Modeling the influence of the nature of spatial heterogeneity on the deformation and failure of porous ductile alloys

A three-dimensional cellular automata approach has been adopted to investigate the effect of the nature of spatial heterogeneity on macroscale material behavior. Spatial heterogeneity was introduced by randomly assigning initial porosities to domains within a material model in line with one of five governing probability distributions. As the spatial distribution of the initial porosity deviated from the homogeneous ideal, the strain field developing within the models became increasingly heterogeneous, the effect being most pronounced at high strains. The variability of the macroscale response similarly increased as the initial porosity distribution deviated from homogeneity, with variation maximized in the family of models in which initial porosities were assigned in line with an extreme probability distribution representing severe pore clustering. Response variation was most pronounced at elevated strains, where the strain localization path exerted a strong influence on the macroscale response. At elevated strains, the average stress supported declined significantly as the initial porosity distribution became increasingly heterogeneous, indicating that the severity of local property disparities plays an important role in the process of strain localization.