Growth of an Infinitesimal Cavity in a Rate-Dependent Solid

[+] Author and Article Information
Rohan Abeyaratne, Hang-sheng Hou

Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139

J. Appl. Mech 56(1), 40-46 (Mar 01, 1989) (7 pages) doi:10.1115/1.3176063 History: Received October 22, 1987; Revised March 22, 1988; Online July 21, 2009


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 = p̂(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.

Copyright © 1989 by ASME
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