高温合金定向凝固过程中枝晶生长与溶质对流数值模拟

目的 针对高温合金叶片在定向凝固过程中容易出现雀斑缺陷,从而导致叶片报废的问题,对定向凝固枝晶生长与溶质对流进行模拟研究,以揭示雀斑缺陷的形成规律。方法 针对CM247LC合金定向凝固过程,采用相场模型模拟凝固过程枝晶生长,采用格子Boltzmann模型模拟溶质浓度差引起的自然对流。采用基于双重网格的GPU并行算法对相场-格子Boltzmann模型进行数值求解。研究在不同晶体取向角度与取向差条件下的枝晶形貌、对流速度及溶质羽流的演变规律。结果 当晶体取向角度不同时,在枝晶生长过程中,液相区域的平均对流速度均表现为周期性变化。当晶体取向角度较大时,随着晶体取向角度的变大,一次枝晶臂间距变大。当枝晶间存在晶体取向差时,溶质羽流倾向于在发散型晶界附近发起;随着晶体取向差的增大,溶质羽流发起时间提前。溶质羽流的形成阻碍了枝晶尖端及附近枝晶侧臂的生长。结论 晶体取向角度对溶质羽流形成的影响较小,较大的晶体取向差对溶质羽流的形成有促进作用。     

Effect of cooling rates on the dendritic morphology transition of Mg–6Gd alloy by in situ X-ray radiography

The effect of cooling rate on the transition of dendrite morphology of a Mg-6 Gd(wt%) alloy was semiquantitatively analyzed under a constant temperature gradient by using synchrotron X-ray radiographic technique. Results show that equiaxed dendrites, including exotic 'butterfly-shaped' dendrite morphology, dominate at high cooling rate(1 K/s). When the cooling rate decreases in the range of 0.5–1 K/s, the equiaxed-to-columnar transition takes place, and solute segregates at the center of two long dendrite arms(LDA) of the 'butterfly-shaped' dendrite. When the cooling rate is lower than 0.3 K/s, directional solidification occurs and the columnar dendritic growth direction gradually rotates from the crystalline axis to the thermal gradient direction with an increase in cooling rate. Meanwhile, interface moves faster but the dendrite arm spacing decreases. Floating, collision and rotation of dendrites under convection were also studied in this work.     

High rate directional solidification and its application in single crystal superalloys

In the present paper there are two parts contributing to the discussion of high rate directional solidification and its application. The first part aims to characterize the high rate directional solidification of various kinds of alloys. It was found that the relevant cooling rate of the high rate directional solidification is defined to be within 1–10³ K/s (solidification rate is 10^-4–10^-1 m/s as G_L= 100 K/cm) and that it is located in the region between the near-equilibrium slow growth rate and the rapid solidification rate beyond the equilibrium condition, whilst at the same time there occurs a series of turning effects of interface stability and morphologies. With the increase in the growth velocity the interface with the plane front evolves to cells and dendrites at the stage of near-equilibrium and with a further increase in growth rate they transformed reversibly from dendrites to cell structure and then to the absolute stability of a planar interface. The change of solute segregation reveals the same from a lowsegregation, then increased and finally reduced again. An explanation based on effective constitutional supercooling about the evolution of interface morphologies with respect to the changes of growth rate is proposed.

The second part is devoted to introducing experimental results for single crystal superalloys using the rate directional solidiication principle. It is shown that the single crystal superalloys CMSX–2 and NASAIR 100 exhibit significant improvement in microstructure segregation and mechanical properties at high temperature both in the as-cast and after-heat-treatment conditions with the high rate directional solidification technique.     

High rate directional solidification and its application in single crystal superalloys

In the present paper there are two parts contributing to the discussion of high rate directional solidification and its application. The first part aims to characterize the high rate directional solidification of various kinds of alloys. It was found that the relevant cooling rate of the high rate directional solidification is defined to be within 1–10³ K/s (solidification rate is 10⁻⁴–10⁻¹ m/s as G_L=100 K/cm) and that it is located in the region between the near-equilibrium slow growth rate and the rapid solidification rate beyond the equilibrium condition, whilst at the same time there occurs a series of turning effects of interface stability and morphologies. With the increase in the growth velocity the interface with the plane front evolves to cells and dendrites at the stage of near-equilibrium and with a further increase in growth rate they transformed reversibly from dendrites to cell structure and then to the absolute stability of a planar interface. The change of solute segregation reveals the same from a low segregation, then increased and finally reduced again. An explanation based on effective constitutional supercooling about the evolution of interface morphologies with respect to the changes of growth rate is proposed.The second part is devoted to introducing experimental results for single crystal superalloys using the rate directional solidification principle. It is shown that the single crystal superalloys CMSX-2 and NASAIR 100 exhibit significant improvement in microstructure segregation and mechanical properties at high temperature both in the as-cast and after-heat-treatment conditions with the high rate directional solidification technique.     

Simulation of dendrite growth of Fe–C alloy using phase field method

采用相场法模拟了Fe--0.5%C合金等温凝固过程中单个枝晶和多个枝晶的生长, 研究了过冷度、各向异性、界面厚度、晶体取向以及扰动对枝晶形貌的影响, 获得了具有二次分枝的枝晶形貌, 再现了枝晶生长过程及枝晶臂之间的竞争生长. 模拟结果表明: 凝固过程中存在溶质富集和枝晶偏析, 枝晶主干溶质浓度最低, 枝晶臂之间的液相浓度最高. 随着过冷度的增大, 枝晶生长加快且分枝发达; 界面厚度直接影响枝晶的生长速度; 各向异性影响枝晶的形态; 晶体取向与坐标轴方向一致时枝晶优先生长;扰动的加入导致枝晶分枝的形成.     

Numerical Simulation of Morphology and Microsegregation Evolution during Solidification of Al-Si Alloy

A stochastic model coupled with transient calculations for the distributions of temperature, solute and velocity during the solidification of binary alloy is presented. The model can directly describe the evolution of both morphology and segregation during dendritic crystal growth. The model takes into account the curvature and growth anisotropy of dendritic crystals. Finite difference method is used to explicitly track the sharp solid liquid (S/L) interface on a fixed Cartesian grid. Two-dimensional mesoscopic calculations are performed to simulate the evolution of columnar and equiaxed dendritic morphologies of an AI-7 wt pct Si alloy. The effects of heat transfer coefficient on the evolution of both the dendrite morphology and segregation patterns during the solidification of binary alloys are analyzed. This model is applied to the solidification of small casting. Columnar-to-equiaxed transition is analyzed in detail. The effects of heat transfer coefficient on final casting structures are also studi     

Effect of transverse static magnetic field on radial microstructure of hypereutectic aluminum alloy during directional solidification

The effect of different scales thermoelectric magnetic convection(TEMC)on the radial solidification microstructure of hypereutectic Al alloy has been investigated under transverse static magnetic field during directional solidification,focusing on the formation of freckle.Our experimental and numerical simulation results indicate that the TEMC circulation at sample scale under transverse static magnetic field leads to the enrichment of solute Al on one side of the sample.The TEMC and the solute enrichment degree increase with the increase of magnetic field when the magnetic field increases to 0.5 T.The enrichment degree of solute elements under magnetic field is affected by temperature gradient and growth rate.The non-uniform distribution of solute Al in the radial direction of the sample results in the non-uniform distribution of primary dendrite arm spacing(PDAS).Moreover,the applied magnetic field can lead to freckle formation and its number increases with the increase of magnetic field.The change of freckle is consistent with the anisotropy TEMC caused by the anisotropy of primary dendrite or primary dendrite network under magnetic field.Finally,the mechanism of synergism effect of the anisotropy TEMC,the distribution of solute Al and the PDAS on freckle formation and evolution is studied during directional solidification under magnetic field.     

Self-consistent modeling of morphology evolution during unidirectional solidification

A self-consistent model is developed to describe the morphology evolution during unidirectional solidification, which shows that, for a given temperature gradient, the interface morphology will go planar → shallow cell → deep cell → dendrite → cell → planar with increasing growth velocity. By examining the interaction of adjacent cells/dendrites, a wide allowable range of primary spacing for given growth conditions is determined, which shows a good agreement with experimental results. Numerical results show that cellular/dendritic and dendritic/cellular transitions appear not at a unique velocity but over a range of velocities, the critical velocity for the transition being dependent on the primary spacing before the transition.     

Self-consistent modeling of morphology evolution during unidirectional solidification

A self-consistent model is developed to describe the morphology evolution during unidirectional solidification, which shows that, for a given temperature gradient, the interface morphology will go planar→shallow cell→deep cell→dendrite→cell→planar with increasing growth velocity. By examining the interaction of adjacent cells/dendrites, a wide allowable range of primary spacing for given growth conditions is determined, which shows a good agreement with experimental results. Numerical results show that cellular/dendritic and dendritic/cellular transitions appear not at a unique velocity but over a range of velocities, the critical velocity for the transition being dependent on the primary spacing before the transition.     

Solidification Microstructures of a Single-crystal Superalloy under Ultra-high Temperature Gradient Conditions

The solidification microstructures and solute segregation of a newly developed hot corrosionresistant single-crystal Ni-base superalloy were investigated with a zone-melting and ultra-highthermal gradient unidirectional solidification apparatus.Compared with the microstructures solidifiedat conventional low thermal gradient conditions,the dendrite arm spacings,the interdendriticmicroporosity and γ/γ' eutectic,and the severity of solute segregation of the single-crystalsuperalloy solidified at ultra-high thermal gradient conditions were considerably reduced.It wasshown that the microstructure solidified under ultra-high thermal gradient condition is ideal for thefull exploitation of the excellent property potentials of single-crystal superalloys.     

Understanding the Heat Transfer and Solidification of Plasma-Sprayed Yttria-Partially Stabilized Zirconia Coatings

A variety of microstructures have been observed in plasma-sprayed yttria-partially stabilized zirconia (YSZ) thermal barrier coatings. Control of the coating microstructures requires a good understanding of the heat transfer and solidification during the process. This article presents a quantitative analysis of heat transfer and solidification of plasma-sprayed YSZ splats. The analysis is based on a simple heat transfer and solidification model that solves a one-dimensional moving boundary problem with consideration of melt undercooling prior to solidification and nonequilibrium crystalline growth kinetics at the moving interface. The solidification morphology is first assumed to be planar, and the stability of the planar interface is examined against the absolute stability velocity calculated from the linear stability theory. Examining the temperature distribution in a solidifying YSZ zirconia splat indicates that a large positive temperature gradient exists in front of the interface, which leads to a stable planar interface and a segregation-free columnar structure, agreeing well with experimental observation. The model also finds that a low interface velocity results from poor heat transfer, which leads to a formation of cells and, therefore, the segregation of yttria. A steady-state dendrite tip growth model is then employed to calculate the radius of the cell tips and thus the cell spacings, which is then compared with experimental observations.     

Influence of directional solidification variables on the microstructure and crystal orientation of AM3 under high thermal gradient

Solid–liquid interface morphologies of a nickel-base single crystal superalloy AM3 were investigated under high thermal gradient. The critical velocities of planar–cellular and cellular–dendritic transition were greatly increased by high thermal gradients. A high thermal gradient was of great benefit to dendrite refinement. Experimental results showed that the primary and secondary dendrite arm spacings decreased with increasing cooling rate. As expected, the segregation of elements was suppressed and the size of the gamma prime (γ′) phase decreased significantly with increasing withdrawal rates. The shape of γ′ in interdendritic region kept cuboidal at higher withdrawal rate. It was found that the withdrawal rates had little influence on the crystallographic orientation in high thermal gradient directional solidification.     

基于三维LBM-CA模型模拟Al-4.7%Cu合金的枝晶形貌和成分分布

建立了三维格子玻尔兹曼方法(LBM)-元胞自动机(CA)耦合数值模型,并用该模型模拟研究了Al-4.7%Cu(质量分数)固溶体合金的凝固过程。该耦合模型采用元胞自动机方法模拟枝晶的生长,同时采用基于分子动力学理论的格子玻尔兹曼方法模拟合金凝固过程中的温度场、流场以及溶质场。模拟结果再现了合金凝固过程中的三维枝晶形貌变化以及溶质富集过程,并将三维流场因素考虑进去,定量研究了自然对流、过冷度对单枝晶形貌和成分分布的影响。研究表明,在纯扩散条件下,枝晶呈现对称的生长现象,模拟自由枝晶稳态生长的尖端速度、尖端半径和过冷度的关系与Lipton-Glicksman-Kurz(LGK)理论模型吻合得较好。在自然对流条件下,枝晶的生长形貌呈现不对称性,即枝晶生长在迎流方向上得到了促进,在顺流方向上受到了抑制。熔体过冷度对枝晶生长的影响较大,过冷度的增加导致枝晶生长加快,二次枝晶增多且呈现出粗化现象,枝晶尖端固液界面处的溶质浓度偏高,加重了溶质偏析。     

亚快速单向凝固晶体生长的非稳态演化

晶体生长中的非稳态演化过程一直是凝固领域人们很少涉及的课题，尤其在胞枝转变之后相当宽范围的亚快速凝固更是少人问津，而非稳态过程对材料最终的组织往往产生在影响，本文采和有机物模拟合金研究了低速及亚快速凝固范围界面形态与一次间距的演化规律，并初步探讨了其演化机制。     

Simulation of equiaxed growth ahead of an advancing columnar front in directionally solidified Ni-based superalloys

Growth of equiaxed grains ahead of an advancing columnar front leads to the formation of as-cast defects, such as stray grains in single crystals or tree rings in vacuum arc remelting (VAR) ingots. In this study a combined cellular automata-finite difference model was applied to simulate dendrite growth and the formation of equiaxed grains in directionally solidified nickel-based superalloys. Realistic dendritic structures and complex solute concentration profiles at the growth front were simulated. It was observed that the solute interaction between primary dendrites occurs well below their tips, while strong solute interaction occurs between the diffusion fields of secondary and tertiary arms. The influence of thermal gradient and growth velocity on CET was investigated and the results were combined on a CET map, showing that a decrease in thermal gradient and an increase in growth rate favour a CET.     

Microstructure and stress rupture properties of single crystal superalloy CMSX-2 under high thermal gradient directional solidification

The interface morphologies of single crystal superalloy CMSX-2 were studied over a range of cooling rate with large variations in withdrawal speeds in directional solidification. A superfine cellular structure was obtained under both high thermal gradient up to 1000 K/cm and fast withdrawal rate up to 1 mm/s. The high rate directional solidification results in reduction in primary and secondary dendrite arm spacing, refinement of γ′ phase, reduced microsegregation of alloying elements and smaller size of γ-γ′ eutectics. The rupture life and plasticity of fine structure samples produced in high thermal gradient directional solidification increase significantly than that in conventional directional solidification process at 1323 K.     

温度梯度对定向凝固Al-4.5%Cu合金一次枝晶间距的影响

使用5kg坩埚下拉式定向凝固设备,对Al-4.5%Cu合金进行定向凝固试验,研究Al-4.5%Cu合金在不同温度梯度下一次枝晶间距的变化规律。结果表明:在其他凝固参数不变时,随着温度梯度的增大,一次枝晶逐渐变小,细密,挺直,基本呈平行状分布,同时计算的一次枝晶间距值与Hunt模型计算值接近,实验测得的一次枝晶间距的回归曲线为:y=2843478.3x2-70217.4x+543.8。用温度梯度较高的实验值来模拟时,可得到1λ=26.7G-0.5-135.9,一次枝晶间距λ1与G-0.5基本呈线性关系,这和Hunt模型分析结果一致。     

溶质梯度系数对二元合金枝晶生长的影响

为了准确描述金属凝固过程中的微观特性,用相场法模拟流场下二元合金的枝晶形貌.结合C.W.Lan提出的耦合流场的相场模型,在溶质场中加入溶质梯度项,研究溶质梯度系数对合金非等温凝固过程中枝晶生长及溶质截留效应的影响.结果表明:随着溶质梯度系数的增大,上游尖端半径和尖端速率都逐渐增大,固相中的溶质浓度显著提高,溶质截留效应更加明显.另外,此模型的计算结果与Oseen-Ivantsov理论符合较好.     

Modelling mixed columnar-equiaxed solidification with melt convection and grain sedimentation – Part I: Model description

Part I of this two-part investigation presents a volume-averaging multiphase solidification model that accounts for mixed columnar-equiaxed solidification, non-dendritic and dendritic crystal growth, nucleation of equiaxed grains, columnar primary dendrite tip tracking, melt flow, sedimentation of equiaxed crystals, and their influence on macrostructure and macrosegregation. Five distinct thermodynamic phases (phase regions) are defined: solid dendrites in equiaxed grains, the interdendritic melt between equiaxed dendrites, solid dendrites in columnar trunks, the interdendritic melt between trunk dendrites, and the extradendritic melt. These five phase regions are quantified by their volume fractions and characterized by their solute concentrations. The five phase regions are grouped into three hydrodynamic phases: equiaxed grains consisting of solid dendrites and interdendritic melt, columnar trunks consisting of solid dendrites and interdendritic melt, and extradendritic melt. The extradendritic melt is separated from the interdendritic melt with a grain envelope, whose profile connects the primary, secondary or tertiary dendrite tips to form a ‘natural’ enclosure of the equiaxed grains or columnar trunks. The envelope is further simplified as a volume-equivalent sphere for equiaxed grains, or as volume-equivalent cylinder for columnar trunks by use of morphological shape factors. Expansion of the envelopes during solidification is determined by dendrite growth kinetics, using the Kurz–Giovanola–Trivedi model for growth of columnar primary dendrite tips and the Lipton–Glicksman–Kurz model for growth of columnar secondary dendrite tips (radial growth of the columnar trunk) and equiaxed primary dendrite tips. The solidification of the interdendritic melt is driven by the supersaturation of the interdendritic melt and governed by the diffusion in the interdendritic melt region. Illustrative process simulations and model verifications are presented in Part II.     

Computer Modeling of the Evolution of Dendrite Microstructure in Binary Alloys During Non-isothermal Solidification

Two-dimensional simulations of the evolution of dendrite microstructure during isothermal and non-isothermal solidifications of a Ni-0.41Cu binary alloy are carried out using the phase-field method. The governing evolution equation for the phase field variable, the solute mole fraction and the temperature are formulated and numerically solved using an explicit finite difference scheme. To make the computations tractable, parallel computing is employed. The results obtained show that under lower cooling rates, the solidification process is controlled by partitioning of the solute between the solid and the liquid at the solid/liquid interface. At high cooling rates, on the other hand, solute trapping takes place and solidification is controlled by the heat extraction rate. An increase in the cooling rate is also found to have a pronounced effect on the dendrite microstructure causing it to change from poorly developed dendrites consisting of only primary stalks, via fully developed dendrites containing secondary and tertiary arms to the diamond-shaped grains with cellular surfaces. These findings are in excellent agreement with experimental observations.