Solidification path calculations of Al-Zn-Mg alloys in Al-rich corner

The solidification paths of Al-Zn-Mg alloys in the Al-rich corner were investigated. The thermodynamic data for the calculation are obtained by direct coupling with the CALPHAD software Thermo-Calc via its TQ6-interface and the COST2 database. The influences of the initial compositions and the extent of solid back diffusion on the solidification path were numerically investigated by sample calculation of the ternary Al-Zn-Mg alloys. The calculation results of solidification paths of the selected alloys: Al-Zn-3 Mg(in wt.%), Al-5 Zn-10 Mg, Al-2.5Zn-15Mg, Al-10Zn-20.5 Mg, Al-8Zn-25 Mg, were: L→(L+α-Al), L→(L+α-Al)→(L+α-Al+TAU), L→(L+α-Al)→(L+α-Al+Al Mg_β), L→(L+α-Al)→(L+α-Al+TAU)→(L+α-Al+TAU+Al Mg_β), L→(L+α-Al)→(L+α-Al+Al Mg_β)→(L+α-Al+TAU+Al Mg_β), respectively. The results show that the initial compositions and the extent of solid back diffusion have a great influence on solidification path, and the amounts of eutectic phase increase with the decrease of the solid back diffusion coefficient. The equilibrium solute partition coefficients for Zn and Mg in alloys are also calculated and their influence on micro-segregation in the primary solidification of Al-5Zn-10 Mg alloy is analyzed.     

The Solidification of Multicomponent Alloys

Various topics taken from the author’s research portfolio that involve multicomponent alloy solidification are reviewed. Topics include: ternary eutectic solidification and Scheil-Gulliver paths in ternary systems. A case study of the solidification of commercial 2219 aluminum alloy is described. Also presented are modifications of the Scheil-Gulliver analysis to treat dendrite tip kinetics and solid diffusion for multicomponent alloys.     

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.     

Numerical solution to T-φ_S-C_L coupling in binary dendrite solidification with any solid-back diffusion effects

1　INTRODUCTIONMostalloymaterialsinengineeringapplicationssolidifyinatemperaturerangeandindendriticman ners.Suchcomplicatedliquid to solid phase changeprocessesareusuallycontrolledsimultaneouslybyheat ,massandmomentumtransfers ,anddeterminedbythealloy snonlinear propertiesofsolidificationthermodynamics/kinetics .Ithasbeenshownthatacontinuumormixtureaveragemodelhasthemathe maticalsuccinctnessandrelativenumerical solutionefficiencyinmodelingthedendriticsolidification trans port phenomena(ST…     

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.     

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.     

Solidification of Aluminum-Zinc Alloys

The solidification of Al?Zn alloys (2 to 70 pet Zn) was investigated at different rates of solidification. The resulting structures were studied; the amounts of nonequilibrium eutectic were measured and compared with the amounts calculated on the assumption of no diffusion in the solid. The compositions of the cored primary constituent were investigated by quantitative autoradiography after activation of the zinc by neutron irradiation. These compositions were also determined from microhardness values.     

Thermo-Calc based multi-component micro-segregation model and solidification paths calculations

On the basis of a multi-length scale modeling,a mixture-averaged multi-component/multiphase microsegregation model was proposed without pre-set function for the micro-scale solute profile.The model exp...     

Modeling equiaxed solidification with melt convection and grain sedimentation—I: Model description

Part I of this two part investigation presents a modified volume-averaged equiaxed solidification model which accounts for nucleation, globular grain growth, globular-to-dendritic transition, dendritic growth, formation of extra- and interdendritic eutectic, grain transport and melt convection, and their influence on microstructure and macrosegregation. Globular grain growth is governed by diffusion around a spherical grain. For the dendritic growth, a “natural” grain envelope smoothly enclosing the primary and secondary dendrite tips is assumed to separate the interdendritic melt from the extradendritic melt. The solid dendrites and interdendritic melt, confined in the “natural” grain envelope, combine to form a dendritic grain. Two “hydrodynamic” phases are considered: the extradendritic melt and the equiaxed grains; and three thermodynamic phase regions are distinguished: the solid dendrites, the interdendritic melt and the extradendritic melt. The velocities of the hydrodynamic phases are solved with a two-phase Eulerian approach, and transport of the mass and solute species of each thermodynamic phase region are considered individually. Growth kinetics for the grain envelope and the interdendritic melt solidification are implemented separately. Simplification of the grain dendritic morphology and treatment of the non-uniform solute distribution in the interdendritic melt region are detailed. Illustrative modeling results and model verification are presented in Part II.     

The real-time,high-resolution x-ray video microscopy of solidification in aluminum alloys

The directional solidification of thin alloy sheets in a Bridgman furnace has been studied by x-radiography using high-brilliance synchrotron x-radiation in combination with a low-noise, fast-readout camera. Spatial resolutions down to 1.5 μm and a temporal resolution of about 0.15 s have permitted real-time video microscopy of microstructural evolution during columnar and equiaxed dendrite growth and eutectic and monotectic growth. The technique has also allowed for direct observations of important solidification phenomena such as dendrite fragmentation and porosity formation, primarily in aluminium alloys. As a result, insights have been gained into mechanisms of dendrite fragmentation, criteria for dendrite tip kinetics and interface stability during transient growth, and microstructure formation mechanisms during monotectic solidification. The results are expected to be important for validation of dendrite growth models. This paper presents a review of the technique as well as examples of images obtained during solidification of aluminum alloys.     

Microstructural evolution during containerless rapid solidification of Ni–Mo eutectic alloys

Ni–45%Mo hypoeutectic, Ni–47.7%Mo eutectic and Ni–50%Mo hypereutectic alloys are rapidly solidified during containerless processing in drop tube. The microstructures of Ni–47.7%Mo eutectic alloy are composed of lamellar eutectic plus anomalous eutectic of Ni and NiMo phases. When the droplet size decreases, the volume fraction of anomalous eutectic becomes larger. The structural morphology transforms into Ni dendrite plus lamellar eutectic in very small droplets which are highly undercooled. The microstructures of Ni–45%Mo hypoeutectic alloy are characterized by primary Ni dendrite plus lamellar eutectic, whereas those of Ni–50%Mo hypereutectic alloy consist of NiMo dendrite plus lamellar eutectic. For both off-eutectic alloys, the experimental results show that the microstructure evolution depends mainly on droplet size. In the case of Ni–45%Mo hypoeutectic alloy, with the decrease of droplet size, the primary Ni phase transforms from dendrites to equiaxed grains. As for Ni–50%Mo hypereutectic alloy, when droplets become smaller and smaller the microstructural transition proceeds from primary NiMo dendrite plus lamellar eutectic to anomalous eutectic. The calculated highest undercoolings of the three alloys are 226, 182 and 135 K, respectively. By classical nucleation theory, Ni phase is the primary phase to nucleate for Ni–47.7%Mo eutectic alloy. The TMK eutectic growth and LKT/BCT dendritic growth theories are applied to analyze the rapid solidification process and investigate the microstructural transition mechanisms. The coupled zone of Ni–Mo eutectic alloy has also been calculated on the basis of TMK and LKT/BCT models, which covers a composition range from 45.7% to 57.1% Mo.     

Exploring dendrite coherency with the discrete element method

The particulate discrete element method (DEM) is used to simulate crystal rearrangement during equiaxed solidification of Al alloys for a range of morphologies across the globular to equiaxed-dendritic transition. It is shown that DEM is able to capture the key experimental results reported in past dendrite coherency studies, namely: the marked increase in resistance to shear at a critical solid fraction, the influence of crystal morphology on dendrite coherency, and that dendrite coherency marks the onset of dilatancy. Dendrite coherency is shown to be the lowest solid fraction at which long-range interconnectivity in the force chain network develops during shear. It is further found that dendrite coherency depends on both the internal solid fraction within dendrite envelopes and the mean shape of envelopes at coherency. The potential to extend DEM to the simulation of mushy-zone mechanics in casting problems is then discussed.     

Solidification of aluminum-rich aluminum-copper alloys

The solidification of aluminum-rich aluminum-copper alloys was investigated for different solidification rates. The measured amounts of nonequilibrium eutectic were compared with the amounts calculated on the assumption of no diffusion in the solid. The morphology of the eutectic was studied and dendritic spacings were measured. Compositions of the cored primary solid solutions were determined by quantitative autoradiography after activation of the solute copper by neutron irradiation.     

Experimental and numerical modeling of equiaxed solidification in metallic alloys

Nucleation undercoolings are measured for the primary dendritic structure and for the eutectic structure in aluminum–copper samples solidified during electromagnetic levitation. The recorded cooling curves are used to determine the heat extraction rate and the solidification times. Metallurgical characterizations consist of composition measurements using a scanning electron microscope (SEM) equipped with energy-dispersive X-ray spectrometry and analyses of SEM images. The distribution maps drawn for the average copper composition, the volume fraction of the eutectic structure and the dendrite arm spacing reveal strong correlations. An equiaxed solidification model based on mass and heat balances is developed for the interpretation of the measurements. The model predicts the effect of diffusion in the liquid and in the solid, as well as the consequences of the recalescences occurring immediately after the nucleation of the primary dendritic structure and the eutectic structure. The nucleation undercooling of the eutectic structure is shown to be a key parameter for a quantitative prediction of the fraction of phases in the solidified samples.     

Simulation of Grain Growth during Solidification of Twin-Roll Continuously Cast Pure Aluminum with a Modified CA Model

基于枝晶生长的基本传输过程和元胞自动机(Cellular Automaton,简称CA)-有限元(Finite Element,简称FE)模型基本原理,建立了适应双辊连续铸轧纯铝薄带工艺特点的凝固过程形核和晶体生长的数学模型。模型耦合了宏观温度场和微观组织模拟计算,考虑了溶质扩散、曲率过冷和潜热释放等重要因素的影响,能够模拟凝固过程中枝晶生长的形态。应用本模型对双辊连续铸轧纯铝薄带凝固过程中等轴晶生长、等轴晶多晶粒生长及柱状晶生长、柱状晶向等轴晶演化进行模拟并与实验结果进行对比,模拟结果与实验结果吻合较好     

As-cast structure refinement of Ti-46Al alloy by hafnium and boron additions

The influence of Hf and B on the solidification structure of cast Ti-46Al alloys was investigated. The results show that the coupling effect of Hf and B changes the solidification structure morphology and strongly refines the grain size. When the Hf+B contents were increased from 0 + 0.0 to 3 + 0.2, 5 + 0.6 and 7 + 1.0 (in at. %), the solidification structure morphology changed from coarse columnar dendrite to fine columnar dendrite,then to equiaxed dendrite, and further to fine near granular grain whilst the average grain size decreased to 20 μm.It is concluded that the columnar dendrite refinement is due to the effect of Hf and B on the decrease of Al diffusion coefficient in the melt. The fine near granular grain formation is attributed to the combined constitutional supercooling formed by AI and B segregation that is strengthened by Hf and B additions at the solid/liquid interface uring solidification, and the TiB2 precipitates acting as heterogeneous nuclei.     

Advanced Solidification Studies on Transparent Alloy Systems: A New European Solidification Insert for Material Science Glovebox on Board the International Space Station

Investigations on solidifying transparent model alloys have served frequently to gain knowledge on physical phenomena occurring during solidification of metallic alloys. However, quantitative results were obtainable in thin samples where convection can successfully be suppressed. Quantitative studies on three-dimensional phenomena not being affected by natural convection are thus only possible under microgravity conditions. Therefore, the European Space Agency (ESA) is planning to launch a new insert for the material science glovebox on board of the International Space Station for studies on solidification phenomena in thick samples. Four different classes of transparent model alloys will be used to address the following scientific topics: (I) columnar to equiaxed transition in solidification processing, (II) novel peritectic structures and in situ composites; (III) solidification along an eutectic path in binary alloys; and (IV) solidification along an eutectic path in ternary alloys. In this article, we give details on the scientific objectives and the operational features ESA??s new solidification device will offer.     

Numerical modeling of solidification morphologies and segregation patterns in cast dendritic alloys

A comprehensive stochastic model for simulating the evolution of dendritic crystals during the solidification of binary alloys was developed. The model includes time-dependent calculations for temperature distribution, solute redistribution in the liquid and solid phases, curvature, and growth anisotropy without further assumptions on the nucleation and growth of dendritic crystals. Stochastic procedures previously developed by Nastac and Stefanescu (Modell. Simul. Mater. Sci. Engng, 1997, 5(4), 391) for simulating dendritic grains were used to control the nucleation and growth of dendrites. A numerical algorithm based on an Eulerian–Lagrangian approach was developed to explicitly track the sharp solid/liquid (S/L) interface on a fixed Cartesian grid. Two-dimensional mesoscopic calculations (i.e. at the dendrite tip length scale) were performed to simulate the evolution of columnar and equiaxed dendritic morphologies including the formation of the columnar-to-equiaxed transition. The effects of solutal and curvature undercoolings on the evolution of both the dendrite morphology and segregation patterns during the solidification of binary alloys were analyzed in detail.     

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。