Thermomechanical analysis of direct chill casting using finite element method

The transient nature of the start-up phase is the most critical phase in the direct chill (DC) casting during which the quality of the ingot is questioned. The hot crack and cold crack are the two major problems in the DC casting which originate during and after the solidification. In this work, the thermal, metallurgical, and the mechanical fields of DC casting are modeled. The attention is focused on the mushy state of alloy where the chances are high for the hot tearing. The heat conduction and metallurgical phase-change phenomenon are modeled together in a strongly coupled manner. An isothermal staggered approach is followed to couple the thermal and mechanical parts within a time step. Finite element method is used to discretize the thermal and mechanical field equations. A temperature-based fixed grid method is followed to incorporate the latent heat. The mushy state of alloy is characterized through the Norton-Hoff viscoplastic law and the solid phase is modeled through the Garafalo law. An axisymmetric round billet is simulated. The casting material is considered as AA1201 aluminum alloy. It is found that all the components of stress and viscoplastic strain are maximum at the billet center. Further, the start-up phase stresses and strains are always higher than the steady state phase. Therefore, the chances of hot crack formation are higher during the start-up phase and specifically at the billet center. It is proved that through the ramping procedure, the vulnerability of start-up phase can be lowered.     

Effects of melt temperature and casting speed on the structure and defect formation during direct-chill casting of an Al-Cu alloy

A thorough experimental investigation of the effects of melt temperature and casting speed on the structure and defect formation during the steady and nonsteady stages of direct-chill (DC) casting of an Al-2.8 pct Cu alloy is performed. In addition, the temperature and melt-flow distributions in the sump of billets cast at different melt temperatures are numerically simulated and used in the discussion on the experimental results. Apart from already known phenomena such as the coarsening of the structure, deepening of the sump, and increased probability of bleed-outs during DC casting with increased casting temperature, a few new observations are made. The increased melt temperature is shown to increase the severity of subsurface segregation, whereas the macrosegregation in the rest of the billet remains virtually unaffected. Hot-tearing susceptibility is strongly diminished by an increased melt superheat. The amount and distribution of “floating” grains is demonstrated to depend on both the melt temperature and the casting speed. The porosity was found to only slightly depend on the melt temperature. The amount of nonequilibrium eutectic in the center of the billet increases with increasing melt temperature. The effects of melt temperature on the dimensions of the sump, transition region, and mushy zone and on the melt-flow pattern in the sump are discussed and used in the interpretation of experimentally observed phenomena. An erratum to this article is available at .     

Deformation Characteristics of Steel Billets with Liquid Core

To investigate the deformation characteristics of billets with liquid core during soft reduction and to clarify the correlation between internal cracks and deformation of the billet in the mushy zone, a fully coupled thermo‐mechanical Finite Element Model was developed in ABAQUS, furthermore, casting and soft reduction tests were carried out in a laboratory strand casting machine. During soft reduction the temperature distribution, the stress and strain states in the billet were calculated, the deformation characteristics of the billet during soft reduction were determined and the relation between internal cracks and equivalent plastic strain as well as maximal principal stress was analysed. The results show that tensile stresses can develop in the mushy zone during soft reduction and the equivalent strain nearby the Zero Ductility Temperature (ZDT) increases with a decreasing solid fraction. Internal cracks can be initiated when the accumulated strain exceeds the critical strain and /or the applied tensile stress exceeds the critical fracture stress during solidification. In addition, the factors (reduction efficiency and internal cracks) that should be considered to determine the optimal parameter for the soft reduction were established.     

Quantification of Input Uncertainty Propagation Through Models of Aluminum Alloy Direct Chill Casting

Insight into transport phenomena in complex solidification processes, such as direct chill (DC) casting, that cannot be found from experimental observation can be gained from numerical simulations. These predictions depend on material, process, and numerical parameters which contain inherit uncertainties due to experimental measurements or model assumptions. A fully transient numerical model of the direct chill casting process of Al-4.5 wt pct Cu was used to examine the propagation of input uncertainty to outputs of interest. The effect of microstructural model parameters, thermal boundary conditions, and material property input uncertainties were examined. Probability density functions were calculated based on these input uncertainties for metrics that characterize the ingot macrosegregation and sump depth. The macrosegregation-level predictions depend strongly on parameters that control the formation of the rigid mushy zone and shrinkage-driven flow. The heat release and transfer in the mushy zone are the dominant factors for determining the sump depth.

     

Development and validation of a thermal model of the direct chill casting of AZ31 magnesium billets

A mathematical model of the direct chill (DC) casting process for magnesium billets has been developed to predict the temperature in the billet, dummy block, and center pin using the commercial finite-element (FE) package, ABAQUS. Boundary conditions used for primary and secondary cooling and interfacial cooling between the billet and dummy block were defined based on the literature and knowledge of the physical phenomena occurring during the process. Temperatures in the billet, mold, and dummy block, as well as sump depth, were measured for a series of casting conditions during a plant trial conducted at Timminco Metals. The data obtained during the plant trial were used to “fine-tune” and validate the model for a variety of industrial casting conditions.     

Floating Grain Formation and Macrosegregation in a 2024 Al Alloy Prepared by Hot-Top DC Casting with a 2024 Al Alloy Insert

For the first time, the method of inserting a 2024 Al alloy rod into a melt of the same alloy during hot-top direct chill casting was used to verify the origin of floating grains and changes in the shape of the sump. Based on the as-cast structure and measured temperature distribution observed, we found that the 2024 Al alloy insert and the grains formed from melt surfaces and the interior walls of the launder or hot-top melted in the high-temperature region of the upper part of the hot-top; additionally, most of the dendrite fragments were captured by feathery grains. We confirmed that the nuclei in the center part of the liquidus isotherm region were able to form coarse-cell dendritic structures in the center part of the slurry zone due to the broad vertical width of this zone. Then, the coarse dendritic structures settled in the mushy zone, and fine dendrites formed in the periphery. In addition, with the insertion of the 2024 Al rod, a hillock-shaped liquidus isotherm was formed in the center part of the slurry zone, and the size of the floating grains in the billet processed with the insert was larger than that in the billet processed without the insert. However, surprisingly, the application of the 2024 Al rod reduced negative centerline segregation because it reduced the horizontal component of shrinkage flow.

     

Influence of Melt Feeding Scheme and Casting Parameters During Direct-Chill Casting on Microstructure of an AA7050 Billet

Direct-chill (DC) casting billets of an AA7050 alloy produced with different melt feeding schemes and casting speeds were examined in order to reveal the effect of these factors on the evolution of microstructure. Experimental results show that grain size is strongly influenced by the casting speed. In addition, the distribution of grain sizes across the billet diameter is mostly determined by melt feeding scheme. Grains tend to coarsen towards the center of a billet cast with the semi-horizontal melt feeding, while upon vertical melt feeding the minimum grain size was observed in the center of the billet. Computer simulations were preformed to reveal sump profiles and flow patterns during casting under different melt feeding schemes and casting speeds. The results show that solidification front and velocity distribution of the melt in the liquid and slurry zones are very different under different melt feeding scheme. The final grain structure and the grain size distribution in a DC casting billet is a result of a combination of fragmentation effects in the slurry zone and the cooling rate in the solidification range.     

Cold-Cracking Assessment in AA7050 Billets during Direct-Chill Casting by Thermomechanical Simulation of Residual Thermal Stresses and Application of Fracture Mechanics

Thermally induced strains and stresses developed during direct-chill (DC) semicontinuous casting of high strength aluminum alloys can result in formation of micro-cracks in different locations of the billet. Rapid propagation of such micro-cracks in tensile thermal stress fields can lead to catastrophic failure of ingots in the solid state called cold cracking. Numerical models can simulate the thermomechanical behavior of an ingot during casting and after solidification and reveal the critical cooling conditions that result in catastrophic failure, provided that the constitutive parameters of the material represent genuine as-cast properties. Application of fracture mechanics, on the other hand, can help to derive the critical crack length leading to failure. In the present research work, the state of residual thermal stresses was determined in an AA7050 billet during DC casting by means of ALSIM5. Simulation results showed that in the steady-state conditions, large compressive stresses form near the surface of the billet in the circumferential direction, whereas in the center, the stresses are tensile in all directions. Magnitudes of von Mises effective stresses, the largest component of principal stresses and the fracture mechanics concepts, were then applied to investigate the crack susceptibility of the billet.     

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.     

A mathematical model of the heat and fluid flows in direct-chill casting of aluminum sheet ingots and billets

A finite-element method model for the time-dependent heat and fluid flows that develop during direct-chill (DC) semicontinuous casting of aluminium ingots is presented. Thermal convection and turbulence are included in the model formulation and, in the mushy zone, the momentum equations are modified with a Darcy-type source term dependent on the liquid fraction. The boundary conditions involve calculations of the air gap along the mold wall as well as the heat transfer to the falling water film with forced convection, nucleate boiling, and film boiling. The mold wall and the starting block are included in the computational domain. In the start-up period of the casting, the ingot domain expands over the starting-block level. The numerical method applies a fractional-step method for the dynamic Navier-Stokes equations and the “streamline upwind Petrov-Galerkin” (SUPG) method for mixed diffusion and convection in the momentum and energy equations. The modeling of the start-up period of the casting is demonstrated and compared to temperature measurements in an AA1050 200×600 mm sheet ingot.     

电磁搅拌对水平连铸圆坯质量的影响

试验和分析了电磁搅拌(S-EMS、F-EMS)对连铸圆坯的中心等轴晶区比率、中间裂纹、缩孔、疏松的影响。结果表明,电磁搅拌后圆铸坯中平均中心等轴晶的比率比未经电磁搅拌的明显提高,中间裂纹和缩孔明显降低,搅拌强度适中时,疏松也会明显降低。     

Mathematical modelling of fluid flow,heat transfer and solidification phenomena in continuous casting of steel

A steady state, two-dimensional mathematical model for continuous billet casting operations has been developed. Towards this, governing equations of fluid flow and heat transfer together with their appropriate set of boundary conditions were derived and solved numerically via a control volume based implicit finite difference procedure (e.g., SIMPLE). The effect of various assumptions and procedures applied to modelling of turbulence phenomena, thermal buoyancy, flow through the mushy zone, free surface conditions etc., on the sensitivity of the computed results was investigated computationally. Of all these, modelling of heat and fluid flow phenomena in the mushy region was found to have relatively more effect on the predicted results. In addition to these, a set of three different billet casting operations reported in literature were simulated mathematically and direct comparisons were made between predicted and observed solidified shell profiles. Such comparisons demonstrated reasonable to excellent agreement between theory and experiments.     

Characterization of the flow in the molten metal sump during direct chill aluminum casting

A recent analytical model for the liquid aluminum flow in a direct chill (DC) casting sump has been investigated and the scaling coefficients evaluated. The magnitudes of flow-field features, such as the depth of the temperature stratification in the sump and the velocity of the metal in the thermal boundary layer close to the solidification front, have been calculated. The results broadly agree with recent full numerical calculations of the flow in the sump. The variation of these essential flow features has been investigated across a range of typical ingot sizes, casting speeds, and superheats, and critical macro-casting-parameter combinations have been identified. The limitations of the model are discussed and the possible effects the identified structure has on macrosegregation are briefly explored. Finally, the influence on the flow field of the method of feeding the ingot is investigated, and it is concluded that the model and these results are not invalidated if the feeding is nonuniform over the top surface of the sump.     

Solidification dynamics under random external-temperature fluctuations

The nonlinear dynamic mechanisms of solid-phase formation with a phase transition region are studied under periodic and random fluctuations of the cooling-boundary temperature. It is theoretically shown that a mushy zone can form even at close liquid and cooling-boundary temperatures due to random temperature field fluctuations. The growth of a solid phase with the mushy zone is investigated as a function of the autocovariance characteristics of random noises.     

连铸流动与凝固耦合模拟中糊状区系数的表征及影响

分析提出了连铸流动与凝固耦合数值模拟中, 钢液在两相区流动时的糊状区系数(A_mush)与渗透率的关系; 通过建立大方坯连铸结晶器三维耦合数值模型, 揭示了不同糊状区系数对钢液流动、传热与凝固进程的影响, 以及早期相关研究结果差异的源头.结果表明: 糊状区系数越大, 钢液在糊状区内的流动阻力越强, 凝固时钢液流动速度降低越快.采用较大的糊状区系数时, 糊状区呈较窄的"带状"分布在固液相之间; 当糊状区系数较小时, 糊状区范围变大, 钢液在结晶器内温降过快, 自由液面处出现过冷现象, 凝固坯壳局部发生重熔.结合实验数据验证与模型分析, 认为糊状区系数取值1×108~5×108 kg·m-3·s-1可以较可靠地揭示连铸结晶器内的实际凝固现象.      

Hot tearing criteria evaluation for direct-chill casting of an Al-4.5 pct Cu alloy

Predicting the occurrence of hot tears in the direct-chill (DC) casting of aluminum alloys by numerical simulation is a crucial step for avoiding such defects. In this study, eight hot tearing criteria proposed in the literature have been implemented in a finite-element method simulation of the DC casting process and have been evaluated. These criteria were based on limitations of feeding, mechanical ductility, or both. It is concluded that six criteria give a higher cracking sensitivity for a higher casting velocity and that five criteria give a higher cracking sensitivity for the center location of the billet. This is considered in qualitative accordance with casting practice. Seven criteria indicate that use of a ramping procedure (lower casting speed during start-up phase) does not make a significant difference. However, in industrial practice, this is a common procedure, needed for avoiding hot cracking. Only one criterion is in qualitative accordance with casting practice, but it fails to quantitatively predict the hot tearing occurrence during DC casting.     

20CrMnTi连铸瞬态与平均冷速条件下凝固原位观察

 宽淬透性带和大尺寸TiN析出物严重危害20CrMnTi齿轮钢的产品质量,其控制的关键基础是掌握连铸过程中凝固组织演变行为机理。传统高温激光共聚焦扫描显微镜(HT-CSLM)原位观察研究通常将糊状区冷却速率设定为固定值,这不能有效反映连铸凝固过程中冷却速率的变化。为此,以国内某钢厂20CrMnTi 160 mm×160 mm小方坯为研究对象,首先通过二维切片凝固传热计算,确定内弧表面下方20、40、60 mm位置处糊状区的热历程、瞬态与平均冷却速率,进而设计HT-CSLM试验升温与降温方案。然后,开展这些位置处糊状区瞬态与平均冷却速率条件下HT-CSLM试验,研究揭示不同冷却条件下20CrMnTi的凝固过程、δ晶粒生长动力学和包晶相变机制。最后,通过电子探针分析(EPMA),考察冷却条件对凝固组织尺寸的影响规律。结果表明,由于凝固潜热的补偿,内弧皮下20、40、60 mm位置处初始凝固阶段冷却速率较小,凝固中后期逐渐增大,且越深入方坯内部越显著。这些位置处的平均冷却速率分别为102.81、44.63和34.93 ℃/min。δ晶粒率先从钢液中析出,其平均生长速率随着冷却速率的提升而增大。在瞬态冷却速率条件下,随着凝固的进行,瞬时生长速率呈增大的趋势,但是在平均冷却速率条件下瞬时生长速率则略微降低。这是因为在瞬态冷却速率条件下,糊状区冷却速率由慢至快,不断补偿了凝固潜热,同时初始形核数量少,生长空间大,溶质过冷度的影响相对较弱。当熔体温度降低至包晶相变临界温度时,δ晶粒快速转变为γ晶粒,即发生块状转变,导致固相率迅速增加,且伴随有部分γ晶粒快速聚合。整体上讲,包晶相变临界温度随着冷却速率的增大而降低,但是也受溶质初始含量的影响。此后,剩余液相向γ相转变,直至完全凝固。晶粒半径随着冷却速率的提升而减小,且在平均冷却速率条件下比瞬态冷却速率条件更小,这取决于初始凝固阶段的形核数量。     

As-Cast Residual Stresses in an Aluminum Alloy AA6063 Billet: Neutron Diffraction Measurements and Finite Element Modeling

The presence of thermally induced residual stresses, created during the industrial direct chill (DC) casting process of aluminum alloys, can cause both significant safety concerns and the formation of defects during downstream processing. Although numerical models have been previously developed to compute these residual stresses, most of the computations have been validated only against measured surface distortions. Recently, the variation in residual elastic strains in the steady-state regime of casting has been measured as a function of radial position using neutron diffraction (ND) in an AA6063 grain-refined cylindrical billet. In the present study, these measurements are used to show that a well-designed thermomechanical finite element (FE) process model can reproduce relatively well the experimental results. A sensitivity analysis is then carried out to determine the relative effect of the various mechanical parameters when computing the as-cast residual stresses in a cylindrical billet. Two model parameters have been investigated: the temperature when the alloy starts to thermally contract and the plasticity behavior. It is shown that the mechanical properties at low temperatures have a much larger influence on the residual stresses than those at high temperatures.     

连铸二冷区铸坯表面测温综述

连铸工艺是从液态钢水到固态铸坯的传热凝固过程,温度是其中的一个重要控制参数。在二冷区,铸坯表面温度是设计二冷配水制度的重要依据,铸坯表面温度的控制是确保铸坯质量的重要手段。对现有的连铸二冷区铸坯表面温度测量方法进行了综述,着重介绍了红外测温的原理和方式,同时对红外点温仪的应用和红外热像仪的研究做了详细的分析和总结,并对未来发展方向提出了一些观点和看法。     

Analysis of Mould,Spray and Radiation Zones of Continuous Billet Caster by Three‐dimensional Mathematical Model based on a Turbulent Fluid Flow

An analysis of mould, spray and radiation zones of a continuous billet caster has been done by a three‐dimensional turbulent fluid flow and heat transfer mathematical model. The aim was to reduce crack susceptibility of the billets and enhance productivity of the billet caster. Enthalpy‐porosity technique is used for the solidification. Turbulence is modelled by a realizable k‐ε model. The three‐dimensional mesh of the billet is generated by Gambit software, and Fluent software is used for the solution of equations. In various zones, different standard boundary conditions are applied. Enhanced wall treatment is used for the turbulence near the wall. In the mould region, Savage and Prichard expression for heat flux is applied. In the spray cooling zone, the heat transfer coefficient for surface cooling of the billet is calculated by knowing the water flow rate and the nozzle configuration of the plant. The model predicts the velocities in the molten pool of a billet, the temperature in the entire volume of billet, the heat transfer coefficient in the mould region, the heat flux in the cooling zone and radiation cooling zone, and the shell thickness at various zones. The model forecasts that the billet surface temperature up to the cutting region is above the austenite‐ferrite transformation temperature (which is accompanied by large volume change). The model predicts a temperature difference of maximum 700 K between the centre and surface of the billet. The entire solidification takes place at 11.0 m length at 3.0 m/min. For the same casting arrangement, increasing the casting speed up to 4.0 m/min has been explored. Based on the simulation results, recommendations to alter the spray water flow rate and spray nozzle diameter are presented to avoid a sudden change of temperature.