Journal of Nondestructive Evaluation

, Volume 16, Issue 4, pp 187–192 | Cite as

Dependence of Ultrasonic Velocity on Porosity and Pore Shape in Sintered Materials

  • Dino N. Boccaccini
  • Aldo R. Boccaccini


A new approach to predict the longitudinal and transverse ultrasonic velocities in porous materials is presented. The model is based on a previously derived Young's modulus-porosity correlation assuming spheroidal geometry of the pores. It is also assumed that the Poisson's ratio of porous materials does not change significantly with porosity. The longitudinal and transverse ultrasonic velocities are given as functions of the Young's modulus, Poisson's ratio, density of the pore-free material and of the porosity and axial ratio (z/x) of the spheroidal pores. Experimental data drawn from the literature on different porous sintered materials including SiC, Al2O3, YBa2Cu3O7−x, porcelain, sintered iron, Si3N4, and sintered tungsten, were used to verify the model. A strong relationship between pore shape and the slope of the ultrasonic velocity–porosity curve was confirmed. In general, the calculated values are in fairly good agreement with the experimental data. When the actual shape (axial ratio) of the pores was known, the approach was shown to predict the experimental data better than a similar model derived by Phani. It is suggested that the present approach, coupled with the measurement of the ultrasonic velocity, may constitute a simple nondestructive technique to gain knowledge of the morphology of the porosity in sintered materials.

Ultrasonic velocity porous materials pore shape elastic constants spheroidal model 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    D. S. Kupperman and H. B. Karplus, Am. Ceram. Soc. Bull. 63: 1505 (1984).Google Scholar
  2. 2.
    G. Y. Baaklini, E. R. Generazio, and J. D. Kiser, J. Am. Ceram. Soc. 72: 383 (1989).Google Scholar
  3. 3.
    J. S. Thorp and T. G. Bushell, J. Mater. Sci. 20: 2265 (1985).Google Scholar
  4. 4.
    A. K. Maitra and K. K. Phani, J. Mater. Sci. 29: 4415 (1994).Google Scholar
  5. 5.
    K. K. Phani, J. Mater. Sci. 31: 272 (1996).Google Scholar
  6. 6.
    E. A. Dean, J. Am. Ceram. Soc. 66: 847 (1983).Google Scholar
  7. 7.
    A. R. Boccaccini, G. Ondracek, P. Mazilu, and D. Windelberg, J. Mech. Behav. Mater. 4: 119 (1993).Google Scholar
  8. 8.
    K. K. Phani, Am. Ceram. Soc. Bull. 65: 1584 (1986).Google Scholar
  9. 9.
    R. C. Rossi, J. Am. Ceram. Soc. 51: 433 (1968).Google Scholar
  10. 10.
    J. C. Wang. J. Mater. Sci. 19: 809 (1984).Google Scholar
  11. 11.
    R. W. Rice, in Treatise on Materials Science and Technology, Vol. 11, R. K. McCrone, ed. (1977), pp. 199–381.Google Scholar
  12. 12.
    A. S. Wagh, J. P. Singh, and R. B. Poeppel, J. Mater. Sci. 28: 3589–3593 (1993).Google Scholar
  13. 13.
    P. Mazilu and G. Ondracek, in Thermal Effects in Fracture of Multiphase Materials, Proc. Euromech Colloquium 255,K. Herrman and Z. Olesiak, eds. (Springer Verlag, Heidelberg, Tokyo, New York, 1989), pp. 214–230.Google Scholar
  14. 14.
    G. Ondracek, Rev. Powder Metall. Phys. Ceram. 3: 205 (1987).Google Scholar
  15. 15.
    A. R. Boccaccini, G. Ondracek, and O. Postel, Silic. Indust. 59: 295–299 (1994).Google Scholar
  16. 16.
    A. R. Boccaccini and G. Ondracek, in Proc. IUTAM Symposium on Microstructure-Property Interactions in Composite Materials, R. Pyrz, ed. (Aalborg, Denmark, August 1994), pp. 23–25 (Kluwer Academic Publishers, 1995), pp. 27-38.Google Scholar
  17. 17.
    N. Ramakrishnan and V. S. Arunachalam, J. Am. Ceram. Soc. 76: 2745–2752 (1993).Google Scholar
  18. 18.
    R. W. Zimmerman, Mech. Mater. 12: 237–247 (1991).Google Scholar
  19. 19.
    M. Arnold, A. R. Boccaccini, and G. Ondracek, J. Mat. Sci. 31: 1643–1646 (1996).Google Scholar
  20. 20.
    A. R. Boccaccini, J. Am. Ceram. Soc. 77: 2779–2781 (1994).Google Scholar
  21. 21.
    N. Ramakrishnan, J. Am. Ceram. Soc. 77: 2782 (1994).Google Scholar
  22. 22.
    R. W. Rice, J. Mater. Sci. 31: 1509–1528 (1996).Google Scholar
  23. 23.
    Engineered Materials Handbook, Vol. 4, Ceramics and Glasses, (ASM International, 1991), p. 30.Google Scholar
  24. 24.
    Materials Science and Technology, Vol. 11: Structure and Properties of Ceramics,M. Swain Vol. ed. (VCH Weinheim, New York, Basel, Cambridge, Tokyo, 1994), p. 777.Google Scholar
  25. 25.
    T. Shields, personnal communication (1996).Google Scholar
  26. 26.
    H. Salmang and H. Scholze, Keramik, Teil 1(Springer Verlag, Berlin-Heidelberg, 1982) p. 231.Google Scholar
  27. 27.
    Materials Science and Technology, Vol. 8: Structure and Properties of Nonferrous Alloys,K. H. Matucha, Vol. ed. (VCH Weinheim, New York, Basel, Cambridge, Tokyo, 1994), p. 600.Google Scholar
  28. 28.
    J. P. Panakkal, H. Willems, and W. Arnold, J. Mater. Sci. 25: 1397–1402 (1990).Google Scholar

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • Dino N. Boccaccini
    • 1
  • Aldo R. Boccaccini
    • 2
  1. 1.Facultad Regional San RafaelUniversidad Tecnológica NacionalSan RafaelArgentina
  2. 2.Fachgebiet WerkstofftechnikTechnische Universität IlmenauIlmenauGermany

Personalised recommendations