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.
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March 1989
Research Papers
Growth of an Infinitesimal Cavity in a Rate-Dependent Solid
Rohan Abeyaratne,
Rohan Abeyaratne
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139
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Hang-sheng Hou
Hang-sheng Hou
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139
Search for other works by this author on:
Rohan Abeyaratne
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139
Hang-sheng Hou
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139
J. Appl. Mech. Mar 1989, 56(1): 40-46 (7 pages)
Published Online: March 1, 1989
Article history
Received:
October 22, 1987
Revised:
March 22, 1988
Online:
July 21, 2009
Citation
Abeyaratne, R., and Hou, H. (March 1, 1989). "Growth of an Infinitesimal Cavity in a Rate-Dependent Solid." ASME. J. Appl. Mech. March 1989; 56(1): 40–46. https://doi.org/10.1115/1.3176063
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