Interactions of spherical precipitates in an anisotropic matrix

Abstract

Elastic interactions between two anisotropic spherical precipitates embedded in an anisotropic elastic medium and their asymptotic behavior are investigated on the basis of an elastic field for two spheres. It is confirmed that an interaction energy between two spherical anisotropic precipitates (not necessarily identical to each other) separated by a large distance | d | is of order (| d | −3) or higher. Numerical computations are performed for the cases of two identical misfitting anisotropic precipitates in an anisotropic matrix of cubic symmetry. It is observed that far-field interactions (| d | ⪢ a) depend on the anisotropic factor H = C 12 + 2 C 44 − C 11, of the matrix. When the factor H is positive as in fcc elements, the far-field interactions are attractive between the two precipitates aligned along 〈100〉 directions of the matrix while repulsive along 〈100〉 directions. In contrast, the far-field interactions are attractive along 〈111〉 directions and repulsive along 〈100〉 directions whrn the factor H of the matrix is negative as in bcc elements. It also appears that the near-field (| d | ≈ 2 a) interactions are strongly dependent on the direction of the alignment of the precipitates, and the differences between the elastic moduli of the precipitates and those of the matrix.