Precipitation in powder-metallurgy, nickel-base superalloys: review of modeling approach and formulation of engineering methods to determine input data

Methods for determining the various thermodynamic and kinetic parameters required for the modeling of γ′ precipitation in powder-metallurgy (PM), nickel-base superalloys are summarized. These parameters comprise the composition of the γ′ phase, the γ′ solvus temperature/equilibrium solvus approach curve, the free energy (∆G*) associated with the decomposition of the γ matrix to form γ′, the γ/γ′ interfacial energy σ, and an effective diffusivity for use in nucleation, growth, and coarsening calculations. Techniques to obtain the material data include phase extraction (for the average composition of γ′) and heat-treatment/quantitative metallography (for a two-parameter fit of the solvus approach curve). With regard to ∆G*, two methods, one based on the instantaneous composition of the γ and γ′ phases and the other on the enthalpy of transformation and the solvus temperature, are summarized. It is shown that the interfacial energy σ can be determined from the nucleation-onset temperature as indicated by on-cooling specific-heat measurements. Last, the use of a limited set of static-coarsening measurements to estimate the effective diffusivity is described. The application of the various protocols is illustrated for typical first-, second-, and third-generation PM superalloys, i.e., IN-100, René 88, and LSHR/ME3, respectively.