Elstic energy changes accompanying gamma-prime rafting in nickel-base superalloys

Eshelby's equivalent inclusion method is applied to the case of a single, inhomogeneous, ellipsoidal precipitate in an infinite matrix to study the morphological changes of the gamma-prime precipitates in nickel-base superalloys due to the influence of lattice constant misfit, elastic inhomogeneity and anisotropy, applied stress, and interfacial energy. The energy-minimizing inclusion shapes depend very sensitively on the degree of elastic inhomogeneity, on the sense and magnitude of the applied stress, and on the sense of the lattice constant misfit. The interfacial energy contribution can dominate that of elastic strain energy for small precipitate sizes, elastically compliant systems, nearly homogeneous alloys, and/or nearly isotropic materials. Calculations are carried out for two well-characterized nickel-base alloys: a Ni–13.5Al alloy (positive misfit, elastically hard inclusions) studied by Miyazaki et al. and CMSX-3 (negative misfit, elastically soft inclusions) studied by Pollock. The Eshelby energy calculations correctly predict the precipitate morphologies observed by Miyazaki et al. and by Pollock.