Evolution of elliptical voids in power-law viscous solids

The evolution of an isolated elliptical-cylindrical void contained in a power-law viscous matrix is investigated. For linearly viscous solids, the void evolves through a sequence of (rotating) ellipses, and Eshelby's equivalent inclusion method is applied to exactly determine the history of shape, orientation and volume of the void as a function of time or remote strain. For non-linearly viscous matrix materials, the void evolution is idealized as proceeding through a sequence of elliptical shapes, and a numerical procedure developed by Lee and Mear (Lee: B.J., Mear, M.E., 1992. Mechanics of Materials 13, 337) is utilized to simulate finite deformations of the void. Detailed studies are presented first for the growth and collapse of initially circular voids, after which the role of initial void shape is investigated by considering the evolution of initially elliptical voids. Results are also presented for the evolution of the void volume fraction for solids containing a dilute concentration of randomly oriented elliptical voids. The findings of the study have relevance to modeling ductile fracture as well as to modeling the final stages of the densification of powder metal compacts. (C) 1999 Published by Elsevier Science Ltd. All rights reserved.