Simulation of plastic deformation induced texture evolution using the crystallographic homogenization finite element method

A semi-implicit elastic/crystalline viscoplastic finite element (FE) method based on a “crystallographic homogenization” approach is formulated for a multi-scale analysis. In the formulation, the asymptotic series expansion is introduced to define the displacement in the micro-continuum. This homogenization FE analysis is aimed at predicting the plastic deformation induced texture evolution of polycrystalline materials, the constituent microstructure of which is represented by an assembly of single crystal grains. The rate dependent crystal plasticity model is adopted for the description of microstructures. Their displacements are decomposed into two parts: the homogenized deformation defined in the macro-continuum and the perturbed one in the micro-continuum. This multi-scale formulation makes it possible to carry out an alternative transition from a representative micro-structure to the macro-continuum. This homogenization procedure satisfies both the compatibility and the equilibrium in the micro-structure. This developed code is applied to predict the texture evolution, and its performance is demonstrated by the numerical examples of texture evolution of FCC polycrystalline metals.