Effect of void locking by inclusions upon the plastic behavior of porous ductile solids—I: theoretical modeling and numerical study of void growth

The aim of this work is to model the effect of inclusions upon void growth in porous ductile metals. This effect arises from the fact that when such a material is subjected to low tensile, or compressive mean stresses, voids can undergo compressive stresses in some directions; then, if they are still in contact in these directions with the inclusions they originated from, void shrinkage is hindered by the inclusions. A numerical yield surface is first derived through limit-analysis of some RVE, accounting for presence of some rigid inclusion, and compared to the (also numerical) yield surface without inclusion. Using then, as a basis, the Gologanu–Leblond–Devaux (GLD) model accounting for void shape effects but not for influence of inclusions, an analytical approximate model is developed, taking into account both void shape effects and influence of inclusions. This model consists of a macroscopic yield criterion analogous to that of the GLD model, depending upon the porosity and the void shape parameter, a flow rule obeying normality, and evolution equations for the internal parameters. It contains four adjustable coefficients. Two of these are determined through consideration that the yield surface with effect of inclusions should be tangent to the GLD yield surface for a certain “critical” stress state. The other two are adjusted so as to get the best possible fit between the analytical yield surface (with effect of inclusions) and the supposedly exact numerical one. The model is finally critically assessed through comparison of its predictions with results of FE simulations performed in ideal-plasticity (in order for the comparison with the theory developed with this hypothesis to be fully meaningful).