A crack at the interface of two power-law hardening materials-Antiplane case

The singular behavior near the crack tip at the interface between two power-law hardening materials is studied for the case of antiplane deformation. The stress-strain curves for both materials are approximated by segments that additively combine the perfectly plastic and linear elastic behaviors in such a way that within each segment the traction is continuous across the interface. The overall solution is obtained by summing a sufficiently large number of segments, leading to an integral representation. For power-law hardening materials with different hardening exponents, n₁ and n₂, two asymptotic solutions are obtained. One is the near crack tip asymptotic solution, which shows that the interfacial stress singularity near the crack tip is - l/(n+1),where n = max (n₁, n₂). The other one is obtained under the condition that one material is much harder than the other material, and can be considered as a rigid body.