Finite element modeling of porous ductile solids with non-uniform void size distributions

In this study, we use micromechanics-based modeling to investigate the effect of a non-uniform void size distribution on the plastic flow and fracture behavior of porous ductile solids. We perform 2D plane strain finite element simulations of statistical volume elements containing between 3 × 3 and 22 × 22 uniformly-spaced voids of varying sizes, using two different modeling approaches: (i) resolving the voids spatially and (ii) using a porous plasticity model and spatially varying the initial porosity. For each sample size, thirty statistical volume elements are generated through random sampling from a log-normal void size distribution to quantify the variation for a given number of voids. The macroscopic behavior and microstructural evolution are analyzed under different imposed stress states. Our findings indicate that non-uniform void sizes have negligible effects on initial yielding and behavior before peak stress, but the strain at which maximum stress is attained varies. Beyond peak stress, there is a significant variation in the macroscopic stress–strain response and void growth between the statistical volume elements. Mean failure strain decreases and scatter diminishes as sample size increases, but even large samples retain scatter in failure strain. We achieve tremendous speed-up using models with porous plasticity while producing results comparable to models with spatially resolved voids. This suggests that a cost-effective modeling approach, where the voided subregions of the model are described using a porous plasticity model and spatially varying initial porosity, facilitates simulations of 3D volume elements with a statistically representative number of voids.