Phase-field modeling with CALPHAD and CVM for microstructural evolution of Ni-base superalloy

To perform a quantitative simulation using the Phase Field Method (PFM) in a real alloy system, a new strategy of modeling the microstructure evolution of Ni-base superalloy is proposed in the present paper. In this strategy, the Calculation Phase Diagram (CALPHAD) method and Cluster Variation Method (CVM) are combined with the PFM, in which the four sub-lattice model is used to evaluate the free energy density, while CVM is used to calculate some parameters, such as the lattice misfit and gradient coefficients in phase-field equations. The microstrucrure evolution of a Ni-Al binary alloy at the temperature of 1000K has been simulated; the elastic energy due to the lattice misfit and elastic inhomogeneity between γ and γ′ phases have also been taken into account. The simulated microstructures are formed by cuboidal coherent γ′ precipitates with a strong alignment in a certain direction, and all the precipitates are single-domain particles. The influence of the volume fraction of the γ′ phase on the final microstructures is also investigated. Results show that with the increasing of the volume fraction, the size distribution of the precipitates becomes broader and the aspect ratio of the cuboidal coherent precipitates becomes smaller, which may result from the interactions between the precipitates that become stronger because of the high-volume fraction. Moreover, the directional coarsening phenomenon of Ni-Al alloy with 18at. %Al has been reoccurred with this strategy when the various external stress conditions are applied, which shows the same conclusion as Pineau's directional coarsening map.