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