The role of elastic anisotropy on the macroscopic constitutive response and yield onset of cubic oligo- and polycrystals

Abstract

The single crystal elastic anisotropy is one of the most important properties affecting the macroscopic response of polycrystalline materials, both in the elastic regime and the early stages of plastic deformation. In this work, the impact of monocrystalline parameters on the mechanical behaviour of cubic polycrystals is studied in detail. The analysis is conducted with an RVE-based computational homogenisation framework which includes several original strategies and criteria developed to enable the efficient statistical analysis of virtual micro-structures. In particular, these developments include a stress-driven adaptation to the usually employed strain-driven homogenisation approach, used to study the plastic polycrystalline response in stress space. The effects of number of grains and realisations considered, finite element mesh discretisation level, and algorithms used to generate both the grain morphology and orientation distribution are also assessed. Considering a number of materials with cubic symmetry, expressions for the number of grains required for an elastically isotropic response are deduced, along with bounds for the homogenised elastic stiffness components of oligocrystals, in both cases as a function of the monocrystalline elastic anisotropy. In the plastic domain, multiple microscopic and macroscopic criteria to describe the yield onset of such polycrystals are evaluated and compared. This is done for both elastically isotropic and anisotropic polycrystals, where once again the effect of different levels of monocrystalline elastic anisotropy are evaluated. The numerically derived yield surface of isotropic polycrystals is fitted to both Tresca and von Mises yield functions, and for anisotropic oligocrystals, the statistical bounds for the expected distribution of micro-yield stresses are deduced, in terms of both the number of grains and of the level of single crystal elastic anisotropy. The results obtained are thus a step towards clarifying the effect of important micro-structural parameters in establishing the minimum representative volume element (RVE) size for metallic alloys in elasto-plastic applications.