Re-examination of the elastic strain energy of an incoherent ellipsoidal precipitate

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Department of Materials Science and Engineering


The elastic strain energy of an incoherent ellipsoidal precipitate in either an isotropic or an anisotropic matrix is re-evaluated as a function of the ellipsoidal aspect ratio (β) using the method of Eshelby. An incoherent interface means an essentially disordered interphase boundary structure and therefore such a precipitate is stressed in a purely hydrostatic fashion along the precipitate:matrix interface. The general behavior of the strain energy found by Nabarro and by Kröner is again observed: that is, the strain energy becomes zero as β → 0 (disk), while reaching its maximum value when β equals unity (sphere). However, comparison of the results of the Kröner approach with the exact results shows a noticeable error in Kroner's results. It is found that the Kröner approach is correct only when the matrix is elastically isotropic and the precipitate shape is one of three special cases, i.e. disk, sphere and needle (β→ ∞). As an example, when β = 0.1, the error is found to vary up to 48%, depending upon the severity of the anisotropy of the matrix. © 1978.

Publication Title

Acta Metallurgica