Finite Element Analysis of Thermal and Mechanical Behavior in a Slab Continuous Casting Mold

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1 , pp Finite Element Analysis of Thermal and Mechanical Behavior in a Slab Continuous Casting Mold Xudong LIU and Miaoyong ZHU School of Materials & Metallurgy, Northeastern University, Shenyang , P. R. China. xdliu80110@163.com (Received on June 13, 2006; accepted on September 5, 2006) Three-dimensional (3-D) finite-element heat-transfer and thermal stress models ere established to predict temperature, distortion and thermal stress in a continuous casting mold for steel slabs during operation. The effects of copper plate thickness, ater slot depth, nickel layer and casting speed on temperature, distortion and thermal stress of copper plate ere analyzed in detail. The results sho that during casting, a maximum temperature, about 285 C, as found just near the meniscus of the centre of hot copper surface, and decreasing the thickness of copper plate and nickel layer, and increasing ater slot depth are available in decreasing the copper plate temperature, therefore improving the mold life. The maximum distortion of ide and narro copper faces are mm and 1.01 mm, respectively, and it increases ith increasing copper plate thickness and casting speed, and decreasing ater slot. Nickel layer thickness has little effect on distortion and much effect on thermal stress. KEY WORDS: slab continuous casting mold; finite element model; copper plate temperature; distortion; thermal stress. 1. Introduction During continuous casting of steel, large temperature gradients develop across the copper plates, hich causes distortions and thermal stresses. Although the amount of distortion is small, it ill greatly affect the heat transfer beteen the shell and the mold since the size of the gap beteen them ill be changed. The mold plates must ithstand this stress reliably ithout cracking, otherise any ater leaking through the mold ould be a catastrophe. Therefore, it is important to have an in-depth understanding the thermal and mechanical behavior of the copper mold. Many studies have been carried out to understand the thermal and mechanical behavior of conventional slab-casting molds over the past years. 1 4) Thomas et al. 4 6) applied a three-dimensional elastic-plastic-creep finite-element model to predict temperature and distortion and residual stress in a continuous casting mold for steel slabs. Samarasekera et al. 7 10) applied mathematical models, combined ith in-plant measurements, to predict the temperature field and shape of the molds as a function of operating design variables. O Conner and Dantzig 11) applied an elastic-plastic-creep finite element model to predict temperature, thermal distortion, stress, and hot face cracks in a funnelshaped mold for casting thin slabs. The above-mentioned orks have shon that temperature and distortion of the mold are important to mold life and steel quality. The present study aims to quantify slab mold temperature, distortion and stress during operation as a function of design variables and operating conditions, such as copper plate thickness, ater slot depth, nickel layer thickness and casting speed, using three dimensional finite-element models of heat transfer and thermal stress, and to provide an insight into slab mold behavior. 2. Mathematical Model Formulation 2.1. Finite Element Models In order to simulate the thermal and mechanical behavior of slab mold, the folloing assumptions ere made in the formulating of the model: (1) The mechanical and thermal properties of mold copper and steel backup plate are isotropic. Since the physical properties such as density and heat capacity of copper mold change little ith the temperature blo 400 C, the influence of temperature on physical properties is negligible. The thermal conductivity of the mold copper is dependent on temperature. (2) Heat transfer beteen the cooling ater and the mold copper is at steady-state. The ater in the cooling channel is in plug flo, and nuclear boiling of the cooling ater is negligible. (3) The top and bottom of mold are considered to be adiabatic, and heat absorption by the mold poder above meniscus is negligible. (4) A perfect bonding exists beteen the mold copper and steel backup plate. The steel backup plate is assumed to be elastic only, and the mold copper is modeled as a bilinear elastoplastic material governed by the von Mises yield criterion. Based on above-mentioned assumptions, models for calculating temperature, distortion and stress in typical slab 2006 ISIJ 1652

2 Fig D finite element modeling: (a) quarter mold model, and (b) finite element mesh. Table 1. Mold geometry and operating conditions. Table 2. Thermal properties of copper, nickel, steel and ater. Table 3. Thermomechanical properties of copper, nickel, and steel. casting molds during steady operation conditions ere established. The mold for slab casting includes four separate copper plates and steel backup plates. Because of symmetry, it as modeled using a representative 3-D quarter-mold model, as shon in Fig. 1(a), and a typical finite element mesh for the model is shon in Fig. 1(b). Mold geometry and operating conditions are given in Table 1, and the thermal and thermomechanical properties of copper, nickel, and steel are given in Table 2 and Table 3, respectively Heat Flo Model During operation, temperature of copper plate, T, is calculated by solving the steady heat conduction equation using nonlinear-temperature finite elements, since the thermal conductivity of the mold copper is dependent on temperature. λ( T ) λ( T ) x x y y z λ( T ) z 0...(1) Where, l is the thermal conductivity of the steel or copper. In the finite element models, the top and bottom of mold and cold face of steel backup plate are considered to be adiabatic. The heat flux on the mold hot faces as a function of distance across and don the mold, 4) and the coefficients of function are determined by the heat flux equilibrium of cooling ater. Thus, the relevant boundary conditions are (i) top and bottom of mold λ( T ) 0...(2) z ISIJ

3 (ii) cold face of steel backup plate for ide face, λ( T ) 0...(3) y for narro face, λ( T ) 0...(4) x (iii) hot face of mold above meniscus for ide face, λ( T ) q ( z 08. ) MW/m 2 y (0.8 z 0.9 m)...(5) for narro face, λ( T ) q ( z 0. 8) MW/m 2 x (0.8 z 0.9 m)...(6) (iv) hot face of mold belo meniscus for ide face, λ T MW/m 2 q z y (0.0 z 0.8 m)...(7) for narro face, λ T MW/m 2 q z x (0.0 z 0.8 m)...(8) To simulate the larger interfacial gaps near the corners, heat flux beneath the meniscus from 30 mm along the offcorner to the corner region of the ide face and narro face decreased to 70% of standard ide face and narro face values. 4) (v) cooling ater slot of mold q h (T T )...(9) Where, T is temperature of cooling ater, and its distribution in the ater slot from the inlet to the outlet don the mold as considered to be linear. The ater slot heat transfer coefficient, h, is determined from the folloing dimensionless correlation. 5) h λ ρ u d d µ...(10) Cµ λ here, d is hydraulic diameter of slot, l is thermal conductivity, m is viscosity, r is density and C is specific heat of cooling ater. Symmetry planes of the heat flo model are insulated (q 0). The simulation as conducted using a commercial finite element analysis package ANSYS TM. The mold copper and steel backup plate ere described using three-dimensional eight-node brick thermal solid elements, referred to in the ANSYS manual as SOLID70. In order to ensure the consistency of results, the element and mesh size ere kept the same for all calculations, hile the number of elements varied ith the design variables Stress Model Displacements, stresses, and strains are calculated by solving the standard equilibrium, constitutive, and straindisplacement equations using the finite element method. For a slab casting mold, the steel backup plate as assumed to exhibit thermoelastic behavior, and the mold copper plate as considered to be thermoelastic-plastic. The isotropic linear elastic stress strain relation can be expressed by the constitutive equation as follos: s ij 2Ge ij [le kk (3l 2G)aDT]d ij...(11) In this relation, l and G are Lamé coefficients for the copper and steel plates, a is the coefficient of thermal expansion and d ij is Kronecker s delta. The copper and steel plates of a slab casting mold often sho very different behaviors, therefore, different mathematical models are required for the simulation. Plasticity of the mold copper as considered for the calculation of thermal stresses during operation, since the temperature gradients is usually large enough to induce plastic deformation. Therefore, the total strain in the copper plate can be expressed as the sum of an elastic strain, a thermal strain, and a plastic strain, i.e. e ij e ij e e ij p e ij T. Plasticity as modeled using the isotropic-hardening viscoplastic relation ith ε p e εij 3 2 Φ( ε )...(12) Φ( εe) σy E E εe...(13) E E here, S ij is the deviatoric stress tensor, s y is the yield stress, E and E 1 are Young s modulus and linear hardening slope respectively, and e e is the von Mises equivalent strain. A temperature change DT may induce a thermal strain of a magnitude e ij T adtd ij...(14) The 3-D quarter-mold model includes separate domain for the mold coppers and steel backup plates hich are coupled mathematically at interface here they are connected mechanically by 144 and 18 steel bolts for ide and narro face of mold, respectively. The cold side of the steel backup plates is mathematically fixed. Boundary conditions include ferrostatic pressure loads over all hot-face surfaces. The mechanical boundary conditions are free at upper and loer ends of mold, due to the upper and loer ends of mold are not fixed and prevented from expanding. Finally, rigid body motion is prevented by constraining the symmetry planes from normal displacement. The finite element method as used to solve Eqs. (11) (14) ith boundary conditions, and the displacement, stress, strain can then be calculated. Finite element analysis e Sij ISIJ 1654

4 Fig. 2. The distribution of calculated heat flux and temperature at the centre of hot copper surface in the direction of mold length. Fig. 3. Temperature distribution at position of thermocouple in (a) narro face and (b) ide face of copper plate. Fig. 4. Temperature distribution ( C) on transverse section of copper plate through (a) ide face, and (b) narro face. of thermal mechanical behavior of slab casting mold as conducted by using ANSYS TM. The mold copper and steel backup plate ere described using three-dimensional eightnode brick structural solid elements, referred to in the ANSYS manual as SOLID45. Fig. 5. The distribution of calculated distortion at the centre of hot copper surface in the direction of mold length. 3. Results and Discussion 3.1. Temperature, Distortion and Stress Distribution in Mold Copper The typical temperature and distorted shape of the quarter mold during operation are shon in Figs. 2 5 for standard conditions given in Tables 1 3. Figure 2 shos the distribution of heat flux and calculated temperature at the centre of hot copper surface in the direction of mold length. There is a peak heat flux at the meniscus here a maximum temperature value can be found, and another maximum temperature as at mid-height of copper mold. This is because the copper surface as be coated ith a 3 mm thickness layer of nickel to reduce the mold ear in the loer portions of the hot face, here mold ear is usually greater due to the greater ferrostatic pressure of the molten steel. Nickel possesses a loer thermal conductivity than copper, hich induces a higher temperature in the loer portions of the mold hot face. Within about 50 mm from the mold exit, the temperature increases by about 25 C, though a continuously decreasing heat flux profile. Such effect, neglected in previous heat flo models, is due to the end of the ater slot 25 mm above the mold exit, hich indirectly validates this novel prediction of the model. To verify the predictions of the model, the predicted temperature values of mold copper ere compared ith available experimental measurements, as shon in Fig. 3. To measure the temperature distribution in casting direction, the bottom and top ro thermocouples are fixed in copper plate 500 mm and 700 mm above the mold exit, respectively. Figure 3 shos that both temperature distributions in narro and ide face are in a good agreement. The highest temperature can be found at the corner of the mold narro face, since the distance beteen cooling ater slots and the edge of the narro face is relatively large. Near the edge of the ide face, hoever, temperature decreases ith increasing the distance from ide face centerline due to no heat flux transferred across the copper plates. Thus, care should be especially taken in designing the cooling ater slots on the narro face, and an oblique cooling ater slot can be designed to ensure the enough cooling to the narro face edge. The calculated temperature distribution on transverse section of copper plate is shon in Fig. 4. Water slots often have a larger spacing across bolt locations, hich lead to a ISIJ

5 higher local temperature, and this is also shon in Fig. 3. So, deeper ater slots adjacent to bolts ere often made to avoid temperature increase. An almost linear temperature gradient is established in the copper plates beteen the hot face and roots of the cooling ater slots, hile the temperature gradients beteen the cold face and the roots of the cooling ater slots are relatively large. Figure 5 shos the distribution of calculated distortion don the centerline of hot copper surface, and the distortion is y-displacement for ide face and x-displacement for narro face. The maximum thermal distortions of ide and narro face are mm and 1.01 mm, respectively. As there are ater sockets at the ide and narro steel backup plates as shon in Fig. 1, decreasing the length of ater socket ill increase the rigidity of steel backup plates and greatly decrease the distortion of mold copper. In the present mold, the length of ater socket at narro steel backup plates is larger than that of ide ones. The distribution of calculated thermal Von Mises stress s at the centre of hot copper surface in the direction of mold length is shon in Fig. 6. Although, larger distortion is found in narro hot face, smaller von Mises stress can be calculated in narro hot face of mold copper, due to smaller rigidity restriction of steel backup plates. To remove the effects of both mold ear and permanent distortion, the mold copper plates need to be remachined. Mold ear is usually greater in the loer portions of the hot face, due to the greater ferrostatic pressure of the molten steel. Thus, a large thermal stress produces in the copper plates beteen the mid-height and the exit of mold due to the mismatch of thermal expansions beteen the nickel layer and copper plate, especially for the interface. Figure 7 shos thermal stress distribution on transverse section of copper plate through ide and narro face. Thermal stress depends mainly on the temperature gradient and the coefficient of thermal expansion. Although the temperature gradient is almost linear close to the edge of mold hot face, the thermal stress gradient is larger due to the difference in the coefficient of thermal expansion of the nickel layer and copper plate. A larger thermal stress gradient can be also found at ater slot roots, here the temperature gradient is larger due to the more cooling action of ater Effect of Copper Plate Thickness Five copper plate thicknesses ere chosen to study the effect on thermal and mechanical behavior of copper plate, and the calculated results are shon in Figs. 8 and 9. It can be seen that decreasing thickness of copper plates loers the hot face temperature, and correspondently decreases in both distortion and thermal stress. Decreasing 5 mm of copper plate thickness can loer about 32 C maximum temperature and 0.18 mm maximum thermal distortion of hot face. Figure 9 shos that the effect of copper plate thickness on thermal stress and distortion at don part of mold hot face is more distinct than that of the upper part. This is because that the mismatch of thermal expansions beteen the nickel layer and copper plate incurred the larger thermal stress Effect of Water Slot Depth Copper temperature depends mainly on the heat flux transferred across the interfacial gap from the molten steel, and on the minimum distance beteen the copper hot face and the root of the nearest ater slot. Thus, ater slot depth has a critical effect on temperature and accompanying thermal distortion and stress in the mold. Locations in the mold here cooling slots are farther from the surface, thus give rise to the higher hot face temperature, that is, the shalloer ater slot incurs higher hot face temperature. Fig. 6. The distribution of calculated thermal Von Mises stress at the centre of hot copper surface in the direction of mold length. Fig. 8. Effect of copper plate thickness on temperature don centerline of hot ide face ISIJ Fig. 7. Thermal stress distribution (MPa) on transverse section of copper plate through (a) ide face, and (b) narro face. 1656

6 Fig. 9. Effect of copper plate thickness on (a) distortion and (b) thermal stress don centerline of hot narro and ide face. Fig. 10. Temperature distribution ( C) on transverse section of copper plate ith different ater slot depth: (a) 12 mm and (b) 24 mm. Fig. 11. Thermal stress distribution (MPa) on transverse section of copper plate ith different ater slot depth: (a) 12 mm and (b) 24 mm. Fig. 12. Effect of ater slot depth on (a) distortion and (b) thermal stress don centerline of hot ide face. The effects of ater slot depth on temperature distribution on transverse section of copper plate are shon in Fig. 10. It can be seen that the trend of temperature distribution is almost similar, and the temperature of the hot face decreases ith increasing ater slot depth. While the temperature increases near the roots of ater slot due to the short distance from the hot face. During operation, the different coefficient of thermal expansion and temperature gradient in the copper plate generate thermal stress, and it is clear that this stress concentrates at the roots of the ater slots and in the nickel layer, hich is more obvious for the copper plate ith deeper ater slot, as shon in Fig. 11. Deeper ater slot has the potential to decrease temperature as ell as the thermal distortion on the hot face of copper plate, especially for maximum distortion, as shon in Fig. 12, hile it has a slight effect on thermal stress of hot ISIJ

7 face, especially at the upper part of the mold Effect of Nickel Layer Mold ear is usually greater in the loer potions of the hot face of copper plates, and it can be improved by coating the copper surface ith a 1 3 mm layer of sacrificial nickel plating. While relatively less effort has been made to understand the effect of nickel layer thickness on the thermal and mechanical behavior of slab molds. The nickel layer as usually neglected in some mathematical models, and the physical properties of nickel layer ere treated as a part of effective physical properties of copper plates. In the present ork, the effect of nickel layer thickness on the thermal and mechanical behaviors of slab mold are numerically studied, and the effects of nickel layer are shon in Figs. 13 and 14. The figures indicate that the thicker nickel layer incurred higher temperature, due to the loer thermal conductivity of nickel, and the effect on thermal stress is greatest. The incremental thermal stress is about 500 MPa as nickel layer is coated in the copper plate, as shon in Fig. 14(b). The temperature increases by about 15 C ith the 1 mm increment of nickel layer thickness, hich has a potential to increase the thermal stress value of mold copper. The nickel layer thickness has little effect on the thermal distortion of copper plates Effect of Casting Speed Casting speed has much effect on the distribution of heat flux on the mold hot faces, hich affects the distribution of temperature and thermal distortion of copper mold. Figure 15 shos the effect of casting speed on temperature don the hot face centerline, and it indicates the higher casting speed incurred higher temperature, due to the higher heat flux through the copper mold, hile the increments of temperature decrease ith increasing casting speed. Within about 50 mm from the mold exit, hoever, the predicted temperature increments increase ith increasing casting speed, due to the end of the ater slot 25 mm above mold exit. The casting speed has a more effect on the temperature distribution at the loer part of copper mold than that of the upper part, hich causes a more thermal distortion increase as shon in Fig. 16. The maximum distortions increase by Fig. 13. Effect of nickel layer on temperature don centerline of hot ide face. Fig. 15. Effect of casting speed on temperature don centerline of hot narro face. Fig. 14. Effect of nickel layer on (a) distortion and (b) thermal stress don centerline of hot ide face. Fig. 16. Effect of casting speed on (a) distortion and (b) thermal stress don centerline of hot narro face ISIJ 1658

8 about 0.06 mm ith 0.4 m/min increment of casting speed. It implies that the casting speed has little effect on the thermal stress on the part of copper mold hot face ithout nickel layer, hile much effect on the part ith nickel layer. 4. Conclusions (1) To peak temperatures are found at the centre of hot copper surface, one at the meniscus ith a peak heat flux and another at interface beteen copper plate and nickel layer. Within about 50 mm of the mold exit, temperature increases by about 25 C due to the end of the ater slot 25 mm above mold exit. Decreasing the length of ater socket can increase the rigidity of steel backup plates and greatly decrease the distortion of mold copper. (2) Decreasing 5 mm of copper plate thickness can loer about 32 C maximum temperature and 0.18 mm maximum thermal distortion of hot face. Thermal stress concentrates at the roots of the ater slots and in the nickel layer, hich is more obvious for the copper plate ith deeper ater slot. (3) The effect of nickel layer on thermal stress is greatest, and the increment is about 500 MPa hen nickel layer is coated in the copper plate, hile it has little effect on the thermal distortion of copper plates. Acknoledgements The authors are especially grateful to the National Natural Science Foundation of China (Grant No ) and Program for Ne Century Excellent Talents in University (NCET ). REFERENCES 1) E. G. Wang and J. C. He: Sci. Technol. Adv. Mater., 2 (2001), ) M. Janik and H. Dyja: J. Mater. Process. Technol., (2004), ) M. Janik, H. Dyja, S. Berski and G. Banaszek: J. Mater. Process. Technol., (2004), ) B. G. Thomas, G. Li, A. Moitra and D. Habing: 80th Steelmaking Conf. Proc., Vol. 80, ISS, Warrendale, PA, (1997), ) J. K. Park, I. V. Samarasekera, B. G. Thomas and U. S. Yoon: 83rd Steelmaking Conf. Proc., Vol. 83, ISS, Warrendale, PA, (2000), 9. 6) J. K. Park, C. S. Li, B. G. Thomas and I. V. Samarasekera: 60th Electric Furnace Conf., Vol. 60, ISS, Warrendale, PA, (2002), ) C. Cho, I. V. Samarasekera, B. N. Walker and G. Lockhart: Ironmaking Steelmaking, 29 (2002), No. 1, 61. 8) I. V. Samarasekera and J. K. Brimacombe: Ironmaking Steelmaking, 1 (1982), 1. 9) J. K. Brimacombe and I. V. Samarasekera: I&SM, 10 (1979), ) I. V. Samarasekera and J. K. Brimacombe: Can. Metall. Q, 18 (1979), ) T. G. O Conner and J. A. Dantzig: Metall. Mater. Trans. B, 25B (1994), ISIJ