Approximation of the Strain Field Associated With an Inhomogeneous Precipitate—Part 1: Theory

[+] Author and Article Information
W. C. Johnson, J. K. Lee

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

Y. Y. Earmme

Department of Mechanical Science, Korea Advanced Institute of Science, P.O. Box 150, Cheong Ryang Ri, Seoul, Korea

J. Appl. Mech 47(4), 775-780 (Dec 01, 1980) (6 pages) doi:10.1115/1.3153789 History: Received January 01, 1980; Revised May 01, 1980; Online July 21, 2009


Two independent methods are derived for the calculation of the elastic strain field associated with a coherent precipitate of arbitrary morphology that has undergone a stress-free transformation strain. Both methods are formulated in their entirety for an isotropic system. The first method is predicated upon the derivation of an integral equation from consideration of the equations of equilibrium. A Taylor series expansion about the origin is employed in solution of the integral equation. However, an inherently more accurate means is also developed based upon a Taylor expansion about the point of which the strain is to be calculated. Employing the technique of Moschovidis and Mura, the second method extends Eshelby’s equivalency condition to the more general precipitate shape where the constrained strain is now a function of position within the precipitate. An approximate solution to the resultant system of equations is obtained through representation of the equivalent stress-free transformation strain by a polynomial series. For a given order of approximation, both methods reduce to the determination of the biharmonic potential functions and their derivatives.

Copyright © 1980 by ASME
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