Skip to main content
SpringerLink
Log in

Hot Tearing Modeling: A Microstructural Approach Applied to Steel Solidification

  • Published:
Metallurgical and Materials Transactions B Aims and scope Submit manuscript

Abstract

Hot tearing during solidification processes has been deeply investigated in past and recent years through testing, modeling, and development of a number of macroscopic hot tearing criteria. The objective is predicting the crack occurrence during industrial solidification processes, which, in the steel production, are mainly ingot and continuous casting. The present work is inspired by the criterion proposed in the work of Bellet et al.[1] called CBC criterion, from which the methodological approach and experimental data used for calibration, related to nine carbon steels, have been derived. The proposed hot tearing criterion adopts as parameters: primary and secondary arm spacing, the mechanical resistance near the solidus temperature, the solidification parameters G (gradient) and v (dendrite tip velocity), the brittle range extension in the dendritic front and the temperature of formation of manganese sulfides. The new formulation is an attempt to substitute to brittle temperature range and steel content, appearing in the CBC criterion, the dendritic structure characteristics, in the aim of: (a) moving toward a generalized expression of the cracking index applicable to different steel classes; (b) introducing the dependence of the crack susceptibility on the cooling conditions. The agreement of the new hot tearing index values with the experimental ones is of the same kind as that of the CBC criterion, indicating that the parameters and the dependences adopted in the new criterion make a sense. Further study and experimental work are needed to assess the influence of the microstructure morphology on the hot cracking sensitivity and to check the suitability of the approach to a wider range of steel compositions.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Abbreviations

k 0 :

solid/liquid partition coefficient

g s :

solid fraction

g scoal :

solid fraction at coalescence point

m, n :

exponents

m l :

liquidus slope

r :

cooling rate at the dendrite tip

v :

solidification rate

A, C, f 1, f 2 :

fitting factors

C 0 :

nominal mass fraction of solute

C eut :

eutectic mass fraction of solute

C l :

liquid mass fraction of solute at the solid/liquid interface

D l :

solute diffusivity in the liquid

G :

temperature gradient at the dendrite tip

G br :

temperature gradient in the brittle zone

PDAS:

primary dendrite arm spacing

R, r 0 :

radius (mm)

R tip :

dendrite tip radius

SDAS, λ 2 :

secondary dendrite arm spacing

T (K):

absolute temperature

T liq :

liquidus temperature

T m :

melting temperature of pure iron

T MnS :

temperature of Manganese sulfides formation

γ sl :

solid–liquid interface energy

γ gb :

grain boundary energy

ε cr :

critical strain

ε R :

strain to rupture

\( \dot{\varepsilon } \) :

strain rate

φ :

fitting factor

σ 1 pct :

stress at 1 pct strain

σ δ1 pct :

stress at 1 pct strain of delta-ferrite

σ γ1 pct :

stress at 1 pct strain of austenite

Γsl :

Gibbs–Thomson coefficient

ΔT :

solidification interval

ΔT br :

brittle temperature interval

References

  1. M. Bellet, O. Cerri, M. Bobadilla, Y. Chastel: Metall. Mater. Trans. A, 2009, vol. 40A, pp. 2705-2717.

    Article  Google Scholar 

  2. J. Campbell: “Complete Casting Handbook”, Butterworth-Heinemann, Oxford, 2011.

    Google Scholar 

  3. J. Dantzig, M. Rappaz: “Solidification”, EPFL Press, Lausanne, 2010.

    Google Scholar 

  4. R. A. Rosenberg, M. C. Flemings, H. F. Taylor: Trans. AFS, 1960, vol. 68, pp. 518-528.

    Google Scholar 

  5. O. Cerri: Doctoral Thesis, Mines-Paris Tech, Sophia Antipolis, France, 2011, http://pastel.archives-ouvertes.fr.

  6. O. Cerri, Y. Chastel, M. Bellet: ASME J. Eng. Mater. Technol., 2008, vol. 130, pp. 1-7.

    Google Scholar 

  7. M. Bobadilla, B. Chamont, C. Gatellier, and J.M. Jolivet: Commission des Communautés Européennes, Convention n°7210-CA/316, RE 88/023, 1988.

  8. D. Senk, S. Stratemeier, B. Boettger, K. Goelher, I. Steinbach, Advanced Engineering Materials, 2010, vol. 12, no. 3, pp. 94-100.

    Article  Google Scholar 

  9. Y. M. Won, T-J. Yeo, D. J. Seol, K. H. Oh, Metall. Mater. Trans. B, 2000, vol. 31B, pp. 779-794.

    Article  Google Scholar 

  10. J. Miyazaki, T. Mori, and K. Narita: Second Process Technology Conference, Chicago, 1981, vol. 2, pp. 35–43.

  11. H. Fujii, T. Ohashi, and K. Hiromoto: Tetsu-to-Hagane´, 1976, vol. vol. 206, pp. 81-89.

    Google Scholar 

  12. K. Narita, T. Mori, K. Ayata, and J. Miyajaki: Tetsu-to-Hagane, 1978, vol. 64, p. S152.

    Google Scholar 

  13. B. T. Matsumiya, M. Ito, H. Kajioka, S. Yamaguchi, Y. Nakamura, Transactions ISIJ, 1986, vol. 26, pp. 540-546.

    Article  Google Scholar 

  14. T.W. Clyne and G.J. Davies: “Solidification and Casting of Metals”, TMS, Warrendale, PA, 1977.

    Google Scholar 

  15. M. Rappaz, J.M. Drezet, and M. Gremaud: Metall. Mater. Trans. A, 1999, vol. 30A, pp. 449–56.

    Article  Google Scholar 

  16. C. Monroe, C. Beckermann, Materials Science and Engineering A, 2005, 413-414, pp. 30-36.

    Article  Google Scholar 

  17. M. M’Hamdi, A. Mo, C. L. Martin, Metall. Mater. Trans. A, 2002, vol. 33, pp. 2081–2093.

    Article  Google Scholar 

  18. V. Mathier, J-M. Drezet, M. Rappaz, Modelling and Simulation In Materials Science and Engineering, 2007, 15, pp. 121–134.

    Article  Google Scholar 

  19. O. Ludwig, J-M. Drezet, C.L. Martin, M. Suery, Metall. Mater. Trans. A, 2005, vol. 36, pp. 1525–1535.

    Article  Google Scholar 

  20. S. Koric, B.G. Thomas, Journal of Materials Processing Technology, 2008, 197, pp. 408–418.

    Article  Google Scholar 

  21. P.F. Kozlowski, B.G. Thomas, J.A. Azzi, H. Wang, Metall. Trans. A, vol. 23, 1992, pp. 903-918.

    Article  Google Scholar 

  22. H. Zhu: Ph.D. Thesis, University of Illinois, 1993.

  23. P.J. Wray, Metallurgical and Materials Transactions A, 1976, vol. 7, pp. 1621-1627.

    Article  Google Scholar 

  24. T. Suzuki, K.H. Tacke, K Wunnenberg and K. Schwerdtfeger, Ironmaking and Steelmaking, 1988, vol. 15(2), pp. 90-100.

    Google Scholar 

  25. T.Z. Kattamis and M.C. Flemings, Trans. AIME, 1965, 233, pp. 992-999.

    Google Scholar 

  26. M. Bobadilla, J. Lacaze, and G. Lesoult: Scand. J. Metall., 1996, vol. 25, pp. 2-10.

    Google Scholar 

  27. M. Rappaz, S.A. David, J.M. Vitek, and L.A. Boatner: Metall. Trans. A, 1990, vol. 21A, pp. 1767-82.

    Article  Google Scholar 

  28. J. Miettinen, Metall. and Mater. Trans. B, 2000, vol. 31B, pp. 365-379.

    Article  Google Scholar 

  29. J. Miettinen, S. Louhenkilpi, and J. Laine: IDS User manual, version 1.3.1.

  30. J. Miettinen: Metall. Trans. A, 1992, Vol 23A, pp. 1155.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centro Sviluppo Materiali S.p.A, Rome, Italy

    Maria Rita Ridolfi (Senior Scientist)

Authors
  1. Maria Rita Ridolfi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Maria Rita Ridolfi.

Additional information

Manuscript submitted May 10, 2013.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ridolfi, M.R. Hot Tearing Modeling: A Microstructural Approach Applied to Steel Solidification. Metall Mater Trans B 45, 1425–1438 (2014). https://doi.org/10.1007/s11663-014-0068-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11663-014-0068-1

Keywords

Search

Navigation