Abstract
The J2 corner theory proposed by Christoffersen et al. was applied to the interaction problem between a crack tip and voids. CT specimens with voids near the crack tip were analyzed by the finite element method using the finite deformation theory. The results were compared with those by the infinitesimal theory and those by the J2 flow theory. First, it is pointed out that the finite deformation theory is necessary to apply the J2 corner theory to the crack problem. It is also shown that the results by the J2 corner theory give larger displacement fields than those by the J2 flow theory. Especially, the difference between these two theories is recognized clearly on the interaction pattern between a crack and a void. By changing the distance between a crack tip and a void, the displacement fields were compared with each other. It is noticed that the interaction effects appear differently with the change of the distance. When the distance is small, the effects of two singularities (a crack tip and a void) overlap each other and behaves as a single singularity. It is estimated that the fracture criterion may be satisfied locally in this region before the macroscopic fracture criterion is satisfied. It is concluded that the application of the J2 corner theory is preferable for the analysis of the localization or the bifurcation problems.
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