Plane strain near-tip fields for elastic-plastic interface cracks

Abstract

The plane strain problem of a stationary interface crack between two dissimilar ductile solids is studied asymptotically, where the ductile solids are assumed to be incompressible, elastic perfectly plastic, and obey the J2-flow theory of plasticity. Candidate asymptotic crack-tip assemblies of plastic and elastic sectors are proposed, and all associated admissible near-tip fields are presented. It is found that when the crack tip is fully surrounded by plastic sectors, then only isolated, mode 1 type solutions exist. When an elastic sector appears along the crack flank in one solid and all other sectors in the two solids are plastic, a two-parameter family of solutions exists, which produces crack-tip stress variations similar to those of the mixed-mode as well as mode I slip-line fields for homogeneous ductile materials. When each of the two solids contains an elastic sector along the crack flank, the crack-tip solutions are found to belong to a four-parameter family, which also resembles mixed-mode and mode I solutions for homogeneous solids. For completeness, the special case of ductile/rigid interfaces is also studied, and several one-parameter families of crack-tip solutions are obtained, which are complementary to those already published in the literature.