Consider the double cantilever beam specimen shown in the figure, where the crack centered in the beam of height 2 h has a length of a , and a load P is applied to open the crack. Assume that the material is linearly-elastic and that the crack grows straight forward. Consider a rectangular path shown in the second figure: start on the top crack face, (1) go up to the top at h , (2) go to the right past the crack tip, (3) go down to the bottom at − − 2 h , (4) go along the bottom to the left, and (5) go back up to the bottom crack face. The J-integral is zero along many parts of this path. The material is effectively unloaded behind the crack, so both the strain energy density and traction are zero along (1) and (5), and hence the J-integral. Along (2) and (4) one has n 1 = 0 as well as t = 0 (no traction on the free surface), so the J-integral is zero on (2) and (4) as well. This leaves only (3); assuming one is far enough from the crack on (3), the traction term is zero since u 1 = 0 and σ σ 12 = 0 far from the crack, leaving