The Role of Side Arcing in the Global Energy Partition during Vacuum Arc Remelting of INCONEL 718

Non-steady-state ensemble arc behavior has been observed during the Vacuum Arc Remelting (VAR) of 508-mm-diameter ingots of INCONEL 718. The liquid metal flow in the melt pool of a 508-mm ingot during VAR has been simulated under two alternative sets of conditions: (1) a steady-state axisymmetrical arc distribution, as has been typically used in modeling work previously; and (b) a transient asymmetrical arc distribution. Due to the computational requirements, neither mass flux nor solidification were modeled; instead, the pool shape was fixed from measurements from a 508-mm-diameter ingot, and a constant pool wall temperature of 1609 K was used. The transient simulation assumed a localized Gaussian arc whose effective center was located at a distance of 0.1 m from the ingot centerline; this simulation rotated clockwise around the centerline with a period of 36 seconds. The steady-state model was simulated with axisymmetrical distributions of current and power input to the pool top surface calculated by time averaging the transient current and power inputs. The standard k-ε solver of ANSYS CFX 5.6 software was used for both simulations. The transient model results suggest that 5 seconds of asymmetrical arc behavior is enough to change the pool from steady state to transient and that, after 30 seconds, the flow is almost fully developed (at least to the accuracy of the model) and dominated by the Lorentz force. Aspects of the model results agree with key features of the melt pool observed during VAR. This article is based on a presentation given at the International Symposium on Liquid Metal Processing and Casting (LMPC 2007), which occurred in September 2007 in Nancy, France.

---

A Multiscale Transient Modeling Approach for Predicting the Solidification Structure in VAR-Processed Alloy 718 Ingots

This paper describes the development and validation of a comprehensive multiscale modeling approach capable of predicting at the mesoscopic scale level the ingot solidification structure and solidification-related defects commonly occurring during the vacuum arc remelting (VAR) process. The approach consists of a coupling between a fully transient macroscopic code and a mesoscopic solidification structure code. The predictions from the multiscale model, including grain morphology and size and columnar-to-equiaxed transition, were validated against experimental measurements for a 20-inch (508 mm) diameter VAR alloy 718 ingots. The validated model was then used to investigate the effects of melting rate and ingot diameter on the solidification structure of VAR processed 718 ingots.     

Ti2AlNb合金锭真空自耗过程宏观偏析的数值模拟

Ti₂AlNb合金锭的真空电弧重熔(VAR)是一种超高温且不透明冶金过程,很难对这一过程中的熔体流动行为和宏观偏析的形成过程进行试验研究。发展了基于欧拉多相流的电磁场、温度场、流场、溶质场的多场强耦合数学模型,研究了真空自耗过程中的多物理场相互作用机制,对Ti₂AlNb合金锭中成分偏析形成过程及分布规律进行了预测。模拟结果表明,电磁力主要分布于熔池表面,自感电磁力推动金属液由中心向下流动而加深熔池;搅拌电磁力的离心效应则大幅提升熔池的温度场均匀度,促使熔池内金属液中的溶质混合均匀。尽管铸锭外围和中心分别形成了大范围的正、负偏析区,但区域内的成分较为均匀。在搅拌和沉降的作用下,金属熔池中的等轴晶极大地缩短了铸锭中的柱状晶区。该模型的模拟结果在熔池深度与宏观偏析分布方面与试验结果吻合良好,可进一步应用于预测和研究工业级大型铸锭中的成分偏析。     

Study of the Formation Mechanism of A-Segregation Based on Microstructural Morphology

A model that combines a cellular automaton (CA) and lattice Boltzmann method (LBM) is presented. The mechanism of A-segregation in an Fe-0.34 wt pct C alloy ingot is analyzed on the basis of microstructural morphology calculations. The CA is used to capture the solid/liquid interface, while the LBM is used to calculate the transport phenomena. (1) The solidification of global columnar dendrites was simulated, and two obvious A-segregation bands appeared in the middle-radius region between the ingot wall surface and the centerline. In addition, the angle of deflection to the centerline increased with the increasing heat dissipation rate of the wall surface. When natural convection was ignored, the A-segregation disappeared, and only positive segregation was present in the center and bottom corner of the ingot. (2) Mixed columnar–equiaxed solidification was simulated. Many A-segregation bands appeared in the ingot. (3) Global equiaxed solidification was simulated, and no A-segregation bands were found. The results show that the upward movement of the high-concentration melt is the key to the formation of A-segregation bands, and remelting and the emergence of equiaxed grains are not necessary conditions to develop these bands. However, the appearance of equiaxed grains accelerates the formation of vortexes; thus, many A-segregation bands appear during columnar–equiaxed solidification.     

Quasi-steady-state characteristics of solidification of alloys made from VT3-1 alloy during vacuum arc remelting

Numerical calculations are presented of the depth of a liquid pool, time of local solidification, and temperature gradient in the axial region of an ingot during vacuum arc remelting (VAR) of VT3-1 titanium alloy (Ti-6.5Al-2.5Mo-1.5Cr-0.5Fe-0.3Si) corresponding to quasi-equilibrium conditions. Calculations were carried out for ingots of diameters D = 400, 800, and 1200 mm in the ranges of mass melting rates \(\dot M\) = 0.5–12.0, 0.5–35.0, and 1.5–30.0 kg/min, respectively. It is found that the depth of the liquid pool (H, mm) linearly increases with increasing \(\dot M\) and is virtually independent of D in the conditions under consideration and, therefore, can be presented as a unique dependence H = 66.63 \(\dot M\) + 71.91. A finite depth of the liquid pool at a zero mass melting rate is associated with that the state \(\dot M\) = 0 corresponds to a finite current of the arc, which holds a part of metal in the liquid state. It is shown that the time of local solidification depending on \(\dot M\) has a minimum associated with various physical processes, which determine the kinetics of the solidification front at small and large solidification rates. In relative units, which correspond to a minimum, these dependences are identical for all considered diameters of the ingot. In addition, based on autoradiographic investigations of solidification of VT3-1 alloy under the VAR conditions, critical values of the temperature gradient (G) and velocity of motion of the crystallization front (v) along the ingot axis, which determine the passage from the column structure to the equiaxial one, are determined. Starting from these results, the plots v(G) are constructed, which turn out to be very useful in the development of remelting modes, excluding the appearance of some type of liquation process. It is revealed that at the specified ingot diameter, the dependence v(G) is decreasing and, at the specified temperature gradient, the velocity of motion of the solidification front decreases as D increases, which indicates an increase in D for the smelting of the ingots of highly-doped alloys.     

USS122G钢锭真空电弧重熔工艺的数值模拟

 超高强度不锈钢以其超高强度和良好的韧性以及优异的耐腐蚀性能而广泛地应用在航空、航天等领域。真空自耗重熔(VAR)作为生产超高强度不锈钢铸锭的主要生产技术,具有去除钢中有害杂质、改善钢中元素偏析的功能。为了研究新型Cr-Co-Ni-Mo合金体系超高强度不锈钢USS122G的真空电弧重熔过程,通过工艺仿真优化软件(Melf-Flow-VAR),对VAR过程的宏观传热、传质和流动现象进行模拟,建立USS122G合金VAR过程的二维轴对称数学模型,预测了不同冷却速度下的温度场和熔池形貌,并着重分析了特定熔速下的温度场、流场的演变,有无氦气冷却的元素宏观偏析情况,最后以模拟工艺制备了USS122G合金660 mm铸锭进行验证。结果表明,熔速增加,熔池深度加深,熔池形貌由低熔速扁平状圆弧状高熔速深“U”变化,熔炼速率为4.5 kg/min的熔池形貌具有较窄的糊状区,在此熔速下,熔池形貌呈现圆弧状,且真空自耗炉的输入功率较低,流场模拟结果显示流体的流动方向沿边部向下,中部向上,在铸锭右侧呈现顺时针运动规律;模拟熔池在达到稳态后深度为132 mm,此时模拟熔池深度与实测结果基本一致;在熔炼过程中Cr和C元素均发生正向偏析,采用氦气冷却的铸锭中元素偏析程度较小,在距钢锭1/2R处到边部Cr和C元素分布规律与模拟结果吻合较好。本项研究成果为钢的工业化稳定生产提供了可靠的数据支撑。     

A Multiscale 3D Model of the Vacuum Arc Remelting Process

A three-dimensional, transient, multiscale model of the VAR process is presented, allowing novel simulations of the influence of fluctuations in arc behavior on the flow and heat transfer in the molten pool and the effect this has on the microstructure and defects. The transient behavior of the arc was characterized using the external magnetic field and surface current measurements, which were then used as transient boundary conditions in the model. The interactions of the magnetic field, turbulent metal flow, and heat transfer were modeled using CFD techniques and this “macro” model was linked to a microscale solidification model. This allowed the transient fluctuations in the dendritic microstructure to be predicted, allowing the first coupled three-dimensional correlations between macroscopic operational parameters and microstructural defects to be performed. It was found that convection driven by the motion of the arc caused local remelting of the mushy zone, resulting in variations in permeability and solute density. This causes variations in the local Rayleigh number, leading to conditions under which freckle solidification defects will initiate. A three-dimensional transient tracking of particle fall-in was also simulated, enabling predictions of “white spot” defects via quantification of the trajectory and dissolution of inclusions entering the melt.     

On the Modeling of Thermal Radiation at the Top Surface of a Vacuum Arc Remelting Ingot

Two models have been implemented for calculating the thermal radiation emitted at the ingot top in the VAR process, namely, a crude model that considers only radiative heat transfer between the free surface and electrode tip and a more detailed model that describes all radiative exchanges between the ingot, electrode, and crucible wall using a radiosity method. From the results of the second model, it is found that the radiative heat flux at the ingot top may depend heavily on the arc gap length and the electrode radius, but remains almost unaffected by variations of the electrode height. Both radiation models have been integrated into a CFD numerical code that simulates the growth and solidification of a VAR ingot. The simulation of a Ti-6-4 alloy melt shows that use of the detailed radiation model leads to some significant modification of the simulation results compared with the simple model. This is especially true during the hot-topping phase, where the top radiation plays an increasingly important role compared with the arc energy input. Thus, while the crude model has the advantage of its simplicity, use of the detailed model should be preferred.     

On the Dissolution of Nitrided Titanium Defects During Vacuum Arc Remelting of Ti Alloys

The elimination of high interstitial defects (also known as hard-α inclusions) is of great importance to the titanium industry. This article presents a model capable of simulating the motion and dissolution of such defects during their residence in the pool of a vacuum arc remelted (VAR) ingot. To predict the complete history of that inclusion, the study couples a dissolution model of the defect and a Lagrangian particle-tracking model. This numerical tool is implemented in SOLAR (solidification during arc remelting), a computational fluid dynamics code developed at the Nancy School of Mines in the framework of an important research project conducted during the last 15 years, which aims to study and optimize the VAR process. The dissolution model numerically solves the nitrogen diffusion equation in a spherical inclusion and in thermal equilibrium with the surrounding fluid. The computational domain is divided into a central zone (α phase) and a surrounding layer (β phase), which appears because the diffusion of nitrogen into the liquid pool causes some solidification. The dissolution kinetics strongly depend on the liquid temperature and velocity of the inclusion. The model can compute the nitrogen profile in the defect at each moment as well as the thickness of the different layers; therefore, it can compute the overall size of the inclusion. The trajectory model consists of solving Newton’s law of motion. Because the inclusion size is large, the consequence of fluid-flow turbulence is to modify the local flow around the inclusion so that the drag is affected. Results presented and discussed in this article include a parametric study of the influence of the pool thermohydrodynamics, the relative inclusion–fluid density, and the initial diameter of the defect as it enters the melt pool. Finally, an example of the full history of an inclusion during triple VAR illustrates the possibility to remove such a defect effectively by dissolving it in the liquid phase.     

Numerical simulation of dendrite white spot formation during vacuum arc remelting of INCONEL718

White spot is the term for a particulate dispersion lean in niobium found in vacuum arc remelted (VAR) ingots of niobium containing nickel-based superalloys, such as INCONEL718, that can be detrimental to the mechanical properties. While spot can result from exogenous fragments that fall into the VAR melt pool and remain incompletely melted. In this study, white spot formed when dendrite clusters fall-in from the shrinkage pipe of vacuum induction melted (VIM) electrodes is considered by simulations. The motion and dissolution of the dendrite cluster particles were simulated in the framework of a macroscopic heat and fluid flow model of the VAR process. Two scales of heat and mass transfer are considered within the cluster: interdendritic solute diffusion within particles and the thermal interaction between the particle and the bulk convective melt. The dissolution behavior of dendrite cluster fall-in was investigated for a range of initial particle conditions including solid fraction, Nb content, drop height, and initial temperature. The operational window where the exogenous particles completely dissolve was determined as a function of cluster size, density, and location. It was found that particles smaller than 3 mm are completely dissolved under all conditions simulated in this study. All factors studied demonstrated significant influence on particle dissolution. Particles with a solid fraction less than 0.5, a Nb content greater than 4 pct, or an initial temperature greater than 1400 K are likely to be dissolved immediately after entering the melt pool. Drop height and initial density had the greatest effect on particle dissolution.     

Dissolution and Interface Reactions between Palladium and Tin (Sn)-Based Solders: Part I. 95.5Sn-3.9Ag-0.6Cu Alloy

The interface microstructures and dissolution behavior were studied, which occur between 99.9 pct Pd substrates and molten 95.5Sn-3.9Ag-0.6Cu (wt pct, Sn-Ag-Cu) solder. The solder bath temperatures were 513 K to 623 K (240 °C to 350 °C). The immersion times were 5 to 240 seconds. The IMC layer composition exhibited the (Pd, Cu)Sn₄ (Cu, 0 to 2 at. pct) and (Pd, Sn) solid-solution phases for all test conditions. The phases PdSn and PdSn₂ were observed only for the 623 K (350 °C), 60 seconds test conditions. The metastable phase, Pd₁₁Sn₉, occurred consistently for the 623 K (350 °C), 240 seconds conditions. Palladium-tin needles appeared in the Sn-Ag-Cu solder, but only at temperatures of 563 K (290 °C ) or higher, and had a (Pd, Cu)Sn₄ stoichiometry. Palladium dissolution increased monotonically with both solder bath temperature and exposure time. The rate kinetics of dissolution were represented by the expression At ⁿ exp(?H/RT), where the time exponent (n) was 0.52 ± 0.10 and the apparent activation energy (?H) was 44 ± 9 kJ/mol. The IMC layer thickness increased between 513 K and 563 K (240 °C and 290 °C) to approximately 3 to 5 µm, but then was less than 3 µm at 593 K and 623 K (320 °C and 350 °C). The thickness values exhibited no significant time dependence. As a protective finish in electronics assembly applications, Pd would be relatively slow to dissolve into molten Sn-Ag-Cu solder. The Pd-Sn IMC layer would remain sufficiently thin and adherent to a residual Pd layer so as to pose a minimal reliability concern for Sn-Ag-Cu solder interconnections.     

Solidification of a Vacuum Arc-Remelted Zirconium Ingot

As the quality of vacuum arc-remelted (VAR) zirconium ingots is directly linked to their chemical homogeneity and their metallurgical structure after solidification, it is important to predictively relate these factors to the operating conditions. Therefore, a detailed modeling study of the solidification process during VAR has been undertaken. To this purpose, the numerical macromodel SOLAR has been used. Assuming axisymmetrical geometry, this model is based on the solution of the coupled transient heat, momentum, and solute transport equations, under turbulent flow conditions during the remelting, hot-topping, and cooling of a cylindrical ingot. The actual operating parameters are defined as inputs for the model. Each of them, mainly the melting current sequence, melting rate sequence, and stirring parameters (current and period), is allowed to vary with time. Solidification mechanisms recently implemented in the model include a full coupling between energy and solute transport in the mushy zone. This modeling can be applied to actual multicomponent alloys. In this article, the macrosegregation induced by solidification in a zirconium alloy ingot is investigated. In order to validate the model results, a full-scale homogeneous Zy4 electrode has been remelted, and the resulted ingot has been analyzed. The model results show a general good agreement with the chemistry analyses, as soon as thermosolutal convection is accounted for to simulate accurately the interdendritic fluid flow in the central part of the ingot.     

Segregation Development in Multiple Melt Vacuum Arc Remelting

A numerical model of the vacuum arc remelting (VAR) process was used to study multistage VAR processes. The studies of low and high power 3XVAR confirmed the results of the single stage process studies for Ti-10-2-3: (1) high arc power results in strong electromagnetically driven flow and undesirably high macrosegregation; (2) low arc power does not generate significant Lorentz forces and the flow is dominated by weaker buoyancy forces, which cause less segregation; and (3) even short-lived changes in process conditions during the run may result in a switch of the flow regime in low power cases from buoyancy driven to electromagnetically driven. The switch of flow regime results in an increase in macrosegregation levels and a change in the pattern of solute redistribution. The most significant finding in the studies of 3XVAR processing of Ti-10-2-3 is the small effect of the electrode composition distribution on ingot segregation development. In both low and high power VAR cases, macrosegregation levels and patterns in the final ingots were similar to those demonstrated assuming a uniform electrode for that final case. However, for low power cases, nonuniformities in the electrode composition may strongly affect the final ingot macrosegregation. The nonuniformity in the composition of the electrode results in the formation of additional buoyancy forces within the liquid pool, which can cause a switch from buoyancy driven flow to the undesirable electromagnetically driven flow regime and a drastic change in segregation development. This article is based on a presentation given at the International Symposium on Liquid Metal Processing and Casting (LMPC 2007), which occurred in September 2007 in Nancy, France.     

基于数值模拟的镍基高温合金电渣重熔工艺优化

利用MeltFlow软件对镍基高温合金电渣重熔过程进行数值模拟计算,探究了电渣重熔过程中温度场、流场、熔池形貌及微观组织的分布特点,通过工业试验验证模拟的准确性,定量分析熔速对熔炼过程的影响规律,提出了一种改善铸锭凝固质量的工艺优化方法。结果表明,渣池内的温度相对较高且分布均匀,熔池形貌近似“V”型。铸锭一次枝晶间距从中心到边缘沿径向逐渐减小,而二次枝晶间距没有明显差别。对比试验数据,数值模拟结果误差较小,可以准确预测镍基高温合金电渣重熔过程中的熔池形貌和枝晶间距。随着熔化速率的减小,金属熔池深度降低,ESR铸锭二次枝晶间距逐渐减小,且宏观偏析程度得到改善,黑斑产生概率逐渐降低。控制熔化速率由0.47 kg/min降低至0.45 kg/min,有利于获得凝固质量较好的镍基高温合金电渣重熔铸锭。     

Simulation of convection and macrosegregation in a large steel ingot

Melt convection and macrosegregation in casting of a large steel ingot are numerically simulated. The simulation is based on a previously developed model for multicomponent steel solidification with melt convection and involves the solution of fully coupled conservation equations for the transport phenomena in the liquid, mush, and solid. Heat transfer in the mold and insulation materials, as well as the formation of a shrinkage cavity at the top, is taken into account. The numerical results show the evolution of the temperature, melt velocity, and species concentration fields during solidification. The predicted variation of the macrosegregation of carbon and sulfur along the vertical centerline is compared with measurements from an industrial steel ingot that was sectioned and analyzed. Although generally good agreement is obtained, the neglect of sedimentation of free equiaxed grains prevents the prediction of the zone of negative macrosegregation observed in the lower part of the ingot. It is also shown that the inclusion of the shrinkage cavity at the top and the variation of the final solidification temperature due to macrosegregation is important in obtaining good agreement between the predictions and measurements.     

Mathematical modeling of a melt pool driven by an electron beam

Physical vapor deposition (PVD) assisted by an electron beam is one of several methods currently used to apply thermal barrier coatings (TBCs) to aircraft components subjected to high-temperature environments. The molten pool of source material inherent in this process shall be the subject of analysis in this investigation. A model of the melt pool and the ingot below shall be generated in an effort to study the fluid flow and heat transfer within the pool. This model shall incorporate all of the following mechanisms for heat transfer into and out of the melt pool/ingot system: electron-beam impingement upon the melt pool surface, absorption of latent heat of evaporation at the melt pool surface, radiation from the melt pool surface, loss of sensible heat carried off with the vapor, and cooling by the crucible containing the melt pool/ingot. Fluid flow within the melt pool model shall be driven by both natural convection and by surface tension gradients on the melt pool surface. Due to the complexity of the differential equations and boundary equations governing the model, this detailed study shall be performed through a finite element analysis. Reduced order models of the system will be generated from this investigation. An analysis will also be performed to ascertain the error introduced into these models by uncertainty in the thermophysical property data used to generate them.     

Liquid Inclusions in Heat-Resistant Steel Containing Rare Earth Elements

Abundant thermodynamic data of pure substances were incorporated in the coupled thermodynamic model of inclusion precipitation and solute micro-segregation during the solidification of heat-resistant steel containing rare earth elements. The liquid inclusions Ce_2x Al_2y Si_1?x?y O _z (0 < x < 1, 0 < y < x and z = 1 ? x ? y) were first introduced to ensure the model more accurately. And the computational method for generation Gibbs free energy of liquid inclusions in molten steel was given. The accuracy of accomplished model was validated through plant trials, lab-scale experiments, and the data published in the literature. The comparisons of results calculated by FactSage with the model were also discussed. Finally, the stable area of liquid inclusions was predicted and the liquid inclusions with larger size were found in the preliminary experiments.     

Chemically Induced Solidification: A New Way to Produce Thin Solid-Near-Net Shapes

In situ observation of the solidification of high-carbon steel (4 wt pct C) through decarburization has been carried out as a feasibility study into reducing high-power usage and high CO₂ production involved in steel making. Decarburization has been carried out under both air and pure N₂ atmospheres at temperatures of 1573 K and 1673 K (1300 °C and 1400 °C). A solidified shell of around 500 μm was formed with carbon concentrations reduced down to 1 pct in as short as 18 seconds.