Nonlinear Analysis of Interfacial Cracks

Abstract

Asymptotic analysis is developed for the problem of a plane strain crack lying on the interface of an elastic-plastic (or elastic-creeping) material and a rigid substrate. The nonlinear plastic (creep) response is taken to follow a power-law hardening relation. In contrast to other recent analyses, we have found asymptotic solutions for a continuous variation of crack-tip mode-mix that agree well with full-field solutions. These crack-tip displacements and stresses are variable-separable in polar coordinates r and θ and exhibit a singularity in stress of σ ∝ r ^-1/(n+1) as r → 0, where n is the hardening exponent. The angular variations of these asymptotic fields have been calculated using a finite difference scheme. Unlike the full range of mixed-mode solutions that exist for a homogeneous crack in a power-law hardening material, there appears to be a narrow range around the pure tensile mode for which solutions do not exist. That latter range increases somewhat as the hardening exponent n increases.