Developing techniques for modeling spatially heterogeneous materials

摘要

The macroscale properties of materials evolve under the influence of phenomena arising across a broad spectrum of length scales, with spatial heterogeneity strongly influencing processes at all length scales. In order to fully investigate the effect of spatial heterogeneity on macroscale material behavior, it is necessary to formulate models that capture the interactions between microscale material phenomena and the mesoscale linkage processes that govern macroscale behavior. In order to accomplish this, a Cellular Automata (CA) based approach has been developed, in which a material volume is divided into an array of discrete domains, with each domain being randomly assigned an individual value for a property of interest. This approach has been applied to model deformation in particulate reinforced metal matrix composites (PR MMCs) and failure in ductile aluminum alloys. The nature of spatial heterogeneity has been found to strongly influence flow stresses in PR MMCs, consistent with experimental observations. The severity of local property disparities has been found to strongly influence the variability of material response, with the effect being most pronounced at high plastic strains in ductile aluminum alloys. Future development of techniques for modeling heterogeneous materials requires the application of rigorous statistical techniques for the characterization of spatial heterogeneity in material microstructures. Quadrat and distance based techniques that show potential for characterizing microstructural heterogeneity are discussed.