Abstract: The path independent integrals in the field of fracture mechanics have received considerable attention in recent years since Rice proposed the well known J integral in 1968. On the one hand, Herrmann and Herrmann (1981) pointed out that the integrals L and M provide a more natural description of energy release rate associated with plane cracks than the integrals J 1(≡J) and J 2 . On the other hand, Chen (1985), Chen and Hasebe (1994,1995) found that there is a simple and inherent relati...