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Simulation on solidification structure of 72A tire cord steel billet using CAFE method

Male, born 1985. He gained his Ph.D from the University of Science and Technology Beijing in 2011. His research interest mainly focuses on solidification simulation including heat transfer, structure formation and macro-segregation.E-mail: jingcailiang@163.comReceived: 2011-03-23; Accepted: 2011-10-12

*Jing Cailiang

*Jing Cailiang1, Xu Zhigang1, Wang Ying2, and Wang Wanjun1

(1. School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing 100083, China;

2. Technology Center of Xingtai Iron & Steel Co., Ltd., Xingtai 054027, Hebei, China)

Generally speaking, making a large number of industrial experiments is impracticable for metallurgical enterprises.

So, simulation of solidification structure is one of the hottest technologies in metallurgical field. With this method, only a few experiments are needed to predict the solidification microstructure and mechanical properties of castings, which results in low costs and therefore great application potential [1]. However, up to now the applications of this technology have been mainly focused on ingot casting [2, 3]. There have been few attempts to simulate solidification structure formation in continuous casting for two reasons. First, the forced flow in the melt during solidification is too complex to be simulated， such as electromagnetic stirring (EMS), bulging, soft reduction and so on. Second, during the solidification of steel, heterogeneous transformations such as the peritectic reaction and subsequent phase transformation occur. These phenomena make the modeling of solidification structure formation in continuous casting difficult.

Center segregation is one of the most important influencing factors for tire cord steel which can cause abruption, hydrogen

Abstract: The solidification microstructure has an important effect on the mechanical properties of castings. Therefore, an FE (Finite Element) – CA (Cellular Automaton) coupling model was developed for the simulation of solidification structure during the continuous casting process of 72A tire cord steel. In the model, the effect of phase transformation (l→g→a ) during solidification was considered based on a thermodynamic database. The effect of electromagnetic stirring (EMS) was determined by increasing both the thermal conductivity and crystal formation rate in the liquid phase. The results show that the cooling curves and solidification structure calculated by this model agree well with the experimental results. The optimum pouring temperature range for tire cord steel casting was also discussed based on the present model. By comprehensive consideration of billet quality and smooth production, the pouring temperature should be controlled at about 1,495 under the casting conditions of the local plant in this study.

Key words: tire cord steel; solidification structure; CAFE method; phase transformation; EMSCLC numbers: TG142/TP391.9 Document code: A Article ID: 1672-6421(2012)01-053-07

embitterment, quench crack and so on [4]. So far, the prediction of the billet’s center segregation is very difficult because of its complex formation mechanism [5, 6]. However, the relationship between the solidification structure and the center segregation has been widely reported [7, 8]. If the effects of the casting process parameters on the solidification structure were clear, the prediction of the billet’s center segregation could be achieved. Therefore, it is desirable to develop a mathematical model to simulate solidification structure formation during casting process.

Based on the above idea, the FE (Finite Element) – CA (Cellular Automaton) coupling model was developed to simulate the solidification structure of tire cord steel billet under the casting conditions of a local plant, in which the effects of phase transformation (l→g→a ) and electromagnetic stirring (EMS) on the solidification process were taken into consideration. The optimum pouring temperature range for tire cord steel casting was also discussed based on the present model.

1 Casting equipment and processThe main casting equipment and technologies for tire cord steel plant can be listed as follows: (1) 9 m - arc bow type continuous caster; (2) 4-strand T-type tundish; (3) billet mould of 150 mm × 150 mm; (4) final electromagnetic stirring (F-EMS); (5) protective casting technology, such as long nozzle casting with argon gas shielding, submerged nozzles,

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and mold flux. The 72A tire cord steel was chosen in this study, and its

main chemical composition is shown in Table 1.

2 Model description

2.1 Consideration of phase transformationIn this study, a pairwise mixture model [shown in Eq. (1)] based on the thermodynamic database from CompuTherm LLC was used to calculate the thermo-physical properties of 72A tire cord steel at different temperatures; including thermal conductivity, density, enthalpy, liquidus, solidus, etc., which

were later coupled in the heat transfer model. By this method, the effect of different phases during solidification process is taken into consideration.

where P and Pi are the thermo-physical properties of one phase and pure element, respectively; Ωv is a binary interaction parameter; and xi and xj are the mole fractions of elements i and j.

The main chemical composition of 72A tire cord steel (shown in Table 1) was input into the database (provided by ESI Company), and the calculated results of thermo-physical properties of 72A are shown in Fig. 1. It can be seen that the change of the thermo-physical properties with temperature is not simple; there are obvious mutational points when phase transitions appear. Therefore, this setting method can reflect the solidification process more accurately than constant or simple function treatment.

Table 1: Main chemical composition of 72A tire cord steel (%)

Fe C Si Mn P S

Bal. 0.71 0.22 0.46 0.012 0.012

Fig. 1: Calculated thermo-physical properties of 72A tire cord steel

2.2 Heat transfer model of FE(1) Geometric modeling and mesh generationThe solidification and heat transfer process of the billet was

simulated based on a slice moving method: a 150 mm × 150 mm billet slice was moving down from the mold. The slice was first cooled in the mold by heat transfer from the slice to the mold. Then, the slice was cooled at the secondary cooling zone by spray which was divided into four zones with different heat transfer conditions to enhance the accuracy of the heat transfer calculation. Finally, the slice was cooled in air, and the heat extraction from the slice in this region was calculated by radiation. In the heat transfer calculation, the heat flow

condition at the surface of the billet was changed with the lapse of time by synchronizing with the movement of the billet.

By comprehensive consideration of calculation precision and calculation time, the slice was set 10 mm thick, and the computational domain of 150 mm × 150 mm × 10 mm was divided into 10,827 nodes and 46,775 elements as shown in Fig. 2.

(2) Treatment of boundary conditionsIt is assumed that the temperature is uniform in the slice

at the initial time, and it is equal to the pouring temperature. The cooling parameters in different locations are treated as equivalent heat flux, which are set as the boundary conditions

( )∑ ∑∑ ∑>

−Ω+=i ij v

jivjiii xxxxPxP (1)

(a) (b)

(c) (d)

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in the heat transfer model. The specific treatment methods in the different locations are listed in Table 2.where,

q - specified flux, kW·m-2; l - distance from the top of the mold, m; v - casting speed, m·min-1; β - a constant which depends on the casting parameter,

kW·m-2·min-1/2; h - heat transfer coefficient, W·m-2·K-1; w - water flow rate, L•m-2•min-1; a - a correction factor; Tw - temperature of the cooling water, K; σ - Stefan-Boltzmann constant, 5.67 × 10-8 W·m-2·K-4; ε - radiation coefficient; Tb, T a - temperature of the bi l le t surface and the

environment, respectively, K.

equiaxed morphologies can be calculated by the KGT model [11]. Based on the marginal stability criterion, one obtains:

(3)

where, V - growth velocity of a dendrite tip; Γ - Gibbs-Thomson coefficient; PC - Peclet number for solute diffusion; D - diffusion coefficient in liquid; m - liquidus slope;

C0 - initial concentration; k0 - partition coefficient;

Iv(PC) - Ivantsov function and G - temperature gradient. For the dendrite growth regime, the imposed temperature

gradient, G, has little effect on the growth velocity of a dendrite tip and can be regarded as zero.

Temperature at the dendrite tip, T tip, was expressed as follows:

(4)

where T0 is the melting point of pure Fe (1,538 ) and r is the dendrite tip radius. The relationship between the undercooling at the dendrite tip and the growth velocity can be calculated from Eqs. (3) and (4) by substituting an arbitrary value of the Peclet number into Eqs. (3) and (4). In the simulation process, in order to accelerate the velocity of computation, the KGT model is fitted giving the following equation:

(5)

where ΔT is the total undercooling of the dendrite tip; a2 and a3 are the coefficients of the multinomial of dendrite tip growth velocity, which are calculated to be a2 = 0 and a3 = 1.22942 × 10-5 m•s-1•K-3 based on the data of partition coefficient, liqudus slope, diffusivity in liquid and Gibbs-Thomson coefficient of Fe-X (X = C, Si, Mn, P, S) alloys (Table 4).

2.4 Consideration of EMSGenerally, electromagnetic stirring (EMS) is used to reduce the centerline segregation in the continuous casting process. In order to evaluate the effect of the fluid flow due to EMS on heat flow in the billet, the accurate flow pattern in the molten steel must be known. However, at present, it is difficult to calculate accurately combining fluid flow and heat transfer with the CA procedure due to very large computational load.

Two methods have been reported for incorporating the effect of EMS into the heat transfer calculation. (1) Changing the thermal conductivity of the liquid during electromagnetic stirring [14, 15]. In this method, it is considered that the thermal

Fig. 2: Griddling of the computational domain

Table 2: Calculation method of boundary conditions [9]

Zone Boundary condition Calculation formula

Mold q

Secondary cooling q = h(Tb-Tw)

Air cooling ε = 0.7

2.3 Model of CA(1) Heterogeneous nucleationA continuous nucleation distribution function, dn/d(ΔT), is

used to describe the grain density change, dn, which is induced by an increase in the under-cooling, d(ΔT). The distribution function, dn/d(ΔT), is described by Eq. (2) [10].

(2)

where ΔT is the calculated local under-cooling, ΔTmax is the mean under-cooling, ΔTσ is the standard deviation, nmax is the maximum nucleation density which can be reached when all the nucleation sites are activated during cooling. Unless otherwise stated, the nucleation parameters used in this calculation are those listed in Table 3.

(2) Dendrite tip growth kineticsIn castings, the growth kinetics of both columnar and

Table 3: Nucleation parameters used in the calculation ΔTmax (K) ΔTσ (K) nmax (m

-3)

Surface nucleation 1 0.1 108

Volume nucleation 3.5 1 109

tip

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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. [16], the thermal conductivity of solid was used in the solid region and the mushy zone when fraction of solid, fs > 0.7, and the effective thermal conductivity of liquid with fluid flow was used in the liquid region and the mushy zone when fs < 0.3. In the mushy zone when 0.3 ≤ fs ≤ 0.7, the thermal conductivity was assumed to change linearly with fs. The exact value of the thermal conductivity in liquid with EMS is not clear since the value varies with the flow velocity of the liquid. It requires testing several times to find an appropriate value to represent the real casting conditions in the simulation. Mizikar [15] used a thermal conductivity of liquid which is 7.5-times higher than that of solid; while a 10-times higher thermal conductivity was used

in Minoru’s study [14]. In the present simulation, a 5-times higher thermal conductivity was assumed after many tests. The schematic diagram is shown in Fig. 3(a). (2) Changing the crystal formation rate in bulk liquid [3]. In this method, it is considered that the crystal formation rate would increase due to the contribution of the fragmentation of dendrites caused by EMS, which should be incorporated into the nucleation model. However, the accurate effect of the fragmentation of dendrites is difficult to describe because of the complex mechanism of fragmentation due to fluid flow. Generally, the value of effective crystal formation rate was determined by reproducing the area of equiaxed crystals as same as that experimentally observed in real billet. In this simulation, the effective crystal formation rate was set at 25 cm-2·s-1 higher than that of heterogeneous nucleation in liquid.

Table 4: Materials properties of 72A cord steel alloys used in this simulation

Alloying Element C Si Mn P S

Partition coefficient (k0) [12] 0.35 0.52 0.75 0.06 0.025

Liqudus slope (m) [12] -60 -8 -5 -34 -40

Diffusivity in liquid (m2·s-1) [3,13] 2.0 × 10-8 2.4 × 10-9 2.4 × 10-9 4.7 × 10-9 4.5 × 10-9

Gibbs-Thomson coefficient, Γ (m•K) [3] 1.9 × 10-7 1.9 × 10-7 1.9 × 10-7 1.9 × 10-7 1.9 × 10-7

(a) Setting of thermal conductivity (b) Setting of crystal formation rate

2.5 Coupling process of FE and CAThe aim of combining the FE and CA calculations into a single model in this work is to ensure the microstructure development is a function of the thermal field, and simultaneously the influence of the latent heat release of the grains could be considered. New nuclei are formed randomly in the bulk volume when the local temperature falls below the critical temperature. The crystallographic orientation of the crystal growth is randomly chosen from predefined orientation classes. The crystallographic orientation <100> is selected preferentially. The growth of grains is realized by capturing the neighboring cells which have the same crystallographic orientation as the matrix cell, and this calculation method can realize the competition of crystal growth. The detailed introduction can be seen in the paper by Gandin and Desbiolles [17].

3 Results and discussion

3.1 Examination of modelTo examine the effectiveness of the present model, a continuous casting experiment was carried out under the same conditions as in the simulation. The cooling parameters and holding time were calculated by the method mentioned in 2.2; and the results are listed in Table 5.

The surface temperature of the billet at different locations was measured using an infrared pyrometer. The solidification structure of a transverse section of billet was etched using 1:1 HNO3-HCl reagent. The comparison between experimental results and simulated results are shown in Fig. 4 and Fig. 5.

It can be seen from Fig. 4 that the simulated results agree well with the surface temperature of the billet measured in the

Fig. 3: Schematic of the effect of EMS

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continuous casting experiment. The macrostructure of the billet is shown in Fig. 5(a) from which about 7% equiaxed crystal ratio can be observed. Figures 5(b) and (c) show the simulated macrostructure of the continuously casting billet with and without EMS. In the simulation without EMS, a smaller region of equiaxed grains (about 5%) is formed in the center of the billet as shown in Fig. 5(b). The equiaxed crystal ratios in the simulation with EMS agree very well with the experimental result, which indicates the treatment method of EMS in this model is feasible.

Therefore, the heat transfer process and solidification structure of 72A tire cord steel billet can be accurately simulated by the present model.

3.2 Model applicationOne purpose of this study is to define the optimum pouring temperature range to obtain a low degree of segregation in the tire cord steel billet. Generally, the lower limit pouring temperature for smooth production should be the maximum temperature decline in the tundish during the casting process plus the liquidus of 72A steel (1,478 ). The temperature variation of liquid steel in the tundish during three times of casting (1#, 2# and 3#) are shown in Fig. 6, from which it can be seen that the maximum temperature decline is about 12 . Therefore, the lower limit pouring temperature of the plant for 72A tire cord steel is about 1,490 .

The 19 billet transverse samples selected randomly in the warehouse of the plant were subjected to fine grinding and polishing to obtain a smooth surface finish. The billet samples were etched with 1:1 HNO3-HCl reagent to reveal the macrostructure from which the area fraction of chill, columnar and equiaxed zones were measured. After acid etching, samples for chemical analysis were obtained by the conventional drilling technique. Then, the maximum segregation of carbon was

Table 5: Cooling parameters and holding time

Length (m) 0.78 0.92 2.51 2.51 2.51 2.19 Holding time (s) 19.5 23.6 62.8 62.8 62.8 55.0Boundary condition β = 230 h = 921.5 h = 590.0 h = 397.2 h = 317.1 ε = 0.7

Parameter MoldSecondary cooling

Air coolingⅠ Ⅱ Ⅲ Ⅳ

Note: Pouring temperature: 1,510 ; Casting speed: 2.4 m•min-1; EMS parameters: 340 A, 20 Hz

Fig.4: Simulated and measured results of surface temperature of billet

Fig. 6: Temperature variation of molten steel in tundish during three times of casting (1#, 2# and 3#)

correlated to the percentage area of equiaxed zone in the billet samples as shown in Fig. 7. From Fig. 7, it is evident that the degree of center segregation tends to decrease with an increase in equiaxed zone, and it can be seen that an equiaxed zone

(a) Macrostructure of billet with EMS (b) Without EMS (c) With EMS

Fig. 5: Observed (a) and simulated macrostructures (b), (c)

(a) (b) (c)

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ratio of at least 20% is required to obtain the degree of centre segregation of no more than 1.08 (the contract requirement is 1.1 while the internal control of the plant is 1.08).

4 Conclusions(1) A CAFE model was developed to s imulate the

solidification structure of 72A tire cord steel billets during the continuous casting process. The effect of phase transformation was considered by calculating the thermo-physical properties by a pair-wise mixture model. The effect of EMS was taken into consideration by increasing the thermal conductivity and crystal formation rate in the liquid phase. Results showed that simulations of solidification structure and cooling curve show a good agreement with those observed and measured in real billets.

Fig. 7: Variation of degree of centerline segregation of carbon with equiaxed zone ratio

(a) 1,520 (b) 1,510 (c) 1,500

(d) 1,497 (e) 1,492 (f) 1,490

Fig. 8: Simulated macrostructures of 72A steel at different casting tempreatures

(2) The simulations showed that the equiaxed crystal ratio decreases with the increase of pouring temperature. Even if the pouring temperature is 1,520 , the equiaxed crystal ratio is still about 5% because of the EMS; at the lower limit temperature of 1,490 , a 60% equiaxed crystal ratio is obtained, which is the greatest ratio for this plant.

(3) Considering the actual conditions in the plant, a pouring temperature of about 1,495 (with a superheat of 17 ) is required for casting in order to get the desired solidification structures of at least 20% equiaxed crystal ratio which corresponds to a centre segregation of less than 1.08 degree in the billet.

In order to get the critical pouring temperature, simulations were performed with different pouring temperatures from 1,490 to 1,520 under the current cooling parameters, and the simulated results are shown in Fig. 8.

It can be seen from Fig. 8 that: (1) The equiaxed crystal ratio increases with the decrease of pouring temperature, which reflects the general rule; (2) Even if the pouring temperature is 1,520 (a superheat of 42) as shown in Fig. 8(a), the equiaxed crystal ratio is still about 5%, which indicates that the EMS did play a role; (3) When the pouring temperature is 1,490 [Fig. 8(f)], the equiaxed crystal ratio is about 60%, which indicates that the equiaxed crystal ratio of 72A billet under the current casting parameters and equipment level could be no more than 60% in this plant; (4) The pouring temperature corresponding to a 20% equiaxed crystal ratio is 1,497 [Fig. 8(d)]. Considering the temperature fluctuations, the pouring temperature of 72A tire cord steel should be controlled at about 1,495.

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This work was supported by the National Basic Research Program of China (grant No. 2010CB630806).

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