A high-throughput statistical homogenization technique to convert realistic microstructures into idealized periodic unit cells

Abstract

Metal alloys frequently contain distributions of second-phase particles that deleteriously affect the material behavior by acting as sites for void nucleation. These distributions are often extremely complex and processing can induce high levels of anisotropy. The particle length-scale precludes high-fidelity microstructure modeling in macroscale simulations, so computational homogenization methods are often employed. These, however, involve simplifying assumptions to make the problem tractable and many rely on periodic microstructures. Here we propose a methodology to bridge the gap between realistic microstructures composed of anisotropic, spatially varying second-phase void morphologies and idealized periodic microstructures with roughly equivalent mechanical responses. We create a high-throughput, parametric study to investigate 96 unique bridging methods. We apply our proposed solution to a rolled AZ31B magnesium alloy, for which we have a rich dataset of microstructure morphology and mechanical behavior. Our methodology converts a µ-CT scan of the realistic microstructure to idealized periodic unit cell microstructures that are specific to the loading orientation. We recreate the unit cells for each parameter set in a commercial finite element software, subject them to macroscopic uniaxial loading conditions, and compare our results to the datasets for the various loading orientations. We find that certain combinations of our parameters capture the overall stress–strain response, including anisotropy effects, with some degree of success. The effect of different parameter options are explored in detail and we find that excluding certain particle populations from the analysis can give improved results.