Modeling the Grain Size Effect using Gradient Hardening and Damage in Crystal (Visco) Plasticity

Among the important properties that affect the macroscopic behavior of a polycrystalline material (metal) are the size and morphology of the grains, the volume fraction of different phases, and the subgrain material modeling. In this contribution we put emphasis on the modeling and numerical simulation of the grain size dependence on the macroscopic response (in terms of onset of yielding, hardening/softening characteristics, etc.). To this end, we formulate a subgrain material model that comprises crystal (visco)plasticity, crystal damage and gradient hardening. The crystal damage is assumed to be driven by inelastic slip in each slip system. Furthermore, the gradient hardening gives a contribution from each slip system which is added to the well established local hardening. In particular, we investigate the effect of different inter-grain conditions on the gradient hardening variable. These conditions model the misfit of crystal orientations in two neighbor grains and allow plastic slip to be transferred to different degree. Clearly, ”micro-clamped” and ”micro-free” conditions are two well-known extreme cases. The grain interaction in a Representative Volume Element is resolved using finite elements. In order to solve the arising coupled field equations (for the displacements and the gradient hardening in the slip systems) a so-called dual mixed FE algorithm is adopted. Dirichlet boundary conditions on the RVE (corresponding to a given macro-scale deformation gradient) are adopted, and various prolongation conditions inside the RVE are investigated: The classical Taylor assumption, Generalized Taylor assumption (to grain boundaries only) and a fully unconstrained local displacement field. All computations are restricted to 2D