Macrosegregation and thermosolutal convection-induced freckle formation in dendritic mushy zone of directionally solidified Sn-Ni peritectic alloy

Compared with the growing applications of peritectic alloy,none research on the freckle formation during peritectic solidification has been reported before.Observation on the dendritic mushy zone of Sn-36 at.％Ni peritectic alloy during directional solidification at different growth velocities shows that the freckles are formed in two different regions:region Ⅰ before peritectic reaction and region Ⅱ after peritectic reaction.In addition,more freckles can be observed at lower growth velocities.Examination on the experimental results demonstrates that both the temperature gradient zone melting(TGZM)and Gibbs-Thomson(G-T)effects have obvious influences on the morphology of dendritic network during directional solidification.The current theories onKI Rayleigh number Ra characterizing the thermoso-lutal convection of dendritic mushy zone to predict freckle formation through the maximum of Ra can only explain the existence of region Ⅰ while the appearance of region Ⅱ after peritectic reaction cannot be predicted.Thus,a new Rayleigh number RaP is proposed in consideration of evolution of dendritic mushy zone by both effects and peritectic reaction.Theoretical prediction of RaP also shows a maximum after peritectic reaction in addition to that before peritectic reaction,thus,agreeing well with the freckle formation in region Ⅱ.In addition,more severe thermosolutal convection can be predicted by the new Rayleigh number RaP at lower growth velocities,which further demonstrates the reliability of RaP in describing the dependence of freckle formation on growth velocity.     

温度梯度条件下糊状区的凝固行为研究

利用一个垂直的定向凝固装置,研究了Al-6wt%Cu合金在温度梯度约12K/mm条件下,糊状区在保温不同时间并激冷后得到的微观组织及成分分布特征.SEM/EDX分析表明,糊状区在保温时间内将发生自发的、以扩散机制为主的、类似TGZM效应的凝固过程.完全凝固后所形成的成分梯度与温度梯度的对应关系对于预测定向凝固过程中固液相界面温度以及相平衡测定具有重要意义.     

Modelling convection in solidification processes using stabilized finite element techniques

Solidification of dendritic alloys is modelled using stabilized finite element techniques to study convection and macrosegregation driven by buoyancy and shrinkage. The adopted governing macroscopic conservation equations of momentum, energy and species transport are derived from their microscopic counterparts using the volume‐averaging method. A single domain model is considered with a fixed numerical grid and without boundary conditions applied explicitly on the freezing front. The mushy zone is modelled here as a porous medium with either an isotropic or an anisotropic permeability. The stabilized finite‐element scheme, previously developed by authors for modelling flows with phase change, is extended here to include effects of shrinkage, density changes and anisotropic permeability during solidification. The fluid flow scheme developed includes streamline‐upwind/Petrov–Galerkin (SUPG), pressure stabilizing/Petrov–Galerkin, Darcy stabilizing/Petrov–Galerkin and other stabilizing terms arising from changes in density in the mushy zone. For the energy and species equations a classical SUPG‐based finite element method is employed with minor modifications. The developed algorithms are first tested for a reference problem involving solidification of lead–tin alloy where the mushy zone is characterized by an isotropic permeability. Convergence studies are performed to validate the simulation results. Solidification of the same alloy in the absence of shrinkage is studied to observe differences in macrosegregation. Vertical solidification of a lead–tin alloy, where the mushy zone is characterized by an anisotropic permeability, is then simulated. The main aim here is to study convection and demonstrate formation of freckles and channels due to macrosegregation. The ability of stabilized finite element methods to model a wide variety of solidification problems with varying underlying phenomena in two and three dimensions is demonstrated through these examples. Copyright © 2005 John Wiley & Sons, Ltd.     

Effects of dendritic arm coarsening on macroscopic modelling of solidification of binary alloys

Abstract

A pure macroscopic two-dimensional numerical model has been developed, capable of capturing the effects of dendritic arm coarsening on the transport phenomena occurring during a binary alloy solidification process. The general continuum conservation equations are aptly modified to take into account shrinkage induced fluid flow. Simultaneously, the effective permeability of the mushy zone is numerically modelled according to the microscopic coarsening kinetics. Moreover, a new nodal latent heat updating algorithm is proposed that takes into account dendritic arm coarsening considerations. The numerical results are first tested against experimental results reported in the literature, corresponding to the solidification of an Al-Cu alloy in a bottom cooled cavity. It is concluded that dendritic arm coarsening leads to an increased effective permeability of the mushy region as well as an enhanced eutectic fraction of the solidified ingot. Consequently, an enhanced macrosegregation is predicted, compared with that dictated by shrinkage induced fluid flow alone. Physical insights are also developed regarding the effects of various parameters on the overall macrosegregation.     

强磁场下Cu-50%Ag合金定向凝固过程中的组织及固液界面形貌演变

目的 研究强磁场下Cu-50%(质量分数)Ag合金定向凝固过程中的组织演变、固液界面形貌变化及溶质迁移行为,分析强磁场对金属凝固过程的作用机制,为强磁场下的金属材料制备提供理论借鉴和指导。方法 在不同的凝固速率与磁场条件下进行定向凝固和淬火实验,对合金的定向凝固组织、糊状区与固液界面形貌以及溶质分布行为进行考察。结果 强磁场破坏了凝固组织的定向生长,使凝固组织转变为枝晶与等轴晶共存的形貌;强磁场诱发了熔体对流,减少了糊状区中溶质的含量;强磁场改变了固液界面处的溶质分布和固液界面形貌,破坏了固液界面的稳定性。结论 强磁场通过洛伦兹力和热电磁力的共同作用,诱发了糊状区内液相的纵向环流,改变了固液界面及糊状区中的组织形貌与元素分布。     

Diffusion-induced abnormal tertiary dendrite during peritectic solidification in a temperature gradient

1.Introduction Dendritic structure are commonly encountered during solidification [1-4], especially in systems freezing with relatively low entropies of transformation [1,5].Generally speaking, the dendritic structure is composed of primary dendrite stem, secondary branch and even tertiary and higher order dendrite arms [1].Different kinds of models have been proposed for describing the growth of primary dendrite [1-5] and secondary dendrite arms [1,6,7].In recent decades, dendritic growth of many industrial important peritectic alloys featured by peritectic reaction L+α→β have been witnessed [8-10].The dendritic growth is more complex during peritectic solidification due to the involvement of peritectic β phase.     

Numerical study on directional solidification of AlSi alloys with rotating magnetic fields under microgravity conditions

A global thermal model of the ARTEX facility, developed with the modeling tool CrysVUn, is presented. The model is validated with experimental data obtained under microgravity conditions during the TEXUS39 mission. Numerical studies are then reported, in which the effects of a rotating magnetic field are investigated during directional solidification of binary AlSi7 alloys. It appears that beyond a certain magnetic field strength a macrosegregation effect is resulting, leading to the development of a liquid channel inside the mushy zone.     

Transport Properties and Transport Phenomena in Casting Nickel Superalloys

Nickel superalloys that are used in the high-temperature regions of gas-turbine engines are cast by directional solidification (DS). In the DS processes, the castings are cooled from below, and three zones exist during solidification: (1) an all-solid zone at the bottom, (2) a “mushy zone” that is comprised of solid and liquid material, and (3) an overlying all-liquid zone. Computer simulations can be useful in predicting the complex transport phenomena that occur during solidification, but realistic simulations require accurate values of the transport properties. In addition to transport properties, the thermodynamic equilibria between the solid and liquid during solidification must also be known with reasonable accuracy. The importance of using reasonably accurate estimations of the transport properties is illustrated by two-dimensional simulations of the convection during solidification and the coincidental macrosegregation in the DS castings of multicomponent Ni-base alloys. In these simulations, we examine the sensitivity of the calculated results to measured partition ratios, thermal expansion coefficients, and viscosities that are estimated by regression analyses and correlations of existing property data.     

Effects of Re on surface eutectic formation for Ni-base single crystal superalloys during directional solidification

Effects of Re on the formation of surface eutectics have been investigated by using Ni-base single crystal superalloys with different Re additions. It was found that Re promotes the segregation of Al and Ta to the eutectic melt, leading to an increase of the surface and internal eutectics. In addition, the addition of Re also increased the freezing range, the local solidification time, and the permeability of the dendritic network within the mushy zone. These factors ultimately promoted the outflow of the interdendritic residual liquid with the action of solidification shrinkage, and led to the formation of more surface eutectics. In contrast, the addition of Re had no obvious influence on the surface eutectic microstructures.     

糊状区渗氮对Cr10Mn9Ni0.7合金氮含量及凝固相变过程的影响

研究了糊状区保温对Cr10Mn9Ni0.7合金凝固过程和氮含量及相变过程的影响。结果表明,随着糊状区保温时间的延长,铸锭中的氮含量逐渐升高,同时铸锭中的气孔率逐渐降低。当氮气压力为0.1 MPa时,氮含量由0.17%升高到0.23%,而气孔率则从1.86%降至1.37%;当氮气压力为0.4 MPa时,氮含量由0.29%升高到0.37%,而气孔率从1.41%降至1.06%。糊状区保温的增氮机制可归结为:在糊状区保温会促进包晶反应进程,使更多的铁素体转变为奥氏体;同时糊状区保温能够提高残留液相中的氮含量,进而提高"通道状"奥氏体中的氮含量。糊状区保温能够消除铁素体阱,从而降低气孔率。     

Continuum model for predicting macrosegregation in dendritic alloys

“Macrosegregation” represents a class of defects in cast products of serious concern to both alloy producers and users. Many types of macrosegregation result from thermosolutal convection in the solid plus liquid and all-liquid regions of a solidifying alloy, and this has spurred modeling and simulations, which treat the solid plus liquid region (i.e., the mushy zone) as a porous medium of variable porosity and permeability. Simulations include scenarios in which the convection is strong enough to make channels in the mushy zone region, and these channels lead to localized segregates known as “freckles”. Using Pb-10 wt.% Sn as a model alloy, we simulated vertical solidification with various solidification rates. By sufficiently increasing the cooling rate at the bottom surface, convection can be suppressed enough to prevent the formation of freckles. The simulation is an example of relating microstructural metrics to a macroscopic property of the porous medium used in continuum theory. In this case, the property is the permeability, which is governed by two microstructural metrics: the volume fraction of liquid and a characteristic length in the dendritic microstructure. Permeability data, relevant to columnar dendritic solidification, are reviewed, and recommendations for future work on determining the permeability in terms of microstructural metrics are given.     

Microstructure evolution of peritectic Al-18 at.％Ni alloy directionally solidified in high magnetic fields

The effect of a high magnetic field on the microstructural evolution of a peritectic Al-18 at.％Ni alloy during directional solidification and its dependence on pulling speed were investigated.At a low pulling speed,the application of a 2 T magnetic field triggered the appearance of a primary Al3Ni2 phase.At higher pulling speeds,a high magnetic field application induced primary Al3Ni2 phase segregation that formed close to the central alloy regions.For all pulling speeds,the application of a high magnetic field induced bulk Al3Ni/Al eutectic formation on the upper and lower parts of the alloys,and promoted elongated growth of the peritectic Al3 Ni phase along the magnetic field direction.Microstructural analysis indicated that microstructural evolution that was induced by high magnetic fields can be attributed to solute migration and melt flow that is regulated by magnetic,Lorentz,and thermoelectric magnetic forces and their coupling effects during peritectic solidification.     

Tailoring of dendritic microstructure in solidification processing by crucible vibration/rotation

Directional solidification of alloys, which allows the independent control of growth parameters (pulling velocity, temperature gradient), is an experimental method of choice for the investigation of many fundamental problems (e.g. microstructure formation and selection, segregation of chemical species) encountered in the processing of structural materials. Upward directional solidification is carried out on hypoeutectic Al-Ni alloys, under natural and controlled fluid-flow conditions. First, the influence of natural convection on solidified dendritic microstructure is analyzed as a function of growth parameters. Then, directional solidification experiments with axial vibration are performed. It results that crucible vibration can be used to either damp or control fluid flow in the melt, and thus tailor columnar or “equiaxed” dendritic mush. Advanced modeling and numerical simulation are essential to clarify and quantify the various physical effects. Microgravity benchmark experiments under diffusion transport, and possibly with crucible rotation, are foreseen using the Materials Science Laboratory of ESA on ISS.     

定向凝固钛铝合金熔体与铸型界面反应研究展望

钛铝合金是性能优异的高温合金,在航空航天领域有广泛的应用前景,但由于其熔体具有较高的活性,制备时熔体与所有已知的铸型材料会发生不同程度的反应,限制了钛铝合金铸件的发展.定向凝固技术作为制备高精度钛铝合金的新工艺,使铸件组织定向排列,可以进一步提高钛铝合金的使用性能,因此如何调控凝固过程中钛铝合金熔体与铸型材料间的界面反应成为目前有关定向凝固钛铝合金研究的一个热点.从目前国内外关于钛铝合金熔体与铸型材料间界面反应的研究出发,综述了定向凝固过程中铸型材料、涂层成分、工艺参数及合金元素等对界面反应的影响,介绍了界面反应的理论水平,系统收集了界面反应的各项研究结果.     

等轴晶移动对宏观偏析影响的数值模拟

建立了自由等轴晶移动对宏观偏析影响的数学模型,对铸锭凝固过程中的对流和溶质分布进行了数值模拟.在模型中按照临界固相分数将糊状区分为紧密树枝晶和自由等轴晶两个不同的区域.对带冒口铸钢锭的宏观偏析进行了数值模拟,并同实验结果进行了比较.与假设糊状区内固相静止的模型相比,考虑等轴晶移动的模型得到的溶质分布结果与实验结果更接近.在凝固过程中,等轴晶随液体流动并在铸锭的底部中心聚集,在凝固后的铸锭中形成锥形的负偏析.还发现,在铸锭的中心靠上的区域形成正偏析,在铸锭的外部区域形成负偏析.     

Solute distribution at the solid-liquid interface during steady-state peritectic solidification

The solute distributions at the solid-liquid interface during steady-state directional solidification of two contrasting peritectic systems were examined in detail by electron probe microanalysis. In the Al-Al₃Ti system the peritectic transformation plays a negligible part in the solidification reaction whereas in the Cd-Cd₃Ag system the peritectic transformation dominates. Knowing this, the solid-liquid interface profile during solidification can be predicted with reasonable accuracy on the assumption of equilibrium at all points on the solid-liquid interface. In the Cd-Cd₃Ag system the composition of the peritectic product is rapidly equilibrated by solid-state diffusion. A diffusion coefficient is estimated.     

Experimental analysis of the columnar-to-equiaxed transition in directionally solidified Al–Ni and Al–Sn alloys

Experiments were carried out to investigate the columnar-to-equiaxed transition (CET) during the upward vertical directional solidification of hypoeutectic Al–Ni and Al–Sn alloys. For the growth conditions examined both the thermal and solutal profiles inside the mushy zone and in the overlying melt ahead of the dendrite tips are expected to be stable, since the solute enrichment increases the melt density, and no solute movement induced by convection will affect the CET. From the experimental thermal profiles, tip cooling rates, tip growth rates and thermal gradients have been determined. It was found that the CET occurs for a critical value of cooling rate, with the columnar growth prevailing throughout the casting for cooling rates higher than such critical value, which for a particular binary alloy system is independent of the solute concentration in the hypoeutectic range. For Al–Sn and Al–Ni alloys the critical cooling rates were found to be 0.30 K/s and 0.16 K/s, respectively.     

Dendritic Growth Pattern and Dendritic Network Distortion in the Platform of a Ni-based Superalloy

The pattern of dendritic growth and distortion of dendritic network in the platform have been investigated by one mold casting with different platform length during directional solidification. As the platform length elongates, the symmetry of dendritic growth along left and right edges gradually worsens in platform base. While the platform length reaches 14 mm, the distortion of dendritic network is first observed in outward platform. It is found that the distortion of dendritic network along platform inside is more serious than that along platform edges. Both [001] deviation and accumulated misorientation along platform inside, up to 9~ and 16.3~, respectively, are far greeter than those along left-outward-right edges. The deformation of dendritic network in a platform may be caused by the asymmetry of the solidification front at the mush zone.     

Growth kinetics in levitated and quenched Nd-Fe-B alloys

We investigated the growth kinetics and the effect of quenching conditions on rapid solidification of undercooled Nd-Fe-B melts with compositions near the Nd-₂-Fe₁₄-B (2-14-1) phase. We prepared melt drops of various undercooling levels (up to 300 K below the liquidus temperature) were prepared by the electromagnetic levitation method and subsequently quenched them onto chill substrates. We measured the solidification kinetics of the undercooled melts in situ using a high-resolution Si photodiode. In accordance with the nucleation theory, the properitectic γ-Fe phase nucleates at first during the undercooling process. There were two different solidification routes, with the observed route depending on the undercooling level of the levitated melt prior to quenching. The peritectic reaction is favored in melts with high undercooling levels prior to quenching. Low previous undercooling levels lead to primary solidification of the 2-14-1 phase on quenching. The thickness of the homogeneous 2-14-1 phase zone, grown directly at the substrate side, depends strongly on the undercooling level prior to solidification. We estimated the growth velocity of the 2-14-1 phase from temperature-time-characteristics to be of the order of 1 mm/s. These investigations give rise to improved understanding about the high sensitivity of the microstructure of Nd-Fe-B alloys on different rapid solidification procedures     

Volume change during the solidification of SG iron: comparison between experimental results and simulation

In order to understand the shrinkage behaviour of spheroidal graphite (SG) iron during solidification, a volume change kinetic model was set up to simulate the volume change during the eutectic solidification, which was presented in an earlier paper. Furthermore in the present work experiments were carried out for comparison with theoretical prediction. The microstructure of the mushy zone during the solidification of SG cast iron was obtained by the quenching method and analysed by normal metallography and image analysis. The results show that the mushy zone exists in front of the interface between the liquid and the solid. The study by quantitative stereology shows that the graphite fraction in the mushy zone has the same trend as that of the theoretical prediction and the silicon content in cast iron strongly influences graphitization during the solidification. A heat-transfer model to stimulate the heat transfer of the experimental apparatus was developed. A modified Rappaz’s model was used to simulate the eutectic growth under fully equilibrium conditions. The theoretical prediction has been compared with the experimental results, and found to be in good agreement with each other. This revised version was published online in November 2006 with corrections to the Cover Date.