Stress Distribution in and Around Spheroidal Inclusions and Voids at Finite Concentration

[+] Author and Article Information
G. P. Tandon, G. J. Weng

Department of Mechanics and Materials Science, Rutgers University, New Brunswick, NJ 08903

J. Appl. Mech 53(3), 511-518 (Sep 01, 1986) (8 pages) doi:10.1115/1.3171804 History: Received May 29, 1985; Online July 21, 2009


A simple, albeit approximate, close-form solution is developed to study the elastic stress and energy distribution in and around spheroidal inclusions and voids at finite concentration. This theory combines Eshelby’s solution of an ellipsoidal inclusion and Mori- Tanaka’s concept of average stress in the matrix. The inclusions are taken to be homogeneously dispersed and undirectionally aligned. The analytical results are obtained for the general three-dimensional loading, and further simplified for uniaxial tension applied parallel to the axis of inclusions. The ensuing stress and energy fields under tensile loading are illustrated for both hard inclusions and voids, ranging from prolate to oblate shapes, at several concentrations.

Copyright © 1986 by ASME
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