Journal of Materials Science

, Volume 22, Issue 1, pp 257–263 | Cite as

Young's modulus of porous brittle solids

  • K. K. Phani
  • S. K. Niyogi


A new equationE =E0 (1 −aP) n whereE andE0 are the Young's moduli at porosity,P, and zero, respectively, a andn are material constants, has been derived semi-empirically for describing the porosity dependence of Young's modulus of brittle solids. The equation satisfies quite well the exact theoretical solution for the values of Young's moduli at different porosities for model systems with ideal and non-ideal packing geometry. The equation shows excellent agreement with the data Onα- andβ-alumina over a wide range of porosity. Unlike the existing porosity-elastic modulus equations, the proposed equation satisfies the boundary conditions and is inherently capable of treating isometric closed pores as well as non-isometric interconnected pores. The parameters a and n provide information about the packing geometry and pore structure of the material.


Polymer Boundary Condition Porosity Brittle Pore Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R. M. Spriggs,J. Amer. Ceram. Soc. 44 (1961) 628.Google Scholar
  2. 2.
    F. P. Knudsen,ibid. 45 (1962) 94.Google Scholar
  3. 3.
    I. Soroka andP. J. Sereda,ibid. 51 (1968) 337.Google Scholar
  4. 4.
    R. D. Carnahan,ibid. 51 (1968) 223.Google Scholar
  5. 5.
    D. F. Porter, A S. Reed andDavid Lewis III,ibid. 60 (1977) 345.Google Scholar
  6. 6.
    D. P. H. Hasselman,ibid. 45 (1962) 452.Google Scholar
  7. 7.
    J. C. Wang,J. Mater. Sci 19 (1984) 801.Google Scholar
  8. 8.
    R. L. Coble andW. D. Kingery,J. Amer. Ceram. Soc. 39 (1956) 377.Google Scholar
  9. 9.
    J. R. G. Evans, R. Stevens andS. R. Tan,Trans. J. Brit. Ceram. Soc. 83 (1984) 43.Google Scholar
  10. 10.
    K. K. Schiller, in “Mechanical Properties of Non-Metallic Brittle Materials”, edited by W. H. Walton (Butterworth, London, 1958) p. 35.Google Scholar
  11. 11.
    F. P. Knudsen,J. Amer. Ceram. Soc. 42 (1959) 376.Google Scholar
  12. 12.
    J. B. Wachtman Jr, W. E. Tefft, D. G. Lam Jr andR. P. Stinchfield,J. Res. Nat. Bur. Stand. 64A (1960) 213.Google Scholar
  13. 13.
    David Lweis III,Ceram. Bull. 57 (1978) 434.Google Scholar
  14. 14.
    W. H. Duckworth, J. K. Johnston, L. R. Jackson andH. Z. Schofield, “Mechanical properties of Ceramic Bodier”, Rand Report No. R-209, Bottelle Memorial Institute, Columbus, Ohio (1950).Google Scholar
  15. 15.
    R. M. Spriggs andT. Vasilos, “Effect of grain size and porosity on transverse bend strength and elastic modulus of hot pressed alumina and magnesia”, paper presented at the Sixty Third Annual Meeting, The American Ceramic Society, Toronto, Ontario, Canada, 24 April (1961).Google Scholar
  16. 16.
    S. M. Lang, “Properties of High-temperature ceramics and cermets — Elasticity and Density at Room Temperature”, National Bureau of Standards Monograph no. 6 (NBS, Washington, 1960) p. 45.Google Scholar
  17. 17.
    H. Z. Schofield, J. F. Lynch andW. H. Duckworth, “Fundamental Studies of Ceramic Materials”, Final Summary Report, Bottelle Memorial Institute Report to office of Naval Research, Navy Dept. Contract No. N5 ORL - 111, 31 March (1949).Google Scholar
  18. 18.
    B. L. Majumder,Trans. Indian Ceram. Soc. 11 (1952) 168.Google Scholar
  19. 19.
    D. H. Chung, “Elastic and Anelastic Properties of Fine Grained Polycrystalline Alumina at Elevated Temperatures”, Bulletin of Research Department, Monthly Report No. 297, State University of New York College of Ceramics at Alfred University March (1961).Google Scholar
  20. 20.
    J. K. Mackenzie,Proc. Phys. Soc. (London) 63B (1950) 2.Google Scholar
  21. 21.
    D. P. H. Hasselman andR. M. Fulrath,J. Amer. Ceram. Soc. 47 (1964) 52.Google Scholar
  22. 22.
    K. K. Phani, S. K. Niyogi, A. K. Maitra andM. Roy Choudhury,J. Mater. Sci. 21 (1986) 4335.Google Scholar

Copyright information

© Chapman and Hall Ltd. 1987

Authors and Affiliations

  • K. K. Phani
    • 1
  • S. K. Niyogi
    • 1
  1. 1.Central Glass and Ceramic Research InstituteCalcuttaIndia

Personalised recommendations