Mode I, Plane Stress Crack Initiation and Growth in Elastic-Plastic Solids: A Finite Element Analysis

Abstract

A detailed finite element analysis of crack initiation and stable crack extension is performed under Mode I plane stress, small-scale yielding conditions. A small strain, J2 incremental plasticity theory is employed and both elastic-perfectly plastic materials and power law hardening materials are considered. Some issues pertaining to the stationary plane stress crack problem, such as the range of dominance of the asymptotic stress and deformation fields and the amount of non-proportional loading near the crack tip are addressed. Special attention is devoted to the perfectly plastic idealization, by performing a separate singular finite element analysis, to clarify some details about the asymptotic fields near the stationary crack tip. The full-field numerical solution is used to simulate synthetic (optical) caustic patterns at different distances from the crack tip, which are compared with experimental observations and with asymptotic analytical results. A nodal release procedure is used to simulate quasi-static crack extension. It is found that the asymptotic angular extent of the active plastic zone, surrounding the propagating crack tip, is from θ = 0 to about θ = 45° for the perfectly plastic case. The near-tip angular stress distribution within the active plastic zone is in good agreement with the variation in a centered fan, as predicted by a preliminary asymptotic analysis by Rice, for the perfectly plastic case. It is also observed that the σrr stress component has a strong radial variation within the active plastic zone. The angular extent of active yielding around the moving tip increases with hardening, while its maximum radial extent ahead of the tip decreases. Clear evidence of an elastic unloading region following the active plastic zone is found, but no secondary (plastic) reloading along the crack flank has been numerically observed for any level of hardening. The crack tip opening profile during growth is obtained for various levels of hardening. A ductile crack growth criterion is employed to investigate the nature of the J resistance curves under plane stress. Finally, the influence of hardening on the potential for stable crack growth is examined.