多元多相合金的热力学描述及其在凝固过程中的应用
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摘要
科学研究和工业生产实践中所用的金属材料大多数是具有复杂成分的多元多相合金,对这类材料凝固原理及其组织形成的研究有重要的实际意义。能否将凝固模型应用于生产实际,关键就取决于对多元合金凝固组织的模拟是否成熟。本论文主要结合热力学计算技术,对多元多相合金凝固过程中的溶质分凝现象及其对凝固组织和溶质偏析的影响进行了较为深入的研究。
溶质分凝是凝固过程中的重要伴随现象,对凝固过程中的成分偏析及组织形成有着决定性的影响。在多元合金中由于存在复杂的溶质相互作用,用实验相图分析溶质分凝行为并不方便。本文首先从热力学角度出发,建立了溶质分凝因数的热力学计算模型。详细讨论了Al-Cu二元合金和Al-Si-Mg三元合金凝固过程中溶质的分凝行为。结合计算热力学技术,对溶质分凝因数的预测很好地吻合于实验结果。
为了快速提取系统的热力学信息,减少计算时间,应用Levenberg-Marquardt算法进行了相图的计算。Levenberg-Marquardt算法采用目标函数的二阶导数,它能够实现计算精度和收敛速度的较好结合。该方法适合于求解二元以及多元合金中的相平衡问题。
研究了工业中广泛应用的Al-Si-Mg三元合金凝固过程中的溶质分凝行为,确定了该合金凝固过程中溶质分凝因数与固相分数的定量关系。发现分凝因数随固相分数的变化而显著变化,并且远远偏离其二元系中的数值。定量预测了不同凝固条件下Al-Si-Mg合金的凝固路径及共晶分数。其结果与采用二元分凝因数的预测结果偏差较大,而与实验结果接近。
结合溶质分凝的分析,研究了冷却速率对AI-2.06 wt%Si-1.58 wt%Mg合金凝固过程的影响。实验和理论分析均发现,在低的冷却速率下,其凝固过程为:L→L_1+Fcc_Al→L_1+Fcc_Al+Si→L_1+Fcc_Al+Si+Mg_2Si,而在较高的冷却速率下,其凝固过程为:L→L_1+Fcc_Al→L_1+Fcc_Al+Mg_2Si→L_1+Fcc_Al+Si+Mg_2Si。改变凝固速率可以使多元合金的凝固过程按照不同的路径进行,从而达到控制析出相种类的目的。
耦合热力学计算技术,提出了多元合金凝固界面的稳定性判据。以Al-0.34
Metallic materials in engineering applications are mostly multi-component and multi-phase alloys. The application of solidification modeling to practical technology is closely linked to our ability to model the microstructure development in multi-component alloys. In this work, the solute partition behavior and its influence on the solidification process of multi-component alloys were studied in detail based on the Calphad technology.A complete thermodynamic model for the accurate calculation of the partition coefficients in solidification process was described. The model was applied to Al-Cu binary alloy and Al-Si-Mg ternary alloy, and the predicted partition coefficients were compared with some former experimental data. Good agreement between the calculation results and the experimental data demonstrates the validity of the present thermodynamic model for the prediction of the partition coefficients in solidification process.The Levenberg-Marquardt method, the best algorithm to obtain the least-square solution of non-linear equations, was applied to calculate the stable phase equilibria. It was used for the prediction of solidification of ternary Al-Si-Mg system. The calculated phase equilibria agree well with the experimental results.The variation of solute partition coefficient was studied in dendritic solidification process of Al-Si-Mg alloys. It was found that the partition coefficient changed greatly during solidification process, which should have important influence on the formation of the microsegregation and the precipitation of various phases. The solidification path and eutectic fractions were predicted by employing the binary partition coefficients and Calphad technology separately. The results showed that great errors had been introduced by assuming the partition coefficient as a constant. By coupling Calphad method with microscale solidification model, the predicted solidification path and the eutectic fraction of Al-Si-Mg alloys agree well with the experimental results.
The effect of cooling rates on the solidification process of Al-2.06 wt% Si-1.58 wt% Mg alloy was experimentally investigated. It was found that the solidification sequences were L->Li+Fcc_Al->Li+Fcc_Al+Si-±Li+Fcc_Al+Si+Mg2Si under low cooling rate and L-+Li+Fcc_Al-*Li+Fcc_Al+Mg2Si-*Li+Fcc_AlJrSi+Mg2Si under high cooling rate, respectively.A method to predict the solid-liquid interface stability during unidirectional solidification was developed by coupling M-S model with Calphad method. The method was applied to Al-0.38wt% Zn and Al-0.34wt% Si-0.14wt% Mg alloys, and the predicted results were compared with some former experimental data. The good agreement between the calculation results and the experimental data demonstrates the superiority of the present method to the classical model based on constant partition coefficient assumptions.The conventional theory of constrained dendrite growth for binary alloys was extended to multi -component alloys based on the Calphad method with considerations of the solute interactions in each phase. The variable solute partition coefficients and liquidus slopes under different tip undercooling were calculated in detail for a series of Al-Si-Mg alloys. The influence of variable partition coefficients on the kinetics of dendrite growth was demonstrated quantitatively. The primary dendrite spacing, the most important microstructure scale, was predicted in several Al-Si-Mg alloys. By comparing the results with the experimental results of former researchers, the present method was proved to be a superior method for the prediction of primary dendrite arm spacing.By using the concept of solute diffusion layer thickness, the back diffusion flux was easily obtained without the time consuming finite difference scheme. The application of the simplified model to Al-Cu-Mg alloys was studied in detail. The good agreement between the experimental results and the calculated values shows that this simplified model is suitable for the prediction of dendrite arm coarsening during solidification of multi-component alloys.Taking into account the effect of solute interactions on both phase equilibria and diffusion behaviors in each phase, the conventional theory of constrained dendrite
growth for binary alloys was extended to multicomponent alloys. The variable solute partition coefficients and the diffusion matrix were obtained based on the thermodynamic databases and the diffusion mobility coefficients during the dendrite growth process in multi-component alloys. The calculated data were used to evaluate the influence of multi-component diffusion on the kinetics of dendrite solidification of Cu-Sn-Zn ternary alloys.The solute redistribution during the rapid solidification of multi-component alloys was theoretically studied based on thermodynamic analyses. Transportation processes of the two solutes were taken into account to determine the compositions on the both sides of the growth interface. The analysis of the interface diffusion process reveals that the solute partition at the growth interface depends on the diffusion coefficient, growth rate, the solute partition ratios in the two binary sub-systems. After the analysis of the diffusion processes in the bulk liquid and solid, the solute distribution profiles in the directionally solidified samples were obtained. From the results, the path for the interface composition variation was calculated. It was found that the path was dependent on the diffusion coefficients of the solutes in the liquid.
溶质分凝是凝固过程中的重要伴随现象,对凝固过程中的成分偏析及组织形成有着决定性的影响。在多元合金中由于存在复杂的溶质相互作用,用实验相图分析溶质分凝行为并不方便。本文首先从热力学角度出发,建立了溶质分凝因数的热力学计算模型。详细讨论了Al-Cu二元合金和Al-Si-Mg三元合金凝固过程中溶质的分凝行为。结合计算热力学技术,对溶质分凝因数的预测很好地吻合于实验结果。
为了快速提取系统的热力学信息,减少计算时间,应用Levenberg-Marquardt算法进行了相图的计算。Levenberg-Marquardt算法采用目标函数的二阶导数,它能够实现计算精度和收敛速度的较好结合。该方法适合于求解二元以及多元合金中的相平衡问题。
研究了工业中广泛应用的Al-Si-Mg三元合金凝固过程中的溶质分凝行为,确定了该合金凝固过程中溶质分凝因数与固相分数的定量关系。发现分凝因数随固相分数的变化而显著变化,并且远远偏离其二元系中的数值。定量预测了不同凝固条件下Al-Si-Mg合金的凝固路径及共晶分数。其结果与采用二元分凝因数的预测结果偏差较大,而与实验结果接近。
结合溶质分凝的分析,研究了冷却速率对AI-2.06 wt%Si-1.58 wt%Mg合金凝固过程的影响。实验和理论分析均发现,在低的冷却速率下,其凝固过程为:L→L_1+Fcc_Al→L_1+Fcc_Al+Si→L_1+Fcc_Al+Si+Mg_2Si,而在较高的冷却速率下,其凝固过程为:L→L_1+Fcc_Al→L_1+Fcc_Al+Mg_2Si→L_1+Fcc_Al+Si+Mg_2Si。改变凝固速率可以使多元合金的凝固过程按照不同的路径进行,从而达到控制析出相种类的目的。
耦合热力学计算技术,提出了多元合金凝固界面的稳定性判据。以Al-0.34
Metallic materials in engineering applications are mostly multi-component and multi-phase alloys. The application of solidification modeling to practical technology is closely linked to our ability to model the microstructure development in multi-component alloys. In this work, the solute partition behavior and its influence on the solidification process of multi-component alloys were studied in detail based on the Calphad technology.A complete thermodynamic model for the accurate calculation of the partition coefficients in solidification process was described. The model was applied to Al-Cu binary alloy and Al-Si-Mg ternary alloy, and the predicted partition coefficients were compared with some former experimental data. Good agreement between the calculation results and the experimental data demonstrates the validity of the present thermodynamic model for the prediction of the partition coefficients in solidification process.The Levenberg-Marquardt method, the best algorithm to obtain the least-square solution of non-linear equations, was applied to calculate the stable phase equilibria. It was used for the prediction of solidification of ternary Al-Si-Mg system. The calculated phase equilibria agree well with the experimental results.The variation of solute partition coefficient was studied in dendritic solidification process of Al-Si-Mg alloys. It was found that the partition coefficient changed greatly during solidification process, which should have important influence on the formation of the microsegregation and the precipitation of various phases. The solidification path and eutectic fractions were predicted by employing the binary partition coefficients and Calphad technology separately. The results showed that great errors had been introduced by assuming the partition coefficient as a constant. By coupling Calphad method with microscale solidification model, the predicted solidification path and the eutectic fraction of Al-Si-Mg alloys agree well with the experimental results.
The effect of cooling rates on the solidification process of Al-2.06 wt% Si-1.58 wt% Mg alloy was experimentally investigated. It was found that the solidification sequences were L->Li+Fcc_Al->Li+Fcc_Al+Si-±Li+Fcc_Al+Si+Mg2Si under low cooling rate and L-+Li+Fcc_Al-*Li+Fcc_Al+Mg2Si-*Li+Fcc_AlJrSi+Mg2Si under high cooling rate, respectively.A method to predict the solid-liquid interface stability during unidirectional solidification was developed by coupling M-S model with Calphad method. The method was applied to Al-0.38wt% Zn and Al-0.34wt% Si-0.14wt% Mg alloys, and the predicted results were compared with some former experimental data. The good agreement between the calculation results and the experimental data demonstrates the superiority of the present method to the classical model based on constant partition coefficient assumptions.The conventional theory of constrained dendrite growth for binary alloys was extended to multi -component alloys based on the Calphad method with considerations of the solute interactions in each phase. The variable solute partition coefficients and liquidus slopes under different tip undercooling were calculated in detail for a series of Al-Si-Mg alloys. The influence of variable partition coefficients on the kinetics of dendrite growth was demonstrated quantitatively. The primary dendrite spacing, the most important microstructure scale, was predicted in several Al-Si-Mg alloys. By comparing the results with the experimental results of former researchers, the present method was proved to be a superior method for the prediction of primary dendrite arm spacing.By using the concept of solute diffusion layer thickness, the back diffusion flux was easily obtained without the time consuming finite difference scheme. The application of the simplified model to Al-Cu-Mg alloys was studied in detail. The good agreement between the experimental results and the calculated values shows that this simplified model is suitable for the prediction of dendrite arm coarsening during solidification of multi-component alloys.Taking into account the effect of solute interactions on both phase equilibria and diffusion behaviors in each phase, the conventional theory of constrained dendrite
growth for binary alloys was extended to multicomponent alloys. The variable solute partition coefficients and the diffusion matrix were obtained based on the thermodynamic databases and the diffusion mobility coefficients during the dendrite growth process in multi-component alloys. The calculated data were used to evaluate the influence of multi-component diffusion on the kinetics of dendrite solidification of Cu-Sn-Zn ternary alloys.The solute redistribution during the rapid solidification of multi-component alloys was theoretically studied based on thermodynamic analyses. Transportation processes of the two solutes were taken into account to determine the compositions on the both sides of the growth interface. The analysis of the interface diffusion process reveals that the solute partition at the growth interface depends on the diffusion coefficient, growth rate, the solute partition ratios in the two binary sub-systems. After the analysis of the diffusion processes in the bulk liquid and solid, the solute distribution profiles in the directionally solidified samples were obtained. From the results, the path for the interface composition variation was calculated. It was found that the path was dependent on the diffusion coefficients of the solutes in the liquid.
引文
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