Theoretical models for void coalescence in porous ductile solids. II. Coalescence “in columns”

Abstract

As in the preceding paper, one studies coalescence of cavities in periodically voided ductile solids through consideration of a cylindrical representative volume element (RVE) containing a spheroidal void and subjected to some axisymmetric loading. However we now study the case where the major stress applied is no longer the axial one but the lateral one, so that the strain is mainly horizontal. This case has not been considered before in either FE micromechanical studies or theoretical models. It is envisaged here through both approaches. The basic idea of the model is that owing to the type of loading considered, the voids gradually concentrate along vertical columns. This is accounted for by schematizing the RVE as made of two coaxial cylinders, a highly porous, central one surrounded by a sound one. Just as in the case of coalescence in layers, the authors' recent extension of Gurson's model accounting for void shape is used to describe the behavior of the central zone whereas the sound one obeys von Mises' criterion. However, there is a major difference, namely that the sound outer region cannot become rigid here, since this would prohibit global flow. As a result, there is no more a sharp transition from pre-coalescence to coalescence but a gradual one. Comparison of the model predictions with the FE results exhibits a good agreement for a wide range of triaxialities.