Phase-field modeling of γ′-precipitate shapes in nickel-base superalloys and their classification by moment invariants

Abstract

We develop a phase-field model for the simulation of precipitate microstructure pattern formation in nickel-base superalloys. The model accounts for the local effects from inhomogeneous and anisotropic elastic deformations, which mainly result from the lattice misfit between the precipitates and matrix phase. Further, in each time-step, we consider the chemical driving force for precipitate ripening to instantaneously equilibrate to a homogeneous value, leading to conserved phase volumes. The model is applied to study the equilibrium shape of a 2D single γ′-particle embedded in the γ-matrix with varying lattice misfit and γ/γ′ interface energies. Further, we apply the method of moment invariants to quantify the resulting equilibrium shapes of precipitates, which turns out to be a size independent characterization of the particle shape. Resulting values for the 2D moment invariants of experimental as well as simulated particle shapes are discussed and compared. Considering ideally spherical particles, we find that large values for the γ/γ′-interface width lead to systematic deviations in the resulting moment invariants.