多元合金凝固微观组织的相场法模拟研究
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摘要
铸件的力学性能优劣和使用寿命主要取决于铸件在凝固过程中所形成的微观组织,有效地控制铸件成型过程中微观组织的形成具有非常重要的科学与工程意义,但是由于成型过程需要控制大量的参数,全部用实验手段不太现实,因而微观组织演化过程的数值模拟为铸件成型控制和多元合金材料的研制提供了一个有效的新途径。微观组织的数值模拟可以有效地降低新合金材料的开发成本,缩短开发周期,少量的实验既可达到合金的凝固组织预测和力学性能控制,又可获得主要工艺参数与合金凝固组织的定量关系,为成型过程的工艺控制和合金凝固组织的改善提供了可靠依据。
相场法是一种计算技术,它能使研究者直接模拟微观组织的形成。相场模型中包括一组描述温度场、浓度场和相场有序参数的方程,相场法借助相场与其它外部场的耦合,在金属充型和凝固过程中,有效地将微观与宏观尺度相结合,能够比较真实地模拟凝固过程。
在参阅国内外相场理论的基础上,完善二元合金凝固过程中枝晶生长的二维相场模型,在模型中考虑溶质扩散与各向异性对枝晶形貌的影响,考虑固-液界面存在的大量结构起伏和能量起伏对组织生长的影响,并对微观组织形成模拟中的若干现象进行分析和讨论。在单晶粒生长的相场模型的基础上,引入方向系数,提出了二元及多元合金多晶粒生长的相场模型。推导分析多相场共晶生长的相场模型,实现合金共晶组织生长过程的模拟。
讨论了相场方程的时域离散与空间离散,优化了相场法数值模拟的初始条件、边界条件、稳定性条件及其数值求解方法。基于交互式大型工程测试和复杂数值计算结果的可视化工具Tecplot,采用Visual C++自行编程将计算结果数据转换成Tecplot标准输入文件,实现了相场法微观组织模拟的可视化软件系统。该系统既可有效处理计算中相关的复杂数据结构,还可实现计算结果的逼真显示及图象和动画的处理,方便地分析模拟结果的特征、规律。
使用提出的二元合金多晶粒生长的相场模型,以Al-Cu合金为例,模拟了二元合金等温凝固过程中多个晶粒的生长过程。研究了二元合金凝固过程中多个晶粒枝晶的竞争生长机制。观察分析了多个枝晶与单个枝晶生长形貌的差别、晶粒之间的溶质分布状况。结果表明：在枝晶生长的初期,各个枝晶之间还没有相互影响的时候,枝晶的生长都和单个枝晶生长的情况相同,符合经典理论。在枝晶生长的后期,由于枝晶间的相互影响,枝晶的生长形貌不再符合Ivantsov理论。晶粒在生长的过程中释放出潜热,潜热使得该区域过冷度较低,导致主枝晶向过冷度大的区域生长,最终造成主枝晶的抑制和弯曲。由于凝固过程的溶质再分配,溶质富集在枝晶生长的界面前沿。溶质富集在这些区域,造成这个区域的熔点降低,从而导致实际过冷度的减小,使得这些区域凝固的比其他区域晚,最后形成晶界。
使用提出的多元合金多晶粒生长的相场模型,以Al-Cu-Mg合金为例,模拟了多元合金等温凝固过程中多个晶粒的生长过程。研究比较了Al-Cu合金和Al-Cu-Mg合金在相同凝固条件下微观组织的变化。结果表明：多元合金多个晶粒共同生长时与二元合金类似,有竞争生长的现象,溶质富集在枝晶生长的界面前沿等区域。多元合金的各种溶质在溶剂(基体)中的扩散系数越大,溶质在晶粒中的分布越均匀。定性的展现了孕育剂细化晶粒机制对Al-Cu-Mg晶粒的形状和尺寸的影响、合金之间的合金成分和微观组织的关系(Al-Cu合金vs.Al-Cu-Mg合金)。合金成分的改变并没有十分明显的改变枝晶的形貌,初始晶核数量的大小对枝晶形貌有很大的影响。在Al-Cu-Mg合金中Mg改变了溶质Cu晶粒中的分布,加重了晶粒中Cu的溶质偏析。
在多元合金多晶粒生长的相场模型的基础上耦合温度场,提出了一个多元合金多晶粒非等温生长的相场模型,并对Al-Cu合金与Al-Cu-Mg合金的凝固进行模拟,研究分析了其微观组织形貌的变化,以及温度场、溶质场的分布。结果表明：在忽略温度梯度的情况下,凝固时潜热的释放使凝固界面前沿的液体温度升高,由于枝晶生长的速度要大于热量传递的速度,使热量在凝固界面前沿累积,因此造成凝固的前沿上温度最高,、后凝固的区域要比先凝固的区域温度高。在模拟中加入了冷却速度和外部温度梯度,外部温度梯度随着晶粒的生长发生变化,这是由凝固潜热和热量传递造成的。初始温度不同,对凝固的速度有很大的影响,过冷度越大,模拟区域的固相率越大,凝固速度越快。
推导分析了多相场共晶生长的模型,使用该模型模拟研究了CBr4-C2C16合金凝固过程中共晶组织的演化。结果表明：初始共晶层片和过冷度等参数选择适当时,共晶层片保持稳定界面,平行向前生长。在凝固前沿由于溶质再分配和溶质在液相中不能及时的扩散均匀,导致与理论计算的浓度值相比,在已凝固的区域中α相中的溶质浓度偏高、β相中的溶质浓度偏低。
The mechanical properties and serving life of castings depend on the microstructures in solidification, it is very important and realistic to control the formation of microstructures effectively in molding, but there has many controlling parameters, it is unpractical to test them by experiment, the method of numerical prediction is therefore essential for any processing activity. It is well known that the numerical simulation can reduce consumptions, predict solidified microstructures and materials behavior by fewer experiments, obtain the quantitative relationship between mayor processing parameters and the microstructures, and it can offer a credible basis to evaluate and optimize the castings processing so as to improve their quality.
The phase field method is a computing technology, the investigators can simulate the microstructures directly with it. The phase-field model includes a set of equations to depict the phase field, temperature field and solute diffusion field, the phase-field method for simulating the processing of solidification is developed by coupling phase field, temperature field, flow field, and other accessional fields, the microcosmic scales and macrocosmic scales are combined during mold filling and solidifying of the castings.
Take the influence of structural fluctuation and energetic fluctuation in interface to dendrite growth, improved binary phase-field model, studied the influence of different anisotropy coefficients、undercooling on shapes of dendrites and distribution of solute for single grain. A new phase-field model for dendrite growth of multiple grains in binary and multicomponent alloys has been developed based on the Ginzberg-Landau theory and phase-field model of single grain.
The time discretization and the space discretization of the phase-field equation were discussed in this paper, the initial conditions, boundary conditions, stable conditions and their solution methods were presented. In the process of simulation, the Visual C++ code was used to calculate the program and visible software Tecplot was used to achieve the vision of results, the visible system of the phase-field simulation was achieved. The complicated data base can be transacted effectively in this system, and the characteristic and the discipline of simulation results can be analyzed conveniently.
Using the binary alloys dendrite growth of multiple grains phase model, taking Al-Cu alloy for example, coupled the concentration field, simulated the dendritic growth process of multiple grains during isothermal solidification. The result of simulation showed dendritic competitive growth of multiple grains, and reappears the process of dendrite growth in practical solidification. Comparing the simulated of multiple grains microstructure and single grain, we can see that the single dendrite growth and the multiple dendrite growth without other grains influences on side are agree with the classical theory (Ivantsov theory);in the region of competitive growth, multiple grains influenced interactive, they growth aren't agree with the classical theory. The regions between the secondary arms and grains have the highest concentration, while the grain itself has a low concentration. These features show good agreement with the composition distribution given by the real equiaxed dendrite growth.
Using the multicomponent alloys dendrite growth of multiple grains phase model taking Al-Cu alloy and Al-Cu-Mg alloy for example, coupled the concentration field, simulate the dendritic growth process of multiple grains during isothermal solidification. The result shows, the predicted dendritic morphology is affected by density of seed, the higher seed density it is, the more refined and globular grains become. Qualitative effects like the grain refining mechanisms of inoculants and the effect on the grain size and dendritic morphology in Al-Cu-Mg alloy, the effect of the relation between alloy composition and microstructure (Al-Cu alloy vs. Al-Cu-Mg alloy) have been shown. A conclusion can be drawn after comparing the simulated result of Al-Cu alloys and Al-Cu-Mg alloys, that the composition change (adding Mg to Al-Cu alloy in order to get Al-Cu-Mg alloy) do not significantly change the shape of grains. That solute Mg changes the concentration distributing of solute Cu in equiaxed dendrite and increases concentration of Cu in grains. That means solute Mg will increase the microsegregation of solute Cu in grains.
A new phase-field model of dendritic growth of non-isothermal solidification is developed based on the phase-field model of isothermal solidification of multicomponent alloy with multiple grains, in connection with the temperature field. Taking Al-Cu-Mg alloy for example, we simulated the dendritic growth process of multiple grains during multicomponent alloy solidification. The simulation showed dendritic competitive growth of multiple grains, and reproduced the process of dendrite growth in practical solidification. The release of latent heat of alloy solidification can be showed in simulation. In same grain, the temperature of the region of earlier solidification was less than the region of late solidification. The velocity of solidification increased with the augment of temperature of undercooling.
Deduce and analyse phase-field model of eutectic solidification, using the model, taking CBr4-C2Cl6 alloy for example, simulated the eutectic growth process of alloy solidification. The result shows, the eutectic lamellar growth is parallel and steady with fitting parameters. In front of the solidification interface the diffuse and distribution of solute influence the concentration of solute in solid phase, induce the concentration of solute in a phase is higher andβphase is lower than value of steady state.
相场法是一种计算技术,它能使研究者直接模拟微观组织的形成。相场模型中包括一组描述温度场、浓度场和相场有序参数的方程,相场法借助相场与其它外部场的耦合,在金属充型和凝固过程中,有效地将微观与宏观尺度相结合,能够比较真实地模拟凝固过程。
在参阅国内外相场理论的基础上,完善二元合金凝固过程中枝晶生长的二维相场模型,在模型中考虑溶质扩散与各向异性对枝晶形貌的影响,考虑固-液界面存在的大量结构起伏和能量起伏对组织生长的影响,并对微观组织形成模拟中的若干现象进行分析和讨论。在单晶粒生长的相场模型的基础上,引入方向系数,提出了二元及多元合金多晶粒生长的相场模型。推导分析多相场共晶生长的相场模型,实现合金共晶组织生长过程的模拟。
讨论了相场方程的时域离散与空间离散,优化了相场法数值模拟的初始条件、边界条件、稳定性条件及其数值求解方法。基于交互式大型工程测试和复杂数值计算结果的可视化工具Tecplot,采用Visual C++自行编程将计算结果数据转换成Tecplot标准输入文件,实现了相场法微观组织模拟的可视化软件系统。该系统既可有效处理计算中相关的复杂数据结构,还可实现计算结果的逼真显示及图象和动画的处理,方便地分析模拟结果的特征、规律。
使用提出的二元合金多晶粒生长的相场模型,以Al-Cu合金为例,模拟了二元合金等温凝固过程中多个晶粒的生长过程。研究了二元合金凝固过程中多个晶粒枝晶的竞争生长机制。观察分析了多个枝晶与单个枝晶生长形貌的差别、晶粒之间的溶质分布状况。结果表明：在枝晶生长的初期,各个枝晶之间还没有相互影响的时候,枝晶的生长都和单个枝晶生长的情况相同,符合经典理论。在枝晶生长的后期,由于枝晶间的相互影响,枝晶的生长形貌不再符合Ivantsov理论。晶粒在生长的过程中释放出潜热,潜热使得该区域过冷度较低,导致主枝晶向过冷度大的区域生长,最终造成主枝晶的抑制和弯曲。由于凝固过程的溶质再分配,溶质富集在枝晶生长的界面前沿。溶质富集在这些区域,造成这个区域的熔点降低,从而导致实际过冷度的减小,使得这些区域凝固的比其他区域晚,最后形成晶界。
使用提出的多元合金多晶粒生长的相场模型,以Al-Cu-Mg合金为例,模拟了多元合金等温凝固过程中多个晶粒的生长过程。研究比较了Al-Cu合金和Al-Cu-Mg合金在相同凝固条件下微观组织的变化。结果表明：多元合金多个晶粒共同生长时与二元合金类似,有竞争生长的现象,溶质富集在枝晶生长的界面前沿等区域。多元合金的各种溶质在溶剂(基体)中的扩散系数越大,溶质在晶粒中的分布越均匀。定性的展现了孕育剂细化晶粒机制对Al-Cu-Mg晶粒的形状和尺寸的影响、合金之间的合金成分和微观组织的关系(Al-Cu合金vs.Al-Cu-Mg合金)。合金成分的改变并没有十分明显的改变枝晶的形貌,初始晶核数量的大小对枝晶形貌有很大的影响。在Al-Cu-Mg合金中Mg改变了溶质Cu晶粒中的分布,加重了晶粒中Cu的溶质偏析。
在多元合金多晶粒生长的相场模型的基础上耦合温度场,提出了一个多元合金多晶粒非等温生长的相场模型,并对Al-Cu合金与Al-Cu-Mg合金的凝固进行模拟,研究分析了其微观组织形貌的变化,以及温度场、溶质场的分布。结果表明：在忽略温度梯度的情况下,凝固时潜热的释放使凝固界面前沿的液体温度升高,由于枝晶生长的速度要大于热量传递的速度,使热量在凝固界面前沿累积,因此造成凝固的前沿上温度最高,、后凝固的区域要比先凝固的区域温度高。在模拟中加入了冷却速度和外部温度梯度,外部温度梯度随着晶粒的生长发生变化,这是由凝固潜热和热量传递造成的。初始温度不同,对凝固的速度有很大的影响,过冷度越大,模拟区域的固相率越大,凝固速度越快。
推导分析了多相场共晶生长的模型,使用该模型模拟研究了CBr4-C2C16合金凝固过程中共晶组织的演化。结果表明：初始共晶层片和过冷度等参数选择适当时,共晶层片保持稳定界面,平行向前生长。在凝固前沿由于溶质再分配和溶质在液相中不能及时的扩散均匀,导致与理论计算的浓度值相比,在已凝固的区域中α相中的溶质浓度偏高、β相中的溶质浓度偏低。
The mechanical properties and serving life of castings depend on the microstructures in solidification, it is very important and realistic to control the formation of microstructures effectively in molding, but there has many controlling parameters, it is unpractical to test them by experiment, the method of numerical prediction is therefore essential for any processing activity. It is well known that the numerical simulation can reduce consumptions, predict solidified microstructures and materials behavior by fewer experiments, obtain the quantitative relationship between mayor processing parameters and the microstructures, and it can offer a credible basis to evaluate and optimize the castings processing so as to improve their quality.
The phase field method is a computing technology, the investigators can simulate the microstructures directly with it. The phase-field model includes a set of equations to depict the phase field, temperature field and solute diffusion field, the phase-field method for simulating the processing of solidification is developed by coupling phase field, temperature field, flow field, and other accessional fields, the microcosmic scales and macrocosmic scales are combined during mold filling and solidifying of the castings.
Take the influence of structural fluctuation and energetic fluctuation in interface to dendrite growth, improved binary phase-field model, studied the influence of different anisotropy coefficients、undercooling on shapes of dendrites and distribution of solute for single grain. A new phase-field model for dendrite growth of multiple grains in binary and multicomponent alloys has been developed based on the Ginzberg-Landau theory and phase-field model of single grain.
The time discretization and the space discretization of the phase-field equation were discussed in this paper, the initial conditions, boundary conditions, stable conditions and their solution methods were presented. In the process of simulation, the Visual C++ code was used to calculate the program and visible software Tecplot was used to achieve the vision of results, the visible system of the phase-field simulation was achieved. The complicated data base can be transacted effectively in this system, and the characteristic and the discipline of simulation results can be analyzed conveniently.
Using the binary alloys dendrite growth of multiple grains phase model, taking Al-Cu alloy for example, coupled the concentration field, simulated the dendritic growth process of multiple grains during isothermal solidification. The result of simulation showed dendritic competitive growth of multiple grains, and reappears the process of dendrite growth in practical solidification. Comparing the simulated of multiple grains microstructure and single grain, we can see that the single dendrite growth and the multiple dendrite growth without other grains influences on side are agree with the classical theory (Ivantsov theory);in the region of competitive growth, multiple grains influenced interactive, they growth aren't agree with the classical theory. The regions between the secondary arms and grains have the highest concentration, while the grain itself has a low concentration. These features show good agreement with the composition distribution given by the real equiaxed dendrite growth.
Using the multicomponent alloys dendrite growth of multiple grains phase model taking Al-Cu alloy and Al-Cu-Mg alloy for example, coupled the concentration field, simulate the dendritic growth process of multiple grains during isothermal solidification. The result shows, the predicted dendritic morphology is affected by density of seed, the higher seed density it is, the more refined and globular grains become. Qualitative effects like the grain refining mechanisms of inoculants and the effect on the grain size and dendritic morphology in Al-Cu-Mg alloy, the effect of the relation between alloy composition and microstructure (Al-Cu alloy vs. Al-Cu-Mg alloy) have been shown. A conclusion can be drawn after comparing the simulated result of Al-Cu alloys and Al-Cu-Mg alloys, that the composition change (adding Mg to Al-Cu alloy in order to get Al-Cu-Mg alloy) do not significantly change the shape of grains. That solute Mg changes the concentration distributing of solute Cu in equiaxed dendrite and increases concentration of Cu in grains. That means solute Mg will increase the microsegregation of solute Cu in grains.
A new phase-field model of dendritic growth of non-isothermal solidification is developed based on the phase-field model of isothermal solidification of multicomponent alloy with multiple grains, in connection with the temperature field. Taking Al-Cu-Mg alloy for example, we simulated the dendritic growth process of multiple grains during multicomponent alloy solidification. The simulation showed dendritic competitive growth of multiple grains, and reproduced the process of dendrite growth in practical solidification. The release of latent heat of alloy solidification can be showed in simulation. In same grain, the temperature of the region of earlier solidification was less than the region of late solidification. The velocity of solidification increased with the augment of temperature of undercooling.
Deduce and analyse phase-field model of eutectic solidification, using the model, taking CBr4-C2Cl6 alloy for example, simulated the eutectic growth process of alloy solidification. The result shows, the eutectic lamellar growth is parallel and steady with fitting parameters. In front of the solidification interface the diffuse and distribution of solute influence the concentration of solute in solid phase, induce the concentration of solute in a phase is higher andβphase is lower than value of steady state.
引文
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