On Eshelby's Elastic Interaction in Two-Phase Solids

Abstract

As their sizes grow, domains that are harder than the matrix change their shapes from spheres to other shapes to cancel anisotropic elastic fields produced by other domains. Harder domains then tend to be elastically isotropic, and the adjusted shapes are ellipsoids in the dilute case. Eshelby's interaction exists only among spheres and disappears after such shape adjustment. Furthermore, shape changes of softer domains are much more drastic and take place even in single precipitate cases. These conclusions generally hold under the coherent condition, whether the order parameter is conserved or not.