Quantitative comparison of the phase-transformation kinetics in a sharp-interface and a phase-field model

A sharp-interface model, which provides an accurate description of diffusional phase-transformation kinetics [C. Bos, J. Sietsma, Scripta Mater. 57 (2007) 1085–1088], is used to evaluate the transformation kinetics as calculated by a diffuse-interface multi-phase-field model, in particular the effect of the interface thickness will be investigated. This is done for the isothermal austenite-to-ferrite transformation in a C–Mn steel, using the simple geometry of a single ferrite grain growing in the bulk of the austenite matrix. For the sake of computation time, this analysis is limited to one- and two-dimensional space, although it can be extended to three-dimensional space straightforwardly. Small deviations of the numerical phase-field profile from the analytical stationary solution, used to match the phase-field equation to the equation for the sharp-interface kinetics, results in a lower effective interface mobility compared to the input value. This deviation, more pronounced in the early stage of transformation, can be minimised by reducing the grid size, while keeping the number of interface grid points constant. During stationary growth, a good agreement was found between phase-field and sharp-interface solution, although a small deviation of about 7% still remains if six grid points are chosen for the interface width. This deviation could not be reduced further by a better grid resolution, but can be overcome by a higher number of grid points within the diffuse interface.