Modelling of the austenite–ferrite phase transformation by solving a diffusion equation with a moving boundary was the main aim here. Particular emphasis was placed upon testing to what extent models based upon solving the diffusion equation were capable of properly describing the kinetics of transformation. Mathematical and numerical models describing γ−α phase transformation for granular ferrite were created. These models were based upon the solution of Fick’s second law for the 1-dimensional, 2-dimensional (circle in circle, regular hexagon in regular hexagon) and 3-dimensional (sphere in sphere) cases. The models developed were solved by using the finite difference, as well as the finite element, methods. The results of numerical simulations for ferrite volume fraction, ferrite grain size and carbon segregation ahead of the transformation front were compared with experimental data.

Numerical Solution of the Diffusion Equation with Moving Boundary Applied to Modelling of the Austenite–Ferrite Phase Transformation. M.Pernach, M.Pietrzyk: Computational Materials Science, 2008, 44[2], 783-91