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High Temperature Materials and Processes

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Volume 36, Issue 7

Issues

Influence of Secondary Cooling Mode on Solidification Structure and Macro-segregation Behavior for High-carbon Continuous Casting Bloom

Kun Dou / Zhenguo Yang
  • State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing, Beijing 10083, China
  • Special Steel Plants, Laiwu Iron and Steel Co., Ltd., Laiwu 271104, Shandong, China
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/ Qing Liu
  • Corresponding author
  • State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing, Beijing 10083, China
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/ Yunhua Huang
  • Institute for Advanced Materials and Technology, University of Science and Technology Beijing, Beijing 100083, China
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/ Hongbiao Dong
Published Online: 2017-07-19 | DOI: https://doi.org/10.1515/htmp-2016-0022

Abstract

A cellular automaton–finite element coupling model for high-carbon continuously cast bloom of GCr15 steel is established to simulate the solidification structure and to investigate the influence of different secondary cooling modes on characteristic parameters such as equiaxed crystal ratio, grain size and secondary dendrite arm spacing, in which the effect of phase transformation and electromagnetic stirring is taken into consideration. On this basis, evolution of carbon macro-segregation for GCr15 steel bloom is researched correspondingly via industrial tests. Based on above analysis, the relationship among secondary cooling modes, characteristic parameters for solidification structure as well as carbon macro-segregation is illustrated to obtain optimum secondary cooling strategy and alleviate carbon macro-segregation degree for GCr15 steel bloom in continuous casting process. The evaluating method for element macro-segregation is applicable in various steel types.

Keywords: carbon macro-segregation; cellular automaton–finite element method; solidification structure; secondary cooling mode; continuous casting

Introduction

As an important type of high-carbon steel, solidification structure and macro-segregation of GCr15 steel in continuous casting process have obvious influence on the quality of the final rolled products [1]. Desired solidification structure can be obtained by optimization of solidification parameters, for which numerical simulation is an economic and desirable way.

Over the past decades, several models for predicting the solidification structure formation have been developed, including stochastic models such as the Monte Carlo method [2] and cellular automaton (CA) method [3, 4] and deterministic models like the phase-field method [5, 6] Many attempts have been carried out to simulate solidification structure formation of alloys using these methods. However, applications of these models are mainly focused on ingot casting [7, 8] and few attempts have been made in simulating solidification structure formation in continuous casting. Two reasons account for this. First, forced flow in melt during solidification is too complex to be simulated, such as electromagnetic stirring (EMS), bulging, soft reduction and so on. Second, complex transformations such as peritectic reaction occur during the solidification of steel, which make modeling of solidification structure in continuous casting very difficult. The formation mechanism of carbon macro-segregation is closely associated with solidification structure for continuous casting of steel while the variation of secondary cooling mode would have obvious impact on the solidification structure such as columnar-to-equiaxed transition (CET), dendrites orientation, grain size (GS) [9, 10]. Hence, it would be necessary to illustrate the impact of various secondary cooling modes on solidification structure characteristics and describe the formation mechanism of carbon macro-segregation in GCr15 steel continuous casting process.

In this paper, the cellular automaton–finite element (CA–FE) coupling model [11, 12] is used to simulate the solidification structure of GCr15 steel bloom under different secondary cooling modes in continuous casting process, in which the variation of thermophysical parameters during solidification and the effect of EMS are taken into consideration. On this basis, industrial tests under the same casting condition are conducted to obtain specimens for carbon segregation and solidification structure analysis. Finally, the relationship between carbon macro-segregation and solidification structure evolution under different secondary cooling modes is discussed.

Thermophysical properties calculation

A simple pair-wise mixture model (shown in eq. (1) [13]) based on the thermodynamic database from Procast software is used to calculate the thermophysical properties of GCr15 steel at different temperatures, including thermal conductivity, density, enthalpy, etc. The calculated results are coupled into the FE model later.[13] P=XiPi+ij>iXiXjvΩVXiXjV(1)

where P and Pi are the thermophysical properties of one phase and pure element, respectively. ΩV is the binary interaction parameter, Xi and Xj are the mole fractions of elements i and j.

Chemical compositions of GCr15 steel are given in Table 1. Temperature dependences of enthalpy, density, thermal conductivity and fraction of solid are calculated by importing them into the thermodynamic database, as depicted in Figure 1. It could be seen that variation of enthalpy, density and thermal conductivity with temperature indicated several turning points, e. g. the range of 1,613–1,723 K and 893–1,043 K corresponds to the phase transformation l → γ and γ → α, respectively.

Table 1:

Main chemical compositions for GCr15 steel (wt. %).

Calculated thermophysical properties of GCr15 steel.
Figure 1:

Calculated thermophysical properties of GCr15 steel.

Numerical model

In the present model, the CA method is combined with heat transfer calculation during the continuous casting process. The CA–FE model simulating the solidification structure mainly includes heat transfer model, nucleation model and dendrite tip growth kinetics.

Heat transfer model

A two-dimensional unsteady state heat transfer equation is available as eq. (2) [14]: ρcTt=xkTx+ykTy(2)

where ρ is density, c is specific heat, keff is thermal conductivity. The evolution of latent heat during solidification is incorporated to the calculation by using the effective specific heat method, shown in eq. (3). Cp=CpLdfsdT(3)

where Cp is the effective specific heat, L is the latent heat and fs is the solid fraction.

The heat transfer model based on the moving slice method is established to simulate the solidifications of GCr15 steel. Figure 2 shows the boundary conditions of the heat transfer model during the continuous casting process. The section size of slice is the same as the bloom, 260 mm × 300 mm and the thickness is 10 mm. In this research, the secondary cooling zone is divided into five segments according to water flow rate, such as foot roller zone, I zone, II zone, III zone and IV zone.

Schematic illustration of boundary conditions and the slice moving method.
Figure 2:

Schematic illustration of boundary conditions and the slice moving method.

The length, boundary conditions and calculated formula are listed in Table 2. In Table 2, T, Tw, Te are the temperature of the bloom surface, the water temperature in the secondary cooling zone, the environment temperature of the air cooling zone, respectively, K; qm, qk,i and qa are the heat flux of mold, segment i in secondary cooling zone and air cooling zone, respectively, kW/m2; t is the holding time in the mold, s; β is a coefficient about the conditions of the mold, kW/(m2 s1/2); hi is the heat transfer coefficient of segment i in the secondary cooling zone, W/(m2 K); Wi is the sprayed water density of segment i in secondary cooling zone, L/(m2 min); σ is Stefan–Boltzmann constant, W/(m2 K4); ε is the radiation coefficient. The heat flux of mold is assumed to be a function of the casting speed and the distance from the meniscus. The most important parameter that affects the mold heat flux qm is the mold dwell time (equivalent to distance below the meniscus) neglecting the steel grade, entry nozzle geometry, mold flux, etc.

Table 2:

Boundary conditions and the calculated formula of GCr15 steel.

In the secondary cooling zone, the surface heat flux qk,i is proportional to the heat transfer coefficient hi as well as the difference between the surface temperature and the temperature of cooling water. The radiative heat transfer to the atmosphere is neglected in water cooling zone.

Nucleation model

Nucleation can be divided into homogeneous nucleation and heterogeneous nucleation during solidification process. In the present study, the continuous heterogeneous model [17] is applied. A continuous nucleation distribution function, dn/d(∆T), is used to describe the grain density change, dn is induced by increase of the undercooling, d(∆T). The distribution function is expressed by eq. (4) [17]. dndΔT=nmax2πΔTσexp12ΔTΔTmaxΔTσ2(4)

where ΔT is the calculated local undercooling, K; ΔTmax is the mean undercooling, K; ΔTσ is the standard deviation, K; nmax is the maximum nucleation density which can be reached when all the nucleation sites are activated while cooling, m−3.

Gaussian distribution is used to describe heterogeneous nucleation both at the mold surface and in the bulk of the melt. Two such functions are shown in Figure 3 [3].

Nucleation site distributions for nuclei formed at the mold wall (indexed as “s”) and in the bulk of the liquid (indexed as “v”) [3].
Figure 3:

Nucleation site distributions for nuclei formed at the mold wall (indexed as “s”) and in the bulk of the liquid (indexed as “v”) [3].

Dendrite tip growth

The growth kinetics of both columnar and equiaxed morphologies can be calculated. The KGT (Kurz, Givoanola, Trivedi) model [18, 19] is used as the model of growth kinetics of a dendrite tip in the GCr15 steel. Based on the marginal stability criterion, eq. (5) is obtained. V2A+VB+C=0(5)

where A=π2/P2D2, B=mC0(1k0)c/D[1(1k0)Iv(P)], C = G, Γ is the Gibbs–Thomoson coefficient (Γ=1.9×107), V is the growth velocity of a dendrite tip, P is the Peclet number for solute diffusion, D is the diffusion coefficient in the liquid, m is the liquidus slope, C0 is the initial concentration, k0 is the partition coefficient, Iv(P) is the Ivantsov function, ξc = π2/(k0p) and it closes to unity at low temperature gradient, G is the temperature gradient. For the dendrite growth regime, G has little effect on the growth velocity V and can be regarded as zero.

Ttip is the temperature at the dendrite tip, T0 is the melting point of GCr15 steel (T0 = 1,630 K), ∆T is the undercooling temperature at a tip of dendrite (∆T= Ttip − T0), ∆T is expressed as eq. (6). ΔT=mC01111k0IvP+2r(6)

where r is the dendrite tip radius. The relationship between the undercooling ∆T and growth velocity V can be calculated by substituting an arbitral value of the Peclet number into eqs. (5) and (6). The material properties of GCr15 steel used in the simulation are given in Table 3.

Table 3:

Materials properties of GCr15 steel used in the simulation.

In order to accelerate the computation velocity during the simulation process, KGT model is fitted and the following equation (eq. (7)) is gained. v(ΔT)=a2ΔT2+a3ΔT3(7)

where a2 and a3 are the fitting coefficients of the KGT model, both of them reflect the growing velocity of the dendrite tip. ΔT is the total undercooling of the dendrite tip. Using the simulation and based on Table 3, the calculated values of a2 and a3 are 0 and 1.354 × 10−5m/(s K3).

Effect of EMS

EMS is generally used to reduce the centerline segregation in the continuous casting process. To evaluate the effect of the fluid flow due to EMS on heat flow in the bloom, accurate flow pattern in the molten steel melt should be known. However, at present, it is difficult to combine accurate calculation of fluid flow with heat transfer calculation and the CA procedure due to very large computational load. Two methods have been reported for incorporating the effect of fluid flow into heat transfer calculation.

  1. Changing thermal conductivity of liquid during EMS [22, 23, 24]. By this means, it is considered that the thermal conductivity of molten steel with EMS is larger than that without EMS. Based on the solid–liquid coexisting zone model proposed by Takahashi et al. [24], thermal conductivity of solid is used in the region of solid and the mushy zone with solid fraction (fs) larger than 0.7 while the effective thermal conductivity of liquid with fluid flow is used in the liquid region and mushy zone with fs < 0.3. In the mushy zone with 0.3 ≤ fs ≤ 0.7, thermal conductivity is assumed to change with fs linearly, as shown in Figure 4. The exact value of the thermal conductivity in liquid with EMS is not clear since it varies with the flow velocity of the liquid. Hence, several testing are required to find an appropriate one to describe the real casting conditions in simulation. Mizikar [22] used a 7.5 times higher thermal conductivity while a 10 times higher thermal conductivity was used in Yamazaki’s study [25]. In the present simulation, an 8.5 times higher thermal conductivity is assigned after many tests.

  2. Changing crystal formation rate in bulk liquid [8, 26]. In this way, it is considered that the crystal formation rate would increase due to the contribution of fragmentation of dendrites caused by EMS, which should be incorporated into the nucleation model. However, accurate effect of the dendrites fragmentation is difficult to describe because of the complex mechanism of fragmentation caused by fluid flow. In this simulation, the effective crystal formation rate is set to 25 cm−2 s−1 higher than that of heterogeneous nucleation in liquid.

Schematic illustration of solid–liquid coexisting zones during the solidification of steel.
Figure 4:

Schematic illustration of solid–liquid coexisting zones during the solidification of steel.

Model validation

To prove the accuracy of the established model, industrial test and numerical simulation for GCr15 steel continuous casting blooms are conducted under the same casting condition, shown in Table 4. Bloom surface temperatures at typical positions in the continuous casting process are measured using infrared radiation thermometer, comparisons between measured and calculated bloom surface temperatures are shown in Figure 5, which shows well accuracy in temperature distribution calculation.

The calculated temperature profiles with measured data points.
Figure 5:

The calculated temperature profiles with measured data points.

Table 4:

Casting parameters used for model validation.

Besides, bloom samples are sliced and etched by H2O–50 %HCl reagent for solidification structure observation and equiaxed crystal ratio (ECR) calculation. The calculation method for ECR is illustrated in eq. (8). ECR=SEST×100%(8)

where SE is the area of equiaxed crystal zone, ST is the total area of bloom cross section.

The observed and calculated solidification structures are shown in Figure 6(a) and (b). The typical solidification structures include three parts: outer chill zone, intermediate columnar zone and central equiaxed crystal zone. It can be seen from Figure 6 that the simulated solidification structures by CA–FE model are compatible with the actual results and the experimentally observed and simulated ECR are about 23 %. This result indicates that the selected nucleation parameters are reasonable and the present model can be used to simulate the solidification structure during continuous casting of GCr15 steel.

Morphology of actual/simulated GCr15 steel bloom (cross section).
Figure 6:

Morphology of actual/simulated GCr15 steel bloom (cross section).

Results and discussion

Solidification structure evolution under different secondary cooling modes

In the actual continuous casting process of GCr15 steel bloom, five different types of secondary cooling modes are usually applied. The water distribution profiles under five different cooling modes are illustrated in Figure 7. Values of the five axes (Qi) represent the water flow rate of segment i in the secondary cooling zone, L/min, which is calculated as eq. (9).

Water distribution profiles in five different secondary cooling modes.
Figure 7:

Water distribution profiles in five different secondary cooling modes.

Wi=QiAi(9)

where Wi is the sprayed water density of segment i in secondary cooling zone, L/(m2 min) (seen in Table 2); Ai is the sprayed area of segment i, m2.

Here, in this paper, the water distribution profiles from Figure 7 are used in the boundary condition calculation for secondary cooling zone as in Table 2 while other parameters are the same as Table 4.

Influence of secondary cooling mode on equiaxed crystal ratio and grain size

The water distribution of various secondary cooling modes are input into the CA–FE model and the cross-sectional morphology of solidification structure for GCr15 steel continuous casting bloom is shown in Figure 8(a)–(e). It could be observed that with the change of cooling intensity, the central equiaxed crystal area varies evidently. The increased cooling intensity leads to rise of undercooling at solid/liquid phase interface, which contributes to growth of dendrites thus inhibiting the formation of central equiaxed crystals. To quantitatively describe the influence of secondary cooling mode on solidification structure of GCr15 steel bloom, ECR and average grain diameter (Dm) are adopted as quantify indexes. Dm is calculated as eq. (10) based on the assumption that all dendrites are spherical.

Morphologies of solidification structure for GCr15 steel bloom at various secondary cooling modes (one-fourth cross section): (a) super weak cooling, (b) weak cooling, (c) mild cooling, (d) strong cooling and (e) super strong cooling.
Figure 8:

Morphologies of solidification structure for GCr15 steel bloom at various secondary cooling modes (one-fourth cross section): (a) super weak cooling, (b) weak cooling, (c) mild cooling, (d) strong cooling and (e) super strong cooling.

Dm=2ANπ(10)

where A is the area of calculation, N is the nuclei number in the calculation area, which can be obtained from CA–FE calculation.

Figure 9(a) and (b) describes the variation of ECR and Dm at different secondary cooling modes.

Equiaxed crystal ratios and average grain diameters of GCr15 steel bloom under different secondary cooling modes.
Figure 9:

Equiaxed crystal ratios and average grain diameters of GCr15 steel bloom under different secondary cooling modes.

It could be known from Figure 9(a) and (b), when the secondary cooling mode varies from super weak cooling to super strong cooling, ECR drops from 35.4 % to 10.44 % while Dm enlarges from 1.56 mm to 1.99 mm, correspondingly.

Influence of secondary cooling mode on secondary dendrite arm spacing

The evolution of secondary dendrite arm spacing (SDAS) at the cross-sectional direction of the GCr15 steel bloom under different secondary cooling modes is shown in Figure 10(a)–(e).

Evolution of SDAS for GCr15 steel bloom under different secondary cooling modes (µm): (a) super weak cooling, (b) weak cooling, (c) mild cooling, (d) strong cooling and (e) super strong cooling.
Figure 10:

Evolution of SDAS for GCr15 steel bloom under different secondary cooling modes (µm): (a) super weak cooling, (b) weak cooling, (c) mild cooling, (d) strong cooling and (e) super strong cooling.

It could be deduced from Figure 10 that under all types of secondary cooling mode, SDAS at the cross-sectional direction of the GCr15 steel bloom increases from bloom edge to center. During the steel continuous casting process, the chill zone of the continuous casting bloom forms due to rapid cooling in the mold, after which large quantities of dendrites grow toward bloom center with the dendrite tip undercooling and dendrite growth velocity decrease gradually until the CET occurs. SDAS in typical positions of the bloom (Figure 11) is analyzed statistically as in Figure 12.

Sample points for SDAS analysis of GCr15 steel bloom.
Figure 11:

Sample points for SDAS analysis of GCr15 steel bloom.

Evolution of SDAS at different sample points for GCr15 steel bloom.
Figure 12:

Evolution of SDAS at different sample points for GCr15 steel bloom.

It could be observed from Figure 12 that under certain secondary cooling mode, SDAS value increases from bloom edge to center. Take the super weak cooling mode as an example, with the sample point change from C11 to C0, the SDAS value increases from 67.27 µm to 96.57 µm. With the secondary cooling mode changes, SDAS value of the same sample point decreases with the strengthening of cooling intensity. For sample point C0, with the secondary cooling mode varying from super weak cooling to super strong cooling, the SDAS value decreases from 96.57 µm to 93.02 µm.

Considering above results, the secondary cooling mode for GCr15 steel continuous casting could be suitably controlled to obtain finer grains and favorable equiaxed grain structures regarding the final blooms.

Carbon macro-segregation evolution under different solidification structure characteristics

The formation of carbon macro-segregation for GCr15 steel bloom could be clarified in both macro- and microscale. In micro perspective, liquid steel solidifies as dendrites and the dendrite arm spacing determines the diffusion distance of solute elements which causes the micro-segregation behavior of elements. Relative research [27, 28, 29] have proved that minimizing SDAS would contribute to alleviating the micro-segregation degree of elements thus improving the uniformity of element distribution in macroscale. In macroscale, strong and developed columnar dendrites would stimulate cracks between dendrite tips and cause the occurrence of central segregation. Properly enlarging the ECR would be useful in eliminating such defects. Considering above facts, it is necessary to study the influence mechanism of solidification structure characteristics on carbon macro-segregation.

Influence of secondary dendrite arm spacing (SDAS) on carbon macro-segregation

Samples of GCr15 steel bloom are obtained for carbon macro-segregation analysis. The sample positions areillustrated as in Figure 13. In the meantime, solidification structure characteristics for GCr15 steel bloom under the same casting condition are calculated using the model established above.

Sample points for carbon segregation and SDAS analysis.
Figure 13:

Sample points for carbon segregation and SDAS analysis.

Carbon segregation index is defined as eq. (10). Kc=CC(10)

where C is the average carbon content of the bloom, C is the local carbon content of the sample point.

The evolution of SDAS and carbon segregation index at various sample points from bloom side to center is illustrated in Figure 14.

Evolution of SDAS and carbon segregation index at different locations.
Figure 14:

Evolution of SDAS and carbon segregation index at different locations.

It could be observed from Figure 14 that the carbon segregation index increases with the development of SDAS from bloom wide side to center. At sample point C20 (10 mm from bloom wide side), the SDAS value is 27.94 µm and Kc is 0.95. At sample point C0 (130 mm from bloom wide side), the SDAS value is 95.23 µm and Kc is 1.24. Above all, increase of SDAS promotes the diffusion distance and stimulates the nonuniform distribution of carbon element. In the GCr15 steel continuous casting process, proper secondary cooling mode could be selected to control the growth of dendrite and refine SDAS to improve bloom quality.

Influence of equiaxed crystal ratio on carbon macro-segregation

In order to study the influence of ECR on carbon macro-segregation behavior of GCr15 steel bloom, industrial tests are conducted to obtain bloom samples under five different secondary cooling modes shown as Figure 7. The samples are then etched by H2O–50 %HCl reagent for structure observation and ECR estimation. Morphologies for central region of the bloom cross sections under various secondary cooling modes are illustrated in Figure 15.

Morphologies for horizontal direction of GCr15 steel bloom under various secondary cooling modes (a) super weak cooling, (b) weak cooling, (c) mild cooling, (d) strong cooling and (e) super strong cooling.
Figure 15:

Morphologies for horizontal direction of GCr15 steel bloom under various secondary cooling modes (a) super weak cooling, (b) weak cooling, (c) mild cooling, (d) strong cooling and (e) super strong cooling.

It could be clearly observed from Figure 15 that with the increase of secondary cooling intensity, the porosity and segregation in central region has become more severe and micro-cracks even occur under the strong cooling mode. These phenomena indicate that stronger cooling intensity enlarges the area of columnar dendrite and reduces the compactness degree of central region of the bloom.

On this basis, the ECR and the carbon segregation index at different locations (seen in Figure 16) of the above five samples are measured as in Figures 17 and 18, respectively. When the secondary cooling intensity transforms from weak to strong mode, the measured ECR drops from 33.2 % to 10.05 % and the carbon segregation index decreases to some extent but then gradually increases. For instance, at point C0, Kc under super weak cooling mode is 1.27 then it stabilizes at about 1.109 before increasing to 1.18 under super strong cooling mode. Moreover, under certain cooling mode, Kc increases from bloom side to center, which explains the formation of central segregation of solute elements.

Sample points for carbon segregation index analysis.
Figure 16:

Sample points for carbon segregation index analysis.

Measured results for equiaxed crystal ratio of GCr15 bloom.
Figure 17:

Measured results for equiaxed crystal ratio of GCr15 bloom.

Carbon segregation index at different positions.
Figure 18:

Carbon segregation index at different positions.

Considering above results, it is evident that when the cooling intensity becomes stronger, the ECR decreases while Kc decreases first and then increases. Apparently, there exists the optimum secondary cooling mode in the transformation process of cooling intensity for the bloom to keep low-carbon segregation level while obtaining relatively high ECR and finer grains.

Summary

In order to determine the optimum cooling mode for improving the quality of GCr15 steel continuous casting bloom, the evolution of ECR, GS, SDAS as well as carbon segregation index at typical sample position with the change of secondary cooling intensity is summarized as in Figure 18.

It could be clearly observed from Figure 19 that the optimum secondary cooling water intensity is between 0.26 L/kg and 0.30 L/kg, in which the GCr15 steel bloom would have relatively higher ECR, finer grain as well as SDAS while the carbon segregation degree is low. Above all, for GCr15 steel bloom studied in this paper, the secondary cooling process should be controlled within weak/mild cooling mode (secondary cooling water intensity between 0.26 L/kg and 0.30 L/kg) to keep low carbon macro-segregation degree and to improve the comprehensive performance of final products.

Summary of characteristic parameters under different secondary cooling mode.
Figure 19:

Summary of characteristic parameters under different secondary cooling mode.

Conclusions

A coupled CA–FE model has been used to simulate the solidification structure in continuous casting process of high-carbon GCr15 steel bloom. The present model is validated by experimental data. This study simulated the effect of secondary cooling intensity on the solidification structure of GCr15 steel bloom. Besides, industrial test is conducted to investigate different secondary cooling water intensity on the macro-segregation of GCr15 steel. Based on the CA–FE simulation and industrial test, the following conclusions can be drawn:

  1. It is found that the ECR and bloom compact degree (GS, SDAS) changes in the opposite direction at different secondary cooling intensities. The ECR would be improved with weak cooling intensity. Intensive cooling intensities could improve the compactness of the bloom.

  2. For the high-carbon GCr15 steel bloom in this research, the optimum secondary cooling water intensity is between 0.26 L/kg and 0.30 L/kg to reduce the carbon macro-segregation and to improve bloom compact degree in the continuous casting process.

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About the article

Received: 2016-01-27

Accepted: 2016-05-31

Published Online: 2017-07-19

Published in Print: 2017-07-26


The authors would like to acknowledge the financial support for this study provided by Key Research & Development Foundation (No. 41614014) and Independent Research & Development Foundation (No. 41602023) of State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing, China.


Citation Information: High Temperature Materials and Processes, Volume 36, Issue 7, Pages 741–753, ISSN (Online) 2191-0324, ISSN (Print) 0334-6455, DOI: https://doi.org/10.1515/htmp-2016-0022.

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