Effect of cooling structure on thermal deformation of copper plate in continuous casting mold

Abstract: A three-dimensional finite element thermoelastoplastic structural model of the slab continuous casting mold was established, and the influence of the copper plate deformation and the cooling structure of the mold on it was calculated. The cooling structure and thermal load determine the deformation behavior of the hot surface of the copper plate. The deformation amount of the copper plate depends on the geometric parameters of the cooling structure, and there is a small deformation mutation at the copper-nickel boundary. The maximum deformation of the center line of the wide hot surface occurs at 100 mm below the meniscus, and the maximum deformation of the narrow surface occurs at the end of the meniscus and cooling water tank, and the deformation curves on both sides of the copper-nickel boundary have obvious curvature fluctuations. When the copper plate is thickened by 5 mm, the maximum centerline deformation can increase by 0. 05 mm. The nickel layer has no obvious effect on the centerline deformation. A thickness change of 1 mm only causes a maximum decrease of 0. 01 mm on the narrow surface. The cooling water tank also has a small impact on the centerline deformation. The water tank is deepened by 2 mm and the maximum centerline deformation is reduced by 0. 02 mm.

Keywords: continuous casting; copper mould tube; deformation; thermal analysis; finite element method

A large amount of sensible heat and latent heat of solidification of molten steel in continuous casting are lost in the primary cooling zone, causing the copper mould tube to bear a huge thermal load and causing elastic, plastic deformation and high-temperature creep of the copper plate of the mold. Not only does thermal fatigue shorten the service life of the copper mould tube, it also causes changes in the contact state between the copper mould tube wall and the initial solidification shell, which directly affects the metallurgical effect of the copper mould tube. Despite being restrained by fastening bolts and cooled by cooling water, this amount of thermal deformation is relatively small. However, when the width of the meniscus slag channel is in the range of 10-2 to 10-1mm, it is still the key to determining the process behavior of lubrication, friction, heat transfer and shell solidification, and is even an important basis for taper design. Therefore, revealing the deformation rules of the copper mould plate under specific temperature loads and analyzing the influence of cooling structural parameters are crucial to theoretical research on high-quality steel continuous casting and mold metallurgy. Many previous studies have focused on the shrinkage deformation of solidified shells. Based on the elaboration of metal solidification and crack formation mechanisms, they provide a reference for cooling mechanism and taper optimization, which can be regarded as an “inverse problem” of cooling structure design. As a large-scale metallurgical reactor, the structure of the copper mould tube produced is difficult to change, and it should be examined from the perspective of “positive problems”. That is, based on specific heat transfer boundary conditions, the thermal stress and thermal deformation laws of the copper mould plate are calculated and analyzed to provide support for designing appropriate structures. Thomas et al. used a steady-state heat transfer finite element model to calculate the hot surface and corner temperatures of the slab mold copper plate, proposed an empirical equation for the corner temperature, and optimized the cooling water tank design based on this. Based on the analysis of the heat flow characteristics of the billet mold, Chow et al. clarified the mold taper requirements, and combined the deformation of the copper plate and the casting section size to design a taper suitable for higher drawing speeds. Park et al. used the indirect coupling method to apply the measured heat flow density to the thin slab mold, and then analyzed the mechanical behaviors such as deformation and residual stress of the funnel-shaped and straight mold copper plates. When the casting operation is stable, the deformation of the mold largely depends on the primary cooling effect, but research so far still lacks exploration of the intrinsic relationship between the two. This paper establishes a three-dimensional finite element solid model of the slab copper mould tube, and calculates the influence of cooling structure parameters such as the deformation of the copper mould tube copper plate, the thickness of the copper plate and nickel layer, and the depth of the cooling water tank, in order to provide a basis for exploring a suitable copper mould tube cooling structure.

1 Calculation model

1. 1 Physical model

Figure 1 shows the physical model of the slab continuous casting mold. In order to enhance the primary cooling effect, the water tank near the corner of the narrow surface is tilted 15° to the wide surface. This feature is often ignored in previous studies, but its influence on the corner temperature of the copper plate is obvious. Considering symmetry, 1/4 of the copper mould tube was selected to build a three-dimensional finite element solid model, and the finite element commercial software ANSYS was used to complete the meshing of the solid model. To ensure accuracy, the nickel layer, cooling water tank, water cave and other locations were all meshed. ,as shown in picture 2.

Figure 1 Physical model of slab continuous casting mold

Figure 2 Finite element solid model of the copper mould tube

1. 2 Mathematical model

The heat transfer in the continuous casting mold is complex. This article examines steady-state casting, and its heat transfer control equation is:

In the formula: λ is the thermal conductivity of the medium, W·m-1·℃ – 1. T is temperature, ℃. x, y and z are the coordinate positions perpendicular to the narrow surface and wide surface and parallel to the drawing direction respectively, and the coordinate origin is the geometric center of the mold outlet.

The solution boundary conditions are: (1) The top and bottom surfaces of the copper mould tube and the cold surface of the back plate water tank are at constant temperature; (2) The heat flow on the hot surface of the effective height copper plate complies with the square root law of heat transfer, and the heat flow on the hot surface on the meniscus is linear; (3) There is surface convection heat transfer between the copper plate and the cooling water. Among them, the heat flow above the meniscus and in the effective height range is determined by equation (2) and equation (3) respectively, and its equation coefficients are determined based on the thermal balance principle. In addition, considering the air gap existing between the contact surfaces near the corners of the mold, it is believed that the heat flow gradually decreases by 30% from a distance of 30 mm from the corner area to the corners.

In the formula: q is the heat flow density, W·m-2; a1, a2 and a3 are the equation coefficients. hw is the convection heat transfer coefficient, W·m-2·℃-1. Tw is the cooling water temperature, ℃-1. λw is the thermal conductivity of the cooling water, W·m-1 ·℃-1. dw is the equivalent diameter of the cooling water tank, m. ρw is the density of cooling water, kg·m-3. vw is the cooling water velocity, m·s-1; μw is the cooling water viscosity, Pa·s; Cw is the cooling water specific heat capacity, J·kg-1·℃-1.

Because the connection between the copper plate and the steel back plate is relatively complex, the basic assumptions for calculation are: (1) The copper plate and the back plate are tightly combined, and the internal stress caused by the fixing bolts is ignored. (2) The mechanical and thermal properties of the copper plate and the back plate are isotropic; (3) The back plate has low temperature and high rigidity. Consider that the back plate is elastic and the copper plate is elastic-plastic. The thermoelastoplastic stress-strain constitutive equation of the mold copper plate is expressed as

In the formula: σij is the stress, Pa; εij is the strain; L1 and L2 are Lamé coefficients; εkk is the positive strain of the node; β is the thermal expansion coefficient, ℃-1; ΔT is the temperature change, ℃; δij is the Kronecker function. Among them, the stress and strain of the copper plate include elastic, plastic and thermal strains:

Where: εe, εp and εt are elastic, plastic and thermal strains. ε0 is the effective strain. Sij is the skewness tensor; E is the Young’s modulus, Pa. Et is the linear hardening modulus, Pa; σy is the yield strength, Pa.

The solution boundary conditions are: (1) The cold surface of the wide-surface back plate is fixed; (2) The centerline profiles of the wide-surface and narrow-surface are fixed. (3) At a distance of 100 mm from the inlet and outlet of the crystallizer, the cold surface clamping force of the narrow back plate is 60. 1 and 74. 9 MPa respectively; (4) The inner wall of the copper plate bears the static pressure of molten steel.

2 Calculation results and analysis

Based on the above model, the literature calculated the temperature field of the copper plate of the copper mould tube and compared it with the temperature value measured by the thermocouple, confirming that the results are credible and the model is reliable. This article uses ANSYS software to convert the solid model into a thermal stress structural model, and uses the temperature field of the copper plate as a thermal load to calculate its thermodynamic behavior. It is applied to the solid structure model at one time to simulate the deformation of the copper plate. The calculation operating conditions are casting SPHC ([C] ≤ 0. 08%) steel at a pulling speed of 1. 6 m·min-1. The copper mould tube material properties are shown in Table 1. In addition, based on the surface of the mold copper plate, the deformation toward the cast slab side is defined as positive and vice versa as negative.

Table 1 Copper mould tube material properties

MaterialEt / GPaE / GPaβ /10-6  – 1σy / MPa
 copper    11. 0 128. 015. 2( 15℃) 330. 0 (20℃) 
15. 7 (71℃)280. 0 (200℃)
16. 5 ( 127℃)240. 0 (350℃)
17. 6 (227℃)165. 0 (500℃)
18. 3 (327℃) 
nickel73. 0230. 016. 7(20~200℃)700. 0 (20~400℃)
steel200. 011. 7(20~200℃)

2.1 Normal deformation of hot surface

Commonly used metal materials follow the von Mises yield criterion, and their unit deformation is described by the shape change specific energy theory. The deformation of the copper plate caused by the von Mises equivalent stress is shown in Figure 3 in three-dimensional and contour form, where 0 deformation represents the base plane of the hot surface of the copper plate. The hot surface deformation of the wide surface is more uniform than that of the narrow surface because the narrow surface is significantly affected by the shrinkage and air gap of the corner shell. Moreover, the end surfaces on both sides of the narrow surface are in contact with the wide surface and are not free ends. The expansion and extension are limited, and the deformation energy cannot be released along the tangent direction of the hot surface and superimposed on the relatively free normal direction of the hot surface. The wide hot surface expands to the side of the billet as a whole due to thermal stress. Among them, the deformation of the far corner is relatively large, with the maximum value corresponding to the fastening bolt position about 100 mm below the meniscus, which is about 0. 34 mm, and is blocked by the cooling water tank to form six equal deformation ring areas. The deformation below the meniscus gradually decreases, and the relatively low deformation at the corresponding position of the cooling water tank makes the iso-deformation curve appear wavy. It is not until the isovalue curve near the crystallizer outlet that it becomes smooth, and the deformation at the end of the cooling water tank increases, which is about 0. 15 mm, and then drops to about 0. 08 mm at the exit. The deformation from the near corner to the corner of the hot surface gradually decreases, until a slight negative deformation occurs at the contact point with the narrow surface, which is about – 0. 008 mm. The middle part of the contact area between the wide surface and the narrow surface end face has resisted the tangential expansion of the narrow surface due to the expansion and rigidity of the copper plate itself. It still shows very slight deformation towards the casting billet, and the distribution is relatively uniform, with a maximum value of about 0. 06 mm. , corresponding to the maximum deformation position of the hot surface, and the remaining parts are about 0. 01 ~ 0. 04 mm; a “triangular area” of negative deformation toward the cold surface of the copper plate appears from the bottom of the crystallizer to the outlet, with the maximum deformation reaching – 0. 13 mm. On the one hand, the weak cooling effect makes the thermal deformation of the copper plate smaller, and on the other hand, it is caused by the narrow surface deformation energy being released at the free end.The narrow surface expands toward the slab side due to thermal stress, forming a minimal negative deformation zone only at the exit corner of the mold, with a maximum value of -0.10 mm; the maximum positive deformation of the narrow surface occurs at the middle meniscus position, which is approximately 0 . 40 mm, which is higher than the maximum value of the wide surface. The positive deformation gradually decreases along the drawing direction, rebounds to the end of the cooling water tank, and then continues to decrease. The meniscus area, the copper-nickel boundary area and the end area of the cooling water tank respectively form closed equal deformation curves, which together with the constrained superimposed deformation make the deformation in the middle of the narrow surface appear irregular. The isovalue curve from the near corner to the corner gradually becomes gentle, and the closed isodeformation curve near the copper-nickel boundary should be a narrow inverted taper design to ensure full contact between the crystallizer wall and the shell surface. Calculations show that the thermal deformation trend of the copper plate is relatively fixed under a specific thermal load, and the amount of deformation depends on the cooling effect. The following is a quantitative analysis of the influence of cooling structure parameters on the deformation of the copper plate by examining the deformation of the copper plate at the center line of the hot surface.

Figure 3 Normal displacement distribution of the hot surface of the copper plate of the mold (a) wide surface; (b) narrow surface

2.2 Influence of copper plate thickness

Figure 4 shows the effect of copper plate thickness on the centerline deformation of the hot surface. As the copper plate thickens, the deformation of the centerline of the hot surface increases, and the thicker the copper plate, the greater the increase. The maximum increment of the wide surface occurs in the maximum deformation area of 100 mm under the meniscus. The deformation increments of the copper plate from 30 to 35 mm and from 45 to 50 mm are approximately 0. 03 and 0. 06 mm respectively. The maximum increment of the narrow surface not only occurs on the meniscus, but also occurs near the copper-nickel boundary. This is because the copper-nickel boundary area forms a relatively high closed equal deformation curve. The deformation increments of the copper plate from 30 to 35 mm and from 45 to 50 mm are approximately 0. 03 and 0. 05 mm respectively. In addition, the higher curvature of the deformation curve near the meniscus and the end of the cooling water tank indicates that primary cooling and heat flux have a greater impact on the deformation of the copper plate. Among them, the deformation amplitude of the end of the narrow surface water tank is higher than that of the wide surface. This should be caused by the shrinkage of the wide surface causing a larger air gap near the outlet of the narrow surface copper mould tube, and the cooling effect is more obvious. The difference in thermal physical parameters between copper and nickel has little effect on deformation, and only small deformation protrusions appear at the boundary between copper and nickel. And when the copper plate is thin, the protrusions are not obvious and the deformation curve is smoother. The deformation protrusions are more obvious when the copper plate is thicker than 45 mm.

Figure 4 Effect of the thickness of the mold copper plate on the normal displacement of the center line of the hot surface (a) wide surface; (b) narrow surface

2.3 Influence of nickel layer thickness

Figure 5 shows the effect of nickel layer thickness on the centerline deformation of the hot surface. Because the nickel layer is thin, thickness changes have little effect on the deformation of the copper plate, and because the narrow surface deformation is limited, the nickel layer thickness has a greater impact on the narrow surface deformation than the wide surface. As the nickel layer thickens, the deformation from the boundary between wide copper and nickel to the end of the crystallizer outlet water tank decreases slightly, but it is not obvious. As the nickel layer thickens in the area above the narrow-surface copper-nickel boundary, the deformation decreases relatively significantly. The maximum deformation caused by a 1 mm change in the thickness of the nickel layer can reach 0. 01 mm. The deformation gradually decreases below the copper-nickel boundary, and increases with the increase in the thickness of the nickel layer from the area 350 mm away from the mold outlet to the end of the water tank. Therefore, an excessively thick nickel layer will lead to an increase in the curvature of the centerline deformation curve, which can easily cause metal fatigue and is not conducive to the use of the equipment.

Figure 5 Effect of the thickness of the nickel layer of the mold on the normal displacement of the center line of the hot surface (a) wide surface; (b) narrow surface

2.4 Influence of cooling water tank depth

If the size of the copper mould tube cooling water tank changes, the cooling water flow rate and the temperature difference between the inlet and outlet water of the cooling system will inevitably change. It is difficult to quantitatively calculate the impact of water tank size. Based on the current constant water flow rate and water temperature difference, this study examines the impact of the cooling water tank size on the stress distribution of the copper plate and proposes auxiliary analysis results. Since the change in the width of the cooling water tank will significantly affect the deformation resistance of the copper plate itself, only the effect of the depth of the cooling water tank on the deformation of the center line of the hot surface is examined, as shown in Figure 6. As the depth of the cooling water tank increases, the deformation of the center line of the hot surface decreases; the maximum deformation of the wide surface is 100 mm below the meniscus. For every 2 mm change in the cooling water tank, the maximum deformation changes by 0. 02 mm; the maximum deformation of the narrow surface occurs. At 100 mm below the meniscus and near the copper-nickel boundary, the maximum deformation is also close to 0. 02 mm. In actual casting, although a deep cooling water tank will carry away more heat, it will bring the bottom of the water tank closer to the hot surface of the copper plate, which can easily cause nucleate boiling of the cooling water, reduce cooling efficiency, concentrate thermal stress, and produce scale. Figure 6 shows that deepening the water tank does not significantly reduce the deformation of the copper plate, so the current water tank design is reasonable.

Figure 6 Effect of the depth of the cooling water tank of the copper mould tube on the normal displacement of the center line of the hot surface (a) wide surface; (b) narrow surface

3 Conclusion

The hot surface deforms more uniformly on the wide surface than on the narrow surface, and the whole expands toward the side of the slab. The far corner deforms greatly and is blocked by the cooling water tank to form an equal deformation ring area. The maximum deformation of 0.34 mm occurs at the tightening bolt position 100 mm below the meniscus, and gradually decreases along the drawing direction. The relatively low deformation of the cooling water tank makes the equal deformation curve appear wavy, which tends to be smooth near the crystallizer outlet. The deformation at the end of the cooling water tank rebounded to about 0. 15 mm, and then dropped to about 0. 08 mm at the outlet; the deformation from the near corner to the corner of the hot surface gradually decreased, until a slight negative deformation occurred at the contact with the narrow surface, which was about -0. 008 mm.

The narrow surface also expands toward the billet side, forming a minimal negative deformation zone only at the exit corner of the mold, with a maximum value of -0. 10 mm. The maximum positive deformation of the narrow surface appears at the middle meniscus, which is about 0. 40 mm, which is higher than the maximum value of the wide surface. It gradually decreases along the drawing direction, rises to the end of the cooling water tank, and then continues to decrease. The meniscus area, the copper-nickel boundary area and the end area of the cooling water tank respectively form closed equal deformation curves. The superposition of the deformation constrained by the wide surface makes the deformation of the middle part of the narrow surface appear irregular, while the iso-stress curves from the near corner to the corner gradually become gentle.

As the copper plate thickens, the centerline deformation of the hot surface increases. The thicker the copper plate, the greater the increase. When the copper plate is thickened by 5 mm, the maximum centerline deformation increases by 0. 05 mm. The thickness of the nickel layer and the depth of the cooling water tank have relatively little impact on the centerline deformation. A 1 mm change in the nickel layer thickness only causes a maximum decrease of 0. 01 mm on the narrow surface. The cooling water tank is deepened by 2 mm, and the maximum center line deformation is reduced by 0. 02 mm.

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