Computer Simulation of Solidification Transport Behaviours in Blade‐Like Castings under Transverse Static Magnetic Fields up to 25T

Numerical simulation of solidification transport phenomena/processes in a TiAl alloy blade‐like casting, under transverse magnetic fields of different strengths, was carried out. The simulation was based on a continuum solidification model and the computer codes developed by the authors. The simulation results show that, although the liquid flow in the bulk liquid region can be suppressed efficiently, the feeding flow in the mushy zone caused by the volume contraction, due to solidification shrinkage and thermal/solutal expansion, cannot be suppressed even under an ultra‐strong magnetic field up to 25T. This indicates that the forces driven by volume contraction are much stronger than those caused by the gravity. The natural convection can delay the directional solidification process, while the applied static magnetic field accelerates it to some extent, by weakening the natural convection. The magnetic field changes the coupled heat and species mass transfer to a diffusion type mechanism. The natural convection may be the cause for horizontal segregation. An ultra‐strong magnetic field is not necessary to achieve sufficient suppression of natural convection.     

Effects of a High Magnetic Field on the Microstructure of Ni-Based Single-Crystal Superalloys During Directional Solidification

High magnetic fields are widely used to improve the microstructure and properties of materials during the solidification process. During the preparation of single-crystal turbine blades, the microstructure of the superalloy is the main factor that determines its mechanical properties. In this work, the effects of a high magnetic field on the microstructure of Ni-based single-crystal superalloys PWA1483 and CMSX-4 during directional solidification were investigated experimentally. The results showed that the magnetic field modified the primary dendrite arm spacing, γ′ phase size, and microsegregation of the superalloys. In addition, the size and volume fractions of γ/γ′ eutectic and the microporosity were decreased in a high magnetic field. Analysis of variance (ANOVA) results showed that the effect of a high magnetic field on the microstructure during directional solidification was significant (p < 0.05). Based on both experimental results and theoretical analysis, the modification of microstructure was attributed to thermoelectric magnetic convection occurring in the interdendritic regions under a high magnetic field. The present work provides a new method to optimize the microstructure of Ni-based single-crystal superalloy blades by applying a high magnetic field.     

Influence of Forced/Natural Convection on Segregation During the Directional Solidification of Al-Based Binary Alloys

We analyzed the columnar solidification of a binary alloy under the influence of an electromagnetic forced convection of various types and investigated the influence of a rotating magnetic field on segregation during directional solidification of Al-Si alloy as well as the influence of a travelling magnetic field on segregation during solidification of Al-Ni alloy through directional solidification experiments and numerical modeling of macrosegregation. The numerical model is capable of predicting fluid flow, heat transfer, solute concentration field, and columnar solidification and takes into account the existence of a mushy zone. Fluid flows are created by both natural convection as well as electromagnetic body forces. Both the experiments and the numerical modeling, which were achieved in axisymmetric geometry, show that the forced-flow configuration changes the segregation pattern. The change is a result of the coupling between the liquid flow and the top of the mushy zone via the pressure distribution along the solidification front. In a forced flow, the pressure difference along the front drives a mush flow that transports the solute within the mushy region. The channel forms at the junction of two meridional vortices in the liquid zone where the fluid leaves the front. The latter phenomenon is observed for both the rotating magnetic field (RMF) and traveling magnetic field (TMF) cases. The liquid enrichment in the segregated channel is strong enough that the local solute concentration may reach the eutectic composition.     

Phase‐Field Simulation of Solidifying Microstructure in the Presence of a Convective Field

Here we present a contribution to the microstructure based design of new steel alloys by a careful investigation of multiphase microstructure solidification in a convective field. To this end we present an extension of the quantitative phase‐field model proposed in [1] to investigate the influence of hydrodynamic convection on the growth of eutectic/peritectic alloys. We study directional solidification of a eutectic alloy under the influence of a shear flow ahead of the solidifying front. We mainly investigate the growth of a eutectic lamellar structure. We show that the imposed flow tilts the whole lamellar structure away from the flow direction. Moreover, we show that forced flow alters the growth morphology of Fe‐Ni peritectic alloys, having a strong influence on the nucleation of the peritectic phase. Based on these investigations, a scale relation between the strength of flow and the solid volume fraction is derived. Further we propose an application of these models as an alternative approach to study heterogeneous nucleation kinetics in the solidification of peritectic materials systems.     

强制对流影响下Fe?C合金定向凝固微观组织的相场法研究

定向凝固技术能够获得特定柱状晶结构,对于优化合金轴向力学性能具有非常显著的效果。本文采用耦合流场的相场模型模拟了定向凝固过程中枝晶的生长过程,研究了各向异性系数、界面能对定向凝固枝晶生长的影响以及强制对流作用下枝晶的生长行为。数值求解过程中,选用基于均匀网格的有限差分方法对控制方程进行离散,实现了格子中标记点算法（MAC）和相场离散计算方法的联合求解。处理微观速度场和压力场耦合时,采用MAC算法求解Navier-Stokes方程和压力Poisson方程,采用交错网格法处理复杂的自由界面。结果表明:随着各向异性系数的增大,枝晶尖端生长速度增大,曲率半径减小,枝晶根部溶质浓度逐渐降低;随着界面能的增大,枝晶尖端曲率半径增大,当界面能为最大（0.6 J·m?2）时,凝固呈现平界面的凝固方式向前推进;强迫对流对定向凝固枝晶生长方向影响较大,上游方向定向凝固枝晶粗大且生长速度更快,其现象随流速的增大而愈加明显。      

外磁场在定向凝固过程中的应用研究

以磁场对合金凝固组织的影响为基础,综述了近年来交变磁场和稳恒磁场在定向凝固过程中的应用和发展,总结了外磁场对定向凝固过程中合金微观组织的作用机制,并展望了今后的研究方向。     

相场法在金属凝固过程的应用现状

相场法是在计算材料学中发展最快的一种强大的计算方法,以基本的热力学和动力学为输入,可用于模拟和预测材料的介观尺度形貌和微观结构的演变。首先总结了相场模型的历史发展、物理基础、数学表达及其数值求解,其次分析了相场法在纯物质、二元合金、多组分系统以及定向凝固、增材制造等领域中的应用情况,最后对相场法进行了总结及展望,并指出相场法发展应趋向于超大尺度相场模拟技术,更高效算法的开发,相场模型与热力学、动力学数据库的结合,工业应用的探索以及与实验观察技术的进一步结合。     

超磁致伸缩材料的研究新进展

近年来,稀土超磁致伸缩TbDyFe材料的研究进展迅速,既有新的研究方向如材料力学性能、合金的凝固过程、磁畴取向的分布、组分处于准同型相界的合金的性能等,也有传统的如热处理时施加高磁场及应力处理、新热处理方法等方面。此外,科研人员不断开发出新的稀土超磁致伸缩材料合金体系,即不同元素对TbDyFe体系的部分取代与添加,主要有Pr、Nd、Sm、Gd、Ho和Er等稀土元素及第八族的Co元素。     

Solidification of metallic alloys under magnetic fields

The present paper is aimed at showing how solidification of metallic alloys can be influenced by AC or DC magnetic fields through various types of effects. The application of AC magnetic fields leads to the generation of either fluid flows or vibration. It has been shown both numerically and experimentally that the electromagnetically-driven flows created by travelling or rotating magnetic fields promoted segregations and influenced their distribution. The flow may also promote the CET thanks to its effects on both the temperature and solute fields as well as the possible fragmentation mechanism. As far as DC magnetic fields are concerned, it was known that they usually exert a damping of the bulk fluid flows. However, it has been shown recently that for some alloys high intensity magnetic field interacts with the small thermoelectric current to create significant electromagnetic forces which are responsible for strong liquid metal flows both in the bulk and in the mushy zone. Orientation changes as well as possible modifications of thermodynamic properties were also observed.     

Natural Convection and Columnar-to-Equiaxed Transition Prediction in a Front-Tracking Model of Alloy Solidification

A meso-scale front-tracking model (FTM) of nonequilibrium binary alloy dendritic solidification has been extended to incorporate Kurz, Giovanola, and Trivedi (KGT) dendrite kinetics and a Scheil solidification path. Model validation via comparison with thermocouple measurements from a solidification experiment, in which natural convection is limited by design, is presented. Via solution of the flow field due to natural thermal buoyancy, it is shown that resultant liquid-phase convection creates conditions in which equiaxed solidification is favored. Comparison with simulations in which casting solidification is diffusion controlled show that natural convection has greatest effect at intermediate times, but that at early and late stages of columnar solidification, the differences are relatively small. It is, however, during the time of greatest divergence between the simulations that the authors’ predictive index for equiaxed zone formation is enhanced most by convection. Finally, the columnar-to-equiaxed transition is directly simulated, in directional solidification controlled by diffusion. This article is based on a presentation made in the symposium entitled “Solidification Modeling and Microstructure Formation: in Honor of Prof. John Hunt,” which occurred March 13–15, 2006 during the TMS Spring Meeting in San Antonio, Texas, under the auspices of the TMS Materials Processing and Manufacturing Division, Solidification Committee.     

Flow effects on the dendritic microstructure of AlSi-base alloys

Fluid flow changes heat and mass transport during solidification, thereby affecting the evolution of the microstructure. In order to quantify effects of convection, it is important that fluid flow can be modified experimentally. We performed directional solidification experiments with binary AlSi alloys of different compositions, using a microgravity environment for diffusive solidification and adding rotating magnetic fields to generate flow. Flow velocities up to 10 mm/s and various solidification velocities were realized while maintaining a constant temperature gradient at the solid-liquid interface. The microstructure observed in samples processed on earth and in space is characterized by primary and secondary dendrite arm spacing and the fractal dimension of the dendrites. It is found that fluid flow usually accelerates growth and coarsening of the dendritic structures and leads to new kinetic laws. The branching of dendritic networks, however, is hardly affected by flow.     

An Improved Model for the Flow in an Electromagnetically Stirred Melt during Solidification

A mathematical model for simulating the electromagnetic field and the evolution of the temperature and velocity fields during solidification of a molten metal subjected to a time-varying magnetic field is described. The model is based on the dual suspended particle and fixed particle region representation of the mushy zone. The key feature of the model is that it accounts for turbulent interactions with the solidified crystallites in the suspended particle region. An expression is presented for describing the turbulent damping force in terms of the turbulent kinetic energy, solid fraction, and final grain size. Calculations were performed for solidification of an electromagnetically stirred melt in a bottom chill mold. It was found that the damping force plays an important role in attenuating the intensity of both the flow and turbulent fields at the beginning of solidification, and strongly depends on the final grain size. It was also found that turbulence drops significantly near the solidification front, and the flow becomes laminarized for solid fraction around 0.3.     

Comparison of nucleation and growth mechanisms in alloy solidification to those in metallic glass crystallisation — relevance to modeling

The development of microstructure during phase transformations is often best understood by considerations of nucleation in the parent material followed by growth of the new phase. This is a mature research field in alloy solidification, thanks to extensive investigations of nucleation and dendritic growth in cooling alloy melts. Bulk metallic glasses, on the other hand, typically do not form crystals on cooling from above the liquidus to below the glass transition temperature, resulting in very strong hard materials. As BMG toughness can be enhanced by a crystallising anneal, the study of nucleation and growth of crystals in viscous multi-component liquids has become an important topic for study. Such devitrification can lead to crystalline-glass composites or bulk nano-crystalline alloys, and the micro- or nano-structure is controlled by phenomena such as diffusion of solute and heat, and impingement dynamics. The relevance of solidification theories of nucleation, growth and impingement to crystallisation in amorphous alloys is discussed in this paper. The effects of the key differences between phase transformations in alloy casting processes and those in alloy devitrification on development of computational models for process simulation are highlighted.     

Casting of High Alloy Steels in the Mushy State

In order to broaden the field of application for the innovative thixocasting process, much research is dedicated to the thixocasting of high melting point alloys. The wide property range of modern high alloy steels combined with the productive semi‐solid die casting process opens up new fields of application. The Foundry Institute of the Aachen University has therefore been concentrating on the research of the possibilities and limits of high pressure die casting of high alloy steels in the semi‐solid state. This paper gives an overview of the current work dedicated to thixocasting of steel alloys by a high pressure die casting machine at the Foundry‐Institute of the Aachen University of Technology. In order to understand and describe the material properties in the semi‐solid state, basic test specimens have been investigated. Weak points of tool preheating as well as directional solidification of the produced parts can be controlled by numerical simulation of the temperature distribution inside the dies. In consideration of the outstanding flow properties of semi‐solid steels more complex geometries with accurately defined applications are now being investigated. Extensive metallographical analyses of the pre‐material, the reheated billets and the produced parts have been done to evaluate the viability of the process. The mechanical properties of the specimens outline the outstanding potential of the thixocasting process.     

Relationship between crystal growth mode, preferred orientation and magnetostriction of (Tb0.3Dy0.7)Fe1.95 alloys

The relationship between crystal growth mode, preferred orientation and magnetostrictive properties of (Tb0.3Dy0.7)Fe1.95 alloys was investigated at different directional solidification rates. The results showed that preferred orientation had a strong influence on the characteristics of (Tb0.3Dy0.7)Fe1.95 alloys. At lower solidification rates, the sample with <110> preferred orientation showed larger low-field magnetostriction and apparent compressive stress effect. The excessive solidification rate resulted in failure of preferred orientation and a poor magnetostrictive performance. With an increase in solidification rates, the crystal growth modes changed gradually from cellular and primary dendrite morphology to developed dendritic morphology. In addition, domain configurations were observed using magnetic force microscopy, and the change of magnetostrictive properties was interpreted in terms of revealing the domain configurations.     

Microstructure Formation in AlSi7Mg Alloys Directionally Solidified in a Rotating Magnetic Field

To produce high stressed automotive components like engine frames and cylinder heads in foundry industry often AlSi7Mg alloys are used. During mould filling and casting melt flow affects the development of the microstructure, which defines the mechanical properties. In this paper the microstructure formation in AlSi7Mg0.3 and AlSi7Mg0.6 alloys during directional solidification is investigated. To induce a forced melt flow a rotating magnetic field is applied. For that purpose a Bridgman‐type gradient furnace is equipped with a rotary ring magnet. For detailed investigation of the shape of the solid‐liquid interface and the primary dendrite spacing a decanting device is used. As a result, the forced melt flow substantially changes the dendritic solidification microstructure. The rotating magnetic field generates a radial secondary flow in and ahead of the mushy zone, which causes an enrichment of eutectics in the centre of the samples. At lower solidification velocities this locally leads to the transition to mixed columnar‐equiaxed or even to equiaxed growth. In that case the solid‐liquid interfaces of the decanted samples show a significant depression in the centre part. In the out‐of‐centre region columnar growth still exists and the primary dendrite spacing decreases with increasing melt flow.     

Determination of single crystals' elastic constants from the measurement of ultrasonic velocity in the polycrystalline material

In order to determine the crystal elastic properties and to investigate the influence of external factors such as applied stresses, magnetic fields and temperature on the elastic properties, sufficiently large single crystals are required. However, for some materials, such large single crystals are difficult to grow. In view of this difficulty, an attempt has been made to determine the elastic constants of cubic crystals from ultrasonic velocities measured in polycrystalline textured materials. Based on the ultrasonic-velocity measurement and the orientation distribution function (ODF) of crystallines in the polycrystalline aggregate, the single crystals' elastic constants can be obtained.     

Solidification of Silicon for Solar Cells

Silicon is the dominating material in solar cells. Monocrystalline and multicrystalline cells have approximately equal market shares and are produced from wafers, cut from single crystals produced by Czochralski (CZ) pulling or from polycrystalline ingots made by directional solidification, respectively. The present paper reviews how demands for lower cost, better yield, higher efficiency and use of less pure silicon in solar cells are addressed by advanced solidification processing. In monocrystalline solar silicon, careful growth control results in less point defects, and better efficiency. Continuous- or semi-continuous CZ growth processes are being developed for better productivity and lower cost. In multicrystalline solar silicon, extended defects such as dislocations and grain boundaries decrease efficiency, particularly in combination with new, less expensive, but more contaminated silicon feedstock. This problem is addressed by control of nucleation and growth of ingots with larger grains, preferred grain orientation and lower dislocation density.     

Influence of Pressure Field in Melts on the Primary Nucleation in Solidification Processing

It is well known that external fields applied to melts can cause nucleation at lower supercoolings, fragmentation of growing dendrites, and forced convection around the solidification front. All these effects contribute to a finer microstructure of solidified material. In this article, we analyze how the pressure field created with ultrasonic vibrations influences structure refinement in terms of supercooling. It is shown that only high cavitation pressures of the order of 10⁴ atmospheres are capable of nucleating crystals at minimal supercoolings. We demonstrate the possibility of sononucleation even in superheated liquid. Simulation and experiments with water samples show that very high cavitation pressures occur in a relatively narrow zone where the drive acoustic field has an appropriate combination of pressure amplitude and frequency. In order to accurately predict the microstructure formed by ultrasonically assisted solidification of metals, this article calls for the development of equations of state that would describe the pressure-dependent behavior of molten metals.     

纵向磁场拉制硅单晶的工艺研究

用常规CZ法拉制的硅单晶质量与VLSI对材料的要求有较大差距。MCZ法可以抑制硅熔体的热对流,因而改变了硅单晶的氧含量和其他性能。作者采用VMCZ法详细地研究了磁场对硅熔体波动、温度起伏的影响,进而研究了磁场对热场分布、磁场对硅单晶中杂质的分布、磁场对硅单晶中氧、碳含量、磁场对硅单晶中微缺陷等的影响。发现:VMCZ的结果与资料报导的HMCZ数据相比有较大差别。通过调整拉晶参数也只能有限度地改善硅单晶的性能。