclear axial and lateral strains obtained during unconfined compression of single-attached chondrocytes (). Based on the nearly one-to-one correlation of cellular and nuclear strains observed in that study, we hypothesized the in situ nuclear stiffness is similar to that of the cytoplasm. Further, the effects of changing both cytoplasmic and nuclear Poisson's ratios were explored to investigate the validity of the commonly used assumption of cellular incompressibility.An axisymmetric model of the chondrocyte (height=10 μm, width=12 μm) with a nuclear inclusion (radius=2.5 μm) was created using ABAQUS 6.7.1 (). The aforementioned geometric parameters were chosen to closely resemble an attached chondrocyte seeded for 3 h (). Both the nucleus and cytoplasm were modeled as isotropic linearly elastic solids. This elastic model was chosen, since the experimental data for cytoplasmic and nuclear strains were reported at equilibrium (), corresponding to long-time behavior of a viscoelastic solid (). Along the cell bottom, 4 μm of membrane was placed in frictionless contact with a rigid substrate. Preliminary analysis showed that substrate adhesiveness had no effect on the cytoplasmic and nuclear mechanical properties determined. Finally, the cell membrane was placed in frictionless contact with the compression platen. A reference point was created for the platen to which a 25 nN load was applied. The cytoplasm and nucleus consisted of 522 and 144 axially symmetric four node-reduced integration continuum elements (CAX4R), respectively. This was determined sufficient for convergence, as a model containing 2123 and 561 elements (cytoplasm and nucleus, respectively) yielded identical results.To determine the combination of cytoplasmic and nuclear stiffnesses and Poisson's ratios that best-matched observed cytoplasmic and nuclear strains (), a root-mean-square difference cost function was used, defined asδRMS=(εAxialModel(Nuc)-εAxialExperimental(Nuc))2+(εAxialModel(Cyto)-εAxialExperimental(Cyto))2+(εLateralModel(Nuc)-εLateralExperimental(Nuc))2+(εLateralModel(Cyto)-εLateralExperimental(Cyto))2δRMS was calculated for each combination of material properties. Lower δRMS values indicate that the model output more closely matched the previously reported data., cytoplasmic and nuclear strains were measured experimentally through the analysis of immunocytochemistry of cells fixed under a 25 nN compressive load. Cytomechanical testing was performed using a previously validated creep cytoindentation apparatus (), which applies controlled compressive loads onto single adherent cells. Cell to platen contact was determined by a 5 nN preload, followed by compression to 25 nN. At equilibrium deformation, chondrocytes were fixed with paraformaldehyde. After fixation, a phalloidin stain was applied for the cytoskeleton and a Hoescht's stain was applied for the nucleus. Both loaded and unloaded (control) cells were imaged with a confocal microscope, followed by three-dimensional image reconstructions. The use of fluorescent staining to examine cellular and nuclear deformations and strains has been previously described in the literature (In an initial coarse search, cytoplasmic and nuclear Young's moduli were varied parametrically at 0.5 kPa increments from 1 to 7 kPa for combinations of Poisson's ratios shown in . These search parameters were guided by literature values for Poisson's ratios and cellular stiffness (), as well as preliminary analyses confirming Young's moduli less than 1 kPa and Poisson's ratios less than 0.3 yielded higher δRMS values.Based on results from the coarse search, Young's moduli were refined to increment 0.25 kPa from 3 to 5.5 kPa for νCyto=νNuc=0.5 and νCyto=0.4, νNuc=0.5. Simulations were also performed for the cell without a nuclear inclusion to examine the contribution of the nucleus. For these cases, the cell was considered to be an isotropic linearly elastic solid with the same initial physical dimensions as before. For the cell model, cost function values were calculated using only cytoplasmic axial and lateral strains.Due to the inherent variability in any cell mechanics technique and analysis, the finite element model was examined for its sensitivity to slight changes in the experimental data of . The following three cases were studied: (1) increased axial and lateral cytoplasmic strains by 5%; (2) decreased axial and lateral nuclear strains by 5%; and (3) increased cytoplasmic strains by 5% and decreased nuclear strains by 5%. Finite element analysis was performed on the aforementioned cases for νCyto=νNuc=0.5 to yield stiffness values for the cytoplasm and the nucleus. shows minimum values computed from the cost function for each combination of Poisson's ratios, and the values of cytoplasmic and nuclear Young's moduli for which the minimum was obtained. From the initial coarse search, the ratio of cytoplasmic to nuclear stiffness was either ∼1.4 (EYCyto=3.5 kPa, EYNuc=5 kPa) or ∼1.1 (EYCyto=4 kPa, EYNuc=4.5 kPa) depending upon Poisson's ratios used. The minimum δRMS, or case most closely matching the experimental data, occurred for νCyto=νNuc=0.5, i.e., both cytoplasm and nucleus incompressible. shows the cell in its undeformed and deformed states for this minimum δRMS case. Comparing cases where cytoplasmic and nuclear Poisson's ratios were held equal, there was little effect of Poisson's ratio on δRMS, though the νCyto=νNuc=0.3 case had a different “best fit” Young's moduli than the νCyto=νNuc=0.4 or νCyto=νNuc=0.5 cases. shows a 3-D plot of δRMS as a function of EYCyto and EYNuc for νCyto=νNuc=0.5. In this refined search, the minimum Young's moduli were determined to be EYCyto=3.75 kPa and EYNuc=5.25kPa, with δRMS=0.02276. In the refined search for νCyto=0.4 and νNuc=0.5, minimum Young's moduli were determined to be EYCyto=4.0kPa and EYNuc=4.75kPa, with δRMS=0.02572. Without a nuclear inclusion, EYCell=4.25kPa, which did not change for νCell=0.4 or 0.5.Finally, experimental strains were varied to ascertain the effects of the experimental measurements on the ratio of cytoplasmic to nuclear stiffnesses. Slight changes in the experimental data of did not yield substantial differences in the calculated stiffness for the cytoplasm and nucleus. In the case. where the experimentally measured axial and lateral cytoplasmic strains were increased by 5%, the Young's moduli were determined to be EYCyto=3.0kPa and EYNuc=5.5kPa. In the alternative case, where the experimentally measured axial and lateral nuclear strains were decreased by 5%, the Young's moduli were determined to be EYCyto=3.5kPa and EYNuc=6.0kPa. Finally, when the cytoplasmic strains were increased by 5% and nuclear strains decreased by 5%, the Young's moduli were determined to be EYCyto=3.0kPa and EYNuc=6.0kPa, yielding a nuclear to cytoplasmic stiffness ratio of 2.0.Using a finite element approach, this study investigated in situ mechanical properties of the nucleus. Young's moduli and Poisson's ratio were parametrically changed for the cytoplasm and nucleus, and predicted cellular and nuclear strains were compared to known experimental results during unconfined cytocompression (). It was found that the experimental data were best-matched when EYCyto=3.75kPa, EYNuc=5.25kPa, and both cytoplasm and nucleus were incompressible. These results suggest that the ratio of nuclear to cytoplasmic stiffness is less than previously reported for single cells (). Moreover, changing Poisson's ratio had little effect on the model.Examining nuclear mechanical properties is an important step toward understanding cellular mechanotransduction. Nuclear physical characteristics change in response to an applied load on native tissue (). Enclosed within the nucleus, chromatin is organized by the nuclear lamina (). Due to cellular deformations, mechanical linkages between cytoskeleton and nuclear lamina may lead to changes in chromatin conformation/alignment and/or 3-D spatial orientation of transcription factors. Thus, understanding how the nucleus senses and responds to forces provides insight into possible gene regulatory mechanisms.The results presented in this study have applicability to current finite element models of cell–matrix interactions. These models predict the local mechanical environment of chondrocytes under various loading conditions (). When considering the cell without a nuclear inclusion, cellular Young's modulus was minimally greater than the cytoplasm itself. Moreover, the in situ difference between cytoplasmic and nuclear stiffnesses during compression is small, and variations in Poisson's ratio had little effect on Young's moduli (i.e., EYCyto=3.75kPa, EYNuc=5.25kPa for νCyto=νNuc=0.5 versus EYCyto=4kPa, EYNuc=4.75kPa for νCyto=0.4, νNuc=0.5). These results suggest that assumptions of cellular homogeneity and incompressibility may be valid simplifications for theoretical models describing chondrocytes. Supporting these simplifications, no volume change has been measured experimentally in single chondrocytes subjected to unconfined compression at strain levels below ∼30–35% (Several explanations exist for why our results differ from previously reported nuclear and cellular stiffnesses. We observed a nuclear to cytoplasmic stiffness ratio of ∼1.1 or ∼1.4 depending on the assumed combination of Poisson's ratios, whereas prior results from micropipette aspiration testing of chondrocytes and isolated nuclei suggest this ratio is 3–4 (). However, in comparison to the free-floating state in micropipette aspiration, cytoskeletal rearrangements during cell attachment for unconfined cytocompression may cause alterations in nuclear structure and decreased stiffness. Moreover, when tested in situ, connections between the nuclear lamina and cytoskeleton are intact, resulting in a more integrated mechanical framework between the cytoplasm and nucleus. Further, the cellular stiffness under compression is greater than previous micropipette aspiration results with single chondrocytes (), in which tensile forces dominate. Prior literature has confirmed that cell stiffness is greater during bulk cell compression than during local aspiration of the cell membrane (It is further important to note that the stiffness values for single chondrocytes calculated in this study coincide with measurements obtained by Knight and Bader () for cells compressed within alginate constructs. In both unconfined cytocompression and cell compression within constructs, single cells must withstand compressive forces applied onto the whole cell, and thus a similar mechanical response is expected. Additionally, the predicted stiffness value of the overall cell using our model is 2–3 times greater than previous unconfined compression results for single chondrocytes (). Since our finite element model represents the cell as an ellipsoid, which more accurately resembles the geometry of attached chondrocytes than a cylinder (), the increased stiffness is likely an effect of modeling the changing contact surface area. The contact area between the cell (represented by our geometry) and the platen in the compressed state at equilibrium is 28% of that obtained assuming the entire cell's cross-section is in contact under compression (cylindrical geometry). Thus, for the same applied force, the stress experienced by our cell would be approximately 3.6 times greater than that of a cell with an assumed cylindrical geometry. Smaller contact area results in increased stress and, hence, greater cell stiffness.Several assumptions were made for this model which could limit its representation of physical reality. First, the assumption of a spherical nucleus can potentially affect the resultant properties of the cytoplasm and nucleus. Changes in nucleus size, morphology, uniformity, and connections with the cytoplasm may alter the stress distributions applied on the nucleus, thereby changing the calculated stiffness of the nucleus. For instance, a larger contact area between the nucleus and cytoplasm could decrease the stress in the nucleus, resulting in a lower nuclear stiffness. In addition, preferential interactions between the nucleus and cytoskeleton could result in non-uniform nuclear deformations, changing the calculated stiffness values. In this study, we choose to assume a simple spherical geometry because previous finite element modeling () have used or suggested, respectively, a spherical nucleus. An additional limitation is that the cell is assumed to be in frictionless contact with the platen, which is inherently difficult to verify experimentally. This may result in variations in cell stiffness and, thus, different cytoplasmic to nuclear stiffness ratios. However, as mentioned in the previous paragraph, the high cell stiffness reported in this study may also be due to a more accurate representation of cellular geometry (). Finally, this model assumed both the cytoplasm and nucleus to be isotropic materials. Differences in the Poisson's ratio between principal directions can alter the axial and lateral strains and, thus, the calculated material properties. However, the experimental results presented by suggest a deviation from isotropy only at loads 50 nN or greater. At the 25 nN load case examined in this study, the experimental Poisson's ratio values for the cell and nucleus were 0.45 and 0.42, respectively. These values have been confirmed with other experimental testing modalities, generally yielding Poisson's ratios between 0.3 and 0.5 (). Thus, based on previous experimental work at the low loads and strains examined in our model, anisotropy was not considered. In the future, this model can be adapted to include consideration of varying nuclear morphologies, cytoskeletal and nuclear interactions, frictional contact between the cell and the compressing platen, and anisotropies.In conclusion, this study elucidated a combination of chondrocyte cytoplasmic and nuclear stiffnesses and Poisson's ratios which simulated previous results for unconfined cytocompression. In situ, nuclear stiffness was determined to be 40% more than the cytoplasm, which is lower than previously reported (). Moreover, little effect of Poisson's ratio on the model's behavior was observed, and the incompressible case best-matched the prior experimental data. These results have implications in understanding the basis of cellular mechanotransduction.Experimental implementation of a self-tuning control system for decentralised velocity feedback► Experimental implementation of decentralised self-tuning broadband vibration control. ► Decentralised velocity feedback loops are tuned to maximise their absorbed power. ► Absorbed power is estimated only using the feedback error signal. ► Maximising the absorbed power roughly minimises the structure's kinetic energy. ► An algorithm automatically adjusts the gains of each independent control unit.This paper is concerned with the self-tuning of multiple local velocity feedback loops in a decentralised arrangement. If ideal force actuators are used, the stability of each local control loop is independent of feedback gain, thus the feedback control gain can be adjusted to minimise the response of any structure where it is attached. This paper is concerned with the automatic adjustment of the local feedback gain to maximise its own absorbed power. It follows on from a promising simulation study of this tuning strategy The idea of using fundamental physical quantities such as power to individually tune the feedback controller is an intuitively appealing one and has been investigated by a number of authors In this paper we first describe the experimental set-up used to implement multiple local feedback loops on a small panel. Electromagnetic actuators are used that react off a separate framework and thus reasonably approximate ideal force devices. Although it is acknowledged that such a framework may not be available in many applications, and alternative actuators, such as inertial devices, may need to be used, we are seeking here to establish the feasibility of self-tuning in multiple feedback loops and the complexities involved in the implementation with other actuators will be considered separately.Care is taken to reduce excessive phase shift to allow stable operation over a wide range of feedback gains. This allows the transition from optimum active damping towards the cancellation of the structure's motion at control position, called here active pinning, to be demonstrated experimentally. Real time control with two feedback loops is then investigated by measuring with the estimated kinetic energy of the panel and the total power absorbed by each controller for a wide range of the two feedback gains. This paper demonstrates for the first time, in practice, that maximising the absorbed power really is a reasonable approximation to minimising the kinetic energy. Finally an automatic method of adjusting the two feedback gains is described so that their local absorbed power is minimised.The smart panel demonstrator built for this study consists of a 1 mm thick rectangular aluminium panel with dimensions 0.412×0.312 m2. As shown in , miniature voice coils actuators (H2W Technologies, model NCC01-04-001), consisting of a coil and a permanent magnet, are placed between the panel and a reactive frame. Although the panel is equipped with 9 voice coils only two have been used during the experiment described here. Since the coils are lighter than the magnets, they were attached to the panel, whereas the permanent magnets were attached to the rigid reactive frame. In this way the passive effect of the actuator on the panel is minimised. Each of the nine coil and magnet pairs is equipped with a piezoelectric accelerometer closely located with the coil. All the accelerometers are used to measure the response of the structure under control. The sensor–actuator control units are arranged as shown in the scheme of as (○) and Ch1 and Ch2 indicate the location of the two active channels.The panel's kinetic energy has been estimated aswhere |vi|2 is the mean squared value of the velocity measured at the ith accelerometer monitoring position, M is the mass of the panel and I is the number of monitoring positions. Eq. gives a good approximation of the kinetic energy of the panel in the frequency range where the distance between adjacent monitoring positions is smaller than half-wavelength. This estimate of the kinetic energy of the panel is used here to evaluate the performance of the controller, even though it is not used in the tuning process.(b), the panel is clamped between two aluminium frames. The frames have a width of 32 mm, but they have different thicknesses: 25 mm for the bottom frame and 10 mm for the top one. The clamping frame and the panel are mounted on one side of a Perspex box, which was left open during the experiments to avoid strong coupling between the panel and the volumetric mode of the cavity. The panel was excited by a shaker placed in the box. A force sensor was placed between the shaker and the panel to measure the primary force produced by the shaker. The physical properties and geometry of the smart panel and the main characteristics of the transducers are summarised in . The charge output of each accelerometer was amplified using a charge amplifier. The charge amplifiers are equipped with a high pass filter with cut-off frequency of 10 Hz and an electrical integrator in order to obtain a measurement of the velocity. shows a scheme of the experimental set-up of the self-tuning control unit. The velocity signal was amplified using a power amplifier and fed back to the voice-coil actuator. The gain of the amplifier was set to the maximum value. A digital taper-potentiometer was used to attenuate the velocity signal fed back to the actuator. The potentiometer is composed of 256 resistive sections, so that between each resistive section and both ends of the potentiometer are outputs tap points. The tap point of the resistive array is set by an 8-bit digital control signal. The control of the device was accomplished via a 3-wire serial port interface using the digital output of a data acquisition device. The attenuation provided by the potentiometer was in the range 0 dB to −48 dB with 256 possible linear steps. However, only 23 steps where selected in order to have −2 dB attenuation between successive steps.For direct local velocity feedback, the secondary force at each position, fi, is proportional to the measured velocity, vi, in each channel via a feedback gain, gi. The power absorbed by this controller is then given bywhere the symbol ⁎ indicates complex conjugate. The system is made self-tuning by using an algorithm that sequentially varies the control gain of each loop, estimates the absorbed power and adapts the control gain to maximises this power. The algorithm used in the experiments, at the kth iteration, can be written aswhere sgn[ ] signifies the sign of the parameter in brackets, ΔPi and Δgi are the differences in power absorbed and control gain between two consecutive iterations for the ith controller, with all the other control gains fixed. The parameter α(k) is the step by which the gain is increased at the kth iteration. When the power absorbed starts to decrease, the algorithm reduces the control gain by half a step and so α(k) is given bywhere the initial value of α for k=0 must be specified. More details and simulation results can be found in Ref. The velocity waveform is directly fed back to the actuator but the power is estimated off line, using the mean square velocity, and the control gain is changed in response to this estimate. Thus the tuning does not introduce any phase lag in the feedback. The panel was excited with a shaker, fed with white noise signal in the frequency band of 10–1000 Hz. The velocity measured by the sensor was acquired for 10 s and sampling frequency of 3 kHz using the analogue input of the data acquisition device. The acquired velocity signal was digitally filtered with a high-pass filter with cut-off frequencies of 52 Hz. The filter reduces the noise level at low frequency and the mains at 50 Hz, especially for high values of control gain when the measured velocity is very low. The power was calculated as the mean product of the measured velocity signal and the signal driving the actuator. This was implemented by taking the product of the velocity signal before the attenuator and that after it. The control algorithm iteratively changes the attenuation, estimates the power and adapts towards the attenuation that maximises the power absorbed by the control unit, as described in Ref. In this section the response of the controller is described in more detail. If the control-sensor pairs are dual and collocated, constant gain feedback loops are in theory unconditionally stable In order to analyse the stability of the feedback loop, the control system has been notionally divided into the blocks shown in , and the FRF of each component of the system has been measured. In this way it is easier to identify the effect of each element on the overall stability of the control loop. The reactive force actuators are made of miniature coil and magnet pairs, which have their own dynamics. The electrical admittance of the actuator, represented in by the first block, has been measured taking the voltage input signal U as reference and measuring the current I which is proportional to the force generated by the actuator (a) shows that the coil behaves like a low pass filter with a cut-off frequency of 7.3 kHz. The phase is about zero up to 200 Hz above which it starts to drop due to the inductance of the coil. The small peaks visible in the plot are due to the response of the panel. The maximum phase lag, of about −70°, occurs at around 8 kHz where the phase starts to increase again.The structural response is represented by the second block in . Since the applied force is proportional to the current, the main part of the FRF curve in (b) is what one would expect from the point excitation of a structure, with a phase between 0° and −180°. The response is characterised by resonances followed by anti-resonances. An additional phase lag of 180° appears at around 35 kHz due to the natural frequency of the B&K accelerometer.The measured FRF of the integrator in the charge amplifier is plotted in (c) when the cut-off frequency of the high pass filter is set to 10 Hz. The plots show that the integrator behaves almost like an ideal integrator over the frequency band of interest, producing the desired 90° phase shift.The amplifier used to amplify the sensors signal is the LDS PA25E voltage amplifier, its FRF is shown in (d) when the amplification gain is set on the maximum value. The response of this amplifier is almost constant at all the frequencies except for the offset of a high pass filter with a cut-off frequency of 4 Hz. shows the directly measured open loop FRF (solid line) and the one predicted using the individual measured responses of each element of (dashed line). The plot shows that the prediction is in reasonable experimental agreement with the measurement.In this section the stability of the controller is first assessed, using the Nyquist criterion. Initially the stability of a single channel system is analysed independently and then the stability of the two channel control system is studied using the generalised Nyquist criterion for multiple feedback loops. This section also describes experimental results on the performance of the control system. Firstly, real time control with a single control unit is investigated by measuring the estimated kinetic energy of the panel and the power absorbed by the controller for wide range of the feedback gain. Secondly, results on a two channels control system are discussed in order to verify possible interaction between control units.The single channel system taken as an example is number 1, placed close to the centre of the panel, although the results for channel 2 are similar and can be found in (a) shows the Nyquist plot of the sensor–actuator open loop FRF when the control gain is adjusted to the maximum value used in the experiment. (b) shows a zoom at the origin of the Nyquist plot of the sensor–actuator open loop FRFs. The plots show that the loci cross the left hand side of the diagram, indicating that the system is only conditionally stable. The gain margin, which is the maximum increase in gain that can be tolerated before the system gets unstable, given by the inverse of distance δ in (b), is about 10 dB when the control gain is set at its maximum. shows the sorted eigenvalues of the fully populated 2×2 matrix containing the sensors–actuators open loop FRFs of the two channels. The magnitude of these eigenvalues increases linearly with the feedback gains if they are assumed to be equal In this section results for real time control using control unit number 1 are discussed. (a), shows the power spectral density (PSD) of the kinetic energy of the structure from the measured velocities of the panel, estimated from the integrated outputs of the 9 accelerometers, for different values of control gain corresponding to 0, −15 and −50 dB of attenuation in the signal fed back to the actuator. (b) shows the same results obtained from numerical simulations of clamped–clamped aluminium panel of the same dimensions when the kinetic energy is calculated as the sum of the mean squared velocities at the position of the nine accelerometers using the mathematical model described in Ref. (a) and (b) represents the response of the panel for the control gain that minimises the frequency averaged response of the panel. If the control gain exceeds this value, the response of the panel increases again (dotted-line), at other frequencies, eventually creating a new set of resonance frequencies. This is due to the fact that the control loop is pinning the panel at a control position and thus the resonance frequencies of the point-constrained clamped panel are shifted up. Since the control unit is placed in the centre of the panel only the first mode is most influenced by the controller and the first resonance due to the pinning appears at around 136 Hz.The measured and simulated results are different in a number of aspects, however. The measured resonance frequencies of the uncontrolled structure are lower than the resonances calculated in the simulation. This is because the experimental boundary conditions do not produce perfect clamping. The experimental panel is clamped between two aluminium frames fixed with screws and has the first resonance frequency at about 58 Hz, compared with a calculated value of 62 Hz with fully clamped edges, although the results are close enough to make the comparison useful.To obtain broadband control, the estimated kinetic energy and power absorbed by the controller have been averaged over the frequency band from 10 to 1000 Hz. (a) shows the measured total kinetic energy of the panel, normalised to the total kinetic energy without control, plotted against the feedback gain, which is normalised by the maximum gain used in the experiment, while (c) shows the measured total power absorbed by the control unit. The measurement units of the absorbed power have been omitted because the control gain used to estimate the absorbed power is the measured attenuation introduced by the potentiometer, not the real overall value of gain as shown in . The experimental results show that the optimum value of the control gain which minimises the total kinetic energy is about −13 dB and produces a reduction in total kinetic energy of about −2.4 dB. The control gain which maximises the total power absorbed is about −17 dB and produces a reduction in the total kinetic energy of the panel of about −2.2 dB. Therefore, maximising the absorbed power produces a global structural response which is only about 0.2 dB higher than when the global response itself is minimised. This suggests that a good level of performance can be achieved with broadband excitation by maximising the power absorbed by the controller. Moreover the gradient of the total kinetic energy is very small around its minimum which means that a small error in the tuning of the control gain it does not significantly affect the total response of the structure. (b) and (d) shows the same results obtained from numerical simulations. The control gain in the simulation is normalised to the maximum control gain used in the experiments. Simulation and experimental results are in reasonable agreement. The major difference is that the maximum reduction in the response of the panel in simulation is about −1.6 dB, which is 1.8 dB less than the reduction achieved in the experiments. This could be due to the fact that the control unit in the experimental set-up is not placed exactly symmetrically compared with the actual modal shapes, so that the control unit in the experimental set-up is able to marginally control modes that are uncontrollable in the simulations.In this section the real time control of a two channels control system is discussed. In this case the estimated total kinetic energy of the structure and the total power absorbed by the two control units have been measured for a wide range of combination of the two control gains. (a) shows the total kinetic energy of the panel, estimated as the sum of mean squared velocities measured by the nine monitoring sensors normalised to the estimate total kinetic energy without control, while (c) shows the total power absorbed by the two control units as a function of the two control gains. The experimental results show that the combination of feedback gains that achieves a maximisation of total power absorbed by the two control units corresponds reasonably well to those that result in the minimisation of the total kinetic energy of the structure. A detailed analysis of (a) and (c) shows that the minimum of the kinetic energy is about −3.7 dB when the two control gains are set to −17 and −15 dB. The power absorbed by the two control units produces a reduction of −3.5 dB in the total kinetic energy of the panel when the two control gains are set to −15 dB and –15 dB. These results suggest that, for broadband disturbances, controlling the response of the panel by locally tuning each control loop to maximise its own absorbed power results in global reduction of the panel's response, as seen earlier in Ref. (b) and (d). A summary of the comparison between experimental and simulation results is shown in shows the measured (on the left) and simulated (on the right) values of the individual power absorbed by the two control units as a function of the two control gains. The results show that the power absorbed by each control unit is reduced when both control units are tuned to their combined optimal values, compared with the power absorbed when they are individually tuned in the absence of the other. The simultaneous maximisation of the local power in both control units, however, converges to the maximisation of the total absorbed power, as shown in (d). An important aspect of the experimental curves in (b), as far as a practical algorithm is concerned, is that if all the other control gains are fixed, the local power absorbed by one loop is still maximised by a single value of its control gain. Thus the adaptation can be performed as long as the estimation of the power absorbed by one channel is made when the control gain of the other is not varied. The self-tuning algorithm described in Ref. have shown that for broadband stationary excitation a similar control performance is achieved minimising the total kinetic energy of the plate or maximising the power absorbed by each of the feedback loops. This suggests that reductions in the overall vibration can be obtained by adapting the local feedback gains of the control units to maximise the total power absorbed by each control unit. In this section we describe the performance of the algorithm to maximise the power absorbed by each of the two control units, as described in Ref. shows the convergence of the algorithm in terms of the two control gains when their initial values are (a) both set to −50 dB and (b) when the control gain 1 is set to −25 dB and control gain 2 is set to −50 dB. In this example, the initial value of α, which is the step by which the attenuation is decreased at the first iteration, is 13 dB and each iteration takes about 20 s. The algorithm is programmed to stop adjusting when α becomes smaller than 2 dB, which is the limit of resolution in this case. As shown in the optimum control gains which maximises the total absorbed power are g1=−15 dB and g2=−15 dB. shows that the final setting of the two control gains in both cases is within ±4 dB of their optimum, a range of feedback gains that would result in a maximum error in the minimisation of the total kinetic energy of the structure of about 0.5 dB. Higher precision in the adaptation is difficult to achieve with the current arragement due to noise in the measurement of the control velocity. (a) shows that the algorithm converges after 22 iterations to −15 dB of attenuation for both channels. (b) shows that the algorithm converges after 21 iterations to −13 dB for channel 1 and −15 dB for channel 2. When multiple feedback units are tuned simultaneously, the power absorbed by one control unit is influenced by the other, as seen in . Therefore, the individual power absorbed by one control unit must be re-estimated, keeping the other gain constant, before this control gain is varied. One limitation of the current algorithm is thus that some global synchronisation is required for multichannel control systems to ensure the loops adapt sequentially. It may be possible to communicate the measured absorbed power between units, which would allow more global tuning strategies. Another limitation is that the level of disturbance is assumed to be constant from one step to the next so that the measured change in power is due to the change in gain rather than a change in disturbance. The performance of this self-tuning system could also be improved by reducing the noise in the measurements, so that a shorter acquisition time would be required to obtain the same accuracy. shows the PSD of the measured kinetic energy of the panel for the uncontrolled structure (solid line), when the power absorbed by the two control units is maximised (dashed line) and when the maximum control gains are implemented. The plot shows that the response of the structure is damped at the first few resonances when the power absorbed by each control unit is maximised and the first mode is fully controlled. For very high control gain the two control units are able to begin to pin the panel, so that new resonances appears in the spectrum of the structural response (dotted-line).If all nine control units installed on the panel were used, it would be necessary to include additional monitoring sensors in the estimation of the panel's kinetic energy to correctly account for the modes generated when the controller pins the structure at the control positions. In this case, simulation results with 49 monitoring sensors have shown that the total reduction in estimated kinetic energy of the panel obtained with 9 active control units is about 7.4 dB when the power absorbed by all the controllers is maximised, compared with a reduction of 8.1 dB if the 9 control gains are adjusted to minimise the kinetic energy.This paper has described the experimental implementation of a simple approach to automatically tune the frequency-independent gains of decentralised velocity feedback control loops, using only the measured error sensor signal. Previous work Experimental results for a single channel system using control unit number 2. The measured and predicted open loop FRF's are shown in , indicating the a gain margin of 10 dB. The measured and simulated PSD of the estimated kinetic energy is also shown in frictional force on rake face of ECT [N]ratio of shear stress at cutting edge and workpiece shear flow stressfriction factor at cutting edge of the toolheat flux into the tool from rake face [W/m2]heat generated in primary deformation zone [W]heat generated in secondary deformation zone [W]assumed heat flux into the tool from rake face [W/m2]energy partition entering the chips in primary deformation zonefriction energy partition into workpiecetransverse rupture strength of tool material [N/mm2]average tool temperature at the tool–chip interface [°C]thermal diffusivity of tool material [m2/s]prow angle of the workpiece directly in front of the tool [°]shear strain in the primary deformation zonefriction coefficient between workpiece and toolslip-line field angle for friction on stable build-up [°]With the advance in aviation engine technology, more and more difficult-to-cut materials are widely used in new engines, and this presents a higher demand on the processing capabilities for parts. Among the difficult-to-cut engine materials, nickel-based superalloys play an important role, and they are widely employed in aircraft engines and in the hot end components of various types of gas turbines with its high strength, strong corrosion resistance and excellent thermal fatigue properties and thermal stability (). However, its low thermal conductivity, large material plasticity, and hardening issues often result in a high cutting temperature, large cutting forces, and excessive tool wear, thereby restricting the machining efficiency.It is of evidence that most of the cutting energy is consumed by the elastic deformation, plastic deformation and friction converted to heat. argued that only a handful of energy is used for both the formation of new surface and the potential in the form of lattice distortions, thus the cutting energy consumed is considered to be all converted into heat. Consequently, different methods have been applied to investigate the cutting temperature, including analytical methods, experimental methods, numerical methods, mixed methods (including the reverse method), and heat source methods. Due to the complexity in the analytical calculation of the coated cutting tool temperature, the frequently employed analytical method is established based on the equivalent parameter method of the thermal physical parameters of coatings, and then the heat distribution and tool temperature rise equations of uncoated cutting tools are used for calculation.While for the thermal conduction analysis of coated tools, reported a new and basic geometric analysis of 3-D chips in the absence of deformation after separation from the tool rake face. numerically modeled the milling temperature by discretizing the chip thickness in the time frame during one tool revolution and using a finite difference method to predict the steady-state tool and chip temperature at each time. It should be noted that the issue of steady state modeling approach is the maximum chip thickness location. investigated thermodynamically activated effects influencing the behavior of the multi-layered coated tool rake face during orthogonal cutting of ferromagnetic and paramagnetic steels. performed numerical/theoretical analysis of dry machining to study the impact of different coating layers on the machining process. applied the accessible know-how concerning coated cutting tools and their behavior in a wide range of different machining tasks to improve the systematic selection and development of coatings for specialized cutting operations.Focusing on the effects of coating on the heat distribution and thermal conductivity, proposed a model of heat transfer in the cutting tool. An issue about whether it is appropriate to apply the heat distribution formula of uncoated tools also for coated tools was unclear. Currently, a method to solve the heat distribution of coated cutting tools has not yet established. conducted the investigation into the tool–chip contact interface temperature during turning different materials with various coated tools, indicating that the different workpiece materials and coating materials result in a variable cutting temperature.Specifically, the following explanations can be connected to the mechanism of cutting temperature using the coated tools: (1) suggested that the optimization of coating structure serves to reduce the friction coefficient at the tool–chip interface, thereby reducing the tool–chip interface temperature. For the easy-to-cut materials, the coating material with a low coefficient of thermal conductivity results in the easy conduction of heat to the chips; while for the difficult-to-cut materials, in theory, the coating should be applied to a material with high thermal conductivity so that the heat is easily transferred into the tool; (2) the further research by indicated that a low coefficient of thermal conductivity both for the tool and the workpiece results in a small contact length, thereby resulting in a decreasing tool–chip contact length, where the coating acts as a thermal barrier role; (3) verified that the lower temperature of the coated cutting tool is attributed to the decreased cutting force and tool–chip contact area; and (4) observed that a good coating friction performance, a low coefficient of friction and a small tool–chip contact area result in a decreasing coated cutting tool temperature. The above interpretations for the coated cutting tool temperature are associated with the research methods in each study. Therefore the heat generation and distribution of coated tools is worthy of further exploration. established two models with respect to the heat conduction analysis of coated tools, and dealt with a variety of tests and simulation analysis on coated tools. Because of the different research methods, scholars still hold different opinions on such a fact whether the coating influences the thermal conductivity of the tool. The first view argues that the coating only influences the thermal conductivity of the tool in the transient state, and almost has no impact in the steady state, e.g. the influence by Al2O3 coating is negligible. The second view claims that the coating has no influence on the thermal conductivity of the tool substrate in continuous cutting. However, in interrupted cutting such as milling, claimed that the internal heat conduction of the coating plays the role of a thermal barrier on the tool. The third view supported by believes that the coating influences the thermal conductivity of the tool, and reduces the tool's substrate temperature. If the coating influences the tool temperature and what characteristics the coating material with a thermal barrier has still should be investigated further. Owing to the obvious physical sense of the analytical method, it is therefore necessary to take advantage of the analytical method for the thermal conductivity analysis of the coated tools.Cutting heat is generated at three different deformation regions. For the coated tools concerned, the cutting heat transmitted to the tools is achieved through the tool–chip contact zone. Partial heat conducted to the tool leads to the tool temperature rise, and the rest is taken away by the fixed tool holder and the air. proposed a concept that divides the ball-end mill flutes into numerous wedge-shaped elemental cutting tools (ECT), and this concept has been applied in the modeling of tool temperature as well as cutting forces. The geometry of a ball-end milling cutter is shown in . In this model, it is assumed that the two adjacent points form an ECT. Each ECT performs an independent oblique cutting process ((a, left)), so the cutting forces and heat generation for each ECT can be obtained individually (For each ECT, it should be known that the chip load varies due to the rotation of the cutter. The varying chip load not only results in varying heat generation, moreover, it makes the chip-tool contact area change with time (. The cutting tool is considered to be a rectangular insert and this assumption has been adopted in stated that in order to assess the effectiveness of the thermal analysis of the machining process, steady state conditions should be achieved in the numerical simulation. However, the simulation needs to be run for a much longer cutting period on the order of a half second (). In fact, only few milliseconds of cutting time can be simulated, even in the case of 2-D simulations of orthogonal cutting conditions. Therefore, . In addition, in order to reach the steady-state conditions and to complete the outer boundary conditions during the numerical simulation, the contact heat conduction between tool and tool holder is assumed to be executed in the form of convective heat transfer.Note that the thermal property parameters of material are temperature-dependent. Set the coefficient of thermal conductivity of the tool material as k(T), and kc(T) and ks(T) denote the thermal conductivity coefficients of the tool coating and the substrate, respectively. Assuming the tool coating provides good bonding to the substrate, there is no additional thermal resistance; no specific internal heat is generated within the tool body; ambient temperature is T∞. In the Cartesian coordinate system, the steady-state heat conduction differential equations of a coated tool are listed as follows:• Heat conduction differential equations−kc(T)∂T∂x|x=0,y1≤y≤y2=h0T−T∞|x=0,y1≤y≤y2−kc(T)∂T∂y|y=0,x1≤x≤x2=h0T−T∞|y=0,x1≤x≤x2 indicate that the temperatures generated at the interface of coating and substrate are identical. Eqs. show that the heat flux is continuous in correspondence to inter boundary surface.As mentioned above, cutting heat is generated at three different deformation regions. argued that the primary and secondary deformation zones have the largest influence on the tool temperature when the cutting tool is sharp. Therefore, when performing the calculation of the tool temperature, only the heat in the primary and secondary deformation zones is considered.Tool temperature calculation follows such principles:In a machining operation, the heat transmitted to the tool is given by the sum of two parts as shown in . The first part is given by the heat conducted into the workpiece subtracted from the heat generated in the primary deformation zone, while the rest transmits to the chips. This part of heat is assumed transmitting to the tool. The second part is the heat generated in the secondary deformation zone and is assumed transmitting to the tool completely.Among the parameters to be set in the numerical simulation, the global HTC at the tool–chip interface plays a relevant role because it directly governs the temperature evolution (). A portion of the heat flowing to the tool from the primary and secondary deformation zones that should be taken away by the chips is assumed to be dissipated from the cutting tool in the form of global heat transfer, as shown in The tool temperature is the result of superposition of the above two effects as shown in The global HTC is a partitioning coefficient which governs heat transfer at the tool–chip interface. shows the heat generation and dissipation in the machining operation, in which (a) exhibits the heat propagation in the bodies and toward the environment ((b) illustrates the relationship among the assumed heat flow in the tool, the heat taken away by chips, and the actual heat flow in the tool (The assumed heat flowing to the tool is determined by Eq. where, Qp and Qs represent the heat generated in the primary and secondary deformation zones, respectively, and Rch is the energy partition entering the chips in the primary deformation zone.The assumed heat flux entering the tool from the rake face is determined by Q1 divided by the tool–chip contact area (Ac).Qp is determined by the shear force on the shear plane (Fs) multiplied by the shear velocity on the shear plane (vs).Energy partition entering the chips in the primary deformation zone is given by Eq. where, hw denotes the chip thickness before deformation (equals to the feed rate in milling process), and γsh means the shear strain in the primary deformation zone and is given by Eq. where αn is the tool normal rake angle, and ϕn is the normal shear angle.Frictional force Fγ is determined by Eq. The heat generated in the secondary deformation zone is listed as follows (Notice that λh, the chip deformation coefficient represents the ratio of chip thickness after and before deformation, and the relationship between three kinds of velocity is vs=vch−vc.Since the contact surface temperature of the chip can be considered to be nearly independent of the global HTC at the tool–chip interface (h), the physical property of h is only considered in the calculation of Q2 (where Ac is the tool–chip contact area, Tt−c is the average tool temperature at the tool–chip interface, and Tc is the initial temperature of chips. The global HTC plays a direct role as far as Q2 is concerned. Once Q1 and Q2 determined, the actual heat flowing to the tool can be expressed by Eq. Finally, the heat flux flowing to the tool from the rake face is obtained.It is well documented that the magnitude of tool temperatures, calculated using the heat flux model, was very sensitive to the h value used (). Thus the h value must be determined by estimation of the heat flux into the tool. A combination of analytical calculation, tests, and numerical calculation can be employed to determine the h value, and this method has been applied in the study by . The steps in the present study are as follows:Step 2: Set h equal to a tentative value.Step 3: Establish a two-dimensional tool model using the partial differential equation toolbox of Matlab. Input the physical parameters of the tool into the heat conduction equation by using the heat conduction equation established above.Step 4: Apply h1 into the contact boundary between the tool and the cutter bar in accordance with the model. Furthermore, apply the calculated q0 and h into the tool–chip contact length as the boundary conditions at the tool–chip interface. Finally, mesh the tool model and obtain the tool temperature distribution by numerical calculation.Step 5: Compare the calculated tool temperature on the rake face with the measured values. If the error is greater than 1%, change the h value, and this change depends on the size of the error value. If the error is relatively great (e.g., larger than 100 °C), the numerical change of h could be larger (e.g., change steps to be 1 × 104 |
W/(m2 |
K)), otherwise the numerical change of h could be small (e.g., change steps to be 1 × 103 |
W/(m2 |
K)). Repeat steps (3), (4), and (5) until the error to be lower than 1%. The flow chart is illustrated in Fcw=L∫0VB(1−τ0σ0)τ0dx+L∫VB(1−τ0σ0)VBμσ0VB−x2VBdx,ifVB<VB*Fcw=L∫0VB(1−τ0σ0)τ0dx+L∫VB(1−τ0σ0)VBμσ0VB−x2VB2dx,ifVB>VB*where σ0 and τ0 are the normal and shear stress at the tool nose, which can be calculated by the slip-line field (σ0=K1+π2−2ρ−2ϕ+2γ+sin(2γ−2ϕ),ifVB<VB*K1+π2−2ρ−2ϕ+2ηw+sin(2ηw),ifVB>VB*τ0=Kcos(2γ−2ϕ),ifVB<VB*Kcos(2ηw),ifVB>VB*γ=ηp+ϕ−sin−1(2sin(ρ)sin(ηp))ηp=0.5cos−1(mp)ηw=0.5cos−1(mw)Variable mp is the friction factor at the cutting edge, and equals to the ratio of the shear stress at the cutting edge and the workpiece shear flow stress K. assumed that mp approaches unity due to the adhesive nature of contact at the tool cutting edge. Variable ρ is the prow angle of the workpiece directly in front of the tool. If the ratio of uncut chip thickness to the width of cut is greater than 5%, the prow angle is negligible () and this is still applicable to Inconel 718 workpiece since small changes (10–20%) in the friction factor only result in 0.2–0.3% deviation of the frictional forces.The experimental shear angle values are determined by the following geometrical equation relating to the cut and uncut chip thicknesses,The experimental shear flow stress values can be obtained using model as given in the following equation, argued that since the axial depth of cut is constant for a given pass, the radial width of cut becomes the major parameter to predict the cutting force. ϕ is the shear angle, L is the width of tool cutting edge. The friction coefficient μ between the workpiece and the tool is equivalent to the friction coefficient at the tool–chip interface, because the workpiece and the chips have the same material as well as cooling conditions. Therefore, the friction coefficient μ, given by Eq. , can be solved through the frictional force and normal force in the case of a sharp tool. The forces perpendicular and parallel to the shear plane are then given by Eqs. Through geometric considerations, the far field angle is found to be:VB* is the critical wear land width when plastic flow is generated, this value can be determined by the experimental observation (where tu denotes the uncut chip thickness.where αt is the thermal diffusivity of tool material.Tests with sharp and worn tools under different feed rates are conducted for validation of the proposed model. The details of workpiece material, cutting tool material and coating, machine tool, experimental parameters, and thermal properties of the materials are described.The workpiece material used in the milling tests is Inconel 718 which has experienced the rough and semi-finish machining. The dimension of the workpiece with a blade shape is 397 mm × 113.4 mm × 26.2 mm. This Inconel 718 blade consists of convex and concave surfaces and trailing and leading edges. It contains a significant amount of iron, niobium, and molybdenum along with lesser amount of aluminum and titanium. The material has a chemical composition of 50–55% Ni(+Co), 17–21% Cr, 4.75–5.5% Nb(+Ta), 2.8–3.3% Mo, 1% Co, 0.2–0.8% Al, 0.35% Si, 0.35% Mn, 0.3% Cu, 0.08% C, 0.006% B and balance Fe (weight percent) (). The nominal ultimate tensile strength of the material is 1240 MPa, and the nominal hardness is 36 HRC (355 HV10). shows the semi-finishing workpiece to be machined by two tests with constant feed rate by a sharp tool (test 1) and variable feed rate by the same tool without obvious wear (test 2).The machine tool used in the milling tests is a five-axis Starragheckert LX 151. A rotating multicomponent dynamometer (Kistler 9123C) is mounted on the machine tool spindle to measure the three cutting force components. The voltage signal from the charge amplifier is fed to an analog to digital converter card, and it is recorded in the computer. The voltage signals are then multiplied to the appropriate scale factor for each channel to obtain the experimental force data. A sampling rate of 10,000 Hz is used to collect enough data points of the forces in tests.The workpiece is mounted through the fixture. An infrared camera Type HY-2688 is used to measure the cutting temperature distribution. This instrument can automatically measure and capture the maximum temperature in the full screen with the temperature range of 0–800 °C. Temperature resolution is 0.07 °C at the external temperature of 20 °C. The infrared camera is adapted into the machine tool, and the camera lens aims at the cutting area with a distance of 0.5 m through the door-crack. In order to make an accurate measurement during the milling process using the infrared camera with a calibrated temperature range of 250–800 °C, the emissivity at different temperatures is calibrated. The calibrated value remains at 0.3 when the coated carbide tool temperature is below 550 °C. When the tool temperature exceeds 550 °C, the emissivity sharply increases, then trends to be stable, and ultimately remains at 0.65. The setup of the machining experiment is shown in claimed that the increasing need for manufacturing of parts with complex surfaces and geometries brings additional challenges such as tool accessibility and contouring. Improper selections of process parameters result in low productivity or unacceptable part quality. One of the most important parameters in machining is the feed rate. Generally, constant feed rate is used in freeform surface machining operations (). However, in most cases the tool–workpiece engagement varies along the tool path resulting in cutting force fluctuations. presented the layout of a tool path calculation based on the NURBS, and designed a NURBS interpolator with minimal feed fluctuation and continuous feed modulation capability. The relevant literatures by indicated that feed rate optimization based on cutting force prediction can improve the quality and productivity. stated that the dimensional accuracy of the final surface becomes as important as the productivity of the machining process. Thus the productivity and the product quality for the planning of the finish milling operations should be focused. In test 1, constant feed rates including 445 mm/min at the convex and concave surfaces and 371 mm/min at the trailing and leading edges with a greater curvature are employed in practical operations by a sharp tool. The transitions of feed rate from 445 mm/min to 371 mm/min and then to 445 mm/min take place at the trailing and leading edges of the blade, successively. In test 2, the same tool observed without obvious wear was adopted. The feed rates at concave and convex surface are set to be variable in the range of 232–900 mm/min and 445–900 mm/min, respectively, and the values at the trailing and leading edges remain at 371 mm/min. The schematic diagram of feed rate by the independently developed RCStoCL software modules is illustrated in . Due to the 0.5 mm of finish allowance of this blade, an axial depth of cut 0.5 mm coupled with a cutting speed of 35 m/min are selected and kept unchanged in the two tests. All the machining operations are executed in dry conditions.Offline variable scheduling has long been of considerable interest as it is derived from the mechanistic cutting force model (). To maintain constant cutting load not only leads to smooth and reliable machining process, but also is of great significance for improving the processing quality ( evaluates a tool load to guide feed rate selection and the distance error of the machined surface. The feed rate optimization research by employed the average cutting forces which were determined by the MRR model to plan the feed rate. Limited to just the size of the cutting forces, simulated the milling forces through the instantaneous cutting force model, adopted the milling force constraints to control the variance of instantaneous milling forces, and used appropriate optimization strategies to optimize the feed rate. A recent work by presents a new and comprehensive strategy for planning minimum cycle time tool trajectories subject to both machining process related constraints, and also limitations of the feed drive control system. illustrates the optimized feed rate at the convex and concave surfaces of a blade based on the milling force constraints without considering the influence of tool wear. presents the thermal conductivities of the tool and workpiece for heat flux calculations. In addition, two important heat transfer coefficients required for cutting heat flux calculations are given in presents the experimental cutting forces by test 1. Owing to the much smaller radial component of force Fz in z-axis direction, only the feed component of force Fy in y-axis direction and the vertical component of force Fx in x-axis direction are considered in this work. In (a), when a sharp coated carbide tool is used to conduct the experiment with constant feed rate of 445 mm/min at convex and concave surfaces and constant feed rate of 371 mm/min at trailing and leading edges, the cutting forces show a slightly increasing trend and remain below 150 N. The entire machining process approximates to 18 cycles and the machining time to complete the machining area lasts about 500 s. To further analyze the individual machining cycle from the first leading edge to the next leading edge shown in (b), the cutting tool passes the convex and concave surfaces, and the maximum cutting force appears at the trailing edge of the blade which corresponds to the transition of feed rate from 445 mm/min to 371 mm/min. It is well observed that the cutting forces at the concave surface are much smaller than that at the convex surface. This is opposite to the experimental results by who explained that when a ball nose mill cuts a curved surface, a concave surface may engage with a longer cutting edge than a convex surface does, resulting in increase at the cutting forces. The explanation for the phenomenon in the present work can be associated with the curvature of the blade and the machining method. The larger curvature of the blade results in greater cutting forces, and the down milling strategy at the concave surface generates smaller cutting forces than that of the up milling strategy at the convex surface.After the completion of test 1, no obvious tool wear is observed (see tool wear photo in (a)), and the tool continues to be used for test 2. In the case of variable feed rate as shown in , the cutting forces, especially the feed component of force, strongly fluctuate and the maximum reaches nearly 500 N in the later phase. A sudden fracture of cutting tool happens after the machining process experiences 15 cycles, and excessive tool wear is observed in test 2 (see tool wear photo in (a)). Thus the entire machining time only lasts about 315 s in the cut-in phase. If no tool fracture occurs, the final machining time will be about 350 s. In order to determine the reference cutting force which is considered to avoid the tool fracture, a formula using the transverse rupture strength given by where RF represents the force considered to avoid fracture of the tool, SF means a safety factor, which is used to make up for unpredictable factors such as cutter geometry error or cutter material variation, TRS means the transverse rupture strength of the tool material, and S is the equivalent cross-section area. In this paper, SF of 0.0064 was determined in , and carbide tool with TRS of 3600 N/mm2 was used.where dt denotes the diameter of the cutting tool, and here 10 mm is used.The calculated reference cutting force is 452.2 N, slightly smaller than the maximum cutting force in (a). This well explains the tool fracture.Relative to the maximum cutting forces appeared at the trailing and leading edges of the blade in test 1, the cutting forces observed in (b) show a smooth transition at these two edges since the cutting forces are relatively smaller. The maximum cutting forces appear in the middle of the concave and convex surfaces, respectively, corresponding to the greater feed rate.Based on the cutting forces obtained, this sub-section plans to calculate the heat flux and estimate the cutting temperature. As mentioned in Section , no obvious tool wear is observed after finishing test 1, thus only heat flux into the tool from the rake face is considered to cause the temperature rise of the cutting tool. In accordance with the flow chart for the determination of global HTC shown in shows the calculated heat flux and global HTC within individual machining cycle which corresponds to the maximum cutting forces in different positions of the blade in (b). It is worth outlining that the tool–chip contact length is calculated to approximate 0.6 mm in all tests by the expression lc= |
1.92tc |
− 0.09tu (), although it is influenced by feed rate. The chip deformation coefficient, denoting the ratio of cut chip thickness (tc) to uncut chip thickness (tu) was given a mean value of 1.25 (). Temperature-dependent thermal conductivities are used in the simulations. The heat conduction coefficients of tool coating and substrate are selected as 14.5 W/(m K) and 48.5 W/(m K) at 300 °C, respectively. The ambient temperature is set to 20 °C., a dependence of the global HTC on the tool–chip interface temperature obtained by the tests and the total heat flux into the cutting tool from the rake face by the numerical calculation can be identified. For this reason, a statistical regression technique is used to fit the data, and the regression expression of global HTC is written as follows:Because of the chip obstruction in direct sensing the tool–chip interface temperature, the tool–chip interface temperature Tt–c is substituted by the maximum tool temperature Tc captured. This assumption is relatively reasonable because the maximum tool temperature separating from the tool–chip interface is only 10% smaller than the maximum tool rake face temperature ( show the estimated and measured tool temperature distribution at different positions of the blade within one machining cycle in test 1. It can be seen that, although the feed rate at the trailing and leading edges is smaller than that at the convex and concave surfaces, the temperature values at the two edges are much higher than that at the two surfaces, especially the temperature at the concave surface. The reason for the much lower temperature at the concave surface, on the one hand, is attributed to the measurement error caused by the viewing angle restrictions of the infrared camera. On the other hand, it is owing to the smooth cutting which is caused by the smaller curvature at concave surface. This can be validated by the small and stable force variance in (b). Furthermore, the estimated results in indicate that the temperature peak occurs at the tool tip, and this is a natural consequence of the modeling approach used in Section . Obviously, the results do not agree with the findings in other literatures, e.g., argued that the maximum temperature is not located right at the tool tip but at the middle of the tool–chip contact area. The difference could be attributed to the fact that the proposed model fails to consider both the chip movement and the tool wear behavior on rake face. In actual machining, the heat flux distribution along the tool–chip contact length must be necessarily non-uniform ( claimed that a parabolic heat flux would be more realistic. Note that the final drop at the tool–chip interface in is attributed to the decrease in the tool–chip contact length at the end of the cut, thus these points experience more heat loss due to air convection than heat input due to cutting. More importantly, it is intuitively observed in that the TiAlN coating influences the thermal conductivity of the tool, and 4 μm of coating thickness significantly reduces the temperature of the tool substrate. This supports the third view on whether the coating influences the thermal conductivity of the tool mentioned in Section shows the calculated heat flux and global HTC within individual machining cycle in different positions of the blade in , the global HTC shows the same behavior depending on the feed rate and tool wear state, which result in a correlated distribution of temperature and heat flux on the rake face. It is well observed that the determined coefficient is positively correlated to the total heat flux into the tool and negatively correlated to the tool–chip interface temperature. This indicates that greater feed rate and tool wear volume result in more heat into the tool and also accelerate the convective heat transfer when cooling in air. This is supported by work that the air cooling influenced the cutting temperature and enhanced the heat dissipation at the tool surface, and therefore, reduced the tool surface temperature. It is known that the total heat flux into the tool is mainly dependent on the feed rate and the tool wear state, and these two factors directly influence the tool temperature rise. shows the overall evaluation of feed rate and tool wear state effects on the tool temperature rise. In this chart, each parameter has been equally weighted. It is well explained that the increase in either feed rate or tool wear volume or the increase in both directly causes the tool temperature rise at different positions of the blade within one machining cycle. To assess the tool wear volume effects on the tool temperature rise, shown in (b) and (d), it has been found that a critical wear width of 0.3 mm leads to 28.3% and 21.3% of tool temperature rise compared to the values by a sharp tool. Correspondingly, an interesting result from (a) and (c), the tool temperature increases sharply. At the convex surface of the blade, the material removal rate (MRR) is nearly doubled (corresponding to nearly doubled feed rate), the tool temperature increases by 41.3%, and even at the concave surface of the blade, this value increases by 136%. This indicates that the tool temperature rise is more sensitive to tool wear volume than to feed rate at the convex surface of the blade, and more sensitive to feed rate than to tool wear volume at the concave surface of the blade. Taking into account the productivity and tool life, an increase in feed rate can be implemented at the convex surface of the blade to enhance the productivity, and the feed rate at the concave surface of the blade should be reduced to control the significant tool temperature rise. shows the blade surface quality after these two tests. After the use of variable feed rate to finish milling of Inconel 718 blade in dry conditions, the machining time to complete the same volume is enhanced by 30%, in other words, the MRR is nearly improved by 43%, although the tool fracture happened in test 2. To further observe the machined surface, the surface roughness along the feed direction in test 2 (average Ra 0.98 μm) is worse than that in test 1 (average Ra 0.61 μm). The explanation for this can be attributed to the tool wear occurred in test 2. Obviously, the worn tool together with higher temperature causes great influence to the workpiece surface quality when a greater and variable feed rate is employed. This is contrary to the investigation of who found that the surface roughness of Inconel 718 lowered with the increasing feed rate in a turning process. One of the interpretations is for the latter fails to consider the tool wear effect. indicates the excessive tool wear takes place after completing test 2 and this can be attributed to the fact that the temperature at the contact zone might raise or exceed the level of the resistivity of the cutting materials. This view is validated by In the proposed thermal model of a coated cutting tool, the close match between the experimental, analytical and numerical results indicates that the approach assuming a portion of the heat flowing to the tool that should be taken away by the chips, to be dissipated from the tool in the form of global heat transfer is feasible. The view on whether the coating influences the thermal conductivity of the tool has also been supported.A new model showing the dependence of the global heat transfer coefficient on two relevant interface process variables such as temperature and total heat flux into the tool is determined under different feed rate and tool wear state effects, fitting the experimental and numerical data. In this way it is possible to implement a proper h function directly in the FE numerical code in order to calculate the real amount of heat that flows between chip and tool as the temperature and total heat flux into the tool are varying during the milling process. This method can also be easily extended to other workpiece materials and machining operations.Estimation of fracture toughness (KIC) using Charpy impact test for Al6061T6 and Al7075T6 alloys subjected to corrosionFracture Toughness (KIC) is an important material property in fracture mechanics. There are numerous literatures that suggest the use of relationship between the fracture toughness (KIC) and impact strength (CVN). In this investigation, the relationship between KIC and CVN was used to determine the fracture toughness of high strength, low density Al6061T6 and Al7075T6 aluminum alloys. Accelerated corrosion was performed on these alloys using salt spray in a closed chamber for 250 h and 500 h. Pitting corrosion followed with exfoliation corrosion was noticed after prolonged exposure time which were responsible for the deterioration of mechanical properties. The experimentation results in degradation of yield strength, tensile strength, and impact strength with increase in exposure time. The yield and the impact test results were considered to estimate fracture toughness using the relations proposed by Rolfe and Barsom, Weld Research Council (WRC) and Robert and Newton. The KIC results were validated analytically using Compact Tension (CT) and Single Edge Notched Bend (SENB) specimens. The results show that, KIC decreases with increase in exposure time for all the combinations considered. Further, it was relatively observed that Al7075T6 is more susceptible to corrosion than Al6061T6.Aluminum alloys are potential replacement for conventional high strength metallic materials from decades. Their peculiar metallurgical properties of precipitation and dispersion permit their use in wide range of applications specially in components of aircraft and space shuttles to storage vessels Aluminum alloys Al6061T6 and Al7075T6 aluminum alloys purchased from Hindalco Industries Limited’ (Aditya Birla Group) were considered to investigate the effect of salt spray corrosion on impact strength and fracture toughness. shows the chemical composition of the alloys.The tensile and impact test specimens were machined following ASTM E8 The test specimens were exposed to accelerated salt spray as per ASTM B117 It was observed from the regular inspection that, inhomogeneous white and grey patches were formed at the end of 250 h of corrosion ((a, c)). The prolonged exposure resulted in pitting which visibly became larger and began to coalescence and propagate below the surface resulting exfoliation of the superficial layers The effect of salt spray corrosion on tensile properties was investigated on both alloys at 250 and 500 h of exposure with reference to the as-received sample. (a) and (b) represents the stress–strain curves for the respective alloys of 6061 and 7075. It was observed that yield strength and tensile strength decreases with exposure time in both the alloys. For Al6061, at 500 h of exposure a 29% decrease in yield strength and 19% decrease in tensile strength was observed. For Al7075, at 500 h of exposure a 28% decrease in yield strength and 33% decrease in tensile strength was observed. There was significant decrease in elongation at yield and elongation at break with increase in exposure time. The Charpy impact test was conducted to examine the influence of salt spray. The impact strength CVN show decreasing trend with increase in exposure hours. The data of yield strength σys and the impact strength CVN were used to estimate the fracture toughness KIC.The variations of σys and CVN with corrosion duration are shown in The linear elastic plane strain fracture toughness is estimated using the relationship between KIC and CVN. According to Rolfe-Barsom According to Welding Research Council (WRC) − 1981, According to Roberts R and Newton C, at WRC in 1984 where KIC represents fracture toughness in Pam, CVN is impact strength in J/m2, and σys is yield stress (tension) in N/m2To analyse the variation of fracture toughness using the relationship between KIC and CVN proposed by Rolfe –Barsom, WRC, and Robert-Newton The variation of fracture toughness with exposure time is plotted as shown in . The magnitude of KIC for Al7075 decreases significantly after 250 h of exposure in all the three cases. The overall decrease of KICat the end of 500 h of exposure for Al6061 is 31.65%, 30.21% and 30.47% and for A7075 the KICdecreases by 28.4%, 30.66%, and 28.4%.The fracture toughness values obtained from Rolfe-Barsom (Eqn. ) were identical when compared with the values of WRC (Eqn. ). Analytical computation was done using the CT and SENB (.) in accordance with the standards of ASTM E 399 to estimate linear elastic plane strain fracture toughness KICThe yield stress obtained by the tensile test was considered as the critical stress at the crack tip and the critical load ‘P’ was calculated based on Priest equations For, CT and SENB specimens KIC is estimated using the following equations:wherefaW=2+aW0.886+4.64aW-13.32aW2+14.72aW3-5.6aW41-aW32wherefaW=3aW1.99-aW1-aW2.15-3.93aW+2.7aW221+2aW1-aW32The fracture toughness for Al6061T6 and Al7075T6 alloys estimated using Eqn.6. and Eqn. 7. is tabulated as shown in The KIC shows a decreasing trend in both the alloys for CT and SENB specimens and the variations are shown in that, the magnitude of KIC for Al7075 decreases significantly after 250 h of exposure in both the cases. The overall decrease in KICat the end of 500 h of exposure for Al6061T6 is 29.13%, and 29.11% and for A7075T6, the fracture toughness decreases by 28.31%, and 28.29% for CT and SENB specimens respectively. The analytically obtained KIC values are compared with the values obtained from KIC – CVN relations as shown in it is observed that, the KIC of both the alloys decreases with increase in exposure duration for all the cases. Collectively it can be stated that, there is significant decrease in fracture toughness which results in pre-mature failure. It is also evident from the comparison () that the stress raisers at the root of ‘V’ notch of impact specimen are critically equivalent to the stress at the crack tip in CT and SENB specimens In this investigation, Al6061T6 and Al7075T6 aluminum alloys were exposed to accelerated salt spray for the durations of 250 and 500 h and following conclusions were drawn,The tensile and yield strength of the alloys decreases with increase in exposure duration. The salt spray has significant effect on mechanical behaviour occurring due to exfoliation of passive layers and formation of pits.There is a considerable decrease in impact strength of the alloys and there is consequent reduction in fracture toughness in accordance with the KIC – CVN relations.The analytical results obtained from CT and SENB specimens are in agreement with the KIC – CVN equations proposed by Rolfe –Barsom, WRC and Robert-Newton and can be used to estimate linear elastic plane strain fracture toughnessKIC.S. Sunil Kumar: Conceptualization, Formal analysis, Investigation, Methodology, Writing - original draft. Neelakantha V. Londe: Conceptualization, Supervision. K. Dilip Kumar: Conceptualization, Supervision. Mohammed Ibrahim Kittur: Writing - review & editing.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.Quantized prediction of coefficients of thermal expansion of 3-D CNT-Graphene junctioned carbon nanostructuresA computational finite element analysis based on a structural molecular mechanics approach was conducted to predict effective coefficients of thermal expansion (CTE) of a novel three-dimensional carbon nanostructure, pillared graphene structure (PGS), which is constituted with several graphene sheets and single-walled carbon nanotubes. Four sets of representative unitcell models were developed atomistically having different geometric parameters of pillar length and inter-pillar distance in the PGS. Periodic boundary conditions were applied to periodic unitcell geometries to yield consistent results. Parametric study shows that both pillar length and inter-pillar distance significantly affect the effective in-plane and through-thickness CTEs. The PGS with smaller inter-pillar distance and larger pillar length yields higher in-plane CTEs, while that with larger inter-pillar distance and smaller pillar length yields higher through-thickness CTE. The calculation yields negative through-thickness CTE at low temperatures (T<100 K) for all sets of PGSs, which is associated with the curvature at the junction.A pillared graphene structure (PGS) is a novel carbon nanostructure that possesses superior three-dimensional (3-D) multifunctional properties, such as mechanical, thermal and electrical properties and hydrogen storage capability. The PGS consists of graphene and carbon nanotube (CNT) constitutive elements as basal planes and pillars, respectively, which are interconnected to form 3-D network with CNT-graphene junctions. shows schematic views of four different unitcells of the PGSs with various geometric parameters of pillar (CNT) lengths and their inter-pillar distances. The unitcells are periodic in geometry so that they can duplicate in 3-D directions to fill the space. In the PGS, the carbon atoms are connected not only in the planar directions but also inter-layer direction, so good and tailorable transport properties can be achieved in the 3-D directions. This innovative 3-D carbon nanostructure was considered for an efficient hydrogen storage media [] because of its large surface area, and also indicated possible enhancement of both in-plane and through-thickness conductivities [], not only because of the superior properties of graphite and CNTs, but because of low interfacial resistance at the CNT-graphene junctions as well. Furthermore, these properties can be tailorable with the adjustable geometric parameters of the pillar lengths and their distances.Although this ideal 3-D network formation is not trivial to achieve experimentally, experimental work has already been pursued to fabricate and characterize the innovative 3-D carbon nanostructure. Graphene multi-layers were combined perpendicularly with upper ends of vertically aligned multi-walled carbon nanotubes (MWNTs) using chemical vapor deposition (CVD) synthesis with a bi-layer catalyst consisting of a cobalt (Co) film on a titanium nitride (TiN) film []. A CVD growth process was used to fabricate CNT pillars on large-area graphene layers using C2H2 or CH4 gas as a carbon source on an Fe-nanoparticle-decorated thin layer of e-beam-evaporated copper film deposited on a SiO2/Si substrate []. The CNT pillars were grown on graphene oxide (GO) and reduced graphene oxide (RGO) by using the CVD method with acetonitrile as the carbon source and nickel nanoparticles as the catalyst, forming a 3-D porous nanostructure of specific surfaces as high as 352 m2/g []. This work discovered that the amount and length of the CNT pillars connecting the RGO layers were controlled by changing the amount of the nickel metal catalyst and the time of CVD. The CVD method was also used to fabricated a hybrid film consisting of multilayer graphene connecting to vertical CNTs on a Si substrate [Meanwhile, several computational efforts were made to predict the multiphysical properties of the PGS with various computational methods. The hydrogen storage capability was predicted by density functional theory (DFT) []. This study revealed that this novel 3-D nanoporous material can be designed to have tunable pore sizes and surface areas, and when doped with lithium cations, can reach D.O.E's volumetric requirement for mobile applications under ambient conditions. 3-D effective thermal conductivities were predicted by atomistic molecular dynamics simulations []. This study investigated the influence of geometric aspects (e.g., CNT pillar length and the interpillar distance) on phono scattering at the CNT-graphene junctions, which could provide a significantly low resistance for 3-D thermal transport because of the carbon atoms of the same atomic mass and hybridization at the junction. The electrical transport behaviors in the PGS were studied by the DFT simulations []. The first-principles calculations identified governing transport mechanisms between metallic and semiconducting nanotubes and two graphene layers. For metallic CNTs, the conductance is nearly independent of the tube length, but changes strongly with the link structure, while the opposite occurs for semiconducting CNTs, where the conductance in the tunneling regime is mainly controlled by the tube length and independent of the link structure. 3-D effective mechanical properties, such as Young's modulus, shear modulus and Poisson's ratio, were predicted by a structural molecular mechanics method using a finite element (FE) analysis []. This study revealed a significant influence of the curved CNT-graphene junctions and discontinuous arrangement of the CNT pillars on the effective mechanical properties. Among four representative unitcell models considered, the PGSs with shorter CNT pillars yield higher planar Young's and shear moduli, while those with smaller inter-pillar distance yield higher through-thickness moduli. It was also found that the curved CNT-graphene junction resulted in negative in-plane Poisson's ratios, which could offer an opportunity of designing auxetic materials. Recently, a computational study using combined molecular mechanics and molecular dynamics simulations was conducted to predict stiffness and strength of the PGS subject to tensile and compressive loading []. It was found that non-hexagonal carbon-carbon (C-C) rings at the CNT-graphene junctions were highly probable sites of damage initiation, which could result in catastrophic failure subject to the tensile loading. Furthermore, because of columnar nature of the PGS, they are susceptible to buckling damage subject to the compressive loading.Among numerous computational efforts for predicting the multiphysical properties of the PGS, the structural molecular mechanics method is desirable because of its efficient computational scheme in dealing with huge system size without losing atomistic resolution, such as the investigation of issues associated with CNT chirality, curved CNT-graphene junctions, etc. This structural molecular mechanics approach has been used to predict mechanical elastic properties and elastic buckling of various carbon nanostructures, such as single-layer graphene, multi-layer graphite and single-walled and multi-walled CNTs []. The similar approach has also been applied to investigate the mechanical properties and elastic buckling of 2-D super carbon nanostructures []. The structural molecular mechanics method was also used to predict thermo-mechanical properties of the CNTs, such as heat capacity [], coefficient of thermal expansion (CTE) [Because of the 3-D property enhancement in terms of thermal and electrical transport properties, the PGSs can potentially be used as nano-reinforcement in multifunctional composites and nanocomposites. During the fabrication process, these (nano)composites are exposed to heating and cooling cycles, which might cause thermally-induced prestresses in the composites because of thermal mismatch between the PGS and the filling matrix. The thermal mismatch is typically attributed to the difference in their CTEs. Furthermore, the CTE mismatch can cause damage initiation when subjected to thermal cycles during operation. Therefore, it is essential to assess the CTE properties of PGS in order to utilize it properly as the multifunctional composites material.Although many aspects of the PGS properties have been discussed in the literature as stated above, to the authors' knowledge, none has been performed to study the CTE subject to temperature variation. In the present study, we have predicted the 3-D effective CTEs of the PGS by using computational models based on the structural molecular mechanics method combined with molecular mechanics simulations. The atomistic molecular mechanics simulation was conducted to form the CNT-graphene junctions and relax the whole carbon structures to a minimal energy configuration. These minimized structures were converted into a beam model having nodal points on the carbon atom sites for the structural molecular mechanics simulations. The 3-D effective CTEs of the PGS were then predicted with the vibrational eigen analysis combined with a partition function from statistical thermodynamics as well as a theory of quantum mechanics, which will be explained in detail later. Considering the fact that the eigen frequency analysis needs to be conducted to obtain natural frequencies of the PGS of all possible modes, computational efficiency is a significant factor in choosing the analysis method. In this aspect, the current simulation approach is appropriate as an efficient method. Parametric study was conducted with the various geometric parameters of the pillar length and the inter-pillar distances to determine the critical parameters that affect the effective in-plane and through-thickness CTEs of the PGS.The first step in modeling the PGS is to create the junction between the CNT and the graphene layer. A circular hole, whose diameter is similar to that of the CNT, was created in the graphene layer, as shown in (a) and (b). In order to avoid atomic vacancies and minimize defects at the junction, it is desired to have the sum of chiral vectors of a single-walled CNT (i.e., n+m) be equal to the number of inner vertices along the hole in the graphene layer. A single-walled CNT was then brought vertically to the graphene sheet near the hole. In the present study, we used (6, 6) CNT, whose diameter is approximately 0.8 nm. With this disconnected junction, an atomistic molecular mechanics simulation was then conducted to form the transitional junction between these two constituents. We utilized an energy minimization scheme built in the LAMMPS software [] using an adaptive intermolecular reactive empirical bond order (AIREBO) potential function [] to obtain an equilibrium configuration of this junctioned nanostructure with minimal energy. (c) shows the minimized CNT-graphene junction using the (6, 6) CNT and the holed graphene sheet. The simulation results in smooth and curved junction. (d) shows that the junction consists of several non-hexagonal carbon rings. In this case, six heptagons exist around the CNT-graphene junction. The formation of these heptagonal rings is a consequence of introducing curvature at the junctions and is governed by Euler's rule of polygons, which gives relationship between vertices, edges, faces and genus [After the formation of the CNT-graphene junction, a representative unitcell of the PGS was built by performing several geometrical manipulations such as translation, rotation, mirror-imaging, etc. In forming the representative unitcell model, we designed the model to be periodic in x-, y- and z-directions so that the model can be expanded in the three spatial directions without creating any missing or duplicate C-C bonds. This entire unitcell is then relaxed again by the LAMMPS software using a modified Morse potential function [] to make certain that the atomic topology (distance, angles, etc.) among the carbon atoms is at minimal energy configuration. After the final relaxation, these structures were used as a starting point for the structural molecular mechanics simulations.We considered four sets of PGSs having two graphene interlayer distances (pillar length = 1.21 nm and 3.25 nm) and two separation distances between the CNT pillars (inter-pillar distance = 2.36 nm and 3.94 nm). The inter-pillar distance is measured between center locations of two neighboring pillars (CNTs). shows top, side and isometric views of the four PGSs with their number of atoms and C-C bonds of each model. The pillar length and inter-pillar distance as well as the dimensions of the unitcell models for the four sets of PGS are listed in . Note that z is the through-thickness (pillar) direction.The 3-D CTE (αi) is expressed as the thermal strain (εi) induced by temperature variation (ΔT), so thatHere, α1 and α2 are in-plane CTE parallel to the graphene layers, and α3 is through-thickness CTE parallel to the CNT pillars. The thermal strain is an engineering strain, which is expressed as εi=ui,j . We assume that the effective thermal strain (ε¯i) is the ratio of the change of a length (ΔLi) in a given direction to the overall length (Li) in that direction, so thatThe effective CTE (α¯i) is then written asα¯i=1ΔT(ΔLiLi)=1Li(ΔLiΔT)=1AiLi(AiΔLiΔT)=1V(ΔVΔT),where V is the volume of the PGS. According to a thermodynamic relationship,where S and p are entropy and pressure in the PGS, Eq. α¯i≈−1V(ΔSΔpi)T=−1V(S2−S1pi2−pi1)T,(i=1,2,3),where the superscripts, 1 and 2, represent two stages under two different pressures. Therefore, Sk is the entropy state subject to pik pressure condition.According to statistical thermodynamics, the entropy can be expressed with a partition function (Z) aswhere kB is the Boltzmann's constant. Note that internal energy (Ei) and heat capacity (Cv) can also be obtained with the partition function asMeanwhile, the thermal transport in the carbon nanostructures in the graphene, CNT and PGS is carried by vibrational oscillators (or phonons) of various frequencies (ω). By relating the quantum mechanics of phonons, the partition function can be expressed as a product of individual partition functions due to each phonon via vibrational frequencies, so thatZ=∏j=13n−cexp(−ℏωj/2kBT)1−exp(−ℏωj/kBT),where ℏ is the Planck's constant, n is the number of carbon atoms and c is the number of constraints in the model system. The entropy is then expressed with the frequencies asS=kB∑j=13n−c[ln{exp(−ℏωj/2kBT)1−exp(−ℏωj/kBT)}+ℏωj2kBTexp(ℏωj/kBT)+1exp(ℏωj/kBT)−1].Therefore, in order to calculate the CTEs from Eqs. ), we need to obtain the vibrational natural frequencies of all possible vibrational modes in the PGS under two different deformational stages subject to two different pressure loads.To obtain the vibrational frequencies of phonons, we conducted an eigen frequency analysis using the structural molecular mechanics method and calculated natural frequencies of the PGS of all possible modes. The structural molecular mechanics modeling technique is established based on an assumption that the PGS carbon nanostructure is a frame-like structure, whose C-C bonds between two nearest-neighboring carbon atoms are treated as a beam element, whereas an individual atom acts as the nodal point of the related load-bearing beam members, as (b) shows. Because of the complex bond network in this carbon nanostructure, numerical analysis schemes, such as the FE method, are used in the calculation of the CTEs. FE nodes and elements were obtained from carbon atom sites and C-C bonds, respectively, as minimized from the molecular mechanics simulations stated above. The beam FE member has six degrees of freedom (three translational and three rotational) at each nodal point (i and j), and the corresponding nodal forces and moment components, as In formulating an elemental stiffness matrix of the beam, we need to evaluate its material and sectional properties such as Young's modulus (E), shear modulus (G), length (L), cross-sectional area (A), second moments of inertia with respect to its local y and z axes (Iy, Iz), and polar moment of inertia (J). Among them, the C-C bond length is well known to be 0.142 nm. Other properties can be obtained by considering energy equivalence between potential energy due to the covalent C-C bond interactions from the molecular model, and strain energy for axial stretching, flexural bending and torsional twisting of the beam element from the structural mechanics. In this way, it is possible to correlate the material and sectional properties of the beam element with the molecular force field constants of the C-C bond [where kr, kθ and kτ are the force field constants for the axial stretching, flexural bending and torsional twisting, respectively. The suggested values of the force field constants are kr=6.52×10−7 N/mm, kθ=8.75×10−10 N-mm/rad2 and kτ=2.78×10−10 N-mm/rad2 []. With a further assumption that the C-C bond has a circular beam section with a diameter (d), the material and sectional properties in Eq. d=4kθkr,E=kτ2L4πkθ,G=kr2kτL8πkθ2,A=πd24,Iy=Iz=πd464,J=πd432.Similarly, we can obtain an elemental mass matrix using a lumped mass scheme for the FE method. The lumped mass matrix scheme is an appropriate choice because the carbon atoms are located only at the nodal points. With the mass of the carbon atom being mc=12 g/mol, the lumped elemental mass matrix can be formulated with nonzero diagonal terms of mc/3.Based on the equation of motion for an undamped system, a system of equations for free vibrational motion can be written aswhere M and K are global mass and stiffness matrices of the PGS, respectively, and u¨ and u are nodal acceleration and displacement vectors, respectively. The global stiffness and mass matrices of the PGS are obtained from the elemental stiffness and mass matrices of the individual C-C bond, which are modeled as the beam finite elements.For a linear system, the solution of the free vibrations in Eq. where qi is an eigenvector representing the mode shape of the i-th natural frequency, ωi is the i-th natural circular frequency (radians per unit time), and t is time. Eq. The vibrational frequencies and mode shapes are then obtained from non-trivial solution of the eigenvalue problem of Eq. The solution of the eigenvalue problem results in up to m values of ω2 and m eigenvectors qi which satisfy Eq. , where m is the number of degrees of freedom (DOF) (3 times the number of nodal points) minus the number of constraints. The total number of vibrational modes of each model is shown in It is worth noting that the current approach based on the harmonic approximation of the deformation modes may not be appropriate for specific geometries such as very long CNTs. Instabilities such as buckling could occur and thus lead to failure of current model, especially when the temperature is high. However, the nanostructure of concern in this paper is the pillared graphene structure, whose CNT length is limited by the presence of the graphene layers. Therefore, it is anticipated that the instability behaviors of the CNT pillars would not drastically change at high temperatures in the case of the PGS nanostructures.The periodic geometry was ensured when we generated the unitcell models as stated in the previous section. With the periodic geometry in the unitcell models, we applied periodic boundary conditions with six constraint conditions for three translational and three rotational degrees of freedom for each pair of nodes that reside along the boundaries. Boundary nodes with two C-C bonds at one side are paired with those with a single C-C bond at the other side of the boundary. The periodic boundary conditions can be described by the following relations:{ui|x=xmin=ui|x=xmax,θi|x=xmin=θi|x=xmax,ui|y=ymin=ui|y=ymax,θi|y=ymin=θi|y=ymax,ui|z=zmin=ui|z=zmax,θi|z=zmin=θi|z=zmax,(i=x,y,z)The periodic geometry and the periodic boundary conditions were implemented into a commercial FE software, Ansys []. The eigenvalues and eigenvectors were calculated with the Ansys using a block Lanczos eigenvalue extraction method [], which is suitable for symmetric systems of equations with large number of DOFs as in the case of the PGS. The stated method employs an automated shift strategy, combined with Sturm sequence checks, to extract the number of eigenvalues requested. The Sturm sequence check also ensures that the requested number of eigenfrequencies beyond the user supplied shift frequency is found without missing any modes.With the present method, we calculated both effective in-plane (α¯1 and α¯2) and through-thickness (α¯3) CTEs of the four different types of PGSs (PGS_I, PGS_II, PGS_III and PGS_IV) shown in . Before evaluating the CTEs, we first study the cell-size effect by calculating heat capacity (Cv) of the PGS_IV using Eq. . We considered both a unitcell model and two multicell models (2 by 2 by 2 and 3 by 3 by 3) of the PGS. As shows, all three models yield nearly identical results of Cv over wide ranges of temperature, and the Cv values approach to the asymptote of 3kB with the increase of the temperature. This result indicates that in the case of the PGS, the unitcell model can capture nearly all the high-energy low-frequency modes that contribute to the accurate prediction of the thermomechanical properties including the Cv and thus the CTEs. Therefore, further analyses were conducted only with the unitcell models. show variation of in-plane (α¯1) and through-thickness (α¯3) CTEs of the four PGSs as a function of temperature. We also calculated α¯1 of a single graphene layer, and compared with a dotted line in . The parametric study conducted with various geometry parameters indicates that PGSs with smaller inter-pillar distance and larger pillar length yield higher α¯1, while PGSs with larger inter-pillar distance and smaller pillar length yield higher α¯3. It was also found that α¯3 (see ) is an order of magnitude of larger than α¯1 (see ) for all types of PGS studied. Note from that α¯1 of all four PGSs are larger than that of the graphene because the curved CNT-graphene junctions in the PGS could contribute the additional in-plane deformation subject to temperature increase. By decreasing pillar length and/or increasing inter-pillar distance, α¯1 of PGS would approach to that of the graphene (or graphite).We found that all CTEs are significantly dependent on the temperature at low temperature, but becomes less affected by the temperature at high temperature. We also found that α¯3 can have negative values at low temperatures (T<100 K). The negative CTE means that the PGS can contract with the increase of temperature, and expand with the decrease of temperature. The negative CTE can be explained as follows: With the increase of temperature, the graphene layers and CNT pillars expand in the in-plane and through-thickness directions, respectively. When the graphene layer expands laterally, the holes near the curved graphene-CNT junctions tend to expand in the radial direction, resulting in increasing the diameter of the holes and thus attributing to reducing the spacing between the two graphene layers and pillar length. Consequently, when the thermal expansion of the CNT pillars due to the temperature increase is smaller than the reduction of the pillar length due to the expansion of the graphene layers, the PGS can have a negative thermal expansion in the through-thickness direction, which occurs in the low temperature range. Otherwise, α¯3 becomes positive as shown at higher temperatures. It was reported in previous computational research by others that multi-layered graphite [] can have negative in-plane CTEs at the low temperatures.Since α¯3 tends to be negative at low temperature and then becomes positive as the temperature increases, the PGS can have zero CTE at certain temperatures. shows the temperatures at which α¯3 becomes zero. It can be seen that the temperature at the zero CTE is significantly dependent on the inter-pillar distance rather than the pillar length.We have conducted the computational study to predict the 3-D effective CTEs of the 3-D novel carbon structure, PGS, by using computational models based on the structural molecular mechanics method combined with atomistic molecular mechanics simulations. The atomistic molecular mechanics simulation was conducted to form the CNT-graphene junctions and relax the whole carbon structures to a minimal energy configuration. The carbon atom sites and carbon-carbon bonds from the minimized molecular structures were used to generate nodal points and beam elements in an FE model, respectively. We used the material and sectional properties of the beam element, which were obtained from the literature, based on the energy equivalence between the potential energy of the atomistic interactions and the strain energy of the beam deformations.The eigen analysis was then conducted to obtain the vibrational natural frequencies of all possible vibrational modes in the PGS to determine the CTEs. The periodic boundary conditions were applied to the unit cell of the PGS. The results of the unit cell were compared with those of the multicell models. From the heat capacity calculation, we found that the unitcell model can yield sufficiently accurate results as compared to the multicell models when the proper periodic boundary conditions were applied to the periodic unitcell geometry.The 3-D effective CTEs of the PGS were then predicted by utilizing the partition function from statistical thermodynamics as well as the theory of quantum mechanics. We found that all CTEs are significantly dependent on the temperature in low temperature region, but become less affected by the temperature at higher temperatures. The parametric study was conducted with the four representative unitcell models having different values of pillar length and inter-pillar distance to determine the critical parameters that affect the effective in-plane and through-thickness CTEs of the PGS. The parametric study shows that the pillar length and the inter-pillar distance significantly affect the effective in-plane and through-thickness CTEs. Overall, the PGS with smaller inter-pillar distance and larger pillar length yields higher in-plane CTEs, while that with larger inter-pillar distance and smaller pillar length yields higher through-thickness CTE. It was found that the through-thickness CTE of the PGS is an order of magnitude of larger than in-plane CTE for all types of PGS studied. We also found that through-thickness CTEs can have negative values at low temperatures (T<100 K). The temperature at the zero CTE is also significantly dependent on the inter-pillar distance rather than the pillar length. One can find the benefit of controlling the CTEs with the zero or negative CTEs for thermal, electronic, photonic and structural applications. For example, if one were to mix a negative CTE material with a positive CTE one, it could be possible to make a zero CTE composite material. Examples of such composite materials are Invar (FeNi36, a nickel-iron alloy with very low CTE), and fiber-reinforced composites with carbon fibers having the negative CTE. As the thermal expansion causes many problems in engineering, and in everyday life, there may be many potential applications for materials with controlled CTE property.Effect of in-situ formed Pr-coated Al2O3 nanoparticles on interfacial microstructure and shear behavior of Sn-0.3Ag-0.7Cu-0.06Pr/Cu solder joints during isothermal agingOur previous research has already demonstrated the positive effect of in-situ formed Pr-coated Al2O3 NPs by developing a novel method of simultaneously doping 0.06 wt% surface-active rare-earth (RE) Pr and 0.06 wt% Al2O3 nanoparticles (NPs) into Sn-0.3Ag-0.7Cu solder. It not only addressed the issue of poor interface bonding between ceramic reinforcement (Al2O3 NPs) and solder, but also simplified the most-used modified technology of pre-decorating ceramic NPs with metals to enhance interface bonding. In this study, we focused on investigating the effect of in-situ formed Pr-coated Al2O3 NPs on the evolution of interfacial microstructures and resultant shear forces of the joints soldered with SAC0307-0.06Pr-0.06Al2O3 during solid state aging. The experimental results were compared with those of Sn-0.3Ag-0.7Cu-0.06Pr and Sn-0.3Ag-0.7Cu-0.12Al2O3. It was found the joint soldered with SAC0307-0.06Pr-0.06Al2O3 possessed a delayed growth of interfacial Cu6Sn5 IMCs and an enhanced shear force. This is attributed to a synergistic relationship established between Pr atoms and Al2O3 NPs, in the form of Pr-coated Al2O3 NPs, which effectively pinned the growth and development of interfacial IMCs during high temperature aging treatment. Theoretical analysis showed that the growth constants of total interfacial IMCs (DT) at the SAC0307-0.06Pr-0.06Al2O3/Cu interface was approximately 0.64 × 10−10 cm2/s, about 47.1% and 37.3% smaller than those at the interfaces of SAC0307-0.06Pr/Cu (1.21 × 10−10 cm2/s) and SAC0307-0.12Al2O3/Cu (1.02 × 10−10 cm2/s). Even after 840 h' aging treatment, the fractograph of the shear failure joint soldered with SAC0307-0.06Pr-0.06Al2O3 still exhibited a typical ductile fracture with smaller dimples than that soldered with SAC0307-0.06Pr.The development of lead-free solders, driven by WEEE and RoHS directives, has been attached much importance to because of the existence of toxic Pb in Sn-Pb solder []. Sn-Ag-Cu high-Ag solder becomes the most promising substitute due to its good comprehensive properties []. However, its inferior drop reliability due to large bulk Ag3Sn and high price of noble metal-Ag limit its usage and thus promoting the application of Sn-Ag-Cu low-Ag solder []. The Ag content in Sn-Ag-Cu solder is lowered down, even to 0.3 wt%, which, however, triggers other issues, especially excessive growth of interfacial IMCs, thus distinctly decreases the joint's resistance to thermal fatigue []. Hence, in order to expand the application of low-Ag solder, its long-term thermal reliability should be taken seriously. As is well-known, one of the most critical factors that influence the joint reliability is the growth of interfacial IMCs during soldering and aging process, which should be well-controlled [Methods of substrate finishes, such as electrolytic Ni(Pd)/(immersion) Au [] are commonly taken to impede the growth of interfacial IMCs because these coating metals can effectively hinder atom diffusion at the interface. However, defects of black pads or pinholes generating at the Ni/Au interface after electroless nickel immersion gold (ENIG) process obviously degraded the joint reliability. In addition, complex preparation process also increases the production cost. Another effective and economical approach to control the growth of interfacial IMCs is minor alloying for solder [] and several satisfactory modified results have been reported. Various alloying metals were used, including Ni []. Among them, RE elements are the most effective modified additives for low-Ag solder since they are surface-active and inclined to be adsorbed on the grain surface of interfacial IMCs, hindering Cu and Sn atom diffusion at the interface. Recently, with the development of nanotechnology, nanomaterials (e.g., metals []) by virtue of their much higher surface free energy than bulk counterparts are becoming more and more popular to be selected as foreign reinforcements for solder. It can be concluded that for metal nanomaterials (e.g., Fe), although they are easy to be dissolved into solder and thus improves the wettability of solder, they can lead to the formation of bulk IMCs (e.g., FeSn2) either in solder matrix or at interface, which may ruin the joint reliability, particularly in a long-term service. Fortunately, carbon-based and ceramic nanomaterials performed outstandingly in restraining IMCs' growth and enhancing mechanical properties. Nai et al. [] reported that a 0.01 wt% carbon nanotubes (CNT) addition into Sn-3.5Ag-0.7Cu solder effectively hindered the growth of interfacial IMCs during aging at 150 °C and the average shear strength of the isothermally aged composite solder joints were still superior to those of the non-doped ones. Tang et al. [] reported that with aging temperature and time increased, the thickness of IMC layers of both TiO2-containing and TiO2-free solder joints increased. However, the thickness of overall IMC layer of TiO2-containing solder joint is much thinner than that of TiO2-free solder joint. The most severe issue that remained to be resolved is their poor bonding with solder matrix which may generate micro-pores and eventually ruin the joint reliability. In order to solve these issues, researchers began to make a precoating for carbon-based nanomaterials to strengthen the interface bonding with solder. Chen et al. [] successfully added Ni-CNTs into Sn-Ag-Cu solder and found the nanocomposite solder had a 19.7% and 16.9% improvement in microhardness and shear strength, respectively, when compared to the unreinforced solders. However, the synthesis of Ni-GNS process was complex, including (1) ultrasonic dispersion, (2) sensitization and activation, and (3) electroless Ni plating. Up to now, few researches were conducted on incorporating surface-modified ceramic NPs into solder, which is of great potential since the ceramic NPs are low cost, natural abundance and easy-availability. In our previous study [], Al2O3 ceramic NPs were selected as foreign additives to modify properties of Sn-0.3Ag-0.7Cu low-Ag solder and RE Pr was used as the surface-modified metal for Al2O3 NPs. Due to the surface-active characteristic of RE Pr atoms, they will be spontaneously adsorbed on the surface of Al2O3 NPs and form Pr-coated Al2O3 NPs, a core-shell structure which not only strengthen the interface bonding between Al2O3 NPs and solder, but also effectively inhibit the growth of interfacial IMC growth, and therefore enhancing the mechanical properties of solder. In addition, the incorporation technology is much more simple than the traditional pre-coating process because of the spontaneous adsorption of Pr atoms on the surface of Al2O3 NPs, which makes it possible to directly add them into solder. However, it should be noted that the content of these additives should be well managed or bulk hard and brittle IMCs, such as PrSn3 or Al2O3 agglomerations may emerge, which will degrade the mechanical properties of solder. It has already been demonstrated that when the addition content of Pr and Al2O3 NPs approached 0.06 wt% at the same time, the nanocomposite solder will attain a superior properties with refined microstructure. Although this novel nanocomposite solder has been successfully developed and also displayed a much more enhanced mechanical properties than the non-modified one, the high temperature joint reliability hasn't been studied, which is particularly critical to ensure its long-term normal work.Hence, in this work, a high temperature (150 °C) environment was exerted on the SAC0307-0.06Pr-0.06Al2O3 solder for different hours to study its high temperature joint reliability, evaluated with the shear force of corresponding solder joint. For comparison, the joint reliabilities of SAC0307-0.06Pr and SAC0307-0.12Al2O3 solders were also investigated and cited, respectively. In order to fully understand the synergistic effect of Pr and Al2O3 NPs on the high temperature joint reliability of SAC0307 solder, their growth kinetics of interfacial IMCs between solder and Cu substrate during solid-state reactions were explained in detail.Raw materials of Sn, Ag, and Cu (purity: 99.95 wt%) are melted to synthesize SAC0307 alloy in a vacuum furnace (T: 900 ± 10 °C). To avoid RE Pr oxidation, SAC0307-5Pr alloy were fabricated through firstly melting Sn5Pr with SAC0307 alloy. Afterwards, SAC03070.06Pr alloy was obtained by diluting SAC0307-5Pr with SAC0307 ingots. (a) shows the SEM image of commercially-available Al2O3 NPs. Clearly, they are regular-shaped with mean size of ∼50 nm ((b)). Their XRD analyzed results were shown in (c), which indicated that they were α-Al2O3 NPs without impurities according to JCPDS card No. 042-1468. In order to dope 0.06 wt% Al2O3 NPs (∼50 nm) into SAC0307-0.06Pr solder, a Cu foil with Al2O3 NPs wrapped in was placed on the bottom of one crucible with SAC0307-0.06Pr ingots covering on it. Then, a high-frequency induction heating technique was employed to melt the alloy protected by nitrogen (600 °C; 5 min). Joint specimens for high temperature storage (HTS) test were prepared by soldering 0805 ceramic resistors attached on a printed circuit board (PCB) (Cu/Ni/Au coating) using water-soluble flux. According to the Department of Defense of the USA (MIL-STD-883) and IPC-Association Connecting Electronics Industries (IPC-SM-785), all the joint samples were stored in a furnace at a constant high temperature of 150 °C for different hours (72-840 h). STR-1000 Micro-joint strength tester (Rhesca Co., Ltd, Japan) was used to measure the shear forces of the joints. Each measurement was repeated five times and the average value was finally taken. After shear force test, the fracture morphology of joints were observed by scanning electron microscopy (SEM) equipped with Energy Dispersive Spectrometer (EDS).To know the microstructure-property relationship, interfacial samples for high temperature storage experiment were also prepared by soldering representative solders (SAC0307-0.06Pr; SAC0307-0.06Pr-0.06Al2O3 NPs) on Cu substrate. For microstructure observation and phase identification, backscattered electron (BSE) imaging technique equipped with EDS analysis was employed. In addition, the Image Pro-plus software was also applied to measure the thickness of interfacial IMC layer. presents the SEM images of cross-sectional microstructure at SAC0307-0.06Pr/Cu interface aged at 150 °C for different hours. As shown in (a), after 72 h' aging treatment, IMCs of Cu6Sn5 and nano-sized Ag3Sn in the microstructure of SAC0307-0.06Pr solder had a little coarsening. With aging time gradually extended to 840 h ((b)-(f)), Cu6Sn5 and Ag3Sn IMCs with large size emerged. Note that as aging time prolongs, more and more Pr atoms migrate to gather nearby the interface and react with Sn to form PrSn3 phases, as shown in the magnified SEM image in . Clearly, whiskers with various shapes (e.g., buds, curly) can be observed. The EDS analyzed result showed the region marked with red rectangle in (a) contains a high concentration of elemental O besides elemental Sn and Pr. It suggests a severe oxidation of PrSn3 (Sn−RE(s)+O2(g)→RE−O(s)+Sn(s)(1)), a root cause for whiskers' growth. Detailed growth mechanism was given with the aid of the schematic diagram in . As analyzed above, PrSn3 phase exposing to the air is inclined to be oxidized following reaction (1). So, lattice expansion of PrSn3 phase occurs which induce some small cracks, enabling the internal PrSn3 phase continues to be oxidized. Consequently, many free Sn atoms are produced, moving along grain boundaries towards these small gaps and then spontaneously agglomerating with each other, forming Sn crystals. In this case, if compressive stress produced by lattice expansion is high enough, these Sn crystals will be squeezed out from the weak points or cracks of Pr oxides and finally forming Sn sprouts or whiskers with diverse morphologies. Note that the extra lateral stress provided by the growth of interfacial IMC layer also contributes more or less to squeezing whiskers []. For the interfacial microstructures of SAC0307-0.06Pr-0.06Al2O3/Cu aged from 0 to 528 h ((a)-(d)), the IMCs (Ag3Sn + Cu6Sn5) in them were still much more refined when compared with those in the interfacial microstructures of SAC0307-0.06Pr/Cu ((a)-(d)). With aging time extended to 840 h, IMCs of Ag3Sn and Cu6Sn5 ripened ((e) and (f)). But their sizes were still much smaller than those in the interfacial microstructure of SAC0307-0.06Pr solder ((e) and (f)). In this case, a few black particles emerge adhering to Cu6Sn5 IMCs, as shown in the magnified SEM image in (a). After a detailed EDS analysis of region C, these black particles were preliminarily judged as Al2O3 agglomerations based on the Al/O atom ratio ((b)). Note that elemental Pr with a very low intensity also emerges. To further confirm it, EDS mapping analysis is conducted and the results are shown in (c)–(h). It is clear that the mappings of elemental Al and O exhibit a relative bright signal at the location of black agglomerations ((f) and (g)), strongly demonstrating that they are Al2O3 agglomerations. Note that at the site of Al2O3 agglomerations, the mapping of elemental Pr also displays bright signal, suggesting the existence of RE Pr. So, it excludes the suppose that the emergence of Pr peaks in the EDS analysis is due to the signal-to-noise ratio from the electron microscope. In other words, it demonstrates the formation of Pr-coated Al2O3 NPs, one type metal-coated ceramic structure. This structure is conducive to the wettability and mechanical properties of the solder. This is because the free Pr atoms outside can work as a bridge between Al2O3 NPs and solder matrix and the nano-Al2O3 ceramic inside can effectively hinder the movements of grain boundaries and dislocations.The evolution of IMCs in the microstructures of SAC0307-0.06Pr and SAC0307-0.06Pr-0.06Al2O3 solder during aging process can be explained with the aid of . For SAC0307-0.06Pr solder, it's clear that the surface-active Pr atoms are uniformly adsorbed on the grain surfaces of IMCs to pin their growth before aging treatment ((a)-(Ⅰ)), as demonstrated by our previous research []. However, a long-term high temperature aging treatment accelerates the atom diffusion, resulting in the initial combination of Sn and Pr atom ((a)-(Ⅱ)) due to their greatest difference in the electronegativity among all the binary groups (]). In this case, the amount of free Pr atoms that can pin the IMCs' growth decreases a lot. As shown in (a)-(Ⅲ), a continuous aging treatment further accelerates the atom diffusion and PrSn3 IMC is produced as the Pr/Sn atom ratio satisfies that of PrSn3 phase. Thus the inhibited effect on IMCs' growth is largely degraded and IMCs with large size emerge. (b) presents the coupling effects of Pr atom and Al2O3 NP on the IMCs' growth in the microstructure of SAC0307-0.06Pr-0.06Al2O3 solder subjected to aging treatment. As illustrated in (b)-(Ⅰ), it's clear that a large portion of surface-active Pr atoms are adsorbed on the surfaces of Al2O3 NPs to form Pr-coated Al2O3 NPs. Due to the surface-active Pr atoms outside, these Pr-coated Al2O3 NPs can be adsorbed on the grain surfaces of relative IMCs, pinning their growth. Hence, a synergetic relationship is established between Pr atom and Al2O3 NP for the microstructure refinement. After a certain hours' aging treatment, atom diffusion become reactive, thus leading to the emergence of Sn-Pr combinations and few Al2O3 agglomerations ((b)-(Ⅱ)). In this case, Pr-coated Al2O3 NPs still hold their original state, and refining the microstructure. This reveals a retaining of synergetic relationship between Pr atom and Al2O3 NP. After a longer hours' aging treatment ((b)-(Ⅲ)), more Al2O3 agglomerations appear accompanied with few damage of Pr-coated Al2O3 NPs. So, a competitive relationship is established between Pr atoms and the remaining Pr-coated Al2O3 NPs owing to the decreased capacity of saturated adsorption on grain surfaces. Consequently, the refined effect on IMCs is weakened but still larger than that on IMCs in SAC0307-0.06Pr solder, manifested as a delay in the IMCs' growth in SAC0307-0.06Pr-0.06Al2O3 solder. show the BSE images of morphology and thickness evolution of interfacial IMC layer at the interfaces of SAC0307-0.06Pr/Cu and SAC0307-0.06Pr-0.06Al2O3/Cu, respectively. As shown in (a), with the initial 72 h' aging treatment, a continuous interfacial IMC layer with many scallop-shaped Cu6Sn5 protrudings emerging at the SAC0307-0.06Pr/Cu interface. As aging treatment prolongs to 840 h, the radius of Cu6Sn5 enlarges and its number is evidently decreased ((b)-(f)). Note that for the joint at each aging stage, a newly wave-shaped interfacial IMC layer with darker colour contrast also forms and lies at the bottom of Cu6Sn5 IMC layer, as identified to be Cu3Sn via EDS analysis ( summarizes the calculated thickness of interfacial IML producing and developing at the interfaces of SAC0307-0.06Pr/Cu and SAC0307-0.06Pr-0.06Al2O3/Cu after each aging period. Clearly, the thickness of interfacial IML (Cu6Sn5+Cu3Sn) at the SAC0307-0.06Pr-0.06Al2O3/Cu interface was much smaller than that at the SAC0307-0.06Pr/Cu interface after each period of aging treatment. For instance, after aged for 840 h, the thickness of interfacial Cu6Sn5 and Cu3Sn IML at the SAC0307-0.06Pr-0.06Al2O3/Cu interface grew to 2.1 and 2.48 μm, about 18.1% and 39.5% thinner than those developed at the SAC0307-0.06Pr/Cu interface, respectively. It is well-known that the development of interfacial IML is supposed to be a diffusion-controlled process, as described by the following classic diffusion formula [where xt is the thickness of interfacial IML aged for t, x0 is the initial thickness, D means the diffusion coefficient, revealing the growth rate of interfacial IMC layer. It can be obtained from the slope of linear fitted curve between interfacial IML thickness and aging time, as shown in . The following relationship can be obtained:T(SAC0307-0.06Pr-total)=2.87+0.11t;T(SAC0307-0.06Pr-Cu3Sn)=0.15+0.14t,T(SAC0307-0.06Pr-0.06Al2O3-total)=1.71+0.08t;T(SAC0307-0.06Pr-0.06Al2O3-Cu3Sn)=0.022+0.087t.Clearly, the growth constants of total interfacial IMCs (DT) and Cu3Sn (DCu3) at the SAC0307-0.06Pr-0.06Al2O3/Cu interface decrease from 1.21 × 10−10 cm2/s to 0.64 × 10−10 cm2/s, and from 1.96 × 10−10 cm2/s to 0.76 × 10−10 cm2/s, respectively. When compared with those growing at the SAC0307-0.12Al2O3/Cu interface [], the value of DT and DCu3 was decreased by and,respectively. gives the illustration of morphology and thickness evolution of interfacial IMCs to better understand the coupling effect of Pr and Al2O3 NPs on the interfacial IMCs' growth. As shown in (a)-(Ⅰ), before aging treatment, the surface-active Pr atoms are prone to be adsorbed on the grain surfaces of interfacial Cu6Sn5 IMCs at the SAC0307-0.06Pr/Cu interface and thus pinning their growth. After a period of aging treatment, the atom diffusion is accelerated, which lead to the first combination of Sn and Pr atom and form Sn-Pr phase ((a)-(Ⅱ)). In this case, the growth of interfacial Cu6Sn5 IMC is still impeded due to the pinning effect caused by the remaining Pr atoms. Note that the growth of interfacial Cu3Sn IMCs is also hindered. This can be explained from the standpoint of thermodynamics. Minor addition of Pr has a decrease in the diffusion flux of Sn due to their Sn-affinity characteristic []. It's well-known that the main factor that dominates the growth of interfacial Cu6Sn5 is the diffusion flux of Sn according to its formation mechanism (6Cu+5Sn→Cu6Sn5 (4); 2Cu3Sn+3Sn→Cu6Sn5 (5)). However, the development of Cu3Sn mainly relies on the Cu diffusion flux based on its formation methods of 3Cu + Sn→Cu3Sn (6) and Cu6Sn5+9Cu→5Cu3Sn (7). Although Pr addition into solder doesn't distinctly affect the Cu diffusion flux, its effect on Sn diffusion flux is obvious, which can impede the growth of interfacial Cu6Sn5 IMCs. So, both ways (R. (6) and (7)) to form interfacial Cu3Sn IMCs are hindered indirectly. A further aging treatment contributes to more formations of Sn-Pr phase, leading to a decrease in the amount of free Pr atoms. Hence, the inhibition effect contributed by free Pr atoms on the growth of interfacial Cu6Sn5 and Cu3Sn IMCs is obviously weakened. (b) presents the coupling effects of free Pr atoms and Al2O3 NPs on the interfacial Cu6Sn5 and Cu3Sn growth at the SAC0307-0.06Pr-0.06Al2O3/Cu interface. Without aging treatment, Pr-coated Al2O3 NPs are prone to distribute uniformly on the grain surfaces of interfacial Cu6Sn5 IMCs and pinning their growth ((b)-(Ⅰ)). In this case, a synergetic relationship is established between Pr atoms and Al2O3 NPs. After a long term aging treatment, accelerated atom diffusion occurs, causing the emergence of minor combinations of Sn and Pr and few Al2O3 agglomerations ((b)-(Ⅱ)). Note that Pr-coated Al2O3 NPs still remain their original structure, thus pinning the interfacial Cu6Sn5 IMCs' growth. In addition, the growth of interfacial Cu3Sn IMCs can also be hindered by decreasing the Sn diffusion flux, as explained above. However, a longer aging treatment damages the metal-coated ceramic structure due to the emergence of Al2O3 agglomerations ((b)-(Ⅲ)). Hence, a competitive relationship is established between Pr atoms and the remaining Pr-coated Al2O3 NPs due to the decreased capacity of saturated adsorption on grain surfaces. So, the refined effect on IMCs is weakened but still larger than that on interfacial IMCs at the SAC0307-0.06Pr-0.06Al2O3/Cu interface, manifested as a much thinner interfacial IMC layer at its interface.Shear test was performed to evaluate the coupling effects of rare earth Pr and Al2O3 NPs on the high-temperature joint reliability of SAC0307 low-Ag solder. gives the corresponding shear forces of this two kinds of solder joints as a function of aging time. As can be seen, the initial aging treatment decreases the shear forces of both joints soldered with SAC0307-0.06Pr and SAC0307-0.06Pr-0.06Al2O3. Note that the decrease rate of shear force for SAC0307-0.06Pr/Cu solder joint is a bit larger than that for SAC0307-0.06Pr-0.06Al2O3/Cu solder joint. However, as aging time prolongs, the shear forces of both solder joints decrease rapidly. Even so, the shear force of the joint soldered with SAC0307-0.06Pr-0.06Al2O3 is still higher than that of the joint soldered with SAC0307-0.06Pr. After 840 h' aging treatment, the shear forces of SAC0307-0.06Pr/Cu and SAC0307-0.06Pr-0.06Al2O3/Cu solder joints are decreased by 56.1% and 38.5%, respectively. This joint reliability enhancement is probably owing to the refined microstructure as well as the inhibited growth of interfacial IMCs contributed by the synergetic relationship between Pr atoms and Al2O3 NPs, as mentioned above.To further understand the fracture behaviors of the joints, the SEM images of their fracture surfaces are given in . Clearly, slant dimples parallel to the shear direction emerge on the fracture surface of SAC0307-0.06Pr/Cu joint aged for just 72 h ((a)). In addition, the EDS analysis of region E ((g)) shows that the composition of fracture surfaces is almost pure Sn. It indicates that the fracture occurs at the bulk solder. With aging time extended to 528 h, the size of slant dimples gradually becomes larger, and these joints still crack at the bulk solder ((e)). Note that there emerges an area with darker colour and a more smooth surface in this case (marked with red rectangle). The EDS analysis of point F in this area verified they are Cu6Sn5 IMCs according to the corresponding Sn/Cu ratio ( (h)). It implies that the shear crack goes through from the bulk solder to the interfacial Cu6Sn5 IMCs. With aging time increasing to 840 h, the fracture morphology of the aged joint displays more coarse and superficial dimples. It's clear that a protrusion with whiskers distributed on it grows out. This is related with the hard and brittle Sn-Pr phase formed by the accelerated migration and gathering of Pr atoms under high temperature, as demonstrated by EDS analysis of Point G ((i)). In addition, an area full of uniform and fine IMCs can also be observed, as identified to be Cu3Sn via EDS technique ( (j)). So, this implied that with aging time extended to a certain level, the fracture transfers from the bulk solder to the interfacial Cu6Sn5 IMCs and even to the Cu3Sn IMCs, as shown in . It is ascribed to the rapid growth of interfacial IMCs of Cu6Sn5 and Cu3Sn with aging time, aggravating the influence of thermal expansion mismatch among solder, interfacial IMCs of Cu6Sn5 and Cu3Sn, thus triggering the cracks. Therefore, with aging time extended, the failure mode of Sn-0.3Ag-0.7Cu-0.06Pr/Cu solder joint changes from the ductile to the mixed ductile and brittle. gives the SEM images of fracture morphology of SAC0307-0.06Pr-0.06Al2O3/Cu solder joints aged at 150 °C for different hours. For the initial 72 h, the fracture surface displays a plenty of dimples with much smaller size than that of SAC0307-0.06Pr/Cu joint ((a)). Note that the shear direction here doesn't reflect in the shape of dimples, implying SAC0307-0.06Pr-0.06Al2O3 has a higher modulus of elasticity. As aging time prolongs to 840 h, the size of dimples on the surface fracture of SAC0307-0.06Pr-0.06Al2O3 solder increases ((b)-(f)), indicative of a degradation in the ductility. Even so, their average sizes at each aging period are still smaller than those of dimples on the fracture surface of SAC0307-0.06Pr solder joint. This suggests the joint soldered with SAC0307-0.06Pr-0.06Al2O3 displays a constant better high-temperature mechanical stability than that soldered with SAC0307-0.06Pr solder. Note that some newly grown fine IMCs also emerge at the bottom of dimples on the fracture surfaces of SAC0307-0.06Pr-0.06Al2O3 solder ( (f)), as shown in the magnified SEM image of (a). By analyzed region J with EDS technique, they are identified to be Cu6Sn5 IMCs according to the Sn/Cu atom ratio ((b)). In addition, Point K (the bright IMCs) and L (the dark region) were also selected to be analyzed by EDS technique and corresponding results preliminarily show that they are Al2O3 agglomeration and Pr oxidizes, respectively ((c) and (d)). To further ascertain them, an EDS mapping analysis was also taken, as shown in (e)-(j). Clearly, the IMCs staying on the bottom of dimples mainly contain elemental Sn and Cu judged by their relatively bright colour in this region ((e) and (g)). In addition, the existence of Al2O3 agglomeration and Pr oxidizes can also be ascertained from the EDS mapping of Al, Pr, and O ((h)-(j)). These Al2O3 agglomerations and Pr oxidizes are inclined to induce cracks and accelerate the fracture process. So, a ductile failure mode for the joint soldered with SAC0307-0.06Pr-0.06Al2O3 can be ascertained and the detail pathway for it is illustrated in . The fracture pathways of these two kinds of solders are consistent with the view proposed by Deng [] that the shear strength of one solder joints is mainly dependent on the mechanical properties of the solder itself but not the thickness of interfacial IMCs. However, as interfacial IMCs grow large enough, they may become the dominant role in inducing cracks.In this work, changes of high-temperature (150 °C) interfacial microstructures and shear forces of SAC0307-0.06Pr/Cu and SAC0307-0.06Pr-0.06Al2O3 nanoparticles (NPs)/Cu solder joints were investigated and compared. The conclusions can be drawn as follows:After each time of aging treatment, SAC0307-0.06Pr-0.06Al2O3 always exhibits a more refined microstructure with smaller sizes of β-Sn phases and Cu6Sn5 IMCs than SAC0307-0.06Pr solder. This is attributed to a synergistic relationship established between Pr atom and Al2O3 NP, in the form of Pr-coated Al2O3 NP, which can delay microstructure coarsening through absorbing on the grain surface, exerting pinning effect.During aging process, two interfacial IMC layers (Cu6Sn5+Cu3Sn) were formed and gradually developed at solder/Cu interfaces and their thicknesses increased with aging time. Theoretical analysis showed the growth constants of total interfacial IMCs (Cu6Sn5+Cu3Sn; DT) and Cu3Sn (DCu3) IMCs of SAC0307-0.06Pr-0.06Al2O3 solder can be decreased from 1.21 × 10−10 cm2/s to 0.64 × 10−10 cm2/s, and from 1.96 × 10−10 cm2/s to 0.76 × 10−10 cm2/s, respectively. The decreased value of DT is mainly attributed to the pinning effect exerted by Pr-coated Al2O3 NPs on the grain boundaries' motions. The suppressed mechanism for interfacial Cu3Sn IMCs is indirectly, mainly through decreasing the concentration gradient of Sn atoms at the Cu6Sn5/Cu3Sn interface by Pr-coated Al2O3 NPs.A delay in microstructure coarsening and a much slower growth rate of interfacial IMC layer with aging time are responsible for higher shear force of SAC0307-0.06Pr-0.06Al2O3/Cu solder joint than that of SAC0307-0.06Pr/Cu solder joint. Even after 840 h' aging treatment, SAC0307-0.06Pr-0.06Al2O3/Cu solder joint still displayed a typical ductile fracture mode, while the fracture mode for SAC0307-0.06Pr/Cu solder joint transformed from ductile to a mixed of ductile and brittle.Mechanical properties of a bi-continuous Cu–Cr3C2 compositeA series of new Cu–Cr3C2 composites with a three-dimensionally continuous interpenetrating micro-structure was fabricated by porous carbide preforms using a metal infiltration process. The micro-structure and mechanical properties of the composites were investigated. Increasing the carbonisation temperature of the preforms resulted in an increase in the volume fraction of the reinforcing carbide phase and an increase in the Vickers hardness. The average value of Young’s modulus increased from 162 GPa to 202 GPa as the carbonisation temperature of the preforms increased from 1000 °C to 1300 °C. The flexural strength of the composites ranged from 710 MPa to 820 MPa, and the fracture toughness ranged from 14.8 MPa·m1/2 to 19.5 MPa·m1/2.Chromium carbide is widely used as a reinforcement phase in bulk composites and thick deposited coatings employed in extreme environments such as those involving high temperature, high wear and high corrosivity A number of Cu–Cr3C2 composites have been described in the literature In our previous study, we developed an infiltration process in which a porous Cr3C2 structure was used as a preform for the preparation of Cu–Cr3C2 composites ], where Eo is the Young׳s modulus of bulk Cr3C2 and P is the porosity, and the Vickers hardness increased from 20 to 90 kg/mm2 when the average pore size of the carbide preforms increased from 0.8 μm to 3.5 μm.In this study, we expanded on our previous work by fabricating Cu–Cr3C2 from porous Cr3C2 preforms prepared at four different temperatures, which therefore showed four different porosities. We then characterised the mechanical properties of these four types of Cu–Cr3C2 composites, including the Young׳s modulus, Vickers hardness, flexural strength and fracture toughness. The results were compared to values predicted by the mixture model.Commercial chromium oxide (Cr2O3) powder (Alfa Aesar, USA, -325 mesh, purity of 98+%) and 10 wt% polyethylene glycol (PEG-400) were mixed by ball milling in ethanol for 24 h, then dried and uniaxially compressed in a cylindrical mould under a pressure of 20 MPa to form disc-shaped samples with a diameter of 38 mm. The disc-shaped samples were pre-sintered at 150 °C for 1 h and then heated to 1000 °C for 2 h in a tube furnace (GSL 1200X, MTI Corporation); carbide preforms were subsequently obtained by carbonising samples in a tube furnace (GSL 1600X, MTI Corporation) at either 1000 °C, 1100 °C, 1200 °C or 1300 °C for 20 h; during the sintering process a carbonaceous gas mixture (10% CH4, 40% Argon and H2 for balance, Praxair Canada) was flowed through the tube furnace at a rate of 60 ml/min.The porous carbide preforms were set into an alumina crucible with pure copper powder placed on top. The crucible was covered with an alumina plate and then heated in a tube furnace (GSL 1600X, MTI Corporation) in hydrogen gas as a protective environment. The temperature of the furnace was increased from ambient temperature to 1250 °C at a heating rate of 5 °C/min and held at 1250 °C for 10 h, then cooled at a cooling speed of 5 °C/min.The sectional morphologies of the four types of composites were examined using a field emission scanning electron microscope (FE-SEM, Zeiss, EVO-MA15). The composite samples were cut and ground to rectangular shapes with dimensions of 35 mm×8 mm×1 mm such that their moduli could be characterised by dynamic mechanical analysis (DMA 8000, Perkin Elmer) at 1 Hz and room temperature to a displacement of 0.01 mm using the three-point bending mode. Five samples of each composite were prepared. The hardness of the composites was measured by a micro indentation hardness tester (Buehler, USA, IndentaMet 1100 Series) with a load of 100 g. Three samples were prepared for each composite, and ten points were measured for each sample.Flexural strength and fracture toughness measurements were conducted in accordance with ASTM C1161-02c and ASTM E1820-11, respectively. To prepare the samples, surfaces parallel to the length were sanded with SiC paper, and the surface intended for loading was finely polished using a diamond slurry (average particle size 0.5 μm). The flexural strength was measured on a FPZ100 testing machine with three point bending fixtures (Heckart, Germany), with a support span of 20 mm. The flexural strength S was calculated using the following equation:where P is the fracture load, L is the span, and b and d are the width and thickness of the specimen, respectively. The formula was obtained from ASTM C1161-02c: Standard test method for flexural strength of advanced ceramics at ambient temperature.Single edge notch bending specimens were prepared for fracture toughness testing. A V-shaped notch (with root radius of 10 µm) was formed in the center of one face of each beam, to a depth of 0.5W (where W is the beam thickness). Beams were mounted with the notched surface oriented on the opposite face to the loaded surface, with an outer sample span of 16 mm. Samples were loaded at a cross-head speed of 0.5 mm/min. Fracture toughness was calculated based on the following equations from the literature [In this equation, L is the length of the support span in the three-point bending apparatus, B is width of the specimen, and Y is a function dependent on the ratio between the notch length (α) and the thickness of the specimen (W), as described in the following equation [Y=1.964−2.387(aW)+13.711(aW)2−23.250(aW)3+24.129(aW)4. The dark-grey and light-grey areas observed in the XRD images correspond to the chromium carbide and copper phases (a–d). In addition, some black holes can be observed in the images, and the number of holes increased with increasing temperature. Based on the location of the holes (most of which were within the carbide phase), it is inferred that these holes were closed pores that were formed during the sintering process of the carbides. These closed pores are speculated to affect the mechanical properties of our composites.The Young׳s modulus of the Cu–Cr3C2 composites was tested by the DMA system, which has shown to be a useful and simple method for characterising the modulus of ceramics shows the effect of the carbonisation temperature of the Cr3C2 preforms on the Young׳s modulus and Vickers harness of our composites. The average value of the Young׳s modulus increased from approximately 162–202 GPa as the carbonisation temperature of the preforms increased from 1000 °C to 1300 °C. As indicated in our previous study, the Young׳s modulus of the unfilled Cr3C2 ranged from only 4.3 GPa to 11.0 GPa (depending on porosity) , from composites 1 to 4, the average size of each phase increased monotonically from approximately 0.8 μm to 3.5 μm, while the porosity decreased and then increased slightly. As Young׳s modulus increased monotonically from samples 1 to 4, it appears that this property is dependent primarily on the average size of each phase. The presence of voids in the composites could also play a role.A similar trend was also observed with respect to the Vickers hardness (also shown in ), which ranged between HV 257.7 kg/mm2 and HV 316.9 kg/mm2 as the carbonisation temperature of the carbide preforms was increased from 1000 °C to 1300 °C. The composite with the lowest average hardness was the one for which the preform was sintered at 1100 °C, which corresponds to the composite with the lowest volume fraction of Cr3C2. The volume fractions of hard phase Cr3C2 in the four composites was shown to be 42.1%, 36.3%, 39.9% and 42.9% for carbonisation temperatures of 1000 °C, 1100 °C, 1200 °C, and 1300 °C, respectively. As shown in , the Vickers hardness was mainly related to the volume fraction of the hard phase in the composites. This pattern differed from the trends observed previously for the Vickers hardness of unfilled carbides The high hardness values measured for our Cu–Cr3C2 composites agree well with values reported in the literature. Larsson et al. determined the hardness HV of chromium carbide–copper composites with volume fractions of 54% and 60% chromium carbide to be 750 kg/mm2 and HV 850 kg/mm2, respectively Many models have been developed to describe the relationship between the mechanical properties of composites those of their components, such as the upper bound of “rule of mixtures” and the lower bound of “rule of mixtures”where M is a specific mechanical property, V is the volume fraction of component, the subscripts c, r and m represent the composite, the reinforcement and metal phase, respectively. Actually, most of the models can be summarised to a “generalised mixture rule” (GMR), which was proposed by Ji in 2004 where i represents the ith phase, composites consist of N phase, J refers to a micro-structural exponent that is a scaling, fractal parameter controlled by the nature of interface boundaries, phases geometry, size distribution, continuity, connectivity and so on. When the composites consist of only two phases, the expression can be simplified as follows:When the phases are well-adhered and well-ordered (for example, the phases consist of anisotropic, aligned particles or layers of material), J=1, and Eq. . When the phases are weakly adhered and are irregular in shape, J=−1, and Eq. . In other cases, the value of J is between −1 and 1 (except 0) for real materials.The correlations between the Young׳s modulus and the Vickers hardness to the volume fraction of reinforcement Cr3C2 in our composites were fit by using the OriginPro 8.5 software program, as shown in (a) and (b), respectively. It can be observed that all of the experimental data for both the Young׳s modulus and Vickers hardness were scattered between the two ideal curves (J=1 and J=−1). The values of J=0.288 and 0.156 were fit from the Young׳s modulus (a) and Vickers hardness (b) measurements, respectively, which may offer a promising approach for the prediction of the Young׳s modulus and Vickers hardness of this type of Cu–Cr3C2 composite. In this case, J was mainly controlled by the copper and chromium carbide interface boundary, closed pore, phase geometry and connectivity and so on.Flexural strength and fracture toughness are two other important mechanical properties of brittle materials. Generally, metals have higher fracture toughness and lower flexural strength than ceramics; ceramic–metal mixtures tend to exhibit intermediate values. shows the effect of the carbonisation temperature of the Cr3C2 preforms on the flexural strength and fracture toughness of the Cu–Cr3C2 composites. The average value of the flexural strength dropped from 820 MPa to 710 MPa as the carbonisation temperature was increased from 1100 °C to 1200 °C, and then it rose slightly to 729 MPa when the temperature was increased to 1300 °C. Typically, ceramics exhibit higher flexural strength than metals. The flexural strength of the composites was generally dependent on the volume fraction of the ceramic phase, but in our composites, the one with the lowest volume fraction of carbide phase (at 1100 °C) presented the highest average flexural strength. Peng et al. also observed a similar correlation in interpenetrating Si3N4–Al composites , the average value of fracture toughness (KIC) did not change considerably as the carbonisation temperature of the carbide preforms was elevated from 1000 °C (19.3 MPa m1/2) to 1100 °C (19.5 MPa m1/2); upon further heating to 1300 °C, the fracture toughness decreased slightly to 14.8 MPa m1/2. Generally, metals are much tougher than ceramics: the higher the volume fraction of the ductile metal phase is, the higher the fracture toughness of composites becomes. However, as shown in , material 3 exhibits a higher volume fraction of ductile copper than does material 1, but its fracture toughness is lower than that of material 1. This discrepancy should be attributed to differences in micro-structure and average grain size and the fact that close pores caused the KIC of material 1 to be higher than that of material 3. Based on the values measured for materials 2–4, it can still be concluded that the fracture toughness of the Cu–Cr3C2 composites was mainly affected by the volume fraction of the ductile metal phase. Larsson et al. indicated a fracture toughness 8 MPa m1/2 for the Cu–Cr3C2 composites containing 40% copper shows the morphologies of crack tips on the four different Cu–Cr3C2 composites after the three-point bending test. It can be observed that most of the cracks extended along the interface between the carbide and copper phases, whereas only a few crossed through the brittle carbide phase. Cracking generally starts from locations with weak micro-strength. In our composites, the stress was concentrated at the ceramic–metal interface and near the defects introduced by unfilled close pores, which made those locations weaker than those within the Cr3C2 and copper grains. These findings explain why crack propagation was observed mostly along the Cu and Cr3C2 interface and sometimes traversing the close pores in Cr3C2 grains.The new Cu–Cr3C2 composites examined in this study possess a homogeneous, bi-continuous micro-structure. The Vickers hardness of the composites was mainly affected by the volume fraction of reinforcement Cr3C2 in the composites, which was increased from HV 257.7 kg/mm2 to HV 316.9 kg/mm2 when the volume fraction of the carbide phase increased from 36.3% to 42.9%. The average value of the Young׳s modulus increased from 162 GPa to 202 GPa as the carbonisation temperature for the preforms increased from 1000 °C to 1300 °C. The flexural strength of the composites was measured to be in the range of 710–820 MPa. The value of this property depended comprehensively on the volume fraction, micro-structure and binding strength of the components in the composites. Metal infiltration can greatly improve the fracture toughness of chromium carbide ceramics, and the KIC of our Cu–Cr3C2 composites can reach as high as 19.5 MPa m1/2.Quality retention in strawberries dried by emerging dehydration methodsIn this study the effectiveness of drying methods – vacuum microwave drying (VMD), hot air drying (AD), convective air drying combined with vacuum microwave drying (AD-VMD) and osmotic dehydration followed by vacuum microwave drying (OD-VMD) – and their effects on both physicochemical and structural changes in strawberries are compared. Drying performance was assessed by drying rate, moisture content and water activity, while changes in quality attributes of strawberries were determined by measuring color, texture, microstructure, shrinkage and rehydration ratio. A maximum drying rate of 6.74 × 10− 4 |
kg water/(kg dry matter s) was found for microwave-assisted drying, which results into a product of intermediate water activity. Combining VMD with osmotic dehydration or air drying did not improve drying efficiency. VMD yields an elastic product of improved mechanical resistance with just a slight loss of color and an appropriate rehydration performance. Preliminary dehydration using hot air or sucrose solution was not able to improve most of the quality attributes of strawberries.Drying of foods is particularly important for handling and distribution of raw materials with high moisture content and limited shelf-life such as fruits and vegetables. The main objective of drying of food products is to remove free water to a level where microbial spoilage is reduced and where a shelf stable, less perishable product is ensured. Fruits dehydrated by convective drying should have a moisture content of 20–25%, i.e. 0.33 kg water/kg dry matter to assume a prolonged shelf-life (In drying, applied external heat evaporates surface moisture, while internal moisture may be forced to the surface and then evaporated. Moisture can also be evaporated internally and then transported to the surface. The transfer of heat depends on the air temperature, air humidity, air flow rate, pressure, surface area, the physical nature of the material as well as its composition and the process by which the heat is transferred to the material be it by conduction, convection or by radiation (). In addition, diffusion is the dominant physical mechanism governing moisture movement in strawberry drying (). Most conventional dryers operate at atmospheric pressure under steady drying conditions using hot air as a drying medium and convection as the mode of heat transfer (). Besides, convective drying consists of passing heated air through layers of products, such as apples, plums, herbs and vegetables (). Convective drying has several limitations, e.g. non-uniform product quality (), case hardening of the product surface (), significant change of color compared with the original product () and changes in physical, chemical and sensory attributes (), which gives rise to low drying performance and high operating costs. Other traditional methods of drying are, although inexpensive, slow and unpredictable, or slow and expensive. Therefore, emerging drying methods based on the potential of microwaves have been studied to reduce drying time while preserving the quality for a number of food products () can be further improved by combining pretreatments such as osmotic dehydration or convective drying, with microwave-convective or microwave-vacuum drying.Strawberries (Fragaria ananassa) are one of the most delicate and perishable fruits with a very high respiration rate, weight loss and susceptibility to fungal attack. Strawberries are highly valued due to their sensory properties, particularly sweetness and aroma attributes being determinant for their quality (). On the other hand, color is the key property governing the initial acceptability of any food, while mechanical properties are one of major interest in order to characterize the first bite and microstructure of food. Therefore, the food industry is looking for new alternative, inexpensive preservation methods yielding minor alterations in the main attributes of processed strawberry fruits.The purpose of this study was to compare the effectiveness of drying methods – vacuum microwave drying (VMD), hot air drying (AD), convective air drying combined with vacuum microwave drying (AD-VMD) and osmotic dehydration followed by vacuum microwave drying (OD-VMD) – for strawberries and to compare both physicochemical and structural changes caused by these methods that would affect final product quality.Fresh strawberries (Fragaria ananassa, cv. San Andreas), harvested in 2011 and 2012, were supplied by Agrofrutillas San Pedro S.A. (Melipilla, RM, Chile). After removing unripe and damaged fruits, berries were selected according to size and color. After removal of stem and sepals of individual, unwashed strawberries, these were stored at 5 °C for maximum 24 h.Analyses of the composition of fresh strawberries were done in triplicate according to the recommendations of . Moisture content of strawberries was determined by gravimetry using an oven (Gallenkamp, hotbox oven, size one, UK) for 48 h at 70 °C and an analytical electronic balance FA2104N with an accuracy of ± 0.0001 g (AOAC 20.013). Soluble solids were measured with a refractometer (Abbe Atago N-1e, Japan) (AOAC 932.12). The pH of puréed strawberries was measured with a pH-meter (OAKTON, pH 510 series, Singapore) (AOAC 981.12). Diluted solution of puréed strawberries was titrated with 0.01 N NaOH, using phenolphthalein as indicator, where titratable acidity was expressed as weight percentage of citric acid in fresh sample (AOAC 942.15). Strawberry samples were characterized by an initial moisture content of 90.4 ± 1.3% (w/w), soluble solids of 8.0 ± 0.8 °Brix, pH of 3.56 ± 0.11 and tritatable acidity of 0.85 ± 0.13% (w/w).Drying experiments were performed at the maximum load of the drying equipment. Strawberry samples were dried to a mean final moisture content of 28% wet basis. These samples were cooled to ambient temperature, packed and stored at 5 °C for evaluating water activity, color, texture, structure and rehydration performance. Four drying techniques were investigated in this study.In convective air drying (AD), 12.7 kg of strawberries was air dried at 70 °C for 10 h in the Proctor-062 tray dryer (Proctor & Schwartz Corp., Philadelphia, PA, USA), using vertical air flow through six trays in a closed circuit. The air velocity inside the drying cavity was kept constant at 1.70 m/s with a relative humidity of air of about 5%. The sample was weighed using an electronic balance (Gibertini, TMB25AR, Gibertini, Italy) with an accuracy of 0.1 g. Weighing intervals of 5 min were used during the first hour of drying, 15 min for the second hour, 30 min for the third hour and then 1 h until the end of the process.Vacuum microwave drying (VMD) of strawberries was done using a custom made, Airmax lab-scale microwave vacuum dryer (700 W, 2450 MHz) (). In the cavity of the microwave oven, three static horizontally stapled acrylic trays (width: 10–13 cm; length: 17 cm) covered with adsorbent paper and supported by rear and front acrylic disks (diameter: 14 cm) were used to distribute a sample of maximum 250 g of strawberries. Individual berries were separated 1 cm from each other to allow individual drying. Trays were completely covered by a vertical cylindrical container (diameter: 18 cm; length: 24 cm; thickness: 6 mm) made of black polyethylene, which allows passage of microwaves. This container was adjusted to a circular slot at the rear side of the oven for hermetical sealing during operation, where sub-atmospheric pressure was provided by a vacuum pump. Condenser with refrigeration liquid (− 10 °C) and condensate trap were connected in-line with the vacuum hose to remove moisture from sub-atmospheric air before reaching the vacuum pump. Absolute pressure was controlled by a manometer and maintained in the range of 10 to 70 mm Hg by the vacuum pump and a vent for air inlet. Four probes of optical fiber (model TMI4, FISO Technologies Inc., Canada) for temperature measurement were inserted in the center of different berries. The vacuum microwave drying system operated for 3 h at a temperature of 50 ± 1 °C, removing the excess of microwave heat by recirculation of cold water between two polypropylene containers outside the vacuum chamber and by using an on–off temperature control system for the magnetron after the first 20 min after starting each experiment. Then the microwave control system was switched off, but the vacuum drying conditions were maintained for one extra hour.A heating oven with mechanical convection (Binder FD 53, Tuttlingen, Germany) was used in the preliminary drying step using an air temperature of 50 °C and an air velocity of 1.0 m/s. The drying system consisted of a horizontal airflow through three trays arranged as a closed circuit. For air heating, electrical resistances of 1200 W were used and manually set into operation by a digital thermostat. A digital hygro thermometer anemometer (Omega Engineering, Inc., model HHF710, Stamford, CT, USA) was used to measure air temperature and velocity. A sample of about 1.1 kg of fresh strawberries was weighed using a semi-analytical balance with a resolution of 0.1 g. Weighing intervals of 2 h were used for 48 h until the moisture content became 50% (w/w) followed by the vacuum microwave drying operation.After applying a vacuum pulse (70 mm Hg absolute pressure for 10 min) at the beginning of the process, osmotic dehydration (OD) was carried out at atmospheric pressure and ambient temperature for 4 h. Five 80 g samples of strawberries were taken and mixed with a sucrose solution of 60% (w/w) that was used as hypertonic solution, being the ratio of solution–fruit (12.5:1 (v/w)) high enough to avoid significant changes in concentration of the solution over time. Mass transfer was enhanced by shaking at 140 rpm (orbital shaker, Ilshin Lab. Co. Ltd., South Korea). Afterwards, dehydrated strawberries (250 g) were drained, rinsed with distilled water to remove the excess of sucrose solution and the excess of external moisture was removed with adsorbent paper. Then fruits were put on a previously weighed drying tray in order to continue drying by using vacuum microwave heating (VMD).In order to account for the performance of each drying method, the drying rate was calculated from the amount of water removed by dehydration per kilogram of dry matter per second of operating each dryer at full load.where W0, W(t) and Wd are the initial weight of the sample, its weight after dehydration and its dry mass, respectively, and Δt is the time interval of dehydration.The portable instrument ms1 Set aw (Novasina, Lachen, Switzerland) was used to measure the water activity at 26 ± 0.3 °C of the following strawberry samples: VMD (4 h), VMD (2 h), VMD (3 h) and raw material. Prior to using the device, the instrument was calibrated using saturated salt solutions of known relative humidity. Moisture content of strawberry samples was determined in triplicate in the Gallenkamp hotbox oven (OVB-300-010 N, Gallenkamp, London, UK) at 70 °C until constant weight (The Guggenheim, Anderson and de Boer (GAB) model (Eq. (2)) was used to describe dry basis moisture content (X) as function of water activity (aw):where C and K are constants and X0 is the monolayer moisture content on dry basis (kg/kg). Model parameters were estimated by direct nonlinear weighted regression analysis using the SPSS 15.0 software for Windows. Fitting of the parameters was carried out by minimizing the sum of the residual error. Regression procedure was started by using the values reported by (Color of fresh and dehydrated strawberries was measured by means of the degree of redness or greenness (± |
a), the degree of yellowness or blueness (± |
b) and the degree of lightness (L), using the Color Quest II Hunterlab colorimeter (Hunter Associates Laboratory, Inc., Reston, VA, USA). This instrument was calibrated at the beginning of each experiment with a white ceramic plate. Results were expressed in a⁎, b⁎ and L⁎ color coordinates of the Commission Internationale de l'Eclairage (CIE). Values of hue (h0), chrome (C⁎) and difference of color to fresh sample (ΔE) were calculated from a⁎, b⁎ and L⁎ values by the following equations (where Δa |
= (a⁎f |
− |
a⁎0), Δb |
= (b⁎f |
− |
b⁎0) and ΔL |
= (L⁎f |
− |
L⁎0). The subscripts 0 and f indicate fresh and dehydrated states, respectively. Each strawberry was scanned at three different locations using ten fruits per treatment.Texture characteristics of strawberries were measured by the Instron Universal Testing Machine (ID 4467 H 1998, Instron Co., Norwood, MA, USA). At least ten replicates per treatment were carried out. Compression tests were performed using a cylindrical plunger with a diameter of 3.21 mm and a crosshead speed of 10 mm/min, where the applied force was plotted against deformation. Texture was evaluated in terms of maximum force to rupture (Fcrit) and Young's modulus or apparent modulus of elasticity (E). The rupture point agrees with the point in the force–deformation curve at which the loaded specimen shows visible or invisible failure in the form of breaks or cracks. This point was detected by a continuous decrease of the load in the force–deformation diagram (). Apparent modulus of elasticity was calculated from the force–deformation data before rupture and geometry data of plunger and each specimen, considering loading of a spherical indenter on a curved surface and assuming a Poisson's ratio of 0.42 for strawberries (Structural features of parenchyma tissue were examined after preparing strawberry sections according to . Radial fruit sections were cut from mid-way between the epidermis and the core of similar sized berries in cubes of approximately 1 cm. Four cubes were randomly chosen for microscopic examination. Samples were fixed in an aqueous solution of formaldehyde (3.8% v/v), acetic acid (5.0% v/v) and ethanol (48% v/v) for at least five days. Samples were dehydrated by immersion in ethanol solutions (50%, 60%, 70% and 80%) for 2 h, followed by immersion in ethanol (96%) for 12 h. Washing was done by dipping the samples for 1 h in a solution of ethanol (67%) and benzene (33%), for 3 h in a solution of ethanol (50%) and benzene (50%), for 1 h in a solution of ethanol (67%) and benzene (33%), for 0.5 h and 10 min in pure benzene. Dehydration was completed by three-fold immersion of the cubes in a solution of benzene (50%) and paraffin (50%) for 2 h, followed by immersion in pure paraffin for 12 h at 60 °C in order to vaporize solvent from the samples. Dehydrated material was fixed and saturated with liquid paraffin. After polymerization samples were cut by a rotary Minot microtome into 12 μm thick slices. These slices were first fixed by glycerinated albumin in a droplet of water. Samples were dried at 40 °C for 12 h in order to remove residual water. Fixation stage was finished by the immersion of samples in pure dimethyl-benzene and in a solution of dimethyl-benzene (50%) and ethanol (50%) for 10 min and in ethanol solutions (96%, 80% and 60%) for 5 min. Slices were stained with alcoholic safranin for 2 d and washed with water. Then an alcoholic picric acid solution was applied for 20 s in order to enhance the differentiation between microstructures of strawberry tissue, followed by the neutralization with alcoholic ammonia solution and by two-fold hydration with pure ethanol for 10 min. Microscopic examinations were done using the Zeiss Axiostar Plus microscope (Carl Zeiss Microscopy, Oberkochen, Germany) with a digital camera (Cannon PowerShot A620, 7.1 MP) connected to a computer with an image analysis program (ZoomBrowser Ex 5.5).Shrinkage of strawberries was expressed in terms of the ratio of the difference between initial (V0) and final volumes (Vf) per initial volume:Volume was calculated from the polar (dp), first equatorial (de,1) and second equatorial (de,2) diameters according to the following function:Diameters were measured using a digital Vernier caliper (Caliper, 150 × 0.05 mm, Stanford professional) with an accuracy of 0.01 mm. Each value was the average of ten measurements.Rehydration of strawberry samples was done in a thermally isolated container filled with about 5 L of distilled water. The temperature of water inside the container was set at 20 °C. Strawberry samples (100 g) were put in two plastic tied up sieves and immersed for 12 h. After rehydration samples were shaken twice to drain attached water and weighed afterwards, using the Shimadzu BL320H (Shimadzu Co., Tokyo, Japan) electronic balance. In order to account for rehydration performance, the rehydration coefficient was defined as the ratio between the amounts of water absorbed after rehydration to the amounts of water removed by dehydration (where Wr, Wd and W0 are the weight of the sample after rehydration, its weight after dehydration and before rehydration, and its initial weight, respectively.Analysis of variance was performed to assess statistically significant differences between dehydration treatments for the quality attributes of strawberries at a confidence level of 95% (p |
< 0.05) using Statgraphics Centurion XVI version 16.1.15 (Statpoint Technologies, Inc., Warrenton, VA, USA). Differences on the mean values were assessed by Duncan's multiple range test at a significance level of p |
< 0.05 to discriminate among the means using the Fisher's least significant difference procedure.The drying rate for dehydrated strawberry samples is shown in . It is evident that water removal from fruit is dependent on the drying method. The drying rate for hot air drying was found to be 6.0 × 10− 4 |
kg water/(kg dry matter s). This value agrees with the maximum drying rate for convective drying of strawberries at 65 °C as reported by , where the drying rate decreased with moisture content. The drying rate determined for microwave assisted drying was about 12% higher than the convective air drying rate (). Microwave treatment results into internal water heating and evaporation due to ionic conduction and dipolar rotation of charged and dipolar species, respectively (). Evaporation that occurs inside the product creates additional partial pressure and concentration gradients (). Both ordinary concentration diffusion and pressure diffusion act as additional driving forces to enhance mass flux of water and thus the effective water diffusion rate during microwave-assisted drying (). Thus microwave application is able to reduce the drying time of strawberries. Although the moisture content decreased from 90% (wet basis) to 75% (wet basis) after osmotic pretreatment, the drying rate decreased significantly compared to VMD without osmotic pretreatment. Decrease of the dielectric constant after osmotic pretreatment yields a reduced absorption of microwave energy by the product (). Due to less microwave coupling with the osmotically treated product, the time taken to remove moisture increased, therefore reducing drying rate (). Strawberry freezing previously to microwave-convective drying at 55 °C and 1.7 W/g with or without osmotic dehydration was able to increase maximum drying rates by approximately ten times () compared to data of our study. Freezing of raw material seems to affect the structure of plant tissue enhancing drying performance. However, no information has been provided about the impact of microwave application on the structural changes and mechanical properties of these fruits. Combined treatment of VMD with osmotic dehydration or air drying is able to reduce the moisture content of dehydrated strawberries further on (), but this improvement is coupled to lower drying rates (). At the advance of drying, moisture gradients within the product are smoothen down, which hinders moisture transport by diffusion out of the product and thus decreasing drying rates. shows the results of physicochemical analyses done to the strawberry samples. High moisture content (90.43 ± 1.30 g water/100 g product) of fresh fruit is related to high water activity (aw |
= 0.92). Soluble solids, amongst others organic acids, were concentrated after water removal reducing water activity down to between 0.70 and 0.80. This intermediate water activity yields into dry, firm and flexible products without growth of most of the bacteria, yeast and molds (). The water sorption isotherm of strawberries after VMD dehydration is shown in . The first part of the isotherm represents the monolayer of water molecules strongly bound to the primary adsorption sites by high energy hydrogen bonds. The second part of the isotherm, which is almost linear and falls approximately between aw of 0.2 and 0.7, corresponds to the binding of several layers of water molecules superimposed on each other, attached by hydrogen bonds of decreasing energies. The third part of the isotherm for aw greater than 0.7 represents water retained in micropores by capillarity (). As can be observed, sorption data of water activity and equilibrium moisture content were well fitted by the GAB model with a mean relative error of 0.76%. In our study, the monolayer moisture content X0 was 0.075 g water/g solids. This value was close to that reported by other authors for freeze-dried straw berries (). The value of the monolayer moisture content is of particular interest, since it indicates the amount of water that is strongly adsorbed to specific sites of the food surface, which may be related to food stability. The value of constant K of the GAB model was 1.078, near to 1, demonstrating multilayer properties similar to bulk liquid water for the dehydrated strawberry samples. The value of the C constant was 17.45, which suggests a difference of sorption enthalpy or energy of interaction between monolayer and multilayer molecules at the sorption sites. The values of the parameters of the GAB model for VMD strawberries were close to those of freeze-dried strawberries (X0: 0.102 g water/g solids; K: 1.01; C: 18.81) (). This suggests that both vacuum microwave drying and freeze-drying modify the internal and porous structures, including capillaries of strawberry tissue in a similar way.Only minor color difference could be observed between vacuum microwave dehydrated strawberries and untreated fruit (). This color change was mainly due to the differences in chrome properties, where no statistically significant differences between raw material and VMD samples were found for hue and lightness. Color changes due to the loss of chrome may be attributed to thermal degradation of anthocyanins during strawberry dehydration (). Anthocyanins were more sensitive to dehydration than polyphenols (). Osmotic and air treatment previous to VMD did not provide a better quality of strawberries in terms of color retention. Air-dried samples had the lowest chrome, indicating less saturation and a pale appearance that is contrary to the vivid color of fresh strawberries. Air pretreated strawberries were more yellow and less red compared with other samples as evidenced by the higher hue value (). Anthocyanins are relatively more labile due to oxidation reactions that occur with air drying (). Moreover, there was a significant reduction of luminosity for OD-VMD provoked by the substitution of air by the impregnation solution after applying the vacuum pulse, followed by the contraction and deformation of intercellular spaces (). On the other hand, least color change after applying osmotic pretreatment to strawberries as reported by was due to their lack of temperature control during VMD, where osmotic pretreatment resulted into a decrease of the dielectric constant for this kind of strawberries. Differences between experimental conditions of microwave drying make it difficult to compare literature data.Strawberry drying by using hot air of 70 °C promoted the loss of mechanical resistance of the samples (). Vacuum microwave-assisted dehydrated samples, with or without air pretreatment at 50 °C, yielded the highest rupture point values in the loaded species (). The firmness of plant-derived material depends on cell turgor. The decrease in firmness resulted from changes in cell wall structure, losses of hydrostatic pressure within the cells and tissue damage caused by thermal processing at 70 °C (). Structure disruption and folding surfaces could be observed in micrograph c. Similar results were reported for thermal processing of strawberries at 70 and 95 °C with a decrease of 90% of firmness (). On the other hand, mechanical resistance of strawberries dehydrated by vacuum microwave heating with osmotic pretreatment decreased by 60% compared with strawberries without pretreatment (). According to micrographs b and d, tissue structures of both samples were rather similar despite osmotic pretreatment. Dehydrated strawberries show some loss of cell turgor compared with fresh fruit (a). However, in osmotic dehydration sucrose passes through the cell wall and accumulates between the cell wall and the cell membrane, where this hypertonic solution leads to a flux of water through the cell membrane, and as a consequence some shrinkage and loss of the integrity of cell structure due to plasmolysis (). Minor ultrastructural differences might explain the lower mechanical resistance of VMD samples with osmotic pretreatment. Furthermore, the high Young's modulus of air pretreated microwave-assisted dehydrated strawberries found in this study () represents a less chewy product and seems to be related to the low moisture content of this sample. Elastic behavior of the tested fruit species depends upon the moisture content and dehydration method applied.Internal vaporization of water during vacuum microwave heating yields a more open structure and lower shrinkage degree as the result of vapor expansion within the product. The more open, spongy structure of vacuum microwave heated strawberries improves the accessibility and effective water diffusivity during rehydration, which results into better rehydration performance except for fruits that received osmotic pretreatment (). Sucrose leaching during the rehydration operation may explain worse rehydration performance of OD-VMD samples.Dehydration of strawberries by microwave-assisted heating under vacuum conditions was able to create the highest water flux out of the product. This drying method results into an elastic product of improved mechanical resistance, showing only a slight loss of color and an appropriate rehydration performance. Preliminary dehydration techniques making use of hot air or sucrose solution did not improve most of the quality attributes, neither the drying rate of strawberries. The temperature of the drying process was a critical factor that affected the quality of microwave dried strawberries in terms of rehydration, color, shrinkage and microstructure.Compatibilization of immiscible poly(lactic acid)/poly(ε-caprolactone) blend through electron-beam irradiation with the addition of a compatibilizing agentThe aim of this study was to compatibilize immiscible poly(lactic acid) (PLA)/poly(ε-caprolactone) (PCL) blend by using electron-beam radiation method with the addition of a compatibilizing agent. Glycidyl methacrylate (GMA) was chosen as the compatibilizing agent, in the expectation that the GMA plays a role as a monomeric compatibilizer and a reactive agent at the interface between the PLA and the PCL phases. Compatibilization process has been investigated through the melt mixing of the PLA/PCL and the GMA by using a twin-screw extruder and the exposure of the PLA/PCL/GMA mixture to electron-beam radiation at room temperature. The melt mixing process was performed to locate the GMA at the interface, thereby expecting a finer morphology due to the GMA as the monomeric plasticizer. The exposure process was carried out to induce definite interfacial adhesion at the interface through electron-beam initiated cross-copolymerization by the medium of the GMA as the reactive agent. To investigate the results of this compatibilization strategy, the morphological, mechanical, and rheological properties of the blend were analyzed. The morphological study clearly showed the reduced particle size of dispersed PCL domains and significantly improved interfacial adhesion by the electron-beam irradiation with the addition of the GMA. The stress–strain curves of the blends irradiated at less than 20 kGy showed the typical characteristics of ductile materials. The tensile properties of the blend were strongly affected by the dose of irradiation.► PLA/PCL blend was compatibilized by the electron-beam irradiation with the addition of GMA. ► GMA played the role of a monomeric compatibilizer and a reactive agent at the interface. ► Definite interfacial adhesion was produced through radiation initiated cross-copolymerization. ► The stress–strain curves of blends irradiated at less than 20 kGy showed a ductile behavior.Biobased and biodegradable polymers have been attracting ever-increasing attention due to the environmental requirements for the reduction of carbon dioxide emission and the safe and effective disposal of used plastics into the waste stream (). Poly(lactic acid) (PLA) is an important biobased and biodegradable polymer, which now can be found in most of single-use disposable items and is produced from non fossil renewable resources by fermentation of polysaccharide (). PLA has high modulus and tensile strength at break comparable to those of many petroleum-based plastics, but its brittleness is a big drawback for its application to various commercial items such as automobile parts or home electronics (). According to recent studies the soft biodegradable polymer PCL has been blended with PLA to overcome the brittleness (It is well known that polymer blending is an excellent strategy for modifying the drawbacks of polymers. Unfortunately, most polymer pairs are thermodynamically immiscible. Therefore, the most important point in preparing polymer blends is assigning good dispersion and compatibility to the immiscible polymer blends (). For the PLA/PCL blend system, in previous works () revealed that the PLA/PCL blend was a thermodynamically immiscible blend, which results in poor dispersion and interfacial adhesion. Considerable efforts have been made to enhance the compatibility between PLA and PCL by using generally known compatibilization strategies such as the addition of a polymeric compatibilizer and reactive compatibilization method. The addition of PLA-g-PCL or PLA-b-PCL copolymer as the polymeric compatibilizer () is one of the common ways to improve the interfacial adhesion; however, it is almost impossible for all the added copolymer molecules to reach the interface during melt blending. Therefore, in most cases, a number of the copolymer molecules preferentially form micelles in the immiscible polymers rather than locating at the interface; consequently, the compatibilization effect is low (). Another preferred strategy of compatibilization is to form a block, graft, or crosslinked copolymers at the interface through covalent bond formation in situ during the reactive compatibilization step. There are two distinct processes available for copolymer formation at the interface, which are a direct process for the polymers that have reactive functionalities and a mediation process by addition of a reactive compatibilizer (). Frequently, however, the added reactive compatibilizer reacts with the individual polymers. Therefore, self-copolymerization of each polymer may compete with cross-copolymerization at the interface between the immiscible polymers. For the case of the PLA/PCL blend, the mediation process by addition of a reactive compatibilizer strategy was preferred among the compatibilization strategies in recent studies (In more recent years, exposure of polymers or polymer blends to high-energy radiation at room temperature has been newly introduced to modify their properties by changing the molecular structure of polymers or to improve the compatibility of blends (), polymers can be classified into two groups when they are irradiated. One group contains crosslinking dominated polymers and the other contains chain scission dominated polymers. For the field of the polymer blends, radiation processing, of course, leads to crosslinking or chain scission of one or more of the constituent polymers. These effects result in the modification of the blend's properties. The crosslinking dominated polymers have been relatively preferred in comparison with the chain scission dominated polymers because the former can achieve a good interfacial adhesion through a crosslinking or a grafting reaction at the interface between the pair of polymers (It was reported that PLA is classified the group of chain scission dominated polymers. For this reason, the high-energy radiation method seemed to be considered an unsuitable compatibilization strategy for the blend of PLA continuous phase though there were some studies () it was found that PLA can be modified with minimal amount of radiation induced chain scission by the addition of a functional monomer and applied this strategy to enhance compatibility for the immiscible PLA/PCL blend (). So far, there are few studies on the immiscible PLA/PCL blend compatibilized by electron-beam irradiation with the addition of a compatibilizing agent.In this study, to enhance the compatibility of the immiscible PLA/PCL blend the electron-beam irradiation strategy with the addition of the compatibilizing agent was adopted. The morphological, rheological, and mechanical properties were studied to observe the effects of this compatibilization strategy on the compatibility of the immiscible PLA/PCL blend. We also proposed electron-beam initiated reaction mechanisms, which were believed to be occurred at the interface, to explain interfacial phenomena.Poly(lactic acid) (NatureWorks® PLA Polymer 2002D) with a specific gravity of 1.24 and a melt flow index of 5–7 g/10 min (measured at 210 °C at a load of 2.16 kg) was obtained from NatureWorks LLC. Polycaprolactone (TONE-787) was obtained from Dow/Union Carbide. Glycidyl methacrylate (GMA) was provided by Sigma-Aldrich (WI, USA).The blend ratio of PLA and PCL was chosen to be 80/20 in weight percent and the amount of GMA content was fixed at 3 parts per hundred parts of resin (phr) based on the total mass of PLA and PCL. PLA, PCL and GMA were mixed in a plastic bag before being extruded in a twin-screw co-rotating extruder (SM PLATEK Co. Ltd., TEK 30, Korea). Screw diameter was 30 mm with 36:1 L/D ratio. The extruder was operated at 150 rpm with a constant feed rate of 15 kg/hr. The barrel and die temperatures were set at 160–190 °C and 185 °C, respectively. The extrudate was cooled in chilled water (∼20 °C) and cut into pellets with diameter less than 1 mm. The pellets and then dried for 24 h at 50 °C prior to the electron-beam irradiation. In addition, PLA/PCL blend without GMA was also prepared under the same preparation conditions as the PLA/PCL blend with GMA for morphological comparison purpose.The mixture of the PLA/PCL and the GMA with maximum chip diameter of 1 mm was irradiated using a commercial electron-beam accelerator (ELV-0.5, BINP, Russia, with a maximum beam current of 40 mA and beam energy of 0.5–0.7 MeV) under a nitrogen atmosphere. The irradiation doses were 5, 10, 20, 50, and 100 kGy, which were controlled by varying both the beam currents of 0.5–10 mA and the conveyor speeds of 1–2 m/min, and the irradiation dose was measured by dosimetry film (B3 WINdose Dosimetry, GEX Co.) and dosimeter (GENESYS 20, Thermo SCIENTIFIC Co.). Acceleration energy was 0.7 MeV and the effective penetration depth was about 2 mmm for the substrate with 1 g/cm3 of density (). The irradiated samples were dried in an oven at 50 °C for 12 h to eliminate any residual radicals.The morphology of the blend was studied by observing both the cryogenic and tensile fracture surfaces using a scanning electron microscope (SEM, Hitachi model s-4200, Japan). The mechanical properties of the blend were determined using INSTRON 4464 tensile tester (INSTRON). Tests were performed on tensile bars (type II) that were compression molded according to the KS M3600 test method using a hot press (Model 3851-O, Carver Inc.) at a set temperature of 200 °C and a molding pressure of 10 MPa. The experiment was performed at room temperature with a gauge speed of 10 mm/min and a gauge length of 35 mm. The average value determined from 6 tests was employed as the tensile value. The rheological property was measured using an ARES (Advanced Rheometric Expansion System: Rheometric Scientific Co. Ltd. US) rotational rheometer. The equipment was run in the parallel plate configuration at a strain of 2% in the frequency range of 0.1–100 rad/s.It is essential for compatibilization of immiscible polymer blends that the compatibilizer must locate at the interface to be effective (). In comparison with a polymeric compatibilizer, a monomeric compatibilizer can diffuse more easily to the interface between the phases of the immiscible polymers. In this study, the GMA was chosen as a monomeric compatibilizer, hoping to develop the finer morphology of the PLA/PCL blend by the GMA located at the interface. exhibits morphological differences between the unirradiated PLA/PCL blends with and without the GMA. The decrease in the size of dispersed PCL particles by addition of the GMA reveals that the added GMA localizes at the interface between the PLA and the PCL phases, lowers the interfacial tension by wetting the interface, and, thereby, develops the finer dispersion of PCL domains. shows the schematic morphology at the interface between the PLA matrix and the PCL dispersion developed by the addition of the GMA before electron-beam irradiation. There can be free GMAs as well as reacted GMAs, which reacted with the chain ends of the PLA or the PCL, as illustrated in ). Naturally, the existence of both the reacted GMA and the free GMA at the interface contribute to producing finer dispersion morphology as the compatibilizer. Nevertheless, the effect of the GMA on the interfacial adhesion is difficult to ascertain from the morphological change illustrated in the . Thus, we observed the change in storage modulus of the blend irradiated with and without electron beam. It was already reported that the effect of the interfacial adhesion on the change in rheological properties of blends (). If there is no improvement in interfacial adhesion by the addition of the GMA, the values of storage modulus of the PLA/PCL blend would be between the values of the PLA and the PCL. As seen in , the storage modulus of the PLA/PCL blend containing the GMA (0 kGy irradiated sample) is higher than those of both the pure PLA and PCL at a lower frequency range due to the enhanced interfacial adhesion. However, the modulus of the blend is lower than that of PLA at a higher frequency range because the interfacial interaction between the two phases is not enough to keep a physical network between the PLA matrix and the PCL dispersion against to a shear stress across the interface. Therefore, just by the addition of the GMA as the monomeric compatibilizer is successful to develop the finer dispersion of the PCL dispersed phase, but partly successful to get the sufficient interfacial adhesion to transfer the shear stress across the interface.Accordingly, the electron-beam radiation method was applied to the PLA/PCL blend to get the definite interfacial adhesion in expectation of cross-copolymerization by the medium of the GMA as the reactive agent, which was located at the interface by the melt mixing. exhibits the cryofracture and the tensile fracture surfaces of the PLA/PCL blends with and without irradiation. The cryofracture surfaces ((a) and (b)) display that the size of the dispersed PCL particles is decreased by the electron-beam irradiation. Moreover, there is clear evidence of the electron-beam initiated cross-copolymerization at the interface because the voids between the PLA matrix and the PCL particles seems to be filled with a substance and partial junctions exist (see the arrows in (b)), which are not in the unirradiated blend.Meanwhile, the tensile fracture micrographs of both the unirradiated and 10 kGy irradiated blends display the images for ductile fracture, as shown in (c) and (d), respectively. However, there are subtle morphological differences between the unirradiated and the 10 kGy irradiated blends. The tensile fracture morphology of the unirradiated blend exhibits that the PLA matrix was highly deformed by tensile stress but the PCL particles embedded in the elongated big holes was hardly deformed due to the insufficient interfacial adhesion to transfer the tensile stress across the interface. On the other hand, the tensile fracture of 10 kGy irradiated blend exhibits highly elongated morphology and even it is difficult to discern the elongated PCL particles from the deformed PLA matrix. In addition, there are many small holes instead of the elongated big holes, which exist in the surface of the unirradiated sample. This, of course, means that the interfacial adhesion is sufficient to transfer the tensile stress across the two phases due the greatly enhanced interfacial adhesion. Furthermore, the storage modulus of the blends irradiated at 10 kGy is higher than those of the pure PLA and PCL over the entire range of frequency due to the enhanced interfacial adhesion, as shown in . From these morphological and rheological results, we can clearly confirm that the interfacial adhesion between the PLA matrix and the PCL dispersion was greatly enhanced by the electron-beam irradiation. This excellent interfacial adhesion, in turn, seems to be caused by the electron-beam radiation initiated cross-copolymerization with the medium of the GMA placed at the interface by the melt mixing.Therefore, we proposed the reaction mechanisms of the electron-beam radiation initiated cross-copolymerization with the medium of the GMA at the interface in represent the free radicals formed by hydrogen abstraction at the quaternary carbon atom sites of PLA () and at arbitrary carbon atom sites of PCL ( also represent the free radicals formed by radiolysis of the GMA, which are reacted with the PLA or the PCL. estimates the cross-copolymerization at the interface, which can be taken place between the PLA. Meanwhile, various kinds of reactions also can occur by irradiation due to the existence of the free GMA at the interface, for example, homo-polymerization of the free GMA, grafting reaction of the free GMA with the PLA or the PCL, and the cross-copolymerization between PLA and PCL phases.Mechanical properties of blends are very important for their practical applications in a plastic industry and highly depend on their compatibility. As mentioned above, PLA is very brittle in spite of its high modulus and tensile strength at break. Thus, eventually, the purpose of this PLA blend study is also the improvement of the brittle behavior of PLA, combined with trying to minimizing the deterioration of the other mechanical properties such as the modulus and the tensile strength at break. represent the changes in tensile properties with respect to irradiation dose and the addition of the GMA. The tensile strength at break and modulus of the PLA/PCL blend increase with increasing irradiation dose up to 20 kGy, whereas those are decreased by higher dose over 20 kGy and then remain virtually constant with the irradiation dose. However, the elongation decreases gradually with increasing irradiation dose up to 20 kGy and then that remains constant, as shown in . The increases in tensile strength and modulus of the blend irradiated at 20 kGy are 140% and 30% comparing to the values for unirradiated sample, respectively. Whereas, the highest increase in elongation occurs at the unirradiated blend: the elongation is approximately 6 times higher than that of the pure PLA. Moreover, the stress–strain curves of the blends irradiated up to 10 kGy are showing the typical behavior of ductile materials, but that of the blend irradiated at 20 kGy becomes brittle, as shown in . These changes in mechanical properties and the stress–strain behavior are closely related to the chemical changes of the constituent polymers by electron-beam irradiation.As mentioned in introduction section, although the PLA is chain scission dominated polymer, chain branching is superior to chain scission when the PLA is irradiated at less than a certain dose in the presence of the GMA (). At a higher dose, however, the chain scission reaction is prevalent vice versa in the radiation induced reactions. In contrast with the PLA, the PCL is an easily crosslinking-type polymer even at low dose (). Consequently, for this blend system, to confirm the relationships between the chemical changes by irradiation and the changes in tensile properties of the blend is very difficult because all the reactions occur simultaneously (). However, it is true that crosslinking increases the modulus but decreases elongation of polymer. Thus, the decrease in elongation by irradiation is believed to be due to the crosslinking of the dispersed PCL domains () and strong interfacial adhesion enough to transfer the stress across the interface between the PLA matrix and the PCL domains. The decrease in modulus and tensile strength at higher dose seems to be caused by the degradation of the PLA matrix.In this work, we studied the effect of electron beam irradiation with presence of compatibilization agent on the compatibility of the immiscible PLA/PCL blend by observing the morphological, mechanical, and rheological properties of the blend. Morphological and rheological results indicated clearly that the GMA located well at the interface and behaved as a good monomeric compatibilizer for developing a finer morphology, whereas the interfacial adhesion was insufficient to transfer stress across the interface. Accordingly, electron-beam irradiation process was applied to get sufficient interfacial adhesion and, in turn, this strategy was very successful. The effect of the electron-beam irradiation on the interfacial adhesion was well illustrated by the morphologies of both the cryofracture and the tensile fracture surfaces. The stress–strain curves of the blends irradiated at less than 20 kGy showed the characteristics of ductile materials. The tensile strength at break and the modulus increased to a maximum at the dose of 20 kGy, whereas the highest increase in elongation was obtained at 0 kGy irradiated blend.In comparison with the in situ reactive compatibilization strategy of the mediation process, this strategy can locate a compatibilizing agent better at the interface by minimizing self-reaction with the constituent polymers and can compatibilize an immiscible blend more definitely through the electron-beam radiation initiated cross-copolymerization with the medium of the compatibilizing agent placed at the interface. However, to employ electron-beam irradiation strategy effectively for compatibilizing the immiscible polymer blends the chemical changes of the constituent polymers should be carefully controlled by the addition of suitable additives.Strengthening mechanism in a high-strength carbon-containing powder metallurgical high entropy alloyA carbon-containing FeCoCrNiAl0.5 high entropy alloys (HEAs) with high tensile strength was fabricated by powder metallurgy (P/M) method. The P/M process includes gas atomization and hot extrusion of pre-alloyed HEA powder. The microstructural evolution and mechanical properties were systematically investigated using X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM) and tensile tests. The results showed that the gas-atomized HEA powder was of dual phase, including face centered cubic (fcc) phase and B2 phase. Hot extrusion caused the precipitation of M23C6 carbides, the formation of dislocations and the refinement of microstructure. The as-extruded HEA exhibited a tensile strength as high as 1093 MPa and an elongation of ∼12.4%. The contributions of different strengthening mechanisms were quantitatively calculated, and it was found that the grain boundary strengthening and the dislocation strengthening are the main strengthening mechanism.Developing high strength and low cost materials is a constant goal for material scientists. Recently, a new kind of alloys referred as high entropy alloys (HEAs) have received considerable attentions due to their unique structures and excellent mechanical properties []. Originally, HEAs were designed to mix multiple elements in equiatomic or near-equiatomic ratios, and to form a stable single-phase structure through the effect of the high configurational entropy []. A typical single-phase HEA CrMnFeCoNi exhibits exceptionally high damage tolerance and fracture toughness even at cryogenic temperatures []. Nevertheless, a number of studies show that a single-phase matrix only with intrinsic characteristics of HEAs is relatively weak in strength for practical applications []. Motivated by these findings, various strengthening mechanisms have been introduced by thermo-mechanical treatments to enhance the strength of HEAs. For example, the increment of yield strength about 100 MPa was obtained in an Al0.3CrFeCoNi HEA by grain boundary strengthening []. The yield strength of a CrMnFeCoNi HEA increases from 170 MPa to 360 MPa, when the grain size decreases from 155 μm to 4 μm []. Nanocrystalline Al7.5Fe25Co25Ni25Cu17.5 HEA produced by mechanical alloying (MA) and spark plasma sintering (SPS) exhibits a very high compressive strength []. In addition to the grain boundary strengthening, the precipitation strengthening is another way to strengthen HEAs. For example, homogeneous L12 Ni3(Ti, Al)-type precipitates in the (FeCoNiCr)94Ti2Al4 HEA contribute a strength increment of about 320 MPa []. The precipitations of hard σ and μ intermetallic phases were introduced in CoCrFeNiMox HEAs by thermo-mechanical treatments, producing a strength of 1186 MPa and an elongation of 18.9% []. The strength and the ductility of the dual-phase Fe80-xMnxCo10Cr10 HEAs both increase with the decrease of the grain size of face centered cubic (fcc) phase and the increased fraction of hcp phase [] made attempts to improve the strength of 1.1 at. % carbon-doped Fe40.4Ni11.3Mn34.8Al7.5Cr6 HEAs by multiple strengthening mechanisms, and found that the reduction in the grain size resulted in a sharp increase in strength, while the precipitation, produced only a slight increase in strength and a decrease in ductility. So far, simultaneous additions of carbon and strong carbide-forming elements, for example, Mo, Nb and Ta, are quite few, which can expect to induce the combination of solid solution strengthening and other strengthening effects.Casting technique is the most widely adopted route for the synthesis of HEAs []; however, the coarse and heterogeneous microstructures need to be improved []. Therefore, an additional thermo-mechanical process becomes a necessary step to optimize the microstructures and enhance the mechanical properties. Besides, the complex alloying composition and the addition of carbon are also a great challenge for casting HEAs. Powder metallurgy (P/M) is recently reported to be a promising way for preparing HEAs []. In this work, a high performance HEA was prepared by hot extruding pre-alloyed powder, and the microstructural evolution and strengthening mechanisms were investigated to achieve in-depth understanding of HEA.High-purity elemental metals of a nominal composition-Al10.5Cr21.1Fe21.1Co21.1Ni21.1Mo2.5C2.5 (at.%) were melted in a vacuum induction furnace. The melt then dropped through a ceramic tube, and was atomized by high pressure argon. The atomization pressure was 4 MPa. The gas-atomized powder was kept in an airtight chamber until cooling down. The composition of powder was analyzed by chemical methods. The oxygen content was determined by the fusion method on a Leco O/N analyzer.The gas-atomized HEA powder was filled into a stainless steel can with dimensions of d 60 mm × 150 mm. The can was degassed for 12 h at 500 °C and sealed in vacuum. The encapsulated powder was subsequently pre-heated at 1150 °C for 1 h, and immediately hot extruded into bars with an extrusion ratio of 6:1. After hot extrusion, the bars were cooled in air.Specimens for analyses were sectioned along the extrusion direction (ED). X-ray diffraction (XRD) tests were performed on a Rigaku D/max 2550VB diffractometer using Cu-Ka radiation. An FEI Quanta 250 field emission gun (FEG) scanning electron microscopy (SEM) with backscattered electron (BSE) mode was employed to examine the microstructures of the as-extruded HEA. Specimens for SEM examination were ground using silicon carbide papers, and then polished using a 0.05 μm colloidal silica suspension. Electron backscatter scattered diffraction (EBSD) measurements were carried out by an FEI Quanta 650 FEG SEM equipped with a fully automatic HKL technology EBSD attachment. Data acquisition and post-processing were performed using both the Aztec and Channel 5 software. For EBSD specimens, vibration polishing was applied for about 4 h after standard metallographic procedure. The foils for transmission electron microscopy (TEM) analyses were thinned using Struers Tenupol 5 in an electrolyte of 25% nitric acid and 75% methanol with a voltage of 10 V at −25 °C. TEM investigations were conducted on electrochemically polished disks using a FEI Tecnai F20 TEM operated at 200 kV.Cylinder specimens for tensile tests, with a gauge size of d 4 mm × 20 mm, were machined from the as-extruded HEA bars along the ED. All specimens were mechanically polished prior to tensile tests in order to remove surface irregularities and to guarantee an accurate determination of the cross-sectional area. The quasi-static tensile tests were performed on an MTS landmark testing machine with a strain rate of 1 × 10−3 s−1.The chemical analyses of the gas-atomized HEA powder (see ) suggest that the real composition is in good agreement with the nominal composition. Additionally, the oxygen content of the powder is as low as 175 ppm, indicating no obvious oxidation during the gas atomization. As shown in , the mean particle diameter (d50) of the gas-atomized HEA powder is about 33.73 μm, with a distribution from several microns to 140 μm. (a) shows the morphology of the gas-atomized HEA powder. It can be seen that the powder is predominantly spherical or near-spherical in shape with some satellite particles. The surface and the internal microstructures of the gas-atomized HEA powder are both dendritic in submicron scale, as shown in (b) and (c), respectively. The X-ray diffraction (XRD) patterns in reveal the phase constitution of the gas-atomized HEA powder. It is clear that the powder consists of fcc phase and B2 phase. shows the XRD patterns and SEM images of the longitudinal section of the as-extruded HEA bars. After hot extrusion, some peaks associated with M23C6 carbide appear in the XRD patterns. The phase composition of the as-extruded HEA consists of fcc phase, B2 phase and M23C6 carbide (see (a)). Meanwhile, the abnormal diffraction peak intensity of fcc phase suggests that the texture along [200] was formed. The gas-atomized HEA powder exhibits a good flowability and deformability during the hot extrusion. The particles were consolidated to nearly full density, and only very few pores can be observed in the microstructure (see (b)). Combined with the XRD patterns, it can be concluded that the main phase is fcc, the grey roughly circular phase is M23C6 carbides, and the dark phase is B2. The high magnification image and corresponding compositional profiles displayed in show that the M23C6 carbide contains high amount of Cr and Mo, and the B2 phase is enriched in Ni and Al. The distribution of the elements in fcc matrix is homogeneous. (a) through (c) are EBSD inverse pole figure (IPF) map, phase color (PC) map and kernel average misorientation (KAM) map, respectively. The average diameter and the volume fraction of each precipitates obtained from EBSD maps are presented in (c) can serve as a measurement of the deformation-induced local orientation gradients inside grains, and a positive relationship exists between the KAM values and dislocation densities. The measured KAM values is about 0.355°. The detailed microstructural analysis in shows that the lattice parameter of fcc phase as measured by selected area diffraction (SAD) is about 0.371 nm. Few annealing twins with coherent boundaries are clearly observed in the fcc phase, and the corresponding SAD patterns reveal the twinning relationship (see (a)). The [001] zone axis (ZA) SAD patterns generated by the Ni, Al-rich phase display the superlattice reflection, and the presence of {001} superlattice spots marked by the arrow in (b) confirms a B2 (ordered bcc) structure. In addition, SAD patterns recorded from the B2 phase together with surrounding fcc phase show the superposition of the [011]fcc ZA SAD from the matrix with the [001]B2 ZA SAD from the precipitate. The relationship between B2 phase and the parent fcc phase is [011]fcc//[001]B2 and {111} fcc//{110} B2, consistent with the Kurdjumov-Sachs (K-S) orientation relationship []. The lattice parameter of B2 phase as measured by SAD is about 0.297 nm. The lattice distortion caused by atomic size difference of the constituent elements and the addition of strong carbide-forming element Mo induce the instability of the fcc matrix, and increase the driving force of phase transformation []. So, M23C6 carbides tend to precipitate in the process of hot extrusion, typical morphologies and corresponding SAD patterns of intergranular M23C6 carbides and intrargranular M23C6 carbides are respectively shown in . The SAD patterns taken from different ZA reveal that M23C6 carbides have an fcc structure, and the lattice parameter of the M23C6 carbides as measured is about 1.102 nm. Accumulated dislocations were observed around the precipitates and the grain boundaries, as shown in , confirming the incompletely dynamic recrystallization of the as-extruded HEA.The engineering stress-strain curve for the HEA is plotted in (a). The as-extruded HEA exhibits a yield strength of 659 MPa, an ultimate tensile strength of 1093 MPa, and an elongation to failure of 12.4%. Micrographs of the fracture surfaces in the inset of (a) indicate basically ductile fracture model through the nucleation and coalescence of fine microvoids. (b) shows the true stress-true strain and strain-hardening rate (dσ/dε) curves. It shows a continuously increasing strain hardening behavior, and the peak strength reaches 1228 MPa. The strain-hardening rate continuously decreases with increasing plastic strain. A direct comparison of the mechanical properties of the HEA with those of several advanced steels and other HEAs (data from Refs. [(c). The ultimate tensile strength of the as-extruded HEA exceeds those of most advanced steels and HEAs, whilst its elongation still remains at an acceptable level of 12%. reveal the typical dislocation configurations in the as-extruded HEA after tensile tests. The dislocations are arranged in planar configuration, forming extended pile-ups and slip bands. Furthermore, the dislocation slip was localized within a limited set of {111} slip planes, as shown in (a). This is similar to earlier studies in binary fcc solid solutions []. In addition, randomly distributed dislocation clusters rather than the regular dislocation configuration can be observed near the grain boundary and precipitates (as seen in (b) and (c), respectively). According to Wang et al. [], the inhibition of the grain subdivision by the grain boundaries and precipitates leads to the transformation from regular dislocation configurations to irregular dislocation configurations.Generally, the mechanical properties of the metallic materials are strongly dependent upon their microstructures. Some studies indicated that the strong localization of the dislocation slip shown in (a) is likely to be associated with the increase in atomic size misfit and solute contents []. The δ parameter is widely used to quantify the atomic size difference in a multicomponent alloy [where ci and ri are the atomic percentage and the atomic radius of the i th component, and n is the number of alloying elements. The δ of the as-extruded HEA is calculated to be 7.84. It means that a severe atomic size misfit will limit the movement of dislocations. But meanwhile, the grain boundaries and precipitates will also apparently affect the dislocation configurations (see (b) and (c)). Combined with the deformation microstructures, it can be deduced that the yield strength of HEA has contributions from a combination of friction stress, solid solution hardening, dislocation hardening, grain boundary hardening and precipitation hardening. In order to qualify the strengthening mechanisms, the following microstructure-related equation is utilized.where σfr are the friction stress, and Δσss, Δσd, Δσgb, Δσp are the strengthening increments from solid solutions, initial dislocations, grain boundaries and precipitates, respectively.The friction stress is the intrinsic lattice resistance to dislocation motion. For the recently emerged HEAs, the relevant study are still not systematic and clear. Even the values needed here for the present HEA are not available in the literature since this HEA has heretofore never been studied. Hence, similar with the approximations made in Ref. [], the rule of mixtures has been used to estimate the friction stress, which is calculated as 139 MPa. For CrMnFeCoNi HEAs [], the friction stress σfr is about 125 MPa, and for (FeCoNiCr)94Ti2Al4 HEAs [], the friction stress σfr is about 165 MPa. So the estimated value is reasonable.For HEAs, the terms “solute” and “solvent” lose their traditional meanings, thus, conventional approaches of measuring the effect of solid solution hardening are unable to precisely quantify the contribution of solid solution hardening in HEAs system. Fortunately, Cr, Fe, Co and Ni elements have nearly the same atomic sizes and the mixing enthalpies of different atom-pairs of these four elements are nearly zero. Atomic radius of Al (rAl = 0.143 nm) is ∼15% larger than those of Cr, Fe, Co and Ni (rCr, Fe, Co, Ni ≈ 0.124 nm), and atomic radius of Mo (rMo = 0.136 nm) is ∼9.6% larger than those of Cr, Fe, Co and Ni. Hence, the current HEA can be treated as a CrFeCoNi solvent matrix containing Mo and Al solutes, and a standard model for substitutional solid solution strengthening based on elastic dislocation solute interactions can be used to estimate the potency of solid solution strengthening [where GM is the shear modulus of CrFeCoNi matrix [], c is the atomic ratio of Mo and Al in fcc matrix (list in ), M is the Taylor factor (3.06 for both fcc and bcc polycrystalline materials). The interaction parameter εs is expressed as:it combines the elastic effect and atomic size mismatch, i.e. εG and εa, whcih are defined respectively as:where aM is the lattice parameter of the CrFeCoNi matrix. The value of εa can be calculated by using data from Refs. [], while the effect of εG is relatively negligible in comparison with εa. Thus, εs and Δσss can be properly estimated. The strength enhancement caused by the solid solution hardening in the current HEA is about 41 MPa. Due to the fact that solvent and solutes cannot be accurately distinguished in HEAs system, the solid solution strengthening is commonly integrated together with the lattice friction stress to study []. Compare with these studies, this value is relatively small. Additionally, some recent studies show that the solid solution strengthening caused by adding 7 at.% Al is also only about 28 MPa for CrMnFeCoNi HEAs. Similarly, the addition of 4 at.% Al and 2 at.% Ti only contributes a solid solution strengthening increment of about 39.8 MPa for CrFeCoNi HEAs. In the present work, the main reason might be the precipitation of Al-rich B2 phase and Mo-rich carbide reduce the solid solution strengthening effects caused by the atomic size differences.] have used the diffusion couple to confirm the sluggish diffusion effect in HEAs. Low diffusion rate leads to high normalized activation energies and low diffusion rate, which exert directly effects on the nucleation and growth of dynamic recrystallization grain. In addition, hot extrusion is a rapid process. Therefore, the completely recrystallized microstructure is hardly obtained, dislocations can still be observed around the precipitates and the grain boundaries (see ). The initial dislocations would impede dislocation motion. According to Taylor hardening model, the relationship can be expressed as [where α is 0.2 for fcc metals, G is the shear modulus, b is the Burgers vector, ρd is dislocation density. Under the assumption that the alloy is elastically isotropic, shear modulus (G) can be calculated as G = E/2(1+υ), where υ is the Poisson's ration (≈0.33), E is the elastic modulus. The value of elastic modulus for the current alloy, measured by using the nanoindentation, is 197 GPa. The magnitude of the Burgers vector is |b|=a0/2, with a0 being the lattice constant. A method based on Kubin and Mortensen [] is used to extrapolate the dislocation density information,where θ is the misorientation angle, u is the unit length. KAM values of the as-extruded HEA is about 0.355°. ρd is calculated to be 5.42 × 1014 m−2. Inserting these values into Eq. , the strength increment from dislocation hardening is evaluated as Δσd = 276.2 MPa.The precipitation strengthening is the resistance from hard particles for passing dislocation. The B2 precipitates and M23C6 carbides in the as-extruded HEA are expected to produce hardening. Because of the large size and high hardness of the B2 phase and M23C6 carbides, the Ashby-Orowan equation for dislocation by-pass mechanism is suitably employed to estimate the precipitation strengthening effect [where f is the volume fraction of precipitates, D is the real spatial diameter of precipitates. The B2 precipitates and M23C6 carbides are consider to be spherical in the model to simplify calculation. presents the average diameter and the volume fraction of each precipitates in the as-extruded HEA. The increment from precipitation strengthening is determined to be Δσp-B2 = 15.4 MPa and Δσp-M23C6 = 34.4 MPa for B2 precipitates and M23C6 carbides in the alloy, respectively., the as-extruded HEA has a grain size of several microns, which is much finer than that of many as-wrought HEAs. The fine microstructure is mainly due to the powder metallurgical process. Firstly, the hot extrusion of pre-alloyed powder is a very fast densification process. During the annealing of HEA powder, the grain growth inside particles is not serious, because the particle size is already small (see ) and the interdiffusion between particles is limited. After annealing, the hot extrusion process only lasted about 10s, so that microstructures of powder particles can be refined through deformation and dynamic recrystallization without grain growth. Secondly, the fine precipitates located in the grain boundaries also effectively suppress the grain growth behavior. It is well known that the small grain size offers a high volume fraction of grain boundaries, which can impede dislocation motion and improve mechanical properties. According to the Hall-Petch equation, the grain boundary strengthening or the Hall-Petch strengthening can be expressed as [where KPH is the Hall-Petch constant and d is the average grain diameter. Due to the similar grain size and phase composition, KPH = 574 MPa μm0.5 in Fe40.4Ni11.3Mn34.8Al7.5Cr6 system is applied to estimate the contribution from grain boundary hardening []. The calculated value of ΔσGB is about 308 MPa.In the present HEA, the calculated values of the quantitative contribution from the solid solution strengthening, precipitation strengthening, dislocation strengthening and grain boundary strengthening are 41.1 MPa, 49.8 MPa, 276.2 MPa and 308 MPa, respectively. It is found that the dislocation strengthening and the grain boundary strengthening are much more effective than other strengthening mechanisms. In addition, the calculated yield strength, in a total of 814 MPa, is greater than the measured yield strength of 659 MPa. The discrepancy may be attributable to a couple of reasons. First, some parameters used for calculation are approximations, or cited from other HEAs. Second, The B2 precipitates are actually elongated along ED direction. These plate-shaped particles produce different resistance to plastic flow as compared to spherical particles. Third, the texture affects the strength of the materials to some extent []. In general, the as-extruded HEA shows excellent mechanical properties due to a good combined strengthening mechanisms, especially the dislocation strengthening and the grain boundary strengthening.In this work, a multiphase structured HEA was fabricated by hot extrusion of gas-atomized powder. Microstructural characterizations and mechanical tests were conducted, and various strengthening mechanisms were analyzed quantitatively. The main conclusions are as follows:HEA with full density and fine microstructures can be effectively processed by hot extrusion of gas-atomized powder. The microstructure of the as-extruded HEA mainly consists of fcc phase, B2 phase and M23C6 carbide.The as-extruded HEA exhibits a tensile strength as high as 1093 MPa, and a reasonable ductility of 12.4% at room temperature.The strengthening mechanisms, including solid solution strengthening, precipitation strengthening, dislocation strengthening and grain boundary strengthening are quantitatively evaluated, and it reveals that the dislocation strengthening and the grain boundary strengthening are the predominant effecting mechanisms.A novel face-centered-cubic high-entropy alloy strengthened by nanoscale precipitatesA new single-phase face-centered-cubic (FCC) Co9Cr7Cu36Mn25Ni23 [atomic percent, similar hereinafter] high-entropy alloy (HEA) was prepared by arc melting. A uniform distribution of nanometer-sized precipitates was achieved. The tensile yield strength, ultimate tensile strength, and elongation were 401 MPa, 700 MPa, and 36%, respectively. The energy-dispersive spectrometer results showed that the nano-precipitates were rich in Co and Cr elements. Moreover, the crystal-forming behavior and the nanoscale-precipitates-forming mechanism were revealed.The nano-precipitates phase forming process.High-entropy alloys (HEAs) contain at least four principal elements and were first proposed by Yeh et al. and Cantor et al. in 2004 []. Today, they continue to attract extensive research attention due to their excellent mechanical properties, good resistance to irradiation damage, good wear resistance, fatigue and corrosion resistance, and stable microstructure against heat treatment []. Often, HEAs possess simple face-centered-cubic (FCC), body-centered-cubic (BCC), or hexagonal-close-packed (HCP) solid-solution structure []. For example, several studies on mechanical properties [] of HEAs have been reported from 2015 to present. These studies have made outstanding contributions to the development and application of HEAs. However, investigations on the phase-forming behavior in HEAs are limited.In this paper, we introduce a novel Co9Cr7Cu36Mn25Ni23 (atomic percent, at. %) HEA. The mechanical properties, phase compositions, microstructures, and chemical distributions of the proposed HEAs are presented. An atom motion model is established to describe the behavior of crystal-forming and nanometer precipitates-forming processes in the proposed HEA. The present results are expected to be useful in developing HEAs with high performance.The alloy was obtained by arc melting from pure metals (purity > 99.8 wt%) under a high-purity argon atmosphere and was smelted seven times to ensure chemical homogeneity. X-ray diffraction (XRD) using CuKα radiation (MXP21VAHF) was employed to identify the phase structures of the HEA. Scanning electron microscopy (SEM) and transmission electron microscopy (TEM) were used to characterize the microstructural morphology. Energy-dispersive spectrometer (EDS) was utilized to study the elemental distribution. For the microstructural observation, the samples were sequentially ground and polished and then underwent electropolishing in a mixture of 90% (volume percent) acetic acid and 10% (volume percent) perchloric acid at room temperature with an applied voltage of 27 V for 15 s. Flat specimens, with the thickness of 1 mm and gauge length and width of 10 mm and 2 mm, respectively, underwent tensile testing at a strain rate of 0.5 mm/min. at room temperature. The strain was measured using an extensometer. shows the mechanical behavior and crystal structure of the Co9Cr7Cu36Mn25Ni23 HEA. (a) presents the XRD patterns of the Co9Cr7Cu36Mn25Ni23 HEA. It shows that the Co9Cr7Cu36Mn25Ni23 HEA has two crystal phases, FCC(225, Cu rich)and FCC(225, Co and Cr rich)crystal structures. (b) exhibits the tensile engineering stress-strain curve, in which the tensile yield strength is 401 MPa, the ultimate strength is 700 MPa, and the elongation is 36%. The tensile yield strength, ultimate tensile strength, and elongation for the Co9Cr7Cu36Mn25Ni23 HEA and other HEAs [(c) and (d). We observed that our proposed HEA has a good combination of tensile yield strength and elongation, while having an ultimate tensile strength similar to the FeCoCoNiMn and Fe50Mn30Cr10Co10 HEAs.For a more elaborate investigation of the phase-forming behavior of the proposed HEA system, microstructures attained by the SEM and elemental distribution determined through EDS are shown in . The crystal grains appear to be a peritectic-structure with a core on the inside [see (b–f)] reveal that Co and Cr are rich in the primary phase area. These two elements have the highest melting point among the five constituent elements. However, Cu, which has a lower melting point, was scanty in this primary phase area. Ni and Mn slightly segregated in the primary phase and crystal areas, respectively.To clearly observe the nanometer precipitates and identify their crystalline structures, the sample was observed through TEM. As presented in , a large amount of nanometer precipitates was found in the Co9Cr7Cu36Mn25Ni23 HEA. The nanometer precipitates, which are several nanometers in size, are diffusely distributed in the matrix. The electron-diffraction spot illustrated in (b) indicate that the proposed HEA has a single FCC (1‾2‾2) crystalline structure. (c) and (d) show the bright-field TEM image with high magnification and the corresponding electron-diffraction spots for (c), in which the nanometer precipitates are seen to be 3–8 nm in diameter and have an FCC (1 1‾1) structure. (e–j) show the HAADF (High-Angle Annular Dark Field) image and the corresponding STEM-EDS elemental maps of Co, Cr, Cu, Mn, and Ni, which reveal that the nanometer precipitates were rich in Co and Cr elements but scanty in Cu.Based on the experimental results, an atom motion model was formulated to describe the crystal-forming behavior in this HEA. The atoms with higher melting points (Co, Cr, and Ni) preferentially precipitated as the primary phase when mixed with a small amount of atoms with low melting points (Cu and Mn), as the temperature decreased. This observation can be verified through the elemental-distribution maps presented in . When the temperature was further reduced, the atoms with lower melting points separated out and attached themselves to the primary phase, which prompted the grains to gradually increase in size and form a whole grain with a peritectic structure [as shown in ]. After the liquid metal solidified and as the temperature dropped, the solid solubilities of Co and Cr were decreased in the matrix, and a part of these element were separated from the supersaturated solid solution, which mainly led to the generation of the nanometer precipitates. The sluggish diffusion effect prevents the further growth of the nanometer precipitates [as presented in (b)]. Furthermore, a mass of nanometer precipitates is pivotal in improving the strength of the proposed HEA.] proposed an empirical criterion based on two physical parameters, i.e., Ω (the ratio of the entropy of mixing to the enthalpy of mixing) and δ (the atomic-size difference), to discuss the formation ability of multi-component HEAs. Accordingly, a stable solid-solution phase formed, when Ω ≥ 1.1 and δ ≤ 6.6%. It should be noted, however, that Ω and δ are correlated parameters, and approximately follow a hyperbolic relation, i.e., δ x LnΩ = constant []. Here, we studied these two parameters for our proposed HEA.The atomic-size difference is defined as [where n represents the number of component elements, ri is the atomic radius of the ith constituent element, and ci represents the atomic percentage of the ith component element.where Tm is the average melting point, ΔSmix is the entropy of mixing, and ΔHmix is the enthalpy of mixing.where (Tm)i is the melting point of the ith constituent element.where Ωij usually equals 4 ΔHijmix, and ΔHijmix is the enthalpy of mixing of the ith and jth component elements.where R is the universal gas constant (8.314 kJ−1 mol−1). Using Eqs. , we obtained δ = 3.1% and Ω = 13.74 for Co9Cr7Cu36Mn25Ni23, which is according to the above criterion, suggesting that this HEA forms a stable solid-solution phase. This prediction is consistent with our observation.Guo et al. reported that valance electron concentration (VEC) is another important parameter for predicting the phase structure of HEAs []. The criterion is that a sole solid-solution phase with an FCC structure is formed when VEC ≥ 8. We find that our proposed HEA has a VEC of 9.24. It implies that the Co9Cr7Cu36Mn25Ni23 HEA would form a single FCC solid-solution phase, which is consistent with our observation.It has been reported by Basu et al. and Rao et al. [] that the interface strengthening caused by a second phase plays an important role in enhancing the mechanical properties of some HEAs, e.g., the BCC-FCC dual-phase AlxCoCrCuFeNi []. Accordingly, in order to evaluate the effect of the nanoscale particles on the strength of our proposed HEA, we estimated the phase interfacial strengthening, Δσint. Based on the continuum dislocation pile-up theory [where b is the Burgers vector, L is the pile-up length (in the present case, the grain size), ν is the Poisson's ratio, and G is the shear modulus. τin is the barrier stress caused by the heterophase interfaces, which can be obtained by Eq. where τK is the Koehler stress caused by the modulus mismatch, τL is related to the lattice mismatch, and τS is due to the stacking-fault difference (both the matrix and the second phase have an FCC structure in our proposed HEA. Thus, the stacking-fault-energy difference is not considered in this study). τK and τL can be obtained by Eqs. τK=GmatrixGnanoparticles−Gmatrixb4πGnanoparticles+Gmatrixhwhere h = 2b,δ=∆aa∗, and a∗ is the mean lattice parameter (ananoparticles+ amatrix)/2, ε = 0.76δ is the residual elastic strain [], d is the interparticle spacing, and G is the average shear modulus.From our experiment, we derived a value of d = 21.0 nm, and L is 21.0 μm, where Gmatrix = 75.39 GPa and Gnanoparticle = 83.26 GPa, ananoparticles = 3.554 Å, amatix = 3.566 Å, and b = 1.443 Å were determined through density-functional-theory calculations. The calculations for the parameters were carried out with the exact muffin‑tin-orbitals method [], and the problem of chemical disorder in alloys was treated within the coherent-potential approximation []. The same numerical settings and methodology reported in Refs. [] were employed here. With these parameters, we obtained a τK of about 297 MPa and a τL of about 419 MPa. Therefore, the phase interfacial strengthening, ∆σint, was calculated to be about 419 MPa based on Eq. We are the first to investigate the Co9Cr7Cu36Mn25Ni23 HEA. We observed that our proposed HEA has a good combination of the tensile yield strength and elongation. A large amount of precipitates, which were several nanometers (3–8 nm) in size, abundant in Co and Cr, and scarce in Cu, were found in the novel HEA. We estimated the additional strength caused by the lattice mismatch and shear-modulus mismatch between the nanoparticles and matrix to be about 419 MPa based on Eq. . The total tensile strength is 700 MPa, which indicates that this alloy also can be strengthened by solution strengthening and grain-boundary strengthening mechanisms.Based on the EDS analysis and the crystal-forming behavior of HEAs, we found that the elements with higher melting points preferentially precipitated as the primary phase, whereas elements with lower melting points were separated out and attached themselves to the primary phase as the temperature was reduced. Moreover, as the temperature dropped, a part of Co and Cr was separated from the supersaturated solid solution and precipitated. The precipitates grew to a size of a few nanometers and further growth was hindered by the sluggish diffusion effect. Therefore, the nanoprecipitates were formed.A three-invariant cap plasticity with isotropic–kinematic hardening rule for powder materials: Model assessment and parameter calibrationThe constitutive modeling of powder is clearly a keystone of successful quantitative solution possibilities. Without a reasonable constitutive model, which can reproduce complicated powder behavior under loading conditions, the computations are worthless. In this paper, a three-invariant cap plasticity model with isotropic–kinematic hardening rule is presented for powder materials. A generalized single-cap plasticity is developed which can be compared with some common double-surface plasticity models proposed for powders in literature. The hardening rule is defined based on the isotropic and kinematic material functions. The constitutive elasto-plastic matrix and its components are derived by using the definition of yield surface, material functions and nonlinear elastic behavior, as function of hardening parameters. The procedure for determination of material parameters is described. Finally, the applicability of the proposed model is demonstrated in numerical simulation of triaxial and confining pressure tests.Powder metallurgy is becoming an increasingly important processing technology for advanced and some conventional materials because of its capability in micro-structural control combined with net shape. The compaction process of powder is of great importance in the industrial manufacturing process where components of rather complicated geometry are being manufactured. Powder metallurgy considers the methods of producing commercial products from metallic powders by pressure. The powder compaction process transforms the loose powder into a compacted sample by increasing density. The magnitude of shrinkage in compaction process depends on the relative density of the compacted specimen. One of the main difficulties in the compaction forming process of powders is a non-homogenous density distribution which has wide ranging effects on the final performance of the compacted part. The variation of density results in cracks and localized deformation in the compact, producing regions of high density surrounded by lower density material, leading to compact failure. Thus, a uniform distribution of the relative density is desired to avoid micro-cracks or fully developed cracks in the compacted specimen. It is therefore important to understand the behavior of powder material by an appropriate constitutive model.A number of constitutive models have been developed for the compaction of powders over the last three decades, including micro-mechanical models The granular material model, which has been used for the modeling of frictional materials, such as soil or rock, is then adopted to describe the behavior of powder and granular materials. This model reflects the yielding, frictional and densification characteristics of powder along with strain and geometrical hardening, which occurs during the compaction process. The experimental results of Watson and Wert The cone-cap model based on a density-dependent Drucker–Prager yield surface and a non-centered ellipse was developed by Haggblad and Oldenburg In the analysis of powder forming problems, the non-linear behavior of powder is adequately described by double-surface plasticity model. However, it suffers from a serious deficiency when the stress-point reaches in the intersection of these two different yield functions. In the flow theory of plasticity, the transition from an elastic state to an elasto-plastic state appears more or less abruptly. For powder material it is very difficult to define the location of yield surface and special treatment should be made to avoid numerical difficulties in the intersection of these two surfaces In the present paper, the single-cap plasticity developed by first author in reference The mechanical behavior of powders involves several interacting micro-mechanical processes. Firstly, at low pressure, particle sliding occurs leading to particle re-arrangement. The second stage involves both elastic and plastic deformation of the particles via their contact areas leading to geometric hardening (i.e. plastic deformation and void closure). Lastly, at very high pressure, the flow resistance of the material increases rapidly due to material strain hardening. Therefore, it is necessary that the constitutive model of powder captures the various behaviors of compaction process. Based on these requirements, the following plasticity model is developed here for both isotropic and kinematic hardening behaviors using the three invariants of stress states, J1, J2D and J3D, asF(σ,α,κ)=ψJ3D2/3+23J2D+ϕdfdϕhfh2J12-ϕd2fd2=0where J1 is the first invariant of stress tensor and J2D and J3D are the second and third invariants of deviatoric stress tensors. α and κ are the kinematic and isotropic hardening parameters, respectively, and fh and fd are material functions, which are functions of hardening parameters. Different combinations of fh and fd lead to different shapes of the yield surface. It should be mentioned that material functions can be decomposed into two parts, the isotropic and kinematic parts, which control the shape of the yield surface. In Eq. , ϕh and ϕd are coefficients, which indicate the effect of material functions fh and fd in yield surface . Parameter ψ causes triangularity of deviatoric trace along the hydrostatic axis. presents the 3D representation of yield surface for the isotropic and kinematic hardening behavior of material.The isotropic and kinematic hardening parameters κ and α evolve with plastic deformation. The evolution of κ is related to the mean stress, and more directly to the plastic volumetric strain εvp aswhile the evolution of α is related to the deviatoric plastic strain ep. As can be expected, the kinematic hardening parameter α={α1α2α3}T can be decomposed in two directions J1 and J2D in meridian plane, which contains two parts as follows:αi=a1exp(a2(epT:ep)a3)+(a4(epT:ep)a3epii)i=1,2,3where the first term controls the movement of yield surface in J1-axis and the second term controls the movement of yield surface in perpendicular direction to J1-axis. a1, a2, a3 and a4 are material parameters. The three components of kinematic hardening parameter α, i.e. α1, α2 and α3, determine the values of the yield surface movements in the directions of principal stresses σ1, σ2 and σ3, respectively.As mentioned earlier, the material functions fh and fd control the size and movement of the yield surface, and are functions of hardening parameters. Then, these functions can be decomposed into two parts, i.e. the isotropic and kinematic parts, asThe isotropic part of material functions fh and fd are the exponential increasing functions of the isotropic hardening parameter κ=εvp, defined aswhere b1, b2, b3, c1, c2 and c3 are the material parameters and δ(εvp) is defined asIn order to determine the kinematic parts of material functions , consider two different stress spaces σi and Ξi; the former is located in the center of the yield surface before kinematic hardening and the later is placed in the center of the yield surface after kinematic hardening. The distance of centers of two coordinate systems can be defined by αi, in which the relationship between the principal stresses in two stress spaces is defined asDefining the parameters J1α and J2Dα similar to the definitions of the invariants of stress and deviatoric stress tensors asConsidering the definition of the principal stresses in two stress spaces, defined by Eq. , the three-invariant single plasticity where JI is the first invariant of stress tensor and JIID and JIIID are the second and third invariants of deviatoric stress tensors in the second stress space, defined as in the absence of third invariants of deviatoric stress with respect to Eq. , the kinematic parts of material functions fh and fd can be therefore written asFinally, the material functions fh and fd can be defined by substituting equations fh=(b1+b2exp(b3εvp))δ(εvp)+1ϕh(2J1αJ1+J1α2)1/2fd=(c1+c2exp(c3εvp))δ(εvp)+1ϕd-23(J2Dα+Jσα)1/2The object of the mathematical theory of plasticity is to provide a theoretical description of the relationship between stress and strain or more commonly, between increments of stress and increments of strain using the assumption that the material behaves plastically only after a certain limiting value has been exceeded. The elasto-plastic constitutive relation in its incremental form can be presented by dσ |
= |
Depdε, with dσ denoting the incremental stress vector, dε the incremental strain vector and Dep the constitutive elasto-plastic matrix. The yield surface F(σ, |
α, |
κ) = 0 determine the stress level at which the plastic deformation begins. The material property matrix Dep is defined aswhere n |
= ∂F/∂σ and ng |
= ∂Q/∂σ are the normal vector to the yield and potential plastic surfaces, respectively, and H is the hardening plastic modulus defined as where dλ is the plastic multiplier and μ=(ep,εvp).In order to derive the constitutive elasto-plastic matrix and its components, we need to calculate De, n, ng and H in Eq. . The normal vector to the yield surface is determined byn=∂F∂σ=∂F∂J1∂J1∂σ+∂F∂J2D∂J2D∂σ+∂F∂J3D2/3∂J3D2/3∂σ∂F∂J1=2J1ϕdfdϕhfh2+ϕd2fd2ϕh3fh32J12J1α-(2/3)(2J1αJ1+J1α2)∂F∂J2D=23+2J12fdϕd2ϕh2fh2∂fd∂J2D-2ϕd2fd∂fd∂J2D∂F∂J3D2/3=ψ+2J12fdϕd2ϕh2fh2∂fd∂J3D2/3-2ϕd2fd∂fd∂J3D2/3The hardening plastic modulus H can be determined by substituting the yield surface H=-∂F∂fh∂fh∂epdepdλ+∂F∂fd∂fd∂epdepdλ+∂F∂fh∂fh∂εvpdεvpdλ+∂F∂fd∂fd∂εvpdεvpdλ∂fh∂ep=-1ϕh(J1+J1α)-(2J1αJ1+J1α2)2∂α1∂ep+∂α2∂ep∂fd∂ep=(α2-α1)3ϕdJ2Dα+Jσα∂α2∂ep-∂α1∂ep+J2Dcosω-3sinω2ϕd3(J2Dα+Jσα)∂α1∂ep-∂α2∂epIn order to demonstrate the performance of the proposed plasticity model in prediction of powder material behavior, the experimental tests must be performed to determine and calibrate the parameters of material functions fh and fd, defined by . These two material functions control the size and movement of the yield surface, and are decomposed into the isotropic and kinematic parts, given by , as functions of the hardening parameters κ and α, or directly the plastic volumetric strain εvp and the deviatoric plastic strain ep. It must be noted that the kinematic hardening parameter α indicates the movement of the yield surface in the direction of J1-axis and perpendicular direction to J1-axis.It is worth mentioning that different values of material functions fh and fd result in different aspects of the yield surface . Consider that the first two terms of Eq. The above equation generally yields to three roots, the points of intersection of yield surface with J1-axis, i.e. J1 |
= ±ϕhfh and one more from fd |
= 0.0, which has been defined in Eq. . If fd |
= 0.0 does not lead to any value for J1, the yield surface of Eq. yields to two roots for J1, i.e. J1 |
= ±ϕhfh, which results in an elliptical shape in meridian plane. The 3D representation of the yield surface in principal stress space for different values of isotropic hardening, where the intersection point of yield surface with J1-axis are −ϕhfh and +ϕhfh. This representation clearly shows how the yield surface grows with densification, eventually becoming independent of the hydrostatic stress J1 at full dense material, where the von-Mises yield surface is generated. This yield surface is very similar to the elliptical yield functions developed by authors for porous metal and sintered powder based on an extension of von-Mises’s concept If fd |
= 0.0 leads to the value of J1 between −ϕhfh and +ϕhfh, the cone-cap yield surface will be produced from Eq. based on the intersection points of J1 |
= −ϕhfh and the value obtained from fd |
= 0.0, as shown in for different values of isotropic hardening. As can be observed from this figure the yield surface grows with densification and reduces to the Drucker–Prager yield function for full dense bodies. This yield surface is very similar to the double-surface cap models, i.e. a combination of Mohr–Coulomb or Drucker–Prager and elliptical surfaces, which has been extensively used by authors to demonstrate the behavior of powder and granular materials presents the effect of parameter ψ in the yield surface that causes triangularity of deviatoric trace along the hydrostatic axis. This yield surface is similar to the irregular hexagonal pyramid of the Mohr–Coulomb and cone-cap yield surface employed by researchers for description of soil and geomaterial behavior The important issue in prediction of powder material behavior is the identification of parameters of the proposed plasticity model. The calibration procedure for three-invariant isotropic–kinematic cap plasticity is carried out based on a series of isostatic and triaxial tests. An organized approach to determine model parameters is to utilize an optimization routine. Mathematically, an objective function and a search strategy are necessary for the optimization. The objective function, which represents the constitutive model, captures the material behavior and can be used in a simultaneous optimization against a series of experimental data. The simplest search strategy is based on the direct search approach, which is proved to be reliable and its relative simplicity make it quite easy to program into the code.For the proposed constitutive model, the total number of 10 material constants need to be determined for the material functions fh and fd. The parameters of isotropic parts of fh and fd (i.e. b1, b2, b3 and c1,c2,c3) are firstly evaluated using the confining pressure test, where the values of J2D and J3D in the yield surface are zero. The parameters of the kinematic parts of fh and fd (i.e. a1,a2,a3 and a4) are then estimated performing the LSM method on the data obtained by a series of triaxial tests. These parameters control different aspects of predicted stress–strain curves obtained numerically by fitting the stress path to the triaxial and confining pressure tests, including: the slope, transition, expansion and contraction.a1: controls the slope of ‘stress–axial strain’ and ‘radial strain–axial strain’ diagrams.a2: controls the slope of ‘radial strain–axial strain’ diagram after dilation.a3: controls the transition of ‘radial strain–axial strain’ diagram before dilation.a4: controls the transition of ‘stress–axial strain’ and ‘radial strain–axial strain’ diagrams, and the slope of ‘stress–axial strain’ curve.b1: controls the transition, expansion and contraction of ‘radial strain–axial strain’ diagram, and the slope, expansion and contraction of ‘stress–axial strain’ curve.b2: controls the transition, expansion and contraction of ‘stress–axial strain’ and ‘radial strain–axial strain’ diagrams, and the slope of ‘radial strain–axial strain’ curve.b3: controls the slope and transition of ‘radial strain–axial strain’ curve, and the slope of ‘stress–axial strain’ diagram.c1: controls the slope, expansion and contraction of ‘stress–axial strain’ and ‘radial strain–axial strain’ diagrams.c2: controls the slope, transition, expansion and contraction of ‘stress–axial strain’ diagram, and the slope of ‘radial strain–axial strain’ diagram.c3: controls the slope of ‘stress–axial strain’ curve, and the slope and transition of ‘radial strain–axial strain’ diagram after dilation.The procedure of parameter determination is performed as follows:Based on the results obtained from the confining pressure test, the values of J1 are evaluated using the yield surface where the values of J2D and J3D are zero. From the values of volumetric strain εv, the elastic and plastic volumetric strains, εve and εvp, are estimated. The parameters b1, b2 and b3 in the isotropic part of fh are computed. The parameters c1, c2 and c3 in the isotropic part of fd are then calculated by a least square method on the data obtained from the confining pressure test.Applying the results of triaxial tests and the isotropic parameters of fh and fd obtained from Step 1, the kinematic parameters of fh and fd, i.e. a1, a2 and a3, in the first term of relation are first estimated. Parameter a4 in the second term of relation is then obtained by performing the least square method on the data obtained from the triaxial tests.The first example refers to a set of triaxial loading paths on a cylindrical grade tungsten powder specimen performed by Alm et al. The material parameters calibrated for the yield surface are as follows:a1=5.0e-10a2=0.7a3=0.01a4=-1.0e-4b1=150.3b2=0.4b3=-0.1c1=580.5c2=17.0c3=-9.5a, the first invariant of stress tensor J1 versus volumetric strain is presented for the hydrostatic pressure test. It shows a good agreement between the model and experimental results. In b, the relevant yield surfaces corresponding to the isotropic hardening behavior has been shown schematically. This representation clearly shows how the yield surface grows with densification isotropically by increasing the hydrostatic pressure. In this figure, the inner circle shows the initial yield surface and the outer one presents the yield surface at the specified point. In order to demonstrate the isotropic and kinematic hardening behaviors in a set of triaxial tests, the variations of axial stress with axial and radial strains are plotted in at different confining pressures. Also plotted in Figs. b are the relevant yield surfaces corresponding to the isotropic and kinematic hardening behavior. As can be observed, the proposed plasticity model captures the behavior of powder in a complete set of triaxial loading paths.The next experimental data are gained from a set of experiments performed by Chtourou et al. The material parameters calibrated for the yield surface are as follows:a1=2.0e-16a2=5.0a3=-0.12a4=-0.04b1=-900.3b2=1.0e-6b3=-4.15c1=600.2c2=7.0c3=-6.6a, the first invariant of stress tensor J1 versus volumetric strain is presented for the hydrostatic pressure test. This result shows a good agreement between the proposed model and experimental results. In b, the isotropic behavior of powder during the expansion of the yield surfaces is demonstrated by increasing the hydrostatic pressure. The variations of the density with the first invariant of stress tensor are plotted in at four different confining pressures. Also plotted in these figures are the isotropic and kinematic behaviors of powder in the triaxial loading paths. It must be noted that in a and b, the precompaction isostatic pressure is set to 207 MPa, while the isostatic pressure of the actual triaxial test are 207 and 276 MPa, respectively. In c and d, the precompaction isostatic pressure and the isostatic pressure are both equal and set to 276 and 345 MPa, respectively. Clearly, the isotropic and kinematic behavior of powder can be observed in a complete set of loading paths.The last example is chosen to demonstrate the performance of the proposed plasticity model in prediction of a set of compaction experiments on iron-based powder (95% by weight) performed by Doremus et al. The material parameters calibrated for the proposed yield surface are as follows:a1=2.0e-17a2=35.16a3=0.08a4=-0.05b1=260.2b2=8.586e-2b3=-9.2c1=610.5c2=1.75c3=-10.85The variation of density with hydrostatic pressure is presented in a for the isostatic test. This evolution is the characteristic of metal powders. It shows a good agreement between the experimental and numerical results for the isostatic compression step. In b, the isotropic hardening behavior of powder is illustrated due to expansion of the yield surfaces by increasing the hydrostatic pressure. Clearly, the effect of confining pressure on isotropic hardening of powder can be observed in this figure. correspond to the complete triaxial compression tests. The variations of the axial stress with axial strain are shown in a at different values of hydrostatic pressure. Also plotted in a is the variation of the density with axial strain at different values of the hydrostatic pressure. Figs. b present the relevant yield surfaces corresponding to the isotropic and kinematic hardening behavior in complete triaxial tests. As can be observed, the proposed model captures the behavior of powder in complete triaxial experiment. This representation clearly shows how the yield surface grows isotropically and moves kinematically by increasing the axial strain.In the present paper, a three-invariant cap plasticity model was developed based on an isotropic–kinematic hardening rule for powder materials. A generalized description of single-cap plasticity was presented which can be compared with some common double-surface plasticity models proposed for powders in literature. Two material functions were introduced to control the size and movement of the yield surface, which are decomposed into the isotropic and kinematic parts as functions of the hardening parameters. The kinematic hardening parameter was defined to indicate the movement of the yield surface in the direction of J1-axis and in the direction of perpendicular to J1-axis. The constitutive elasto-plastic matrix and its components were derived by using the definition of yield surface, material functions and nonlinear elastic behavior, as function of hardening parameters. The calibration procedure for three-invariant isotropic–kinematic cap plasticity was demonstrated based on a series of isostatic, triaxial and uniaxial compression tests. Finally, the applicability of the proposed model was illustrated in modeling of experiments on three different powder components, including: a cylindrical grade tungsten powder specimen, a blend of Alcan 316L stainless steel powder, and an iron-based powder component. The variation of the first invariant of stress tensor with volumetric strain was presented for the hydrostatic pressure test. It was shown how the yield surface grows with densification isotropically by increasing the hydrostatic pressure. Furthermore, the variations of axial stress with axial and radial strains were obtained at different confining pressures corresponding to the set of triaxial tests to present the isotropic and kinematic hardening behavior of powders. Remarkable agreements were observed between experimental and numerical results.∗Correspondingauthor．Prof．,Ph．D． EＧmailaddress:ylheï¼ t．shu．edu．cn (Yô€†°L．He)． Received２５Julyï¼’ï¼�１６;Receivedinrevisedform２５Augustï¼’ï¼�１６; Acceptedï¼’ï¼™Augustï¼’ï¼�１６ Availableonline１５Marchï¼’ï¼�１７ １ï¼�ï¼�６Ｇ７ï¼�ï¼–X/Copyrightâ“’ï¼’ï¼�１７,TheeditorialoficeofJournalofIronandSteelResearch,International．PublishedbyElsevierLimited．Alrightsreserved． InＧsituanalysisofretainedaustenitetransformationinhighＧperformance microＧaloyedTRIPsteel JiＧboPeng１,ï¼’,　HuJiang１,ï¼’,　GongＧtingZhang３,　LiＧbenChen１,ï¼’,　NaＧqiongZhu１,ï¼’,　YanＧlinHe１,ï¼’,∗ , XiaoＧgangLu１,ï¼’,　LinLi１,ï¼’ １SchoolofMaterialsScienceandEngineering,ShanghaiUniversity,Shanghaiï¼’ï¼�ï¼�ï¼�ï¼—ï¼’,China ï¼’StateKeyLaboratoryofAdvancedSpecialSteel,ShanghaiUniversity,Shanghaiï¼’ï¼�ï¼�ï¼�ï¼—ï¼’,China ３PangangGroupResearchInstitute,Panzhihua６１７ï¼�ï¼�ï¼�,Sichuan,China ARTICLEINFO Keywords: TiＧVmicroＧaloyedTRIPsteel Retainedaustenitestability InＧsituanalysis Microstructure ABSTRACT MicrostructuresandmechanicalpropertiesofTiＧVmicroＧaloyedTRIP (transformationＧinduced plasticity)steelwithdifferentcompositionswereinvestigatedbytensiletest,scanningelectron microscopy(SEM),transmissionelectronmicroscopy (TEM), XＧraydiffraction (XRD)and thermodynamiccalculation(TC)．Theresultsindicatedthatthesteelexhibitedhighultimate tensilestrength(１ï¼�ï¼—ï¼™MPa),sufficientductility(２８％)andthehighestproductofstrengthand ductility(３ï¼�２１２MPaô€…°ï¼…)heattreatedafterintercriticalannealingat８ï¼�ï¼�°Cfor３minandbaiＧ niticannealingat４３ï¼�°Cfor５min．Inaddition,thechangeofvolumefractionofretainedaustenＧ ite(VFＧRA)versustensilestrainwasmeasuredusinginＧsituanalysisbyXＧraystressapparatus andmicroＧelectronicuniversaltestingmachine．ItwasconcludedthataＧvaluecouldbeusedto evaluatethestabilityofretainedaustenite(SＧRA)intheinvestigatedTiＧVmicroＧaloyedTRIP steel．ThesmaleraＧvalueindicatedthehigherstabilityofretainedaustenite (SＧRA)andthe highermechanicalpropertiesofTiＧVmicroＧaloyedTRIPsteel． １．Introduction 　Automobileindustryhasmadeeffortstoimprove fuelefficiencywithlightweightstructuralmaterialsin carbodies．TRIP (transformationＧinducedplasticity) steel[１] ,asakindofadvancedhighＧstrengthsteel,is knownforitsexcelentcombinationofhighultimate tensilestrength(UTS)andgoodtotalelongation(TE) becauseofitsmetastableretainedaustenitephasewhich cantransformtomartensiteduringtensiletest． 　AccordingtoZhu[ï¼’] ,theTRIPsteelwithAladdition exhibitstheproductoftensilestrengthandelongation (PSE)ofï¼’ï¼’ï¼�ï¼�ï¼�MPaô€…°ï¼…．Itiswelknownthatthe mechanicalpropertiesofTRIPsteelmainlydepend onthestabilityofretainedaustenite (SＧRA)[３Ｇ７] , whichisdeterminedbyfactorssuchasthecarbon content,grainsize, morphologyanddistributionof retainedausteniteandthesecondphase[８Ｇ１２]．InorＧ dertodevelophighＧperformanceTRIPsteelsforveＧ hicleapplications,microＧaloyingelements(Nb,V, Ti) have been added to produce precipitation strengtheningrecently[１３]．ButstudiesonTRIPsteel withPSEof３ï¼�ï¼�ï¼�ï¼�MPaô€…°ï¼…andsystematicalyevaluaＧ tingSＧRAarelimited．Steelswithdiferentcontentsof C, Al, V,andTiwereinvestigatedbytensiletest, scanningelectronmicroscopy (SEM),transmission electronmicroscopy(TEM),XＧraydifraction(XRD), inＧsituanalysisandthermodynamiccalculation(TC)in currentwork,aimingtostudytheinteractionbeＧ tweenaloying elements, SＧRA and mechanical propertiesforTRIPsteel,andtoprovidetheoretical referencefordevelopingnewgenerationvehicle． ２．ExperimentalMaterialsandProcedure 　Theinvestigatedsteelswerepreparedasa１５ï¼�kg ingotinavacuuminductionfurnace．Thecastingots werehotroledtoathicknessof３ô€†°ï¼•mm,pickled andsubsequentlycoldroledto１ô€†°ï¼’mminthickＧ ness．Thechemicalcompositionsofinvestigated steelsarelistedinTable１．Theinvestigatedsteels wereannealedinasaltbathfurnaceandtheheat treatmentprocesses(HTP)areshowninFigô€†°ï¼‘． 　Mechanicalpropertieswereevaluatedbytakingthe averagevalueofthreeA５ï¼�samplestestedusing 　　　　　　　　　JournalofIronandSteelResearch,Internationalï¼’ï¼”(ï¼’ï¼�１７)３１３ï¼�３２ï¼�　　　　　　　　　　 Table１ Chemicalcompositionsofinvestigatedsteels(massï¼…) Steel C Si Mn Al V Ti N A ï¼�ô€†°ï¼’１ ï¼�ô€†°ï¼˜ï¼˜ ï¼’ô€†°ï¼�８ ï¼�ô€†°ï¼˜ï¼” ï¼�ô€†°ï¼�９５ ï¼�ô€†°ï¼�９４ ï¼�ô€†°ï¼�ï¼�５ B ï¼�ô€†°ï¼’ï¼— ï¼�ô€†°ï¼˜ï¼— １ô€†°ï¼™ï¼— ï¼� ï¼�ô€†°ï¼�９６ ï¼�ô€†°ï¼‘５ï¼� ï¼�ô€†°ï¼�ï¼�５ C ï¼�ô€†°ï¼’８ ï¼�ô€†°ï¼™ï¼� ï¼’ô€†°ï¼�ï¼� １ô€†°ï¼‘ï¼’ ï¼�ô€†°ï¼�８３ ï¼�ô€†°ï¼‘５ï¼� ï¼�ô€†°ï¼�ï¼�５ D ï¼�ô€†°ï¼“１ ï¼�ô€†°ï¼™ï¼‘ ï¼’ô€†°ï¼�ï¼– ï¼�ô€†°ï¼—ï¼– ï¼�ô€†°ï¼�９４ ï¼�ô€†°ï¼�ï¼�ï¼™ ï¼�ô€†°ï¼�ï¼�５ Figô€†°ï¼‘．　Schematicdiagramofheattreatmentprocesses． CMT５３ï¼�５universaltestingmachinewithcrosshead speedofï¼’mm/min．Microstructurewasobservedusing SEM (HITACHIＧS５７ï¼�S)andTEM (JEMＧ２ï¼�１ï¼�F)． HeatＧtreatedsamplesforSEMwerepreparedwithï¼” volô€†°ï¼…nital．FoilsforTEM wereslicedfrombulk specimensandmechanicalypolishedtoabout５ï¼�μm discswithadiameterof３mm．ElectrolyticpolisＧ hingwasconductedusing５volô€†°ï¼…perchloricacidin ethanolatï¼�ï¼’ï¼�°CinatwinＧjetelectrolyticpolisher． Thesize, morphologyanddistributionofprecipiＧ tateswerestudiedbycarbonreplicaextractionand TEMtechnique．Thecarbonfilmwasdepositedon theetchedsurfaceandscoredinto１×１mmsquare gridsbeforeetchingagaininnital,andtheetched surfacewasthenetchedin５volô€†°ï¼…nitalforaround ï¼’ï¼�s．Finaly,thespecimenwasslidintodistiled waterandthereplicaswerecolectedbyacoppernet anddried．Precipitationwasidentifiedbyelectron diffractionpatternsandenergydispersivespectromＧ eter(EDS)analysis．Inaddition,carbideparticles werechemicalyextractedinphosphoricacid(２∶１) atroomtemperatureandfilteredusingamicroＧporＧ ousmembranewithï¼’ï¼�nmapertureanddried．AD/ MAXＧ２５ï¼�ï¼�XＧraydifractometeroperatingatï¼”ï¼�kVand ï¼”ï¼�mAwasusedtodeterminethetypeofprecipitates． 　ThechangeofthevolumefractionofretainedaustenＧ ite (VFＧRA) asafunctionoftensilestrain was measuredusinganXＧraystressapparatus (XＧ３５ï¼�) aidedbymicroＧelectronicuniversaltestingmachine． A３ï¼�sampleswerestretchedwithcrossheadspeedof ï¼�ô€†°ï¼•mm/minusingamicroＧelectronicuniversaltesＧ tingmachine,andVFＧRAinthetensilezoneofthe specimenwasmeasuredwithanintervalofacertain strainby XＧraystressapparatustoobservethe changeofVFＧRAduringtensiletesting． ３．Results 　Figô€†°ï¼’showstheSEMmicrographsofthefoursteels (a)SteelA; 　 (b)SteelB; 　 (c)SteelC; 　 (d)SteelD． Figô€†°ï¼’．　SEM micrographsofinvestigatedsteelsheattreatedafterannealingat８ï¼�ï¼�°C×３minandï¼”ï¼�ï¼�°C×５min． ４１３ 　　　Jô€†°B．Pengetal．/JournalofIronandSteelResearch,Internationalï¼’ï¼” (ï¼’ï¼�１７)３１３ï¼�３２ï¼� heattreatedafterintercriticalannealingat８ï¼�ï¼�°Cfor ３minandbainiticannealingatï¼”ï¼�ï¼�°Cfor５min．Itis foundthatthemicrostructureofthesteelsiscomＧ posedofferrite(F),bainite(B),andretainedausＧ tenite(RA),asmarkedinFigô€†°ï¼’． 　AsshowninFigô€†°ï¼“,thesequenceofPSEforthe investigatedsteelsfromthehighesttolowestissteel D,steelC,steelBandsteelAonthewhole．Among them,steelAexhibitedthehighestUTSandthe lowestTE． 　TheHTPforinＧsituanalysis, whicharerespecＧ tivelychosentoobtainthebestmechanicalproperＧ tiesforthefoursteels,areshowninTable２． 　ThechangeofVFＧRAwasinＧsituanalyzedandthe (a) UTS; 　 (b) TE; 　 (c)PSE． Figô€†°ï¼“．　Tensiletestresultsofinvestigatedsteels． Tableï¼’ HeattreatmentprocessesforinＧsituanalysisofinvesＧ tigatedsteels Steel A B C D HTP ８ï¼�ï¼�°C× ３min ８ï¼�ï¼�°C× ３min ８２ï¼�°C× ３min ８ï¼�ï¼�°C× ３min ï¼”ï¼�ï¼�°C× ５min ４３ï¼�°C× ５min ３７ï¼�°C× ５min ４３ï¼�°C× ５min resultsareshowninFigô€†°ï¼”．ItcanbeseenthatVFＧ RAdecreaseswiththeincreaseofstrain．InaddiＧ tion,retainedaustenitestartedtodecomposewhen theyieldingstresswasreached．Thus,itcouldbe concludedthatthegradualdecompositionofretained austenite wasinducedand performedthe TRIP effect．Moreover,VFＧRAinsteelCandsteelDdeＧ creasedgradualyafteryieldingstressandthetransＧ (a)SteelA; 　 (b)SteelB; 　 (c)SteelC; 　 (d)SteelD． Figô€†°ï¼”．　ChangeofVFＧRAandengineeringstressversusengineeringstrainofinvestigatedsteels． ５１３　　　Jô€†°B．Pengetal．/JournalofIronandSteelResearch,Internationalï¼’ï¼” (ï¼’ï¼�１７)３１３ï¼�３２ï¼� formationofretainedaustenitefinishedwhenengiＧ neeringstrainisaboveï¼�ô€†°ï¼“５．ButforsteelAandsteel B,VFＧRAdroppedsharplyafteryieldingstress,and thetransformationofretainedausteniteinsteelA endedwhilethestrainwaslessthanï¼�ô€†°ï¼’５． 　AccordingtoTableï¼’,theequilibriumsecondphase compositionsofinvestigatedsteelsattheirintercritiＧ caltemperatureswerecalculatedusingTCandthe resultsarelistedinTable３．AsshowninTable３, theequilibriumsecondphasesexistinginsteelsA,B andCareTiCandTiNparticles,whicharedifferent fromsteelDwithVCandAlNprecipitates． Table３ Equilibriumsecondphasecompositionsofinvestigatedsteels Number TiC VC TiN AlN A ï¼�ô€†°ï¼‘９２volô€†°ï¼…５ï¼�ô€†°ï¼•ï¼… V＋２９ô€†°ï¼™ï¼… Ti＋１８ô€†°ï¼–ï¼…C ï¼� ï¼�ô€†°ï¼‘ï¼�３volô€†°ï¼… ７８ô€†°ï¼’ï¼… Ti＋１３ô€†°ï¼–ï¼…C＋７ô€†°ï¼’ï¼… N ï¼� B ï¼�ô€†°ï¼’８１volô€†°ï¼…４２ô€†°ï¼™ï¼… Ti＋３８ô€†°ï¼�ï¼… V＋１８ô€†°ï¼˜ï¼…C ï¼� ï¼�ô€†°ï¼‘３７volô€†°ï¼… ï¼—ï¼—ô€†°ï¼™ï¼… Ti＋１５ô€†°ï¼�ï¼…C＋５ô€†°ï¼”ï¼… N ï¼� C ï¼�ô€†°ï¼’５９volô€†°ï¼…４４ô€†°ï¼�ï¼… Ti＋３６ô€†°ï¼•ï¼… V＋１８ô€†°ï¼™ï¼…C ï¼� ï¼�ô€†°ï¼‘３８volô€†°ï¼… ï¼—ï¼—ô€†°ï¼˜ï¼… Ti＋１５ô€†°ï¼’ï¼…C＋５ô€†°ï¼’ï¼… N ï¼� D ï¼� ï¼�ô€†°ï¼‘３８volô€†°ï¼…６８ô€†°ï¼“ï¼… V＋８ô€†°ï¼™ï¼… Ti＋１７ô€†°ï¼™ï¼…C ï¼� ï¼�ô€†°ï¼�３４volô€†°ï¼… ６５ô€†°ï¼˜ï¼… Al＋３５％ N ４．Discussion 　RelatedstudiespointedoutthatTiCandVCare bothfaceＧcentredcubicstructuralprecipitateswhich havethecrystalographyrelationshipof {CubeＧonＧ Cube((ï¼�ï¼�１)(Ti,V)C‖ (ï¼�ï¼�１)γ[ï¼�１ï¼�](Ti,V)C‖ [１１ï¼�]γ)} withaustenitewhichisalsofaceＧcentredcubicstrucＧ ture[ï¼’,１４] , namely, TiCandVCinaustenitehave highenergyorientationrelationshipwithaustenite, whichresultsindissolutionofcarbidesbecauseof instabilityofprecipitatesfortheincreaseofitssurＧ faceenergy[１５]．Thedissolutionbehaviorincreases thecarbonconcentrationofausteniteintwoＧphase region,whichimprovesSＧRAobviously． 　ForsteelA withthelowestPSE,althoughthe carboncontentofausteniteincreasesduetothedisＧ solutionoftitaniumcarbide,theretainedaustenite isnotstableenoughbecauseofthelowcarbonconＧ tent(ï¼�ô€†°ï¼’１wtô€†°ï¼…)ofmatrixandthelimitedcontent ofdissolvedcarbidesowingtothelowestconcentraＧ tionofTiCprecipitatesaslistedinTable３．TheforＧ mationofmartensite[１６,１７]insteelAheattreatedafＧ terannealingat８ï¼�ï¼�°C×３minandï¼”ï¼�ï¼�°C×５minis showninFigô€†°ï¼•ï¼ŽMartensitedeterioratesthe meＧ chanicalpropertieswithUTSashighas１２ï¼�ï¼�MPa andlow TE, resultinginobviouslylow PSEfor steelA． 　WithoutAladdition,thePSEvaluecanstilreachas highasï¼’ï¼’ï¼�ï¼�ï¼�MPaô€…°ï¼…forsteelB, whichaccounts forthedissolutionofsufficientcontentof(Ti,V)C precipitateslistedinTable３．AsshowninFigô€†°ï¼–, thedensityof(Ti,V)Cdecreasesandthenumberof bigsize(Ti,V)Cparticlesdeclineswhilethesmal size(Ti,V)CprecipitatesincreaseswhenheattreaＧ tedafterannealingat８ï¼�ï¼�°Cfor３min,indicating thatpartof(Ti,V)Cprecipitatesdissolves, which increasesthecarboncontentofausteniteinthetwoＧ phaseregion,enhancingSＧRAinsteelB,andimprovＧ Figô€†°ï¼•ï¼Žã€€TEMmicrographofmartensiteinsteelAheattreated afterannealingat８ï¼�ï¼�°C×３minandï¼”ï¼�ï¼�°C×５min． ingthemechanicalpropertiesofsteelB． 　 According to the results calculated using TC (Figô€†°ï¼—),thecarboncontentofausteniteintwoＧ phaseregionincreasesinsteelCwithAladditionin comparisonwiththatinsteelB,thusthebainite transformationisdelayedduringcontinuouscoolＧ ing;SＧRAafterbainiticannealingisenhanced,reＧ sultingingoodTRIPeffectandimprovingthePSE valueofsteelCto２５ï¼�ï¼�ï¼�MPaô€…°ï¼…． 　SteelDexhibitstheoptimalmechanicalproperties amongalinvestigatedsteels．HeattreatedafteranＧ nealingatintercriticaltemperatureof８ï¼�ï¼�°Cfor３min andbainitictemperatureof４３ï¼�°Cfor５min,thePSE valueofsteelDcanachieve３ï¼�２１２MPaô€…°ï¼…．Asshown inFigô€†°ï¼˜, thevolumefractionofprecipitatesin steelsCandDasafunctionoftemperaturewasfurＧ theranalyzedusingTC．Combinedwiththeresults listedinTable３,thevolumefractionofTiNinsteelC ６１３ 　　　Jô€†°B．Pengetal．/JournalofIronandSteelResearch,Internationalï¼’ï¼” (ï¼’ï¼�１７)３１３ï¼�３２ï¼� (a) TEMmicrographofprecipitatesincoldＧroledsheet; 　 (b) TEMmicrographofprecipitatesinsheetheattreatedafterannealingat ８ï¼�ï¼�°Cfor３min; 　 (c)XRDanalysisofprecipitatesinsheetheattreatedafterannealingat８ï¼�ï¼�°Cfor３min; 　 (d)Particlesize distributionincoldＧroledsheet; 　 (e)Particlesizedistributioninsheetheattreatedafterannealingat８ï¼�ï¼�°Cfor３min． Figô€†°ï¼–．　PrecipitatesanalysisinsteelB． Figô€†°ï¼—．　VerticalsectionofphasediagramforsteelsBandC． isfoundtobeabout１ô€†°ï¼‘×１ï¼�ï¼�３．Inaddition,thevolＧ umefractionofAlNisapproximately２×１ï¼�ï¼�ï¼”, which isfarlessthanï¼’ô€†°ï¼‘×１ï¼�ï¼�３forVC．Consideringthe XRDanalysisresultsofprecipitatesinsteelsCand Dwhenheattreatedafterannealingat８ï¼�ï¼�°C×３min andï¼”ï¼�ï¼�°C×５min(Figô€†°ï¼™),itisconcludedthatTiN particlesmustexistinsteelCandtheAlNparticles maynotprecipitateinsteelD． 　Figô€†°ï¼‘ï¼�showsthefracturesofsteelsCandDheat treatedafterannealingat８２ï¼�°C×３min,３７ï¼�°C×５min and８ï¼�ï¼�°C×３min,４３ï¼�°C×５min,respectively．It isapparentthatquadrateTiNparticlesexistinthe fractureofsteelC,thesizeofwhichisabout２μm, (a)SteelC; 　 (b)SteelD． Figô€†°ï¼˜ï¼Žã€€Volumefractionofprecipitatesininvestigatedsteelsasafunctionoftemperature． ７１３　　　Jô€†°B．Pengetal．/JournalofIronandSteelResearch,Internationalï¼’ï¼” (ï¼’ï¼�１７)３１３ï¼�３２ï¼� (a)SteelC; 　 (b)SteelD． Figô€†°ï¼™ï¼Žã€€XRDanalysisofprecipitatesininvestigatedsteelsheattreatedafterannealingat８ï¼�ï¼�°C×３minandï¼”ï¼�ï¼�°C×５min． Figô€†°ï¼‘ï¼�．　SEM micrographsofinvestigatedsteelsC (a)andD (b)． butAlNparticleshavenotbeenobservedinthefracＧ tureofsteelD．AccordingtoLiandChen[１８] ,the morphologyofTiNmainlydependsonitssize．TiN withgrainsizebelowï¼–nmismainlyspherical,but itstartstoturnintoquadrateshapeduringfurther growth．ThemechanicalpropertiesofsteelCaredeＧ terioratedwhilebigquadrateTiNparticlesprecipitaＧ tedasthecracksourceduringtensiletesting．InconＧ clusion,the mechanicalpropertiesofsteelDare moreexcelentthanthoseofsteelC． 　Itiswelknownthatthemainfactordetermining themechanicalpropertiesofTRIPsteelisSＧRAas mentionedabove[３Ｇ７]．ToevaluateSＧRAsystematiＧ caly,theTRIPeffectformulaisappliedas[１９] : 　　logln fs fsï¼�f é ë êê ù û úúï¼�logk＋mlogε (１) where,fsandfrefertothevolumefractionofthe saturatedmartensiteandthemartensitetransformed duringdeformation,respectively;εrepresentsthe truestrain;mrepresentsthedeformationmodecoＧ efficient, whichremainsstableat１ô€†°ï¼�; andkis characterizedasthecoefficientofSＧRAandthelarＧ gerkvalueindicatesthelowerSＧRA． 　Eqô€†°(１)canbeturnedintoEqô€†°(ï¼’)inthepresent study． 　　 f fs æ è ç ö ø ÷ï¼�１ï¼�exp(ï¼�kε) (ï¼’) 　ConsideringthestrainＧinducedphasetransformaＧ tionofretainedaustenitewithcriticaltruestrain value,Eqô€†°(３)isusedtofitthetransformedVFＧRA asafunctionoftruestrain．yrepresentsthevalueof f/fsandaisequaltok． 　　yï¼�１ï¼�exp[ï¼�a(xï¼�b)] (３) 　ThefittingaＧvalueindicatesSＧRA．ThelargeraＧ valuecorrespondstothelowerstability．brefersto thetruestrainwhenthephasetransformationbegins andxisequaltothetruestrain． 　TheinＧsituanalysisresultsandthefittedcurves ofinvestigatedsteelsareshowninFigô€†°ï¼‘１．Itis foundthattheexponentialfunction (Eqô€†°(３))fits theexperimentaldatawelandaＧvaluecanbeused toevaluateSＧRAintheinvestigatedTiＧVmicroＧalＧ loyedTRIPsteels,namely,thesmaleraＧvalueinＧ dicatesbetterSＧRA．Inaddition,comparisonofaＧ valueandPSEofinvestigatedsteelsisshownin Figô€†°ï¼‘２．ItisconcludedthatthesteelwithsmaleraＧ valueexhibitedbettermechanicalproperties． ５．Conclusions 　 (１)ThebestmechanicalpropertiesofinvestigaＧ ８１３ 　　　Jô€†°B．Pengetal．/JournalofIronandSteelResearch,Internationalï¼’ï¼” (ï¼’ï¼�１７)３１３ï¼�３２ï¼� (a)SteelA; 　 (b)SteelB; 　 (c)SteelC; 　 (d)SteelD． Figô€†°ï¼‘１．　InＧsituanalysisresultsandthefittedcurveofinvestigatedsteels． Figô€†°ï¼‘２．　ComparisonofaＧvalueandPSEofinvestigatedsteels． tedsteelscanbeobtainedforsteelDwhenheattreaＧ tedafterintercriticalannealingat８ï¼�ï¼�°Cfor３min andbainiticannealingat４３ï¼�°Cfor５min,withtenＧ silestrengthreaching１ï¼�ï¼—ï¼™ MPa,elongationreacＧ hing２８％,andthePSEreaching３ï¼�２１２MPaô€…°ï¼…． 　 (ï¼’) Theausteniteheattreatedafterintercritical annealingisnotstableenoughforlowcarbonconＧ tentofmatrix,leadingtotheformationofmartensＧ itewhichisharmfultothemechanicalproperties duetotheweakTRIPeffect．Thecarboncontentof austeniteintwoＧphaseregionincreaseswithAladdiＧ tion,delayingthebainitictransformation,andthe mechanicalpropertiesofthesteelisimproveddueto goodSＧRA． 　 (３)ThemechanicalpropertiesofTiＧVmicroＧalＧ loyedTRIPsteelareimprovedbecauseofthedissoＧ lutionoftitaniumandvanadiumcarbidesduringinＧ tercriticalannealing．Butthemechanicalproperties ofthesteelcanbedeterioratedwhenTiNwithpolyＧ gonparticlesandlargeparticlesprecipitatedasthe cracksourceduringtensiletesting． 　 (ï¼”)Theexponentialfunctionyï¼�１ï¼�exp[ï¼�a(xï¼� b)]fitstheexperimentaldatawelandaＧvaluecan beusedtoevaluateSＧRAintheinvestigatedTiＧV microＧaloyedTRIPsteels．ThesmaleraＧvalueindiＧ catesthehigherSＧRAandthehighermechanical propertiesofTiＧVmicroＧaloyedTRIPsteel． Acknowledgment 　ThisworkwassupportedbytheShanghaiMuniciＧ palScienceandTechnologyCommission(GrantNo． １５DZï¼’ï¼’ï¼–ï¼�３ï¼�ï¼�,１５DZï¼’ï¼’ï¼–ï¼�３ï¼�１)andShanghaiMuniciＧ palNaturalScienceFoundation(１７ZR１４１ï¼�ï¼”ï¼�ï¼�)． ９１３　　　Jô€†°B．Pengetal．/JournalofIronandSteelResearch,Internationalï¼’ï¼” (ï¼’ï¼�１７)３１３ï¼�３２ï¼� References [１] 　Vô€†°F．Zackay,Eô€†°R．Parker, D．Fahr, R．Busch, Trans．ASM ï¼–ï¼�(１９６７)２５ï¼�Ｇ２５９． [ï¼’] 　Nô€†°Q．Zhu,StudyandCalculationofthePrecipitationBehavior ofCarbidesinAutomotiveSteelsandtheMicrostructureand Properties,ShanghaiUniversity,Shanghai,ï¼’ï¼�１３(inChinese)． [３] 　Jô€†°J．Wang,Sô€†°Vô€†°D．Zwaag, Metal．Mater．Trans．A３２ (ï¼’ï¼�ï¼�１) １５２７Ｇ１５３９． [ï¼”] 　S．Traint, A．Pichler,K．Hauzenberger,P．Stiaszny,E．WerＧ ner,SteelRes．７３(ï¼’ï¼�ï¼�ï¼’)２５９Ｇ２６２． [５] 　Nô€†°H．vanDijk, Aô€†°M．Butt,L．Zhao,J．Sietsma,Sô€†°E．OfferＧ man,Jô€†°P．Wright, ActaMater．５３(ï¼’ï¼�ï¼�５)５４３９Ｇ５４４５． [ï¼–] 　L．Samek,E．DeMoor,J．Penning,Bô€†°C．DeCooman, Metal． Mater．Trans．A３７(ï¼’ï¼�ï¼�ï¼–)１ï¼�９Ｇ１２４． [ï¼—] 　F．Hajiakbari, M．NiliＧAhmadabadi,B．Poorganji,T．FuruhaＧ ra, ActaMater．５８(ï¼’ï¼�１ï¼�)３ï¼�７３Ｇ３ï¼�７４． [８] 　L．Samek,E．deMoor,J．Penning,Bô€†°C．deCooman,J．MaＧ ter．Trans．３７(ï¼’ï¼�ï¼�ï¼–)１ï¼�９Ｇ１２４． [ï¼™] 　Dô€†°V．Edmonds,Rô€†°C．Cochrane, Metal．Trans．２１ (１９９ï¼�)１５２７Ｇ １５４ï¼�． [１ï¼�] 　K．Sugimoto, M．Misu, M．Kobayashi, H．Shirasawa,ISIJ Int．３３(１９９３)７７５Ｇ７８２． [１１] 　Gô€†°N．Haidemenopoulos, M．Grujicic, Gô€†°B．Olson, M．CoＧ hen,J．Aloy．Compd．２２ï¼�(１９９５)１４２Ｇ１４７． [１２] 　J．Chiang,B．Lawrence,Jô€†°D．Boyd,Aô€†°K．Pilkey, Mater．Sci． Eng．A５２８(ï¼’ï¼�１３)４５１６Ｇ４５２１． [１３] 　W．Bleck, K．Hulka, K．Papamentelos, Mater．Sci．Forum ２８４Ｇ２８６(１９９８)３２７Ｇ３３４． [１４] 　Qô€†°L．Yong,SecondaryPhasesinSteels, MetalurgicalIndusＧ tryPress,Beijing,ï¼’ï¼�ï¼�ï¼–(inChinese)． [１５] 　Iô€†°E．Locci,Xô€†°C．Guo, Metal．Mater．Trans．A３(１９９１)５７Ｇ ６４． [１６] 　Nô€†°H．vanDijk,Aô€†°M．Butt,L．Zhao,J．Sietsma,Sô€†°E．OfferＧ man,Jô€†°P．Wright,S．vanderZwaag,ActaMater．５３(ï¼’ï¼�ï¼�５) ５４３９Ｇ５４４ï¼�． [１７] 　A．Kammouni, W．Saikaly, M．Dumont,C．Marteau,X．BaＧ no, A．Charai, Mater．Sci．Eng．A５１８(ï¼’ï¼�ï¼�ï¼™)８９Ｇ９５． [１８] 　Yô€†°L．Li, Mô€†°Z．Chen,JournalofBeijingNormalUniversity３５ (１９９９) Noô€†°ï¼‘,３８Ｇ４１(inChinese)． [１９] 　Cô€†°G．Lee,Sô€†°J．Kim,Tô€†°H．Lee,S．Lee, Mater．Sci．Eng．A ３７１(ï¼’ï¼�ï¼�ï¼”)１６． ï¼�２３ 　　　Jô€†°B．Pengetal．/JournalofIronandSteelResearch,Internationalï¼’ï¼” (ï¼’ï¼�１７)３１３ï¼�３２ï¼� (ï¼’) Theausteniteheattreatedafterintercritical annealingisnotstableenoughforlowcarbonconＧ tentofmatrix,leadingtotheformationofmartensＧ itewhichisharmfultothemechanicalproperties duetotheweakTRIPeffect．Thecarboncontentof austeniteintwoＧphaseregionincreaseswithAladdiＧ tion,delayingthebainitictransformation,andthe mechanicalpropertiesofthesteelisimproveddueto goodSＧRA． 　 (３)ThemechanicalpropertiesofTiＧVmicroＧalＧ loyedTRIPsteelareimprovedbecauseofthedissoＧ lutionoftitaniumandvanadiumcarbidesduringinＧ tercriticalannealing．Butthemechanicalproperties ofthesteelcanbedeterioratedwhenTiNwithpolyＧ gonparticlesandlargeparticlesprecipitatedasthe cracksourceduringtensiletesting． 　 (ï¼”)Theexponentialfunctionyï¼�１ï¼�exp[ï¼�a(xï¼� b)]fitstheexperimentaldatawelandaＧvaluecan beusedtoevaluateSＧRAintheinvestigatedTiＧV microＧaloyedTRIPsteels．ThesmaleraＧvalueindiＧ catesthehigherSＧRAandthehighermechanical propertiesofTiＧVmicroＧaloyedTRIPsteel． Acknowledgment 　ThisworkwassupportedbytheShanghaiMuniciＧ palScienceandTechnologyCommission(GrantNo． １５DZï¼’ï¼’ï¼–ï¼�３ï¼�ï¼�,１５DZï¼’ï¼’ï¼–ï¼�３ï¼�１)andShanghaiMuniciＧ palNaturalScienceFoundation(１７ZR１４１ï¼�ï¼”ï¼�ï¼�)． ９１３　　　Jô€†°B．Pengetal．/JournalofIronandSteelResearch,Internationalï¼’ï¼” (ï¼’ï¼�１７)３１３ï¼�３２ï¼� References [１] 　Vô€†°F．Zackay,Eô€†°R．Parker, D．Fahr, R．Busch, Trans．ASM ï¼–ï¼�(１９６７)２５ï¼�Ｇ２５９． [ï¼’] 　Nô€†°Q．Zhu,StudyandCalculationofthePrecipitationBehavior ofCarbidesinAutomotiveSteelsandtheMicrostructureand Properties,ShanghaiUniversity,Shanghai,ï¼’ï¼�１３(inChinese)． [３] 　Jô€†°J．Wang,Sô€†°Vô€†°D．Zwaag, Metal．Mater．Trans．A３２ (ï¼’ï¼�ï¼�１) １５２７Ｇ１５３９． [ï¼”] 　S．Traint, A．Pichler,K．Hauzenberger,P．Stiaszny,E．WerＧ ner,SteelRes．７３(ï¼’ï¼�ï¼�ï¼’)２５９Ｇ２６２． [５] 　Nô€†°H．vanDijk, Aô€†°M．Butt,L．Zhao,J．Sietsma,Sô€†°E．OfferＧ man,Jô€†°P．Wright, ActaMater．５３(ï¼’ï¼�ï¼�５)５４３９Ｇ５４４５． [ï¼–] 　L．Samek,E．DeMoor,J．Penning,Bô€†°C．DeCooman, Metal． Mater．Trans．A３７(ï¼’ï¼�ï¼�ï¼–)１ï¼�９Ｇ１２４． [ï¼—] 　F．Hajiakbari, M．NiliＧAhmadabadi,B．Poorganji,T．FuruhaＧ ra, ActaMater．５８(ï¼’ï¼�１ï¼�)３ï¼�７３Ｇ３ï¼�７４． [８] 　L．Samek,E．deMoor,J．Penning,Bô€†°C．deCooman,J．MaＧ ter．Trans．３７(ï¼’ï¼�ï¼�ï¼–)１ï¼�９Ｇ１２４． [ï¼™] 　Dô€†°V．Edmonds,Rô€†°C．Cochrane, Metal．Trans．２１ (１９９ï¼�)１５２７Ｇ １５４ï¼�． [１ï¼�] 　K．Sugimoto, M．Misu, M．Kobayashi, H．Shirasawa,ISIJ Int．３３(１９９３)７７５Ｇ７８２． [１１] 　Gô€†°N．Haidemenopoulos, M．Grujicic, Gô€†°B．Olson, M．CoＧ hen,J．Aloy．Compd．２２ï¼�(１９９５)１４２Ｇ１４７． [１２] 　J．Chiang,B．Lawrence,Jô€†°D．Boyd,Aô€†°K．Pilkey, Mater．Sci． Eng．A５２８(ï¼’ï¼�１３)４５１６Ｇ４５２１． [１３] 　W．Bleck, K．Hulka, K．Papamentelos, Mater．Sci．Forum ２８４Ｇ２８６(１９９８)３２７Ｇ３３４． [１４] 　Qô€†°L．Yong,SecondaryPhasesinSteels, MetalurgicalIndusＧ tryPress,Beijing,ï¼’ï¼�ï¼�ï¼–(inChinese)． [１ïIn-situ analysis of retained austenite transformation in high-performance micro-alloyed TRIP steelMicrostructures and mechanical properties of Ti-V micro-alloyed TRIP (transformation-induced plasticity) steel with different compositions were investigated by tensile test, scanning electron microscopy (SEM), transmission electron microscopy (TEM), X-ray diffraction (XRD) and thermodynamic calculation (TC). The results indicated that the steel exhibited high ultimate tensile strength (1079 MPa), sufficient ductility (28%) and the highest product of strength and ductility (30212 MPa · %) heat treated after intercritical annealing at 800 °C for 3 min and bainitic annealing at 430 °C for 5 min. In addition, the change of volume fraction of retained austenite (VF-RA) versus tensile strain was measured using in-situ analysis by X-ray stress apparatus and micro-electronic universal testing machine. It was concluded that a-value could be used to evaluate the stability of retained austenite (S-RA) in the investigated Ti-V micro-alloyed TRIP steel. The smaller a-value indicated the higher stability of retained austenite (S-RA) and the higher mechanical properties of Ti-V micro-alloyed TRIP steel.Impact resistance of nacre-like composites diversely patterned by 3D printingMulti-layered composites structured by replicating biological creatures are very promising protective material applicable in various industries for the outstanding mechanical characteristics. Particularly, nacre is the most sought-after creature for biomimicry due to the exceptional impact resistance, secured by hierarchically patterned architecture. Therefore, numerous efforts have been devoted aiming to develop high functional composites by mimicking the nacre. However, optimization of dimensions and material properties for the nacre-like geometry has not been fully investigated thus far. In this study, we utilize a combination of fabrication, testing, and simulation to explore an optimal design of the nacre-like composite. Various types of 3D nacre-like architecture are designed, and corresponding specimens are fabricated using a dual-extruder 3D printer. Under drop weight impact loading, impact performances of each specimen are demonstrated. The test is simulated with finite element models of the nacre-like composite, and the experiment and numerical results are in good agreement. Both results reveal that the nacre-like composite outperforms the monolithic stiff material upon impact. Furthermore, adequate dimensions of each constituent and desirable material properties are determined. This insight on the nacre-like design can be employed as a guideline toward further optimization for a new generation of high-performance material systems.Development of advanced multi-material composites with high impact resistance and energy absorption capacity has attracted much attention in the scientific community due to the rapid growing applications in diverse industrial fields Meanwhile, significant efforts have been devoted to yield a new class of multi-material composites with highly enhanced mechanical properties by mimicking natural materials possessing extremely efficient designs through the biological evolution to fulfill required functions Particularly, the biomimicry has been mainly conducted on damage-tolerant biological structures such as nacre, bone, and animal scale, having a very complex hierarchical geometry, where hard and stiff main constituents in a regular arrangement are bonded by soft or ductile interfaces, revealing high strength and toughness Among the diverse biological materials worth replicating, nacre has been the most sought-after creature in biomimetics due to its exceptionally enhanced fracture toughness and impact resistance compared with mechanical properties of each constituent material Many studies have shown that the nacre-like architectures can yield enhanced mechanical properties, and the corresponding key failure mechanisms like nonlinear deformation have been disseminated by means of fabrication, mechanical testing, and numerical simulation. However, only limited experiments and numerical simulations were conducted with a practical loading such as low-velocity impact, while a simple tensile loading is mostly used in the verification. Besides, optimized dimensions of constituents such as platelets and matrices in the nacre-like design and desirable material properties for each constituent to produce the most enhanced mechanical performances have not been fully disclosed yet. The optimization studies under the practical loadings can be utilized as a foundation for industrial application.In this work, we present an integrative study of dimensions of stiff platelet and soft interlamellar matrix as well as material properties of the matrix enabling impact resistance enhancement by a combination of multi-material 3D printing, drop weight impact test, and finite element analysis. Diverse types of 3D nacre-like composite models are developed for dimensions of each constituent by employing a Voronoi diagram, and corresponding 3D bimaterial specimens are fabricated by means of a dual-extruder 3D printer. Under drop weight impact tests, enhancement of impact resistance obtained from each prototype is investigated through comparisons with the result from a monolithic stiff model. Additionally, the impact test is simulated with a 3D finite element model of the nacre-like composite, and numerical and experiment results are compared. It is expected that this systematic study of the nacre-like architecture could help carrying out optimization of the design, elevating practical usage of biological composites in various industrial fields.By replicating the complex hierarchical architecture found in the nacre, we design five different types of nacre-like composite by manipulating the dimensions of each constituent. The nacre consists of brittle aragonite platelets and soft interlamellar matrices, forming a brick and mortar structure (). The arrangement of the platelets dividing the region of each nacre layer is similar to the cells generated by a Voronoi diagram describes the process of generating a nacre-like structure. First, seeds are regularly located in the center of rectangular grids with a length of α (-(a)). The seeds are randomly shifted by a radius r and an angle θ with a range of 0 to π, and Voronoi cells are generated based on the configuration of the seeds (-(b)). The region is cut by the boundaries of thick black lines to generate the nacre-like design. The Voronoi cells are contracted by a certain gap Wg (-(c)), and the contracted cells resemble the shape of nacre platelets. The remained area by contracting the cells is similar to the shape of interlamellar matrices bonding the platelets, and the area would be filled with soft materials. The nacreous patterns are projected to a height of H, and stacked to form a nacreous multi-layered architecture (-(d)). A thin layer of height h is inserted between the layers generated by projecting the nacreous pattern. Five different models are developed according to this formation process of the nacre-like design with manipulating the parameters α and Wg (). The parameters α and Wg are set as the initial dimension parameters, and those are applied to generate the nacre-like model with initial constituent dimensions (-(a)). Other four nacre-like models are generated with the parameters increased by 1.5 and 2 times, respectively: increased α enlarges the size of platelets (-(b) and (c)), while the interlamellar matrices are thickened by increasing Wg (The three dimensional (3D) printing technique enables precise fabrication of structures with complex geometries In this work, a dual-extruder FDM 3D printer manufactured by Ultimaker was employed to fabricate experiment specimens. Each 3D model of the nacre-like specimens developed in Section was used as input in 3D printing processes.In the fabrication, polylactic acid (PLA), stiff and high strength polymer, was chosen for the hexagonal platelets of the nacre-like composite. Meanwhile, we selected more than one material for the soft interlamellar matrices to evaluate their significance against the impact loading: soft and ductile nylon and thermoplastic polyurethane (TPU) rubber-like material. Both the TPU and nylon have low tensile strength and high ductility, but the nylon has about half the failure strain and nearly twice the strength of the TPU. Parameters such as nozzle and build plate temperatures, and printing speed for printing these three different materials were set according to the manufacturer’s recommendations The temperature of the build plate was kept at 60 °C, while the nozzle temperatures for printing the PLA, TPU, and nylon were maintained at 210 °C, 222 °C, and 245 °C, respectively throughout the printing. The printing speeds for each material were equally set to 10 mm/s considering both printing quality and efficiency. Unlike the PLA and TPU, the nylon has inferior adhesion with the build plate, which highly degrades the overall printing quality. The adhesion between printed nylon and the build plate could be improved by attaching an adhesion sheet provided by Ultimaker on the build plate.According to the 3D printing guideline described in Section , we fabricated the 3D specimens of the nacre-like composites suitable for the drop weight impact test. All the specimens were rectangular shaped, and their dimensions were 60 mm (length) × 60 mm (width) × 7 mm (height) as shown in Specimen 1 is a monolithic specimen made of the stiff material (PLA), and was prepared for comparisons with the nacre-like specimens in terms of the energy absorption capacity against the drop weight impact loading (). For the nacre-like specimens, those have three main layers of a height 2 mm composed of the stiff platelets (PLA) and soft matrices (TPU or nylon), and two soft interlayers of a height 0.5 mm inserted between the main layers. In each main layer, the soft matrices envelop each stiff platelet (-(b) and (c)). These specimens can be categorized into two types by the constituent materials: specimens 2 to 6 have the TPU interlamellar matrices, while the matrices in specimens 7 to 11 are made of nylon. Specimens 2 and 7 have platelets of a diameter 10 mm and matrices of a thickness 0.8 mm, which are initial constituent dimensions because those properly produced the nacre-like geometry within the overall specimen size (-(b) and (c)). Platelets in specimens 3 and 8 have about 2.5 times larger area, while specimens 4 and 9 have 4.5 times larger platelets compared with those of specimens 2 and 7, (). On the other hand, specimens 5 and 10 have the matrix 1.5 times thicker than those of the specimens 2 and 7, while specimens 6 and 11 have 2 times thicker matrix (, the platelet length refers to a distance α from a seed in a platelet to a seed in an adjacent platelet as described in . The platelet area increases by 4.5 times larger when the platelet length is doubled (from the specimens 2 and 7 to specimens 4 and 9, respectively). Also, volume fractions of the matrix in the specimens 2 to 11 are presented, which is determined by the platelet length and matrix thickness. Compared with the original size specimens (the specimens 2 and 7), the specimens 6 and 11 have the highest matrix volume fraction and the specimens 4 and 9 have the lowest matrix volume fraction.To investigate low-velocity impact resistance behavior of the nacre-like specimens fabricated in this work, drop weight impact tests were carried out using an Instron CEAST 9350 drop tower impact tester. The test setup is illustrated in . Firstly, the specimen was clamped by the clamping system consisting of the lower and upper constraints. Those have a central circular hole of an internal diameter 40 mm, leaving the circular free surface of a diameter 40 mm of the specimen exposed to the impactor. The specimen was placed on the lower constraint, and then the pressure of 3 bar was applied on the specimen by the upper constraint.Subsequently, the hemispherical impactor of a diameter 20 mm carrying a total weight of 20.41 kg was dropped from a set height and struck the specimen with the impact velocity 3.13 m/s. As the impactor was in contact with the specimen, the contact force was measured by a piezoelectric load cell embedded in the impactor tup, and the applied impact energy to the specimen was 100 J.When the impactor was in contact with the specimens, the time histories of the contact force were recorded and the damage patterns in the specimens were observed. The impact test was repeated four times, and the four recorded time histories of the contact force were not identical because each 3D printed specimen has a slight difference in the geometry due to 3D printer’s operation tolerance., the monolithic PLA specimen (specimen 1) exhibits brittle failure and sudden collapse of the structure. -(a) and (b) display the damage patterns on the top and bottom faces, respectively, and it is observed that complete perforation through the specimen and spalling on the bottom face occurred. This brittle failure can be analyzed through -(c) presenting the time histories of the contact force. As the failure is in the brittle mode, high contact force of 6 kN was measured at 1 ms, and the specimens were completely perforated at around 3 ms on average. This catastrophic failure of the specimen 1 indicates that it has limited energy absorption and dissipation capacity. In , the average values of absorbed energy for the specimens 1, 2 and 7 against the impact loading are calculated. Due to the insufficient impact energy absorbing capacity, the specimen 1 only absorbed 19.01 J.On the contrary, the sudden collapse and brittle failure were not exhibited in the PLA-TPU nacre-like specimens (specimen 2), and the complete perforation through the specimens did not occur (). It is observed that radial cracks were formed along the interface between the PLA platelets and TPU matrices on the impacted area as shown in -(a) and (b). In addition to this gradual interface debonding and breakage, fracture and deformation partially occurred on the stiff PLA platelets and soft TPU matrices, respectively as the specimen was impacted. This unique mode of failure enables prevention of the sudden collapse of the structure delocalizing the fracture and deformation.Also, this uniqueness can be identified in -(c) presenting the time histories of the contact force exerted on the specimen 2. The contact forces increase linearly up to around 2 kN until 0.5 ms, but those show several slight step changes from 0.5 to 3.5 ms. It indicates that gradual interfacial debonding between the PLA platelets and TPU matrices occurred as the impact proceeded. During this period, the contact forces reached their maximum values (around 3 kN). For the nacre-like (PLA-TPU)-2, there was a larger step change at around 2 ms, implying that the fracture of the PLA platelets was mainly taken place at the corresponding time compared with the other specimens. After 3.5 ms, the contact forces gradually decreased, but the complete failure did not occur. This novel impact resistance behavior governed by the gradual interface debonding can presumably be achieved through embracing the TPU matrices with the nacre-like architecture in the specimen. Consequently, the impact energy dissipating and absorbing capacity of the specimen 2 is significantly enhanced (120%) compared with that of the specimen 1 as presented in The impact resistance behavior of the nacre-like specimen composed of the PLA and nylon (specimen 7) is shown in . The specimen 7 has much degraded impact resistance compared with the specimen 2, although those have the same platelets-matrices architecture. Nevertheless, the specimen 7 still has about 25% higher impact energy absorbing capacity than the specimen 1 as presented in The damage patterns of the impacted specimen 7 are shown in -(a) and (b), where almost complete perforation through the specimen is observed. Compared with the specimen 2, the interface debonding between the PLA platelets and nylon matrices as well as the ductile fracture of the nylon matrices highly occurred, while the brittle fracture of the PLA platelets is similarly exhibited. This failure mode could be a result of lower ductility of the nylon and weaker interfacial bonding force between the PLA and nylon. Consequently, the nylon matrices in the specimen are incapable of yielding an adequate contribution toward resisting the impact.-(c), the time histories of the contact force exerted on the PLA-nylon specimens (specimen 7) are plotted. The contact forces reach the maximum value (around 2 kN) at about 2 ms, and then those gradually decrease until 6 ms. The complete failure did not occur, but the contact forces converged to nearly zero at around 6 ms. Compared with the specimen 2, both the magnitude and duration time of the contact force are reduced in the specimen 7, indicating the energy absorption capacity is degraded.Also, more step changes are observed as the contact forces decrease from 2 to 6 ms. As aforementioned, this is due to the insufficient contribution of the soft matrices in resisting the impact. As the impact progresses, it is assumed that interfacial debonding between the PLA and nylon and ductile failure of the nylon matrices occurred more prematurely.By comparing the experiment results of the specimens 2 and 7, the soft matrices’ role under the drop weight impact and desirable material properties for the constituent can be determined. The soft matrices with the nacre-like design allow enlargement of the contact area underneath the projectile, along with the gradual crack formation at the interfaces, suppressing the sudden collapse of the structure. In the meantime, the stiff platelets are partially fractured and the soft matrices are highly stretched. This large plastic deformation of the matrices without the ductile fracture help maintaining the nacre-like architecture as the impact progresses, delocalizing the damages radially from the path of the impactor. As a result, more impact energy can be dissipated and absorbed.Based on this failure mechanism, a material suitable for the soft matrices is required to have reasonably high ductility and fracture toughness to improve the impact performance. Moreover, it is essential to have the high interfacial bonding force between the component materials. As aforementioned, the nylon has highly deteriorated adhesion with the PLA determined by the damage patterns displaying much larger interface debonding compared with the TPU. Therefore, it is more adequate to adopt the TPU for the matrices rather than the nylon although the nylon has higher elasticity and tensile strength as presented in . Since additional adhesion process is not available in a current dual extruder 3D printing, the interfacial bonding between materials is unavoidably weak as in the PLA-nylon nacre-like specimen. This limitation concerning the material adhesion could be overcome by further development of a 3D printer capable of applying various adhesives selectively between the materials during the fabrication.Significances of the stiff platelet and soft matrix in resisting the low-velocity impact were investigated by the experiment results of the specimens 3 to 6 and 8 to 11. In , the damage patterns observed from the specimens 3 to 6 are presented, and the impact force histories are plotted with the result of the specimen 2. In addition, their energy absorption capacities against the impact loading are also compared with those of the specimens 1 and 2 in -(e), the specimens 3 and 4 reach the maximum contact force earlier at around 1.7 ms and the peak force value is also higher (around 4 kN), and then those show the steeper decrease after the peak, compared with the specimen 2. In a comparison between specimens 3 and 4, the maximum force of the specimen 4 is slightly higher, and more rapid contact force drop is observed in the specimen 4 after the peak. Furthermore, the contact force is dropped to zero at around 6.3 ms only in the specimen 4. This impact resistance behavior is presumably due to the enlargement of the stiff platelets, which reduces the interface length between the platelets and matrices. Therefore, the crack formation along the interface inevitably diminishes, and the interface debonding or breakage is less likely to occur as the impact proceeds. Instead, the brittle fracture of the platelets mainly governs the failure mode of the specimens as shown in -(a) and (b). Consequently, the impact energy dissipating and absorbing capacity is degraded, which can be verified through the absorbed impact energy by the specimens 3 and 4 (34.17 and 32.62 J, respectively) presented in . As the platelets become enlarged, the low-velocity impact resistance of the structure is more likely to deteriorate.On the other hand, the specimens 5 and 6 have much different impact resistance behaviors compared with the specimens 3 and 4 as shown in -(c) to (e). First of all, the impact force histories measured on the specimens 2, 5, and 6 have the analogous trend with the gradual decrease after the blunt peak, except for the steeper decrease in a range from 4 to 8 ms recorded on the specimen 2. Correspondingly, the specimens 2, 5, and 6 have very similar damage mode dominated by the adhesive disjoint between the platelets and matrices rather than the brittle fracture on the platelets as presented in -(c) and (d). However, their impact performances vary and it is clear that the impact resistance improves as the matrices become thicker: the absorbed impact energies are 43.44, 48.30, and 53.20 J for the specimens 2, 5, and 6, respectively as presented in The thickened soft matrices as in the specimens 5 and 6 can withstand further plastic deformation, impeding the ductile fracture of the constituent under the impact. By means of this matrix reinforcement, the nacre-like configuration can be preserved longer, allowing more gradual interface breakage and efficient delocalization of the damages through the structure as the impact progresses. Moreover, the cracks are more likely to initiate and propagate through the thicker matrices, not only at the interfaces, under dynamic loading as the impact. As the damages are initiated on the soft matrices, the crack path can deviate more in the corresponding constituent, and eventually reached to the interfaces. Consequently, the more impact energy is dissipated and absorbed in the structure by means of all of these factors described above functioning together.As the volume fraction of the matrix in nacre-like structure increases, the energy tends to be absorbed more, while the maximum impact force that the composite can tolerate is more likely to decrease. Therefore, it is very important to carefully manipulate the matrix volume fraction according to a particular purpose or usage of the nacre-like composite.This impact performance variation for the constituent dimensions can also be confirmed in showing the damage patterns of the specimens 8 to 11, and the impact force-time curves plotted with that of the specimen 7.Analogous to the failure modes of the specimens 3 to 6, the brittle fracture of the platelets controls the damage pattern of the specimens 8 and 9, whereas the interface disjoints are mainly found in the specimens 10 and 11. However, the amount of perforation is generally larger in the specimens 8 to 11 as can be seen in -(a) to (d). Similarly, the impact force histories of the specimens 3 to 6 and 8 to 11 have the comparable trend, but the measured contact forces are consistently lower in the specimens 8 to 11., in which the impact energies absorbed by specimens 7 to 11 are given. As previously confirmed, enlarging the platelets reduces the impact performance, whereas thickening the matrices absorbs more impact energy. Unintentionally, the specimens 8 and 9 composed of the enlarged platelets are less capable than the specimen 1. This undermined performance of the PLA-nylon nacre-like specimens is originated from the nylon matrices’ low ductility and weak bonding force with the PLA platelets as described in Section . In summary, the impact performance variation depending on the constituent dimensions can be discovered from both the specimens 3 to 6 and 8 to 11, while the specimens 8 to 11 have the deficient capability in absorbing the impact energy.For current dual extruder FDM 3D printers, only limited polymers are available in printing rather than traditional materials used in industries such as ceramic and metal, and thus only the TPU and nylon are chosen for the soft matrices in this work. Accordingly, it is unable to evaluate the performances of nacre-like structures fabricated using the traditional materials and compare them with those of the conventional composites. More options for 3D printing materials will be available including the practical materials as the additive manufacturing technologies develop, and therefore the investigation on the various component materials can be carried out, leading to practical utilization of the nacre-like composite in industries.The low-velocity impact behaviors of the monolithic and nacre-like specimens are simulated by means of a commercially available finite element (FE) code, LS-DYNA. FE models of the monolithic PLA (specimen 1) and PLA-TPU nacre-like specimen (specimen 2) are developed implementing the experiment setup.The clamping system is modeled as shown in : the lower constraint is fixed in all directions, and the upper constraint is fully constrained except for the vertical direction. To fix the specimen, the upper constraint exerts the pressure of 3 bar on the top surface both prior to and during the transient analysis using dynamic relaxation feature of LS-DYNA. For the impactor, only the hemispherical part is modeled for the impactor to alleviate the computational cost, and then the mass is properly modified to implement the actual impactor.Meshing is carried on the 3D models of the specimens 1 and 2 developed in Section . For the specimen 2, the PLA platelets are discretized with hexahedral 8-node solid elements, while tetrahedral 4-node solid elements are used for the TPU matrices to simulate the rubber-like material behavior more precisely (). Mesh density is higher in the matrices because those play a major role in the deformation of the structure, improving the computational accuracy. The specimen 1 is discretized with hexahedral 8-node solid elements with the same size as those of the platelets.Regarding the employment of material models, a couple of material models are carefully selected to increase the calculation accuracy. For the steel impactor and clamps, a rigid material model is used since those have much higher elastic modulus and tensile strength with negligible deformation compared with those of the specimens. The PLA material is modeled using a bilinear elastic-plastic model (MAT 3), which is widely employed to simulate isotropic and kinematic hardening plasticity are used for defining the material model. The strain rate effect of the PLA material is considered by Cowper Symonds strain rate parameters, C and P, in the material model (MAT 3). The values 33 and 6.5 are applied for the C and P, respectively, in accordance with Nishida et al. In order to model the adhesive joint between the platelets and matrices, and simulate subsequent disjoint or debonding at the interface, tiebreak contact algorithm is utilized by which the platelets and matrices in immediate proximity are initially tied together and break apart at critical failure criteria Using the material models and contact algorithms proposed in Section , numerical simulations of the drop weight impact test are carried out, and the numerical results are compared with the experiment results in terms of the impact force histories in . The first specimen among the four monolithic PLA specimens is chosen to compare with the numerical result, and they are plotted together in . Those are in good agreement validating the developed monolithic FE model., the impact forces reach the first peak value (around 4 kN) at about 0.5 ms, and the sudden drops to zero are shown at around 3.2 ms representing that the complete perforation occurs in both the experiment and simulation. Although the experimentally and numerically obtained impact force histories have a slight difference in a range from 1 to 2 ms, those certainly exhibit the brittle failure and sudden collapse of the specimen. shows the comparison of the impact force histories obtained from the experiment and simulation of the specimen 2. As aforementioned in Section , the four specimens show slightly different force-time curves due to the imperfection of the current 3D printing technology. When fabricating a structure with highly complex architecture several times, a small difference in the geometry of each 3D printed specimen is inevitable due to the 3D printer’s operation tolerance. Therefore, an envelope is produced with the four force-time curves, and plotted with the numerical result in The numerically obtained impact force history resides within the envelope, having the negligible difference caused by the complex aspect of the crack initiation and propagation in the actual nacre-like architectures. The unique failure mode of the nacre-like composite enhancing the impact resistance is also observed in the simulation. The numerical contact force reaches the maximum value (around 3.5 kN) at about 3 ms and gradually decreases afterwards, but the force is not dropped to zero implying that the complete perforation on the nacre-like model rarely occurs. A couple of the step changes are also observed, which indicates that the interfaces between the platelets and matrices in the model are gradually debonded, and the constituents are partially fractured and deformed as the impact proceeds.-(b) and (d) show the damage pattern on the impacted area of the nacre-like model observed in the simulation. Similar to the experiment, the cracks are initiated and propagated radially along the interfaces between the platelets and matrices in the simulation. In addition to the interfacial debonding, the partial fracture of the platelets and the large plastic deformation of the matrices are also exhibited. The von Mises stress distribution (MPa) at around 5 ms on the impacted area is demonstrated in -(c) and (e) for an in-depth study of the unique failure mode. The wide distribution of the stress is observed surrounding the impacted area, displaying that the contact area with the projectile is broadened. This is achieved by the progressive debonding and breakage of the adhesive joints between the platelets and matrices, which plays a critical role in the nonlinear large deformation of the specimen. Meanwhile, the TPU matrices manage to maintain the nacre-like configuration by enduring the severe deformation without the ductile failure. Consequently, the damages including the brittle fracture and plastic deformation can be spread out more, resulting in more impact energy dissipation and absorption.Nacre has exceptional fracture toughness and impact resistance compared with its constituent materials due to the unique architecture created by an arrangement of the stiff platelets and soft matrices. In this work, we develop ten types of three-dimensional nacre-like composite model using the Voronoi diagram depending on the constituent dimensions and materials. By means of a dual extruder 3D printer, the corresponding 3D bimaterial specimens are fabricated with two sets of contrasting materials: PLA for the platelet and TPU or nylon for the matrix. The drop weight impact tests are carried out to determine the impact resisting performances of each specimen with the effects of the platelet and matrix, and desirable material properties for the matrix. Additionally, the finite element model of the nacre-like specimen is developed, and the drop weight impact test is numerically simulated using LS-DYNA enabling an in-depth study of the failure mode including stress distribution around the impacted area.In the experiment, the brittle failure and sudden collapse are mainly shown in the monolithic specimen made up of the PLA, resulting in the complete perforation upon the impact. On the other hand, the nacre-like specimen has highly enhanced impact resistance performance exhibiting the unique failure mode, which is governed by gradual interface debonding along with the partial fracture of the platelets and large plastic deformation of the matrices, preventing the complete perforation. These two contrasting damage patterns can also be confirmed through the impact force histories measured during the impact test, and the results agree well with the numerically calculated force-time curves. Also, the uniqueness in the failure mode is accurately simulated, revealing the enlarged contact area and widely distributed stress underneath the projectile. Furthermore, we experimentally demonstrate that the impact performance noticeably varies depending on the dimensions of each constituent. As the stiff platelets become enlarged, the brittle fracture is more likely to govern the failure mode, and the perforation is highly possible to occur, debasing the impact resistance of the nacre-like composite. On the contrary, it is found that more impact energy tends to be dissipated and absorbed as the soft matrices are thickened, allowing further plastic deformation without the ductile fracture of the soft constituent. It is also proven that a material for the soft matrices is required to have high ductility and bonding force with the stiff material, to improve the impact resistance, rather than high elasticity and tensile strength through the experiment results using the TPU and nylon.This study demonstrates that the bimaterial composites with the nacre-like hierarchical architecture are very promising to enhance the impact resistance, and establishes a foundation for optimization of the constituent dimensions and materials in those composites. This is achieved by fully harnessing the additive manufacturing, drop weight impact testing, and finite element analysis, providing a fundamental understanding of the failure process and key factors in the composites. This integration of the techniques can efficiently be exploited in carrying out future work including investigation of a mathematical relationship between the impact performance and constituent dimensions, and further optimization on the nacre-like design created by various pattern-generating algorithms.The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.Kwonhwan Ko: Conceptualization, Methodology, Investigation, Visualization, Writing - original draft. Suyeong Jin: Conceptualization, Methodology, Software, Formal analysis. Sang Eon Lee: Conceptualization, Validation, Formal analysis, Writing - review & editing. Jung-Wuk Hong: Resources, Writing - review & editing, Supervision.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.Supplementary data associated with this article can be found, in the online version, atThe following are the Supplementary data to this article:Very high cycle fatigue of nitrided 18Ni maraging steel sheetThin sheets of nitrided 18Ni maraging steel are tested under cyclic tension (load ratio R |
= 0.1) in the very high cycle fatigue (VHCF) regime. The ultrasonic fatigue testing method with a cycling frequency of about 20 kHz has been further developed for these experiments. Sheet specimens with 0.35 mm thickness are mounted on a carrier specimen, they are pre-stressed and are forced to vibrate jointly. Between 107 and 109 cycles, fatigue cracks are initiated exclusively at internal TiN inclusions. The areas of the crack initiating inclusions projected perpendicular to the applied tensile stress are evaluated. The square root of inclusion areas, (areaINC)1/2 lies between 2.5 μm and 5.3 μm. Considering inclusions as cracks, their stress intensity range is between ΔKINC |
= 1.3 MPa m1/2 and 2.4 MPa m1/2. The sizes of crack initiating inclusions influence fatigue lifetimes. This is considered in a crack propagation model and by presenting lifetimes versus the stress amplitudes multiplied by (areaINC)1/12. A mean lifetime of 109 |
cycles is found at a stress amplitude of 22% of the tensile strength, which is comparable to other high strength steels tested under cyclic tension.Several components and parts used in the transportation industry, in power plants or in medical devices are stressed with very high numbers of load cycles during service. Engine and powertrain components of vehicles for example are often loaded with more than 108 cycles. Driven by the need for an economic and safe design, very high cycle fatigue (VHCF) properties of the employed materials need to be appropriately characterised. Cyclic strength and mechanism of fatigue damage may be different when lifetimes increase from the high cycle fatigue (HCF) to the VHCF regime. No sound method exists to extrapolate HCF data to the VHCF regime, which make experimental investigations necessary.A great impulse for the interest in VHCF of materials were studies on high strength steels, which showed failures and decreasing S–N curves when cycled beyond the classical fatigue limit at 107 cycles Maraging steels show very high strength combined with good toughness, practically no dimension change and no cracking during hardening treatment, good formability and excellent weldability. These benefits compared with heat treatable steels make them potentially attractive for load bearing components stressed in the VHCF regime. Fully reversed tension–compression fatigue tests in the HCF and VHCF regime were performed with four 18Ni maraging steels with different maximum inclusion sizes Maraging steel may be nitrided to improve surface hardness and wear resistance. High hardness and beneficial surface compression stresses in nitrided surfaces can improve the cyclic properties VHCF properties of thin 18Ni maraging steel sheets with nitrided surfaces are studied in the present work. The ultrasonic fatigue testing method with a cycling frequency of approximately 20 kHz is used to study lifetimes up to 109 cycles at load ratio R |
= 0.1. Ultrasonic testing is well suited to perform VHCF investigations within reasonable testing times due to its high testing frequency Cyclic properties of 18Ni maraging steel sheets with nitrided surface are investigated. The chemical composition is in weight-%: Ni 18%, Co 9%, Mo 5%, Ti 0.5% and rest Fe. Specimens are manufactured from coil material in the solution annealed condition. They are precipitation hardened at 480 °C for 2.5 h which leads to the formation of strengthening Ni3Ti and Ni3Mo precipitates. Mechanical properties of the precipitation hardened material in the core of the specimens are tensile strength 2000 MPa, yield strength 1800 MPa and Vickers hardness 580 HV. After the maraging heat treatment the specimens are gas nitrided for 1 h at a temperature below 480 °C. The nitriding treatment produces a surface layer with a depth of the diffusion zone of approximately 30 μm depth. Vickers hardness at the outer surface of the nitriding layer is about 1000 HV.The specimen shape used in the present investigation is shown in . The edges of the sheets in the centres are rounded (rounding radius between 0.09 and 0.10 mm). Cyclic and static stresses are maximal in the centre of the specimen and decrease as the load bearing cross section increases towards the ends of the specimen. The volume and the surface subjected to greater 95% of the nominal stress is 2.7 mm3 and 17.5 mm2, respectively.The experiments have been performed using the ultrasonic equipment described in detail in Ref. However this testing method is not feasible with the present material, as the sheets of 0.35 mm thickness would buckle under ultrasonic loading, leading to undefined bending stresses and premature failure. Therefore the existing setup was further developed as shown in . Rather than vibrating in resonance the thin sheets of 18Ni maraging steel are fixed to a carrier made of Ti6Al4V that is dumbbell-shaped like a conventional ultrasonic specimen (The static preload is realised through bending the carrier out of vertical alignment away from the end stop, fixing the specimen onto the carrier and pulling the titanium rod back towards the end stop so that it is again vertically aligned. The amount of bending for the required static strain is determined with two strain gauges that are attached to both sides of the specimen (, upper right side, detail view) and a scale on the movable end stop to guarantee preloading with load ratio R |
= 0.1 in the successive test. The exact force for pulling the rod back into vertical alignment is applied with a weight that is connected to the titanium rod’s end with a string via a deflection pulley. In its final vertically aligned position the rod does not touch the end stop by a small margin, which serves as a criterion for detecting specimen failure: If the rod does touch the end stop either the specimen’s fixture to the carrier is compromised, the specimen has lengthened through cyclic creep, or failed. However, the material does not show cyclic creep at the investigated stresses. Cyclic stresses in the titanium carrier are low enough to avoid fatigue fracture, due to its long cylindrical centre section that yields much weaker stress intensification than the shorter testing section in the sheet specimen. This effectively rules out invalid detection of specimen failure due to the carrier. Cyclic strain for the consecutive test is measured with both strain gauges. The transverse offset in the specimen due to the bending procedure is virtually zero due to the great relative length of the 2λ titanium rod (0.52 m) and the small yield force (⩽10 N) required for the correct bending moment.Buckling of the specimen would cause premature failure. Consequently it was verified that the strain gauges showed symmetric readings of static and dynamic strain. Additionally, vibration of the specimens perpendicular to the displacement axis has been observed occasionally with an MTI Fotonic Sensor™ fibre optic measurement system.Ultrasonic loading is performed in a pulse-pause fashion to prevent specimen heating. Additional forced-air cooling and temperature supervision with an infrared thermometer ensure that specimen temperature stays close to room temperature.The results of constant amplitude fatigue tests with nitrided 18Ni maraging steel sheets at load ratio R |
= 0.1 are shown in . Experiments are performed at stress amplitudes between 600 MPa and 450 MPa yielding lifetimes between 9.1 × 106 and 1.9 × 109 cycles. Two specimens were cycled at 450 MPa for more than 1.6 × 109 cycles and did not fail, which is indicated with arrows in S–N data are approximated with a straight line in the double logarithmic diagram. The number of cycles to failure N and stress amplitude Δσ/2 are correlated with a power law according to the following equation.With stress amplitudes in MPa, the constant amounts to C |
= 1.52 × 1047 and the exponent to n |
= 14.4. In the investigated regime below 109 |
cycles, the material does not show a fatigue limit.Scatter of data may be quantified using the ratio Tσ of numbers of cycles with 90% fracture probability, N90% and 10% fracture probability, N10% according to the following equation.Fatigue lifetimes measured at all four stress levels are included in the analysis. The influence of the stress amplitude on lifetime is considered using Eq. . A log-normal distribution of fatigue lifetimes is assumed All fracture surfaces were inspected in a Scanning Electron Microscope (SEM). From the 23 fractured specimens, 22 failed with crack initiation at an internal inclusion. In one specimen the fracture surface was deformed during final fracture and the crack initiation location could not be located any more. Thus, internal inclusions are the predominant crack initiating sites in the investigated nitrided 18Ni maraging steel sheets.Energy dispersive X-ray spectroscopy shows that the crack initiating particles in the investigated 18Ni maraging steel are TiN nonmetallic inclusions. The surface area projected perpendicular to the applied tensile stress of each crack-initiating inclusion (subsequently termed areaINC) is determined by evaluating pixels in SEM images with Photoshop®. The square root of the inclusion surface area, areaINC is used to characterise the sizes of the inclusions. The smallest crack initiating inclusion shows areaINC |
= 2.5 μm and the largest 5.3 μm. The distribution of areaINC is presented in shows crack initiation at an internal inclusion that led to failure in the VHCF regime. The crack propagates perpendicular to the applied tensile stress until it reaches a length between 60 μm and 80 μm. Then the crack leaves the perpendicular plane and approximately follows a plane of maximum shear stress. In this regime of accelerated crack growth, transgranular quasi-cleavage fracture is visible. Striations cannot be found anywhere on the fracture surfaces.The fracture surface next to the inclusion with crack propagation perpendicular to the applied tensile stress is named fish-eye fracture surface in the following. The border of the fish-eye is characterised by a change of crack propagation direction into a plane with maximum shear stress. The border has a scraggy shape in the present 18Ni maraging steel, whereas fish-eyes with approximately circular shape are often found in other high strength steels. The area of the fish-eyes varies with the stress amplitude. Mean sizes of the fish-eyes range from areafish-eye |
= 30 μm to 90 μm.The fish-eye fracture surface shows a distinct difference close to the inclusion and at greater crack lengths (). Close to the inclusion the fracture surface appears granular and homogeneous without steps or secondary cracks. In this area, the crack propagation direction cannot be deduced from the fracture surface appearance. This area (marked with a white circle in ) is named inclusion adjacent area (IAA) in the following. The fracture surface enclosing the IAA up to the border of the fish-eye appears rougher and radial secondary cracks indicate the direction of the crack growth. The surface areas of the IAAs are determined evaluating pixels in SEM figures. The sizes vary between areaIAA |
= 14 μm and 25 μm. Lower stress amplitudes associated with longer lifetimes show larger sizes of IAAs.The crack-initiating inclusion may be considered as initial crack. The stress intensity range ΔK of an arbitrarily shaped internal crack may be calculated using Eq. With the stress range Δσ and area=areaINC, the stress intensity range for the crack initiating inclusion, ΔKINC can be calculated. Circles in shows ΔKINC versus the numbers of cycles to failure. The lowest stress intensity range determined for inclusions in two specimens with failures after 1.1 × 109 and 1.8 × 109 cycles, respectively is ΔKINC |
= 1.3 MPa m1/2. The highest stress intensity range ΔKINC |
= 2.4 MPa m1/2 found for three specimens led to failures between 9 × 106 and 1.8 × 107 |
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