Micro-simulation of Solidification on Mild Steel of Welding Pool Base on the Method of Cellular Automata

doi:10.11901/1005.3093.2014.216

Chinese Journal of Materials Research

2014, Vol. 28

Issue (9): 689-696 DOI: 10.11901/1005.3093.2014.216

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Micro-simulation of Solidification on Mild Steel of Welding Pool Base on the Method of Cellular Automata

Min ZHANG(

),Aiyan XU,Qiang WANG,Lulu LI

School of Material Science and Engineering, Xi’an University of Technology, Xi’an 710048

Cite this article:

Min ZHANG,Aiyan XU,Qiang WANG,Lulu LI. Micro-simulation of Solidification on Mild Steel of Welding Pool Base on the Method of Cellular Automata. Chinese Journal of Materials Research, 2014, 28(9): 689-696.

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Abstract

The present model, which described the nucleation and growth of crystals and diffusion of solute atoms during solidification, is extended by means of cellular automata method to simulate the growth morphology of dendrites and the solute distribution during the solidification process of welding pool of Fe-0.05%C binary alloy. Meanwhile, the phase distribution after solidification was simulated on basis of the Fe-C binary phase diagram and according to the principle that different solute concentration corresponds to different phase. Besides, a mathematical model is acquired to describe the relationship between the ratio of α+P to P+Fe₃C_Ⅱ with the parameters such as the solute concentration, the cooling rate and the basal number of nucleation. The results show that the simulated results of the microstructure distribution of weld mild steel is in good agreement with the experimental ones. Therefore, the microstructure model based on changes of solute concentration can effectively predict the real microstructure of weld joint of mild steel. The impact of solute concentration, cooling rate, and the basal number of nucleation on the ratio of α+P to P+Fe₃C_Ⅱ is much obvious, but the effect of each factor is independent relatively. The deduced regressive equation of microstructure control is highly significant, and it can provide data as reference for microstructure optimization of the weld joint.

Key words: metallic materials welding pool cellular automata solute concentration phase structure

Received: 28 April 2014

Fund: *Supported by National Nature Science Foundation of China No.51274162, the National High Technology Research and Development Program of China No.2013AA031303, the Natural Science Foundation of Shaanxi Province No. 2012JM6003, the Incubation of the Education Department of Shanxi Province No.2012JC16 and the Science and Technology Program of Xi'an No. CX12163.

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https://www.cjmr.org/EN/10.11901/1005.3093.2014.216 OR https://www.cjmr.org/EN/Y2014/V28/I9/689

Fig.1 Solidification phase diagram of Fe-C binary alloy

Temperature	Name	Equation
1493<T<1538	Curve a	C l = - 9731.8 + 19.159 T - 0.0126 T 2 + 2.744 × 10 - 6 T 3
	Curve a	m L 1 = ? T L ? C L = ( 19.159 - 0.0252 T + 8.232 × 10 - 6 T 2 ) - 1
	Curve b	C S = - 56.61 + 0.116 T - 7.734 × 10 - 5 T 2 + 1.69 × 10 - 8 T 3
	Curve b	m S 1 = ? T S ? C S = ( 0.116 - 1.547 × 10 - 4 T + 5.07 × 10 - 8 T 2 ) - 1
	Partition coefficient of solid-liquid phases	k 1 = m L 1 m S 1 = 0.116 - 1.547 × 10 - 4 T + 5.07 × 10 - 8 T 2 19.159 - 0.0252 T + 8.232 × 10 - 6 T 2
1153<T<1493	Curve c	C l = - 13.465 + 0.0507 T - 4.089 × 10 - 5 T 2 + 8.864 × 10 - 9 T 3
	Curve c	m L 2 = ? T L ? C L = ( 0.0507 - 8.178 × 10 - 5 T + 2.659 × 10 - 8 T 2 ) - 1
	Curve d	C S = - 5.084 + 0 . 02 6 T - 2.432 × 10 - 5 T 2 + 6.203 × 10 - 9 T 3
	Curve d	m S 2 = ? T S ? C S = ( 0 . 026 - 4.864 × 10 - 5 T + 1.861 × 10 - 8 T 2 ) - 1
	Partition coefficient of solid-liquid phases	k 2 = m L 2 m S 2 = 0.026 - 4.864 × 10 - 5 T + 1.861 × 10 - 8 T 2 0.0507 - 8.178 × 10 - 5 T + 2.659 × 10 - 8 T 2

Table 1 Results of fitting equation

Fig.2 Dendritic morphology of Fe-0.05%C alloy under different growth time (a) t=0.025 s, (b) t=0.5 s, (c) t=1 s, (d) t=2.5 s

Fig.3 Solute concentration of Fe-0.05%C alloy under different growth time (a) t=0.025 s, (b) t=0.5 s, (c) t=1 s, (d) t=2.5 s

Fig.4 simulation and experiment results at the end of solidification of weld pool (a) dendritic morphology, (b) solute concentration in the solid phase, (c) microstructure of simulation, (d) Microstructure of experiment

Fig.5 Proportional change of α+P and P+Fe₃C_II, (a) (b) (c) is effect results at different solute concentration, cooling rate and number of nucleation substrate

Table 2 Regression analysis of variance

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