An enhanced grain-boundary framework for computational homogenization and micro-cracking simulations of polycrystalline materials

Abstract

An enhanced three-dimensional (3D) framework for computational homogenization and intergranular cracking of polycrystalline materials is presented. The framework is aimed at reducing the computational cost of polycrystalline micro simulations, with an aim towards effective multiscale modelling. The scheme is based on a recently developed Voronoi cohesive-frictional grain-boundary formulation. A regularization scheme is used to avoid excessive mesh refinements often induced by the presence of small edges and surfaces in mathematically exact 3D Voronoi morphologies. For homogenization purposes, periodic boundary conditions are enforced on non-prismatic periodic micro representative volume elements (μRVEs), eliminating pathological grains generally induced by the procedures used to generate prismatic periodic μRVEs. An original meshing strategy is adopted to retain mesh effectiveness without inducing numerical complexities at grain edges and vertices. The proposed methodology offers remarkable computational savings and high robustness, both highly desirable in a multiscale perspective. The determination of the effective properties of several polycrystalline materials demonstrate the accuracy of the technique. Several microcracking simulations complete the study and confirm the performance of the method.