A Three-Dimensional Cellular Automata Model for Dendrite Growth with Various Crystallographic Orientations During Solidi
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THE microstructure evolution and solute segregation in alloy solidification have a significant influence on the final casting products. During the past two decades, extensive studies have been carried out on the simulation of microstructure evolution during the solidification process, e.g., the formation of grain morphology, the columnar-to-equiaxed transition, and the microsegregation. Obviously, investigating microstructure evolution is of great importance for high-quality alloy products. The Stephan Sharp interface model,[1] the level set model,[2,3] the phase-field (PF) model[4,5] and the cellular automata (CA) model[6–8] are promising numerical methods for the simulation of microstructure evolution and have reproduced many dendritic features comparable to that observed in experiments. To simulate a solidification process containing N (the total number) grains to grow in liquid metal, however, the sharp interface model checks solid–liquid (SL) interface and requires to solve N sets of partial differentiation equations under N sets of boundary conditions. This method is extremely computing intensive but can provide detailed information on the SL interface. The PF model does not chase the position of the SL interface YAN ZHAO, Ph.D. Student, DENGFU CHEN, Professor, and MUJUN LONG, Lecturer, are with the College of Materials Science and Engineering, Chongqing University, Chongqing 400030, P.R. China. Contact e-mail: [email protected] TANSEL T. ARIF, Ph.D. Student, and RONGSHAN QIN, Senior Lecturer, are with the Department of Materials, Imperial College London, London SW7 2AZ, U.K. Manuscript submitted April 22, 2013. Article published online October 11, 2013. METALLURGICAL AND MATERIALS TRANSACTIONS B
and can simulate the microstructure evolution in the solidification system by solving just one set of partial differentiation equations, regardless of the number of the growing grains. This method requires less computing power and, hence, is suitable for simulating in a bigger system. Due to the assumption of the smooth interface, the PF model loses some geometric details at grain boundaries. The CA model calculates the phase transition by the logical judgment of cell neighborhood rather than solving partial differentiation equations.[9] The method requires much less computational power than that in the PF and sharp interface models, which provides an opportunity to calculate the system with large dimensions in the case of the existing limitation of computing facility. It is worth mentioning that the adaptive mesh refinement can be used in all the methods above. The numerical and analytical CA models for solidification have been developed in the previous studies[10–13] on the basis of assuming either steady-state growth of the dendritic tip or the local velocity of the SL interface obtained from the interface solute balance. Those models need to be further improved to capture more kinetics of the SL interface. Zhao et al.[14] developed the CA model linking the velocity of the SL interface to the phase transition d
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