An assessment of statistical models of competitive growth during transient Ostwald ripening in turbine disc nickel-based superalloys

The ability to accurately predict the time evolution of precipitate size distributions is fundamental to optimising heat treatments and mechanical properties of engineering alloys. Mean-field models of the particle growth rates assume that diffusion fields between neighbouring particles are weakly coupled reducing the problem to a single particle embedded in an effective medium. This regime of behaviour is expected to be satisfied for low volume fraction alloys. However, these assumptions are not fulfilled in many applications of interest where strong interactions between precipitates holds. Correction factors are often introduced to account for the accelerated rate of diffusion caused by the overlapping of diffusion fields between neighbouring precipitates. This paper applies the Wang–Glicksman–Rajan–Voorhees (WGRV) discrete point-source/sink model to compare descriptions of competitive growth. This includes assessing correction factors to the mean-field particle growth rate derived by Ardell, Marqusee and Ross, and Svoboda and Fischer in addition to Di Nunzio's pairwise interaction model. The WGRV model is used as a benchmark to compare different approximations of competitive growth that apply similar assumptions. This is followed by the application of the models to simulate precipitation kinetics during long term aging kinetics observed in the nickel-based superalloys IN738LC and RR1000. It is shown that the competitive growth correction factors are accurate for volume fractions of 20% and under-predict the acceleration of precipitate kinetics predicted at 40%. The WGRV model is able to capture the coarsening kinetics observed in both IN738LC and RR1000 with reasonable accuracy. The WGRV model determines particle growth rates as a function of the immediate neighbourhood and provides an improved prediction of the coarsening behaviour of tertiary particles in RR1000 in comparison to the mean-field approximation, however over-estimates the growth rate of the tertiary particles compared to experimental data.