Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Mathematical modeling of the hot strip rolling of microalloyed Nb, multiply-alloyed Cr-Mo, and plain C-Mn steels

  • 926 Accesses

  • 123 Citations

Abstract

Industrial mill logs from seven different hot strip mills (HSMs) were analyzed in order to calculate the mean flow stresses (MFSs) developed in each stand. The schedules were typical of the processing of microalloyed Nb, multiply-alloyed Cr-Mo, and plain C-Mn steels. The calculations, based on the Sims analysis, take into account work roll flattening, redundant strain, and the forward slip ratio. The measured stresses are then compared to the predictions of a model based on an improved Misaka MFS equation, in which solute effects, strain accumulation, and the kinetics of static recrystallization (SRX) and metadynamic recrystallization (MDRX) are fully accounted for. Good agreement between the measured and predicted MFSs is obtained over the whole range of rolling temperatures. The evolution of grain size and the fractional softening are also predicted by the model during all stages of strip rolling. Special attention was paid to the Nb steels, in which the occurrence of Nb(C, N) precipitation strongly influences the rolling behavior, preventing softening between passes. The present study leads to the conclusion that Mn addition retards the strain-induced precipitation of Nb; by contrast, Si addition has an accelerating effect. The critical strain for the onset of dynamic recrystallization (DRX) in Nb steels is derived, and it is shown that the critical strain/peak strain ratio decreases with increasing Nb content; furthermore, Mn and Si have marginal but opposite effects. It is demonstrated that DRX followed by MDRX occurs under most conditions of hot strip rolling; during the initial passes, it is due to high strains, low strain rates, and high temperatures, and, in the final passes, it is a consequence of strain accumulation.

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

Abbreviations

ε :

true strain

ε :

true strain rate (1/s)

ε a :

accumulated true strain

ε c :

critical strain for the initiation of dynamic recrystallization

ε f :

retained strain present in the material after leaving the finishing train

Z:

Zener-Hollomon parameter = ε · exp(Q def / RT)(1/s)

ε p :

peak strain

T :

absolute temperature (K)

Q def :

activation energy for deformation (J/mol)

X :

fractional softening

t 0.5 :

time for 50 pct softening (s)

R:

gas constant = 8.31 (J/mol·K)

d 0 :

initial grain size (µm)

T nr :

interpass recrystallization stop temperature (K)

t ps :

precipitation start time

T RH :

absolute reheat temperature (K)

T pass :

absolute pass temperature (K)

T :

cooling rate (°C/s)

H :

strip thickness before passes

h :

strip thickness after all passes

σ M :

mean flow stress

X dyn :

fractional softening attributable to dynamic recrystallization

σ ss :

steady-state stress

K :

parameter that converts flow stress to mean flow stress

K s :

supersaturation ratio

t ip :

interpass time

Nbeff :

effective Nb concentration

d :

grain size

d° α :

ferrite grain size when the austenite is unstrained

d γ :

austenite grain size

d α :

ferrite grain size after transformation of deformed austenite

References

  1. 1.

    F. Boratto, R. Barbosa, S. Yue, and J.J. Jonas: in Thermec 88, I Tamura, ed., ISIJ, Tokyo, 1988, pp. 383–89.

  2. 2.

    D.Q. Bai, S. Yue, and J.J. Jonas: Proc. Int. Conf. on Modeling of Metal Rolling Processes, The Institute of Materials, London, 1993, pp. 180–92.

  3. 3.

    D.Q. Bai, S. Yue, W.P. Sun, and J.J. Jonas: Metall. Trans. A, 1993, vol. 24A, pp. 2151–59.

  4. 4.

    T.M. Maccagno, J.J. Jonas, S. Yue, B.J. McCrady, R. Slobodian, and D. Deeks: Iron Steel Inst. Jpn. Int., 1994, vol. 34, pp. 917–22.

  5. 5.

    Microalloying ’75, Int. Symp. on HSLA Steels, Union Carbide Corp., New York, NY, USA, 1977.

  6. 6.

    M. Cohen and W. Owen: Microalloying ’75, Int. Symp. on HSLA Steels, Union Carbide Corp., New York, NY, USA, 1977, pp. 2–8.

  7. 7.

    F.B. Pickering: Microalloying ’75, Int. Symp. on HSLA Steels, Union Carbide Corp., New York, NY, USA, 1977, pp. 9–31.

  8. 8.

    T. Gladman, D. Dulieu, and I.D. McIvor: Microalloying ’75, Int. Symp. on HSLA Steels, Union Carbide Corp., New York, NY, USA, 1977, pp. 32–58.

  9. 9.

    R.D. Stout: Microalloying ’75, Int. Symp. on HSLA Steels, Union Carbridge Corp., New York, NY, USA, 1977, pp. 488–97.

  10. 10.

    P.H.M. Hart, R.E. Dolby, N. Bailey, and D.J. Widgery: Microalloying ’75, Int. Symp. on HSLA Steels, Union Carbide Corp., New York, NY, USA, 1977, pp. 540–51.

  11. 11.

    T.M. Maccagno, J.J. Jonas, and P.D. Hodgson: Iron Steel Inst. Jpn. Int., 1996, vol. 36, pp. 720–28.

  12. 12.

    I.P. Kemp, P.D. Hodgson, and R.E. Gloss: Proc. Int. Conf. on Modeling of Metal Rolling Processes, The Institute of Materials, London, 1993, pp. 149–56.

  13. 13.

    T.M. Maccagno and J.J. Jonas: Iron Steel Inst. Jpn. Int., 1994, vol. 34, pp. 607–14.

  14. 14.

    P.D. Hodgson: in Thermec ’97, T. Chandra and T. Sakai, eds., TMS, Warrendale, PA, 1997, pp. 121–31.

  15. 15.

    P.D. Hodgson: Ph.D. Thesis, University of Queensland, Queensland, Australia, 1993, p. 3.

  16. 16.

    L.N. Pussegoda, P.D. Hodgson, and J.J. Jonas: Mater. Sci. Technol., 1992, vol. 8, pp. 63–71.

  17. 17.

    L.N. Pussegoda, S. Yue, and J.J. Jonas: Metall. Trans. A, 1990, vol. 21A, pp. 153–64.

  18. 18.

    F.H. Samuel, S. Yue, J.J. Jonas, and B.A. Zbinden: Iron Steel Inst. Jpn. Int., 1989, vol. 29, pp. 878–86.

  19. 19.

    E.C. Sarmento and J.F. Evans: Proc. Int. Conf. on Processing, Microstructure and Properties of Microalloyed and Other High Strength Low Alloy Steels, A.J. DeArdo, ed., ISS-AIME, Warrendale, PA, 1992, pp. 105–12.

  20. 20.

    J.J. Jonas: in Recrystallization ’90, T. Chandra, ed., TMS-AIME, Warrendale, PA, 1990, pp. 27–36.

  21. 21.

    A. Schmitz, J. Neutjens, J.C. Herman, and V. Leroy: 40th MWSP Conf., ISS, Warrendale, PA, 1998, pp. 295–309.

  22. 22.

    J. Neutjens, P. Harlet, T. Bakolas, and P. Cantinieaux: 40th MWSP Conf., ISS, Warrendale, PA, 1998, pp. 311–21.

  23. 23.

    R.B. Sims: Proc. Inst. Mech. Eng., 1954, vol. 168, pp. 191–200.

  24. 24.

    J.H. Hitchcock: Roll Neck Bearings, ASME, New York, NY, 1935, Appendix I, p. 33.

  25. 25.

    F. Siciliano, Jr., K. Minami, T.M. Maccagno, and J.J. Jonas: Iron Steel Inst. Jpn. Int., 1996, vol. 36, pp. 1500–06.

  26. 26.

    Y. Misaka and T. Yoshimoto: J. Jpn. Soc. Technol. Plast., 1967–68, vol. 8, pp. 414–22.

  27. 27.

    F. Siciliano, Jr.: Ph.D. Thesis, McGill University, Montreal, 1999, pp. 53–68.

  28. 28.

    K. Minami, F. Siciliano, Jr., T.M. Maccagno, and J.J. Jonas: Iron Steel Inst. Jpn. Int., 1996, vol. 36, pp. 1507–15.

  29. 29.

    T. Senuma and H. Yada: 7th Risø Int. Symp., N. Hansen, D.J. Jensen, T. Leffers and B. Halph, Risø, Roskilde, Denmark, 1986, pp. 547–52.

  30. 30.

    H. Yada: Proc. Int. Symp. on Accelerated Cooling of Rolled Steel, G.E. Ruddle and A.F. Crawley, eds., Pergamon Press, Elmsford, NY, 1988, pp. 105–18.

  31. 31.

    T. Senuma, H. Yada, Y. Matsumura, and T. Futamura: Tetsu-to-Hagane, 1984, vol. 70, pp. 322–29 (in Japanese).

  32. 32.

    A. Kirihata, F. Siciliano, Jr., T.M. Maccagno, and J.J. Jonas: Iron Steel Inst. Jpn. Int., 1998, vol. 38, pp. 187–95.

  33. 33.

    P.D. Hodgson and R.K. Gibbs: Iron Steel Inst. Jpn. Int., 1992, vol. 32, pp. 1329–38.

  34. 34.

    C. Roucoules, S. Yue, and J.J. Jonas: Proc. Int. Conf. on Modeling of Metal Rolling Processes, The Institute of Materials, London, 1993, pp. 165–79.

  35. 35.

    C. Roucoules: Ph.D. Thesis, McGill University, Montreal, 1992.

  36. 36.

    P.D. Hodgson, L.O. Hazeldon, D.L. Matthews, and R.E. Gloss: in Microalloying ’95, M. Korchynsky, A.J. DeArdo, P. Repas and G. Tither, ISS-AIME, Warrendale, PA, 1995, pp. 341–53.

  37. 37.

    R.K. Gibbs, P.D. Hodgson, and B.A. Parker: in Recrystallization ’90, T. Chandra, ed., TMS-AIME, Warrendale, PA, 1996, pp. 585–90.

  38. 38.

    J.J. Jonas and C.M. Sellars: in Future Developments of Metals and Ceramics, J.A. Charles, G.W. Greenwood and G.C. Smith, Institute of Materials, London, 1992, pp. 148–77.

  39. 39.

    D.C. Collinson, P.D. Hodgson, and C.H.J. Davies: Thermec ’97, T. Chandra and T. Sakai, eds., TMS, Warrendale, PA, 1997, pp. 483–89.

  40. 40.

    C. Roucoules, S. Yue, and J.J. Jonas: Metall. Mater. Trans. A, 1995, vol. 26A, pp. 181–90.

  41. 41.

    P.D. Hodgson: Mater. Sci. Technol., 1996, vol. 12, p. 788.

  42. 42.

    C.M. Sellars: Mater. Sci. Technol., 1990, vol. 6, pp. 1072–81.

  43. 43.

    J.H. Beynon and C.M. Sellars: Iron Steel Inst. Jpn. Int., 1992, vol. 32, pp. 359–67.

  44. 44.

    P.D. Hodgson, J.J. Jonas, and S. Yue: Mater. Sci. Forum, 1992, vols. 94–96, pp. 715–22.

  45. 45.

    M. Militzer, W.P. Sun, and J.J. Jonas: Acta Metall. Mater., 1994, vol. 42, pp. 133–41.

  46. 46.

    C.M. Sellars: in Hot Working and Forming Processes, C.M. Sellars and G. Davies, eds., TMS, London, 1980, pp. 3–15.

  47. 47.

    F. Siciliano, Jr. and J.J. Jonas: in Microalloying in Steels, Microalloying in Steels: New Trends, for the 21st Century, CEIT, San Sebastian, Spain, J.M. Rodriguez-Ibabe, I. Gutierrez and B. Lopez, Trans-Tech Publications, Aedermannsdorf, 1998, p. 377; Mater. Sci. Forum, 1998, vols. 284–286, pp. 377–84.

  48. 48.

    S. Kurokawa, J.E. Ruzzante, A.M. Hey, and F. Dyment: Met. Sci., 1983, vol. 17, pp. 433–38.

  49. 49.

    B. Dutta and C.M. Sellars: Mater. Sci. Technol., 1987, vol. 3, pp. 197–206.

  50. 50.

    K.J. Irvine, F.B. Pickering, and T. Gladman: J. Iron Steel Inst., 1967, vol. 205, pp. 161–82.

  51. 51.

    M.G. Akben, I. Weiss, and J.J. Jonas: Acta Metall., 1981, vol. 29, pp. 111–21.

  52. 52.

    F. Siciliano, Jr., T.M. Maccagno, B.D. Nelson, and J.J. Jonas: Thermec ’97, T. Chandra and T. Sakai, eds., TMS, Warrendale, PA, 1997, pp. 347–53.

  53. 53.

    L. Meyer: Z. Metallkd., 1966, vol. 58, p. 334.

  54. 54.

    T.H. Johansen, N. Christensen and B. Augland: Trans. AIME, 1967, vol. 239, pp. 1651–54.

  55. 55.

    F. de Kazinsky, A. Axnas and P. Pachleitner: Jernkont. Ann., 1963, vol. 147, p. 408.

  56. 56.

    D.Q. Bai: Ph.D. Thesis, McGill University, Montreal, 1995, pp. 28–32.

  57. 57.

    E. Valdez and C.M. Sellars: Mater. Sci. Technol., 1991, vol. 7, pp. 622–30.

  58. 58.

    E. Scheil: Arch. Eisenhuttenwes., 1935, vol. 12, p. 565 (cited in Ref. 56).

  59. 59.

    F. Siciliano, Jr. and J.J. Jonas: ABM (Associação Brasileira de Metalurgia e Materiais), 1997, vol. 53, pp. 95–97 (in Portuguese).

  60. 60.

    F. Siciliano, Jr. and J.J. Jonas: The 7th Int. Conf. on Steel Rolling, Tokyo, Nov. 1998, pp. 534–39.

  61. 61.

    M.G. Akben and J.J. Jonas: Proc. Int. Conf. on Technology and Applications of HSLA Steels, ASM, Philadelphia, PA, 1983, pp. 149–61.

  62. 62.

    J.A. Biglou, B.D. Nelson, D.R. Hall, and J.G. Lenard: 37th MWSP Conf., ISS, Warrendale, PA, 1996, pp. 661–68.

  63. 63.

    C.M. Sellars and J.H. Beynon: Proc. Conf. on HSLA Steels, D.P. Dunne and T. Chandra, eds., South Coast Printers, Port Kembla, Australia, 1985, pp. 142–50.

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Siciliano, F., Jonas, J.J. Mathematical modeling of the hot strip rolling of microalloyed Nb, multiply-alloyed Cr-Mo, and plain C-Mn steels. Metall and Mat Trans A 31, 511–530 (2000). https://doi.org/10.1007/s11661-000-0287-8

Download citation

Keywords

  • Ferrite
  • Austenite
  • Material Transaction
  • Critical Strain
  • Strain Accumulation