Asymptotic Analysis of a Mode I Crack Propagating Steadily in a Deformation Theory Material

Abstract

The near-tip asymptotic stress and deformation fields of a crack propagating steadily and quasi-statically into an elastic-plastic material are presented. The material is characterised by J2 -deformation theory, suitably modified to account for unloading and reloading, together with linear strain-hardening. The cases of plane strain and plane stress Mode I are considered. The governing equations are integrated analytically with the assistance of Muskhelishvili’s complex variable formulation. The boundary and continuity conditions then lead to a set of nonlinear algebraic equations in the coefficients of the stress functions to be solved numerically. Explicit results are given for the strength of the singularity, and for the distribution of stress in the plastic loading, elastic unloading, and plastic reloading regions, as functions of the strain-hardening parameter.