Effect of nonuniform porosity on the plastic flow and ductility of metals

The effect of nonuniform void distribution on the plastic flow of porous materials is investigated using finite strain fast Fourier transform (FFT) simulations. The prevalent belief in the literature is that nonuniform void distributions are deleterious for ductility. This belief is supported by limited and difficult-to-conduct experiments and by mean field analyses that smear out the discrete voids. Here, three-dimensional periodic cells containing monodisperse spherical voids embedded in an elastic–plastic matrix with isotropic power-law hardening are deformed to very large strains. Failure at the unit cell level is detected when zones of elastic unloading percolate through the cell. A massively parallel FFT formulation was enhanced to handle high phase-contrast materials and small time increments, introducing acceleration techniques to ensure convergence under finite deformations and fine discretizations. Results show that nonuniform void dispersions can be more ductile than ordered dispersions. The interpretation of the results is based on the competition between a recently uncovered phenomenon termed “distribution softening” and microstructure evolution. Under circumstances where the strain to percolation is small, the initial distribution softening dominates and the ordered (cubic) dispersion constitutes an upper bound to ductility. However, when the strain to percolation is sufficiently large, as would arise for a moderately hardening matrix and moderate levels of superposed hydrostatic pressure, some random dispersions become significantly more ductile than the reference ordered dispersion. The implications of these new findings on modeling ductile fracture in engineering materials are discussed.