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

We investigate the structure of asymptotic crack tip ®elds 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 Taylorʹs dislocation hardening model to strain gradient plasticity. We show that the crack tip ®eld in MSG plasticity does not have a separable form of solution. In contrast, all previously known asymptotic ®elds around stationary crack tips have separable form of solutions such as the classical K ®eld, HRR ®eld, crack tip ®eld in the couple stress theory of strain gradient plasticity, and the crack tip ®eld in the Fleck±Hutchinson phenomenological theory of strain gradient plasticity. The physical signi®cance of this lack of separable solution of the crack tip ®eld 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 ®elds. This diculty can be overcome by combining MSG plasticity theory with a cohesive model of fracture