Phase-field modeling of bimodal microstructures in nickel-based superalloys

The phase-field approach is used to study the formation and ageing of bimodal microstructures in a model Ni-based superalloy. Particular attention is paid to the definition of interfacial energies in the presence of elastic strain fields and to the incorporation of these energies in the phase-field formalism. During a two-step annealing procedure, our model predicts the formation of large anisotropic γ′γ′ precipitates (called secondary precipitates) and small, almost isotropic γ′γ′ precipitates (called tertiary precipitates). Finally, the phase-field model is used to characterize the ageing of tertiary precipitates. In agreement with experiments, we show that the mean size of the tertiary precipitates first grows as t1/3t1/3 and finally reaches a plateau. This peculiar behavior is explained using phase-field simulations with prescribed geometries and with the development of a simple analytic model.