Modeling of Microstructure and Microsegregation in Solidification of Multi-Component Alloys

Driven by industrial demand, extensive efforts have been made to investigate microstructure evolution and microsegregation development during solidification of multicomponent alloys. This paper briefly reviews the recent progress in modeling of microstructures and microsegregation in solidification of multicomponent alloys using various models including micromodel, phase field, front tracking, and cellular automaton approaches. A two-dimensional modified cellular automaton (MCA) model coupled with phase diagram software PanEngine is presented for the prediction of microstructures and microsegregation in the solidification of ternary alloys. The model adopts MCA technique to simulate dendritic growth. The thermodynamic data needed for determining the dynamics of dendritic growth are calculated with PanEngine. After validating the model by comparing the simulated values with the prediction of the Scheil model for solute profiles in the primary dendrites as a function of solid fraction, the model was applied to simulate the microstructure and microsegregation in the solidification of Al-rich ternary alloys. The simulation results demonstrate the capabilities of the present model not only to simulate realistic dendrite morphologies, but also to predict quantitatively the microsegregation profiles in the solidification of multi-component alloys. 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.     

Thermodynamic and Microstructural Modeling of Nb-Si Based Alloys

Nb-Si alloys have gained much attention over the last decade as the next generation alloys for high-temperature aero-engine applications due to their low density and improved mechanical properties. However, the microstructures of these alloys are quite complex and vary significantly with the addition of elements such as Ti and Hf. Hence, an improved understanding of the phase stability and the microstructural evolution of these alloys is essential for alloy design for advanced high-temperature applications. In the present paper, we describe the microstructural evolution modeling results of the dendritic and eutectic solidification of the binary Nb-16 at.% Si alloy, obtained using a Phase-Field simulations performed with MICRESS. The effect of parameters; such as heat extraction rate, the ratio of the diffusivity of the solute in liquid to solid, and the interfacial energy of liquid and solid interface, on the microstructural evolution during dendritic solidification is discussed in detail.     

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.     

Al-Si-Mg三元合金的溶质分凝及其对凝固过程的影响

从热力学角度分析了三元合金凝固过程中的溶质分凝行为, 利用耦合热力学计算技术研究了Al-Si-Mg三元合金溶质分凝因数在凝固过程中的变化规律, 获得了其与固相体积分数的定量关系, 进而预测了不同条件下Al-Si-Mg三元合金的凝固过程和相析出规律. 实验发现三元合金中溶质分凝因数在凝固过程变化巨大, 采用二元系中的参数使得对共晶种类和共晶分数的预测均与实验值有较大偏差. 采用耦合热力学计算技术, 获得了分凝因数在凝固过程中的变化规律, 使预测值更好地吻合于实验结果.     

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.     

A quantitative multi-phase field model of polycrystalline alloy solidification

A multi-phase field model for quantitative simulations of polycrystalline solidification of binary alloys is introduced. During the free-growth stage of solidification, the model exploits the thin-interface analysis developed by Karma [3] in order to realistically capture bulk phase diffusion and the sharp interface corrections predicted by traditional models of solidification. During grain boundary coalescence, the model is constructed to reproduce the properties of repulsive grain boundaries described by Rappaz et al. [29]. The model provides a very simple mechanism for decoupling of solute and concentration fields at steady state, an important feature for calculating grain boundary energies.     

Numerical Simulation of Anomalous Eutectic Growth of Ni-Sn Alloy Under Laser Remelting of Powder BedEI北大核心CSCD

Eutectic is one of the most commonly observed solidification patterns, the growth mor-phology of which is important to materials properties. Anomalous eutectic is typically coarser and globular than lamellar eutectic, which is commonly observed during solidification of binary eutectic alloy, including deep undercooled melt and laser remelting process. The morphological evolution mechanism of anomalous growth is still unknown due to the lack of simulation evidence. During laser remelting process, the anomalous eutectic is sandwiched between lamellar eutectic at the bottom of melt pool. Comparing to deep undercooled melt, laser remelting has simpler temperature field distribution, which can be simplified into directional solidification. Thus, simulations of anomalous eutectic growth in laser remelting process are feasible. In the present work, the anomalous eutectic growth mechanism under laser remelting conditions was simulated using a low mesh induced anisotropy cellular automaton (CA) model. Firstly, a two-dimensional lamellar eutectic CA model of CBr4-C2Cl6 alloy was established, and the morphological transition from 1 lambda O to 2 lambda O was simulated. The calculated results are in good agreement with experiments and phase field simulations. By setting the interface cells containing three phases (alpha, beta and liquid phases), the model can continuously change the alpha and beta phase volume fractions in the CA model, making it easier for the model to capture the instability of lamellar eutectic. Compared with the results of the phase field model, the intermediate 1 lambda O-2 lambda O state of oscillation instability of 1 lambda O and 2 lambda O which is consistent with the experimental results was calculated. Based on the above-mentioned binary eutectic CA model, the lamellar eutectic to anomalous eutectic transition at the bottom of the molten pool was simulated. Under the condition of initial low cooling rate, the fine lamellar eutectic is decoupled, it leads to the overgrowth of beta-Ni3Sn phase. During the subsequent accelerated cooling process, alpha-Ni nucleated in the liquid phase at the front of the solid/liquid interface, and the beta-Ni3Sn phase wrapped around the alpha-Ni phase forming anomalous eutectic morphology. During the laser remelting process, there is indeed a rapid change of solidification rate from zero to scanning speed rate from the bottom to the top of the melt pool, and therefore coincides with the solidification conditions of the variable pulling velocity used in the CA simulations.     

镁合金铸造成形过程宏观／微观模拟

通过研究镁合金压铸过程中界面热,采用热传导反算法确定压铸过程的界面换热系数,研究镁合金压铸过程中工艺参数及凝固过程对铸件界面换热系数的影响规律,建立镁合金压铸过程界面换热边界条件的处理模型,以实现镁合金压铸过程中凝固过程的准确预测。通过实验研究镁合金压铸过程中凝固组织,建立了镁合金压铸过程中形核模型。采用CA方法,建立了镁合金枝晶生长模型,以实现镁合金凝固组织的预测。采用相场方法研究了镁合金枝晶生长形貌。     

相场法对比模拟二元合金等温/非等温凝固过程(英文)

基于熵函数建立二元合金的二维相场模型,采用基于均匀网格的有限差分法求解相场和溶质场控制方程;为了避免时间步长的限定,采用交替隐式差分法(ADI)求解温度场控制方程。对Ni-Cu合金非等温凝固过程的部分特征进行模拟研究,对比分析二元合金等温/非等温凝固过程。模拟结果表明:非等温模型更能有效地模拟二元合金的实际凝固过程,并且随着热扩散系数的减小,非等温相场模型逐渐向等温相场模型回归。     

Evaluation of enthalpy and entropy changes for binary alloy solidification process

Analytical expression of the entropy and enthalpy changes and apparent specific heat capacity of binary alloys in the solidification process are derived. The non-equilibrium lever rule is employed in the assessments of the relative concentration of binary alloys during solidification. The effect of the partial ordering of alloys in the liquid state is ignored and the alloy solidification process is divided into steps in the evaluations. Furthermore, experimental data from the available literature for Al−Cu alloys are employed to check the predictions of the current approaches, which indicates the reasonability of the current expressions.     

Post-solidification Effects in Directionally Grown Al-Ag$$_$$Al-Al$$_$$Cu Eutectics

The post-solidification reactions that take place behind the growth front in directionally solidified ternary eutectic Al-Ag-Cu alloys have a marked influence on the observed room temperature microstructure, obscuring many aspects of the solidification morphology present at the growth front. Quantifying these solid-state processes is necessary for proper interpretation of ex-situ microstructure as an indicator of growth dynamics and operating point selection. In this study, the directional growth structure and phase compositions are quantified as a function of distance from the growth front to describe microstructural changes that occur during cooling in the solid state. The solubility of Ag in the Al(fcc) phase decreases rapidly below the eutectic point, and the excess Ag is accommodated by growth of the Ag₂Al(hcp) phase, mainly by motion of the Al(fcc)-Ag₂Al(hcp) interface. These structural changes are quantified, and compared to the coupled morphology at the solidification front. A cellular automaton method is proposed here to mimic either the forward or reverse solid-state changes, providing a means to estimate many features of the directional growth morphology based on sampling the structure at some known distance from the front.     

MICRO-DESCRIPTION OF THE SOLUTE-FIELD AND THE PHASE-FIELD MODEL FOR ISOTHERMAL PHASETRANSITION IN BINARY ALLOYS

A new phase field method for two-dimensional simulations of binary alloy solidification was studied. A model basing on solute conservative in every unit was developed for solving the solute diffusion equation during solidification. Two-dimensional computations were performed for ideal solutions and Ni-Cu dendritic growth into an isothermal and highly supersaturated liquid phase.     

利用短程序改进Al-Cu熔体的热力学模型

将Al-Cu熔体中的缔合物AlCu3以短程序的形式引入置换溶液模型中，提出了一个Redlich—Kister多项式表示的缔合溶液模型，可以直接用于Thermo—Calc相图计算软件，并用这个模型改进了Al一Cu合金体系中液相的热力学描述，计算了Al-Cu熔体混合焓、固相线和平衡分凝因数结果表明，本模型比目前广泛应用的Saunders模型能给出更好的结果，而且适用于Mg-Sn和In—Sb等二元合金体系液相的热力学描述．     

冷却速度对CuCr25合金凝固过程的影响

研究了不同冷却速度下CuCr25合金的微观组织和凝固过程。随着冷却速度的增加，CuCr25合金的微观组织将变得越来越细。当冷却速度达到10^7K／s时，可获得纳米结构的微观组织。当冷却速度〈10^3K／s时，CuCr25合金的凝固过程为普通凝固过程：如果冷却速度〉10^4K／s，其凝固过程为液相分解凝固过程。在快速凝固过程中，CuCr25合金中没有新相形成。但是，Cu在富Cr相中和Cr在富Cu相中的溶解度有所增加。     

过冷熔体定向凝固过程枝晶生长的相场法模拟

利用二元合金相场模型与溶质场进行耦合计算，以Al-4．5％Cu合金为例模拟了二元合金定向凝固的枝晶生长过程。研究了不同过冷度下二元合金过冷熔体定向凝固时枝晶的演化过程及其溶质场的分布情况。结果表明：利用相场模型可以逼真地模拟枝晶的生长过程，以及界面形貌从平界面向柱状晶生长的转变，可再现枝晶演变过程中相互之间的竞争生长和熔合现象。     

Liquidus projection for the Mo-rich portion of the Mo–Si–B ternary system

The solidification behavior in the Mo-rich portion of the Mo–Si–B ternary system has been examined based on the microstructures of arc-cast alloys. Several solidification characteristics in the Mo-rich portion of the system have been identified using XRD, SEM and TEM. The liquidus projection in the Mo-rich portion includes six primary solidification reactions; five reactions originating from the Mo–Si and Mo–B binary sections (Mo, Mo₂B, βMoB, Mo₃Si and Mo₅Si₃) and one from the ternary-based (Mo₅SiB₂) T₂ phase. The liquidus surface in general descends from the high melting temperature Mo–B binary side to the lower melting temperature Mo–Si binary side. The solidification path of alloys with compositions in the T₂ phase region is always preceded by the peritectic reaction of βMoB+L⇒T₂. In addition, four Class II reactions (four-phase reactions) and one Class I reaction (invariant ternary eutectic reaction) have been identified. The extent of solidification segregation in alloys with compositions in the Mo(ss)+T₂ two-phase field is discussed as it pertains to materials processing.     

最大熵产生原理在非平衡凝固中应用

近年来,最大熵产生原理在物理、化学、生物等领域得到广泛应用,被认为是描述非平衡体系演化的普适性原理;其核心思想是孤立非平衡耗散体系演化总是选择最短路径,以使体系尽可能快地向平衡态演化。非平衡凝固技术在工业生产中应用日益广泛,凝固理论研究却仍集中于近平衡过程;最大熵产生率原理在非平衡凝固中的应用,可推动非平衡凝固理论的发展,进而促进凝固理论的工业应用。总结了近年来最大熵产生原理在非平衡凝固中的应用,包括二元合金非平衡凝固界面动力学模型及多相场模型、多元合金非平衡凝固界面动力学模型、平界面稳定性分析及自由枝晶生长模型。对建立这些模型的热力学过程和相应的数学方法进行了详尽的描述。最后对最大熵产生原理的研究前景进行了展望。     

Effect of melt flow on dendritic growth in AlSi7-based alloys during directional solidification

Abstract

High-strength automotive components are often made of AlSi7-based alloys. A very challenging problem with aluminium casting is the influence of melt flow during solidification, because it affects the microstructure formation and therefore the material properties. The scope of this paper is to investigate the effect of forced melt flow on the evolution of the dendritic microstructure in a binary AlSi7 alloy during directional solidification. Global modelling using the software CrysMAS provides typical flow patterns and velocities. These values are used as boundary condition for the flow in the phase field code MICRESS, which allows the numerical simulation of dendritic array solidification in 2D with applied flow. From solidification experiments in a gradient furnace with applied rotating magnetic field the dendrite shapes are determined. It is found consistently that intense melt flow leads to asymmetric dendrite shapes and the growth behaviour of the dendrite arms is directly correlated with the flow direction.     

A model of solidification microstructures in nickel-based superalloys: predicting primary dendrite spacing selection

A combined cellular automaton-finite difference (CA-FD) model has been developed to simulate solute diffusion controlled solidification of binary alloys. Constitutional and curvature undercooling were both solved to determine the growth velocity of the solid/liquid interface. A modified decentered square/octahedron (in two or three dimensions) growth technique was implemented in the cellular automaton to account for the effect of crystallographic anisotropy. The resulting model is capable of simulating the growth of equiaxed and columnar dendritic grains in 2D and 3D, with the <100> directions either aligned or inclined with the grid. The algorithm used can also be used on coarser grids, with a concomitant loss in resolution, allowing simulation of sufficiently large numbers of dendrites in 3D to investigate the distribution of spacings, as well as average behavior.Simulations were performed for directional solidification with a range of withdrawal velocities and nucleation conditions, but a constant thermal gradient. The simulations capture the full microstructural development and primary spacing selection by both branching and overgrowth mechanisms. The model illustrates that there is a range of possible stable spacings, and that the final spacing is history dependent. It was also found that a minimum deviation from the steady state dendrite spacing is required before the spacing adjustment mechanisms are activated. The influence of perturbing the withdrawal velocity upon the stability of the spacing was also investigated. It was found that perturbations significantly reduce the range of stable primary dendrite spacing.     

Microstructures and liquidus projection of the ternary Ag-Sb-Te system

Ag-Sb-Te alloys are important for thermoelectric applications. Fifty-one Ag-Sb-Te ternary alloys were prepared, and their primary solidification phases were analyzed. The liquidus troughs of the liquidus projection of the ternary Ag-Sb-Te system are determined based on the experimental results and the phase diagrams of the three binary constituent systems. There are 13 primary solidification phase regions. In addition to the three terminal solid solution phases and nine binary compounds, there is one ternary compound, AgSbTe₂. A unique microstructure with bright spherical phases uniformly dispersed in a matrix caused by a miscibility gap in the liquid phase is found in the γ-Ag₂Te primary solidification phase regime. A very fine microstructure with nanometer size Ag₂Te is also observed, resulting from the class I reaction, liquid = δ + Ag₂Te + AgSbTe₂, at 496.5 °C, and the liquid composition of Ag-40.0 at%Sb-36.0 at%Te.