Time-resolved x-ray imaging of aluminum alloy solidification processes

Time-resolved direct-beam X-ray imaging, with intense, coherent, and monochromatic third-generation synchrotron radiation, and a high-resolution fast-readout detector system have been used for in-situ studies of dendritic and eutectic growth processes in Al-Cu alloys. Temporal and spatial resolutions down to 0.25 seconds and 2.5 μm, respectively, were obtained with a field of view up to 1.4×1.4 mm². Solid-liquid interfaces and various phase-specific segregates could be observed, and their dynamics could be traced in a sequence of temporally resolved images formed by phase and amplitude contrast from the sample. This article does not present any detailed analysis of a specific solidification phenomenon; instead, it presents to the scientific community an innovative technique for in-situ monitoring of such a phenomenon in real metallic systems.     

A numerical scheme for solidification of an alloy

In modeling the solidification of an alloy, two central numerical problems are:1. The calculation of thermal and species transport fields which satisfy the conservation equations and are also consistent with the underlying thermodynamics.2. The treatment of local scale solute diffusion.In this paper, in the context of modeling inverse segregation in a uni-directionally solidified casting, a recently proposed implicit⧹explicit time integration scheme for coupling thermal and solutal fields is presented and possible ways of capturing the local scale solute diffusion in a macroscopic model are explored. A key element in this work is the validation of the proposed approach by comparison with a sophisticated similarity solution. © 1998 Canadian Institute of Mining and Metallurgy.     

A general enthalpy method for modeling solidification processes

In the present work, a general implicit source-based enthalpy method is presented for the analysis of solidification systems. The proposed approach is both robust and efficient. The performance of the method is illustrated by application to a number of problems taken from recent metallurgical literature.     

Experiments on the solidification structure of alloy castings

Two related experimental programs on the solidification structure of alloy castings are reported. In the first, the grain structure of catalytically clean Ni?Cu alloys is examined as a function of the degree of supercooling below the equilibrium liquidus. For supercoolings greater than 85°C, the Ni?Cu alloys exhibit a structure which is in accord with previous observations in pure nickel,i. e., the structure is found to be coarse and dendritic in the range 85° to 150°C supercooling, but fine and equiaxed for supercoolings greater than 150°C. However, in the lower range of supercooling (<85°C) the structure is fine and equiaxed. It is concluded that solute elements can promote grain formation in certain castings at supercoolings insufficient to cause heterogeneous nucleation. To study the effect of solute elements on the structure of a solidifying material, castings of pure nickel and aluminum are compared with binary alloys of these base materials. Over the composition ranges studied in both alloy systems, the structure is observed to be related to a parameter which includes the slope of the liquidus, the bulk solute concentration, and the solute distribution coefficient. It is shown or is argued that heterogeneous nucleants are not involved and therefore another mechanism must be operating in determining the structure. In any event, these latter experiments suggest that an effective means of controlling the structure of castings is by appropriate selection of alloying additions on the basis of the alloy variables contained in such a parameter.     

Modeling of micro-macrosegregation in solidification processes

Formerly Visiting Professor at EPFL, is permanently affiliated with the Mineral Resources Research Center, University of Minnesota, Minneapolis, MN 55455.     

A solutal interaction mechanism for the columnar-to-equiaxed transition in alloy solidification

A multiphase/multiscale model is used to predict the columnar-to-equiaxed transition (CET) during solidification of binary alloys. The model consists of averaged energy and species conservation equations, coupled with nucleation and growth laws for dendritic structures. A new mechanism for the CET is proposed based on solutal interactions between the equiaxed grains and the advancing columnar front—as opposed to the commonly used mechanical blocking criterion. The resulting differences in the CET prediction are demonstrated for cases where a steady state can be assumed, and a revised isotherm velocity (V _T ) vs temperature gradient (G) map for the CET is presented. The model is validated by predicting the CET in previously performed unsteady, unidirectional solidification experiments involving Al-Si alloys of three different compositions. Good agreement is obtained between measured and predicted cooling curves. A parametric study is performed to investigate the dependence of the CET position on the nucleation undercooling and the density of nuclei in the equiaxed zone. Nucleation undercoolings are determined that provide the best agreement between measured and calculated CET positions. It is found that for all three alloy compositions, the nucleation undercoolings are very close to the maximum columnar dendrite tip undercoolings, indicating that the origin of the equiaxed grains may not be heterogeneous nucleation, but rather a breakdown or fragmentation of the columnar dendrites. An erratum to this article is available at .     

Interface attachment kinetics in alloy solidification

The current status of our understanding of nonequilibrium interface kinetics during solidification is reviewed. Measurements of solute trapping and kinetic interfacial undercooling during rapid alloy solidification are accounted for by the continuous growth model (CGM) without solute drag. Disorder trapping has been predicted and observed in the rapid solidification of ordered intermetallic compounds. In systems that undergo either solute or disorder trapping, a transition from short-range diffusion-limited to collision-limited growth occurs, which originates in the reduced driving free energy for the formation of such metastable materials, resulting in three orders of magnitude change in the interface mobility. Applications to cellular and dendritic growth are discussed. A correlation is presented for estimating the diffusive speed—the growth rate necessary for substantial solute trapping—for alloy systems in which it has not, or cannot, be measured. The raw data for Si(Bi) solute trapping measurements to which many models have been compared are presented in the Appendix.     

Modeling of multidimensional solidification of an alloy

The solidification of an alloy and pure metal is distinct because of the morphological differences between the respective interfaces. For certain conditions of imposed heat extraction, this dis-tinction can lead to large differences in the times required for complete solidification of the alloy over the pure metal. These conditions are examined in this paper. To do this, a powerful numerical technique to model alloy solidification is introduced which allows for the precise integration of the Scheil equation. The model takes into account the nonlinearity of the fraction liquid with temperature as well as the interface nonlinearity in the heat flow. As a test for the model, accurate temperature profiles from a previously published experiment are numerically simulated. The numerical results are noted to closely match experimental values, and as a con-sequence, contact heat transfer values are tabulated. One- and two-dimensional solidification of aluminum-copper alloys are now simulated for different cooling conditions (i.e., varying Biot numbers). The results obtained indicate the essential differences for alloy solidification at low and high Biot numbers and highlight the importance of properly accounting for the mushy zone.     

铁碳合金凝固过程微观溶质偏析模型分析

为了选择正确的微观溶质偏析模型研究铁碳合金的凝固过程,利用Thermo-Calc商业软件计算了不同碳含量下铁碳合金的固相线温度、液相线温度和碳的平衡分配系数,利用数值方法研究了不同微观溶质偏析模型下铁碳合金的固液界面温度和无量纲液相溶质浓度.数值结果表明:文献中常用的碳平衡分配系数不准确;C lyne-Kurz模型和Sche il模型不能准确地预测固液界面温度,B rody-F lem ings模型不能正确地预测碳偏析,建议采用杠杆模型和大中逸雄模型计算铁碳合金凝固过程的微观溶质偏析.     

Dendritic solidification of magnesium alloy AZ91

The magnesium alloy AZ91 has been studied under different solidification conditions, to establish the details of the as-cast structure. The electron backscattered pattern (EBSP) technique has been used to determine the crystallographic directions of the dendrite stem and the secondary arms. Under unidirectional solidification conditions, two different stem directions were found: at a low temperature gradient and high growth velocity, the dendrites grew in a «11-20» direction, while at higher temperature gradients and lower growth velocities, the growth direction was (2245). Dendrites with «11-20» stems have arms in six directions around the stem, while dendrites with «22-45» stems have three secondary arm directions. The crystallographic directions of the secondary arms are the same as the two stem directions.     

Enthalpies of a binary alloy during solidification

The purpose of the paper is to present a method of calculating the enthalpy of a dendritic alloy during solidification. The enthalpies of the dendritic solid and interdendritic liquid of alloys of the Pb-Sn system are evaluated, but the method could be applied to other binaries, as well. The enthalpies are consistent with a recent evaluation of the thermodynamics of Pb-Sn alloys and with the redistribution of solute in the same during dendritic solidification. Because of the heat of mixing in Pb-Sn alloys, the interdendritic liquid of hypoeutectic alloys (Pb-rich) of less than 50 wt pct Sn has enthalpies that increase as temperature decreases during solidification. For some concentrations of Sn, the enthalpy of the dendritic solid at the solid-liquid interface also increases with decreasing temperature during solidification. Of particular concern, in formulating the energy equation, is the fact that the heat of fusion during solidification increases as much as 80 pct for hypoeutectic alloys and decreases as much as 25 pct for hypereutectic alloys. Thus the often applied assumptions of a constant specific heat and/or a constant heat of solidification could lead to errors in numerical modeling of temperature fields for dendritic solidification processes.     

The solidification behavior of 8090 Al-Li alloy

In this work, the solidification and segregation behaviors of 8090 Al-Li alloy have been investigated with differential thermal analysis (DTA) and the metallographic-electron microprobe method. The results show that 8090 Al-Li alloy has a much more complex solidification path than Al-Li binary alloy due to the addition of many alloying elements and the presence of impure elements. Solidification begins at about 635 °C with the reaction of L → α-Al + L′, and this reaction goes on to termination. The alloying element Cu and impure elements Fe and Si have a strong segregation tendency. During solidification, Cu segregates to the interdendrite and finally forms α-Al + T₂ eutectic. As a result, the solidification temperature range is greatly extended. Iron and Si form the insoluble constituents Al₇Cu₂Fe, AlLiSi,etc., although their concentrations in the alloy are quite low. With the increase of Fe content, there is a eutectic reaction of α-Al/Al₃Fe at about 595 °C. The formation of insoluble constituents is influenced by both concentrations of impure elements in the alloy and the cooling rate.     

Rapid solidification processing of a Mg-Li-Si-Ag alloy

A Mg-13Li-4Si-lAg (wt pct) alloy with improved ductility and thermal stability was developedvia the rapid solidification (RS) processing technique. Silicon was added to the alloy as the third alloying element in order to form a thermally stable intermetallic dispersoid phase required for improved mechanical properties at ambient and elevated temperatures. The microstructure of the as-spun and heat-treated alloy was characterized using differential scanning calorimetry (DSC), X-ray diffraction, scanning electron microscopy (SEM), and transmission electron microscopy (TEM). Microhardness measurements were conducted on as-spun and heat-treated alloy in order to obtain qualitative prop-erty data and to investigate the extent of the degradation of properties at elevated temperatures. It was found that the melt-spun Mg-Li alloy possessed a microstructure consisting of a fine dispersion of Mg₂Si phase in a fine-grained body-centered cubic (bcc) Mg-Li solid solution, resulting in the desired improvements in thermal stability and mechanical properties. Formerly Graduate Student, Department of Materials Science and Engineering, University of California     

Model for controlling processes in the ladle treatment of steel

In Russia, the Bardin Central Research Institute of Metallurgy (TsNIIchermet) has used results obtained from many years of basic research to construct physicochemical models of the processes of deoxidizing, desulfurizing, alloying, and finishing steel in out-of-furnace treatments in accordance with the main chemical reactions that take place. Construction of the models has in turn made it possible to develop a series of software applications designed to solve practical problems that arise in controlling the processes which occur in ladle metallurgy.     

电渣重熔过程中金属凝固的控制方法

分析了表征凝固质量的各种参数及凝固过程参数对凝固质量的影响.讨论了电极熔化速度与凝固质量之间的关系,及如何计算合理的熔化速度.通过数学模拟计算凝固过程的温度场,进而计算二次枝晶间距是获得合理凝固组织的有效手段.     

Directional solidification in a AgCuSn eutectic alloy

An experimental study of microstructures in a directionally solidified, near-eutectic Ag-Cu-Sn alloy has been completed. This material is an important candidate for use as a lead-free solder, and the studies show the origin and velocity dependence of some of the microstructures seen in solder joints. Quantitative stereology and microstructural observation were completed for directional solidification experiments where the sample was moved through a gradient furnace at velocities between 0.826 and 500 μm/s.     

Heat flow model for surface melting and solidification of an alloy

The heat flow model previously developed for a pure metal is extended to the solidification of an alloy over a range of temperatures. The eq11Ations are then applied to rapid surface melting and solidification of an alloy substrate. The substrate is subjected to a pulse of stationary high intensity heat flux over a circular region on its bounding surface. The finite difference form of the heat transfer eq11Ation is written in terM_s of dimensionless nodal temperature and enthalpy in an oblate spheroidal coordinate system. A numerical solution technique is developed for an alloy which precipitates a eutectic at the end of solidification. Generalized solutions are presented for an Al-4.5 wt pct Cu alloy subjected to a uniform heat flux distribution over the circular region. Dimensionless temperature distributions, size and location of the “mushy” zone, and average cooling rate during solidification are calculated as a function of the product of absorbed heat flux,q, the radius of the circular region,a, and time. General trends established show that for a given product ofqa all isotherM_s are located at the same dimensionless distance for identical Fourier numbers. The results show that loss of superheat and shallower temperature gradients during solidification result in significantly larger “mushy” zone sizes than during melting. Furthermore, for a given set of process parameters, the average cooling rate increases with distance solidified from the bottom to the top of the melt pool.     

A melting and solidification study of alloy 625

The melting and solidification behavior of Alloy 625 has been investigated with differential thermal analysis (DTA) and electron microscopy. A two-level full-factorial set of chemistries involving the elements Nb, C, and Si was studied. DTA results revealed that all alloying additions decreased the liquidus and solidus temperatures and also increased the melting temperature range. Terminal solidification reactions were observed in the Nb-bearing alloys. Solidification microstructures in gastungsten-arc welds were characterized with transmission electron microscopy (TEM) techniques. All alloys solidified to an austenitic (γ) matrix. The Nb-bearing alloys terminated solidification by forming various combinations of γ/MC(NbC), γ/Laves, and γ/M₆C eutectic-like constituents. Carbon additions (0.035 wt pct) promoted the formation of the γ/MC(NbC) constituent at the expense of the γ/Laves constituent. Silicon (0.4 wt pct) increased the formation of the yJLaves constituent and promoted formation of the γ/M₆C carbide constituent at low levels (<0.01 wt pct) of carbon. When both Si (0.4 wt pct) and C (0.035 wt pct) were present, the γ/MC(NbC) and γ/Laves constituents were observed. Regression analysis was used to develop equations for the liquidus and solidus temperatures as functions of alloy composition. Partial derivatives of these equations taken with respect to the alloying variables (Nb, C, Si) yielded the liquidus and solidus slopes t(m _L , m _S ) for these elements in the multicomponent system. Ratios of these liquidus to solidus slopes gave estimates of the distribution coefficients (k) for these same elements in Alloy 625.