Numerical study of heat transfer and solidification behavior of gas-atomized Fe-6.5%Si (mass fraction) droplets

During spray atomization process, the heat transfer and solidification of droplets play very important roles for the deposition quality. Due to the difficulties of experimental approach, a numerical model is developed, which integrates liquid undercooling, nucleation recalescence and post-recalescence growth to present the full solidification process of Fe-6.5%Si (mass fraction) droplet. The droplet velocity, temperature, cooling rate as well as solid fraction profiles are simulated for droplets with different sizes to demonstrate the critical role of the size effect during the solidification process of droplets. The relationship between the simulated cooling rate and the experimentally obtained secondary dendrite arm spacing is in excellent agreement with the well-established formula. The pre-constant and exponent values lie in the range of various rapid solidified Fe-based alloys reported, which indicates the validity of the numerical model.     

Non-equilibrium solidification of undercooled droplets during atomization process

Thermal history of droplets associated with gas atomization of melt has been investigated. A mathematical model, based on classical theory of heterogeneous nucleation and volume separation of nucleants among droplets size distribution, is described to predict undercooling of droplets. Newtonian heat flow condition coupled with velocity dependent heat transfer coefficient is used to obtain cooling rate before and after nucleation of droplets. The results indicate that temperature profile of droplets in the spray during recalescence, segregated and eutectic solidification regimes is dependent on their size and related undercooling. The interface temperature during solidification of undercooled droplets rapidly approaches the liquidus temperature of the alloy with a subsequent decrease in solid-liquid interface velocity. A comparison in cooling rates of atomized powder particles estimated from secondary dendrite arm spacing measurements are observed to be closer to those predicted from the model during segregated solidification regime of large size droplets.     

Solidification of undercooled Ni-32.5 wt% Sn eutectic alloy

Bulk Ni-32.5 wt % Sn alloy was undercooled by purification. The solidification characteristics at different undercoolings and the various microstructures were studied. It was found that the two eutectic phases can grow in a matching form, to produce regular eutectic structures if the melt was undercooled by less than 10 K. If the melt was highly undercooled, the dendrite tip velocity of the Ni₃Sn phase was very much larger than that of Ni() phase during recalescence; as a result, the melt did not solidify in the regular eutectic morphology but in the dendrite cluster morphology with Ni₃Sn phase acting as the leading phase in the recalescence stage. The dendrite clusters subsequently developed into anomalous eutectic microstructures by ripening of Ni₃Sn dendrites and growth of Ni() phase between the Ni₃Sn arms. If the undercooling before nucleation was below 130 K, bulk melt of the original composition Ni-32.5 wt % Sn existed between the dendrite clusters after recalescence, which then solidified into regular eutectic microstructures. As a result, the structure of the sample consisted of regular eutectic zones and anomalous eutectic zones. If the undercooling before nucleation was above about 130 K, no bulk melts existed after recalescence, so the structures of the samples were completely anomalous eutectic.     

Progress of Nonequilibrium Solidification Theory

This paper summarized the theory related to nucleation, interface kinetics, micromorphology evolution and microscopic growth during nonequilibrium alloy solidification. Methods for quantitative analysis of nucleation rate, the criterion of marginal stability, nonequilibrium partition coefficient, as well as the relationship between growth rate with undercooling and dendrite tip radius are presented. Some limitations and future developments of nonequilibrium theory are pointed out.     

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。     

Sn-Pb合金微粒的制备和微结构

采用均匀颗粒成型法(Uniform Droplet Spray—UDS)制备出Sn—5％Pb合金微粒，颗粒的粒度分布均匀，性能一致．用非绝热容量法测量了在N2—2％H2气氛下Sn—5％Pb微粒的焓，井分析了颗粒的显微结构，结果表明：Sn—5％Pb微粒具有较大的过冷度和亚稳态结构．     

Comparison of microstructure and solidification behavior of rapid quenching with bulk undercooled superalloy

Microstructure and solidification behavior in rapid quenching (i.e., gas-atomized powders and melt-spun ribbons) of superalloy have been compared with bulk undercooled superalloy. The application of a molten salt denucleating technique combined with thermal cycle enables such investigation over a wide range of undercooling up to 210 K. The microstructure formation has been discussed for both methods of solidification with respect to undercooling, nucleation, and recalescence as well as recrystallization during post-recalescence. Comparison of the observed microstructure and morphologies indicates that the melt-spun ribbons and the gas-atomized powders with cooling rate above 10⁴K sec^–1crystallize only after achieving a large degree of undercooling, which becomes higher and higher with the increase of cooling rate. Furthermore, it should be noted that, grain refinements, which play a decisive role in the undercooled as-solidified structure, however, result from different sources in the rapid quenching process.     

Numerical simulation of the thermal history of droplets during multi-stage atomization

Analyses are made on the characteristics of cooling and undercooled solidification of multi-stage atomized aluminum droplets. Models are established for Newtonian cooling, highly undercooled heterogeneous nucleation and steady-state continuous growth. They are used for numerical simulation of the thermal history of the droplets and the effects of the main atomization process parameters such as the extent of superheat and the speed of the rotating disk. Results show that large undercooling occurs mainly in the later stage of multi-stage atomization while recalescence and rapid quenching take place mainly in the forced cooling stage. The undercooling and cooling rates of the droplets are primarily dependent on the droplet diameter, and the main atomization parameters have little effect on the nucleation and solidification behavior of the droplets.     

Numerical simulation of the thermal history of droplets during multi-stage atomization

Analyses are made on the characteristics of cooling and undercooled solidification of multi-stage atomized aluminum droplets. Models are established for Newtonian cooling, highly undercooled heterogeneous nucleation and steady-state continuous growth. They are used for numerical simulation of the thermal history of the droplets and the effects of the main atomization process parameters such as the extent of superheat and the speed of the rotating disk. Results show that large undercooling occurs mainly in the later stage of multi-stage atomization while recalescence and rapid quenching take place mainly in the forced cooling stage. The undercooling and cooling rates of the droplets are primarily dependent on the droplet diameter, and the main atomization parameters have little effect on the nucleation and solidification behavior of the droplets.     

The solidification process of highly undercooled bulk Cu-O melts

The effect of undercooling on grain structure was investigated in pure copper and alloys up to Cu 0.39wt% 0 (eutectic composition), in which grain refinement does not occur at any degree of bath undercooled when the oxygen content is less than 300 p.p.m. Grain refinement occurs in these alloys when the oxygen content exceeds about 300 p.p.m. and the undercooling prior to nucleation exceeds 100 K without quenching. Fragmentation affects primary, secondary and tertiary dendrite arms during and after recalescence. Quenching after recalescence at various solidification times retains transient grain structures. When the sample, which should have achieved complete grain refinement by furnace cooling, is quenched immediately after nucleation, the structure shows a trace of radiating fan-shaped grains originating from a single point of nucleation.     

Al-4％Cu合金定向凝固枝晶／胞晶转变速率的研究

通过实验和理论对比研究Al-4%(质量分数)Cu合金定向凝固胞晶/枝晶转变过程,得到胞晶/枝晶转变发生在尖端半径变化的拐点处。采用KGT模型与非平衡效应研究与胞晶/枝晶转变过程相对应的高速枝晶/胞晶转变特征。结果表明:尖端半径和界面温度均随抽拉速率的增加而减小,到达临界值后又急速增大。枝晶/胞晶转变发生在尖端半径和界面温度的拐点处,即在尖端半径和界面温度最小时发生转变;溶质截留在枝晶/胞晶转变过程中作用明显,大大减小了微观偏析。     

Solidification of Atomized Liquid Droplets

The overall analysis of the microstructures developed during atomized droplet solidification requires an understanding of the nucleation and growth kinetics as well as the thermal history that operate during processing. Following the subdivision of a liquid volume into droplets, the basic nature of nucleation as a stochastic process and the activity of various catalysts play a major role in determining the droplet microstructure. Droplet thermal history including liquid undercooling and recalescence under the influence of the external cooling rate is another important component of the solidification behavior and microstructure development in alloys and the particle incorporation modes that can be observed in composite processing. The central role of kinetic control and thermal history is highlighted near a phase selection transition where the kinetic competition can result in drastic microstructure changes that are sensitive to slight variations of the processing conditions.     

Modelling of dendritic solidification using finite element method

Abstract

Computer based numerical modelling of solidification is being increasingly used in an effort to develop and improve casting processes, a long term goal of this work being the prediction of microstructural features such as grain shape, size, and dendrite arm spacings throughout a casting. In a numerical heat flow model this can be achieved only through the inclusion of the kinetics of nucleation and dendrite growth. In the present paper strategies for including columnar and equiaxed solidification kinetics into a finite element model are reviewed. A detailed model for columnar solidification is then presented together with results obtained from calculations on an Al–5 wt-%Cu alloy and a multicomponent nickel based superalloy. It is shown that the inclusion of a dendrite tip undercooling is important, particularly in systems having a low Stefan number. Furthermore, the thermal histories in the superalloy can only be accurately calculated if an experimentally determined solid fraction versus temperature relationship is employed. A model for equiaxed solidification is also discussed and results obtained for an Al–5 wt-%Cu alloy outlined. In particular, the effects of heat transfer coefficient, heterogeneous nucleation site density, and nucleation undercooling on the grain size variation along a one dimensional casting have been examined. Finally, it is shown that grain sizes predicted by the present finite element model agree reasonably well with those of a previous numerical model for an Al–7 wt-%Si alloy.

MST/1468     

相场法模拟Zn-Al二元合金凝固过程中的枝晶生长

建立了与温度场和溶质场相耦合的 Zn-Al 二元合金枝晶生长的相场模型,用相场法模拟了枝晶形貌及生长过程。通过分析得到的图像,研究了各向异性强度系数、界面动力学系数以及界面能对枝晶生长形貌和枝晶尖端生长速度的影响。结果表明：随着各向异性强度系数的增大,枝晶生长速率增加,且容易出现二次支臂。此外,界面动力学系数和界面能的增大也会不同程度地加速枝晶生长速率并对二次支臂的产生有着较为明显的促进作用。     

Phase-field modelling on effect of pressure on growth kinetics of Mg–Al–Sn alloy

The effects of pressure on dendritic growth kinetics of Mg–Al–Sn alloy were investigated using a ternary phase-field model coupled with thermodynamics with pressure effects and experiments. The results showed that the improved growth velocity and nucleation rate caused by pressure had the opposite effects on grain size. For one-grain growth, the dendrite was larger and more developed under pressure of 85?MPa than that under ambient pressure owing to larger thermodynamic driving force, and thus higher growth velocity. However, when nucleation was considered in multigrain growth case, the average grain size under pressure was smaller owing to less growth space. Growth velocity decreased with the increase in Sn content, on which pressure had no great influence.     

Microstructure evolution in equiaxed dendritic growth

Microstructure evolution in equiaxed dendritic solidification is investigated through the study of free dendritic growth in a supercooled melt. A detailed measurement of microstructural features (such as side-branch spacings, envelope shape, projection area, and contour length) of freely growing succinonitrile dendrites is performed using images from the microgravity experiment of Glicksman and co-workers. The measurements show that the microstructure evolution of an equiaxed dendrite is divided into two regimes: an initial linear regime and a subsequent non-linear coarsening regime. It is found that unique scaling relations exist between the measured geometry parameters and the primary tip radius or speed for both regimes. The underlying mechanisms involved in dendritic structure evolution are discussed. In addition, using the phase-field method, we perform numerical experiments to investigate the effects of melt convection on equiaxed dendritic growth. The dendrite tip operating state (i.e. the tip velocity and radius) is quantitatively evaluated as a function of the flow velocity and dendrite orientations and compared with Microscopic Solvability Theory. Other structural features (such as the side-branches) of an equiaxed dendrite in the presence of flow are also examined in order to show how convection influences microstructure evolution in equiaxed dendritic growth.     

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.     

A Modified Cellular Automaton Model for the Quantitative Prediction of Equiaxed and Columnar Dendritic Growth

Since the characteristic of dendrite is an important factor determining the performance of castings, a twodimensional cellular automaton model with decentered square algorithm is developed for quantitatively predicting the dendritic growth during solidification process. The growth kinetics of solid/liquid interface are determined by the local equilibrium composition and local actual liquid composition, and the calculation of the solid fraction increment is based on these two compositions to avoid the solution of growth velocity. In order to validate the developed model, quantitative simulations of steady-state dendritic features over a range of undercooling was performed and the results exhibited good agreement with the predictions of LGK（Liptone Glicksman-Kurz） model. Meanwhile, it is demonstrated that the proposed model can be applied to simulate multiple equiaxed dendritic growth, as well as columnar dendritic growth with or without equiaxed grain formation in directional solidification of AleC u alloys. It has been shown that the model is able to simulate the growth process of multi-dendrites with various preferential orientations and can reproduce a wide range of complex dendritic growth phenomena such as nucleation, coarsening of dendrite arms, side branching in dendritic morphologies, competitive growth as well as the interaction among surrounding dendrites.     

Effect of Brownian Coagulation on the Liquid-liquid Decomposition in Gas-atomized Alloy Drops

Modeling and simulation have been carried out for Al-Pb alloys to investigate the Brownian coagulation effect on the microstructure development in a gas-atomized drop during the liquid-liquid decomposition. The results indicate that Brownian coagulation has a weak effect on the nucleation and a relatively strong effect on coarsening the minority phase droplets. The influence of Brownian coagulation on the liquid-liquid decomposition decreases with the increase in the diameter （or the decrease in the cooling rate） of the atomized drop.     

Carbide Formation Process in Directionally Solidified MAR-M247 LC Superalloy

1.IntroductionSeveralphasesforminthesolidificationandcool-.ingprocessofcastsuperalloys['].MCcarbidesand7'precipitatesarethemainphasestoprovidehightemperaturestrengthinthesuperalloys.TheMCcarbidesstrengthengrainboundariesandsub-grainboundariesatelevatedtemperature.Theirvolumefraction,sizeandmorphologyhaveaveryimpor-tanteffectonthemechanicalpropertiesofNi-basesuperalloys['l.Considerable..,..,.h.s[3~14]havebeencarriedoutfromslowtorapidsolidificationconditionstocharacterizethesequenceofformation…