An integral equation approach to the elastic interaction of two precipitates

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Department of Materials Science and Engineering


Assuming a constant stress‐free transformation strain or applied stress field, an integral equation is derived for the elastic distortion associated with two arbitrarily shaped precipitates possessing elastic constants different from those of the matrix phase. The precipitates are embedded in an infinite elastic matrix with the extension to the multi‐inclusion problem being straightforward. The strain field associated with two spherical misfitting precipitates in isotropie media is calculated employing an iterative technique similar to that of Willis. It is shown that when the precipitate is elastically softer than the matrix, the internal strain field behaves qualitatively the same as for the case of a homogeneous system. When the precipitate is more rigid than the matrix, approximating the elastic constants of the precipitate with those of the matrix phase yields a qualitatively inappropriate representation of the strain field.

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Copyright © 1982 WILEY‐VCH Verlag GmbH & Co. KGaA. Publisher’s version of record:

Publication Title

physica status solidi (a)