Numerical modeling of diffusion-controlled phase transformations in ternary systems and application to the ferrite/austenite transformation in the Fe-Cr-Ni system

Abstract

An implicit finite-difference analysis has been used to model the diffusion process in a two-phase ternary system. The system was of finite length, and the interface between the two phases, α and γ, was allowed to move as the α phase grew or dissolved. Equilibrium at the interface was assumed. For simplicity, the diffusion coefficients were assumed to be independent of composition, and the cross-coefficient diffusion terms were assumed to be negligible. The details of the computational process are described. The accuracy of the approach and the major sources of error are examined in detail. The numerical results are in excellent agreement with analytical predictions under the limited conditions for which analytical solutions are available. The computational model was applied to the detailed study of ferrite growth/dissolution in the iron-chromium-nickel ternary system to examine ferrite stability in austenitic stainless steel welds. The starting compositions of the ferrite and austenite were typical of these phases in the as-welded condition, and the isothermal equilibration was followed at 700 °C to 1300 °C. It was found that the transformation to the equilibrium state could be divided into two major stages: the first corresponded to rapid diffusion in the ferrite phase, and the second was due to the more sluggish diffusion within the austenite. The path toward equilibrium was often indirect; sometimes the ferrite grew first before eventually shrinking to the final equilibrium size, whereas at other temperatures the ferrite initially dissolved before growing at a later stage. The results are compared to the limited available experimental data, and behavior that was found experimentally was accurately reproduced by the computations. The results provide hitherto unavailable data on the kinetics of the equilibration process at elevated temperatures near the solidus temperature and also provide insight into details of the transformation behavior.