Elastic-plastic analysis of cracks in pressure-sensitive materials

Abstract

In this paper we present an elastic-plastic analysis of the small-scale yielding crack-tip fields for pressure-sensitive materials. Mode I loading and plane-strain conditions are assumed. The yield criterion is chosen to be a linear combination of the effective stress and the hydrostatic stress. For power-law hardening materials, our elastic-plastic finite element analysis shows that HRR-type crack-tipe fields are obtained not only for μ ⩽ μlim, but also for a range of μ >μhm. Here μlim is referred to as the limit value of a pressure sensitivity parameter μ in Li and Pan [J. Appl. Mech. 57, 40–49 (1990)]. When elastic-perfectly plastic behavior is considered, the finite element results show that elastic sectors exist near the crack tip. The sizes of the elastic sectors vary with μ. Plastic zones are also given for different values of the pressure sensitivity parameter μ and the hardening exponent n. The parameter μ has a significant effect on the plastic zone sizes and shapes. The contribution of the hydrostatic stress in the yield criterion causes the plastic zone boundary in front of the crack tip to extend much farther than that in an incompressible material.