A three dimensional cellular automata model for dendrite growth in non-equilibrium solidification of binary alloy

A three-dimensional (3D) cellular automata (CA) model has been developed for simulation of dendrite growth during non-equilibrium solidification. The heat and mass transports are calculated using 3D finite element (FE) method. The migration of solid/liquid (SL) interface is associated with effective free energy difference incorporating solute trapping and relaxation effects. The non-equilibrium solute partition coefficient involving solute trapping and relaxation effects is used to calculate solute redistribution at SL interface. The interface curvature and anisotropy of surface energy are introduced to represent the characteristics of dendrite tip. The CA model has been applied to simulate the microstructure evolution of Fe-1.5 wt.% C alloy. The grain morphology, solute and temperature distributions, and velocity of dendrite tip are characterized during both isothermal and non-isothermal conditions. The velocity of dendrite tip and secondary dendrite arm spacing during directional solidification are validated and are in good agreements with previous experimental and mathematical results