Section 5.4 - Averaging of Viscoplastic Polycrystalline Materials with the Tangent Self-Consistent Model

Abstract

This chapter describes polycrystal averaging for time-dependent behaviors. Large deformations are considered, and the model is aimed at describing the overall stress-strain response together with the evolution of the internal structure of the material that is hardening of individual crystals, crystallographic texture, and grain morphology. Polycrystal averaging is based on several basic steps: (1) choice of a representative volume element (RVE) containing a large ensemble of grains statistically representative of the polycrystal; (2) characterization of the deformation mechanisms and of the constitutive law of individual grains; (3) description of the initial crystallographic texture and of the initial morphological texture; (4) grain interaction model; and (5) evolution laws for the crystallographic and morphological textures. The averaging scheme presented assumes that the deformation remains uniform within grains and ignores all deformation heterogeneities, such as shear bands and dislocation cells. Despite these simplifications, it is worth noting that the proposed averaging scheme is quite successful in describing the texture evolution and the overall plastic response.