A Fast-Acting Method for Simulating Precipitation During Heat Treatment of Superalloy 718

A fast-acting, mean-field method for simulating precipitation of the γ′′ and γ′ phases during aging of superalloy 718 following super-delta-solvus solution treatment was formulated and validated using observations in the literature. The approach assumed classical (homogeneous) nucleation and diffusion-controlled growth (N&G) of disk/ellipsoidal-shaped-γ′′ and spherical-γ′ particles. For the γ′′ precipitates in particular, the evolution equations for both nucleation and growth incorporated corrections for the non-spherical shape, assuming a fixed aspect ratio. In addition, special attention was paid to the choice of input material properties for simulations. These parameters included the bulk free energies of transformation, particle-matrix (misfit) elastic strain energy (for γ′′), effective diffusivities, and the γ′′–γ and γ′–γ interface energies. The applicability of the diffusivities and interface energies chosen for the N&G simulations was established by their consistency in replicating previously measured rate constants for the diffusion-controlled coarsening of both γ′′ and γ′. The N&G formulation was discretized to obtain numerical (spreadsheet) solutions via the Kampmann–Wagner approach. Simulation results for the temporal evolution of volume fraction and average size of the precipitates showed good agreement with experimental measurements. The sensitivity of model predictions to various input parameters was also quantified.