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

The macroscopic behavior of a polycrystalline material (metal) depends on the characteristicsof the grain structure. Among the important properties are the size and morphologyof the grains, volume fraction of different phases, and the subgrain material modeling. In thiscontribution we put emphasis on the modeling and numerical simulation of the grain size dependenceon the macroscopic response.Within the framework of continuum thermodynamics and finite strains, we formulate a subgrainmaterial model that comprises crystal (visco)plasticity and gradient hardening. The gradienthardening gives a contribution from each slip system which is added to the well establishedlocal hardening. The grain interaction in a Representative Volume Element is resolvedusing finite elements. In order to solve the arising coupled field equations (for the displacementsand the gradient hardening in the slip systems) a so-called dual mixed FE algorithm isadopted. Linear displacements and gradients are assumed in a basic set-up. As an alternative,quadratic displacements are introduced, while the linear gradient approximation is retained.Dirichlet boundary conditions on the RVE (corresponding to a given macro-scale deformationgradient) are adopted, and various prolongation conditions inside the RVE are investigated:The Classical Taylor assumption, Relaxed Taylor assumption (to grain boundaries only) anda fully unconstrained local displacement field. In particular, the two first approaches may beused to provide a good start solution for the fully unconstrained (most general) approach. Allcomputations are restricted to 2D