低碳钢焊缝中心凝固相组织的元胞自动机法模拟*

doi:10.11901/1005.3093.2014.216

材料研究学报

2014, Vol. 28

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

本期目录 | 过刊浏览

低碳钢焊缝中心凝固相组织的元胞自动机法模拟*

张敏(

),徐蔼彦,汪强,李露露

西安理工大学材料科学与工程学院西安 710048

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

引用本文:

张敏,徐蔼彦,汪强,李露露. 低碳钢焊缝中心凝固相组织的元胞自动机法模拟*[J]. 材料研究学报, 2014, 28(9): 689-696.
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[J]. Chinese Journal of Materials Research, 2014, 28(9): 689-696.

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摘要:

基于元胞自动机法扩展了现有的焊接熔池凝固过程形核、生长及溶质扩散模拟模型, 模拟了Fe-0.05%C二元合金焊接过程中枝晶的生长形态和结晶过程中溶质的分布及扩散过程。同时, 以Fe-C二元相图为基点, 根据溶质浓度不同相组织不同原理模拟计算了焊接熔池凝固后相组织的分布, 建立了α+P和P+Fe₃C_Ⅱ两种组织比例值与溶质浓度、冷却速度和形核基底数等参数的数学模型。结果表明: 模拟得到的低碳钢焊缝组织分布与试验结果相符; 基于溶质浓度变化的相组织控制模型能预测实际低碳钢的焊后焊缝组织。溶质浓度、冷却速度和形核基底数对α+P和P+Fe₃C_Ⅱ两种组织比例的影响都较为明显, 影响效果相对独立; 回归分析得到的组织控制方程高度显著, 为焊缝的组织控制提供了一定的数据支持。

关键词 ：金属材料, 焊接熔池, 元胞自动机, 溶质浓度, 相组织

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

收稿日期: 2014-04-28

基金资助:* 国家自然科学基金51274162, 国家高技术研究发展计划(863计划)2013AA031303, 陕西省自然科学基金2012JM6003, 陕西省教育厅产业化培育项目2012JC16和西安市科技计划CX12163资助项目。

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https://www.cjmr.org/CN/10.11901/1005.3093.2014.216 或 https://www.cjmr.org/CN/Y2014/V28/I9/689

图1 Fe-C合金凝固相图

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

表1 拟合方程

图2 Fe-0.05%C合金在生长时间为0.025 s、0.5 s、1 s和2.5 s时的枝晶形貌

图3 Fe-0.05%C合金在时间为0.025 s、0.5s、1 s和2.5 s时的溶质分布

图4 熔池凝固结束时枝晶形貌、固相中溶质浓度、微观组织的模拟结果和实验金相组织

图5 α+P和P+Fe3CII两种组织与溶质浓度、熔体冷却速率和形核基底数的关系

表2 回归方程方差分析

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