CAFE模型机理研究及应用

 摘 要：研究和分析了CAFE法模拟凝固过程微观组织的物理本质、数值计算方法。在CAFE模型中,形核密度用高斯分布来描述;枝晶尖端生长动力学用KGT模型进行计算;枝晶生长的择优取向是<100>方向,并可实现枝晶生长的竞争机制;FE与CA的耦合是通过FE节点和CA元胞之间的插值实现的。应用CAFE法模拟了易切削钢9SMn28的三维微观凝固组织,模拟结果与实验吻合较好。对易切削钢9SMn28进行了成分优化,并对优化结果进行了模拟,有效的改善了9SMn28的凝固组织。     

On the columnar to equiaxed transition in small ingots

The columnar to equiaxed transition (CET) in small ingots of, aluminum alloys was found to occur more easily for alloys with a larger value of the constitutional supercooling parameter (−mC _o (1-k)/k). The CET was found to be completely suppressed by increases in the mold temperature by preheating before casting. These results are discussed in terms of the model proposed by Burden and Hunt that the CET occurs by the effect of the thermal gradient, arising from the slow, solidification of equiaxed dendrites, which increases the undercooling of the columnar dendrites. The application of the model due to Burden and Hunt is shown to require, the use of the ‘big bang’ model for equiaxed nucleation on pouring. A higher density of the nuclei, that grow into equiaxed grains, formed by pouring with lower superheat and into a cold mold, gives a higher thermal gradient immediately in front of the growing columnar grains. Other evidence in favor of the model is briefly discussed.     

微观组织参数及工艺条件对430不锈钢凝固显微结构的影响

在多元合金CAFE模型的基础上,分析了微观组织参数（形核密度、高斯分解参数、Gibbs-Thomson系数等）与430不锈钢凝固过程中晶粒形貌的复杂关系,以及过热度与冷却强度等工艺参数对凝固组织的影响.研究发现,晶粒尺寸和柱状晶向等轴晶转变不仅与体最大形核过冷度有关,也受体形核密度的影响.高斯分解参数和Gibbs-Thomson系数增大时,一次枝晶间距减小,等轴晶范围增大;但当它们增加至一定范围后,其对显微结构的影响逐渐变得不明显.过热度或冷却强度增大时,等轴晶范围减小,但一次枝晶间距的变化不明显.      

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 .     

A three-phase model for mixed columnar-equiaxed solidification

A three-phase model for mixed columnar-equiaxed solidification is presented in this article. The three phases are the parent melt as the primary phase, as well as the solidifying columnar dendrites and globular equiaxed grains as two different secondary phases. With an Eulerian approach, the three phases are considered as spatially coupled and interpenetrating continua. The conservation equations of mass, momentum, species, and enthalpy are solved for all three phases. An additional conservation equation for the number density of the equiaxed grains is defined and solved. Nucleation of the equiaxed grains, diffusion-controlled growth of both columnar and equiaxed phases, interphase exchanges, and interactions such as mass transfer during solidification, drag force, solute partitioning at the liquid/solid interface, and release of latent heat are taken into account. Binary steel ingots (Fe-0.34 wt pct C) with two-dimensional (2-D) axis symmetrical and three-dimensional (3-D) geometries as a benchmark were simulated. It is demonstrated that the model can be used to simulate the mixed columnar-equiaxed solidification, including melt convection and grain sedimentation, macrosegregation, columnar-to-equiaxed-transition (CET), and macrostructure distribution. The model was evaluated by comparing it to classical analytical models based on limited one-dimensional (1-D) cases. Satisfactory results were obtained. It is also shown that in order to apply this model for industrial castings, further improvements are still necessary concerning some details.     

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.     

37Mn5连铸圆坯中心等轴晶率预测

为控制油井管用连铸圆坯的质量,基于薄片移动法建立了连铸圆坯凝固传热数学模型,并应用Procast软件的CA—FE模块对37Mn5钢Ф150mm圆坯凝固组织进行了模拟。中心等轴晶率模拟结果与工业试验检测结果相一致,据此,建立了柱状晶-等轴晶转变判据。基于此判据的中心等轴晶率预测结果表明,降低过热度、提高拉速和降低二冷零段...     

Prediction of Columnar to Equiaxed Transition during Diffusion-Controlled Dendritic Alloy Solidification

A model is presented to predict the columnar to equiaxed transition (CET) in alloy castings. The model is based on a multiphase approach and accounts for heat and solute diffusion, as well as for grain nucleation, growth, and morphology. The model equations are applicable to both columnar and equiaxed dendritic solidification, thus offering an efficient single-domain formulation. A fixed grid, fully implicit finite-difference procedure is employed in the numerical solution, and a novel front tracking technique is incorporated that is also implicit in nature and readily applies to multidimensional situations. Calculations are performed for one-dimensional (1-D) and two-dimensional (2-D) castings of Al-Cu and Sn-Pb alloys. The calculated CET positions are compared with previous measurements in a (1-D) ingot cast under well-controlled conditions, and good agreement is found. The effects of various casting parameters on the CET are numerically explored.     

Columnar to equiaxed transition of metals during solidification by using electric current pulse

 A new approach of applying the Electric Current Pulse (ECP) with parallel electrodes to promotion of the transition from columnar to equiaxed crystals and improvement of macrosegregation was introduced. And the experiments of application of ECP in the different stage of solidification have been carried out. The results show that applying ECP in both the initial and the late stage of solidification can promote the columnar to equiaxed transition (CET). Analysis shows that during solidification application of ECP induce a large number of nuclei around the upper surface, which subsequently showers down into the melt and impinges growth front of the columnar crystal. Therefore the CET occurs. In addition, this method is also employed to influence the solidification processing of bearing steel, the results show that the structrue is changed from columnar to equaixed, indicating that ECP can enhance the homogeneity of structure and composition of bearing steel.     

Observations of the columnar-to-equiaxed transition in stainless steels

Observations are reported for the columnar-to-equiaxed transition (CET) in stainless steel bars which have been solidified slowly and progressively in a horizontal configuration. For ferritic, austenitic, and ferritic/austenitic stainless steels containing more than 0.085 wt pct carbon, CETs occur at about the same distance from the start of solidification at a given growth rate. With increasing growth rates, the transition occurs closer to the start of solidification. At low carbon levels, near 0.02 wt pct carbon, the ferritic/austenitic steel is entirely columnar, in most cases. Adding nickel to the ferritic/austenitic steel, which makes the leading phase austenitic, produces a CET with small equiaxed grains. This suggests that different particles which are effective with austenitic growth become operative as nucleants. The transition from a columnar to an equiaxed structure occurs abruptly across the diameter of the sample. There is extensive fluid flow in the bulk melt, which produces shallow temperature gradients in the melt prior to the onset of solidification. The bulk melt flow does not appear to interact significantly with the melt in the interdendritic region or the melt immediately ahead of this region. The width of the solid/liquid region in the present experiments is observed to be between 10 and 20 mm, depending on the growth velocity and the distance from the start of solidification.     

Columnar to Equiaxed Transition During Solidification of Small Ingot by Using Electric Current Pulse

A new approach to applying the electric current pulse (ECP)with parallel electrodes to the promotion of the transition from columnar crystal to equiaxed crystal and the improvement of macrosegregation was introduced. The ECP was applied to different stages of the solidification. The results showed that the application of the ECP in both the initial stage (the thickness of solidified shell reached 2 mm approximately)and the late stage (the thickness of solidified shell reached 14 mm approximately)of solidification can promote the columnar to equiaxed transition (CET). The analysis showed that during solidification, a large number of nuclei around the upper surface fell off due to ECP, which subsequently showered on the melt and impinged the growth front of the columnar crystal. There-fore, the CET occurred. In addition, this method was also employed to influence the solidification process of bearing steel, and the results showed that the structure was changed from columnar crystal to equiaxed crystal, indicating that ECP can enhance the homogeneity of structure and composition of bearing steel.     

电渣重熔GH984G定向凝固组织CAFE法模拟

 电渣重熔凝固组织的控制直接关系到高温合金的品质与实际生产应用。针对电渣重熔GH984G的定向凝固过程,同时考虑传热和溶质扩散,基于CAFE法与C语言结合,建立了三维电渣重熔凝固过程组织演变的CAFE模型,并对凝固过程温度场和凝固组织演变进行模拟预测。结果表明,铸锭温度场和熔池深度都是首先为较浅平状态,然后不断加深至最后稳定;在电极熔化初始,金属熔池浅平,枝晶生长方向是竖直向上,之后金属熔池不断加深,底部竖直向上的柱状晶方向变为斜向上约26°。同时在铸锭的中心线上出现了等轴晶,等轴晶形核长大后与柱状晶镶嵌生长。此外,随着电极熔速变大,渣金界面上涨速度也随之变大,且熔池深度相应变宽变深。模拟结果与试验结果基本吻合,从而验证了模型与形核参数的适用性。     

On the Mechanism of Natural Convection and Equiaxed Structure during Dendritic Solidification Processes

A new technique has been developed to generate dendritic‐equiaxed structures in aluminium alloy casting processes, not only to improve the mechanical properties but also to study the effect of crystal structure on the chemical and physical properties of alloys to be cast. The investigation combined laboratory experimental work, metallographic examination and mathematic modelling. The laboratory experimental work involved different superheats for Al‐4.5%Cu alloy in cast ingots. Measurements of temperature distributions were conducted to verify the solidification model. A metallographic study combined macro and micro structural evolution of cast ingot samples. Two‐dimensional mathematical models of fluid flow and heat transfer were developed to characterise the natural convection streams and thermal fields. The model predictions were compared to temperature and isotherms measurements where a good agreement was found. The formation of cast structure and columnar, equiaxed transition (CET) and macro segregation phenomena were studied and discussed, based not only on the theories of nucleation but also on the thermal effects in the mushy and liquid zones.     

The effect of alloy composition and welding conditions on columnar-equiaxed transitions in ferritic stainless steel gas-tungsten arc welds

The columnar-equiaxed transition (CET) was investigated in full penetration gas-tungsten arc (GTA) welds on ferritic stainless steel plates containing different amounts of minor elements, such as titanium and aluminum, for a range of welding conditions. In general, the fraction of equiaxed grains increased, and the size of the equiaxed grains decreased with increasing titanium contents above 0.18 wt pct. At a given level of titanium, the equiaxed fraction increased, and the size of the equiaxed grains decreased with increased aluminum content. The CET was ascribed to heterogeneous nucleation of ferrite on Ti-rich cuboidal inclusions, since these inclusions were observed at the origin of equiaxed dendrites in the grain refined welds. Titanium-rich cuboidal inclusions, in turn, were found to contain Al-Ca-Mg-rich inclusions at their centers, consistent with observations by previous investigators for other processes. The welding conditions, in particular, the welding speed, were observed to affect the occurrence of the CET. Increasing the welding speed from 3 to 8 mm/s increased the equiaxed fraction noticeably, but a further increase in speed to 14 mm/s had a smaller additional effect. A finite element model (FEM) of heat transfer was used to examine the role of the welding conditions on the local solidification conditions along the weld pool edge. The results are compared with existing models for the CET. Formerly Postdoctoral Fellow, Department of Mechanical Engineering, University of Waterloo     

Laser Repair of Superalloy Single Crystals with Varying Substrate Orientations

The casting and repair of single-crystal gas turbine blades require specific solidification conditions that prevent the formation of new grains, equiaxed or columnar, ahead of the epitaxial columnar dendrites. These conditions are best determined by microstructure modeling. Present day analytical models of the columnar-to-equiaxed transition (CET) relate the microstructure to local solidification conditions (temperature gradient and interface velocity) without taking into account the effects of (1) a preferred growth direction of the columnar dendrites and (2) a growth competition between columnar grains of different orientations. In this article, the infiuence of these effects on the grain structure of nickel-base superalloy single crystals, which have been resolidified after laser treatment or directionally cast, is determined by experiment and by analytical and numerical modeling. It is shown that two effects arise for the case of a nonzero angle between the local heat flux direction and the preferred dendrite growth axis: (1) the regime of equiaxed growth is extended and (2) a loss of the crystal orientation of the substrate often occurs by growth competition of columnar grains leading to an “oriented-to-misoriented transition” (OMT). The results are essential for the definition of the single-crystal processing window and are important for the service life extension of expensive components in land-based or aircraft gas turbines. 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.     

Influence of Solidification Thermal Parameters on the Columnar-to-Equiaxed Transition of Aluminum-Zinc and Zinc-Aluminum Alloys

Understanding the interaction between the parameters involved in the columnar-to-equiaxed transition (CET) has gained considerable attention over the last two decades in the study of the structure of ingot castings. The present investigation was undertaken to investigate experimentally the directional solidification of Al-Zn and Zn-Al (ZA) alloys under different conditions of superheat and heat-transfer efficiencies at the metal/mold interface. The CET is observed; grain sizes are measured and the observations are related to the solidification thermal parameters: cooling rates, growth rates, thermal gradients, and recalescence determined from the temperature vs time curves. The temperature gradient in the melt, measured during the transition, is between –0.338 °C/mm and 0.167 °C/mm. In addition, there is an increase in the velocity of the liquidus front faster than the solidus front, which increases the size of the mushy zone. The size of the equiaxed grains increases with distance from the transition, an observation that was independent of alloy composition. The observations indicate that the transition is the result of a competition between coarse columnar dendrites and finer equiaxed dendrites. The results are compared with those previously obtained in lead-tin alloys. 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.