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Modeling the formation of longitudinal facial cracks during continuous casting of hypoperitectic steel

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Abstract

The mechanism of formation of longitudinal facial cracks during continuous casting of peritectic steels has been studied using a process modeling approach. First, the delta-to-gamma transformation was modeled, assuming carbon diffusion control. The problem of the moving boundary (delta/gamma interface) was solved by employing a one-dimensional finite-difference method. Second, a heat-transfer model for continuous casting of steel was developed and combined with the phase transformation model. Three heat-flux conditions (i.e., low, medium, and high) were obtained from literature data and assumed as the thermal boundary condition. The delta-to-gamma transformation rate was evaluated as a function of the heat-flux conditions. Finally, the results of the coupled model were adopted to calculate the stresses in the solid shell applying the commercial finite-element program, ABAQUS. The results showed that the transformation from delta to gamma is comparatively rapid due to the high diffusivity of carbon in this temperature range. The variation of the heat flux at the meniscus results in large changes of the transformation rate in the meniscus region. Based on the results of the stress calculations, it was concluded that, in order to generate a longitudinal crack on the solid shell surface, not only the tensile stress caused by rapid transformation (i.e., rapid cooling) but also the presence of hot spots is required. A threshold value of approximately 16 pct was obtained for the retardation of shell growth required to generate longitudinal cracks.

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Abbreviations

C 0 :

initial carbon concentration in the steel, wt pct

C γ :

carbon concentration in the gamma phase, wt pct

C γ|δγ :

carbon concentration of the gamma phase at the delta-gamma interface, wt pct

C γ (T):

equilibrium carbon concentration of gamma phase at temperature T, wt pct

C δ (T):

equilibrium carbon concentration of delta phase at temperature T, wt pct

C n :

concentration in node n of Murray-Landis grid

C pa :

apparent specific heat capacity, J g−1 °C−1

C p :

heat capacity of steel, J g−1 °C−1

C eff p :

effective heat capacity (which takes into account of the latent heat), J g−1 °C−1

CR :

cooling rate, °C s−1

D γ :

diffusion coefficient of carbon in the gamma phase, cm2 s−1

E :

Young’s modulus, GPa

ΔH :

latent heat of solidification of steel, J g−1

k :

thermal conductivity of steel, W m−1 °C−1

L :

length of the steel at temperature T, mm

L 0 :

length of the steel at solidus temperature, mm

q((t)):

heat flux, kW m−2

R:

gas constant, J K−1 mol−1

R γ :

volume fraction of gamma phase, dimensionless

R 0 γ :

initial volume fraction of the gamma phase, dimensionless

S :

solid shell thickness for normal position, mm

S HS :

solid shell thickness for hot spot, mm

t :

time, s

t τ :

transit time, s

T :

temperature, °C

T 0 :

temperature corresponding to a strain-free state, °C

T abs :

absolute temperature, K

T avg :

average temperature of the solid shell, °C

T i :

initial temperature of steel, °C

T liq :

liquidus temperature, °C

T p :

peritectic temperature, °C

T sol :

solidus temperature, °C

T surf :

temperature of the shell surface, °C

T*:

fictitious temperature for ABAQUS calculation (derived from Eq. [24]), °C

v i :

displacement of node i in y direction, mm

V :

velocity of the delta-gamma interface toward the delta phase, mm/s

V c :

casting velocity, m/min

V δ :

velocity of the delta-gamma interface due to the carbon diffusion in the delta phase, mm/s

W :

slab width, mm

x :

distance in x-direction, mm

X n :

node position in Murray-Landis grid

X S :

slab thickness, mm

y :

distance in y-direction, mm

z :

distance in z-direction, mm

α :

thermal expansion coefficient, °C−1

ɛ :

total strain, dimensionless

ɛ th :

thermal strain, dimensionless

ɛ tr :

strain due to transformation, dimensionless

λ :

primary dendrite-arm spacing (grain size), μm

ρ :

density of steel, g cm−3

σ max :

maximum tensile stress at solid shell surface, MPa

σ UTS :

UTS, MPa

References

  1. T. Saeki, S. Ooguchi, S. Mizoguchi, T. Yamamoto, H. Misumi, and A. Tsuneoka: Tetsu-to-Hagané, 1982, vol. 68, pp. 1773–81.

    Google Scholar 

  2. K. Nakai, M. Kawasaki, K. Nakajima, T. Sakashita, and Y. Sugitani: Continuous Casting ’85, The Institute of Metals, London, 1982, paper no. 71.

    Google Scholar 

  3. M. Vereecke, W. Vermeirsch, and U. Meers: 4th Int. Conf. Continuous Casting, Verlag Stahleisen mbH, Düsseldorf, 1988, vol. 1, pp. 128–41.

    Google Scholar 

  4. W.R. Irving and A. Perkins: IRSID Conf. on Continuous Casting, Biarritz, 1976.

  5. J.K. Brimacombe and I.V. Samarasekera: Iron Steelmaker, 1994, vol. 21 (11), pp. 29–39.

    CAS  Google Scholar 

  6. Y.K. Chuang, D. Reinisch, and K. Schwerdtfeger: Metall. Trans. A, 1975, vol. 6A, pp. 235–38.

    Google Scholar 

  7. H. Fredriksson and J. Stjerndahl: Met. Sci., 1982, vol. 16, pp. 575–85.

    Article  CAS  Google Scholar 

  8. D. Murray and F. Landis: Trans. ASME J. Heat Transfer, 1959, vol. 81, pp. 106–12

    CAS  Google Scholar 

  9. R.G. Kamat, E.B. Hawbolt, L.C. Brown, and J.K. Brimacombe: Metall. Trans. A, 1992, vol. 23A, pp. 2469–80.

    CAS  Google Scholar 

  10. H. Bester and K.W. Lange: Arch. Eisenhüttenwes., 1972, vol. 43, pp. 207–13.

    CAS  Google Scholar 

  11. Y. Mimura: Master’s Thesis, The University of British Columbia, Vancouver, 1989.

    Google Scholar 

  12. ASM Handbook, vol. 3, Alloy Phase Diagram, ASM INTERNATIONAL, Materials Park, OH, 1992, section 2, p. 110.

  13. H.D. Brody and M.C. Flemings: Trans. TMS-AIME, 1966, vol. 236, pp. 615–24.

    CAS  Google Scholar 

  14. K. Matsuura, Y. Itoh, and T. Narita: Iron Steel Inst. Jpn. Int., 1993, vol. 33, pp. 583–87.

    CAS  Google Scholar 

  15. K. Matsuura, H. Maruyama, Y. Itoh, M. Kudoh, and K. Ishii: Iron Steel Inst. Jpn. Int., 1995, vol. 35, pp. 183–87.

    CAS  Google Scholar 

  16. K. Matsuura, M. Kudoh, and T. Ohmi: Iron Steel Inst. Jpn. Int., 1995, vol. 35, pp. 624–28.

    CAS  Google Scholar 

  17. K. Matsuura, H. Maruyama, M. Kudoh, and Y. Itoh: Iron Steel Inst. Jpn. Int., 1995, vol. 35, pp. 1483–88.

    CAS  Google Scholar 

  18. J.K. Brimacombe: Can. Metall. Q., 1976, vol. 15, pp. 1–13.

    Google Scholar 

  19. I.G. Saucedo, J. Beech, and G.J. Davies: Met. Technol., 1982, vol. 9, pp. 282–91.

    Google Scholar 

  20. L.A. Baptista: Master’s Thesis, The University of British Columbia, Vancouver, 1979.

    Google Scholar 

  21. R. Davies, N. Blake, and P. Campbell: Proc. 4th Int. Conf. Continuous Casting, Verlag Stahleisen mbH, Düsseldorf, 1988, vol. 2, pp. 645–54.

    Google Scholar 

  22. H.L. Gilles: Steelmaking Conf. Proc., ISS-AIME, Warrendale, PA, 1993, vol. 76, pp. 315–29.

    Google Scholar 

  23. M.M. Wolf: Process Technology Conf. Proc., ISS, Warrendale, PA, 1995, vol. 13, pp. 99–117.

    Google Scholar 

  24. S. Hiraki, K. Nakajima, T. Murakami, and T. Kanazawa: Steelmaking Conf. Proc., ISS-AIME, Warrendale, PA, 1994, vol. 77, pp. 397–403.

    Google Scholar 

  25. J. Konishi: Master’s Thesis, The University of British Columbia, Vancouver, 1996.

    Google Scholar 

  26. H. Nakato and I. Muchi: Tetsu-to-Hagané, 1980, vol. 66, pp. 33–42.

    CAS  Google Scholar 

  27. R.B. Mahapatra, J.K. Brimacombe, and I.V. Samarasekera: Metall. Trans. B, 1991, vol. 22B, pp. 875–88.

    CAS  Google Scholar 

  28. S. Kumar, B.N. Walker, I.V. Samarasekera, and J.K. Brimacombe: Process Technology Conf. Proc., ISS, Warrendale, PA, 1995, vol. 13, pp. 119–41.

    Google Scholar 

  29. J. Dubendorff, J. Sardemann, and K. Wünnenberg: Stahl Eisen, 1983, vol. 103, pp. 1327–32.

    Google Scholar 

  30. S. Chandra, J.K. Brimacombe, and I.V. Samarasekera: Ironmaking and Steelmaking, 1993, vol. 20 (2), pp. 104–12.

    CAS  Google Scholar 

  31. H. Vom Ende and G. Vogt: J. Iron Steel Inst., 1972, vol. 210, pp. 889–94.

    Google Scholar 

  32. S.N. Singh and K.E. Blazek: J. Met., 1974, Oct., pp. 17–27.

  33. H. Mizukami, K. Murakami, and Y. Miyashita: Tetsu-to-Hagané, 1977, vol. 63, p. S652.

  34. G. Shin, T. Kajitani, T. Suzuki, and T. Umeda: Tetsu-to-Hagané, 1992, vol. 78, pp. 587–93.

    CAS  Google Scholar 

  35. W.T. Lankford: Metall. Trans., 1973, vol. 3, pp. 1331–57.

    Google Scholar 

  36. B.G. Thomas, J.K. Brimacombe, and I.V. Samarasekera: ISS Trans., 1986, vol. 7, pp. 7–20.

    CAS  Google Scholar 

  37. P.F. Kozlowski, B.G. Thomas, J.A. Azzi, and H. Wang: Metall. Trans. A, 1992, vol. 23A, pp. 903–18.

    CAS  Google Scholar 

  38. S. Tanaka, K. Mizuchi, M. Miyazaki, H. Takeuchi, and Y. Fukuda: CAMP-ISIJ, 1992, vol. 4, p. 1209.

    Google Scholar 

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Author notes

  1. J. Konishi (Graduate Student, Group Manager) & J. K. Brimacombe (Professor, President)

    Present address: The Centre for Metallurgical Process Engineering, The University of British Columbia, V6T 1Z4, Vancouver, BC, Canada

Authors and Affiliations

  1. Steelmaking Division, Yawata Works, Nippon Steel Corporation, 804-8501, Eukuoka, Japan

    J. Konishi (Graduate Student, Group Manager)

  2. The Centre for Metallurgical Process Engineering, The University of British Columbia, V6T 1Z4, Vancouver, BC, Canada

    M. Militzer (Associate Professor and Dofasco Chair in Advanced Steel Processing)

  3. The University of British Columbia, V6T 1Z2, Vancouver, BC, Canada

    I. V. Samarasekera (Vice President of Research)

  4. CEO, The Canada Foundation for Innovation, Ottawa, ON, Canada

    J. K. Brimacombe (Professor, President)

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  1. J. Konishi
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  2. M. Militzer
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  3. I. V. Samarasekera
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  4. J. K. Brimacombe
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Konishi, J., Militzer, M., Samarasekera, I.V. et al. Modeling the formation of longitudinal facial cracks during continuous casting of hypoperitectic steel. Metall Mater Trans B 33, 413–423 (2002). https://doi.org/10.1007/s11663-002-0053-y

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