Skip to main content
SpringerLink
Log in

Porosity dependence of mechanical properties of solid materials

  • Published:
Journal of Materials Science Aims and scope Submit manuscript

Abstract

The generalized means are used as a simple but elegant mixture rule for providing a unified description of the physical properties of polyphase composites in terms of component properties, volume fractions, and microstructures. This formula is named as the generalized mixture rule (GMR). Taking porous materials as a special class of two-phase composites in which pores are dispersed within a solid framework, the GMR yields a rigorous expression for the porosity dependence of the mechanical properties. Although the GMR is purely mathematical in origin, its connection to the existing theories and its consistence with extensive experimental data suggests that it should have some physical validity as a hypothesis or at least a very handy tool for a general description of the mechanical properties of multiphase materials including porous solids.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S. JI, Mater. Sci. Eng. A366 (2004) 195.

    CAS  Google Scholar 

  2. Idem., J. Geophyis. Res. 109 (2004) DOI: 10.1029/2004JB003124.

  3. R. HILL, J. Mech. Phys. Solids 13 (1965) 213.

    Google Scholar 

  4. A. E. EINSTEIN, Ann. Phys. Lpz. 19 (1906) 289.

    CAS  Google Scholar 

  5. R. BR. ROSCOE, J. Appl. Phys. 3 (1952) 367.

    Google Scholar 

  6. S. K. HYUN, K. MURAKAMI and H. NAKAJIMA, Mater. Sci. Eng. A299 (2001) 241.

    CAS  Google Scholar 

  7. T. ICHITSUBO, M. TANE,H. OGI, M. HIRAO, T. IKEDA and H. NAKAJIMA, Acta Mater. 50 (2002) 4105.

    Article  CAS  Google Scholar 

  8. J. C. RUSS, “Practical Stereology” (Plenum Press, New York, 1986).

    Google Scholar 

  9. L. F. NIELSEN, Mater. Sci. Eng. 52 (1982) 39.

    Google Scholar 

  10. P. BEISS and M. DALGIC, Mater. Chem. Phys. 67 (2001) 37.

    CAS  Google Scholar 

  11. M. EUDIER, Power Metal. 9 (1962) 278.

    Google Scholar 

  12. B. PAUL, Trans. Meta. Soc. AIME 218 (1960) 36.

    CAS  Google Scholar 

  13. L. J. GIBSON and M. F. ASHBY, “Cellular Solids: Structure & Properties” (Pergamon, Oxford, 1988).

    Google Scholar 

  14. R. W. RICE, “Porosity of Ceramics” (Marcel Dekker Inc., New York, 1998).

    Google Scholar 

  15. M. Y. BALSHIN, Akad. Sci. USSR 67 (1949) 831.

    CAS  Google Scholar 

  16. P. WONG, J. KOPLIK and J. P. TOMANIC, Phys. Rev. B30 (1984) 6606.

    Google Scholar 

  17. A. S. WAGH, R. B. POEPPEL and J. P. SINGH, J. Mater. Sci. 26 (1991) 3862.

    Article  CAS  Google Scholar 

  18. R. HAYNES, Powder Metall. 14 (1971) 64.

    Google Scholar 

  19. T. J. GRIFFITHS, R. DAVIES and M. B. BASSETT, ibid. 3 (1979) 119.

    Google Scholar 

  20. K. K. PHANI, Am. Ceram. Soc. Bull. 65 (1986) 1584.

    CAS  Google Scholar 

  21. A. R. BOCCACINI, G. ONDRACEK and E. MOMBELLO, Mater. Sci. Lett. 14 (1995) 534.

    Google Scholar 

  22. K. S. BLANKS, A. KRISTOFFERSSON, E. CARLSTROM and W. J. CLEGG, J. Europ. Ceram. Soc. 18 (1998) 1945.

    Article  CAS  Google Scholar 

  23. R. W. RICE, J. Mater. Sci. 32 (1997) 4731.

    CAS  Google Scholar 

  24. F. P. KNUDSEN, J. Am. Ceram. Soc. 42 (1959) 376.

    CAS  Google Scholar 

  25. R. W. RICE, “Treatise on Materials Science and Technology. Properties and Microstructures” Vol. 11 (Academic Press, New York, 1977) p. 199.

    Google Scholar 

  26. W. H. DUCKWORTH, J. Am. Ceram. Soc. 34 (1951) 1.

    Google Scholar 

  27. R. M. SPRIGGS, J. Ceram. Soc. 44 (1961) 628.

    CAS  Google Scholar 

  28. N. RAMAKRISHNAN and V. S. ARUNACHALAM, J. Am. Ceram. Soc. 76 (1993) 2745.

    Article  CAS  Google Scholar 

  29. R. MCLAUGHLIN, Int. J. Eng. Sci. 15 (1977) 237.

    Article  Google Scholar 

  30. A. N. NORRIS, Mech. Mater. 4 (1985) 1.

    Article  Google Scholar 

  31. W. ZIMMERMAN, ibid. 12 (1991) 17.

    Article  Google Scholar 

  32. D. P. HASSELMAN, J. Am. Ceram. Soc. 45 (1962) 452.

    CAS  Google Scholar 

  33. Z. HASHIN, Ceram. Microstr. 14 (1968) 313.

    Google Scholar 

  34. R.ROSSI, J. Am. Ceram. Soc. 51 (1968) 433.

    Google Scholar 

  35. J. M. LEDERMAN, J. Appl. Polymer Sci. 15 (1971) 693.

    CAS  Google Scholar 

  36. A. N. GENT and A. G. THOMAS, J. Appl. Polymer Sci. 1 (1959) 107.

    CAS  Google Scholar 

  37. L. J. GIBSON and M. F. ASHBY, Proc. R. Soc. Lond. A382 (1982) 43.

    Google Scholar 

  38. N. RAMAKRISHNAN and S. ARUNACHALAM, J. Mater. Sci. 25 (1990) 3930.

    Article  Google Scholar 

  39. O. ISHAI and L. J. COHEN, Int. J. Mech. Sci. 9 (1967) 539.

    Article  Google Scholar 

  40. D. STAUFFER and A. AHARONY, “Introduction to Percolation Theory” (Taylor and Francis, London, 1992).

    Google Scholar 

  41. J. KOVACIK, J. Mater. Sci. Lett. 18 (1999) 1007.

    CAS  Google Scholar 

  42. F. P. KNUDSEN, J. Am. Ceram. Soc. 45 (1962) 94.

    CAS  Google Scholar 

  43. R. M. SPRIGGS, ibid. 45 (1962) 454.

    CAS  Google Scholar 

  44. C. REYNAUD, F. THEVENOT, T. CHARTIER and J. L. BESSON, J. Eur. Ceram. Soc. 25 (2005) in press.

  45. D. F. PORTER, J. S. REED and D. LEWIS III, J. Am. Cer. Soc. 60 (1977) 345.

    CAS  Google Scholar 

  46. J. B. WALSH, W. F. BRACE and A. W. ENGLAND, ibid. 48 (1965) 605.

    CAS  Google Scholar 

  47. Z. HASHIN and S. SHTRIKMAN, J. Mech. Phys. Solids 11 (1963) 127.

    Google Scholar 

  48. B. BUDIANSKY, J. Mech. Phys. Solids 13 (1965) 223.

    Google Scholar 

  49. J. G. BERRYMAN, J. Energy Resour. Tech. 116 (1994) 87.

    Google Scholar 

  50. M. P. CLEARY, I. W. CHEN and S. M. LEE, J. Eng. Mech. 106 (1980) 861.

    Google Scholar 

  51. O. ISHAI and L. J. COHEN, J. Comp. Mater.2 (1968) 302.

    CAS  Google Scholar 

  52. T. KATHRINA, R. ROUND and B. BRIDGE, J. Phys. D: Appl. Phys. 24 (1991) 1673.

    Article  CAS  Google Scholar 

  53. W. Z. SHAO, V. V. IVANOV, L. ZHEN, Y. S. CUI and D. Z. YANG, J. Mater. Sci. 39 (2004) 731.

    CAS  Google Scholar 

  54. P. A. BERGE, B. P. BONNER and J. G. BERRYMAN, Geophysics 60 (1995) 108.

    Article  Google Scholar 

  55. C. H. WEAVER, R. G. BUTTERS and J. A. LUND, Inter. J. Powder Metall. 8 (1972) 3.

    CAS  Google Scholar 

  56. T. KRANTZ, Int. J. Powder Metall. 5 (1969) 35.

    CAS  Google Scholar 

  57. R. M. GERMAN, Inter. J. Powder Metall. Tech. 13 (1977) 259.

    CAS  Google Scholar 

  58. T. E. MATIKAS, P. KARPUR and S. SHAMASUNDAR, J. Mater. Sci. 32 (1997) 1099.

    Article  CAS  Google Scholar 

  59. S. JI, Q. WANG and B. XIA, “Handbook of Seismic Properties of Minerals, Rocks and Ores” (Polytechnic International Press, Montreal, 2002).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Département des Génies Civil, Géologique et des Mines, École Polytechnique de Montréal, Montréal, H3C 3A7, Canada

    Shaocheng Ji & Qi Gu

  2. Laboratory of Marginal Sea Geology, Guangzhou Institute of Geochemistry, Chinese Academy of Sciences, Wushan, Guangzhou, 510640, China

    Bin Xia

Authors
  1. Shaocheng Ji
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qi Gu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bin Xia
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shaocheng Ji.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ji, S., Gu, Q. & Xia, B. Porosity dependence of mechanical properties of solid materials. J Mater Sci 41, 1757–1768 (2006). https://doi.org/10.1007/s10853-006-2871-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10853-006-2871-9

Keywords

Search

Navigation