Numerical simulation of microstructure formation during solidification and heat treatments of Ni-base superalloys
A comprehensive modelling approach has been developed for the simulation of microstructure formation during solidification and heat treatment in Ni-base superalloys. The microsegregation taking place during solidification is simulated using the pseudo-front tracking (PFT) technique. This finite volume method calculates the concentration profiles in primary γ and the proportion of liquid and γ′ in the interdendritic regions. The same model is then used to describe the dissolution of the interdendritic γ′ particles during the subsequent solution heat treatment. The concentrations in primary γ predicted with the PFT model are then used to calculate the evolution of the γ′ precipitates and their size distributions at different locations in a dendrite arm during heat treatment. This is achieved with a precipitate size distribution (PSD) model. The classes of the distribution are created and tracked based on classical nucleation theory and a semi-analytical model for the growth of the precipitates as a function of their radius and the matrix supersaturation. The PFT and PSD models are both coupled with Thermo-Calc, which is used for the computation of the concentrations at the γ/liquid and γ/γ′ interfaces, for the Gibbs-Thomson effect in precipitates, and to calculate non-diagonal diffusion matrices based on a mobility database. The precipitation model was applied to a Ni-Al-Cr alloy and the results were compared with experimental data from the literature. Experimental and simulation results are in good qualitative agreement. The main phenomena taking place during precipitation, i.e. nucleation, growth and coarsening, are well reproduced by the precipitation model. Some discrepancies were observed on the precipitate number density, which were attributed to the homogeneous nucleation model. The full modelling sequence was then applied to Ni-Al in order to assess the influence of an incomplete homogenization heat treatment on the formation of γ′ precipitates.