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An Interface-Enriched eXtended Finite Element-Level Set Simulation of Solutal Melting of Additive Powder Particles during Transient Liquid Phase Bonding

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Abstract

A new numerical simulation model is developed by using an interface-enriched eXtended Finite Element-Level Set (XFE-LS) method to study the solute-induced melting of additive powder particles (APPs) during transient liquid phase (TLP) bonding. The robust model captures rapidly occurring concurrent interfacial events at multiple propagating liquid-solid interfaces to simulate the melting behavior. In contrast to the critical assumption in analytical models, numerical calculations show that solute-transport into the APPs during the equilibration of the liquid composition is a significant factor that affects the APPs melting behavior. Also, the study shows that the solute-transport dependence of extent of APPs melting is influenced by the kinetics of solid-state solute diffusion within the particles. The understanding generated by the numerical analysis has resulted in the use of interlayer powder mixture that contains base-alloy APPs to produce single crystal TLP joint that has matching crystallographic orientations with single crystal substrate material, at a substantially reduced processing time, which has been previously considered unfeasible.

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References

  1. S.D. Duvall and W.A. Owczarski: Weld. J., 1967, vol. 46(9), pp. 423–32.

    Google Scholar 

  2. O.A. Ojo and M.C. Chaturvedi: Metall. Mater. Trans. A, 2007, vol. 38A, pp 356–369.

    Article  CAS  Google Scholar 

  3. D.S. Duvall, W.A. Owczarski, and D.F. Paulonis: Weld. J., 1974, vol. 53(4), pp. 203–14.

    CAS  Google Scholar 

  4. A.A. Shirzadi and E.R. Wallach: Acta Mater., 1999, vol. 47(13), pp. 3551–60.

    Article  CAS  Google Scholar 

  5. K. Tokoro, N. Wikstrom, O.A. Ojo, and M.C. Chaturvedi: Mater. Sci. Eng. A, 2008, vol. 477, pp. 311–18.

    Article  Google Scholar 

  6. B. Dutta and M. Rettenmayr: Metall. Mater. Trans. A, 2000, vol. 31A, pp. 2713–20.

    Article  CAS  Google Scholar 

  7. E. Gamsjager, J. Svoboda, F.D. Fischer, and M. Rettenmayr: Acta Mater., 2007, vol. 55, pp. 2599–2607.

    Article  Google Scholar 

  8. M. Buchmann and M. Rettenmayr: J. Cryst. Growth, 2008, vol. 310, pp. 4623–27.

    Article  CAS  Google Scholar 

  9. Y. Zhou: J. Mater. Sci. Lett., 2001, vol. 20, pp. 841–44.

    Article  CAS  Google Scholar 

  10. Y. Zhou and T. North: Model. Simul. Mater. Sci. Eng., 1993, vol. 1, pp. 505–16.

    Article  CAS  Google Scholar 

  11. T.C. Illingworth and I.O. Golosnoy: J. Comput. Phys., 2005, vol. 209, pp. 207–25.

    Article  Google Scholar 

  12. J.F. Li, P.A. Agyakwa, and C.M. Johnson: J. Mater. Sci., 2010, vol. 45, pp. 2340–50.

    Article  CAS  Google Scholar 

  13. J.M. Melenk and I. Babuska: Comput. Methods Appl. Mech. Eng., 1996, vol. 39, pp. 289–314.

    Article  Google Scholar 

  14. D. Chopp and J. Dolbow: Int. J. Numer. Methods Eng., 2002, vol. 54, pp. 1209–33.

    Article  Google Scholar 

  15. N. Sukumar, D.L. Chopp, N. Moes, and T. Belytschko: Comput. Methods Appl. Mech. Eng., 2001, vol. 190, pp. 6183–6200.

    Article  Google Scholar 

  16. J. Chessa, H. Wang, and T. Belytschko: Int. J. Numer. Methods Eng., 2003, vol. 57, pp. 1015–38.

    Article  Google Scholar 

  17. R. Gracie, H. Wang, and T. Belytschko: Int. J. Numer. Methods Eng., 2008, vol. 74(11), pp. 1645–69.

    Article  Google Scholar 

  18. T.P. Fries: Int. J. Numer. Methods Eng., 2008, vol. 75, pp. 503–32.

    Article  Google Scholar 

  19. T. Belytschko, W.K. Liu, and B. Moran: Nonlinear Finite Elements for Continua and Structures, John Wiley & Sons, New York, 2003, ISBN:0-471-98774-3.

  20. H. Ji and J.E. Dolbow: Int. J. Numer. Methods Eng., 2004, vol. 61, pp. 2508–35.

    Article  Google Scholar 

  21. R. Duddu, D. Chopp, P. Voorhees, and B. Moran: J. Comput. Phys., 2010, vol. 230, pp. 1249–64.

    Article  Google Scholar 

  22. N. Moes, M. Cloirec, P. Cartraud, and J.F. Remacle: Comput. Methods Appl. Mech. Eng., 2003, vol. 192, pp. 3163–77.

    Article  Google Scholar 

  23. S. Soghrati, A.M. Aragón, C.A. Duarte, and P.H. Geubelle: Int. J. Numer. Methods Eng., 2012, vol. 89(8), pp. 991–1008.

    Article  Google Scholar 

  24. N. Sukumar and J. Prevost: Int. J. Solids Struct., 2003, vol. 40, pp. 7513–37.

    Article  Google Scholar 

  25. S. Osher and J. Sethian: J. Comput. Phys., 1988, vol. 79(1), pp. 12–49.

    Article  Google Scholar 

  26. S. Osher and R. Fedkiw: Level Set Methods and Dynamic Implicit Surfaces, Springer, New York, 2003, ISBN: 0-387-95482-1.

  27. A. Ghoneim and O.A. Ojo: Comput. Mater. Sci., 2011, vol. 50, pp. 1102–13.

    Article  CAS  Google Scholar 

  28. A. Ghoneim and O.A. Ojo: Metall. Mater. Trans. A, 2012, vol. 43A(3), pp. 900–11.

    Article  Google Scholar 

  29. P.K. Liao and K.E. Spear: Bull. Alloy Phase Diag., 1986, vol. 7(3), p. 550.

    Article  Google Scholar 

  30. Y. Zhou, W.F. Gale, and T.H. North: Int. Mater. Rev., 1995, vol. 40, pp. 181–96.

    Article  CAS  Google Scholar 

  31. O.A. Idowu, O.A. Ojo, and M.C. Chaturvedi: Metall. Mater. Trans. A, 2006, vol. 37A, pp. 2787–96.

    Article  CAS  Google Scholar 

  32. M.M. Abdelfattah and O.A. Ojo: Metall. Mater. Trans. A, 2009, vol. 40A, pp. 377–85.

    Article  Google Scholar 

  33. Y. Xinjian, B.K. Myung, and Y.K. Chung: Metall. Mater. Trans. A, 2011, vol. 42A, pp. 1310–24.

    Google Scholar 

  34. M.K. Dinkel, P. Heinz, F. Pyczak, A. Volek, M. Ott, E. Affeldt, A. Vossberg, M. Goken, and R.F. Singer: 11th International Symposium on Superalloys, 2008, pp. 211–20.

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Acknowledgment

The authors gratefully acknowledge financial support by NSERC of Canada.

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Correspondence to O. A. Ojo.

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Manuscript submitted March 24, 2012.

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Ghoneim, A., Hunedy, J. & Ojo, O.A. An Interface-Enriched eXtended Finite Element-Level Set Simulation of Solutal Melting of Additive Powder Particles during Transient Liquid Phase Bonding. Metall Mater Trans A 44, 1139–1151 (2013). https://doi.org/10.1007/s11661-012-1412-1

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  • DOI: https://doi.org/10.1007/s11661-012-1412-1

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