Asymptotic Fields of a Perfectly-Plastic, Plane-Stress Mode II Growing Crack

Abstract

The asymptotic near-tip stress and velocity fields are presented for a plane-stress Mode II crack propagating quasi-statically in an elastic-perfectly plastic Mises solid. The solution is found to have fully continuous stress and velocity fields, and a configuration similar to that of the anti-plane strain problem: a singular centered fan plastic sector ahead of the crack, followed by an elastic unloading sector and a constant stress plastic sector extending to the crack flank. The impossibility of a plane-stress Mode I crack solution having these properties is also discussed.