Skip to main content
Log in

Investigating the effects of cooling rate and casting speed on continuous casting process using a 3D thermo-mechanical meshless approach

  • Original Paper
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

In this paper, for the first time, using a three-dimensional (3D) thermo-elastoplastic model, the effects of cooling rate and casting speed on the continuous casting (CC) process are studied. Some significant parameters such as solidified shell thickness, mushy zone thickness, metallurgical length, and residual stress in the CC process under different cooling rates and casting speeds are investigated. All analyses are performed using the meshless local Petrov–Galerkin (MLPG) method. The effective heat capacity method is employed to simulate the phase change process. The von Mises yield function with isotropic hardening is used to simulate the stress state, and material parameters are assumed as temperature dependent. To demonstrate the accuracy and efficiency of the present 3D MLPG method in thermo-mechanical analysis of highly nonlinear solidification problems, the obtained results are compared with an exact analytical solution. Several numerical examples for different cooling rates and casting speeds are provided to investigate their effects on the CC process parameters, as well as on the stress, displacement, and temperature fields induced in the cast material. The results from the analyses can be very useful for the optimal design of CC processes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. ASM: Casting ASM Metal Handbook, vol. 15. American Society of Metals, Metals Park, OH (1998)

  2. Tszeng, T.C., Kobayashi, S.: Stress analysis in solidification processes: application to continuous casting. Int. J. Mach. Tools Manuf. 29, 121–140 (1989)

    Article  Google Scholar 

  3. Weiner, J.H., Boley, B.A.: Elasto-plastic thermal stresses in a solidifying body. J. Mech. Phys. Solids 11, 145–154 (1963)

    Article  Google Scholar 

  4. Tien, R., Kaump, V.: Thermal stresses during solidification on basis of elastic model. ASME J. Appl. Mech. 36, 763–767 (1969)

    Article  Google Scholar 

  5. Manesh, A.A.: Three-dimensional finite element analysis application to continuous casting. J. Mater. Shap. Technol. 8, 179–185 (1990)

    Article  Google Scholar 

  6. Thomas, B.G., Li, G., Moitra, A., Habing, D.: Analysis of thermal and mechanical behavior of copper molds during continuous casting of steel slabs. Iron Steelmak. 25, 125–143 (1998)

    Google Scholar 

  7. Koric, S., Hibbeler, L.C., Thomas, B.G.: Explicit coupled thermo-mechanical finite element model of steel solidification. Int. J. Numer. Methods Eng. 78, 1–31 (2009)

    Article  Google Scholar 

  8. Koric, S., Hibbeler, L.C., Liu, R., Thomas, B.G.: Multiphysics model of metal solidification on the continuum level. Numer. Heat Transf. B Fund. 58, 371–392 (2010)

    Article  Google Scholar 

  9. Wang, T., Li, J., Chen, Z., Wu, L., Cao, Z., Li, T.: Three-dimensional analysis and design of petal-like mould for continuous casting of steels. Ironmak. Steelmak. 40, 25–31 (2013)

    Article  Google Scholar 

  10. Louhenkilpi, S., Laitinen, E., Nieminen, R.: Real-time simulation of heat transfer in continuous casting. Metall. Trans. B 24(4), 685–693 (1993)

    Article  Google Scholar 

  11. Hill, J.M., Wu, Y.H.: On a nonlinear Stefan problem arising in the continuous casting of steel. Acta Mech. 107(1–4), 183–198 (1994)

    Article  MathSciNet  Google Scholar 

  12. Hardin, R.A., Liu, K., Beckermann, C., Kapoor, A.: A transient simulation and dynamic spray cooling control model for continuous steel casting. Metall. Mater. Trans. B 34(3), 297–306 (2003)

    Article  Google Scholar 

  13. Cheung, N., Santos, C.A., Spim, J.A., Garcia, A.: Application of a heuristic search technique for the improvement of spray zones cooling conditions in continuously cast steel billets. Appl. Math. Model. 30(1), 104–115 (2006)

    Article  Google Scholar 

  14. Zhang, J., Chen, D., Wang, S., Long, M.: Compensation control model of superheat and cooling water temperature for secondary cooling of continuous casting. Steel Res. Int. 82(3), 213–221 (2011)

    Article  Google Scholar 

  15. Sun, M., Wang, Y.T., Shen, H.F.: Analysis and optimization of spray nozzles arrangement in slab casting by numerical simulation. J. Iron Steel Res. 4, 013 (2011)

    Google Scholar 

  16. Long, M.J., Chen, D.F.: Study on mitigating center macro-segregation during steel continuous casting process. Steel Res. Int. 82(7), 847–856 (2012)

    Article  Google Scholar 

  17. Luo, W., Yan, B., Xiong, Y., Wen, G., Xu, H.: Improvement to secondary cool-ing scheme for beam blank continuous casting. Ironmak. Steelmak. 39(2), 125–132 (2012)

    Article  Google Scholar 

  18. Zhao, Y., Chen, D., Long, M., Shen, J., Qin, R.: Two-dimensional heat transfer model for secondary cooling of continuously cast beam blanks. Ironmak. Steelmak. 41(5), 377–386 (2013)

    Article  Google Scholar 

  19. Florio, B.J., Vynnycky, M., Mitchell, S.L., O’Brien, S.B.: On the interactive effects of mould taper and superheat on air gaps in continuous casting. Acta Mech. 228(1), 233–254 (2017)

    Article  MathSciNet  Google Scholar 

  20. Nowak, I., Smolka, J., Nowak, A.J.: An effective 3-D inverse procedure to retrieve cooling conditions in an aluminium alloy continuous casting problem. Appl. Therm. Eng. 30(10), 1140–1151 (2010)

    Article  Google Scholar 

  21. Sadat, M., Gheysari, A.H., Sadat, S.: The effects of casting speed on steel continuous casting process. Heat Mass Transf. 47(12), 1601–1609 (2011)

    Article  Google Scholar 

  22. Kumar, M., Roy, S., Panda, S.S.: Numerical simulation of continuous casting of steel alloy for different cooling ambiences and casting speeds using immersed boundary method. Proc. Inst. Mech. Eng. B J. Eng. Manuf. 231(8), 1363–1378 (2017)

    Article  Google Scholar 

  23. Ha, J.S., Cho, J.R., Lee, B.Y., Ha, M.Y.: Numerical analysis of secondary cooling and bulging in the continuous casting of slabs. J. Mater. Process. Technol. 113(1), 257–261 (2001)

    Article  Google Scholar 

  24. Peng, X., Zhou, J., Qin, Y.: Improvement of the temperature distribution in continuous casting moulds through the rearrangement of the cooling water slots. J. Mater. Process. Technol. 167(2), 508–514 (2005)

    Article  Google Scholar 

  25. Zhang, J., Chen, D.F., Zhang, C.Q., Wang, S.G., Hwang, W.S., Han, M.R.: Effects of an even secondary cooling mode on the temperature and stress fields of round billet continuous casting steel. J. Mater. Process. Technol. 222, 315–326 (2015)

    Article  Google Scholar 

  26. Nayroles, B., Touzot, G., Villon, P.: Generalizing the finite element method: diffuse approximation and diffuse elements. Comput. Mech. 10(5), 307–318 (1992)

    Article  MathSciNet  Google Scholar 

  27. Belytschko, T., Lu, Y.Y., Gu, L.: Element-free Galerkin methods. Int. J. Numer. Methods Eng. 37(2), 229–256 (1994)

    Article  MathSciNet  Google Scholar 

  28. Liu, W.K., Jun, S., Zhang, Y.F.: Reproducing kernel particle methods. Int. J. Numer. Methods Fluids. 20(8–9), 1081–1106 (1995)

    Article  MathSciNet  Google Scholar 

  29. Duarte, C.A., Oden, J.T.: Hp-cloud—a meshless method to solve boundary-value problems. Comput. Methods Appl. Mech. Eng. 139, 237–262 (1996)

    Article  Google Scholar 

  30. Babuska, I., Melenk, J.: The partition of unity method. Int. J. Numer. Methods Eng. 40, 727–758 (1997)

    Article  MathSciNet  Google Scholar 

  31. Sukumar, N., Moran, B., Belytschko, T.: The natural element method in solid mechanics. Int. J. Numer. Methods Eng. 43, 839–887 (1998)

    Article  MathSciNet  Google Scholar 

  32. Atluri, S.N., Zhu, T.: A new meshless local Petrov–Galerkin (MLPG) approach in computational mechanics. Comput. Mech. 22, 117–127 (1998)

    Article  MathSciNet  Google Scholar 

  33. Atluri, S.N., Shen, S.: The Meshless Local Petrov–Galerkin (MLPG) Method. Tech Science Press, Henderson (2002)

    MATH  Google Scholar 

  34. Lin, H., Atluri, S.N.: Meshless local Petrov–Galerkin (MLPG) method for convection–diffusion problems. Comput. Model. Eng. Sci. 1, 45–60 (2000)

    MathSciNet  Google Scholar 

  35. Atluri, S.N., Zhu, T.: The meshless local Petrov–Galerkin (MLPG) approach for solving problems in elasto-statics. Comput. Mech. 25, 169–179 (2000)

    Article  Google Scholar 

  36. Sladek, J., Sladek, V., Atluri, S.N.: A pure contour formulation for the meshless local boundary integral equation method in thermoelasticity. Comput. Model. Eng. Sci. 2, 423–433 (2001)

    MathSciNet  MATH  Google Scholar 

  37. Ching, H.K., Batra, R.C.: Determination of crack tip fields in linear elastostatics by the meshless local Petrov–Galerkin (MLPG) method. Comput. Model. Eng. Sci. 2, 273–290 (2001)

    Google Scholar 

  38. Xiong, Y., Long, S., Liu, K., Li, G.: A meshless local Petrov–Galerkin method for elasto-plastic problems. In: Liu, G., Tan, V., Han, X. (eds.) Computational Methods, pp. 1475–1477. Springer, Dordrecht (2006)

    Google Scholar 

  39. Koohkan, H., Baradaran, G.H., Vaghefi, R.: A completely meshless analysis of cracks in isotropic functionally graded materials. Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci. 224, 581–590 (2010)

    Article  Google Scholar 

  40. Rad, M.H., Shahabian, F., Hosseini, S.M.: A meshless local Petrov–Galerkin method for nonlinear dynamic analyses of hyper-elastic FG thick hollow cylinder with Rayleigh damping. Acta Mech. 226(5), 1497–513 (2015)

    Article  MathSciNet  Google Scholar 

  41. Mirzaei, D., Hasanpour, K.: Direct meshless local Petrov–Galerkin method for elastodynamic analysis. Acta Mech. 227(3), 619–632 (2016)

    Article  MathSciNet  Google Scholar 

  42. Kazemi, H., Shahabian, F., Hosseini, S.M.: Shock-induced stochastic dynamic analysis of cylinders made of saturated porous materials using MLPG method: considering uncertainty in mechanical properties. Acta Mech. 228(11), 3961–3975 (2017)

    Article  MathSciNet  Google Scholar 

  43. Vaghefi, R., Hematiyan, M.R., Nayebi, A., Khosravifard, A.: A parametric study of the MLPG method for thermo-mechanical solidification analysis. Eng. Anal. Bound. Elem. 89, 10–24 (2018)

    Article  MathSciNet  Google Scholar 

  44. Li, Q., Shen, S., Han, Z.D., Atluri, S.N.: Application of meshless local Petrov–Galerkin (MLPG) to problems with singularities, and material discontinuities, in 3-D elasticity. Comput. Model. Eng. Sci. 4, 571–586 (2003)

    MathSciNet  MATH  Google Scholar 

  45. Han, Z.D., Atluri, S.N.: Truly meshless local Petrov–Galerkin (MLPG) solutions of traction & displacement BIEs. Comput. Model. Eng. Sci. 4, 665–78 (2003)

    MATH  Google Scholar 

  46. Han, Z.D., Atluri, S.N.: A meshless local Petrov–Galerkin (MLPG) approach for 3-dimensional elasto-dynamics. CMC-Comput. Mater. Con. 1, 129–140 (2004)

    MATH  Google Scholar 

  47. Han, Z.D., Atluri, S.N.: Meshless local Petrov–Galerkin (MLPG) approaches for solving 3D problems in elasto-statics. Comput. Model. Eng. Sci. 6, 169–188 (2004)

    MathSciNet  MATH  Google Scholar 

  48. Sladek, J., Sladek, V., Solek, P.: Elastic analysis in 3D anisotropic functionally graded solids by the MLPG. Comput. Model. Eng. Sci. 43, 223 (2009)

    MathSciNet  MATH  Google Scholar 

  49. Vaghefi, R., Baradaran, G.H., Koohkan, H.: Three-dimensional static analysis of rectangular thick plates by using the meshless local Petrov–Galerkin method. Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci. 223, 1983–1996 (2009)

    Article  Google Scholar 

  50. Vaghefi, R., Baradaran, G.H., Koohkan, H.: Three-dimensional static analysis of thick functionally graded plates by using meshless local Petrov–Galerkin (MLPG) method. Eng. Anal. Bound. Elem. 34, 564–573 (2010)

    Article  MathSciNet  Google Scholar 

  51. Moghaddam, M.R., Baradaran, G.H.: Three-dimensional free vibrations analysis of functionally graded rectangular plates by the meshless local Petrov–Galerkin (MLPG) method. Appl. Math. Comput. 304, 153–63 (2017)

    MathSciNet  Google Scholar 

  52. Zhang, L., Shen, H.F., Rong, Y.M., Huang, T.Y.: Numerical simulation on solidification and thermal stress of continuous casting billet in mold based on meshless methods. Mater. Sci. Eng. A 466, 71–78 (2007)

    Article  Google Scholar 

  53. Vaghefi, R., Nayebi, A., Hematiyan, M.R., Khosravifard, A.: Investigating the effects of mushy zone thickness on residual stresses in alloy solidification. Meccanica 53(4–5), 905–922 (2018)

    Article  Google Scholar 

  54. Beckett, G., Mackenzie, J.A., Robertson, M.L.: A moving mesh finite element method for the solution of two-dimensional Stefan problems. J. Comput. Phys. 168(2), 500–18 (2001)

    Article  MathSciNet  Google Scholar 

  55. Rebow, M., Browne, D.J., Fautrelle, Y.: Combined analytical and numerical front tracking approach to modeling directional solidification of a TiAl-based intermetallic alloy for design of microgravity experiments. In: Roósz, A., Mertinger, V., Barkóczy, P., Hoó, C. (eds.) Materials Science Forum, pp. 243–248. Trans Tech Publications, Zürich (2010)

    Google Scholar 

  56. Voller, V.R., Swaminathan, C.R., Thomas, B.G.: Fixed grid techniques for phase change problems: a review. Int. J. Numer. Methods Eng. 30, 875–898 (1990)

    Article  Google Scholar 

  57. Welch, S.W., Wilson, J.: A volume of fluid based method for fluid flows with phase change. J. Comput. Phys. 160(2), 662–82 (2000)

    Article  Google Scholar 

  58. Nedjar, B.: An enthalpy-based finite element method for nonlinear heat problems involving phase change. Comput. Struct. 80, 9–21 (2002)

    Article  Google Scholar 

  59. Lewis, R.W., Nithiarasu, P., Seetharamu, K.N.: Fundamentals of the Finite Element Method for Heat and Fluid Flow. Wiley, New York (2004)

    Book  Google Scholar 

  60. Hsu, T.R.: The Finite Element Methods in Thermomechanics. Allen & Unwin, Massachusetts (1986)

    Book  Google Scholar 

  61. Zhu, H.: Coupled thermo-mechanical finite-element model with application to initial solidification. Doctoral dissertation, Ph.D. thesis, The University of Illinois at Urbana-Champaign (1996)

  62. Storkman, W.R., Thomas, B.G.: Heat flow and stress models of continuous casting to predict slab shape. In: Modeling of Casting and Welding Processes, Palm Coast, FL. TMS/AIME (1988)

  63. Moitra, A., Thomas, B.G., Storkman, W.R.: Thermo-mechanical model of steel shell behavior in the continuous casting mold. In: EPD Congress (eds) TMS Annual Meeting, pp. 547–577. San Diego, CA, TMS/AIME, Warrendale, PA (1992)

  64. Atluri, S.N., Shen, S.: The meshless local Petrov–Galerkin (MLPG) method: a simple & less-costly alternative to the finite element and boundary element methods. Comput. Model. Eng. Sci. 3, 11–51 (2002)

    MathSciNet  MATH  Google Scholar 

  65. Reddy, J.N.: An Introduction to the Finite Element Method. McGraw-Hill, Singapore (1993)

    Google Scholar 

  66. Vaghefi, R., Hematiyan, M.R., Nayebi, A.: Three-dimensional thermo-elastoplastic analysis of thick functionally graded plates using the meshless local Petrov–Galerkin method. Eng. Anal. Bound. Elem. 71, 34–49 (2016)

    Article  MathSciNet  Google Scholar 

  67. Huespe, A.E., Cardona, A., Fachinotti, V.: Thermomechanical model of a continuous casting process. Comput. Methods Appl. Mech. Eng. 182(3), 439–455 (2000)

    Article  Google Scholar 

  68. Janik, M., Dyja, H., Banaszek, G.: Two-dimensional thermomechanical analysis of continuous casting process. J. Mater. Process Technol. 153–154(1), 578–582 (2004)

    Article  Google Scholar 

  69. Brimacombe, J.K., Sorimachi, K.: Crack formation in the continuous casting of steel. Metall. Mater. Trans. B. 8(2), 489–505 (1977)

    Article  Google Scholar 

  70. Sengupta, J., Thomas, B.G., Wells, M.A.: Understanding the role water-cooling plays during continuous casting of steel and aluminum alloys. In: Conference Proceedings of M&ST, pp. 179–193 (2004)

  71. Cheung, N., Santos, C.A., Spim, J.A., Garcia, A.: Application of a heuristic search technique for the improvement of spray zones cooling conditions in continuously cast steel billets. Appl. Math. Model. 30(1), 104–15 (2006)

    Article  Google Scholar 

  72. Manesh, A.A.: Thermo-elastic stress analysis to predict design parameters of continuous casting. J. Mater. Sci. 27(15), 4097–106 (1992)

    Article  Google Scholar 

  73. Flemings, M.C.: Solidification Processing. McGraw Hill, New York (1974)

    Google Scholar 

  74. Donachie, M.J., Donachie, S.J.: Superalloys: A Technical Guide. ASM International, Russell Township (2002)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to R. Vaghefi.

Ethics declarations

Conflict of interest

The authors declare that there is no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Vaghefi, R., Nayebi, A. & Hematiyan, M.R. Investigating the effects of cooling rate and casting speed on continuous casting process using a 3D thermo-mechanical meshless approach. Acta Mech 229, 4375–4392 (2018). https://doi.org/10.1007/s00707-018-2240-1

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-018-2240-1

Navigation