Some comments about the use of J1 integral criterion

Use of J1 integral criterion in Post Yield Fracture Mechanics is considered. If J1 is path independent, it can be considered as a crack tip singularity characterization and then, as a good criterion for crack initiation. But it is not proved that J1 is path independent in general case. The current practice is to consider a material with a mechanical potential energy, it is to say to suppose that strain energy W is only function of the state of strain, but not of the loading history. It is possible to introduce the defect vector concept (or driving force). The resultants of defect vectors included inside a volume are the surface integrals J vector and L vector. So the general condition for J1 path indepedence can be written. It seems that J1 is path independent for radial loading but the question is still open for more complex ways of loading. What is the effect of material memory on the J1 path dependence