SIMULATION OF γ' PRECIPITATION IN Ni-BASE SUPERALLOYS BY THE IMPLEMENTATION OF DIFFERENTIAL EQUATIONS IN A FINITE ELEMENT CODE

摘要

A model is developed to simulate γ' precipitation in Ni-base superalloys. The model makes use of differential equations to compute simultaneously the mean number of precipitates per unit volume, N, and their mean size, r. Both the nucleation rate, dN/dt, and the growth rate, dr/dt, are implemented in the FEMLAB finite element code as differential equations, taking into account the effective solute supersaturation in the γ matrix, which is computed using the phase diagram simulation software Thermo-Calc. Both the nucleation rate and the growth rate depend on r, N and on temperature, T. After calibration and validation with respect to isothermal experimental measurements, the model can be directly coupled to heat transfer models in FEMLAB to simulate time-dependent non-isothermal problems, such as specific heat treatments of bulk ingots, welding, or the evolution of components during service.