A modified cellular automaton method for polydimensional modelling of dendritic growth and microsegregation in multicomponent alloys

Numerous numerical models for simulating solidification of metals on a microscopic scale have been proposed in the past, among them are most importantly the phase-field method and models based on cellular automata. Especially the models based on cellular automata (adopting the virtual front tracking (VFT) concept) published so far are often only suitable for the consideration of one alloying element. Since industrial alloys are usually constituted of multicomponent alloys, the possibility of applying cellular automata is rather limited. With the aim of enhancing this modelling technique, a new, modified VFT model, which allows for the treatment of several alloying elements, in the low Péclet number regime is presented. The model uses the physical fundamentals of solute and heat diffusion in two dimensions as a basis for determining the solidification progress. By a new and effective approach, based on a functional extrapolation of the concentration gradient, dendritic growth in multicomponent Fe-C-Si-Mn-P-S alloys could be studied. The model shows the typical behaviour of dendritic solidification, such as parabolic tip and secondary dendrite arm formation as well as selection of preferably aligned columnar dendrites. A validation of the model is performed by the evaluation of morphological parameters and comparing them to experimentally determined values. The results for free and constrained dendritic growth effectively demonstrate the capabilities of this new model. The model is especially attractive for bridging the gap between one-dimensional microsegregation models and multidimensional morphology models with regard to modelling the complex interrelations between segregation on a multidimensional level and morphology formation.