A gradient plasticity model for porous metals with random spheroidal voids: Theory and applications

This work deals with the development of a rate-independent, implicit gradient plasticity model for porous metallic materials comprising microstructures with an isotropic distribution of randomly oriented spheroidal voids. We take into account void shape effects via a single constant, the void aspect ratio, which can be used as a calibration parameter for the model. The non-local formulation introduces a characteristic material length, which serves as a regularization parameter and can be estimated by association to a microstructural dimension of the material at hand. The mathematical character of the resulting non-local problem and the conditions for loss of ellipticity are carefully examined. We show, both analytically and numerically, that the proposed model retains the elliptic properties of the governing equations and can provide mesh-independent numerical solutions in the post-bifurcation (softening) regime. This analysis also indicates that the critical localization strain is an increasing function of the void shape. Implementation of the model in the finite element software ABAQUS allows to investigate the effects of the various parameters through the numerical simulation of industrially relevant problems such as the cup-and-cone fracture of cylindrical bars and the Charpy V-notch test. By revisiting the first Sandia Fracture Challenge, we showcase the capability of the model to sufficiently reproduce real-world experimental results while maintaining a manageable number of calibrated parameters.