Simulation of the Dendrite Morphology and Microsegregation in Solidification of Al–Cu–Mg Aluminum Alloys

Since most typical alloys in industrial applications are multicomponent with three or more components, and various CA models proposed in the past mainly focus on the binary alloys, a two-dimensional modified cellular automaton model allowing for the quantitatively predicting dendrite growth of multicomponent alloys in the low Pe′clet number regime is presented. The elimination of the mesh-induced anisotropy is achieved by adopting a modified virtual front tracking method. A new efficient method based on the lever rule is applied to calculate the solid fraction increment of the interfacial cells. The thermodynamic data such as liquidus temperature, the partition coefficients, and the slope of liquidus surface, needed for determining the dynamics of dendrite growth, are obtained by coupling with Pan Engine. This model is applied to simulate the dendrite morphology and microsegregation of Al–Cu–Mg ternary alloy both for single and multidendrites growth. The simulated results demonstrate that the difference of the concentration distribution profiles ahead of the dendrite tip for each alloying element mainly results from the different partition coefficients and solute diffusion coefficients. Comparison with the prediction of analytical model is carried out and it reveals the correctness of the model.Consequently, the difference in interdendritic microsegregation behavior of different components is analyzed.     

基于Thermo-Calc及T-f_S-C_L耦合方法预测Biot≤0.1的合金凝固路径(英文)

将二元合金枝晶凝固传输模型及相应的T-fS-CL耦合求解方法扩展到描述多元合金在Biot≤0.1条件下的凝固。基于提出的扩展模型及算法,提出一种考虑传热影响的预测Biot≤0.1合金凝固路径及微观偏析的方法。该算法与Thermo-Calc热力学计算软件接口程序TQ6相耦合,用于实时计算每次迭代需要的热力学数据。Al-2Si-3Mg三元合金实例计算证实提出的模型及算法和凝固路径与微观偏析预测方法的实用性与可靠性,Al-5.17Cu-2.63Si三元合金凝固实验结果与预测结果的取得较好的一致性。     

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.     

Alloy Thermal Physical Property Prediction Coupled Computational Thermodynamics with Back Diffusion Consideration

Simulation technologies are applied extensively in casting industries to understand the heat transfer and fluid transport phenomena and their relationships to the microstructure and the formation of defects. It is critical to have accurate thermo-physical properties as input for reliable simulations of the complex solidification and solid phase transformation processes. The thermo-physical properties can be calculated with the help of thermodynamic calculations of phase stability at given temperatures and compositions. A multicomponent alloy solidification model, coupled with a Gibbs free energy minimization engine and thermodynamic databases, has been developed. A back diffusion model is integrated so that the solidification conditions, such as cooling rate, can be taken into account. This article was presented at the Multi-Component Alloy Thermodynamics Symposium sponsored by The Alloy Phase Committee of the joint EMPMD/SMD of the Minerals, Metals, and Materials Society (TMS), held in San Antonio, Texas, USA, March 12-16, 2006, to honor the 2006 William Hume-Rothery Award recipient, Professor W. Alan Oates of the University of Salford, UK. The symposium was organized by Y. Austin Chang of the University of Wisconsin, Madison, WI, USA, Patrice Turchi of the Lawrence Livermore National Laboratory, Livermore, CA, USA, and Rainer Schmid-Fetzer of the Technische Universitat Clausthal, Clauthal-Zellerfeld, Germany.     

单相合金凝固过程微观组织的三维数值模拟

基于晶粒形核和生长物理过程及热质基本传输过程，建立了单相合金凝固过程微观组织和微观偏析形成及枝晶形貌演化的三维数学模型，模型中考虑了成分过冷．曲率过冷和各向异性等重要因素．数值模拟结果表明，所建数学模型能够合理反映质点形核、晶粒生长和柱状→等轴晶转变物理过程，温度场．溶质场和微观组织形貌的模拟计算结果合理自由枝晶生长过程的模拟结果表明，各向异性强度对枝晶生长和最终组织形貌具有重要影响：强各向异性趋于得到分支发达的树型结构，内部组织为取向平行排列规则的二次枝晶臂簇；而弱各向异性趋于得到表面凹凸不平的近似正八面体结构．模拟结果还证实枝晶内部存在小的孤立熔池，这有助于揭示微观组织中出现点偏析和微观缩松的根本原因．     

枝晶生长的三维元胞自动机模拟

通过将元胞自动机和有限差分方法相耦合,建立了立方体系金属和合金枝晶生长的三维模型.应用该模型,模拟了Al-Cu合金过冷熔体中自由枝晶的生长和定向凝固条件下Al-Cu合金凝固组织演变过程.模拟结果清楚展现了过冷熔体中自由枝晶的生长过程和定向凝固过程中枝晶的形成与淹没,与理论预测和实验结果相吻合,表明所发展的模型能够较准确...     

A three-dimensional cellular automaton model for dendritic growth in multi-component alloys

A three-dimensional (3-D) cellular automaton model for dendritic growth in multi-component alloys is developed. The velocity of advance of the solid/liquid (S/L) interface is calculated using the solute conservation relationship at the S/L interface. The effect of interactions between the alloying elements on the diffusion coefficient of solutes in the solid and liquid phases are considered. The model is first validated by comparing with the theoretical predictions for binary and ternary alloys, and then applied to simulate the solidification process of Al-Cu-Mg alloys by a coupling of thermodynamic and kinetic calculations. The numerical results obtained show both the free dendrite growth process as well as the directional solidification process. The calculated secondary dendrite arm spacing in the directionally solidified Al-Cu-Mg alloy is in good agreement with the experimental results. The effect of interactions between the various alloying elements on dendritic growth is discussed.     

基于CA模拟焊缝凝固过程枝晶生长的分析

将元胞自动机方法用于焊缝金属凝固组织演变的模拟中,不仅为焊缝微观组织演变的数值模拟开辟了一种新的途径,同时也有助于研究焊接接头组织并依此优化工艺来提高焊件质量.文中研究了焊缝凝固过程中的溶质扩散问题,构建了基于元胞自动机的焊缝枝晶生长速度模型,在此基础上进行了焊缝中心等轴晶和熔池边缘柱状晶生长的模拟.初步计算了焊缝中心等轴晶和熔池边缘柱状晶的生长形态,计算结果明显再现了二次、三次枝晶的生长及竞争生长等微观现象.结果表明,元胞自动机方法是研究和模拟焊缝微观组织的有效手段之一.     

Fe-C合金焊接熔池凝固过程CET转变的数值模拟

基于元胞自动机方法建立了枝晶生长的数值模型,应用该模型模拟了Fe-C合金焊接熔池凝固期间柱状晶向等轴晶(CET)转变过程中枝晶生长形貌与溶质浓度分布状况. 模拟过程主要考虑不同扰动振幅和冷却速率对柱状晶向等轴晶转变的影响. 结果表明,随着时间步长增大,晶粒数逐渐增多,最终趋于稳定值;当冷却速率增加时,生长速度增大,枝晶生长的越充分,显微偏析越严重,而CET转变所需时间越短;当扰动振幅增大时,一次枝晶生长的越细,二次、三次枝晶竞争越激烈.     

定向凝固过程中NH_4Cl-H_2O枝晶生长的数值模拟

建立了一种改进的元胞自动机模型(MCA),通过考虑成分过冷、曲率过冷、择优取向系数、温度梯度和抽拉速度等因素,模拟了不同温度梯度方向、不同择优取向及不同抽拉速度对柱状晶形态的影响.模拟结果较好地刻画了温度梯度和生长方向夹角的变化对一次枝晶臂间距的影响,不同择优生长取向的柱状晶竞争生长过程以及柱状晶尖端分叉机制.为了验证模型的可靠性,使用NH_4Cl-H_2O透明合金进行了定向凝固实验,实验结果和模拟结果吻合较好.     

Modeling of precipitate-free zone formed upon homogenization in a multi-component alloy

A comprehensive model is presented for the simulation of microstructure evolution during industrial solidification and homogenization processing of aluminum alloys. The model combines on the one hand microsegregation due to long-range diffusion during solidification and subsequent heat treatment with, on the other hand, precipitation in the primary Al phase. The thermodynamic data are directly obtained from a CALPHAD (CALculation of PHAse Diagrams) approach to thermodynamic equilibrium in multicomponent systems. The model is applied to the prediction of structure and segregation evolutions in a 3003 aluminum alloy for typical industrial solidification and homogenization sequences. It is shown that: (i) accounting for the nucleation undercooling of the eutectic/peritectic structures solidifying from the melt is essential to retrieval of the measured volume fractions of intergranular precipitates; (ii) calculations of intragranular precipitation are generally not applicable if long-range diffusion is neglected; (iii) the precipitate-free zone can be quantitatively predicted only based on the coupling between intergranular and intragranular precipitation calculations.     

Simulation of α-Al grain formation in high vacuum die-casting Al-Si-Mg alloys with multi-component quantitative cellular automaton method

Al-Si-Mg alloys are the most commonly used material in high vacuum die-casting(HVDC),in which the morphology and distribution ofα-Al grains have important effect on mechanical properties.A multi-component quantitative cellular automaton(CA)model was developed to simulate the microstructure and microsegregation of HVDC Al-Si-Mg alloys with different Si contents(7%and 10%)and cooling rates during solidification.The grain number and average grain size with electron backscatter diffraction(EBSD)analysis were used to verify the simulation.The relationship between grain size and nucleation order as well as nuclei density was investigated and discussed.It is found that the growth of grains will be restrained in the location with higher nuclei density.The influence of composition and cooling rate on the solute transport reveals that for AlSi7Mg0.3 alloy the concentration of solute Mg in liquid is higher at the beginning of eutectic solidification.The comparison between simulation and experiment results shows that externally solidified crystals(ESCs)have a significant effect for samples with high cooling rate and narrow solidification interval.     

定向凝固共晶生长的元胞自动机数值模拟

本文在已有的二元初生相元胞自动机（CA）方法的基础上,针对二元共晶凝固过程提出了改进的元胞自动机（MCA）模型.该模型考虑成分过冷和曲率过冷对界面形态的影响,通过界面溶质浓度守恒来获得共晶α相和β相生长速率,模拟了层片的湮灭、分叉与稳态生长.为了验证模型的可靠性,对常见的CBr₄-C₂Cl₆共晶透明合金进行了模拟,研究了抽拉速率对共晶层片间距大小的影响,模拟结果与文献中的实验结果吻合良好;同时模拟了共晶层片间距调整过程的形貌演化以及层片振荡不稳定性现象.本文将MCA模型扩展到三维定向凝固过程中,研究了共晶形态的层棒状转变机制.     

Atomistic Modeling of Multicomponent Systems

The need to accelerate materials design programs based on economical and efficient modeling techniques provides the framework for the introduction of approximations in otherwise rigorous theoretical schemes. Several quantum approximate methods have been introduced through the years, bringing new opportunities for the efficient understanding of complex multicomponent alloys at the atomic level. As a promising example of the role that these methods might have in the development of complex systems, in this work we discuss the Bozzolo-Ferrante-Smith (BFS) method for alloys and its application to a variety of multicomponent systems for a detailed analysis of their defect and phase structure and their properties. Examples include the study of the phase structure of new Ru-rich Ni-base superalloys, the role of multiple alloying additions in high temperature intermetallic alloys, and interfacial phenomena in nuclear materials, highlighting the benefits that can be obtained from introducing simple modeling techniques to the investigation of complex systems. This article was presented at the Multi-Component Alloy Thermodynamics Symposium sponsored by the Alloy Phase Committee of the joint EMPMD/SMD of The Minerals, Metals, and Materials Society (TMS), held in San Antonio, Texas, March 12-16, 2006, to honor the 2006 William Hume-Rothery Award recipient, Professor W. Alan Oates of the University of Salford, UK. The symposium was organized by Y. Austin Chang of the University of Wisconsin, Madison, WI, Patrice Turchi of the Lawrence Livermore National Laboratory, Livermore, CA, and Rainer Schmid-Fetzer of the Technische Universitat Clausthal, Clauthal-Zellerfeld, Germany.     

A generalized segregation model for concurrent dendritic,peritectic and eutectic solidification

A microsegregation model for the solidification of binary alloys is presented. It accounts for diffusion in all phases, as well as nucleation undercooling and growth kinetics of the solidifying microstructures. It successively considers the occurrence of several phase transformations, including one or several peritectic reactions and one eutectic reaction. Volume-averaged mass conservation equations are coupled with a heat balance assuming a uniform temperature. The model is applied to simulate the solidification of Al–Ni atomized droplets. Coupled with an atomization model, it predicts recalescences, volume fractions of phases as well as average compositions during solidification. It eventually predicts the occurrence of a recalescence during the growth of each microstructure, and the progress of peritectic transformations consuming previously formed solid phases. The influence of several process parameters is evaluated. A comparison with experimental measurements is given, showing variation of phase fractions as a function of particle size for Al–Ni atomized droplets.     

Numerical simulation of microstructure evolution on near eutectic spheroidal graphite cast iron

A multiphase cellular automaton model was developed to simulate microstructure evolution of near eutectic spheroidal graphite cast iron (SGI) during its solidification process, and both dendritic austenite and spheroidal graphite growth models were adopted. To deduce the mesh anisotropy of cellular automaton method, the composition averaging and geometrical parameter were introduced to simulate the spheroidal graphite growth. Solute balance method and decentered square algorithms were employed to simulate austenite dendrites growth with different crystallographic orientations. The simulated results indicate that the graphite nodule grows in a spherical morphology when the surrounding environment of a single graphite nodule is same. However, for two adjacent graphite nodules, the environment is different. The higher the carbon concentration, the faster the growth of graphite. By comparison with experimental results, it is found that the microstructure evolution of near eutectic spheroidal graphite cast iron during solidification process can be reproduced quantitatively by numerical simulation with this model.     

A three-dimensional cellular automaton model for simulation of dendritic growth of magnesium alloy

A numerical model based on the cellular automaton method for the three-dimensional simulation of dendritic growth of magnesium alloy was developed. The growth kinetics was calculated from the complete solution of the transport equations. By constructing a three-dimensional anisotropy model with the cubic CA cells, simulation of dendritic growth of magnesium alloy with six-fold symmetry in the basal plane was achieved. The model was applied to simulate the equiaxed dendritic growth and columnar dendritic growth under directional solidification, and its capability was addressed by comparing the simulated results to experimental results and those in the previously published works. Meanwhile, the three-dimensional simulated results were also compared with that of in two dimensions, offering a deep insight into the microstructure formation of magnesium alloy during solidification.     

Microstructure and microsegregation in directionally solidified Mg–4Al alloy

Directional solidification (DS) of a binary Mg–4Al (wt.%) alloy was carried out to investigate the microstructures and microsegregation under controlled solidification conditions. In directional solidification the microstructure depends on the growth rate V because the cooling rate, which governs the solidification microstructure, is the product of the growth rate and the temperature gradient. The ability to produce simple and uniform microstructures in directional solidification enables us to correlate the formation of the microstructure and its characteristic length scales quantitatively with processing parameters. The morphology of the solid–liquid interface and the microstructure of both the mushy zone and the steady-state region were characterized at different levels of growth rates. With the help of an electron microprobe, microsegregation was determined in a specimen directionally solidified with cooling rates ranging from 0.06 to 0.8 K/s. The calculated microsegregation results based on the Scheil model deviated significantly from the experimental data, which is anticipated since back diffusion was not included due to the lack of diffusivity data.     

Solidification paths of multicomponent monotectic aluminum alloys

Solidification paths of three ternary monotectic alloy systems, Al–Bi–Zn, Al–Sn–Cu and Al–Bi–Cu, are studied using thermodynamic calculations, both for the pertinent phase diagrams and also for specific details concerning the solidification of selected alloy compositions. The coupled composition variation in two different liquids is quantitatively given. Various ternary monotectic four-phase reactions are encountered during solidification, as opposed to the simple binary monotectic, L′ → L′′ + solid. These intricacies are reflected in the solidification microstructures, as demonstrated for these three aluminum alloy systems, selected in view of their distinctive features. This examination of solidification paths and microstructure formation may be relevant for advanced solidification processing of multicomponent monotectic alloys.