Numerical analysis for migration of austenite/ferrite interface during carburization of Fe

During isothermal annealing of the ferrite of a binary Fe–C alloy in an appropriate carburization atmosphere at temperatures of 1020–1180 K, the austenite will be formed as a layer on the surface of the ferrite. The migration behavior of the austenite/ferrite interface during the isothermal carburization was numerically analyzed using the diffusion equation describing the flux balance at the interface. However, the diffusion coefficient of C in the austenite monotonically increases with increasing concentration of C. Thus, the composition dependence of the diffusion coefficient was taken into consideration. For the numerical analysis, Crank–Nicolson implicit method was combined with a finite-difference technique. According to the numerical calculation, the parabolic relationship holds between the migration distance of the austenite/ferrite interface and the annealing time. The composition dependence of the diffusion coefficient yields acceleration of the migration. The numerical calculation satisfactorily reproduces the experimental result of the diffusion controlling migration.