Non-existence of separable crack tip field in mechanism-based strain gradient plasticity

Abstract

We investigate the structure of asymptotic crack tip fields associated with the recently developed theory of mechanism-based strain gradient (MSG) plasticity. The MSG plasticity theory directly connects micron scale plasticity to dislocation theories via a multiscale, hierarchical framework linking Taylor’s dislocation hardening model to strain gradient plasticity. We show that the crack tip field in MSG plasticity does not have a separable form of solution. In contrast, all previously known asymptotic fields around stationary crack tips have separable form of solutions such as the classical K field, HRR field, crack tip field in the couple stress theory of strain gradient plasticity, and the crack tip field in the Fleck–Hutchinson phenomenological theory of strain gradient plasticity. The physical significance of this lack of separable solution of the crack tip field in MSG plasticity is that stresses at a distance on the order of dislocation spacing from a crack tip can no longer be characterized by a single parameter as in classical J-controlled crack tip fields. This difficulty can be overcome by combining MSG plasticity theory with a cohesive model of fracture.