Modified cellular automaton model for modeling of microstructure and microsegregation in solidification of ternary alloys

A modified cellular automaton （MCA） model has been extended to the ternary alloy system by coupling thermodynamic and phase equilibrium calculation engine PanEngine. In the present model the dendrite growth is driven by the difference between the local equilibrium liquidus temperature and local actual temperature, incorporating the effect of curvature. The local equilibrium liquidus temperature is calculated with PanEngine according to the local liquid concentrations of two solutes, which are determined by numerically solving the species transport equation in the domain. Model validation was carried out through the comparison of the simulated values to the prediction of the Scheil model for solute profiles in the primary dendrites. The simulated data with zero solid diffusivity and limited liquid diffusivity were increasingly close to the Scheil profiles as the solidification rate decreased. The simulated microstructure and microsegregation in an Al-Cu-Mg ternary alloy were compared with those obtained experimentally.     

Microstructure,Microsegregation, and Mechanical Properties of Directional Solidified Mg–3.0Nd–1.5Gd Alloy

The microstructure, microsegregation, and mechanical properties of directional solidified Mg–3.0Nd–1.5Gd ternary alloys were experimentally studied. Experimental results showed that the solidification microstructure was composed of dendrite primary a(Mg) phase and interdendritic a(Mg) ? Mg12(Nd, Gd) eutectic and Mg5 Gd phase. The primary dendrite arm spacing k1 and secondary dendrite arm spacing k2 were found to be depended on the cooling rate R in the form k1= 8.0415 9 10-6R-0.279 and k2= 6.8883 9 10-6R-0.205, respectively, under the constant temperature gradient of40 K/mm and in the region of cooling rates from 0.4 to 4 K/s. The concentration profiles of Nd and Gd elements calculated by Scheil model were found to be deviated from the ones measured by EPMA to varying degrees, due to ignorance of the back diffusion of the solutes Nd and Gd within a(Mg) matrix. And microsegregation of Gd depended more on the growth rate, compared with Nd microsegregation. The directionally solidified experimental alloy exhibited higher strength than the non-directionally solidified alloy, and the tensile strength of the directionally solidified experimental alloy was improved,while the corresponding elongation decreased with the increase of growth rate.     

Structure defect prediction of single crystal turbine blade by dendrite envelope tracking model

The structure defects such as stray grains during unidirectional solidification can severely reduce the performance of single crystal turbine blades. A dendrite envelope tracking model is developed for predicting the structure defects of unidirectional solidification turbine blade. The normal vector of dendrite envelope is estimated by the gradient of dendrite volume fraction, and the growth velocity of the dendrite envelope （dendrite tips） is calculated with considering the anisotropy of grain growth. The solute redistribution at dendrite envelope is calculated by introducing an effective solute partition coefficient. Simulation tests show that the solute-build-up due to the rejection at envelope greatly affects grain competition and consequently solidification structure. The model is applied to predict the structure defects （e.g. stray grain） of single crystal turbine blade during unidirectional solidification. The results show that the developed model is reliable and has the following abilities： reproduce the growth competition among the different-preferential-direction grains; predict the stray grain formation; simulate the structure evolution （single crystal or dendrite grains）.     

Effect of Solution Treatment on Microstructure and Corrosion Properties of Mg–4Gd–1Y–1Zn–0.5Ca–1Zr Alloy

The as-cast multi-element Mg–4Gd–1Y–1Zn–0.5Ca–1Zr alloy with low rare earth additions was prepared, and the solution treatment was applied at different temperatures. The microstructural evolution of the alloy was characterized by optical microscopy and scanning electron microscopy, and corrosion properties of the alloy in 3.5% NaCl solution were evaluated by immersion and electrochemical tests. The results indicate that the as-cast alloy is composed of the a-Mg matrix,lamellar long-period stacking-ordered(LPSO) structure and eutectic phase. The LPSO structure exists with more volume fraction in the alloy solution-treated at 440 °C, but disappears with the increase in the solution temperature. For all the solution-treated alloys, the precipitated phases are detected. The corrosion rates of the alloys decrease first and then increase slightly with the increase in the solution temperature, and the corrosion resistance of the solution-treated alloys is more than four times as good as that of the as-cast alloy. In addition, the alloy solution-treated at 480 °C for 6 h shows the best corrosion property.     

Thermodynamic database of the phase diagrams in the Mg-Al-Zn-Y-Ce system

The Mg-Al-Zn-Y-Ce system is one of the key systems for designing high-strength Mg alloys. The purpose of the present article is to develop a thermodynamic database for the Mg-Al-Zn-Y-Ce multicomponent system to design Mg alloys using the calculation of phase diagrams （CALPHAD） method, where the Gibbs energies of solution phases such as liquid, fcc, bcc, and hcp phases were described by the subregular solution model, whereas those of all the compounds were described by the sublattice model. The thermodynamic parameters describing Gibbs energies of the different phases in this database were evaluated by fitting the experimental data for phase equilibria and thermodynamic properties. On the basis of this database, a lot of information concerning stable and metastable phase equilibria of isothermal and vertical sections, molar fractions of constituent phases, the liquidus projection, etc., can be predicted. This database is expected to play an important role in the design of Mg alloys.     

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.     

Effects of Cooling Rate and Component on the Microstructure and Mechanical Properties of Mg–Zn–Y Alloys

The microstructure and mechanical properties of Mg–6Zn–1Y and Mg–6Zn–3Y(wt%) alloys under different cooling rates were investigated. The results show that the second dendrite arm spacing(SDAS) of Mg–6Zn–1Y and Mg–6Zn–3Y is reduced by 32 and 30% with increasing cooling rates(Rc) from 10.2 to 23 K/s, which can be predicted using a empirical model of SDAS=68 R 0:45:45cand SDAS=73 R 0c, respectively. The compressive strength of both alloys increases with increasing the cooling rate, which is attributed to the increase of volume fraction(Vf) of secondary phases under high cooling rate. The interaction of the cooling rate and component with SDAS has been theoretically analyzed using interdependence theory.     

Effect of strontium on columnar growth of dendritic α phase in near-eutectic Al-11.6 %Si alloys

For AI-11.6%Si alloy, the influence of the addition of Sr on the morphology of the dendrite α phase was investigated, and the characteristic parameters of the dendrite α phase, the primary dendrite spacing and the secondary dendrite arm spacing, were also measured. The addition of strontium promotes the columnar dendrite growth and leads to a decrease of both the primary dendrite spacing and secondary dendrite arm spacing with the increase of the content of strontium in the modified near-eutectic AI-Si alloys. It is thought that the addition of Sr leads to a reduction of the solid-liquid interracial energy of the dendrite α phase, consequently resulting in a decrease of the growth undercooling of dendrite tips. And hence, the nucleation of the equiaxed grains in the liquid in front of the columnar dendrite tips is restrained, thus the addition of strontium in AI-Si alloys promotes the growth of the columnar dendrites. The reduction of the solid-liquid interracial energy also leads to the decreases in the primary dendrite spacing and the secondary dendrite arm spacing.     

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.     

Simulation for microstructure evolution of Al-Si alloys in solidification process

The numerical simulation for microstructure evolution of Al-Si alloy in solidification process is carried out with phase field model. The phase field model, solution algorithm and the program of dendrite growth are introduced. The definition of initial condition, boundary condition and the stability condition of differential format are all included. The simulation results show that the evolution of dendrite morphology is as follows： the initial circle nucleus transforms to the rectangle one firstly, then its corners develop to the four trunks and from which the secondary side branches are generated and even the third side branches are produced from secondary ones. The dendrite tip radius decreases quickly at the initial stage and changes slowly at the late stage, which is mainly due to the fact that more and more side branches appear and grow up. The comparisons of dendrite morphology between simulated results and investigations by others are also presented. It is proved that the dendrite morphologies are similar in trunks and arms growth, so the developed phase field program is accurate.     

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.     

Quantitative multi-phase-field modeling of non-isothermal solidification in hexagonal multicomponent alloys

A quantitative multi-phase-field model for non-isothermal and polycrystalline solidification was developed and applied to dilute multicomponent alloys with hexagonal close-packed structures. The effects of Lewis coefficient and undercooling on dendrite growth were investigated systematically. Results show that large Lewis coefficients facilitate the release of the latent heat, which can accelerate the dendrite growth while suppress the dendrite tip radius. The greater the initial undercooling, the stronger the driving force for dendrite growth, the faster the growth rate of dendrites, the higher the solid fraction, and the more serious the solute microsegregation. The simulated dendrite growth dynamics are consistent with predictions from the phenomenological theory but significantly deviate from the classical JMAK theory which neglects the soft collision effect and mutual blocking among dendrites. Finally, taking the Mg-6Gd-2Zn (wt.%) alloy as an example, the simulated dendrite morphology shows good agreement with experimental results.

     

Special features of cyrstallization of steels in the liquidus-solidus temperature range

Conclusions The process of crystallization of alloys of the type of bounded solid solutions occurs successively by two principally different mechanisms of growth of the solid phase. In the period of dendrite growth that ends with the formation of about 65% solid phase the change in the composition of the solid and liquid phases is adequately determined by the position of the equilibrium liquidus and solidus lines, and the amount of the phases is determined by the rule of the equilibrium lever. In the period of solidification of the interdendrite liquid the growth of the solid phase becomes layerwise, and the microsegregation of the components decreases markedly (K ⁱ→1), which makes the equilibrium diagrams not quite informative for the prediction of the final stage of solidification of actual alloys. Translated from Metallovedenie i Termicheskaya Obrabotka Metallov, No. 4, pp. 31–34, April, 2000.     

Modelling dendrite evolution under rapid solidification conditions

Abstract

The evolution of a single dendrite is simulated by the cellular automaton (CA) method, in which the influences of interface velocity on the solute partition coefficient ahead of the interface and liquidus slope are investigated under rapid solidification conditions. Furthermore, the kinetic undercooling ahead of the interface is also taken into account, which is neglected under normal solidification conditions. The simulated dendrite morphology is compared with that of the equilibrium conditions and it is shown that the interface easily loses stability around the dendritic tip causing more and more secondary dendrite arms to appear. In addition, the solute partition coefficient increases when the interface velocity increases, which leads to a decrease in solute microsegregation.     

多元合金耦合热力学数据非等温凝固的相场模拟

研究一种多元合金的非等温相场模型,定量地模拟工业多元合金的真实凝固过程,结合热力学和扩散迁移率的数据来预测整个系统中的相平衡、溶质扩散系数、比热容和放出的潜热。结果表明：这些参数不是常数,它们的值与成分和温度有关。没有这些参数,定量模拟多元合金的凝固几乎是不可能。在这个模型中,界面区域假设是由有同样化学势的固相和液相混合而成的,但组成不同。这个模型中同样考虑反溶质截流。一并将模型应用到工业Al?Cu?Mg合金的各向枝晶自由长大的凝固过程。     

On dendritic solidification of multicomponent alloys with unequal liquid diffusion coefficients

A model has been developed previously by Rappaz and Thévoz (Acta metall., 1987, 35, 1478; 1987, 35, 2929) for the solidification of binary alloys having an equiaxed dendritic morphology. The extension of this model to multicomponent alloys is straightforward if the diffusion coefficients in the liquid of the various solute elements are equal. When they are different however, it becomes necessary to distinguish the concentrations at the dendrite tip position, governing the growth kinetics, from the average concentrations within the interdendritic liquid region. A model is presented which couples the dendrite growth kinetics with an overall solute balance performed at the scale of the grain. The diffusion profile outside the grain envelope is calculated using a Landau transformation and an implicit scheme. The calculated solidification paths during and after recalescence are compared with the Scheil approximation for various conditions. Additionally, a model predicting the secondary dendrite arm spacing in multicomponent alloys is briefly described.     

三维枝晶生长数值模拟及实验验证(英文)

建立了用于模拟立方晶系合金三维枝晶生长的改进元胞自动机模型。该模型将枝晶尖端生长速率、界面曲率和界面能各向异性的二维方程扩展到三维直角坐标系,从而能够描述三维枝晶生长形貌演化。应用本模型模拟在确定温度梯度和抽拉速度条件下三维柱状晶生长过程的一次臂间距调整机制和不同择优取向柱状晶之间的竞争生长。使用NH4Cl?H2O透明合金进行凝固实验,模拟结果和实验结果吻合较好。     

元胞自动机法模拟铝合金三维枝晶生长

以元胞自动机模型为基础,基于晶粒形核和生长的物理过程及热质传输过程,建立了铝合金凝固过程微观组织形成及枝晶形貌演化的三维元胞自动机模型.与传统的元胞自动机不同,该模型不仅考虑了温度场扩散而且考虑了固液相中的溶质扩散、曲率过冷等重要因素.枝晶尖端生长速度与局部过冷度的关系采用KGT(Kurz-Giovanola-Trivedi)模型,温度场和浓度场计算采用有限差分法.使用该模型模拟了单晶生长和多晶生长.模拟结果表明,所建立的模型能够合理反映质点形核、单晶粒生长和多晶粒生长,微观组织形貌的模拟计算结果合理.     

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。     

Modeling the overall solidification kinetics for undercooled single-phase solid-solution alloys. I. Model derivation

Departing from the volume-averaging method, the equiaxed solidification model was extended to describe the overall solidification kinetics of undercooled single-phase solid-solution alloys. In this model, a single grain, whose size is given assuming site saturation, is divided into three phases, i.e. the solid dendrite, the inter-dendritic liquid and the extra-dendritic liquid. The non-equilibrium solute diffusion in the inter-dendritic liquid and the extra-dendritic liquid, as well as the heat diffusion in the extra-dendritic liquid, is considered. The growth kinetics of the solid/liquid interface is given by the solute or heat balance, where a maximal growth velocity criterion is applied to determine the transition from thermal-controlled growth to solutal-controlled growth. A dendrite growth model, in which the nonlinear liquidus and solidus, the non-equilibrium interface kinetics, and the non-equilibrium solute diffusion in liquid are considered, is applied to describe the growth kinetics of the grain envelope. On this basis, the solidification path is described.