DEVELOPMENT OF CELLULAR AUTOMATON MODELS AND SIMULATION METHODS FOR SOLIDIFICATION OF ALLOYS

doi:10.3724/SP.J.1037.2013.00567

Acta Metall Sin

2014, Vol. 50

Issue (6): 641-651 DOI: 10.3724/SP.J.1037.2013.00567

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DEVELOPMENT OF CELLULAR AUTOMATON MODELS AND SIMULATION METHODS FOR SOLIDIFICATION OF ALLOYS

ZHAO Jiuzhou¹(

), LI Lu¹, ZHANG Xianfei²

1 Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016
2 School of Materials Science and Engineering, Shenyang Ligong University, Shenyang 110159

Cite this article:

ZHAO Jiuzhou, LI Lu, ZHANG Xianfei. DEVELOPMENT OF CELLULAR AUTOMATON MODELS AND SIMULATION METHODS FOR SOLIDIFICATION OF ALLOYS. Acta Metall Sin, 2014, 50(6): 641-651.

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Abstract

Dendritic structure is the most frequently observed solidification microstructure of alloys. It has a dominant effect on the mechanical properties of alloys. The formation of the dendritic microstructure has attracted extensive attentions. It has been demonstrated that numerical simulation is a powerful tool for studying the microstructure formation during the solidification of alloys. Various models, such as the front-tracking (FT) model, the phase-field (PF) model and the cellular automaton (CA) model have been proposed to simulate the formation process of dendrite. Compared with other methods, CA is an effective numerical simulation method with high calculation efficiency and clear physical meaning. It is more suitable to be applied to simulate the formation kinetics of the dendritic microstructure of alloys. It has been widely applied in the investigation of the solidification of alloys. This paper makes a detailed introduction to the common process of CA modeling and simulation, the constructing method of CA model and the calculation method for some key parameters such as nucleation rate of nuclei, growth velocity of dendrite, etc. A review of the development of the CA models for the solidification of alloys is carried out. The features and applications of the existing CA models are critically assessed. The applications of the CA models in the investigations of the practical solidification process are summarized. The problems to be solved and the future development of CA models are also pointed out.

Key words: alloy solidification microstructure dendrite numerical simulation cellular automaton

Received: 09 September 2013

ZTFLH:	TG111.4
	TG113.12

Fund: Supported by National Natural Science Foundation of China (Nos.51071159, 51271185 and 51031003)

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	Jiuzhou ZHAO
	Lu LI
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https://www.ams.org.cn/EN/10.3724/SP.J.1037.2013.00567 OR https://www.ams.org.cn/EN/Y2014/V50/I6/641

Fig.1 Neighbors of the cell A in 2D square mesh

(a) Von Neumann (b) Moore

Fig.2 Fig.2 Neighbors of the cell A in 3D cubic mesh^[8]

(a) the nearest neighbors of the cell A (I)

(b~d) the second nearest neighbors of the cell A (II)

(e, f) the third nearest neighbors of the cell A (III)

Fig.3 Distribution of the heterogeneous nucleation sites on the mold wall and in the bulk melt (The subscripts s and v represent the nucleation on the mold wall and in the bulk melt, respectively. ΔT_{s, max} and Δ_{Tv, max} are mean undercooling, Δ_{Ts, σ} and Δ_{Tv, σ} are standard deviation, ns and nv are total density of grains)[13]

Fig.4 Schematic diagram of the S/L interface growth direction(

n^

is the normal vector of the S/L interface, φ is the angle between

n^

and x axis, θ₀ is the anglebetween the crystallographic orientation and x axis)

Fig.5 Schematic illustration of the 2D square algorithm (L(t) is the radius of grain, q is the angle between the preferred orientation and the x axis)^[13]

Fig.6 Illustration of the calculation of solid fraction of an interfacial cell ( Δ^s is the size of the cell, v^x and v^yare the velocities along the coordinate axis)

Fig.7 Calculation of the increment in solid fraction by the motion of planar interface along the normal to the surface (Once the interface covers the distance L_φ ,the cell status becomes solid,

n^

is the normal vector of solid (S) / liquid (L) interface)

Fig.8 Microstructural evolution in directionally solidified Al-11.6%Cu-0.85%Mg alloy (The temperature gradient in front of the S/L interface is 10 K/mm)^[59]

(a) t=1.3 s (b) t=2.7 s (c) t=4 s (d) t=8.7 s (e) t=10.7 s

Fig.9 Dendrite spacing l for directionally solidified Al-11.6Cu-0.85Mg alloys^[59]

Fig.10 Dendrite tip velocities calculated using different diffusion coefficients (Line 1 is the results calculated using the diffusion coefficients considering solute interactions, line 2 is the results calculated using the diffusion coefficients neglecting solute interactions)^[59]

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