APPROXIMATE MODELS FOR DUCTILE METALS CONTAINING NONSPHERICAL VOIDS - CASE OF AXISYMMETRICAL PROLATE ELLIPSOIDAL CAVITIES

THE AIM OF THIS PAPER is to extend the classical Gurson analysis of a hollow rigid ideal-plastic sphere loaded axisymmetrically to an ellipsoidal volume containing a confocal ellipsoidal cavity, in order to define approximate models for ductile metals containing non-spherical voids. Only axisymmetric prolate cavities are considered here. The analysis makes an essential use of an ''expansion'' velocity field satisfying conditions of homogeneous boundary strain rate on every ellipsoid confocal with the cavity. A two-field estimate of the overall yield criterion is presented and shown to be reducible, with a few approximations, to a Gurson-like criterion depending on the ''shape parameter'' of the cavity. The accuracy of this estimate is assessed through comparison with some results derived from a numerical minimization procedure. The two-field approach is also used to derive an approximate evolution equation for the shape parameter; comparison with some finite element simulations reveals a reasonable qualitative agreement, and suggests a slight modification of the theoretical formula which leads to acceptable quantitative agreement. The application of these results to materials containing axisymmetric prolate ellipsoidal cavities with parallel or random orientations is finally discussed.