Multi-scale coupling simulation in directional solidification of superalloy based on cellular automaton-finite difference method

Casting microstructure evolution is difficult to describe quantitatively by only a separate simulation of dendrite scale or grain scale, and the numerical simulation of these two scales is difficult to render compatible. A three-dimensional cellular automaton model couplling both dendritic scale and grain scale is developed to simulate the microstructure evolution of the nickel-based single crystal superalloy DD406. Besides, a macro–mesoscopic/microscopic coupling solution algorithm is proposed to improve computational efficiency. The simulation results of dendrite growth and grain growth of the alloy are obtained and compared with the results given in previous reports. The results show that the primary dendritic arm spacing and secondary dendritic arm spacing of the dendritic growth are consistent with the theoretical and experimental results. The mesoscopic grain simulation can be used to obtain results similar to those of microscopic dendrites simulation. It is indicated that the developed model is feasible and effective.