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.     

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 .     

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.     

Simulation of Solidification Microstructure and Columnar to Equiaxed Transition in Free‐cutting Steel 9SMn28 based on a CAFE Method

The solidification microstructure in 9SMn28 free‐cutting steel is simulated by the finite element – cellular automaton (CAFE) method based on the calculation of convection in a casting. The simulation results are consistent with experimental findings; the simulated crystallisation process conforms to the actual situation. The solidification of 9SMn28 alloy is a volume solidification mode under slow cooling condition. The columnar‐to‐equiaxed transition (CET) is also studied in the CAFE model. The mechanism of the CET in the CAFE model is thermal interaction. The CET is not abrupt but occurs gradually, the long columnar grains are first blocked by elongated grains. The grains become more equiaxed as the thermal gradient is decreased with the development 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.     

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.     

Grain structures in gas tungsten-arc welds of austenitic stainless steels with ferrite primary phase

The grain structures were investigated in full penetration gas tungsten-arc (GTA) welds in sheets of 304 and 321 austenitic stainless steels for a range of welding conditions. In type 321 steel welds, fine equiaxed ferrite dendrites were observed in the ferrite phase. The equiaxed structure was ascribed to heterogeneous nucleation of ferrite on Ti-rich cuboidal inclusions present in this steel, since these inclusions were observed at the origin of equiaxed dendrites. In type 304 welds, the ferrite grains were columnar, except in less complete penetration specimens, where a few coarse equiaxed dendrites appeared to originate from the weld surface. The secondary austenitic grain structure was columnar in both steels. In type 304 steel, the columnar austenitic grain structure did not necessarily correspond to the primary ferrite grains. In type 321 steel, the secondary austenite was columnar despite the equiaxed structure of the primary ferrite. Factors which affect the columnar-to-equiaxed transition (CET) are discussed. The failure to form equiaxed austenitic grains in type 321 steel is ascribed to austenite growing across the space between ferrite grains instead of renucleating on the primary equiaxed ferrite.     

Three-dimensional probabilistic simulation of solidification grain structures: Application to superalloy precision castings

A two-dimensional (2-D) probabilistic model, previously developed for the prediction of microstructure formation in solidification processes, is applied to thin section superalloy precision castings. Based upon an assumption of uniform temperature across the section of the plate, the model takes into account the heterogeneous nucleation which might occur at the mold wall and in the bulk of the liquid. The location and crystallographic orientation of newly nucleated grains are chosen randomly among a large number of sites and equiprobable orientation classes, respectively. The growth of the dendritic grains is modeled by using a cellular automaton technique and by considering the growth kinetics of the dendrite tips. The computed 2-D grain structures are compared with micrographie cross sections of specimens of various thicknesses. It is shown that the 2-D approach is able to predict the transition from columnar to equiaxed grains. However, in a transverse section, the grain morphology within the columnar zone differs from that of the experimental micrographs. For this reason, a three-dimensional (3-D) extension of this model is proposed, in which the modeling of the grain growth is simplified. It assumes that each dendritic grain is an octaedron whose half-diagonals, corresponding to the <100> crystallographic orientations of the grain, are simply given by the integral, from the time of nucleation to that of observation, of the velocity of the dendrite tips. All the liquid cells falling within a given octaedron solidify with the same crystallographic orientation of the parent nucleus. It is shown that the grain structures computed with this 3-D model are much closer to the experimental micrographie cross sections.     

Modeling of equiaxed microstructure formation in casting

A general micro/macroscopic model of solidification for 2-D or 3-D castings, valid for both dendritic and eutectic equiaxed alloys, is presented. At the macroscopic level, the heat diffusion equation is solved with an enthalpy formulation using a standard FEM implicit scheme. However, instead of using a unique relationship between temperature and enthalpy (i.e., a unique solidification path), the specific heat and latent heat contributions, whose sum equals the variation of enthalpy at a given node, are calculated using a microscopic model of solidification. This model takes into account nucleation of new grains within the undercooled melt, the kinetics of the dendrite tips or of the eutectic front, and a solute balance at the scale of the grain in the case of dendritic alloys. The coupling between macroscopic and microscopic aspects is carried out using two time-steps, one at the macroscopic level for the implicit calculation of heat flow, and the other, much finer, for the microscopic calculations of nucleation and growth. This micro/macroscopic approach has been applied to one-dimensional and axisymmetric castings of Al-7 pct Si alloys. The calculated recalescences and grain sizes are compared with values measured for one-dimensional ingots cast under well-controlled conditions. Furthermore, the influence of casting conditions on temperature field, undercooling, grain size, and microstructural spacings is shown to be predicted correctly from axisymmetric calculations with regard to the expected experimental behavior.     

Benchmark Al-Cu Solidification Experiments in Microgravity and on Earth

Metallurgical and Materials Transactions A - Predicting macrosegregation and grain structure, including the columnar to equiaxed transition (CET), in alloy solidification is an ongoing challenge....     

Prediction of the As-Cast Structure of Al-4.0 Wt Pct Cu Ingots

A two-stage simulation strategy is proposed to predict the as-cast structure. During the first stage, a 3-phase model is used to simulate the mold-filling process by considering the nucleation, the initial growth of globular equiaxed crystals and the transport of the crystals. The three considered phases are the melt, air and globular equiaxed crystals. In the second stage, a 5-phase mixed columnar-equiaxed solidification model is used to simulate the formation of the as-cast structure including the distinct columnar and equiaxed zones, columnar-to-equiaxed transition, grain size distribution, macrosegregation, etc. The five considered phases are the extradendritic melt, the solid dendrite, the interdendritic melt inside the equiaxed grains, the solid dendrite, and the interdendritic melt inside the columnar grains. The extra- and interdendritic melts are treated as separate phases. In order to validate the above strategy, laboratory ingots (Al-4.0 wt pct Cu) are poured and analyzed, and a good agreement with the numerical predictions is achieved. The origin of the equiaxed crystals by the “big-bang” theory is verified to play a key role in the formation of the as-cast structure, especially for the castings poured at a low pouring temperature. A single-stage approach that only uses the 5-phase mixed columnar-equiaxed solidification model and ignores the mold filling can predict satisfactory results for a casting poured at high temperature, but it delivers false results for the casting poured at low temperature.     

Using a Three-Phase Deterministic Model for the Columnar-to-Equiaxed Transition

In order to overcome the limitations of previous columnar-to-equiaxed (CET) models, which neglect melt convection and the movement of free equiaxed grains, this article presents a three-phase deterministic CET model. With appropriated multiphase volume-averaging approaches, it is possible to account for nucleation and growth of equiaxed grains ahead of a growing columnar front, the influence of melt convection, and grain sedimentation, and the occurrence of a CET in a casting of engineering scale. Special modeling assumptions ensure that both CET mechanisms, namely, “hard” and “soft” blocking, are tackled. It is highly recommended that both mechanisms should be considered, especially in the situation where grain sedimentation and melt convection are present. Although the current model incorporates almost all the physical variables relevant to a CET event, under special condition of a one-dimensional case, the model still reproduces the results of Hunt’s classical CET approach. 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.     

Macro- and Microstructure Evolution of 5CrNiMo Steel Ingots during Electroslag Remelting Process

A comprehensive mathematical model was established and used to simulate the macro and microstructure evolution during the production process of 5CrNiMo steel ingot by electroslag remelting （ESR） method. Along the ingot height, the macrostructure distribution characteristics changed from vertical, fine columnar grains to tilted, coarse columnar grains, and this transformation process occurred at the very beginning of ESR. In the cross section of the ingot, there were three grain morphology regions and two grain type transition regions from the outside to the center of the ingot. These regions were the fine columnar grain region, columnar competitive growth transition re gion, coarse columnar grain region, columnar to equiaxed grain transition （CET） region, and coarse equiaxed grain region. The influence of the remelting rate on the macrostructure and mlcrostructure was investigated using a series of experiments and simulations. The results showed that a low remelting rate could produce a small grain growth angle （GGA） ; the average secondary dendrite arm spacing （SDAS） firstly decreased and then increased as the remelting rate increased. An excessively high or low remelting rate can increase the GGA and average SDAS in ingots. Thus, the remelting rate should be controlled within a suitable range to reduce composition microsegregation and microshrinkage in the ingot to produce an ESR ingot with satisfactory hot forging performance.     

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.      

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.