Effects of alloy composition and casting speed on structure formation and hot tearing during direct-chill casting of Al-Cu alloys

Effects of casting speed and alloy composition on structure formation and hot tearing during direct-chill (DC) casting of 200-mm round billets from binary Al-Cu alloys are studied. It is experimentally shown that the grain structure, including the occurrence of coarse grains in the central part of the billet, is strongly affected by the casting speed and alloy composition, while the dendritic arm spacing is mostly dependent on the casting speed. The hot cracking pattern reveals the maximum hot-tearing susceptibility in the range of low-copper alloys (1 to 1.5 pct) and at high casting speeds (180 to 200 mm/min). The clear correlation between the amount of nonequilibrium eutectics (representing the reserve of liquid phase in the last stage of solidification) and hot tearing is demonstrated. A casting speed-copper concentration-hot-tearing susceptibility chart is constructed experimentally for real-scale DC casting. Computed dimensions of the solidification region in the billet are used to explain the experimentally observed structure patterns and hot cracking. Thermomechanical finite-element simulation of the solidifying billet was used as a tool for testing the applicability to DC casting of several hot-tearing criteria based on different principles. The results are compared to the experimentally observed hot tearing. It is noted that hot-tearing criteria that account for the dynamics of the process, e.g., strain rate, actual stress-strain situation, feeding rate, and melt flow, can be successfully used for the qualitative prediction of hot tearing.     

Two-phase modeling directed toward hot tearing formation in aluminum direct chill casting

The two-phase mass and momentum conservation equations governing shrinkage-driven melt flow and thermally induced deformation are formulated for the aluminum direct chill (DC) casting process. Two main mechanisms associated with hot tearing formation during solidification and subsequent cooling are thus addressed simultaneously in the same mathematical model. The approach unifies the two-phase mushy zone model outlined by Farup and Mo, the constitutive relations that treat the mushy zone as a viscoplastic porous medium saturated with liquid outlined by Martin et al., and the “classical” mechanics approach to thermally induced deformations in solid (one-phase) materials using the linear kinematics approximation. A temperature field and a unique solidification path are considered as input to the model. The governing equations are solved for a one-dimensional (1-D) situation with some relevance to the DC casting process. The importance of taking into account the transfer of momentum from the liquid phase to the solid phase is then demonstrated through modeling examples. Furthermore, the modeling results indicate that the constitutive law governing the viscoplastic behavior of the solid skeleton of the mushy zone should take into account that the solid skeleton can be compressed/dilated as well as stress space anisotropy. Calculated peak values for liquid pressure and solid stress turn out to correlate to the hot tearing susceptibility measured in casting trials in the sense that trials having the largest cracks are those for which the highest pressures and stresses are computed.     

An A Priori Hot-Tearing Indicator Applied to Die-Cast Magnesium-Rare Earth Alloys

Hot-tearing susceptibility is an important consideration for alloy design. Based on a review of previous research, an a priori indicator for the prediction of an alloy’s hot-tearing susceptibility is proposed in this article and is applied to a range of magnesium-rare earth (RE)-based alloys. The indicator involves taking the integral over the solid fraction/temperature curve between the temperature when feeding becomes restricted (coherency) and that when a three-dimension network of solid is formed (coalescence). The hot-tearing propensity of Mg-RE alloys is found to vary greatly depending on which RE is primarily used, due to the difference in the solidification range. Mg-Nd alloys are the most susceptible to hot tearing, followed by Mg-Ce-based alloys, while Mg-La alloys show almost no hot tearing. The proposed indicator can be well applied to hot-tearing propensity of the Mg-RE alloys. It is expected that the indicator could be used as an estimation of the relative hot-tearing propensity in other alloy systems as well.     

Hot-Tearing Susceptibility of Ternary Mg-Al-Sr Alloy Castings

The susceptibility of Mg-Al-Sr alloys to hot tearing during permanent mold casting was investigated using constrained rod casting (CRC) in a steel mold. The alloys included Mg-xAl-1.5Sr and Mg-xAl-3Sr, where x = 4, 6, or 8 wt pct. The hot-tearing susceptibility (HTS) was determined based on the widths and locations of the cracks in the rods. With the Mg-xAl-1.5 Sr alloys, the HTS decreased significantly with increasing Al content. With the Mg-xAl-3Sr alloys, the trend was similar but not as significant. At the same Al content, the HTS was significantly lower at 3 wt pct Sr than at 1.5 wt pct Sr. To help understand the HTS of these alloys, the solidification path and phase fractions were calculated for each alloy. The HTS was found to increase with increasing fraction solid at the end of primary solidification.     

Linear Contraction Behavior of Low-Carbon,Low-Alloy Steels During and After Solidification Using Real-Time Measurements

A technique for measuring the linear contraction during and after solidification of low-alloy steel was developed and used for examination of two commercial low-carbon and low-alloy steel grades. The effects of several experimental parameters on the contraction were studied. The solidification contraction behavior was described using the concept of rigidity in a solidifying alloy, evolution of the solid fraction, and the microstructure development during solidification. A correlation between the linear contraction properties in the solidification range and the hot crack susceptibility was proposed and used for the estimation of hot cracking susceptibility for two studied alloys and verified with the real casting practice. The technique allows estimation of the contraction coefficient of commercial steels in a wide range of temperatures and could be helpful for computer simulation and process optimization during continuous casting.     

<Emphasis Type="Italic">In-situ</Emphasis> three-dimensional microstructural investigation of solidification of an Al-Cu alloy by ultrafast x-ray microtomography

This article presents the first results of a new experimental technique developed to investigate the evolution of the morphology of the solid and liquid phases during the solidification of a metallic alloy. It consists of ultrafast X-ray microtomography observations of a solidifying aluminum-copper alloy carried out at ESRF. These experiments allow investigating in-situ the formation of the casting microstructure and of the evolution of the morphology of the solid and the liquid phases. It allows also the in-situ determination of the solidification path, of the variation of the copper content in both the liquid and solid phases, and of some other characteristic parameters of the microstructure. Provided that some forthcoming technical improvements on the experimental setup are performed, more quantitative results can be obtained as well as better image quality and resolution.     

Q235B钢板坯连铸凝固传热行为的数值模拟计算

基于涟钢板坯连铸机结构参数和冷却条件,建立了Q235B 230 mm×1 280 mm板坯连铸过程凝固传热的数值模型,研究了铸坯温度分布和坯壳厚度变化规律以及过热度和拉速对铸坯温度和凝固末端位置的影响规律。得出:随过热度和拉速的增加,铸坯中心和角部温度整体呈升高趋势,在其它参数不变的条件下,过热度每升高10℃,铸坯凝固末端和液相消失位置分别后移约0.38 m和0.31 m;拉速每升高0.1 m/min,凝固末端和液相消失位置分别后移2.06 m和1.4 m。通过数值模拟研究,掌握了铸坯温度和凝固末端位置的变化规律。     

TearSim: A two-phase model addressing hot tearing formation during aluminum direct chill casting

A two-phase mathematical model for the study of hot tearing formation is presented. The model accounts for the main phenomena associated with the formation of hot tears, i.e., the lack of feeding at the late stages of solidification and the localization of viscoplastic deformation. The model incorporates an advanced viscoplastic constitutive model for the coherent part of the mushy zone, allowing for the possibility of dilatation/densification of the semisolid skeleton under applied deformation. Based on quantities computed by the model, a hot tearing criterion is proposed where liquid feeding difficulties and viscoplastic deformation at the late stages of solidification are taken into account. The model is applied to study hot tearing formation during the start-up phase for direct-chill (DC) casting of extrusion ingots, and to discuss the effect of different phenomena and process parameters. The modeling results are also compared to experimentally measured hot tearing susceptibilities, and the model is able to reproduce known experimental trends such as the effect of the casting speed and the importance of the design of the starting block.     

Physical modeling of the deformation mechanisms of semisolid bodies and a mechanical criterion for hot tearing

The mechanical response of a semisolid body to an applied, uniaxial strain rate has been expressed as a function of strain by modifying an existing analysis based on an idealized representation of the microstructure. An existing mechanical criterion for hot tearing of the semisolid body has been adapted to the deformation mechanisms. The resulting hot tearing model shows that the strength of the body depends on the strain, the viscosity of the intergranular fluid, the solid fraction, the isothermal compressibility of the fluid, the surface tension of the liquid, the limiting liquid-film thickness for viscous flow and a parameter m, which describes microstructure. The effect of each parameter on the mechanical response and the onset of hot tearing has been examined for ranges of values relevant to aluminum alloys and the direct-chill (DC) casting process. The parameter testing has shown that the mechanical response predicted by the model agrees well with some experimental data for both the mechanisms of fracture and the parameters that govern the process. An adjustment of unknown model parameters to experimental data would permit use of the model as a constitutive law and a fracture criterion for numerical modeling of hot tearing during the solidification of Al alloys by DC casting.     

GCr15轴承钢大方坯凝固过程微观偏析模型及应用研究

建立了考虑δ/γ相变的GCr15轴承钢大方坯连铸凝固两相区溶质微观偏析模型,并应用于220 mm ×260 mm铸坯的凝固传热。结果表明:通过模型可以获得高碳钢精确的固液相线温度,以及温度与固相率的关系;GCr15轴承钢大方坯凝固过程仅析出γ相,凝固末期S、P和C元素的偏析严重;固相率越大,冷却速率对偏析度的影响更明显;S和P元素含量以及冷却速率对零塑性温度（ZDT）影响较大;采用基于凝固传热模型优化的连铸工艺后,铸坯中心碳偏析指数控制在0.961.05,且铸坯未产生内裂纹。     

Modeling of solidification of metal-matrix particulate composites with convection

A multiphase model for the alloy solidification of metal-matrix particulate composites with convection is developed. Macroscopic transport equations are written for each phase, with unknown parameters modeled through supplementary relations pertiment to the solidification of a binary alloy matrix containing a stationary solid phase and generally nonstationary spherical particles. The model is applied to various one- and two-dimensional systems containing an Al-7 wt pct Si/SiC composite. One-dimensional sedimentation results in nonclustering and clustering particle systems show good agreement with experiments. One-dimensional composite solidification results illustrate the effect of particle clustering and cooling direction on the final macroscopic particle distribution. Two-dimensional results in various unreinforced and reinforced systems illustrate macroscopic particle segregation and its effect on buoyancy-driven melt convection and species macrosegregation. Results indicate a nearly uniform particle distribution for relatively small particles due to negligible particle settling prior to entrapment. For relatively large particles, significant particle settling prior to entrapment results in large denuded and packed zones in the casting. Fluid flow and macrosegregation during solidification are substantially reduced in the presence of particles, due to the relatively large interfacial drag exerted on the liquid by the stationary mush and particle phases.     

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.     

Development of the manufacture of billets based on high-strength aluminum alloys

When pressure is applied upon casting as a factor of external impact on melt, the problems related mainly to filling of molds are solved; however, some casting defects cannot be avoided. The experimental results demonstrate that complete compensation of shrinkage under pressure can be achieved by compressing of casting by 8–10% prior to beginning of solidification and by 2–3% during the transition of a metal from the liquid to the solid state. It is mentioned that the procedure based on compressing a liquid metal can be efficiently applied for manufacture of high-strength aluminum alloy castings. The selection of engineering parameters is substantiated. Examples of castings made of V95 alloy according to the developed procedure are given. In addition, the article discusses the problems related to designing of engineering and special-purpose equipment, software, and control automation.     

Contraction of aluminum alloys during and after solidification

A technique for measuring the linear contraction during and after solidification of aluminum alloys was improved and used for examination of binary and commercial alloys. The effect of experimental parameters, e.g., the length of the mold and the melt level, on the contraction was studied. The correlation between the compositional dependences of the linear contraction in the solidification range and the hot tearing susceptibility was shown for binary Al-Cu and Al-Mg alloys and used for the estimation of hot tearing susceptibility of 6XXX series alloys with copper. The linear thermal contraction coefficients for binary and commercial alloys showed complex behavior at subsolidus temperatures. The technique allows estimation of the contraction coefficient of commercial alloys in a wide range of temperatures and could be helpful for computer simulations of geometrical distortions during directchill (DC) casting.     

Mathematical simulation on coupled flow, heat, and solute transport in slab continuous casting process

A three-dimensional comprehensively coupled model has been developed to describe the transport phenomena, including fluid flow, heat transfer, solidification, and solute redistribution in the continuous casting process. The continuous casting process is considered as a solidification process in a multicomponent solid-liquid phase system. The porous media theory is used to model the blockage of fluid flow by columnar dendrites in the mushy zone. The relation between flow pattern and the shape of the solid shell is demonstrated. Double diffusive convection caused by thermal and concentration gradients is considered. The change in the liquidus temperature with liquid concentration is also considered. The formation mechanism of macrosegregation is investigated. Calculated solid shell thickness and temperature distribution in liquid core are compared with the measured quantities for validating the model.     

Modeling on Dendrite Growth of Medium Carbon Steel during Continuous Casting

Dendrite growth is an important phenomenon during steel solidification. In the current paper, a numerical method was used to analyse and calculate the dendrite tip radius, dendrite growth velocity, liquid concentration, temperature gradient, cooling rate, secondary dendrite arm spacing, and the dendrite tip temperature in front of the solid/liquid (S/L) interface for the solidification process of medium carbon steels during continuous casting. The current model was well validated by published models and measurement data. The results show that in the continuous casting process, the dendrite growth rate is dominated by the casting speed. Dendrite growth rate, liquid concentration at the S/L interface, temperature gradient and cooling rate decrease with proceeding solidification and solid shell thickness growth, while other parameters such as dendrite tip radius, secondary dendrite arm spacing, and dendrite tip temperature in front of the S/L interface become larger with solidification progress and solid shell thickness growth. Parametric investigations were carried out. The effects of the stability coefficient, temperature gradient and casting speed on the micro‐structural parameters were discussed. Under the same conditions, higher casting speed promotes coarser secondary dendrite arm spacing and enlarges the dendrite tip radius, while decreasing temperature gradient, reducing the dendrite growth rate and making the solute distribute more uniform.     

An analytical model for optimal directional solidification using liquid metal cooling

In what follows, a model is developed that describes the optimal processing parameters for directional solidification using liquid metal cooling (LMC). The model considers a sample with a flat geometry and, as a first approximation, can be used to treat the flat sections of a turbine blade. The model predicts (1) the optimal withdrawal rate of the casting from the hot zone, (2) the temperature gradient in the liquid at the solidification interface, and (3) the temperature profile along the length of the casting. The model is then used to perform a sensitivity analysis of the LMC process. Cooling bath temperature, baffle thickness, shell thickness, and shell thermal conductivity are shown to have a strong influence on system performance.     

Structural Morphologies and Deformaiton Characteristics of Semi‐solid Type 304 Stainless Steel during Solidificaiton and Remelting

Microstructural evolutions of type 304 stainless steel and the related mechanical property of flow stress in semi‐solid state are investigated. The evolutions of microstructure during solidification, partial remelting of a hot‐rolled billet and partial remelting of a cast billet are compared with respect to structural morphologies in the semi‐solid state. Various structural morphologies, such as the linear and multilayered liquid/austenite/δ‐ferrite structure, globular liquid/δ‐ferrite structure and dendrite structure, are characterized using optical micrographs and an EPMA (electron probe microanalyzer). The various structural morphologies in the semi‐solid state are influenced not only by the phase transformation but also by the previous treatment of type 304 steel, such as hot rolling and casting. Furthermore, a series of hot compression tests are conducted for various combinations of deformation rate and deformation temperature in the semi‐solid state, to measure the flow stress and the change in microstructure resulting from plastic deformation. Flow stress, phase segregation, microfracture and distortion of solid particles during and after the hot compression test are strongly affected by the structural morphology in the semi‐solid state, such as the dendrite structure, nonglobular structure and globular structure. Semi‐solid type 304 stainless steel with dendrite structure exhibits the highest flow stress, which is about three times that of steel with globular structure, although the testing temperature and deformation rate are controlled to be the same. This is a result of the higher bonding force between solid particles and lower fluidity of the liquid phase of the dendrite structure than those of the globular structure, which exhibits excellent fluidity of the liquid phase and rotation of solid particles.     

Modeling of microstructural evolution with tracking of equiaxed grain movement for multicomponent Al-Si alloy

A new model for the simulation of microstructure evolution of multicomponent alloys with equiaxed dendritic and eutectic morphology has been developed based upon the mixture-theory model (continuum approach). The model can account for the effects of natural convection, solidification contraction, solidification kinetics, and grain movement on the solidification microstructure evolution. The novelty of this model is that it includes tracking of equiaxed dendritic and eutectic grains movement during solidification and, thus, eliminates the assumption of uniform grain size in a given volume element, which is standard in current advanced solidification models. This is achieved through the implementation of continuous nucleation laws and of a grain distribution function over the volume element, in addition to solid transport simulation through the energy equation. To track grain movement, rules of tracking grain movement are proposed. The model deals with nonequilibrium solidification and describes competitive growth of primary and eutectic phases. The proposed model was implemented to simulate the microstructural evolution of an Al-Si-Mg alloy (A356) during solidification. An equivalent pseudobinary approach was developed to calculate the solidification parameters required in modeling of this multicomponent alloy. Computational experiments with the new model have demonstrated that significant variations in the volumetric grain density exist throughout the casting because of natural convection. These differences can be traced with the proposed grain tracking technique but not with current solidification models.