Computational rate-independent strain gradient crystal plasticity

Size effects in metal plasticity are widely accepted, and different theoretical approaches to handle the phenomenon are developing in the literature. The present work considers the Fleck and Willis (2009b) framework, and creates a new gradient enhanced rate-independent crystal plasticity FE-implementation. The study considers both energetic and dissipative gradient hardening and strengthening, and adopts a general form of the gradient enhanced effective slip rate. Monotonic and cyclic shearing of an infinite crystal slab containing a single slip system at an angle of 90° to the loading direction is a first benchmark case. A second case considers combined shear and tension in 2D of a constrained HCP single crystal. The HCP crystal is loaded in its basal plane by a so-called butterfly deformation path that inflicts repeated loading and unloading of the three crystallographic slip systems. Finally, the evolution and interaction of multiple plastic zones are demonstrated by considering a notched tensile sample. A direct comparison to visco-plastic (rate-dependent) simulations confirms that the proposed crystal plasticity framework forms a rate-independent limit for the gradient enhanced Fleck–Willis theory. The model response also reduces to that of conventional crystal plasticity in the limit of zero length parameters.