Phase-field simulation of formation of cellular dendrites and fine cellular structures at high growth velocities during directional solidification of Ti56Al44 alloy

A phase-field model whose free energy of the solidification system derived from the Calphad thermodynamic modeling of phase diagram was used to simulate formation of cellular dendrites and fine cellular structures of Ti56Al44 alloy during directional solidification at high growth velocities. The liquid-solid phase transition of L→β was chosen. The dynamics of breakdown of initially planar interfaces into cellular dendrites and fine cellular structures were shown firstly at two growth velocities. Then the unidirectional free growths of two initial nucleations evolving to fine cellular dendrites were investigated. The tip splitting phenomenon is observed and the negative temperature gradient in the liquid represents its supercooling directional solidification. The simulation results show the realistic evolution of interfaces and microstructures and they agree with experimental one.     

Numerical simulaton of cellular/dendritic transition and its growth during unidirectional solidificationin of Ti–Al alloy

采用基于溶质扩散控制模型CA方法对Ti44Al合金定向凝固初始阶段变速冷却过程中胞/枝晶转变过程进行了数值模拟.模拟结果表明,在胞/枝转变过程中,存在胞-枝混合生长区,在一些胞晶相邻面无二次枝晶生长.在给定的冷却速率下,枝晶臂间距大于胞晶臂间距;而在过渡区,枝晶间距达到最大.另外,晶核数量对柱状晶间距产生影响,随着植入晶核数量的增加,柱状晶间距非均匀化程度明显减小.出现过渡区的原因与枝晶生长所引起固/液界面前沿成分波动有关.模拟与实验结果吻合较好.     

Microstructure transition from stable to metastable eutectic growth in Ni–25%Al alloy

The microstructural evolution during directional solidification of the Ni–25%Al (mole fraction) alloy was investigated in the range of growth velocity from 10 to 100 μm/s under a given thermal gradient of 10 K/mm. The solidification microstructures reveal a transition from γ‘–β equilibrium eutectic to γ–β metastable eutectic plus β dendrites. A mixed microstructure of γ‘–β and γ–β eutectics produced at a growth velocity of 25 μm/s illustrates that the transition occurs during the competitive growth between γ and γ' phases. The growth temperature for each phase was considered to understand the microstructure selection during solidification. The experimental results show that a phase or a microstructure solidifying with the highest temperature under a given growth condition is preferentially selected upon solidification. In addition, both stable eutectic and metastable eutectic are shown to coexist and simultaneously grow in the velocity range between 25 and 60 μm/s due to their similar growth temperatures.     

Simulation of microstructure evolution in directional solidification of Ti-45at.%Al alloy using cellular automaton method

The microstructural evolution of Ti-45 at.%Al alloy during directional solidification was simulated by applying a solute diffusion controlled solidification model. The obtained results have shown that under high thermal gradients the stable primary spacing can be adjusted via branching or competitive growth. For dendritic structures formed under a high thermal gradient, the secondary dendrite arms are developed not very well in many cases due to the branching mechanism under a constrained dendritic growth condition. Furthermore, it has been observed that, with increasing pulling velocity, there exists a cell/dendrite transition region consisting of cells and dendrites,which varies with the thermal gradient in a contradicting way, i.e. increase of the thermal gradient leading to the decrease of the range of the transition region. The simulations agree reasonably well with experiment results.     

STRUCTURE EVOLUTION OF DIRECTIONALLY SOLIDIFIED Ti--43Al--3Si ALLOY I. Microstructure Evolution in the Transition Region

对Ti--43Al--3Si (原子分数, %) 合金在3---100 μm/s 的生长速度下进行了系统的定向凝固实验. 研究了生长速度对固/液界面形态及初始过渡区组织演化规律的影响. 合金在3---60 μm/s 的生长速度范围内均以胞晶形态生长, 胞晶间距随着生长速度的增大而减小; 当生长速度达到90 μm/s 时, 开始出现枝晶生长. 在定向凝固初始启动阶段, 存在清晰的热过渡区, 热过渡区内Ti₅Si₃ 相分布及过渡区组织与定向凝固区组织的关联性对于籽晶材料的引晶效果有重要影响. 生长速度在10 μm/s 以内时, 热过渡区内Ti₅Si₃ 相分布连续, 且热过渡区组织与定向凝固区组织的关联性好, 有利于该合金的引晶.     

定向凝固Ti-50Al合金组织演化及其片层取向控制

对Ti-50Al(原子分数,%)合金在较宽的生长速率范围内进行定向凝固实验,研究了生长速率对固/液界面形态、微观组织演化及片层结构形成的影响.发现合金在1-5μm/s的速率范围内均以α胞晶单相生长,最终形成全片层结构;当生长速率达到10μm/s时,在初始凝固的较长距离内为α胞品单相生长,随着凝固的进行,胞晶间溶质逐渐富集,晶间出现从液相析出的γ相,最终不能形成全片层结构;当生长速率大干15μm/s时,合金以α枝晶生长,枝晶间也出现γ相.对各生长速率下形成的片层结构取向的分析表明,片层结构取向与定向凝固启动界面处铸态品粒的取向的历史有关.根据上述规律,以Ti-50Al合金为籽晶和主体合金,选择确保α单相凝吲的生长速率8 μm/s,进行片层取向控制,最终扶得取向与生长方向一致的全片层结构.     

Numerical simulation of dendrite growth in Ni-based superalloy casting during directional solidification process

An understanding of dendrite growth is required in order to improve the properties of castings. For this reason, cellular automaton?finite difference (CA?FD) method was used to investigate the dendrite growth during directional solidification (DS) process. The solute diffusion model combined with macro temperature field model was established for predicting the dendrite growth behavior. Model validation was performed by the DS experiment, and the cooling curves and grain structures obtained by the experiment presented a reasonable agreement with the simulation results. The competitive growth of dendrites was also simulated by the proposed model, and the competitive behavior of dendrites with different misalignment angles was also discussed in detail. Subsequently, 3D dendrites growth was also investigated by experiment and simulation, and both were in good accordance. The influence on dendrites growth of initial nucleus was investigated by three simulation cases, and the results showed that the initial nuclei just had an effect on the initial growth stage of columnar dendrites, but had little influence on the final dendritic morphology and the primary dendrite arm spacing.     

STRUCTURE EVOLUTION OF DIRECTIONALLY SOLIDIFIED Ti--43Al--3Si ALLOY II. Microstructure Evolution in the Steady--State Growth Region

分析了定向凝固Ti--43Al--3Si(原子分数, %) 合金在3---90 μm/s 的生长速度下的稳态生长区组织. 在定向凝固过程中经历下列反应: L→Ti₅Si₃, L→α+Ti₅Si₃, α→α₂(Ti₃Al)+γ(TiAl), α₂→γ+Ti₅Si₃, 其中, α 与Ti₅Si₃ 共晶是合金最显著的凝固行为. 当生长速度大于20 μm/s 时, 还出现L→γ+Ti₅Si₃. 随着生长速度增大, 稳态组织逐渐由粗胞晶向细胞晶、胞状枝晶及枝晶转变, 起稳定α相作用的Ti₅Si₃ 相由低速时分布于α相中逐渐向高速时分布于凝固γ 相中转变, 不利于该合金的引晶. 选择10 μm/s 的初始生长速度, 既能减少到达稳态生长的距离, 又能保证引晶效果.     

Morphologies of intermetallic compound phases in Sn-Cu and Sn-Co peritectic alloys during directional solidification

The morphologies of intermetallic phases (IMCs) during directional solidification of the Sn-Cu (L+Cu₃Sn→Cu₆Sn₅) and Sn-Co (L+CoSn→CoSn₂) peritectic systems were analyzed. The primary Cu₃Sn and peritectic Cu₆Sn₅ phases in Sn-Cu alloy are IMCs whose solubility ranges are narrow, while both the primary CoSn and peritectic CoSn₂ phases in Sn-Co alloy are IMCs whose solubility ranges are nil in equilibrium condition. The experimental results before acid corrosion shows that the dendritic morphology of both the Cu₆Sn₅ and CoSn₂ phases can be observed. The investigation on the local dendritic morphology after deep acid corrosion shows that these dendrites are composed of small sub-structures with faceted feature. Faceted growth of the primary Cu₃Sn and CoSn phases is also confirmed, and a faceted to non-faceted transition in their morphologies is observed with increasing growth velocities. Further analysis shows that the dendritic morphology is formed in the solidified phases whose solubility range is larger during peritectic solidification.

     

Influence of a high magnetic field on columnar dendrite growth during directional solidification

The influence of a high magnetic field on the growth of MnBi, α-Al and Al₃Ni dendrites in directionally solidified Bi–Mn, Al–Cu and Al–Ni alloys have been investigated. Results indicate that the magnetic field changes the dendrite growth significantly. Indeed, the magnetic field aligns the primary dendrite arm and the effect is different for different dendrites. For the MnBi dendrite, an axial high magnetic field enhanced the growth of the primary dendrite arm along the solidification direction; however, for the α-Al and Al₃Ni dendrites, the magnetic field caused the primary dendrite arm to deviate from the solidification direction. At a lower growth speed, a high magnetic field is capable of causing the occurrence of the columnar-to-equiaxed transition (CET). Moreover, it has also been observed that a high magnetic field affects the growth of the high-order (i.e., secondary and tertiary) dendrite arms of the α-Al dendrite at a higher growth speed; as a consequence, the field enhances the branching of the dendrite and the formation of the (1 1 1)-twin planes. The above results may be attributed to the alignment of the primary dendrite arm under a high magnetic field and the effect of a high magnetic field on crystalline anisotropy during directional solidification.     

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.     

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。     

Pb-Bi包晶合金定向凝固微观组织演化

对Pb-(26,28,30,34)Bi(质量分数,%,下同)包晶合金进行平界面生长的低速定向凝固到枝晶状生长的高速定向凝固实验,研究了Pb-Bi包晶合金的微观组织形成及其演化。实验结果表明,在温度梯度G=30K/mm条件下,当凝固速度V=0.25μm/s时,初生α相和包晶β相均以平界面生长,凝固组织的演化过程为:单相初生α相→两相竞争组织→β单相。V=0.5μm/s时,定向凝固组织的演化过程为:单相初生α相→胞状α相+胞间包晶β相→α+β两相竞争组织→β单相。在G=20K/mm条件下,当凝固速度V=1μm/s时,初生α相以胞状领先生长,包晶β相则在胞状α间形核生长,并包裹住α胞。当凝固速度增加至V≥2μm/s时,初生α相由胞状转变为枝晶状,包晶β相则在枝晶间包围α枝晶。     

DZ125高温合金深过冷凝固组织转变规律

采用熔盐净化剂与循环过热相结合的方法,获得了过冷度高达180 K的DZ125高温合金深过冷熔体,研究了合金深过冷凝固的组织演化过程.结果表明,随着过冷度△T的增大,凝固组织经历3次转变过程:当△T<48 K时,合金的凝固组织为普通树枝晶;当48 K≤△T<85 K时,枝晶因再辉发生熟化和重熔,组织转化为第1类粒状晶;当85 K≤△T<160 K时,再辉所产生的重熔效应大大降低,凝固组织为深过冷树枝晶;当△T≥160 K时,发生枝晶破碎及再结晶,凝固组织转变为第Ⅱ类粒状晶.     

Microstructure evolution of Cu-Pb monotectic alloys during directional solidification

1 Introduction Monotectic alloy is an important class of alloy whose binary phase diagram has a miscibility gap, in which the original single liquid will decompose into two distinct immiscible liquids within a few seconds. In the normal gravity field, a …     

Ti-Al合金定向凝固过程中胞/枝晶间距选择的计算机模拟

利用溶质扩散控制模型对Ti-Al合金定向凝固初始阶段变速冷却过程中胞/枝晶转变过程进行了数值模拟。在给定的冷却速率下,枝晶臂间距大于胞晶臂间距,而在过渡区,枝晶间距达到最大。另外,模拟结果也显示,晶核数量对柱状晶间距产生影响,随着植入晶核数量的增加,柱状晶间距非均匀化程度明显减小。出现过渡区的原因与枝晶生长所引起固/液界面前沿成分波动有关。模拟与试验结果吻合较好。     

生长速度与试样直径对定向凝固Ti-46Al-8Nb合金显微组织和硬度的影响

对Ti-46Al-8Nb（摩尔分数,%）合金进行布里奇曼型定向凝固实验,考察生长速度和试样直径对合金显微组织、相变路径和硬度的影响。结果表明,随着生长速度的增加和试样直径的减小,凝固过程由完全β相凝固转变为具有包晶反应的凝固过程,其最终显微组织为α2/γ层片及有α2/γ层片和B2相组成的多相组织。以上结果是由扩散和对流的减弱造成的溶质富集而引起的。包晶反应的发生往往导致严重的溶质偏析,其中溶质Al和Nb的偏析使得层片组织较为粗大。因此,在较高生长速度下发生包晶反应时,合金硬度值急剧下降,硬度曲线随着生长速度的增加呈不连续变化。严重溶质偏析导致的粗大层片组织也使得该成分合金的硬度低于其他Ti Al基合金的硬度。     

Quantitative phase field simulation of deep cells in directional solidification of an alloy

The formation of deep cells after the onset of Mullins–Sekerka instability during the thin-film directional solidification of a succinonitrile/acetone alloy has been simulated quantitatively by phase field modeling. The solute trapping introduced by the diffusive interface is corrected by a simple interface model, so that at the interface the equilibrium segregation is restored and the Gibbs–Thompson relation is satisfied. With the increasing pulling speed, the transitions from planar to λ_c/2 shallow cells, smaller wavelength finite-depth cells, and deep cells are clearly illustrated. The formation of deep cells with change of overall morphologies is performed, and its wavelength transition is consistent with the reported experiments. Furthermore, during the development of a cellular pattern starting from a planar interface, the crossover wavelength under different solidification speeds, where the deformation is comparable to the wavelength, agrees reasonably well with the Warren–Langer theory.     

Phase Selection and Microhardness of Directionally Solidified AlCoCrFeNi2.1 Eutectic High-Entropy Alloy

In the present work, the solidi?cation behaviors and microhardness of directionally solidi?ed AlCoCrFeNi_2.1 eutectic highentropy alloy (EHEA) obtained at different growth velocities are investigated. The microstructure of the as-cast AlCoCrFeNi _2.1 EHEA is composed of bulky dendrites (NiAl phase) and lamellar eutectic structures, indicating that the actual composition of the alloy slightly deviates from the eutectic point. However, it is interesting to observe that the full...     

Cellular/dendritic transition,dendritic growth and microhardness in directionally solidified monophasic Sn-2%Sb alloy

Horizontal directional solidification experiments were carried out with a monophasic Sn-2%Sb (mass fraction) alloy to analyze the influence of solidification thermal parameters on the morphology and length scale of the microstructure. Continuous temperature measurements were made during solidification at different positions along the length of the casting and these temperature data were used to determine solidification thermal parameters, including the growth rate (V_L) and the cooling rate (T_R). High cooling rate cells and dendrites are shown to characterize the microstructure in different regions of the casting, with a reverse dendrite-to-cell transition occurring for T_R>5.0 K/s. Cellular (l_c) and primary dendrite arm spacings (l₁) are determined along the length of the directionally-solidified casting. Experimental growth laws relating l_c and l₁ to V_L and T_R are proposed, and a comparative analysis with results from a vertical upward directional solidification experiment is carried out. The influence of morphology and length scale of the microstructure on microhardness is also analyzed.