SpringerLink
Log in

Undercooling and Cracking During Solidification

  • Original Research Article
  • Published:
Metallurgical and Materials Transactions A Aims and scope Submit manuscript

Abstract

How the solid fraction fS increases with decreasing temperature T during solidification, i.e., the fS(T) of an alloy, can play a critical role in its susceptibility to cracking during solidification as demonstrated by various models of solidification cracking. In the present study the classic analytical modeling of microsegregation during rapid solidification was used to calculate fS(T) using Al–Cu alloys as an example. The present study showed significant undercooling can occur during fast cooling and affect fS(T) significantly. For the purpose of illustration, |dT/d(fS)1/2| near (fS)1/2 = 1 was used in the present study as a simple index for the susceptibility to solidification cracking. The fS(T) calculated by any solidification model (e.g., the present analytical model or a phase-field model with undercooling, or the Scheil–Gulliver model without undercooling) can be used to calculate the curve of T vs (fS)1/2 and hence the index. The present study showed undercooling can increase the index and hence the cracking susceptibility significantly. It can also change the composition most susceptible to solidification cracking.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig 12
Fig. 13

Similar content being viewed by others

References

  1. M.C. Flemings: Solidification Processing, McGraw-Hill, New York, 1974, pp. 34–36.

    Google Scholar 

  2. W. Kurz and D.J. Fisher, Fundamentals of Solidification, Trans Tech Publications, Switzerland, 4th edition, 1998, pp. 122–26.

  3. D.J. Fisher and W. Kurz: Unpublished Research. 1978, Department of Materials, EPFL-Swiss Institute of Technology Lausanne, Switzerland.

  4. S. Kou: Welding Metallurgy, 3rd ed. Wiley, Hoboken, 2021, pp. 323–77.

    Google Scholar 

  5. T.W. Clyne and G.J. Davies: Br. Foundryman, 1981, vol. 74(4), pp. 65–73.

    Google Scholar 

  6. M. Rappaz, J.M. Drezet, and M. Gremaud: Metall. Mater. Trans. A, 1999, vol. 30A, pp. 449–55.

    Article  CAS  Google Scholar 

  7. J. Liu, P. Hu, and S. Kou: Metall. Mater. Trans. A, 2024, vol. 55A, pp. 1435–47.

    Article  Google Scholar 

  8. J. Liu, P. Hu, and S. Kou: Metall. Mater. Trans. A, 2023, vol. 54A, pp. 4342–55.

    Article  Google Scholar 

  9. S. Kou: Acta Mater., 2015, vol. 88, pp. 366–74.

    Article  CAS  Google Scholar 

  10. S. Kou: Transport Phenomena and Materials Processing, Wiley, New York, 1966, pp. 64–67.

    Google Scholar 

  11. S. Kou: Weld. J., 2015, vol. 94, pp. 374s-s388.

    Google Scholar 

  12. T. Soysal and S. Kou: Acta Mater., 2018, vol. 143, pp. 181–97.

    Article  CAS  Google Scholar 

  13. J.D. Dowd: Weld. J., 1952, vol. 31(10), pp. 448s-s456.

    CAS  Google Scholar 

  14. J.H. Dudas and F.R. Collins: Weld. J., 1966, vol. 45(6), pp. 241s-s249.

    Google Scholar 

  15. V. Shankar and J.H. Devletian: Sci. Technol. Weld. Joining, 2005, vol. 10(2), pp. 236–43.

    Article  CAS  Google Scholar 

  16. C. **a and S. Kou: Metall. Mater. Trans. B, 2021, vol. 52B, pp. 460–69.

    Article  Google Scholar 

  17. T. Mukherjee, J.W. Elmer, H.L. Wei, T.J. Linert, W. Zhang, S. Kou, and T. DebRoy: Prog. Mater Sci., 2023, vol. 138, 101153.

    Article  CAS  Google Scholar 

  18. J.H. Martin, B.D. Yahata, J.M. Hundley, J.A. Mayer, T.A. Schaedler, and T.M. Pollock: Nature, 2017, vol. 549(7672), pp. 365–69.

    Article  CAS  PubMed  Google Scholar 

  19. H. Hyer, L. Zhou, A. Mehta, S. Park, T. Huynh, S. Song, Y. Bai, K. Cho, B. McWilliams, and Y. Sohn: Acta Mater., 2021, vol. 208, 116698.

    Article  CAS  Google Scholar 

  20. B. Dovgyy, M. Simonelli, and M. Pham: Mater. Res. Lett., 2021, vol. 9(8), pp. 350–57.

    Article  CAS  Google Scholar 

  21. G. Li, E. Brodu, J. Soete, H. Wei, T. Liu, T. Yang, W. Liao, and K. Vanmeensel: Addit. Manuf., 2021, vol. 47, 102210.

    CAS  Google Scholar 

  22. S. Chandra, X. Tan, R.L. Narayan, C. Wang, S.B. Tor, and G. Seet: Addit. Manuf., 2021, vol. 37, 101633.

    CAS  Google Scholar 

  23. N. Sargent, M. Jones, R. Otis, A.A. Shapiro, J.P. Delplanque, and W. **ong: Metals, 2021, vol. 11(4), p. 570.

    Article  CAS  Google Scholar 

  24. S. Geng, P. Jiang, X. Shao, G. Mi, H. Wu, Y. Ai, C. Wang, R. Han, R. Chen, W. Liu, and Y. Zhang: Acta Mater., 2018, vol. 160, pp. 85–96.

    Article  CAS  Google Scholar 

  25. J. Liu, H.P. Duarte, and S. Kou: Acta Mater., 2017, vol. 122, pp. 47–59.

    Article  Google Scholar 

  26. S.C. Gill and W. Kurz: Metall. Mater., 1995, vol. 43(1), pp. 139–51.

    CAS  Google Scholar 

  27. S.C. Gill and W. Kurz: Acta Metall. Mater., 1993, vol. 41(12), pp. 3563–73.

    Article  CAS  Google Scholar 

  28. M. Zimmermann, M. Carrard, and W. Kurz: Acta Metall., 1989, vol. 37(12), pp. 3305–13.

    Article  CAS  Google Scholar 

  29. S.C. Gill, M. Zimmermann, and W. Kurz: Acta Metall. Mater., 1992, vol. 40(11), pp. 2895–2906.

    Article  CAS  Google Scholar 

  30. B. Giovanola and W. Kurz: Metall. Trans. A, 1990, vol. 21(1), pp. 260–63.

    Article  Google Scholar 

  31. X. Tong and C. Beckermann: J. Cryst. Growth, 1998, vol. 187(2), pp. 289–302.

    Article  CAS  Google Scholar 

  32. W. Kurz, B. Giovanola, and R. Trivedi: Acta Metall., 1986, vol. 34(5), pp. 823–30.

    Article  CAS  Google Scholar 

  33. R. Trivedi, P. Magnin, and W. Kurz: Acta Metall., 1987, vol. 35(4), pp. 971–80.

    Article  CAS  Google Scholar 

  34. J. Xu, X. Lin, Y. Zhao, P. Guo, X. Wen, Q. Li, H. Yang, H. Dong, L. Xue, and W. Huang: Metall. Mater. Trans. A, 2018, vol. 49A, pp. 5118–36.

    Article  Google Scholar 

  35. Y.J. Liang, X. Cheng, and H.M. Wang: Acta Mater., 2016, vol. 118, pp. 17–27.

    Article  CAS  Google Scholar 

  36. T.W. Clyne and W. Kurz: Metall. Trans. A, 1981, vol. 12, pp. 965–71.

    Article  Google Scholar 

  37. Z. Gan, Y. Lian, S.E. Lin, K.K. Jones, W.K. Liu, and G.J. Wagner: Integr. Mater. Manuf. Innov., 2019, vol. 8, pp. 178–93.

    Article  Google Scholar 

  38. T. Billotte, D. Daloz, B. Rouat, G. Tirand, J.R. Kennedy, V. Robin, and J. Zollinger: Materials, 2018, vol. 11(1252), pp. 1–15.

    Google Scholar 

  39. A. Plotkowski, O. Rios, N. Sridharan, Z. Sims, K. Unocic, R.T. Ott, R.R. Dehoff, and S.S. Babu: Acta Mater., 2017, vol. 126, pp. 507–19.

    Article  CAS  Google Scholar 

  40. Z.M. Beiranvand, F.M. Ghaini, H.N. Moosavy, M. Sheikhi, and M.J. Torkamany: Metall. Mater. Trans. A, 2019, vol. 50A, pp. 2835–46.

    Article  Google Scholar 

  41. L.A. Bendersky and W.J. Boettinger: in Rapidly Quenched Metals, S. Steeb and H. Warlimont (eds.), Elsevier, 1985, pp. 887–90.

  42. American Society for Metals: Binary Alloy Phase Diagrams, vol. 1, American Society for Metals, Metals Park, 1986.

    Google Scholar 

  43. G. Kasperovich, T. Volkmann, L. Ratke, and D. Herlach: Metall. Mater. Trans. A, 2008, vol. 39A, pp. 1183–91.

    Article  CAS  Google Scholar 

  44. J.A. Sarreal and G.J. Abbaschian: Metall. Trans. A, 1986, vol. 17(11), pp. 2063–73.

    Article  Google Scholar 

  45. E.J. Michaud, H.W. Kerr, and D.C. Weckman: in Trends in Welding Research, Proceedings of 4th International Conference, 5–8 June 1995, Gatlinburg, TN. ASM International, Materials Park, OH.

  46. J.A. Spittle and A.A. Cushway: Metals Technology, 1983, vol. 10(1), pp. 6–13.

    Article  CAS  Google Scholar 

  47. P.F. Paradis, T. Ishikawa, and S. Yoda: J. Appl. Phys., 2005, vol. 97(5), p. 053506.

    Article  Google Scholar 

  48. X.J. Han, M. Chen, and Y.J. Lü: Int. J. Thermophys., 2008, vol. 29(4), pp. 1408–21.

    Article  CAS  Google Scholar 

  49. J. Liu and S. Kou: Acta Mater., 2016, vol. 110, pp. 84–94.

    Article  CAS  Google Scholar 

Download references

Acknowledgments

The study was supported by the National Science Foundation of the United States (Grant No. DMR 1904503). Soumyadeep Dasgupta, formerly Graduate Student at the University of Wisconsin-Madison supervised by Professor Sindo Kou, is now Graduate Student at the University of Michigan-Ann Arbor.

Author information

Authors and Affiliations

  1. Department of Materials Science and Engineering, University of Michigan, Ann Arbor, MI, 48109, USA

    Soumyadeep Dasgupta

  2. Department of Materials Science and Engineering, University of Wisconsin, Madison, WI, 53706, USA

    Sindo Kou

Authors
  1. Soumyadeep Dasgupta
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sindo Kou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sindo Kou.

Ethics declarations

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dasgupta, S., Kou, S. Undercooling and Cracking During Solidification. Metall Mater Trans A (2024). https://doi.org/10.1007/s11661-024-07486-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11661-024-07486-6

Search

Navigation