Jie Zeng* and Weiqing Chen

Effect of Secondary Cooling Conditions on Solidification Structure and Central Macrosegregation in Continuously Cast High-Carbon Rectangular Billet

Abstract: Solidification structures of high carbon rectan-gular billet with a size of 180 mm × 240 mm in different secondary cooling conditions were simulated using cellu-lar automaton-finite element (CAFE) coupling model. The adequacy of the model was compared with the simulated and the actual macrostructures of 82B steel. Effects of the secondary cooling water intensity on solidification struc-tures including the equiaxed grain ratio and the equiaxed grain compactness were discussed. It was shown that the equiaxed grain ratio and the equiaxed grain compact-ness changed in the opposite direction at different sec-ondary cooling water intensities. Increasing the second-ary cooling water intensity from 0.9 or 1.1 to 1.3 L/kg could improve the equiaxed grain compactness and decrease the equiaxed grain ratio. Besides, the industrial test was conducted to investigate the effect of different secondary cooling water intensities on the center carbon macroseg-regation of 82B steel. The optimum secondary cooling water intensity was 0.9 L/kg, while the center carbon seg-regation degree was 1.10. The relationship between solidi-fication structure and center carbon segregation was dis-cussed based on the simulation results and the industrial test.

Keywords: rectangular billet casting, cellular automaton- finite element method, equiaxed grain ratio, equiaxed grain compactness, carbon macrosegregation

PACS® (2010). 81.30.Fb

DOI 10.1515/htmp-2014-0059Received April 6, 2014; accepted September 10, 2014;published online November 15, 2014

1  Introduction Solidification structure and macrosegregation have great influence on the quality of high carbon steels [1–3]. Wire rod with center cementite network resulting from severe segregation not only shows low ducility in the center portion, but also exhibits cup fracture during drawing. A fundamental task of high carbon steel continuous casting is to optimize the processing parameters to minimize the formation of carbon macrosegregation. The optimization of the process variables may provide a simple low cost solution to controlling macrosegregation [4]. It is known that the secondary cooling conditions at the solid/liquid interface strongly affect grain growing in the mushy zone. Equiaxed grains can prevent the formation of solidifica-tion bridges and redistribute the residual impure liquid. Several experimental investigations show a clear decrease in the center segregation as the equiaxed grain ratio in-creases [5, 6]. However, the effect of secondary cooling water intensity on the compactness of equiaxed grain has not been specially investigated. The compactness of equiaxed grain zone can be evaluated by the grain number or the grain size. High compactness means that the grain number is large or the grain size is small [7]. The liquid flow comes from interdendritic areas and therefore, is highly enriched, which causes the center macrosegrega-tion. This liquid flow from the interdendritic region can be effectively influenced by the equiaxed grain size.

Product quality and production efficiency depend es-sentially on the secondary cooling conditions. The effect of secondary cooling water intensity on the middle size of  180 mm × 240 mm rectangular billets in continuous casting has not been researched before. As is known, different billet sizes require different secondary cooling water intensities in order to reduce center macrosegrega-tion. The billet size less than 160 mm × 160 mm needs in-tensive secondary cooling water intensity in continuous casting. The intensive secondary cooling water intensity can achieve a rapid temperature drop at the surface corre-sponding to the temperature drop at the center when the

*Corresponding author: Jie Zeng: State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing, Beijing 100083, China. E-mail: zengjie2014@126.comWeiqing Chen: State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing, Beijing 100083, China

High Temp. Mater. Proc. 2015; 34(6): 577–583

 J. Zeng and W.Q. Chen, Effect of Secondary Cooling Conditions on Solidification Structure

latter solidifies and, consequently decreases the grain size and prevents V-segregation formation [8]. The bloom continuous casting needs softer secondary cooling water intensity. It is known that “soft” secondary cooling water intensity can minimize alloy components segregation in-tensity and increase the equiaxed grain ratio greatly [9]. So, to the middle size rectangular billet, it is of great im-portance to study the secondary cooling water intensity on the macrostructure and the center segregation.

In the present study, the FE-CA coupling model [3, 10] was used to simulate the solidification structure of high carbon 82B steel, in which different secondary cooling water intensities were taken into consideration. Besides the modeling of solidification structure, industrial test was done in order to investigate the optimum secondary cooling water intensity on the macrosegregation of high carbon 82B steel. Based on the CAFE simulation and in-dustrial test, the effects of the ratio and the compactness of equiaxed grain on the center carbon segregation during continuous casting of high carbon 82B rectangular billet were discussed.

2 Numerical modelIn the present model, the cellular automaton method (CA) was combined with the heat transfer calculation during the continuous casting (CC) process. The CAFE model sim-ulating the solidification structure mainly includes heat transfer model, nucleation model and dendrite tip growth kinetics.

2.1 Heat transfer model

A two-dimensional unsteady state heat transfer equation is available as follows:

ρ λ λ ∂ ∂ ∂ ∂ ∂

= + ∂ ∂ ∂ ∂ ∂ tT T TC

x x y y(1)

where ρ is density, C is specific heat capacity and λ is thermal conductivity. The evolution of the latent heat

during solidification is incorporated to the calculation by using the effective specific heat method, as shown in the following equation.

′ = −

s

p pdfC C LdT

(2)

where ′pC 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 solidification of 82B steel. Fig. 1 shows the boundary conditions of the heat transfer model during the CC process. The section size of  slice is the same as the rectangular billet, 180 mm ×  240 mm and the thickness is 25 mm.

The length, boundary conditions and calculated formula are listed in Table 1. The secondary cooling zone includes 4 spray zone.

2.2 Nucleation model

In the present study, the continuous heterogeneous model [13] is applied. A continuous nucleation distribution

Table 1: The boundary conditions and the calculated formula of 82B steel

Section Length (m) Boundary condition Calculated formula

Mould 0.8 qm3(2.68 ) 10mq tβ= − × [11]

Secondary cooling zone 7.9 q ( )k k wh T T= − 0.851200 10.44h W= + [12]Air cooling zone 10.0 4 4[( 273) ( 273) ]b eq T Tεs= + − + 85.67 10s −= × , 0.8ε = [11]

Fig. 1: Schematic illustration of boundary conditions and the moving slice method

578

J. Zeng and W.Q. Chen, Effect of Secondary Cooling Conditions on Solidification Structure 

function, dn/d (DT ), is used to describe the grain den-sity change, dn is induced by increase of the undercool-ing, d (DT ). The distribution function is expressed by Eq. (3).

ss

D −D = − D D πD

2max max1exp

( ) 22dn n T T

d T TT(3)

where T is the calculated temperature, K; Tl is the liquidus temperature, K; DT is the calculated heat undercooling (DT = T − Tl), K; DTmax is the mean undercooling, K; DT

s is

the standard deviation, K; nmax is the maximum nucle-ation density, m−3.

2.3 Dendrite tip growth kinetics

The KGT (Kurz, Givoanola, Trivedi) model [14, 15] is used as the model of growth kinetics of a dendrite tip in an 82B steel. Based on the marginal stability criterion, Eq. (4) is obtained.

+ + =2 0V A VB C (4)

where π Γ=

2

2 2A

P D, ξ−

=− −

0 0

0

m (1 )[1 (1 ) ( )]

cC kBD k Iv P

, C = G, Г is the

Gibbs-Thomoson coefficient (Г = 1.9 × 10−7), 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, Co is the initial concentration, ko is the partition coefficient, Iv(P) is the Ivantsov function, ξ = π2

0/( )c k P 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 82B steel (T0 = 1470 °C), DT is the under-cooling temperature at a tip of dendrite (DT = Ttip − T0), DT is expressed as follows:

ΓD = − + − −

00

1 2m 11 (1 ) ( ) r

T Ck Iv P

(5)

where r is the dendrite tip radius. The relationship between the undercooling DT and V can be calculated by substitut-ing an arbitral value of the Peclet number into Eqs. (4) and (5). The chemical compositions of high carbon 82B steel and materias properties used in the simulation are given in Table 2.

To accelerate the computation speed, set of values for the undercooling and growth velocity of the dendrite tip are calculated in Eqs. (4) and (5). At last, the following Eq. (6) is obtained.

D = D + D2 32 3( )V T a T a T (6)

where V(DT ) is the growth velocity of the dendrite tip; a2 and a3 are the fitting coefficients. Using the simulation and based on the Table 2, the calculated values of a2 and a3 are 0 and 1.257 × 10−5 m/(s·K3).

3 Model validation

3.1  Heat transfer model validation

The validation of the heat transfer model was performed by a comparison of the calculated surface temperature and the measured temperature at different casting speeds and secondary cooling water intensities, as shown in Fig. 2. The surface temperatures were measured using infrared pyrometer in three different cases. Case 1: the casting speed was 0.9 m/min, the secondary cooling water inten-sity was 0.9 L/kg; case 2: the casting speed was 1.1 m/min, the secondary cooling water intensity was 0.9 L/kg; case 3: the casting speed was 1.0 m/min, the secondary cooling water intensity was 0.5 L/kg. This result indicated that the calculated temperature profiles agreed well with the mea-sured temperatures and the present model can be used to simulate the solidification process in continuous casting of steel.

Table 2: The chemical composition of 82B steel and materials properties used in the simulation

Composition C Si Mn P S

Mass fraction (%) 0.82 0.20 0.70 0.014 0.008Partition coefficient (k0 ) [16] 0.35 0.52 0.75 0.06 0.025Liquidus slope (m) −60 −8 −5 −34 −40Diffusivity in liquid, D (m2/s) [17] 2.0 × 10−8 2.4 × 10−9 2.0 × 10−8 4.7 × 10−9 4.5 × 10−9

579

3.2  CAFE model validation

The validation of the CAFE model was performed by a comparison of the simulated solidification structures and the actual solidification structures under the same CC conditions. The CC conditions were as follows: the casting speed was 1.1 m/min, the secondary cooling water inten-sity was 0.9 L/kg, the superheat was 23 °C. The compari-son between the experimental results and the simulated results are shown in Fig. 3. The typical solidification mac-rostructures include three parts: outer chill zone, interme-diate columnar zone and central equiaxed grain zone. It can be seen from Fig. 3 that the simulated solidification macrostructures by CAFE and the experimental macro-structures agree well and the equiaxed grain ratio in ex-perimentally observed and simulated are about 56%.

4 Results and discussionThe minimum area of equiaxed grain zone was 90 mm ×  40 mm under different CC conditions in this study. Fig. 4 shows the same sample position of center equiaxed grain  zone of the rectangular billet under different con-ditions. The equiaxed grain compactness is defined as the  ratio of  the central equiaxed grain number in the sample to the sample area of 90 mm × 40 mm. The equiaxed grain ratio is calculated by dividing the width of equiaxed grain zone into the whole width of the rect-angular billet. They are used to evaluate the effect of secondary cooling water intensity on the solidification macrostructure.

Fig. 2: The calculated temperature profiles with measured data points at three different cases

Fig. 3: Observed (left) and simulated (right) macrostructure

Fig. 4: Sample position of center equiaxed grain zone of the rectangular billet under different conditions

580  J. Zeng and W.Q. Chen, Effect of Secondary Cooling Conditions on Solidification Structure

4.1  Effect of secondary cooling water intensity on equiaxed grain ratio and equiaxed grain compactness

In this research, the casting speed was 1.1 m/min. Fig. 5 shows the simulated results of 82B steel under dif-ferent  secondary cooling water intensities. In Fig. 5, the equiaxed grain ratio decreases obviously with the in-crease  of cooling intensity. Fig. 6 demonstrates the sim-ulation results of central equiaxed grain under differ-ent  secondary cooling water intensities. The results of  equiaxed grain compactness and equiaxed grain ratio  are shown in Fig. 7. As can be seen from Fig. 7, with  the secondary cooling water intensity increasing by  0.1 L/kg, the equiaxed grain compactness increases

Fig. 5: The simulated solidification structures of 82B steel under different secondary cooling water intensities: (a) 1.1 m/min, 0.9 L/ kg, (b) 1.1 m/min, 1.1 L/kg, (c) 1.1 m/min, 1.3 L/kg

Fig. 6: The simulated solidification structures of center equiaxed grain zone under different secondary cooling water intensities: (a) 1.1 m/ min, 0.9 L/kg, (b) 1.1 m/min, 1.1 L/kg, (c) 1.1 m/min, 1.3 L/ kg

Fig. 7: The calculated equiaxed grain compactness and equiaxed grain ratio of 82B steel under different secondary cooling water intensities

581J. Zeng and W.Q. Chen, Effect of Secondary Cooling Conditions on Solidification Structure 

by  1.46% and the equiaxed grain ratio decreases by 2.67%.

Based on the simulation results, the compactness of equiaxed grain increased and the equiaxed grain ratio decreased with the secondary cooling water intensity in-creasing. The reason is that the increase of secondary cooling water intensity results in a large temperature gra-dient at liquid-solid interface. As the cooling intensity increases, the compactness of center equiaxed grain in-creases much and the equiaxed grain ratio decreases greatly. Secondary cooling water intensity has a great effect on the solidification structure. To obtain the optimal secondary cooling water intensity, both the equiaxed grain compactness and the equiaxed grain ratio should be taken into consideration.

4.2  Influence of secondary cooling water intensity on center carbon segregation

In the continuous casting of high carbon 82B steel, center carbon segregation is the most severe problems encoun-tered in 180 mm × 240 mm rectangular billets. The in-dustrial test was conducted to investigate the effect of different secondary cooling water intensities on the mac-rosegregation of high carbon 82B steel. The 82B steel was produced by a straight curved caster with a billet size of 180 mm × 240 mm. In order to find out the optimum process variables of low carbon segregation index, the in-dustrial test was carried out by varying the secondary cooling water intensity from 0.4 L/kg to 1.3 L/kg while the others were fixed. The casting speed was 1.1 m/min and the superheat was 25 °C. The F-EMS was closed.

The segregation index was evaluated by longitudinal cross section of 180 mm × 240 mm rectangular billet. The carbon segregation was determined by total ten drillings along the center line of the rectangular billet. Each sample was drilled out 4 mm depth with 5 mm diameter drill along the central longitudinal direction. The carbon segregation was defined as C/C0 , where C is center carbon content (drilling test), C0 is carbon content in liquid steel (tundish test).

Fig. 8 shows the relationship between the center carbon segregation and the secondary cooling water in-tensity. The results are shown in Fig. 8 presenting that the carbon segregation degree reduces most effectively at the cooling intensity of 0.9 L/kg. The center carbon segrega-tion degree is aggravated when cooling intensity increases from 0.9 L/kg to 1.3 L/kg. Besides, as the cooling intensity decreases from 0.9 L/kg to 0.4 L/kg, the carbon segrega-tion degree increases from 1.10 to 1.16.

Explanations are made to correlate the experimental carbon macrosegregation data with the simulated solidifi-cation structure based on the CAFE model. The equiaxed grain ratio reduces by about 10.7% as the cooling intensity increases from 0.9 L/kg to 1.3 L/kg. In addition, as the cooling intensity increases from 0.4 L/kg to 0.9 L/kg, the equiaxed grain compactness increases by about 7.3%. Therefore, for the middle size rectangular billet, the mod-erate secondary cooling water intensity is the best result.

The results of this exercise demonstrate that the center segregation has a very close relation with the equi-axed grain ratio and the equiaxed grain compactness. It is  important to adopt the appropriate secondary cooling water intensity in consideration of its effect on center carbon segregation. For the rectangular billet continuous casting, it is necessary to consider both the equiaxed grain ratio and the equiaxed grain compactness for the improve-ment of center carbon segregation.

5 ConclusionsA coupled cellular automaton-finite element (CAFE) model has been used to simulate the solidification struc-ture in continuous casting of high carbon 82B rectangular billet. The present model was validated by experimental data. This study simulated the effect of secondary cooling water intensity on the solidification structure of 82B steel. Besides, the industrial test was conducted to investigate different secondary cooling water intensities on the mac-rosegregation of 82B steel. Based on the CAFE simula-tion and industrial test, the following conclusions can be drawn:

Fig. 8: The measured center carbon segregation degree of 82B steel under different secondary cooling water intensities

582  J. Zeng and W.Q. Chen, Effect of Secondary Cooling Conditions on Solidification Structure

1. It is found that the equiaxed grain ratio and the equiaxed grain compactness changes in the opposite direction at different secondary cooling water inten-sities. The equiaxed grain ratio would be improved with the soft secondary cooling water intensity. Inten-sive secondary cooling water intensity can improve the compactness of central equiaxed grain zone.

2. For the middle size rectangular billet continuous casting, it is considered necessary to optimize the equiaxed grain ratio and the equiaxed grain compact-ness for the improvement of center carbon segrega-tion. The moderate secondary cooling water intensity of 0.9 L/kg is appropriate to reduce the center carbon segregation of high-carbon rectangular billet in con-tinuous casting.

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