Ductile fracture of materials with randomly distributed voids

A reliable determination of the onset of void coalescence is critical to the modelling of ductile fracture. Numerical models have been developed but rely mostly on analyses on single defect cells, thus underestimating the interaction between voids. This study aims to provide the first extensive analysis of the response of microstructures with random distributions of voids to various loading conditions and to characterize the dispersion of the results as a consequence of the randomness of the void distribution. Cells embedding a random distribution of identical spherical voids are generated within an elastoplastic matrix and subjected to a macroscopic loading with constant stress triaxiality and Lode parameter under periodic boundary conditions in finite element simulations. The failure of the cell is determined by a new indicator based on the loss of full rankedness of the average deformation gradient rate. It is shown that the strain field developing in random microstructures and the one in unit cells feature different dependencies on the Lode parameter L owing to different failure modes. Depending on L, the cell may fail in extension (coalescence) or in shear. Moreover the random void populations lead to a significant dispersion of failure strain, which is present even in simulations with high numbers of voids.