An Integral Equation Approach to the Inclusion Problem of Elastoplasticity

[+] Author and Article Information
W. C. Johnson

National Bureau of Standards, A153 Materials, Washington, D.C. 20234

J. K. Lee

Department of Metallurgical Engineering, Michigan Technological University, Houghton, Mich. 49931

J. Appl. Mech 49(2), 312-318 (Jun 01, 1982) (7 pages) doi:10.1115/1.3162086 History: Received September 01, 1981; Revised January 01, 1982; Online July 21, 2009


An integral equation approach is derived for the calculation of the elastoplastic strain field associated with a transformed inclusion of constant stress-free transformation strain and for an inhomogeneity when the far stress field remains elastic. The assumptions of a coherent precipitate and the deformation theory of plasticity are employed although any yield condition and flow rule can be chosen. The complexity of the integral equation is such that an iterative solution scheme is necessary. The technique is applied to a spherical precipitate in a uniform elastic stress field where associated stress and strain fields and plastic zone are calculated. The nature of the plastic relaxation process compares qualitatively with two-dimensional plane stress behavior. Extension of this technique to the nonaxisymmetric problem is also examined.

Copyright © 1982 by ASME
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