A Three-Dimensional Cellular Automata Model for Dendrite Growth with Various Crystallographic Orientations During Solidification

A three-dimensional (3-D) cellular automata (CA) model coupled with the finite-element (FE) method has been proposed to simulate dendrite growth with various crystallographic orientations during solidification. The model introduces a new tracking neighborhood method to resolve the mesh dependency caused by the cubic lattice in the CA model for simulating 3-D dendrite growth. The migration of the solid–liquid (SL) interface is associated with the dendritic preferential orientation and the driving force for the phase transition. The latter is obtained from a thermodynamics database. The local curvature and anisotropy of the surface energy are also incorporated to describe the growth kinetics of the SL interface. The solute transfer is calculated using the FE method. A numerical simulation has been performed on a Fe-1.5 wt pct C alloy. The grain morphologies with various crystallographic orientations and the solute distribution during isothermal solidification are studied and discussed. The simulation results are compared with analytical solutions and experimental results, which are in good agreement.