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Acta Metall Sin  2016, Vol. 52 Issue (10): 1297-1310    DOI: 10.11900/0412.1961.2016.00361
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CELLULAR AUTOMATON MODELING OF MICRO-STRUCTURE EVOLUTION DURING ALLOY SOLIDIFICATION
Mingfang ZHU1(),Qianyu TANG1,Qingyu ZHANG1,Shiyan PAN2,Dongke SUN3
1 Jiangsu Key Laboratory for Advanced Metallic Materials, Southeast University, Nanjing 211189, China
2 Engineering Training Center, Nanjing University of Science and Technology, Nanjing 210094, China
3 Shanghai Key Laboratory of Advanced High-Temperature Materials and Precision Forming, Shanghai Jiao Tong University, Shanghai 200240, China
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Mingfang ZHU, Qianyu TANG, Qingyu ZHANG, Shiyan PAN, Dongke SUN. CELLULAR AUTOMATON MODELING OF MICRO-STRUCTURE EVOLUTION DURING ALLOY SOLIDIFICATION. Acta Metall Sin, 2016, 52(10): 1297-1310.

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Abstract  

Microstructure evolution during solidification is a complex process controlled by the interplay of heat, solute, capillary, thermodynamics and kinetics. Computational modeling can provide detailed information about the interactions between transport phenomena and phase transformation. Thus, it has emerged as an important and indispensable tool in studying the underlying physics of microstructural formation in solidification. During the last two decades, extensive efforts have been dedicated to explore the numerical models based on the methods of phase field (PF), cellular automaton (CA), front tracking (FT), and level set (LS), for the simulation of solidification microstructures. The CA approach can reproduce various realistic microstructure features with an acceptable computational efficiency, indicating the considerable potential for practical applications. It has, therefore, drawn great interest in academia and achieved remarkable advances in the simulation of microstructures. This paper gives an overview of CA based models, spanning from the meso-scale to the micro-scale, for the prediction of microstruc ture evolution during alloy solidification. The governing equations and numerical algorithms of CA based models and derived coupling models are summarized, including the calculations of nucleation, growth kinetics, interface curvature, surface tension anisotropy and crystallographic orientation, thermal and solutal transport, melt convection utilizing the lattice Boltzmann method (LBM), the coupling of CA with control volume (CV) method, the coupling of CA with CALPHAD approach for multi-component alloy systems, as well as the approaches for eliminating the artificial anisotropy caused by the CA square cells. The main achievements in this field are addressed by presenting examples encompassing a wide variety of problems involving dendritic growth in pure diffusion and with melt convection, eutectic solidification, microstructure formation in multi-component alloys, dendritic growth with gas pore formation, and multi-scale simulation. Finally, the future prospects and challenges for the CA modeling of solidification microstructures are discussed.
Key words:  alloy      solidification      microstructure      numerical modeling      cellular automaton     
Received:  05 August 2016     
ZTFLH:     
Fund: Supported by National Natural Science Foundation of China (Nos.51371051 and 51501091) and Fundamental Research Funds for the Central Universities of China (No. 2242016K40008)
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Mingfang ZHU
Qianyu TANG
Qingyu ZHANG
Shiyan PAN
Dongke SUN

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https://www.ams.org.cn/EN/10.11900/0412.1961.2016.00361     OR     https://www.ams.org.cn/EN/Y2016/V52/I10/1297

Fig.1  Nucleation distributions for nuclei formed at the mold wall and in the bulk of the melt (ΔTs,max and ΔTb,max are the mean nucleation undercoolings, ΔTs,σ and ΔTb,σ are the standard deviations; ns and nb are the maximum densities of nuclei; the subscripts s and b indicate the surface of mold wall and the bulk of the melt, respectively)
Fig.2  Schematic diagram of superimposing cellular automaton (CA) cells with control volume (CV) nodes[14]
Fig.3  Simulated equiaxed dendrite evolution of a Ni-0.4%Cu (mass fraction) alloy with a cooling rate of 1.5 K/s
(a) 1.8 s (b) 3.0 s (c) 4.0 s
Fig.4  Simulated columnar dendritic morphologies in pure diffusion (a) and forced convection (b) for an Al-2.0%Mg-1.0%Si (mass fraction) alloy with a cooling rate of 10 K/s and a temperature gradient of 1000 K/m
Fig.5  Simulated morphology evolution for a hypoeutectic spheroidal graphite (SG) cast iron with C0=4.1%C (mass fraction) (Numbers on the figures show the local carbon concentration (mass fraction, %), fs—total solid fraction, T—temperature)
(a) fs=7%, T=1163 ℃ (b) fs=40%, T=1147 ℃ (c) fs=84%, T=1146 ℃ (d) fs=100%, T=740 ℃
Fig.6  Simulated morphology evolution of primary dendrites and eutectic structure for an Al-7%Si-1.5%Mg (mass fraction) alloy with a cooling rate of 5 K/s in Mg solute field (a~d) and Si solute field (e~h)
(a, e) fs=20% (b, f) fs=55% (c, g) fs=83% (d, h) fs=100%
Fig.7  Simulated evolution of dendritic growth with hydrogen pore formation in an Al-7%Si (mass fraction) alloy with a cooling rate of 10 K/s
(a) fs=10% (b) fs =15% (c) fs =30% (d) fs =55% (e) fs =65% (f) fs =80% (g) the final solidified microstructure (h) the experimental micrograph[95]
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