On the multiscale analysis of a two phase material: crystal plasticity versus mean field

In this paper, a comparison is made between two multiscale methods, namely crystal plasticity finite element and mean field on a material composed of two phases. Both methods are used to homogenize a given microstructure. In order to obtain macroscopic behavior, in the mean field approach, a Self-Consistent scheme is used to evaluate stress and strain partitioning among the phases. In this method, an average of the fields is estimated and local distributions cannot be captured. In parallel, crystal plasticity simulations on Representative Volume Elements (RVEs) composed of hexagonal grains are performed. In these simulations, grain orientations are attributed randomly respecting Mackenzie's distribution function in order to achieve isotropic behavior and macroscopic hardening is extracted from the simulations. The results on macroscopic hardening of both methods are compared to distinguish the extents of validity of mean field homogenization. In addition to Self- Consistent, other mean field schemes such as Voigt, Reuss and Bound-Interpolation are compared in terms of efficiency and accuracy. The comparison manifests that Self-Consistent scheme is capable of predicting material behavior well.