Some applications of moving boundary problems in solid state steel metallurgy

Numerous diffusion based phenomena occurring during thermal processing of steel can be modelled with finite difference techniques. This paper aims at reviewing those including one or more moving boundaries and especially phase transformations and precipitation which govern most of the final product properties. Quantitative knowledge of the underlying mechanism is of prime importance for the process control. Modelling the kinetics of precipitation and dissolution of binary particles such as MnS or AIN requires solving Pick's second law in a finite iron matrix for both species forming the particle. The usual CrankNicholson scheme is applied and the interface displacement due to growth or shrinking is handled by a moving grid technique. In this case, local equilibrium is assumed at the interface. In the case of reaustenitisation from ferrite-cementite mixtures, the austenite phase grows from the interface between parent phases. This phase transformation is governed by carbon diffusion and can be modelled using a similar approach as for the precipitation. However, the growth proceeds at two distinct interfaces implying the presence of two moving boundaries. The austenite to ferrite transformation is controlled by both the carbon diffusion and the interface mobility which can be deduced from the chemical potential difference at the interface (no local equilibrium). In this case, a fixed grid scheme was chosen and the time step was adjusted in such a way that the interface always corresponded with a grid point. Transactions on Modelling and Simulation vol 17, © 1997 WIT Press, www.witpress.com, ISSN 1743-355X