Effects of elasticity and pressure-sensitive yielding on plane-stress crack-tip fields

Abstract

The asymptotic plane-stress mode I crack-tip fields under small-scale yielding for pressure-sensitive materials are investigated. The yield criterion for these materials is described by a linear combination of the effective stress and the hydrostatic stress. Plastic dilatancy is introduced by normality flow rule. A closed-form general asymptotic solution for singular centered fan sectors is given as a function of [mu], which is a pressure sensitivity parameter introduced in the yield condition. When elastic-perfectly plastic behavior is considered, the finite element results show the existence of elastic sectors bordering the stress-free crack faces. The near-tip stresses of the finite element results agree well with those of the corresponding asymptotic analysis. The angular spans of the elastic and plastic sectors vary with the value of [mu]. The parameter [mu] also has significant effects on the sizes and shapes of the plastic zones. The contribution of hydrostatic stress in the yield criterion for this class of pressure-sensitive materials extends the boundary of the plastic zone much farther in front of the crack-tip than that for incompressible Mises materials.