Modeling phase transformations in ternary systems: Ferrite dissolution during continuous cooling

Abstract

The diffusion-controlled phase dissolution (or growth) in a ternary system of finite length has been modeled numerically using an implicit finite-difference method. The analysis has been applied to study the ferrite to austenite transformation in austenitic stainless steel weldments. The iron-chromium-nickel ternary system was taken as representative of this class of materials. The effect of system geometry was evaluated by considering planar, cylindrical, and spherical geometries. The numerical analysis was extended to the case of continuous cooling, for a range of cooling rates from 0.1 to 100 K/s. The results provide information on how quickly the system deviates from equilibrium during cooling, and what the final compositions and phase fractions are as a function of cooling rate. In most cases, the deviation from equilibrium, in terms of residual ferrite content and composition, increased as the cooling rate increased, as expected. However, under some conditions, it was found that the lowest cooling rates actually deviated further from equilibrium than intermediate cooling rates. This curious phenomenon was investigated in detail and was explained in terms of the indirect path toward final. Such indirect equilibration is often found during and typical of diffusion-controlled transformation behavior in multi-component systems