Mathematical modelling of the continuous casting of blooms and beam blanks

Daniela Fátima Gomes, Bernardo Martins Braga, Roberto Parreiras Tavares, Maurício Covcevich Bagatini,

Metallurgical and Materials Engineering Department, School of Engineering, Federal University of Minas Gerais, Av. Presidente Antônio Carlos 6627, 31270-901 Belo Horizonte, Brazil.



Defects and discontinuities generated in continuous casting are directly related to heat transfer during the process and the stresses to which the material is subjected. Knowledge of these phenomena is essential for both process safety and the quality of the final product. The aim of this work is to analyze the thermo-mechanical behavior of blooms and beam blanks during continuous casting. The continuous casting machine considered in this study is used to cast both blooms and beam blanks. The secondary cooling can be divided into cooling zone z0, cooling zone z1, cooling zone z2, and cooling zone z3. For each geometry, there are specific molds, z0, z1, z2 (sprays and support rollers), which need to be replaced when there is a geometry shift. The changing of the cooling segments brings security risks for the operators and reduces the continuous casting availability. Therefore, it is desired to have a common z2 for both blooms and beam blanks to reduce operational risk exposure and increase the machine production rate. For this to be possible, it is necessary to assess the temperature and resistance of the solidified skin, the effects of thermal stresses, ferrostatic pressure, and contact stresses. This work is the first step in this study. A thermo-mechanical model was developed for both geometries. The thermal model was verified by temperature measurement and shell measurements of blackouts. Finally, the results were analyzed and compared.

Cite as:

Gomes, D. F., Braga, B. M., Tavares, R. P., & Bagatini, M. C. (2021). Mathematical modelling of the continuous casting of blooms and beam blanks. Computer Methods in Materials Science, 21(3), 149-156.

Article (PDF):


Continuous casting, Mathematical modeling, Beam blanks and blooms


Assunção, C.S., Tavares, R.P., & Oliveira, G.D. (2014). Water distribution assessment applied to mathematical model of continuous casting of steel. Associação Brasileira de Metalurgia, Materiais e Mineração (ABM), 3, 2895–2905.

Bobadilla, M., Jolivet, J.M., Lamant, J.Y., & Larrecq, M. (1993). Continuous casting of steel: a close connection between solidification studies and industrial process development. Materials Science and Engineering A, 173(1–2), 275–285.

Chen, W., Zhang, Y.Z., Zhang, C.J., Zhu, L.G., Lu, W.G., Wang, B.X., & Ma, J.H. (2009). Thermo-mechanical simulation and parameters optimization for beam blank continuous casting. Materials Science and Engineering A, 499(1–2), 58–63.

Hibbeler, L.C., Xu, K., Thomas, B.G., Koric, S., & Spangler, C. (2009). Thermomechanical Modeling of Beam Blank Casting. Iron and Steel Technology, 6(7), 60–73.

Ji, C., Luo, S., & Zhu, M. (2014). Analysis and application of soft reduction amount for bloom continuous casting process. ISIJ International, 54(3), 504–510.

Ji, C., Wu, C., & Zhu, M. (2016). Thermo-Mechanical Behavior of the Continuous Casting Bloom in the Heavy Reduction Process. JOM, 68(12), 3107–3115.

Kozlowski, P.F., Thomas, B.G., Azzi, J.A., & Wang, H. (1992). Simple constitutive equations for steel at high temperature. Metallurgical Transactions A, 23(3), 903–918.

Lee, J.-E., Yoon, J.-K., & Han, H.N. (1998). 3-Dimensional Mathematical Model for the Analysis of Continuous Beam Blank Casting Using Body Fitted Coordinate System. ISIJ International, 38(2), 132–141.

Lee, J.-E., Yeo, T.-J., OH, K.H., Yoon, J.-K., & Yoon, U.-S. (2000). Prediction of cracks in continuously cast steel beam blank through fully coupled analysis of fluid flow, heat transfer, and deformation behavior of a solidifying shell. Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science, 31(1), 225–237.

Liu, Y., Liu, X., Fu, H., Lou, M., & Xie, J. (2017). Effects of process parameters on surface quality, composition segregation, microstructure and properties of QSn6. 5-0. 1 alloy slabs fabricated by HCCM horizontal continuous casting. Journal of Iron and Steel Research International, 24(3), 273–281.

Ma, J., Xie, Z., & Jia, G. (2008). Applying of Real-time Heat Transfer and Solidification Model on the Dynamic Control System of Billet Continuous Casting. ISIJ International, 48(12), 1722–1727.

Mahapatra, R.B., Brimacombe, J.K., & Samarasekera, I.V. (1991). Mold behavior and its influence on quality in the continuous casting of steel slabs: Part II. Mold heat transfer, mold flux behavior, formation of oscillation marks, longitudinal off-corner depressions, and subsurface cracks. Metallurgical Transactions B, 22(6), 875–888.

Meng, Y., & Thomas, B.G. (2003). Modeling Transient Slag-Layer Phenomena in the Shell/mold Gap in Continuous Casting of Steel. Metallurgical and Materials Transactions B: Process Metallurgy and Materials Processing Science, 34(5), 707–725.

Ohba, Y., Kitade, S., & Takasu, I. (2008). Austenite grain refining of as-cast bloom surface by reduction of oscillation mark depth. ISIJ International, 3(3), 3–8.

Qin, Q., Shang, S., Wu, D., & Zang, Y. (2014). Comparative analysis of bulge deformation between 2D and 3D finite element models. Advances in Mechanical Engineering, 6.

Qin, X., Cheng, C., Li, Y., Zhang, C., Zhang, J., & Jin, Y. (2019). A simulation study on the flow behavior of liquid steel in tundish with annular argon blowing in the upper nozzle. Metals, 9(2).

Schmidt, L., & Josefsson, A. (1974). On the Formation and Avoidance of Transverse Cracks in Continuously Cast Slabs From Curved Mould Machines. Scandinavian Journal of Metallurgy, 3(5), 193–199.

Thomas, B.G. (1995). Issues in Thermal-Mechanical Modeling of Casting Processes. ISIJ International, 35(6), 737–743.

Thomas, B.G. (2002). Modeling of the continuous casting of steel – Past, present, and future. Metallurgical and Materials Transactions B: Process Metallurgy and Materials Processing Science, 33(6), 795–812.

Vynnycky, M. (2018). Applied mathematical modelling of continuous casting processes: A review. Metals, 8(11).

Wang, H., Li, G., Lei, Y., Zhao, Y., Dai, Q., & Wang, J. (2005). Mathematical Heat Transfer Model Research for the Improvement of Continuous Casting Slab Temperature. ISIJ International, 45(9), 1291–1296.

Xu, H.L., Wen, G.H., Sun, W., Wang, K.Z., & Yan, B. (2010). Analysis of Thermal Behavior for Beam Blank Continuous Casting Mold. Journal of Iron and Steel Research International, 17(12), 17–22.

Zeng, J., Gan, M., Yan, X., Wang, Q., & He, S. (2020). Mathematical Modeling of Heat Transfer and Deformation of Bloom Tube Mold in Continuous Casting Process. Metallurgical and Materials Transactions B: Process Metallurgy and Materials, Processing Science, 51(1), 213–221.