Field variable diffusion cellular automaton model for dendritic growth with multifold symmetry for the solidification of alloys

Abstract

The substantial mesh dependency caused by the discrete properties of cells and limitations of the sharp interface model are the inherent disadvantages of the cellular automaton (CA) model, which leads to difficulties in simulating dendritic growth with multifold symmetry and random preferred orientations for the solidification of alloys. A novel field variable diffusion CA (FCA) model is proposed by referring to the concept of the gradient energy term for diffuse interfaces in the phase field method. The diffusion equation for the field variable based on the constructed gradient functional is derived using the gradient descent method and is introduced into the CA model to reduce the mesh dependency. The FCA model deals with the solidification/remelting growth kinetics of the solid–liquid interface according to the lever rule and by considering the constitutional supercooling and Gibbs–Thomson effect. Free dendritic growth from undercooled melts and competitive dendritic growth during the directional solidification of Al–4 wt% Cu and Mg–5.26 wt% Al alloys were calculated to validate the accuracy of the FCA model for four-fold, six-fold symmetric dendritic morphologies and growth kinetics. The FCA model can efficiently reproduce multi-equiaxed and columnar dendrites with multifold symmetry and random preferred orientations as well as graphically reveal essential dendritic growth information, such as coarsening of secondary arms and side branch fusion.