A modified J integral for functionally graded materials

The influence of nonhomogeneity on the standard J-integral was analyzed and a modified J-integral which is path independent even in functionally graded materials (FGM) was defined. It is shown that the standard J-integral loses the path independence property in FGMs. When the J-integral domain is small, although the influence of nonhomogeneity is negative, the results of the standard J-integral are not reliable due to the inaccuracy near the crack tip. When the J-integral domain becomes larger, the influence of nonhomogeneity becomes larger and the standard J-integral becomes unstable.