Slip system activity in gradient enhanced crystal plasticity: Grain boundary modelling and bi-crystal response

Abstract

In gradient enhanced crystal plasticity formulations, additional conditions are required on grain boundaries which impact slip system activity in their neighborhood. In the case when gradient effects are caught through a dislocation density tensor, these conditions are prescribed on the flow of this tensor through the boundary or on the dual microforce. Gurtin (2008) proposed to derive the grain boundary behavior from a free energy potential function of a surface dislocation density tensor, the evolution of which equals the balance of flows on both sides. In this case, the response of a bi-crystal is driven by energy minimizing considerations extending the approach developed by Petryk and co-workers to gradient plasticity and grain boundary (GB) behavior: slip activity is then an optimum between deformation accommodation and limitation of accumulated bulk and GB defects energies and depends on their respective moduli. This is illustrated for the one dimensional problem of a bi-layered strip in simple shear and different cases are analyzed in terms of slip system orientations and strain hardening. Still, in the case of low angle GBs, the internal structure is assumed to be constituted of dislocation arrays accommodating the lattice misorientation between the two grains; an intrinsic dislocation density tensor can be associated to this structure and incorporated in the GB modeling.