Plastic slip patterning through rate dependent non‐convex gradient‐enhanced plasticity

Abstract

AbstractThe paper presents a non‐convex rate dependent strain gradient plasticity framework for the description of plastic slip patterning in metal crystals. The non‐convexity is treated as an intrinsic property of the free energy of the material. Departing from explicit expressions for the free energy, the non‐convex strain gradient crystal plasticity model is derived in a thermodynamically consistent manner, including the accompanying slip law. For the numerical solution of the problem, the displacement and the plastic slip fields are considered as primary variables. These fields are determined on a global level by solving simultaneously the linear momentum balance and the resulting slip evolution equation. The slip law differs from classical ones in the sense that it naturally includes a contribution from the non‐convex free energy term, which enables patterning of the deformation field. The formulation of the computational framework is partially dual to a Ginzburg Landau type of phase field modeling approach. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)