On the Surface Stability of a Spherical Void Embedded in a Stressed Matrix

[+] Author and Article Information
Jérôme Colin

Laboratoire de Métallurgie Physique, UMR 6630 du CNRS, Université de Poitiers, BP 30179, 86962 Futuroscope Cedex, Francejerome.colin@univ-poitiers.fr

J. Appl. Mech 74(1), 8-12 (Oct 19, 2005) (5 pages) doi:10.1115/1.2165244 History: Received September 26, 2005; Revised October 19, 2005

The linear stability analysis of the shape of a spherical cavity embedded in an infinite-size matrix under stress has been performed when infinitesimal perturbation from sphericity of the rod is assumed to appear by surface diffusion. Developing the perturbation on a basis of complete spherical harmonics, the growth rate of each harmonic Ylm(θ,φ) has been determined and the conditions for the development of the different fluctuations have been discussed as a function of the applied stress and the order l of the perturbation.

Copyright © 2007 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 3

Critical and most probable modes lc and lM versus applied stress T0

Grahic Jump Location
Figure 2

Growth rate τ versus l for different values of the applied stress T0

Grahic Jump Location
Figure 1

The profile of an initially spherical cavity of radius r0 embedded in an infinite-size matrix under stress is perturbed with the help of a spherical harmonic Yl=5m(θ,φ)



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