NONSINGULAR STRESS AND VELOCITY-FIELDS FOR CRACK-TIP PLASTIC ZONES AND CONDITIONS FOR UNIQUENESS

Non-singular plastic stress and velocity fields, for the tip of a crack of finite thickness and root radius, are developed as an elastic-plastic crack model that is likely to be more physically realistic than the classical infinitesimal crack with a plastic crack-tip singularity. With a non-singular plastic zone the velocity-field equations are not uniquely determined by the boundary conditions, under large geometrical changes, and they must therefore have the form of a wide set of kinematically-admissible velocity fields. These virtual velocity fields are used to establish the critical work-hardening rate to give a sufficient condition for uniqueness of the crack-tip velocity field in elastic-plastic fracture; it is shown that proof of uniqueness of the velocity field is likely to be an essential requirement for the valid application of elastic-plastic fracture mechanics. The elastic infinitesimal-crack model is shown to give an inadequate representation of the 'circumferential' T-stress distribution at the surface of a crack of finite root radius, and this requires the adoption of a finite-thickness elliptical crack model to give approximate consistency between the elastic stress field and the non-singular plastic stress field at the crack tip.