A self-consistent approach to coalescence of cavities in inhomogeneously voided ductile solids

摘要

Several authors have derived values of the 'critical porosity' at the onset of coalescence of cavities in periodically voided ductile metals from numerical finite element simulations of the behavior of the microstructure. Such simulations yield critical porosities which are most often unrea1istically large for real materials. Although there are several reasons for the discrepancy, there is strong evidence that a major factor lies in the fact that real materials do not contain periodic but often strongly inhomogeneous distributions of voids. The aim of this paper is to attack this problem from a theoretical point of view. lt is based on an analytic solution to the model problem of an infinite porous matrix containing some spherical, porous inclusion with a different porosity, and subjected to hydrostatic tension at infinity. The behaviors of both the matrix and the inc1usion are described using Gurson's (l977) famous model for plastic porous solids. Coalescence of voids in both the matrix and/or the inclusion is incorporated in the very simple way suggested by Tvergaard and Needleman (l984), coalescence parameters for a homogeneously voided material (such as the matrix and the inclusion) being assumed to be known. From that solution, one derives a self consistent approach to the behavior, including coalescence, of a porous solid containing zones of different porosities. The resulting predictions for the onset of coalescence in inhomogeneously voided solids are found to be in good agreement with the results of Becker's (l987) finite element simulations of the behavior of such