Al-Cu与Al-Si-Cu合金凝固微观组织的仿真模拟
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摘要
在铸件凝固过程中,晶粒组织的控制是非常重要的,晶粒组织对铸件质量和力学性能有显著的影响。以前,主要依靠半经验公式和实验来控制成型过程的微观组织演变,但会延长产品的生产周期、增加生产成本,也不能直观了解微观组织形貌演变的过程。随着高性能计算设备以及新模拟手段的出现,模拟仿真逐渐成为了预测材料微观组织形貌演变的有效手段。
微观组织模拟已经从半定量、固定点形核的确定性模型发展到了定量、随机形核的随机性模型。本文进行的微观组织模拟采用的是元胞自动机有限元模型,在此模型中,将枝晶尖端生长的动力学和晶向作为过冷度的函数。元胞自动机有限元模型非常适合用来跟踪柱状晶前端的生长情况。
本文解决了微观组织模拟过程中,在界面传热、液相流动以及形核方面仍存在的一些问题,进一步提高了微观组织模拟的精度,使得模拟结果在柱状晶和等轴晶分布、比例、晶粒尺寸方面,更接近实验结果。主要的研究结果有以下几个方面：
(1)基于ProCAST的反求方法,采用实验测得的铸件和模具的温度数据,建立了反热传导求解界面换热系数的模型,求解了Al-2%Cu二元合金、Al-9.75%Si-2%Cu三元合金以及A356铝合金的界面换热系数曲线。并将其代入到合金的微观组织模拟中,改善了以往微观组织模拟采用恒定的界面换热系数值模拟的结果,提高了合金微观组织模拟的精度。
通过实验测得的温度曲线与模拟的温度曲线进行对比,验证所求解的界面换热曲线的准确性,分析了界面换热曲线的变化趋势,讨论了Al-2%Cu二元合金与Al-9.75%Si-2%Cu三元合金界面换热曲线产生差异的原因；另外,还通过反分析模型求解了不同浇注温度下的水冷系统的界面换热系数。
(2)将Eyring模型和Miedema模型相结合,建立了二元以及三元合金液相扩散系数的理论计算模型,改善了以往微观组织模拟中采用固定液相扩散系数的模拟结果,提高了微观模拟的精度。
在Eyring模型中,引入合金黏度随时间变化的曲线,进一步提高了计算的准确性,并将Eyring模型计算的液相扩散系数作为合金的自扩散系数,代入到Miedema模型中进行修正,最终计算出合金真实的液相扩散系数；另外,结合Toop模型,将液相扩散系数的理论计算模型进行扩展,计算了三元合金的液相扩散系数。将理论计算的液相扩散系数与实验测得的数值进行对比,验证了液相扩散系数理论计算模型的正确性。
(3)根据实验条件和铸件材料,基于元胞自动机的形核模型和生长模型,对Al-2%Cu二元合金和Al-9.75%Si-2%Cu三元合金的形核密度以及过冷度进行了研究,选择了合适的微观模拟参数；并采用常温模具中的铸件进行微观组织模拟,模拟的结果与实验结果吻合性很好,验证了基于反求的界面换热系数、计算的液相扩散系数以及确定的微观参数的微观组织模拟模型的正确性。
The control of grain structure is of primary importance in many solidification processes of castings, because the grain structure has influence on the quality of casting and mechanical properties. In the past, the microstructural evolution was researched mainly based on numbers of semi-empirical formulations and experiments, which brought great expense of costs and time. Otherwise, it can not provide a direct view of microstructure development. With the advent of high performance computing devices and new simulated techniques, numerical simulation has been considered as an effective tool for evaluation of microstructure evolutions during the solidification process.
Numerical simulation experiences the stage of semi-quantitative simulation, fixed-points nucleation and deterministic model to quantitative simulation, random nucleation, and stochastic model. The method of microstructure simulation is the cellular automation-finite element (CAFE) model in this article. In the CAFE model, the growth kinetics of the dendrite tips and crystallographic orientation of grains are determined as a function of undercooling. The CAFE model is well suited to track the development of a columnar dendritic front in an undercooled liquid.
This article has optimized and solved some problems of interface heat transfer, liquid-phase diffusion and nucleation which still exist in the microstructure simulation to further improve the accuracy of the CAFE model. The simulated results are in accord with the experimental ones well, and can accurately reflect equiaxed and columnar grains distribution, proportion and size. The main researches are shown as following
(1) The interfacial heat transfer coefficients (IHTC) of Al-2%Cu, Al-2%Cu-9.75%Si and A356alloy are performed based on the inverse method of ProCAST and experimental temperature. The identified IHTC is taken into the CAFE method, which improve the accuracy of microstructure simulation with the constant IHTC. For verifying the IHTC, the temperature distribution was calculated by feeding the determined IHTC into the ProCAST with the same boundary conditions and then compared with the measured temperatures at the corresponding locations. In addition, the IHTC variation with time is analysed, and the differences of IHTC between Al-2%Cu alloy and Al-9.75%Si-2%Cu alloy are discussed. Otherwise, the IHTCs of the experiment with water-cooling system are resolved at different pouring temperatures by the inverse method.
(2) The liquid-phase diffusion coefficients of Al-2%Cu alloy and Al-9.75%Si-2%Cu alloy are calculated by the Eyring model and Miedema model in different temperatures. The CAFE method is performed by the calculated liquid-phase diffusion coefficient, which improve the accuracy of the micro structure simulation based on the constant liquid-phase diffusion coefficients. The viscosity curve variation with temperature is introduced into the Eyring model. The self-diffusion coefficient is calculated by the Eyring model, and the liquid-phase diffusion coefficient is modified by the Miedema model. The liquid-phase diffusion coefficient of Al-9.75%Si-2%Cu alloy is calculated by the Eyring model, Miedema model and Toop model. In order to verify the feasibility of the model, the liquid-phase diffusion coefficients measured with experiments are compared with the calculated data by the Eyring model, Miedema model and Toop model.
(3) According to the experimental conditions and casting material, the nucleation density and undercooling are discussed and selected based on the nucleation and growth model of CAFE in the microstructure simulation. The simulated results using the identified IHTC, calculated liquid-phase diffusion coefficients and suitable microstructure parameters are in accord with the experimental results of normal temperature mold well.
微观组织模拟已经从半定量、固定点形核的确定性模型发展到了定量、随机形核的随机性模型。本文进行的微观组织模拟采用的是元胞自动机有限元模型,在此模型中,将枝晶尖端生长的动力学和晶向作为过冷度的函数。元胞自动机有限元模型非常适合用来跟踪柱状晶前端的生长情况。
本文解决了微观组织模拟过程中,在界面传热、液相流动以及形核方面仍存在的一些问题,进一步提高了微观组织模拟的精度,使得模拟结果在柱状晶和等轴晶分布、比例、晶粒尺寸方面,更接近实验结果。主要的研究结果有以下几个方面：
(1)基于ProCAST的反求方法,采用实验测得的铸件和模具的温度数据,建立了反热传导求解界面换热系数的模型,求解了Al-2%Cu二元合金、Al-9.75%Si-2%Cu三元合金以及A356铝合金的界面换热系数曲线。并将其代入到合金的微观组织模拟中,改善了以往微观组织模拟采用恒定的界面换热系数值模拟的结果,提高了合金微观组织模拟的精度。
通过实验测得的温度曲线与模拟的温度曲线进行对比,验证所求解的界面换热曲线的准确性,分析了界面换热曲线的变化趋势,讨论了Al-2%Cu二元合金与Al-9.75%Si-2%Cu三元合金界面换热曲线产生差异的原因；另外,还通过反分析模型求解了不同浇注温度下的水冷系统的界面换热系数。
(2)将Eyring模型和Miedema模型相结合,建立了二元以及三元合金液相扩散系数的理论计算模型,改善了以往微观组织模拟中采用固定液相扩散系数的模拟结果,提高了微观模拟的精度。
在Eyring模型中,引入合金黏度随时间变化的曲线,进一步提高了计算的准确性,并将Eyring模型计算的液相扩散系数作为合金的自扩散系数,代入到Miedema模型中进行修正,最终计算出合金真实的液相扩散系数；另外,结合Toop模型,将液相扩散系数的理论计算模型进行扩展,计算了三元合金的液相扩散系数。将理论计算的液相扩散系数与实验测得的数值进行对比,验证了液相扩散系数理论计算模型的正确性。
(3)根据实验条件和铸件材料,基于元胞自动机的形核模型和生长模型,对Al-2%Cu二元合金和Al-9.75%Si-2%Cu三元合金的形核密度以及过冷度进行了研究,选择了合适的微观模拟参数；并采用常温模具中的铸件进行微观组织模拟,模拟的结果与实验结果吻合性很好,验证了基于反求的界面换热系数、计算的液相扩散系数以及确定的微观参数的微观组织模拟模型的正确性。
The control of grain structure is of primary importance in many solidification processes of castings, because the grain structure has influence on the quality of casting and mechanical properties. In the past, the microstructural evolution was researched mainly based on numbers of semi-empirical formulations and experiments, which brought great expense of costs and time. Otherwise, it can not provide a direct view of microstructure development. With the advent of high performance computing devices and new simulated techniques, numerical simulation has been considered as an effective tool for evaluation of microstructure evolutions during the solidification process.
Numerical simulation experiences the stage of semi-quantitative simulation, fixed-points nucleation and deterministic model to quantitative simulation, random nucleation, and stochastic model. The method of microstructure simulation is the cellular automation-finite element (CAFE) model in this article. In the CAFE model, the growth kinetics of the dendrite tips and crystallographic orientation of grains are determined as a function of undercooling. The CAFE model is well suited to track the development of a columnar dendritic front in an undercooled liquid.
This article has optimized and solved some problems of interface heat transfer, liquid-phase diffusion and nucleation which still exist in the microstructure simulation to further improve the accuracy of the CAFE model. The simulated results are in accord with the experimental ones well, and can accurately reflect equiaxed and columnar grains distribution, proportion and size. The main researches are shown as following
(1) The interfacial heat transfer coefficients (IHTC) of Al-2%Cu, Al-2%Cu-9.75%Si and A356alloy are performed based on the inverse method of ProCAST and experimental temperature. The identified IHTC is taken into the CAFE method, which improve the accuracy of microstructure simulation with the constant IHTC. For verifying the IHTC, the temperature distribution was calculated by feeding the determined IHTC into the ProCAST with the same boundary conditions and then compared with the measured temperatures at the corresponding locations. In addition, the IHTC variation with time is analysed, and the differences of IHTC between Al-2%Cu alloy and Al-9.75%Si-2%Cu alloy are discussed. Otherwise, the IHTCs of the experiment with water-cooling system are resolved at different pouring temperatures by the inverse method.
(2) The liquid-phase diffusion coefficients of Al-2%Cu alloy and Al-9.75%Si-2%Cu alloy are calculated by the Eyring model and Miedema model in different temperatures. The CAFE method is performed by the calculated liquid-phase diffusion coefficient, which improve the accuracy of the micro structure simulation based on the constant liquid-phase diffusion coefficients. The viscosity curve variation with temperature is introduced into the Eyring model. The self-diffusion coefficient is calculated by the Eyring model, and the liquid-phase diffusion coefficient is modified by the Miedema model. The liquid-phase diffusion coefficient of Al-9.75%Si-2%Cu alloy is calculated by the Eyring model, Miedema model and Toop model. In order to verify the feasibility of the model, the liquid-phase diffusion coefficients measured with experiments are compared with the calculated data by the Eyring model, Miedema model and Toop model.
(3) According to the experimental conditions and casting material, the nucleation density and undercooling are discussed and selected based on the nucleation and growth model of CAFE in the microstructure simulation. The simulated results using the identified IHTC, calculated liquid-phase diffusion coefficients and suitable microstructure parameters are in accord with the experimental results of normal temperature mold well.
引文
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