Modeling of isothermal solid-state precipitation using an analytical treatment of soft impingement

The effects of soft impingement on precipitation are considered. On the basis of a two stage-transformation assumption, a physically realistic analytical model for isothermal solid-state precipitation has been developed. In the modeling, a site saturation of nucleation, an isotropic growth, and a linear approximation for the concentration gradient are assumed. A compact expression has been obtained to describe both one-dimensional and three-dimensional precipitations. Compared with Zener’s model, the present model can be given as an analogous form, but with a time-dependent growth coefficient. A detailed description for the model parameters has been given for the model application. On this basis, model predictions for isothermal ferrite formation in 0.37C–1.45Mn–0.11V micro-alloyed steel and precipitation in an Al–0.2wt.%Sc alloy have been performed; good agreement with the published experimental data has been achieved.