Quasi-static crack growth in materials displaying the Bauschinger effect—I. Steady-state analysis

Abstract

In this paper, steady-state quasi-static crack growth in an elastic-plastic material is analysed under Mode III and Mode I plane stress small-scale yielding conditions using a finite element procedure. The material is assumed to obey an incremental plasticity theory with linear isotropic or kinematic hardening. The influence of the Bauschinger effect on the stress distribution near the crack tip and crack opening profiles is examined. The results show that for Mode III and Mode I plane stress, the near-tip angular stress variation for kinematic hardening dos not deviate significantly from that for isotropic hardening except in the region behind the crack tip. A ductile fracture criterion is used to estimate the ratio Jss/Jc of the far-field J integral for steady-state crack growth to that crack initiation. This ratio is substantially smaller for kinematic hardening (as compared to isotropic hardening) which implies that the Bauschinger effect will diminish the capacity of an elastic-plastic material to sustain stable crack growth under Mode III and Mode I plane stress.