Path-dependent J-integrals under mixed-mode loads of mode I and mode II

Because of its path-independence, the J-integral proposed by Rice is widely applied in fracture mechanics. In this paper, the static and dynamic J-integrals under mixed-mode loads of mode I and mode II are investigated on arbitrary integration paths surrounding the crack tip. The J1 integral is path- independent,but the J2 integral relies on the coordinate of the beginning and the end of the path. For paths that begins and ends at equidistant points from crack tip on different crack surfaces, the value of J-integrals are equal. Numerical analysis based on equivalent integration area method are carried out. The maximum deviation of solution on different paths are less than 1.23%, and the path-dependence of J-integrals is proved.This work may be helpful in fracture toughness tests of materials.