A self-consistent viscoplastic model: prediction of rolling textures of anisotropic polycrystals

Abstract The plastic properties of anisotropic polycrystalline aggregates and polyphase materials are in general non-homogeneous and, as a consequence, so is the local plastic deformation. We present in this work a model that describes the plastic behaviour of non-homogeneous materials composed of anisotropic regions (grains or phases). Our model is based on describing each region as a viscoplastic inclusion embedded in the effective medium represented by the other grains, and incorporates explicitly the grain interaction with its surroundings and the plastic anisotropy of grain and matrix. Within the model the grain response is coupled to the overall response of the polycrystal and the grain deformation may differ from the polycrystal's. A characteristic of our approach is that those deformation systems with lower critical resolved shear stress tend to be more active, and less than five systems per grain are sufficient to accomodate the imposed overall deformation. In this work we explore the consequences and the limits of the model, and its dependence on the assumed rate sensitivity as well. We combine the self-consistent formulation with a volume fraction transfer scheme for treating the reorientation due to twinning, and simulate rolling textures of brass (f.c.c.), Zircaloy (h.c.p.), calcite (trigonal) and uranium (orthorhombic). We compare the results with experimental measurements and Taylor-type predictions, infer information concerning the microscopic deformation mechanisms and discuss the limits of applicability of the approach.