基于枝晶粗化和反向扩散的二元合金微观偏析数学模型

基于典型微观控制单元体(通常指二次枝晶臂间距半长)内的溶质质量守恒关系,建立了适用于枝晶凝固方式的二元共晶/包晶合金微观偏析半解析数学模型,模型中充分考虑了固相反向扩散和枝晶结构粗化对液相溶质浓度的稀释效果。在引入适当的假设条件下,通过严格的数学推导,获得了模型的完整核心控制方程。在推导过程中应用了标准的粗化模型、二次方形式的固相溶质浓度分布以及抛物线固相生长方式等重要假设。其中,采用精度较高的四阶经典龙格—库塔数值微分方法,并结合具体的冷却条件,对模型的常微分核心控制方程进行数值计算。为验证所建微观偏析模型的合理性和适用性,本文针对Al-4.9%Cu二元共晶合金进行了模型研究,通过将本模型的计算结果与已有的实验测试数据以及其它特点各异的微观偏析半解析数学模型的预测结果进行对比分析,表明本文所建立的微观偏析半解析数学模型具有相对较高的预测精度和能力,其预测结果最为接近于实测值。     

多元合金两相区凝固过程的数值仿真研究

基于微观枝晶计算域内的溶质质量守恒关系,推导出适用于枝晶凝固方式的二元合金微观偏析半解析数学模型,并根据简单加合原理对模型进行了多元化扩展,应用扩展后的微观偏析模型,针对浇注钢种(视为Fe-C多元合金)的两相区凝固过程进行了数值仿真计算,通过仿真获得了连铸凝固传热计算中所需要的钢种的非平衡凝固路径及实际固相线温度.研究结果表明,所建立的多元合金两相区凝固计算微观偏析数学模型及其仿真程序,具有较好的合理性和广泛的适用性,可以方便地在连铸过程静态及动态仿真计算中加以耦合运用.     

凝固路径对Al-4.5%Cu合金共晶相体积分数影响的数值模拟研究

通过Al-4.5％Cu合金铸锭显微偏析形成的数值模拟，研究了凝固路径对凝固后铸锭不同位置处共晶相体积分数的影响。在显微偏析模型中考虑了树枝晶粗化、固相溶质逆扩散、枝晶尖端过冷、随温度变化的溶质扩散系数等影响显微偏析形成的动力学因素。数值方法中采用变网格技术跟踪移动界面，通过迭代求解溶质扩散方程和溶质守恒方程计算显微偏析参数。结果表明，不能仅靠局部凝固时间来分析共晶相体积分数的变化，还要考虑凝固路径的影响。     

一种新型潜热处理模型显微偏析数值模拟的应用

在显微偏析数值模拟中,宏/微观模型通过潜热处理相互耦合.潜热模型直接决定着模拟结果的准确性.将近期先进的潜热处理模型引入显微偏析数值模拟,对Al-4.5Cu合金铸锭显微偏析的形成进行了数值模拟.在模型中考虑了树枝晶粗化、固相溶质逆扩散、枝晶尖端过冷、随温度变化的溶质扩散系数等动力学因素,微观数值方法中采用变网格技术跟踪移动界面,通过迭代求解溶质扩散方程和溶质守恒方程计算显微偏析参数.在简化耦合算法的情况下,模拟结果与试验结果符合.     

显微偏析数值模拟的微观模型和数值方法

研究显微偏析数值模拟中的微观模型和数值方法,在微观模型中考虑了树枝晶粗化、固相溶质逆扩散、枝晶尖端过冷、随温度变化的溶质扩散系数等影响显微偏析形成的动力学因素.数值方法中采用变网格技术跟踪移动界面,通过迭代求解溶质扩散方程和溶质守恒方程计算显微偏析参数.并给出了微观计算流程图,这种数值方法可以方便地与宏观计算、相图计算相耦合.模拟算例表明模拟结果与实验结果吻合较好.     

凝固路径对Al-4.5%Cu合金显微偏析参数影响的数值模拟

通过对Al-4.5%Cu合金铸锭显微偏析形成的数值模拟,研究了凝固路径对凝固后铸锭不同位置处显微偏析参数的影响.在显微偏析模型中考虑了树枝晶粗化、固相溶质逆扩散、枝晶尖端过冷、随温度变化的溶质扩散系数等影响显微偏析形成的动力学因素.数值方法中采用变网格技术跟踪移动界面,通过迭代求解溶质扩散方程和溶质守恒方程计算显微偏析参数.结果表明,对于Al-Cu合金,固相扩散主要由溶质扩散速率控制,而非局部凝固时间.显微偏析参数不仅取决于局部凝固时间,还要考虑凝固路径的影响.     

铝基四元合金枝晶组织及微观偏析的数值模拟

建立了基于元胞自动机(CA)和热力学相平衡计算引擎(PanEngine)的二维耦合模型,并应用于铝基四元合金枝晶组织和微观偏析的数值模拟.在该耦合模型中,采用CA方法模拟枝晶组织的演变.以固/液界面的平衡液相线温度和实际温度的差值作为枝晶生长的驱动力,同时考虑了固/液界面曲率的Gibbs-Thomson效应.通过求解溶质传输方程获得固/液界面处三种溶质的液相成分,耦合PanEngine获得固/液界面处的平衡液相线温度及三种溶质的平衡固相成分,为提高计算效率,采用预制数据表格的优化策略将CA与PanEngine进行耦合.将Al-4.5Cu-0.5Mg-1Si(质量分数,%)四元合金凝固时的固相分数随温度的变化以及固相分数和固相成分分布关系的模拟结果与Scheil模型和平衡凝固模型的预测结果进行了对比,结果表明,该模型不仅可应用于模拟多元合金中的枝晶生长形貌,而且能对铝基四元合金系凝固的微观偏析进行定量预测.     

MODELING OF DENDRITIC STRUCTURE AND MICROSEGREGATION IN SOLIDIFICATION OF AL-RICH QUATERNARY ALLOYS

建立了基于元胞自动机(CA)和热力学相平衡计算引擎(PanEngine)的二维耦合模型, 并应用于铝 基四元合金枝晶组织和微观偏析的数值模拟. 在该耦合模型中, 采用CA方法模拟枝晶组织的演变. 以固/液界面的平衡液相线温度和实际温度的差值作为枝晶生长的驱动力, 同时考虑了固/液界面曲率的Gibbs-Thomson效应. 通过求解溶质传输方程获得固/液界面处三种溶质的液相成分, 耦合PanEngine获得固/液界面处的平衡液相线温度及三种溶质的平衡固相成分. 为提高计算效率, 采用预制数据表格的优化策略将CA与PanEngine进行耦合. 将Al-4.5Cu-0.5Mg-1Si(质量分数, %)四元合金凝固时的固相分数随温度的变化以及固相分数和固相成分分布关系的模拟结果与Scheil模型和平衡凝固模型的预测结果进行了对比, 结果表明, 该模型不仅可应用于模拟多元合金中的枝晶生长形貌, 而且能对铝基四元合金系凝固的微观偏 析进行定量预测.     

冷却速率对Mg-Gd-Y-Zr合金凝固组织的影响

通过改变凝固过程中的冷却速率,研究了冷却速率对Mg-Gd-Y-Zr合金凝固组织与成分微观偏析的影响.随冷却速率提高,合金组织明显细化,初生相形貌由粗大等轴枝晶逐渐向细小树枝晶转变,合金凝固过程中形核率增加,合金晶粒尺寸逐渐减小;冷却速率的提高可以降低溶质元素的扩散速率,从而增加合金元素在枝晶干中的固溶度,减轻凝固过程中合金元素Gd与Y的微观偏析,同时使凝固过程中形成的共晶减少,共晶组织分布更加弥散、均匀.     

任意固相反扩散条件下枝晶凝固溶质传输微观／宏观模型化

通过对合金枝晶凝固中有任意固相反扩散条件下微观溶质再分布的模型化,扩展了作者提出的合金凝固传输及宏观偏析连续介质模型。本文微观／宏观统一模型提出的归一化固相反扩散集合参数除了包括合金的固相扩散系数外,还包含了生长枝晶尺度及几何形态参数,凝固速率和溶质分配系数等影响因素。模型的数值计算结果表明,在相同的凝固条件下不同的合金固相扩散能力可对其铸锭的宏观偏析行为产生明显的影响。     

Microstructure and microsegregation in Al-rich Al–Cu–Mg alloys

Microstructure and microsegregation in two directionally solidified Al alloys, Al–3.9Cu–0.9Mg and Al–15Cu–1Mg (in wt%), were investigated for cooling rates between 0.78 and 0.039 K/s. Transverse and longitudinal sections were examined to exhibit dendritic microstructures. Fractions of solids formed were determined using quantitative image analysis and solute redistribution in the primary phase was determined using area scans. The model employed to calculate microsegregation is based on the Scheil model but including solid-state diffusion, dendrite arm coarsening and undercooling of the dendrite tip and the formation of eutectic. The model-calculated results were found to be in good agreement with the experimentally determined concentration distributions in the primary α phase and the amounts of phases formed. It was found that the dendrite morphology was best described by a cylindrical arm geometry and that the accuracy of the phase diagram could have a significant influence on the microsegregation predictions. For the alloy with low copper content, two types of embedded droplets were observed.     

Two-dimensional modelling and experimental study on microsegregation during solidification of an Al–Cu binary alloy

To explain the experimentally observed relation between the cooling rate and the non-equilibrium eutectic fraction obtained during solidification experiments of Al–Cu binary alloys [Eskin DG, Du Q, Ruvalcaba D, Katgerman L. Mater Sci Eng A 2005;405:1–10], a two-dimensional (2-D) microsegregation model, the pseudo-front tracking (PFT) method [Jacot A, Rappaz M. Acta Mater 2002;50:1909–26, Jacot A, Rappaz M. Acta Mater 2002;50:3971, Du Q, Jacot A. Acta Mater 2005;53:3479–93], is employed. The analysis of simulated solidification kinetics, including the grain morphology evolution, coarsening and back diffusion, reveals the pronounced effect of dendrite coarsening on the final non-equilibrium eutectic fraction. Because the 2-D modelling can describe rigorously how the important microstructure feature – dendrite arm spacing – evolves, its predictions are in good agreement with the trend observed in the experiments, which both the classic Brody–Flemings model and the 1-D PFT model have failed to explain.     

Reduction in Microsegregation in Al-Cu Alloy by Alternating Magnetic Field

The microsegregation behavior of the Al-4.5 wt%Cu alloy solidified at different cooling rates under the alternating magnetic field(AMF) was investigated.The experimental results showed that the amount of non-equilibrium eutectics in the interdendritic region decreased upon applying the AMF at the same cooling rate.The change in microsegregation could be explained quantificationally by the modifications of dendritic coarsening,solid-state back diffusion and convection in the AMF.The enhanced diffusivity in the solid owing to the AMF was beneficial for the improvement in microsegregation compared to the cases without an AMF.In contrast,the enhanced dendritic coarsening and forced convection in the AMF were found to aggravate the microsegregation level.Considering the contributions of the changes in above factors,an increase in solid diffusivity was found to be primarily responsible for the reduced microsegregation in the AMF.In addition,the microsegregation in the AMF was modeled using the analytical model developed by Voller.The calculated and experimental results were in reasonable agreement.     

Numerical simulation of microstructure evolution and microsegregation of U-Nb alloy during solidification process

In this work, a cellular automaton model has been developed to simulate the microstructure evolution of U-Nb alloy during the solidification process. The preferential growth orientation, solute redistribution in both liquid and solid, solid/liquid interface solute conservation, interface curvature and the growth anisotropy were considered in the model. The model was applied to simulate the dendrite growth and Nb microsegregation behavior of U-5.5Nb alloy during solidification, and the predicted results showed a reasonable agreement with the experimental results. The effects of cooling rates on the solidification microstructure and composition distribution of U-5.5Nb were investigated by using the developed model. The results show that with the increase of the cooling rate, the average grain size decreases and the Nb microsegregation increases.     

半连续浇铸AZ61合金中枝晶形貌特性

采用彩色金相与能谱对半连续浇铸的AZ61镁合金进行了组织和成分上的观察,发现冷却速率较快的铸锭边部的二次枝晶间距比冷却速率较慢的铸锭心部的二次枝晶间距大,与普通模铸的显微组织呈现的规律不同,并对这一现象进行了理论上的分析讨论。分析认为边部二次枝晶间距的异常增大与二次枝晶臂表面溶质的微观偏析密切相关,粗枝晶臂表面溶质浓度与细枝晶臂表面溶质浓度差值越大,粗枝晶臂的粗化驱动能越大,枝晶的二次枝晶间距就越大。     

相场法定量模拟强迫层流对微观偏析的影响(英文)

采用耦合流场的相场模型,模拟Ni-Cu合金过冷熔体流动对液固界面前沿浓度分布的影响;定量分析强迫层流对迎流方向、垂直流动方向与逆流方向枝晶尖端前沿浓度边界层厚度,浓度最大值和枝晶微观偏析的影响。结果表明:溶质场和流场二者相互影响;枝晶上游侧浓度边界层的厚度较薄,溶质浓度的最大值较小;而枝晶下游侧恰好与此相反。贫Cu区域在迎流方向枝晶臂沿枝晶轴线方向的宽度较大,但Cu原子的浓度较低,微观偏析最严重,枝晶下游侧缩松倾向加剧。     

Influence of coupling with calculation of phase diagrams on microsegregation forming simulation of Al-4.5%Cu alloy

The effect of coupling with calculation of phase diagrams on microsegregation forming simulation was investigated. The traditional simplified phase diagram and calculated phase diagram were introduced into the numerical models respectively and simulation on microsegregation forming of the Al-4.5%Cu alloy ingot was also presented. The simulation results were both compared with the experiment results. The results show that the calculated sencondary arm spacing with these two kinds of phase diagram are almost the same because relationship between the coarsening model and the information of phase diagram is not close. The calculated eutectic phase volume fractions of different locations in the ingot coupled with different phase diagrams are discrepant. The calculated volume fractions are consistent with the experiment results when calculated phase diagram couples, but are far from the experiment results and obviously inacceptable when traditional simplified phase diagram couples. So, coupling with accurate calculated phase diagrams is very significant for microsegregation forming simulation since much information of the phase diagram is used in the models and it can improve the precision of simulation results.