Computational homogenization and micromechanical analysis of textured polycrystalline materials

Abstract

We present a numerical methodology for the thermomechanical analysis of real polycrystalline material microstructures obtained using electron backscatter diffraction techniques. The asymptotic expansion homogenization method is used in conjunction with the finite element method to perform comprehensive micromechanical analyses and determine the effective thermoelastic properties of polycrystalline materials. Smooth grain boundaries are generated from the discretely sampled electron backscatter diffraction data of real polycrystalline materials. The microscale displacements, strains and stresses are related to the macroscale temperature change and strains through 21 distinct characteristic functions. The three-dimensional equilibrium equations at the microscale yield a system of partial differential equations for the characteristic functions which are solved using the finite element method. The effective properties of the polycrystalline material are obtained from the single-crystal thermoelastic properties, crystallographic orientations of the crystallites and the characteristic functions. The proposed methodology is demonstrated by considering electron backscatter diffraction maps of zinc, stainless steel, and natural quartzite rock. Results are presented for homogenized properties such as elastic stiffnesses, thermal expansion coefficients, and seismic wavespeeds, as well as for microscale stress distributions resulting from different macroscale loading conditions. The bulk thermoelastic properties are compared with those obtained using the Voigt, Reuss, Voigt–Reuss–Hill and self-consistent methods. Details are provided regarding a freely available software package that has been developed for the thermomechanical analysis of polycrystalline materials based on the proposed numerical framework.