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Mechanisms and Modeling of Bake-Hardening Steels: Part I. Uniaxial Tension

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Abstract

A physically based model for bake-hardening (BH) steels is developed suitable to predict the BH as well as the macroscopic behavior of strain-aged steels in tensile tests, such as the lower yield stress and the yield point elongation or Lüders strain. A description of the strain aging kinetics is given by considering two aging steps: Cottrell atmospheres formation and precipitation of coherent carbides. The modeling includes the effect of solute carbon content, aging time, temperature, and prestrain. Then, a numerical approach of Lüders phenomenon using finite element (FE) method codes is conducted. The strain aging model is eventually coupled with the previous numerical study thanks to a local mechanical behavior that schematically describes the local dislocation behavior. Simulations of tensile tests are performed and agree well with experiments carried out on aluminum-killed (AlK) and ULC BH steels, in terms of lower yield stress and yield point elongation. Effects of aging treatment, grain size, and strain rate on the macroscopic behavior are particularly enlightened.

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References

  1. A.H. Cottrell and B.A. Bilby: Proc. Phys. Soc., 1949, vol. 62, pp. 49–62.

    ADS  Google Scholar 

  2. A.K. De: Ph.D. Thesis, Ghent University, Ghent, Belgium, 2000.

  3. J.Z. Zhao, A.K. De, and B.C. De Cooman: Metall. Mater. Trans. A, 2001, vol. 32A, pp. 417–23.

    Article  CAS  Google Scholar 

  4. G.T. Hahn: Acta Metall., 1962, vol. 10, pp. 727–38.

    Article  Google Scholar 

  5. F. Garofalo: Metall. Trans., 1973, vol. 4, pp. 1557–61.

    CAS  Google Scholar 

  6. P. Hähner: Appl. Phys., 1994, vol. A58, pp. 41–48.

    ADS  Google Scholar 

  7. F. Yoshida: Int. J. Plast., 2000, vol. 16, pp. 359–80.

    Article  MATH  CAS  Google Scholar 

  8. J.F. Butler: J. Mech. Phys. Solids, 1962, vol. 10, pp. 313–34.

    Article  ADS  Google Scholar 

  9. V. Ballarin, A. Perlade, S. Forest, and X. Lemoine: Metall. Mater. Trans. A, 2006, vol. 37A, DOI 10.1007/s11661-009-9812-6.

  10. S. Harper: Phys. Rev., 1951, vol. 83, pp. 709–12.

    Article  ADS  CAS  Google Scholar 

  11. D. Mac Lean: Grain Boundaries in Metals, Oxford University Press, Oxford, United Kingdom, 1957.

    Google Scholar 

  12. Y. Bergström: Mater. Sci. Eng., 1969, vol. 5, pp. 193–200.

    Google Scholar 

  13. U.F. Kocks: J. Eng. Mater. Technol., 1976, vol. 98, pp. 76–85.

    CAS  Google Scholar 

  14. M. Soler: Ph.D. Thesis, Institut National des Sciences Appliquées de Lyon, Lyon, France, 1998 (in French).

  15. J.M. Rubianes and P. Zimmer: Rev. Metall. Cah. Inf. Technol., 1996, pp. 99–109.

  16. W.C. Leslie and A.S. Keh: J. Iron Steel Inst., 1962, vol. 200, pp. 722–28.

    CAS  Google Scholar 

  17. P. Elsen and H.P. Hougardy: Steel Res., 1993, vol. 64, pp. 431–36.

    CAS  Google Scholar 

  18. L.J. Baker, J.D. Parker, and S.R. Daniel: Mater. Sci. Technol., 2002, vol. 18, pp. 541–47.

    Article  CAS  Google Scholar 

  19. A.K. De, K. De Blauwe, S. Vandeputte, and B.C. De Cooman: J. Alloys Compd., 2000, vol. 310, pp. 405–10.

    Article  CAS  Google Scholar 

  20. H. Tsukahara and T. Iung: Mater. Sci. Eng. A, 1998, vol. 248, pp. 304–08.

    Article  Google Scholar 

  21. S. Graff, S. Forest, J.-L. Strudel, C. Prioul, P. Pilvin, and J.-L. Béchade: Mater. Sci. Eng. A, 2004, vols. 387–389, pp. 181–85.

    Google Scholar 

  22. E. Voce: J. Inst. Met., 1948, vol. 74, pp. 537–62.

    CAS  Google Scholar 

  23. Abaqus, 2004, www.abaqus.com.

  24. Z-set, 2001, www.nwnumerics.com, www.mat.ensmp.fr.

  25. J. Besson, G. Cailletaud, J.-L. Chaboche, and S. Forest: Mécanique Non Linéaire des Matériaux, Hermès, Paris, 2001, pp. 385–420 (in French).

  26. D.V. Wilson: Acta Metall., 1968, vol. 16, pp. 743–53.

    Article  CAS  Google Scholar 

  27. H. Fujita and S. Miyazaki: Acta Metall., 1978, vol. 26, pp. 1273–81.

    Article  CAS  Google Scholar 

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Acknowledgment

The authors are grateful to J.L. Uriarte and O. Bouaziz for helpful discussions.

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Authors and Affiliations

  1. Automotive Applications Research Center, Arcelor-Mittal Montataire, 60761, Montataire, France

    V. Ballarin (Research Engineer)

  2. Automotive Products Research Center, Arcelor-Mittal Maizières, Voie Romaine, 57283, Maizières-lès-Metz, France

    M. Soler (Research Engineer), A. Perlade (Research Engineer) & X. Lemoine (Research Engineer)

  3. Mines ParisTech, Centre des Matériaux, UMR CNRS 7633, 91003, Evry Cedex, France

    S. Forest (CNRS Research Director)

Authors
  1. V. Ballarin
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  2. M. Soler
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  3. A. Perlade
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  4. X. Lemoine
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  5. S. Forest
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Corresponding author

Correspondence to X. Lemoine.

Additional information

Manuscript submitted October 16, 2007.

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Ballarin, V., Soler, M., Perlade, A. et al. Mechanisms and Modeling of Bake-Hardening Steels: Part I. Uniaxial Tension. Metall Mater Trans A 40, 1367–1374 (2009). https://doi.org/10.1007/s11661-009-9813-5

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