Some comments about the J1 integral criterion in post yield fracture mechanics

Several criteria have been proposed for Post Yield Fracture Mechanics. One of the most interesting ones is the J1 integral. When the behavior of material is elastic (even non-linear) it can be shown that J1 is not path dependent (for a straight crack without thermal stresses). For this reason, it may be considered that J1 characterizes the crack tip singularity. Extension is easy to deformation-type elastic plastic material, but there is no proof of path independence for flow-type plastic material (incremental plasticity or creep). Experimental results are often given as a proof of J1 criterion validity. But there is no experimental value of a contour integral and assumptions are made in the use of experimental results. The main assumption implies that the received mechanical work (strain energy) is not dependent of the loading history (is only dependent of mechanical state). In order to have an empirical idea of the J1 path independence, it is possible to make computations with finite elements method. Some results are given and it seems that no noticeable path dependence is seen with simple shapes and radial (proportional) loading. A few cases with complex way of loading are also studied