Skip to main content
SpringerLink
Log in

Phase-field simulation of microstructure evolution in electron beam additive manufacturing

  • Regular Article
  • Published:
The European Physical Journal E Aims and scope Submit manuscript

Abstract.

Electron beam additive manufacturing (EBAM) is an emerging additive manufacturing technology with extremely high energy beam. The rapid solidification in the molten pool is of interest but not fully understood. In EBAM, with both large thermal gradient and cooling rate, the microstructure evolution during solidification is difficult to be described. The quantitative multi-phase-field model provides an effective way to reveal the dynamic evolution of dendrites in the molten pool of EBAM. In this study, the thermal profile is interpolated from the macroscale simulation at each time-step, to couple the realistic thermal evolution in the molten pool. The microstructure evolution and competitive growth have been investigated in details. Simulations of dendrite arrays with the same orientation showed how the growth velocity and the primary spacing of columnar dendrites depend on thermal gradient and cooling rate. The results are in agreement with theoretical models qualitatively. Moreover, the Gaussian nucleation model was introduced so as to give a better prediction of the microstructure in EBAM.

Graphical abstract

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

Similar content being viewed by others

References

  1. C. Körner, Int. Mater. Rev. 61, 361 (2016)

    Article  Google Scholar 

  2. L.E. Murr et al., Mater. Charact. 60, 96 (2009)

    Article  Google Scholar 

  3. S. Das, Adv. Eng. Mater. 5, 701 (2003)

    Article  Google Scholar 

  4. P.J. Prescott, F.P. Incropera, in Advances in Heat Transfer, edited by D. Poulikakos (Elsevier, 1996) p. 231

  5. V.R. Voller, A.D. Brent, C. Prakash, Int. J. Heat Mass Transfer 32, 1719 (1989)

    Article  ADS  Google Scholar 

  6. X. He, J. Elmer, T. Debroy, J. Appl. Phys. 97, 084909 (2005)

    Article  ADS  Google Scholar 

  7. W. Kurz, D.J. Fisher, R. Trivedi, Int. Mater. Rev. 64, 311 (2019)

    Article  Google Scholar 

  8. J. Parthasarathy, B. Starly, S. Raman, A. Christensen, J. Mech. Behav. Biomed. Mater. 3, 249 (2010)

    Article  Google Scholar 

  9. R. Cunningham, S.P. Narra, T. Ozturk, J. Beuth, A.D. Rollett, JOM 68, 765 (2016)

    Article  Google Scholar 

  10. S. Bontha, N.W. Klingbeil, P.A. Kobryn, H.L. Fraser, Mater. Sci. Eng. A 513-514, 311 (2009)

    Article  Google Scholar 

  11. S.M. Gaytan, L.E. Murr, F. Medina, E. Martinez, M.I. Lopez, R.B. Wicker, Mater. Technol. 24, 180 (2009)

    Article  Google Scholar 

  12. P. Heinl, A. Rottmair, C. Koerner, R.F. Singer, Adv. Eng. Mater. 9, 360 (2010)

    Article  Google Scholar 

  13. M. Koike, K. Martinez, L. Guo, G. Chahine, R. Kovacevic, T. Okabe, J. Mater. Process. Technol. 211, 1400 (2011)

    Article  Google Scholar 

  14. W.J. Boettinger, J.A. Warren, C. Beckermann, A. Karma, Annu. Rev. Mater. Res. 32, 163 (2002)

    Article  Google Scholar 

  15. A. Karma, W.-J. Rappel, Phys. Rev. E 57, 4323 (1998)

    Article  ADS  Google Scholar 

  16. S.G. Kim, W.T. Kim, T. Suzuki, Phys. Rev. E 60, 7186 (1999)

    Article  ADS  Google Scholar 

  17. Z. Wang, J. Wang, G. Yang, Scr. Mater. 61, 915 (2009)

    Article  Google Scholar 

  18. C.A. Gandin, M. Rappaz, Acta Mater. 45, 2187 (1997)

    Article  Google Scholar 

  19. H. Yin, S.D. Felicelli, L. Wang, Acta Mater. 59, 3124 (2011)

    Article  Google Scholar 

  20. C. Guo, J. Li, H. Yu, Z. Wang, X. Lin, J. Wang, Acta Mater. 136, 148 (2017)

    Article  Google Scholar 

  21. D. Montiel, L. Liu, L. Xiao, Y. Zhou, N. Provatas, Acta Mater. 60, 5925 (2012)

    Article  Google Scholar 

  22. V. Fallah, M. Amoorezaei, N. Provatas, S.F. Corbin, A. Khajepour, Acta Mater. 60, 1633 (2012)

    Article  Google Scholar 

  23. Z. Wang, T. Jing, H. Dong, IOP Conf. Ser.: Mater. Sci. Eng. 529, 012003 (2019)

    Article  Google Scholar 

  24. X. Gong, K. Chou, JOM 67, 1176 (2015)

    Article  ADS  Google Scholar 

  25. S. Sahoo, K. Chou, Addit. Manuf. 9, 14 (2016)

    Google Scholar 

  26. L. Wu, J. Zhang, JOM 70, 2392 (2018)

    Article  Google Scholar 

  27. J.D. Hunt, Solidification and Casting of Metals (The Metal Society, 1979) p. 3

  28. M.H. Burden, J.D. Hunt, J. Cryst. Growth 22, 99 (1974)

    Article  ADS  Google Scholar 

  29. I. Steinbach, F. Pezzolla, B. Nestler, M. Seeßelberg, R. Prieler, G. Schmitz, J. Rezende, Physica D: Nonlin. Phenom. 94, 135 (1996)

    Article  ADS  Google Scholar 

  30. J. Eiken, B. Böttger, I. Steinbach, Phys. Rev. E 73, 066122 (2006)

    Article  ADS  Google Scholar 

  31. S.G. Kim, Acta Mater. 55, 4391 (2007)

    Article  Google Scholar 

  32. S. Gyoon Kim, W. Tae Kim, T. Suzuki, M. Ode, J. Cryst. Growth 261, 135 (2004)

    Article  ADS  Google Scholar 

  33. C. Guo, J. Li, Z. Wang, J. Wang, Mater. Des. 151, 141 (2018)

    Article  Google Scholar 

  34. J. Li, Z. Wang, Y. Wang, J. Wang, Acta Mater. 60, 1478 (2012)

    Article  Google Scholar 

  35. L. Nastac, J.S. Chou, Y. Pang, International Symposium on Liquid Metals Processing and Casting, edited by A. Mitchell, L. Ridgway, M. Baldwin (TMS, Warrendale, PA, 1999) p. 207

  36. L. Nastac, CFD Modeling and Simulation in Materials Processing (Wiley-TMS, New York, 2012) pp. 123--130

  37. Y. Qian, W. Yan, F. Lin, Engineering 5, 746 (2019)

    Article  Google Scholar 

  38. W. Yan, Y. Qian, W. Ge, S. Lin, W.K. Liu, F. Lin, G.J. Wagner, Mater. Des. 141, 210 (2018)

    Article  Google Scholar 

  39. Z. Wang, J. Li, J. Wang, J. Cryst. Growth 328, 108 (2011)

    Article  ADS  Google Scholar 

  40. C.A. Gandin, M. Eshelman, R. Trivedi, Metall. Mater. Trans. A 27, 2727 (1996)

    Article  Google Scholar 

  41. M. Rappaz, C.A. Gandin, Acta Metall. Mater. 41, 345 (1993)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, 710072, Xi’an, P.R. China

    Shuo Chu, Chunwen Guo, Tongxin Zhang, Yueting Wang, Junjie Li, Zhijun Wang & Jincheng Wang

  2. Department of mechanical engineering, Tsinghua University, 100084, Beijing, P.R. China

    Ya Qian & Haiyan Zhao

Authors
  1. Shuo Chu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chunwen Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tongxin Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yueting Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Junjie Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Zhijun Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Jincheng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Ya Qian
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Haiyan Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Junjie Li or Zhijun Wang.

Additional information

Publisher’s Note

The EPJ Publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chu, S., Guo, C., Zhang, T. et al. Phase-field simulation of microstructure evolution in electron beam additive manufacturing. Eur. Phys. J. E 43, 35 (2020). https://doi.org/10.1140/epje/i2020-11952-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epje/i2020-11952-1

Keywords

Search

Navigation