Growth of an Infinitesimal Cavity in a Rate-Dependent Solid

Abstract

This study examines the effect of rate dependence on growth of an infinitesimal cavity in a homogeneous, isotropic, incompressible material. Specifically, a sphere containing a traction-free void of infinitesimal initial radius is considered, its outer surface being subjected to a prescribed uniform radial nominal stress p, which is suddenly applied and then held constant. The sphere is composed of a particular class of rate-dependent materials. The large strains which occur in the vicinity of the void are accounted for in the analysis, and the problem is reduced to a nonlinear initial value problem, which is then studied qualitatively through a phase plane analysis. The principal results of this paper consist of two equations that are derived between the applied stress p and the cavity radius b: p = pˆ(b) and p = p(b). The first of these describes a curve which separates the (p, b)-plane into regions where cavitation does and does not occur. The second describes a curve which further subdivides the former subregion—the post-cavitation region—into domains where void expansion occurs slowly and rapidly.