Modeling of interdendritic strain and macrosegregation for dendritic solidification processes: Part I. Theory and experiments

In the first part of this two-part article, mathematical models have been developed to characterize temperature, interdendritic stain, and segregation distributions during dendritic solidification. This aims to predict the effect of interdendric strain associated with sudden changes in the cooling conditions on the macrosegregation distributions, i.e., the combined effect of interdendric strain and macrosegregation on the dendritic structure. These theoretical models were verified on a laboratory scale. Four laboratory ingots of 0.53 and 0.9 wt pct C steels were cast horizontally and unidirectionally in a static mold under cooling conditions designed to approximate those in the continuous-casting process. Thermocouples recorded temperatures in the ingot at different locations from copper chill. The ingots were examined for macro-microstructure, and the extent of carbon macrosegregation was determined by wet chemical analysis. The experimental results indicate that static mold with sudden changes in the cooling conditions on the copper chill provides an approximately similar structure and macrosegregation profiles to those in a continuous-casting process. It is concluded that these cooling conditions have a significant effect on the fluctuated macrosegregation phenomenon. The sudden drop in the heat flux on the chill causes a positive segregation, whereas a sudden increase in heat flux results in a negative segregation. Also, the metallographic examination shows that there is high inelastic deformation of the dendrites due to the sudden drop in heat flux on the chill.     

Heat Flow and Solidification Modeling of Industrial Scale,Ingot Casting Operation

A model, based on the concept of effective thermal conductivity, was developed to study thermal fields and the resultant solidification behavior of large, round, industrial size ingots. In this, flow and turbulence phenomena during mold filling as well as subsequent solidification were not modeled explicitly but their influence was accounted for by artificially raising the thermal conductivity of solidifying steel. Thus, a conduction like equation embodying a conjugate approach was applied to simultaneously predict the evolution of temperature fields in the mold as well as in the solidifying ingot following teeming. Prior to comparing model predictions against industrial scale measurements, sensitivity of calculations to grid size, time step height, convergence criterion etc. were rigorously assessed. Similarly, modeling of interfacial resistance, chemical reactions and heat effects in the hot top as well as their influence on predicted results were evaluated computationally. Embodying mixed thermal boundary conditions (free convection + radiation) at the mold wall, temperature fields during solidification of two different industrial large ingots were predicted numerically. Parallely, mold wall temperature was monitored as a function of time and surface temperature of ingot was measured at the instant of mold stripping using hand held, radiation pyrometers. Incorporating relevant operating conditions (viz., mold dimensions and size, ingot and hot top dimensions and material, initial mold and liquid temperature etc.) into the calculation scheme, predictions were made via a computational procedure developed in-house and results thus obtained were compared against equivalent industrial scale measurements. Very reasonable agreement between the two was demonstrated.     

The use of water cooling during the continuous casting of steel and aluminum alloys

In both continuous casting of steel slabs and direct chill (DC) casting of aluminum alloy ingots, water is used to cool the mold in the initial stages of solidification, and then below the mold, where it is in direct contact with the newly solidified surface of the metal. Water cooling affects the product quality by (1) controlling the heat removal rate that creates and cools the solid shell and (2) generating thermal stresses and strains inside the solidified metal. This work reviews the current state-of-the-art in water cooling for both processes, and draws insights by comparing and contrasting the different practices used in each process. The heat extraction coefficient during secondary cooling depends greatly on the surface temperature of the ingot, as represented by boiling water-cooling curves. Thus, the heat extraction rate varies dramatically with time, as the slab/ingot surface temperature changes. Sudden fluctuations in the temperature gradients within the solidifying metal cause thermal stresses, which often lead to cracks, especially near the solidification front, where even small tensile stresses can form hot tears. Hence, a tight control of spray cooling for steel, and practices such as CO₂ injection/pulse water cooling for aluminum, are now used to avoid sudden changes in the strand surface temperature. The goal in each process is to match the rate of heat removal at the surface with the internal supply of latent and sensible heat, in order to lower the metal surface temperature monotonically, until cooling is complete.     

Heat transport and solidification in the electromagnetic casting of aluminum alloys: Part II. Development of a mathematical model and comparison with experimental results

In this second article of a two-part series, a mathematical model for heat transport and solidification of aluminum in electromagnetic casting is developed. The model is a three-dimensional one but involves a simplified treatment of convective heat transport in the liquid metal pool. Heat conduction in the solid was thought to play a dominant role in heat transport, and the thermal properties of the two alloys used in measurements reported in Part I (AA 5182 and 3104) were measured independently for input to the model. Heat transfer into the water sprays impacting the sides of the ingot was approximated using a heat-transfer coefficient from direct chill casting; because this heat-transfer step appears not to be rate determining for solidification and cooling of most of the ingot, there is little inaccuracy involved in this approximation. Joule heating was incorporated into some of the computations, which were carried out using the finite element software FIDAP. There was good agreement between the computed results and extensive thermocouple measurements (reported in Part I) made on a pilot-scale caster at Reynolds Metals Company (Richmond, VA).     

车轮钢圆坯表面温度和坯壳厚度的数值分析

采用分段线性的结晶器和二冷拉矫段热流密度表示方法,对车轮钢圆坯的宏观凝固过程进行了流场、温度场和凝固的耦合数学模拟.计算结果与实测数据吻合,表明数学模型可靠准确地反映了实际情况.由于拉速变化引起计算空间内质量流量的变化,圆坯的表面温度和坯壳厚度受拉速强烈影响.二冷拉矫段热流密度的变化反映了散热方式随温度变化进行的自我调节.保温段对圆坯表面温度回升有明显影响,并将凝固终点推后大约1 m.     

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.     

小方坯连铸机喷淋结晶器的研究

建立小方坯喷淋结晶器凝固传热数学模型，模拟计算了铸坯温度场、坯壳厚度、热流场，坯壳与铜壁间气隙厚度。计算坯壳厚度与实测坯壳厚度基本吻合；与普通水缝式结晶器相比，铸坯温度场均匀，坯壳厚度均匀，冷却强度有所提高。     

New narrow-wall design for the mold of continuous slab-casting machines

A mathematical model of ingot solidification is developed for a continuous slab-casting machine. This provides the basis for a new triplanar design of the narrow copper walls in the mold, with variable taper over the height. The ingot profile required to minimize copper wear in the lower part and ensure sufficient thickness in the upper part is calculated.     

On the development of a three-dimensional transient thermal model to predict ingot cooling behavior during the start-up phase of the direct chill-casting process for an AA5182 aluminum alloy ingot

The control of the heat transfer during the start-up phase of the direct-chill (DC) casting process for aluminum sheet ingots is critical from the standpoint of defect formation. Process control is difficult because of the various inter-related phenomena occurring during the cast start-up. First, the transport of heat to the mold is altered as the ingot base deforms and the sides are pulled inward during the start-up phase. Second, the range of temperatures and water flow conditions occurring on the ingot surface as it emerges from the mold results in the full range of boiling-water heat-transfer conditions—e.g., film boiling, transition boiling, nucleate boiling, and convection—making the rate of transport highly variable. For example, points on the ingot surface below the point of water impingement can experience film boiling, resulting in the water being ejected from the surface, causing a dramatic decrease in heat transfer below the point of ejection. Finally, the water flowing down the ingot sides may enter the gap formed between the ingot base and the bottom block due to butt curl. This process alters the heat transfer from the base of the ingot and, in turn, affects the surface temperature on the ingot faces, due to the transport of heat within the ingot in the vertical direction. A comprehensive mathematical model has been developed to describe heat transfer during the start-up phase of the DC casting process. The model, based on the commercial finite-element package ABAQUS, includes primary cooling via the mold, secondary cooling via the chill water, and ingot-base cooling. The algorithm used to account for secondary cooling to the water includes boiling curves that are a function of ingot-surface temperature, water flow rate, impingement-point temperature, and position relative to the point of water impingement. In addition, a secondary cooling algorithm accounts for water ejection, which can occur at low water flow rates (low heat-extraction rates). The algorithm used to describe ingot-base cooling includes both the drop in contact heat transfer due to gap formation between the ingot base and bottom block (arising from butt curl) as well as the increase in heat transfer due to water incursion within the gap. The model has been validated against temperature measurements obtained from two 711×1680 mm AA5182 ingots, cast under different start-up conditions (nontypical “cold” practice and nontypical “hot” practice). Temperature measurements were taken at various locations on the ingot rolling and narrow faces, ingot base, and top surface of the bottom block. Ingot-based deflection data were also obtained for the two test conditions. Comparison of the model predictions with the data collected from the cast/embedded thermocouples indicates that the model accounts for the processes of water ejection and water incursion and is capable of describing the flow of heat in the early stages of the casting process satisfactorily.     

Theoretical analysis of the possibility of controlling the solidification conditions in a continuously cast ingot

It is shown that the solidification conditions in an entire continuously cast ingot cannot be controlled by varying the thermal conditions of cooling the ingot surface. The methods that can intensify the heat transfer in the solidifying melt should be applied in the most problematic axial zone of the ingot.     

Research on segregation control for round billet of anti-sulfur steel

The carbon segregation that occurs in a round billet leads to instability in the anti-sulfur steel pipe.The maximum difference in the C content of these billets can reach 0.08%,and the equiaxed grain ratio is about 37.0%.In this paper,reasonable casting and mixing parameters were obtained by a study of the casting process,mold electromagnetic stirring,and the final electromagnetic stirring process.First,a mathematical model was established for the solidification and heat transfer of round-billet continuous casting using the characteristics of the continuous-casting process for sulfur-resistant steel pipes.The relationship between the casting speed,cooling-water ratio,and thickness of the shell at the final stirring position was analyzed.Then,the electromagnetic force and the liquid steel flow velocity were simulated and used to obtain reasonable parameters for the mold and final electromagnetic stirring.Through optimization of the casting and electromagnetic stirring technologies,the equiaxed grain ratio of the continuous-casting round billet increased to 53.4%and the maximum difference in the C content of the billet reduced to 0.031%.     

Heat-Transfer Measurements in the Primary Cooling Phase of the Direct-Chill Casting Process

Thermal modeling of the direct-chill casting process requires accurate knowledge of (1) the different boundary conditions in the primary mold and secondary direct water-spray cooling regimes and (2) their variability with respect to process parameters. In this study, heat transfer in the primary cooling zone was investigated by using temperature measurements made with subsurface thermocouples in the mold as input to an inverse heat conduction algorithm. Laboratory-scale experiments were performed to investigate the primary cooling of AA3003 and AA4045 aluminum alloy ingots cast at speeds ranging between 1.58 and 2.10 mm/s. The average heat flux values were calculated for the steady-state phase of the casting process, and an effective heat-transfer coefficient for the global primary cooling process was derived that included convection at the mold surfaces and conduction through the mold wall. Effective heat-transfer coefficients were evaluated at different points along the mold height and compared with values from a previously derived computational fluid dynamics model of the direct-chill casting process that were based on predictions of the air gap thickness between the mold and ingot. The current experimental results closely matched the values previously predicted by the air gap models. The effective heat-transfer coefficient for primary cooling was also found to increase slightly with the casting speed and was higher near the mold top (up to 824 W/m²·K) where the molten aluminum first comes in contact with the mold than near the bottom (as low as 242 W/m²·K) where an air gap forms between the ingot and mold because of thermal contraction of the ingot. These results are consistent with previous studies.     

大方坯连铸过程凝固规律

通过建立425mm×320mm连铸大方坯二维凝固传热数学模型,模拟了凝固坯壳的长大过程,并通过窄面射钉实验对数学模型进行了验证,精确得到了任意位置处大方坯凝固坯壳的厚度分布情况及最终凝固终点的位置,发现经典的凝固平方根定律对于连铸大方坯的凝壳长大进程不再适用.回归宽面中心坯壳厚度与凝固时间平方根的关系式发现,结晶器弯月面至二冷区出口,近似为线性关系,符合平方根定律,二冷区出口至凝固终点,二者为非线性关系,不再符合平方根定律.      

C9213钢锭传搁时间表的研制

应用钢锭冷凝过程二维数学模型，研究了Ｃ９２１３钢锭的冷凝规律，制订出了“Ｃ９２１３钢锭传搁时间表”，定量地分析了各盘钢锭间的热状态差异，对第１、２盘钢锭的装炉温度提出了修正。     

连铸喷淋结晶器的传热数学模型

针对铸坯在结晶器内的凝固特性，建立了喷淋冷却结晶顺的传热数学模型。并数值计算了普通循环水冷结晶器与喷淋冷却结晶器的冶金参数，讨论分析，比较了两种冷却方式的冶金效果。     

中锰钢高温热塑性研究

摘要：采用真空感应炉熔炼中锰钢,经铸铁模冷却至室温铸锭内部存在大量的微观裂纹,实验表明中锰钢高温热塑性极差。而采用铸铁模冷却至700℃后,置于700℃马弗炉随炉冷却至室温铸锭内部微观裂纹消失。将试样经过热轧锻造后,中锰钢的热塑性较为良好。研究表明铸锭中柱状晶发达以及凝固过程产生的微观裂纹是造成热塑性极差的主要原因,铸铁模快冷引起的热应力和铸锭完全凝固700℃以后相变应力是造成铸坯内部裂纹的主要因素。生产过程推荐采用结晶器、二冷段相对弱冷工艺措施降低铸坯产生裂纹风险性。     

The implementation of a mathematical model to characterize mold metal interface effects in metal casting

The formation of the air gap at the mold⧹metal interface during casting is responsible for considerable changes in local cooling rates. Often, boundary conditions input to a mathematical model have routinely been guessed at (often inaccurately) or have been determined experimentally, both of which can introduce difficulties in predicting solidification history. A novel technique which minimizes the error associated with selecting boundary conditions without experimentation is proposed. Advance knowledge of air gap formation and its correlation to the heat transfer coefficient at the mold⧹metal interface is used to formulate a coupled mathematical model which determines the growth of the air gap and predicts the instantaneous cooling conditions at a given mold wall. The accuracy of the simulation is consequently improved and the need to match experimental boundary conditions is eliminated. This paper presents the current results of an ongoing research program. © 1998 Canadian Institute of Mining and Metallurgy.     

大型扁型钢锭模的裂纹分析及结构优化设计

针对大型灰铸铁扁型钢锭模早期裂纹报废问题，采用计算机模拟计算技术对ＦＺ２５ｔ钢锭模使用过程的温度场、热应力和裂纹敏感系数的变化过程进行了数值计算分析，并优化了结构设计。     

The effect of cooling rate from the melt on the recrystallization behavior of aluminum alloy 6013

In most commercial operations, the plant metallurgist likely has little control over the solidification rate of the process. However, solidification rate is affected by the dimensions of the ingot, and product form (plate ingot vs extrusion billet, for example) determines the dimensions of the ingot to be cast. Consequently, understanding the effects of solidification rate might be useful in explaining differences in microstructure that are often observed in various product forms cast from equivalent compositions. To provide this microstructural information, the effect of cooling rate from the melt on the microstructural changes in hot-rolled and solution heat treated (SHT) aluminum alloy 6013 was investigated. The range of cooling rates in this investigation is comparable to what might be observed through the thickness of a plate ingot. Over the cooling rate range investigated (0.5 to 5 K/s), recrystallization behavior of the alloy appears to be primarily affected by the size and number density of the coarse α(AlFeMnSi) constituent particles, which act as sites for particle stimulated nucleation (PSN) of recrystallized grains. At intermediate cooling rates (1.5 K/s), the resistance to recrystallization is at a minimum. As the cooling rate increases beyond 1.5 K/s, the number of particles available for PSN decreases; thus, there is a decrease in the fraction of recrystallized grains after heat treating. On the other hand, as the cooling rate is decreased from 1.5 K/s, the size of the constituents increases; however, their number decreases, once again leading to a decrease in the fraction of recrystallized grains observed after heat treatment.