Influence of porosity on cavitation instability predictions for elastic–plastic solids

Abstract

Cavitation instabilities have been found for a single void in a ductile metal stressed under high triaxiality conditions. Here, the possibility of unstable cavity growth is studied for a metal containing many voids. The central cavity is discretely represented, while the surrounding voids are represented by a porous ductile material model in terms of a field quantity that specifies the variation of the void volume fraction in the surrounding metal. As the central void grows, the surrounding void volume fractions increase in nonuniform fields, where the strains grow very large near the void surface, while the high stress levels are reached at some distance from the void, and the interaction of these stress and strain fields determines the porosity evolution. In some cases analysed, the porosity is present initially in the metal matrix, while in other cases voids nucleate gradually during the deformation process. It is found that interaction with the neighbouring voids reduces the critical stress for unstable cavity growth.

Effects of shape on unstable growth of cavities interacting with surrounding small voids

“…4 shows a clear difference between the curves for the the five different initial geometries of the central voids analysed. As was discussed in [5] for the initially spherical void, the rapid load drop at 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 Fig. 5b shows that rapid void growth has started from the sharp end of the surface of the central void.…”

“…For strain controlled nucleation, Chu and Needleman [18] have proposed the following expressions for the nucleation coefficients A and B The analyses in [5] accounted for the dependence of elastic properties on porosity, by using expressions derived by Tandon and Weng [19], but it was found that this reduced elastic stiffness had negligible effect. Very similar results were obtained by using linear interpolations of the expressions for…”

“…According to (6), final ductile failure occurs when f reaches F f . In the present studies, as in [5], final failure is represented in terms of a small yield surface technique, in which expression (10) is used until…”

“…Recent studies have also considered the interaction with neighbouring voids, either represented as discrete voids of different size (Tvergaard [4]), or represented in terms of a ductile porous material model (Tvergaard and Vadillo [5]). The initial shape of the cavity analyzed has usually been taken to be spherical, but effects of initially prolate or oblate spheroidal shapes have been analysed by Tvergaard and Hutchinson [6].…”

“…The purpose of the present paper is to extend the study of Tvergaard and Vadillo [5] to consider an initially spheroidal void, interacting with other small voids in the surrounding material. A unit cell model is analyzed, with a central spheroidal void discretely represented and with a population of small voids in the surrounding metal represented in terms of the generalized Gurson model (Gurson [13], Tvergaard [14]).…”