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

Other conference contribution, 2006

The macroscopic behavior of a polycrystalline material (metal) depends on the characteristics of the grain structure. Among the important properties are the size and morphology of the grains, 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. Within the framework of continuum thermodynamics and finite strains, we formulate a subgrain material model that comprises crystal (visco)plasticity and gradient hardening. The gradient hardening gives a contribution from each slip system which is added to the well established local hardening. 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. 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 deformation gradient) are adopted, and various prolongation conditions inside the RVE are investigated: The Classical Taylor assumption, Relaxed Taylor assumption (to grain boundaries only) and a fully unconstrained local displacement field. In particular, the two first approaches may be used to provide a good start solution for the fully unconstrained (most general) approach. All computations are restricted to 2D.