Theoretical models for void coalescence in porous ductile solids. I. Coalescence “in layers”

Abstract

This paper and its companion address the problem of theoretically predicting coalescence of cavities in periodically voided ductile solids. One considers, as in several previous finite element (FE) studies, a cylindrical representative volume element (RVE) containing an initially spheroidal void and subjected to some axisymmetric loading. We consider here the case where the major stress applied is the axial one so that the strain is mainly vertical. As a consequence, voids gradually concentrate in horizontal bands. Coalescence corresponds to a sudden concentration of the deformation in these regions. In the model, one considers the RVE as made up of three layers, a highly porous one containing the void surrounded by two sound ones; the strain rate and stress fields are considered as homogeneous in each region. A recent model proposed by the authors, analogous to that of Gurson but accounting for void shape, is used to describe the behavior of the central layer while the outer ones obey von Mises' criterion. Two regimes are possible according to whether the sound zones are plastic or rigid; the first one corresponds to the pre-coalescence period while the second one corresponds to coalescence. The simple model thus obtained is entirely analytic. Comparisons with various FE simulations are presented for several initial porosities, void shapes and triaxialities, and the predictions of the model are found to agree quite well with the numerical results.