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Metallurgical and Materials Transactions A

, Volume 50, Issue 3, pp 1323–1332 | Cite as

Modelling of Inclusion Effects on Macrosegregation in Solidifying Steel Ingot with a Multi-phase Approach

  • Duanxing Cai
  • Fengli Ren
  • Honghao Ge
  • Hee-Soo Kim
  • Jun LiEmail author
  • Jianguo Li
Article
  • 164 Downloads

Abstract

A multi-phase dendritic solidification model coupled with Euler–Lagrange framework has been established to characterize the effect of inclusions on macrosegregation in steel ingots. The present model includes many important solidification phenomena such as columnar growth, nucleation, growth of equiaxed and dendritic structure of equiaxed crystals, crystal sedimentation, and melt thermal-solutal convection. A dense discrete phase is employed to simulate the motion of the inclusions and their interaction with fluid flow. Fractal theory is applied to consider the morphology of the inclusion clusters. Based on this model, the effects of the inclusion size and cluster morphology have been investigated for the solidification of a 55-ton industrial Fe-0.33 wt pct C ingot. The results show that inclusions around 15 to 20 μm enhance the macrosegregation significantly, while neither small (i.e. 5 μm) nor large (i.e. 30 μm) inclusions have any obvious influence on the macrosegregation. It’s shown how the compactness of the inclusion cluster plays a dominant role in macrosegregation. The mechanism of how the inclusions affect macrosegregation is also discussed. This study provides valuable information for the control of casting defects caused by inclusions.

Nomenclature

c0

Initial concentration (wt pct)

cref

Reference concentration (wt pct)

Cls, Clc

Species exchange (kg m−3 s−1)

Dl

Diffusion coefficient (m2 s−1)

fl, fs, fenv, fc, fp

Volume fraction (1)

\( \overrightarrow {{g_{l} }} \),\( \overrightarrow {{g_{s} }} \)

Reduced gravity (m s−2)

H*

Volume heat transfer coeff. (W m−3 °C−1)

Δhf

Latent heat (J kg−1)

kl, ks, kc

Thermal conductivity (W m−1 °C−1)

m

Slope of the liquidius in phase diagram (°C)

n

Grain number density (m−3)

Qls, Qlc, Qcs,

Energy transfer (J m−3 s−1)

Senv

Surface area concentration of envelope (m−1)

\( \dot{T} \)

Cooling rate (°C s−1)

\( \overrightarrow {{u_{l} }} \),\( \overrightarrow {{u_{s} }} \),\( \overrightarrow {{u_{p} }} \)

Velocity (m s−1)

vRc

Columnar growth speed in radius direction (m s−1)

vtip

Dendrite tip velocity (m s−1)

\( \varGamma_{\text{env}} \)

Envelope transfer rate (kg m−3 s−1)

ρl, ρs, ρc, ρp

Density (kg m−3)

cl, cs, cc

Species concentration (wt pct)

cmix

Mix concentration (wt pct)

cp

Specific heat (J kg−1°C−1)

ds, denv

Diameter of solid and envelop (m)

G

Temperature gradient (K m−1)

H

Heat transfer coefficient (W m−2 °C−1)

hl, hs, hc

Enthalpy (J kg−1)

k

Solute partitioning coeff. (1)

Mls, Mlc

Net mass transfer rate (kg m−3 s−1)

Ne

Grain production rate by nucleation (m−3 s−1)

p

Pressure (N m−2)

SsSc

Surface area concentration of solid and columnar phase (m−1)

T

Temperature (°C)

t

Time (s)

Uls, Ulc, Ulp, Ucs,

Momentum exchange rate (kg m−2 s−2)

vRs

Solid phase growth speed (m s−1)

μl, μs

Viscosity (kg m−1 s−1)

λ1

Columnar grain space (m)

Subscripts

l

Liquid phase (melt)

env

Grain envelope

p

Discrete particle phase

s

Solid phase (solid skeleton)

c

Columnar phase

cl

Cluster

Notes

Acknowledgments

This work is sponsored by National Key Research and Development Program of China (No. 2017YFB0305300) the Joint Funds of the National Natural Science Foundation of China (No. U1660203), National Natural Science Foundation of China (No. 51404152), Shanghai Pujiang Program (No. 14PJ1404800).

References

  1. 1.
    R. Mehrabian, M.A. Keane and M.C. Flemings: Metall. Mater. Trans. B, 1970, vol. 1, pp. 3238-41.Google Scholar
  2. 2.
    M. G. Worster: Annu. Rev. Fluid Mech. 2003, vol. 29, pp. 91-122.CrossRefGoogle Scholar
  3. 3.
    M. Wu and A. Ludwig: Acta Mater., 2009, vol. 57, pp. 5621-31.CrossRefGoogle Scholar
  4. 4.
    D. Li, X. Chen, P. Fu, X. Ma, H. Liu, Y. Chen, Y. Cao, Y. Luan and Y. Li: Nat. Commun., 2014, vol. 5, p. 5572.CrossRefGoogle Scholar
  5. 5.
    M. T. Rad, P. Kotas and C. Beckermann: Metall. Mater. Trans. A, 2013, vol. 44, pp. 4266-81.CrossRefGoogle Scholar
  6. 6.
    S.M. Copley, A.F Giamei, S.M. Johnson, and M.F. Hornbecker: Metall. Mater. Trans. B, 1970, vol. 1, p. 3455.Google Scholar
  7. 7.
    M. C. Flemings and G. E. Nereo: Macrosegregation, Part I, 1967, vol. 242, pp. 1449-61.Google Scholar
  8. 8.
    T. Fujii, D. R. Poirier and M.C. Flemings: Metal. Mater. Trans. B, 1979, vol. 10, pp. 331-39.CrossRefGoogle Scholar
  9. 9.
    C. Y. Wang and C. Beckermann: Metall. Mater. Trans. A, 1996, vol. 27, pp. 2754-64.CrossRefGoogle Scholar
  10. 10.
    H. Combeau, M. Založnik and S. Hans: Metall. Mater. Trans. B, 2009, vol. 40, pp. 289-304.CrossRefGoogle Scholar
  11. 11.
    M. Wu and A. Ludwig: Metall. Mater. Trans. A, 2006, vol. 37, pp. 1613-31.CrossRefGoogle Scholar
  12. 12.
    J. Li, H. Ge, M. Wu, A. Ludwig and J. Li: Acta Metall. 2016, vol. 52, pp. 1096-1104.Google Scholar
  13. 13.
    H. Ge, F. Ren, J. Li, Q. Hu, M. Xia and J. Li: J. Mater. Process. Technol., 2018, vol. 252, pp. 362-69.CrossRefGoogle Scholar
  14. 14.
    M. Ahmadein, M. Wu, and A. Ludwig: J. Cryst. Growth, 2015, vol. 417, pp. 65–74.CrossRefGoogle Scholar
  15. 15.
    H. Dong and P.D. Lee: Acta Mater., 2005, vol. 53, pp. 659–68.CrossRefGoogle Scholar
  16. 16.
    M. Wu, A. Ludwig and A. Kharicha: Appl. Math. Model., 2016, vol. 41.Google Scholar
  17. 17.
    H. Ge, F. Ren, J. Li, X. Han, M. Xia and J. Li: Metall. Mater. Trans. A, 2017, vol. 48, pp. 1139-50.CrossRefGoogle Scholar
  18. 18.
    Y. Cao, Y. Chen and D. Li: Acta Mater. 2016, vol. 107, pp. 325-36.CrossRefGoogle Scholar
  19. 19.
    L. Zhang: JOM, 2013, vol. 65, pp. 1138-44.CrossRefGoogle Scholar
  20. 20.
    B.G. Thomas, Q. Yuan, S. Mahmood, R. Liu and R. Chaudhary: Metall. Mater. Trans. B, 2014, vol. 45, pp. 22-35.CrossRefGoogle Scholar
  21. 21.
    J. Li, M. Wu, A. Ludwig and A. Kharicha: Int. J. Heat Mass Trans., 2014, vol. 72, pp. 668-679.CrossRefGoogle Scholar
  22. 22.
    A. Kitagawa, Y. Murai and F. Yamamoto: Int. Jou. Multiphase Flow 2001, vol. 27, pp. 2129-2153.CrossRefGoogle Scholar
  23. 23.
    H. Ge, J. Li, X. Han, M. Xia and J. Li: J. Mater. Process. Technol., 2016, vol. 227, pp. 308-17.CrossRefGoogle Scholar
  24. 24.
    W. Kurz, B. Giovanola and R. Trivedi: Acta Metal.,1986, vol. 34, pp. 823-30.CrossRefGoogle Scholar
  25. 25.
    J.A. Spittle: Int. Mater. Rev., 2006, vol. 51, pp. 247-69.CrossRefGoogle Scholar
  26. 26.
    S. Han, C. Chang and H. Lee: Scr. Mater., 2005, vol. 53, pp. 1253-1258.CrossRefGoogle Scholar
  27. 27.
    W.E. Steward, R.B. Bird, and E.N. Lightfoot: Transport Phenomena, Wiley, New York, 1960.Google Scholar
  28. 28.
    C.Y. Wang, S. Ahuja, C. Beckermann and H.C. de Groh Iii: Metall. Mater. Trans. B, 1995, vol. 26, pp. 111–19.Google Scholar
  29. 29.
    H. Shibata, D.R. Poirier and T. Emi: Isij Int., 1998, vol. 38, pp. 339-47.CrossRefGoogle Scholar
  30. 30.
    H. Tozawa, Y. Kato, K. Sorimachi, and T. Nakanishi: Isij Int., vol. 39, pp. 426-434, 1999.CrossRefGoogle Scholar
  31. 31.
    J. Wu, J. Pang, C. Dong and Y. Xu: Altas of Large Castings and Forgings Defects, Mechanical Industry Press, Beijing, 1990pp. 17–33.Google Scholar
  32. 32.
    F. Ren, H. Ge, D. Cai, J. Li, Q. Hu, M. Xia, and J. Li: Metall. Mater. Trans. A, 2018.  https://doi.org/10.1007/s11661-018-4892-9.
  33. 33.
    J. Li, M. Wu, J. Hao and A. Ludwig: Comput. Mater. Sci., 2012, vol. 55, pp. 407-418.CrossRefGoogle Scholar
  34. 34.
    L. K, S. Eck, M. Kharicha, M. Wu, and A. Ludwig, Cast Metals, 2013, vol. 22, pp. 172–74.Google Scholar

Copyright information

© The Minerals, Metals & Materials Society and ASM International 2019

Authors and Affiliations

  • Duanxing Cai
    • 1
  • Fengli Ren
    • 1
  • Honghao Ge
    • 2
  • Hee-Soo Kim
    • 3
  • Jun Li
    • 1
    • 5
    Email author
  • Jianguo Li
    • 1
    • 4
  1. 1.School of Materials Science and EngineeringShanghai Jiao Tong UniversityShanghaiChina
  2. 2.Institute of Laser Advanced ManufacturingZhejiang University of TechnologyHangzhouChina
  3. 3.Department of Materials Science & EngineeringChosun UniversityGwangjuKorea
  4. 4.Collaborative Innovation Center for Advanced Ship and Deep-Sea ExplorationShanghai Jiao Tong UniversityShanghaiChina
  5. 5.Department of EngineeringUniversity of LeicesterLeicesterUK

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