Fe-C合金等温凝固过程的相场法模拟
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摘要
Fe-C合金系是目前应用最为广泛的工程结构材料,其力学性能的优劣和使用寿命的长短,与合金铸件在凝固过程中所形成的微观组织有关。用相场法进行合金凝固时微观组织所形成过程的模拟,对优化工艺参数、提高铸件质量,不仅具有重要的理论学术意义,而且也具有重要的工程应用价值。
本文采用KKS(Kim,Kim,Suzuki.)模型,基于自由能泛函数推导了纯金属、单相二元合金及多元合金的相场控制方程,并重点对Fe-0.5mol%C单相二元合金等温凝固的相场控制方程和溶质控制方程进行推导。相场模型中考虑了界面各向异性,并引入了诱发侧向分支的扰动项,也为模型确定了合适的边界条件和初始条件等,采用基于均匀网格的有限差分法对控制方程进行了离散。采用基于Visual C++6.0平台的C语言进行编程,实现了用Tecplot10.0和Origin7.0将模拟结果以及凝固特征参数可视化。
研究了晶粒的长大过程及各向异性强度对枝晶形貌的影响。结果表明,晶体生长初期,晶粒形貌为球状,随着计算时间的推移,晶粒形貌由球状经星形向枝晶形状转变,最后形成复杂的树枝晶;在不考虑成分过冷的时候,各向异性是使晶粒形貌以枝晶方式生长的最主要原因。
研究了过冷度、各向异性强度和扰动强度对枝晶生长形貌的影响。结果表明,随着过冷度的减小,枝晶主干细化,各向异性程度增大,晶粒生长速度减小,溶质扩散层厚度增加,枝晶的最高溶质浓度降低,溶质梯度减小;随着各向异性的增加,晶粒由海藻状转变为枝晶状,枝晶生长速度也随之增大;扰动是引发枝晶的侧向分支的主要原因。各向异性强度和扰动强度均对枝晶溶质分布的影响并不显著。
分析了枝晶生长过程中溶质分布情况。结果表明,溶质分布情况均与实际枝晶的溶质分布情况相一致。
为了考核模拟结果,对Fe-C合金的凝固过程进行实验研究,并对试样进行了微观组织分析。结果表明,模拟结果与实际凝固结果基本一致,验证了相场模型的正确性。
Fe-C alloy system is the most widely used material for the engineering structures at present time. The mechanical properties and durability property of the alloy lie on the solidification microstructures in the casting process. Modeling of the alloy microstructure formation using phase-field model will help to evaluate and optimize the castings processing technology so as to improve their quality.
Adopted KKS model and based on free energy function, the phase-field model of pure metal, binary single-phase alloy and multiple components alloy are derived respectively. Emphasis on derived the equation of phase-field and solute-field of binary single-phase alloy of the Fe-0.5mol%C under isothermal condition. The interface anisotropy is taken into account and a term of noise to produce the side-branches is introduced into the phase-field model. The initial conditions and boundary conditions is determined too. In order to solve the phase-field and solute-field equations used Finite Difference Formulas on uniform mesh. The computational program is programed by using Visual C++6.0. The vision result of simulation is achieved by using Tecplot 10.0 software and the curve of solidification characteristic parameter is showed by using Origin 7.0 software.
The grain growth process and the influence of anisotropic intensity on dendrite morphologies are investigated. The results show that during the early stages of growth, the morphology of crystal grain is spherical, with increasing of time, the grain morphologies will transform into star shape from spheric shape, and then change as complex dendrite morphologies. The grain morphologies trend to dendritic by anisotropism.
The influences of undercooling, anisotropic intensity and noise intensity on dendrite growth are investigated. The results show that with decreasing of undercooling, the morphology of dendritic trunk will become thinner, while anisotropic degree is increased, the speed of dendrite growth is decreased, thickness of solute diffusion layer is increased. The maximum solute concentration is decreased, the solute gradient is decreased. With increasing of anisotropic intensity, the grain morphology is transformed from seaweed to dendrite, and the speed of dendrite growth is increased. The main reason of dendrite side-branches is caused by the noise intensity. The influence of anisotropic intensity and noise intensity on the solute distribution of dendrite is not significant.
The solute distribution on dendrite growth process is also investigated. The results show that the solute distribution of simulation is same as the actual case.
In order to confirm the result from computer simulation, the solidification process of Fe-C alloy is carried on experimentally, and the microstructure of testing sample is studied in detail. The results show that the simulation results are almost same as the experimental results, which indicates that the conclusion results from the phase-field model simulation is successful.
本文采用KKS(Kim,Kim,Suzuki.)模型,基于自由能泛函数推导了纯金属、单相二元合金及多元合金的相场控制方程,并重点对Fe-0.5mol%C单相二元合金等温凝固的相场控制方程和溶质控制方程进行推导。相场模型中考虑了界面各向异性,并引入了诱发侧向分支的扰动项,也为模型确定了合适的边界条件和初始条件等,采用基于均匀网格的有限差分法对控制方程进行了离散。采用基于Visual C++6.0平台的C语言进行编程,实现了用Tecplot10.0和Origin7.0将模拟结果以及凝固特征参数可视化。
研究了晶粒的长大过程及各向异性强度对枝晶形貌的影响。结果表明,晶体生长初期,晶粒形貌为球状,随着计算时间的推移,晶粒形貌由球状经星形向枝晶形状转变,最后形成复杂的树枝晶;在不考虑成分过冷的时候,各向异性是使晶粒形貌以枝晶方式生长的最主要原因。
研究了过冷度、各向异性强度和扰动强度对枝晶生长形貌的影响。结果表明,随着过冷度的减小,枝晶主干细化,各向异性程度增大,晶粒生长速度减小,溶质扩散层厚度增加,枝晶的最高溶质浓度降低,溶质梯度减小;随着各向异性的增加,晶粒由海藻状转变为枝晶状,枝晶生长速度也随之增大;扰动是引发枝晶的侧向分支的主要原因。各向异性强度和扰动强度均对枝晶溶质分布的影响并不显著。
分析了枝晶生长过程中溶质分布情况。结果表明,溶质分布情况均与实际枝晶的溶质分布情况相一致。
为了考核模拟结果,对Fe-C合金的凝固过程进行实验研究,并对试样进行了微观组织分析。结果表明,模拟结果与实际凝固结果基本一致,验证了相场模型的正确性。
Fe-C alloy system is the most widely used material for the engineering structures at present time. The mechanical properties and durability property of the alloy lie on the solidification microstructures in the casting process. Modeling of the alloy microstructure formation using phase-field model will help to evaluate and optimize the castings processing technology so as to improve their quality.
Adopted KKS model and based on free energy function, the phase-field model of pure metal, binary single-phase alloy and multiple components alloy are derived respectively. Emphasis on derived the equation of phase-field and solute-field of binary single-phase alloy of the Fe-0.5mol%C under isothermal condition. The interface anisotropy is taken into account and a term of noise to produce the side-branches is introduced into the phase-field model. The initial conditions and boundary conditions is determined too. In order to solve the phase-field and solute-field equations used Finite Difference Formulas on uniform mesh. The computational program is programed by using Visual C++6.0. The vision result of simulation is achieved by using Tecplot 10.0 software and the curve of solidification characteristic parameter is showed by using Origin 7.0 software.
The grain growth process and the influence of anisotropic intensity on dendrite morphologies are investigated. The results show that during the early stages of growth, the morphology of crystal grain is spherical, with increasing of time, the grain morphologies will transform into star shape from spheric shape, and then change as complex dendrite morphologies. The grain morphologies trend to dendritic by anisotropism.
The influences of undercooling, anisotropic intensity and noise intensity on dendrite growth are investigated. The results show that with decreasing of undercooling, the morphology of dendritic trunk will become thinner, while anisotropic degree is increased, the speed of dendrite growth is decreased, thickness of solute diffusion layer is increased. The maximum solute concentration is decreased, the solute gradient is decreased. With increasing of anisotropic intensity, the grain morphology is transformed from seaweed to dendrite, and the speed of dendrite growth is increased. The main reason of dendrite side-branches is caused by the noise intensity. The influence of anisotropic intensity and noise intensity on the solute distribution of dendrite is not significant.
The solute distribution on dendrite growth process is also investigated. The results show that the solute distribution of simulation is same as the actual case.
In order to confirm the result from computer simulation, the solidification process of Fe-C alloy is carried on experimentally, and the microstructure of testing sample is studied in detail. The results show that the simulation results are almost same as the experimental results, which indicates that the conclusion results from the phase-field model simulation is successful.
引文
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