Journal of Materials Science

, Volume 44, Issue 5, pp 1219–1236 | Cite as

Moving finite-element mesh model for aiding spark plasma sintering in current control mode of pure ultrafine WC powder

  • G. MaizzaEmail author
  • S. Grasso
  • Y. Sakka


The intricate bulk and contact multiphysics of spark plasma sintering (SPS) together with the involved non-linear materials’ response make the process optimization very difficult both experimentally and computationally. The present work proposes an integrated experimental/numerical methodology, which simultaneously permits the developed SPS model to be reliably tested against experiments and to self-consistently estimate the overall set of unknown SPS contact resistances. Unique features of the proposed methodology are: (a) simulations and experiments are conducted in current control mode (SPS-CCm); (b) the SPS model couples electrothermal and displacement fields; (c) the contact multiphysics at the sliding punch/die interface is modeled during powder sintering using a moving mesh/moving boundary technique; (d) calibration and validation procedures employ both graphite compact and conductive WC powder samples. The unknown contact resistances are estimated iteratively by minimizing the deviation between predictions and on-line measurements (i.e., voltage, die surface temperature, and punch displacement) for three imposed currents (i.e., 1,900, 2,100, 2,700 A) and 20 MPa applied pressure. An excellent agreement is found between model predictions and measurements. The results show that the SPS bulk and contact multiphysics can be accurately reproduced during densification of ultrafine binderless WC powder. The results can be used to benchmark contact resistances in SPS systems applicable to graphite and conductive (WC) powder samples. The SPS bulk and contact multiphysics phenomena arising during sintering of ultrafine binderless WC powders are finally discussed. A direct correlation between sintering microstructure, sintering temperature, and heating rate is established. The developed self-consistent SPS model can be effective used as an aiding tool to design optimum SPS experiments, predict sintering microstructure, or benchmark SPS system hardware or performances.


Contact Resistance Spark Plasma Sinter Spark Plasma Sinter Process Punch Displacement Electric Contact Resistance 



This work was supported by World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan.


  1. 1.
    Munir ZA, Anselmi-Tamburini U, Ohyanagi M (2006) J Mater Sci 41:763. doi: CrossRefGoogle Scholar
  2. 2.
    Keum YT, Jeon JH, Auh KH (2002) J Ceram Proc Res 3:195Google Scholar
  3. 3.
    Leuenberger G, Ludwig R, Apelian D (2002) J Non-Destr Eval 21:111CrossRefGoogle Scholar
  4. 4.
    Zhang J, Zavaliangos A, Kraemer M, Groza JR (2002) In: Lawley A, Smugeresky JE, Smith L (eds) Process modeling in powder metallurgy and particulate materials: Proceedings of the 2002 international conference on process modeling powder metallurgy and particulate materials, Newport Beach, CA, pp 208–215, 28–29 October 2002Google Scholar
  5. 5.
    Zhang J, Zavaliangos A, Groza JR (2003) In: International conference on powder metallurgy and particulate materials, Las VegasGoogle Scholar
  6. 6.
    Zhang J, Zavaliangos A, Groza JR (2003) In: Cornwall RG, German RM, Messing GL (eds) Proceedings of sintering 2003, Materials Research Institute, Pennsylvania State University, University Park, PA, 14–17 September 2003Google Scholar
  7. 7.
    Zhang J, Zavaliangos A, Groza JR (2003) P/M Sci Tech Briefs 5:5Google Scholar
  8. 8.
    Zhang J (2003) Numerical simulation of sintering under electric field. PhD Thesis, Drexel University, Philadelphia, PAGoogle Scholar
  9. 9.
    Anselmi-Tamburini U, Garay JE, Munir ZA, Tacca A, Maglia F, Spinolo G (2004) J Mater Res 19:3255CrossRefGoogle Scholar
  10. 10.
    Zavaliangos A, Zhang J, Krammer M, Groza JR (2004) Mater Sci Eng A 379:218CrossRefGoogle Scholar
  11. 11.
    Anselmi-Tamburini U, Gennari S, Garay JE, Munir ZA (2005) Mater Sci Eng A394:139CrossRefGoogle Scholar
  12. 12.
    Anselmi-Tamburini U, Garay JE, Munir ZA (2005) Mater Sci Eng. A 407:24CrossRefGoogle Scholar
  13. 13.
    Vanmeensel K, Laptev A, Hennicke J, Vleugels J, Van der Biest O (2005) Acta Mater 53:4379CrossRefGoogle Scholar
  14. 14.
    Cincotti A, Locci AM, Orru’ R, Cao G (2007) AIChE J 53:703CrossRefGoogle Scholar
  15. 15.
    Olevsky E, Froyen L (2006) Scr Mater 55:1175CrossRefGoogle Scholar
  16. 16.
    Maizza G, Grasso S, Sakka Y, Noda T, Ohashi O (2007) Sci Tech Adv Mater 8:644CrossRefGoogle Scholar
  17. 17.
    COMSOL Multiphyscs (2006) AC/DC Module, User’s Guide Vers.3.3a, AugustGoogle Scholar
  18. 18.
    Savvatimskiy AI (2005) Carbon 43:1115CrossRefGoogle Scholar
  19. 19.
    Loeb AL (1954) J Am Ceram Soc 37:96CrossRefGoogle Scholar
  20. 20.
    Austin JB (1941) Ceram Abstr 20:45Google Scholar
  21. 21.
    Sahimi M, Tsotsis TT (1999) Ind Eng Chem Res 36:3043CrossRefGoogle Scholar
  22. 22.
    Willims WS (1998) JOM 50:62CrossRefGoogle Scholar
  23. 23.
    Reeber RR, Wang K 1999) J Am Ceram Soc 82:129CrossRefGoogle Scholar
  24. 24.
    Toyo Tanso Co. Ltd. Tokyo private communicationGoogle Scholar
  25. 25.
    Holm R (1967) Electric contacts: theory and application. Springer, New YorkCrossRefGoogle Scholar
  26. 26.
    Nishimoto K, Saida K, Tsuduki R (2001) J Jpn Inst Met 65:747CrossRefGoogle Scholar
  27. 27.
    Luo X, Chung DDL (2001) J Tribol 123:683CrossRefGoogle Scholar
  28. 28.
    Xie G, Ohashi O, Yamaguchi N, Wang A (2003) Metall Mater Trans A 34:2655CrossRefGoogle Scholar
  29. 29.
    Bahrami M, Culham JR, Yovanovich MM (2004) J Heat Transf 126:896CrossRefGoogle Scholar
  30. 30.
    Bahrami M, Culham JR, Yovanovich MM, Schneider GE (2004) J Thermophys Heat Transf 18:218CrossRefGoogle Scholar
  31. 31.
    Song Q, Zhang W, Niel B (2005) Weld J 84:73Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Dipartimento di Scienza dei Materiali ed Ingegneria ChimicaPolitecnico di TorinoTorinoItaly
  2. 2.Graduate School of Pure and Applied SciencesUniversity of TsukubaTsukubaJapan
  3. 3.World Premier International Research Center Initiative (WPI Initiative) on Materials Nanoarchitronics (MANA) and Nano Ceramics CenterNational Institute for Materials Science (NIMS)Tsukuba, IbarakiJapan

Personalised recommendations