Mathematical modeling of particle segregation during centrifugal casting of metal matrix composites

A one-dimensional transient heat-transfer model coupled with an equation for force balance on particles is developed to predict the particle segregation pattern in a centrifugally cast product, temperature distribution in the casting and the mold, and time for complete solidification. The force balance equation contains a repulsive force term for the particles that are in the vicinity of the solid/liquid interface. The solution of the model equations has been obtained by the pure implicit finite volume technique with modified variable time-step approach. It is seen that for a given set of operating conditions, the thickness of the particle-rich region in the composite decreases with an increase in rotational speed, particle size, relative density difference between particles and melt, initial pouring temperature, and initial mold temperature. With reduced heat-transfer coefficient at the casting/mold interface, the solidification time increases, which, in turn, results in more intense segregation of solid particulates. Again, with increased initial volume fraction of the solid particulates in the melt, both the solidification time and the final thickness of the particulate-rich region increase. It is noted that for Al-Al₂O₃ and Al-SiC systems, in castings produced using finer particles, lower rotational speeds, and an enhanced heat-transfer coefficient at the casting/mold interface, the volume fraction of particles in the outer layer of the casting remains more or less the same as in the initial melt. However, for castings produced with coarser particles at higher rotational speeds and reduced heat-transfer coefficients at the casting/mold interface, intense segregation is predicted even at the outer periphery of the casting. In the case of the Al-Gr system, however, intense segregation is predicted at the innermost layers.     

Heat transfer-solidification kinetics modeling of solidification of castings

A close examination of the recent developments in the field of computer simulation of solidification process reveals that a combination of both macroscopic and microscopic models is necessary in order to accurately describe the solidification of castings. Currently available macroscopic models include models that describe heat transfer from metal to mold, fluid flow of liquid metal during mold filling, and stress field in the casting. At the microscopic level, the models should include more intricate issues such as solidification kinetics and fluid flow in the mushy zone. Although significant progress has been accomplished over the years in each field, the task of including all of these models into a comprehensive package is far from being complete. This paper describes the state of the art on coupling the macroscopic heat transfer (HT) and microscopic solidification kinetics (SK) models and introduces thelatent heat method as a more accurate method for solving the heat source term in the heat conduction equation. A new method for calculation of fraction of solid evolved during solidification based on computer-aided cooling curve analysis (CA-CCA), as well as a method based on nucleation and growth kinetics laws, is discussed. A new nucleation model based on the concept of instantaneous nucleation, which is used to describe equiaxed eutectic solidification of commercial alloys, has been introduced. It is demonstrated that the instantaneous nucleation model agrees well with the experimental results in terms of cooling curves and of evolution of the fraction of solid during solidification. Validation results are also shown for SK models that are based on CA-CCA coupled with HT models for eutectic Al-Si and gray cast iron alloys.     

Metal-Mold interfacial heat transfer

During the solidification of metal castings, an interfacial heat transfer resistance exists at the boundary between the metal and the mold. This heat transfer resistance usually varies with time even if the cast metal remains in contact with the mold, due to the time dependence of plasticity of the freezing metal and oxide growth on the surface. The present work has studied interfacial heat transfer on two related types of castings. In the first type, a copper chill was placed on the top of a cylindrical, bottom gated casting. Using the techniques of transducer displacements and electrical continuity, a clearance gap was detected between the solidified metal and the chill. The second type of casting had a similar design except that the chill was placed at the bottom. Owing to the effect of gravity, solid to solid contact was maintained at the metal-chill interface, but the high degree of interface nonconformity resulted in a relatively low thermal conductance as indicated by solution of the inverse heat conduction problem. Finally, the influence of interfacial heat transfer on solidification time with three mold ma-terials is compared by a numerical example, and criteria for utilizing Chvorinov's rule are discussed. Formerly Graduate Student.     

Electrospark alloying of the titanium alloy VT6 with tungsten-free hard alloys

The mass transfer kinetics and alloying elements distribution in a coating layer on the titanium alloy VT6 were investigated, as well as the properties of the layer after electrospark alloying with tungsten free electrodes based on the refractory compounds of titanium and zirconium nitride. !t was shown that the microhardness of the alloyed layer is 3-S times, and of the heat affected zone 1.5-2.0 times greater than that of the initial material. The resistance of the coated samples to high-temperature oxidation was also substantially higher.     

22MnB5钢溶质分配系数及TiN析出对微观偏析的影响

为了提高凝固过程中溶质微观偏析模型计算的准确性,基于溶质分配系数及夹杂物析出对溶质偏析的重要影响,定量分析了溶质分配系数以及TiN析出对凝固过程溶质元素含量的影响,为微合金高强钢凝固过程研究提供理论参考.针对22MnB5钢建立了耦合TiN析出热力学模型的溶质微观偏析模型,并探究了温度及钢液凝固路径对溶质分配系数的影响规...     

Heat flow parameters affecting the unidirectional solidification of pure metals

Unidirectional solidification of pure metals has been studied as a function of liquid superheat, heat transfer coefficient of the metal/mold interface(h _i ), and mold material. Experimental results show that the position of the solid/liquid interface (X) varies with time (l) following the relationshipX(t) = A . t ^1/2 -B, where, for a fixed metal,B is a constant only dependent on the superheat through a parabolic law andA is another constant that is independent of the superheat but dependent on the mold heat sink capacity,i.e., mold material and coefficienth _i At the same time, it has been calculated that the constantA varies withh _i through an error-function type law tending asymptotically to Lyubov’s exact analytic solution.     

Thermomechanics of the cooling stage in casting processes: Three-dimensional finite element analysis and experimental validation

A thermomechanical three-dimensional (3-D) finite element analysis of solidification is presented. The heat transfer model is based on a multidomain analysis accounting for noncoincident meshes for the cast part and the different mold components. In each subdomain, a preconditioned conjugate gradient solver is used. The mechanical analysis assumes the mold is rigid. A thermoelastic-viscoplastic rheological model is used to compute the constrained shrinkage of the part, resulting in an effective local air gap width computation. At each time increment, a weak coupling of the heat transfer and mechanical analyses is performed. Comparisons of experimental measurements and model predictions are given in the case of a hollow cylindrical aluminum alloy part, showing a good quantitative agreement. An application to an industrial aluminum casting is presented, illustrating the practical interest of thermomechanical computations in solidification analysis.     

Theoretical and experimental investigations on macrosegregation caused by mixing in the liquid bulk melt

An improved model describing the macrosegregation caused by mixing in the liquid bulk melt is presented. This model includes the mass transfer between the interdendritic liquid and the bulk melt which takes place additionally to the mass transfer via the boundary layer in front of the dendrite tips. Further, laboratory experiments on macrosegregation of iron-carbon alloys are described. The experiments were carried out in a unidirectional solidification device with 1,5 kg melts. During the solidification process the liquid melt was stirred by a ceramic blade stirrer with rotational speeds between 180 and 720 min^?1. The melts were supperheated above the liquidus temperature by amounts between 3 and 80 K. The solidification velocities were 2 to 6 mm/min. The experiments could satisfactorily be described by the model using an exchange factor α for the amount of additional mass transfer. The exchange factor increases with decreasing amounts of superheating and solidification velocity and with increasing stirring speed.     

低碳钢薄板坯高速连铸保护渣研究与优化

 针对低碳钢薄板坯高速连铸过程中保护渣液渣层过薄、黏结报警频发、铸坯表面纵裂纹过多等问题,在充分考虑高拉速下低碳钢凝固收缩特性的基础上,确定了保护渣润滑与传热性能的优化方向并开展了工业试验。将保护渣碱度从1.10提高到1.30,Li₂O质量分数从0.57%提高到1.06%,Na₂O质量分数从5.48%提高到8.16%,碳质量分数由7.71%降低到6.72%。对2种保护渣的流变性能和渣膜3层结构进行了深入研究,发现优化后保护渣渣膜中的液渣层比例增加,渣膜润滑系数α增大;同时,渣膜中的结晶层比例也有一定程度的提高,渣膜热阻系数β增大,从而使保护渣的润滑性能和控制传热能力均得到改善。从矿相分析结果看出,保护渣碱度的提高在一定程度上会促进硅灰石的析出,导致渣膜结晶率提高、热阻增大,进而起到控制传热的目的。生产实践表明,在拉速提高后,使用新型保护渣基本避免了黏结和裂纹的产生,生产效率和铸坯质量均得到显著提高。     

Crystallization features of solid slag films of ultrahigh- basicity mold fluxes for continuous casting

The ultrahigh- basicity mold flux for industrial application(binary basicity of 1. 74) was selected and solidified by an improved water- cooled copper probe. Different probe immersion times were adopted to analyze the solidification process of films. The growth speeds and closed porosities of solid films were measured. The crystallization processes by solidification and devitrification were also analyzed, respectively. The results indicate that the growth speed of the solid slag film during the initial solidification period (0-15s) is 79. 9??m/s. 2CaO??SiO2??NaF with small spherical shapes is the primary crystal which leads to devitrification. The average devitrification speed of the glassy film is 65??m/s, and the primary crystal in the outer layer of solid films is lathlike cuspidine(3CaO??2SiO2??CaF2). The growth of the lathlike cuspidine in the outer layer of films increases the closed porosity and decreases the effective thermal conductivity of solid slag films.     

Analytical,numerical, and experimental analysis of inverse macrosegregation during upward unidirectional solidification of Al-Cu alloys

The present work focuses on the influence of alloy solute content, melt superheat, and metal/mold heat transfer on inverse segregation during upward solidification of Al-Cu alloys. The experimental segregation profiles of Al 4.5 wt pct Cu, 6.2 wt pct Cu, and 8.1 wt pct Cu alloys are compared with theoretical predictions furnished by analytical and numerical models, with transient h _i profiles being determined in each experiment. The analytical model is based on an analytical heat-transfer model coupled with the classical local solute redistribution equation proposed by Flemings and Nereo. The numerical model is that proposed by Voller, with some changes introduced to take into account different thermophysical properties for the liquid and solid phases, time variable metal/mold interface heat-transfer coefficient, and a variable space grid to assure the accuracy of results without raising the number of nodes. It was observed that the numerical predictions generally conform with the experimental segregation measurements and that the predicted analytical segregation, despite its simplicity, also compares favorably with the experimental scatter except for high melt superheat.     

软接触电磁连铸过程中结晶器及初生坯壳的传热

为了解高频磁场对软接触电磁连铸结晶器及初生坯壳传热行为的影响,用有限元二维数值模拟方法计算了软接触连铸过程中结晶器及初生坯壳的传热.得知在高频磁场（f=20 kHz）作用下,电磁场的感应加热会减少连铸初生坯壳的厚度、提高连铸坯的表面温度,并大幅度提高分瓣结晶器铜壁的温度.     

Convection in the two-phase zone of solidifying alloys

The analysis is applicable to alloy solidification which proceeds horizontally to the center of a mold. The model follows the growth of the solid-liquid zone adjacent to the chill face (the initial transient), the movement of the zone across the mold, and the region of final solidification adjacent to the centerline (the final transient). During solidification the density of the liquid varies across the twophase zone. Consequently, there is natural convection which is treated as flow through a porous medium. The equations for convection are coupled with the equation of solute redistribution between the phases in order to calculate macrosegregation after solidification is complete. Results were computed for alloys which show: (1) “inverse segregation≓ at a cooled-surface; (2) macrosegregation resulting from solidification with the initial transient, a period with a complete two-phase zone, and a final transient; and (3) macrosegregation when the width of the two-phase zone exceeds the semi-width of the mold.     

Determination of interface heat transfer coefficient between aluminum casting and graphite mold

To produce castings of titanium, nickel, copper, aluminum, and zinc alloys, graphite molds can be used, which makes it possible to provide a high cooling rate. No die coating and lubricant are required in this case. Computer simulation of casting into graphite molds requires knowledge of the thermal properties of the poured alloy and graphite. In addition, in order to attain adequate simulation results, a series of boundary conditions such as heat transfer coefficients should be determined. The most important ones are the interface heat transfer coefficient between the casting and the mold, the heat transfer coefficient between the mold parts, and the interface heat transfer coefficient into the environment. In this study, the interface heat transfer coefficient h between the cylindrical aluminum (99.99%) casting and the mold made of block graphite of the GMZ (low ash graphite) grade was determined. The mold was produced by milling using a CNC milling machine. The interface heat transfer coefficient was found by minimizing the error function reflecting the difference between the experimental and simulated temperatures in a mold and in a casting during pouring, solidification, and cooling of the casting. The dependences of the interface heat transfer coefficient between aluminum and graphite on the casting surface temperature and time passed from the beginning of pouring are obtained. It is established that, at temperatures of the metal surface contacting with a mold of 1000, 660, 619, and 190°C, the h is 1100, 4700, 700, and 100 W/(m² K), respectively; i.e., when cooling the melt from 1000°C (pouring temperature) to 660°C (aluminum melting point), the h rises from 1100 to 4700 W/(m² K), and after forming the metal solid skin on the mold surface and decreasing its temperature, the h decreases. In our opinion, a decrease in the interface heat transfer coefficient at casting surface temperatures lower than 660°C is associated with the air gap formation between the surfaces of the mold and the casting because of the linear shrinkage of the latter. The heat transfer coefficient between mold parts (graphite–graphite) is constant, being 1000 W/(m² K). The heat transfer coefficient of graphite into air is 12 W/(m² K) at a mold surface temperature up to 600°C.     

无氟连铸结晶器保护渣的结晶性能

 结晶器与连铸坯间的保护渣膜直接影响着连铸坯的润滑及传热,而保护渣的结晶性能是影响润滑和传热的重要因素。通过测定保护渣的结晶温度、结晶率和结晶体几何尺寸,研究了碱度和TiO2含量对含钛无氟保护渣结晶性能的影响规律。结果表明：加大碱度和增加TiO2含量都能明显提高保护渣的结晶倾向性。     

Furnace atmosphere effects on casting of eutectic superalloys

Control of furnace atmosphere is a key factor in the use of silica-bonded alumina shell molds for the directional solidification of eutectic superalloys reinforced with tantalum monocarbide whiskers. The use of a furnace atmosphere which is simultaneously oxidizing to aluminum in the eutectic alloy and reducing to silica phases in the mold results in the formation of an alumina barrier layerin situ at the metal/mold interface and an absence of silica phases in the mold region adjacent to this barrier layer. The presence of this microstructure permits castings of eutectics at metal temperatures up to 1750°C.     

Mold Simulator Study of Heat Transfer Phenomenon During the Initial Solidification in Continuous Casting Mold

In this paper, mold simulator trials were firstly carried out to study the phenomena of the initial shell solidification of molten steel and the heat transfer across the initial shell to the infiltrated mold/shell slag film and mold. Second, a one-dimensional inverse heat transfer problem for solidification (1DITPS) was built to determine the temperature distribution and the heat transfer behavior through the solidifying shell from the measured shell thickness. Third, the mold wall temperature field was recovered by a 2DIHCP mathematical model from the measured in-mold wall temperatures. Finally, coupled with the measured slag film thickness and the calculations of 1DITPS and 2DIHCP, the thermal resistance and the thickness of liquid slag film in the vicinity of the meniscus were evaluated. The experiment results show that: the total mold/shell thermal resistance, the mold/slag interfacial thermal resistance, the liquid film thermal resistance, and the solid film thermal resistance is 8.0 to 14.9 × 10^?4, 2.7 to 4.8 × 10^?4, 1.5 to 4.6 × 10^?4, and 3.9 to 6.8 × 10^?4 m² K/W, respectively. The percentage of mold/slag interfacial thermal resistance, liquid film thermal resistance, and solid film thermal resistance over the total mold/shell thermal resistance is 27.5 to 34.4, 17.2 to 34.0, and 38.5 to 48.8 pct, respectively. The ratio of radiation heat flux is around 14.1 to 51.9 pct in the liquid slag film.     

亚包晶钢板坯连铸保护渣凝固结晶行为的研究

对≤1.3 m/min常规拉速(TCaO/SiO₂=1.19)和≥1.5 m/min高拉速(TCaO/SiO₂=1.40)0.07～0.10C亚包晶钢板坯用两种保护渣(%:2.54～3.0Al₂O₃、7.34～8.35Na₂O、8.83～8.87F、0.79～3.00Li₂O)降温凝固过程中结晶特性以及结晶对熔渣粘度的影响进行了研究,得出高拉速保护渣在凝固之前有明显的结晶行为,结晶矿相主要为枪晶石(3CaO·2SiO2·CaF₂);常规拉速保护渣在凝固温度以上时,没有明显的结晶现象。与常规拉速保护渣相比,高拉速保护渣完全凝固后晶粒粗大,组织中有大量空隙,有利于增加渣膜热阻,减缓结晶器传热。TCaO/SiO₂=1.40保护渣在结晶温度以上时,具有较低的粘度,有利于结晶器润滑;结晶温度以下时,粘度迅速增加,有利于增加固渣膜厚度,减缓结晶器传热。     

Solidification Microstructure of Aluminum AA 6016-T4 Resistance Spot Welds Using a Short-Pulse Technique

The influence of the duration of the current pulse on the solidification microstructure of resistance spot welded (RSW) samples of aluminum alloy 6016-T4 with the short-pulse technique was investigated through experiments and numerical modeling. Microstructure was analyzed in terms of morphology and size, and primary and secondary dendrite arm spacing were measured on experimental samples. A reduction in pulse width resulted in a fine, columnar-dendritic microstructure in the outer regions of the fusion zone as well as a larger equiaxed-dendritic zone in the fusion zone center. A two-dimensional, axisymmetric finite element model of the spot welding process with new methods for calculation of the solidification parameters G (thermal gradient in the solid behind the solid–liquid interface) and R (velocity of the solid–liquid interface) was used for investigation of influence of pulse time on solidification microstructure and comparison to experimental results. Morphological trends in the solidification structure showed good agreement between experiments and simulations, and the influence of the pulse duration on the solidification parameters evolved because of changing heat transfer conditions. Simulated solidification data suggest that the solidification of aluminum during RSW falls in the regime of rapid solidification.