Deformation field of a misfitting inclusion

J.D. Eshelby (1957, 1959) has calculated the deformation field associated with an ellipsoidal inclusion in a state of homogeneous strain within an infinite matrix. Since most real precipitates occur with facets, the strain within such an inclusion is not uniform. Thus, plate precipitates of θ′ in Al-Cu and η in Al-Au have coherent broad faces with mismatches of 1.34 and 4.95 % respect- ively and semicoherent or disordered interfaces at the edges with residual mismatches of about ?4.3 and ?1.00% normal to the broad faces. The deformation field in the matrix around such precipitates has been calculated using Kelvin's (1848) result for the stress field due to a point force. The calculations show the existence of high stresses near the edges of the precipitates where they have an appreciable misfit. Unlike the case of an ellipsoidal inclusion, the stress fields of these precipitates have dilatational components which can affect the diffusion of solute atoms to them and, thus, the kinetics of interface migration. The behavior of alloys containing these precipitates indicates that the moduli of the precipitates are somewhat greater than those of the matrices. The present calculations, based on the assumption that the two moduli are the same, underestimate the actual deformation field in the matrix. In real systems, therefore, the effects of the deformation field on misfit dislocation nucleation and kinetics of interface migration are likely to be somewhat greater in general.