Advertisement

Journal of Materials Science

, Volume 32, Issue 21, pp 5653–5659 | Cite as

Elastic-plastic indentation stress fieldsusing the finite-element method

  • G CARE
  • A. C FISCHER-CRIPPS
Article

Abstract

The finite-element method is used to model the elastic-plastic indentation response of a flat extensive specimen for the case of a spherical indenter. The work highlights several interesting finite-element modelling techniques and provides insight into the physical processes involved in elastic-plastic indentation of certain structural ceramics. Full details of the stress distribution are given and compared with the results of elastic formulae. This work has particular application to the modelling of physical phenomena of deformation in ceramic materials in machining, wear, bearings and hardness testing.

Keywords

Contact Pressure Plastic Zone Penalty Factor Load Increment Specimen Material 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    H. HERTZ, J. Reine Angew. Math. 92 (1881) 156.Google Scholar
  2. 2.
    Idem., in "Hertz's miscellaneous papers' Macmillan, London, 1896) Chapter 5. (translation and reprint in English of [1]).Google Scholar
  3. 3.
    F. AUERBACH, Ann. Phys. Chem. (Leipzig) 43 (1891) 61.CrossRefGoogle Scholar
  4. 4.
    Idem., in “Miscellaneous documents of the House of Representatives for the First Session of the Fifty-Second Congress”, Vol. 43 (18911892) (Government Printing Office, Washington DC) p. 207.Google Scholar
  5. 5.
    R. HILL, E. H. LEE and S. J. TUPPER, Proc. R. Soc. A 188 (1947) 273.CrossRefGoogle Scholar
  6. 6.
    R. HILL, “The mathematical theory of plasticity” (Clarendon, Oxford, 1950).Google Scholar
  7. 7.
    D. M. MARSH, Proc. R. Soc. A 279 (1964) 420.CrossRefGoogle Scholar
  8. 8.
    L. E. SAMUELS and T. O. MULHEARN, J. Mech. Phys. Solids 5 (1957) 125.CrossRefGoogle Scholar
  9. 9.
    T. O. MULHEARN, ibid. 7 (1959) 85.CrossRefGoogle Scholar
  10. 10.
    K. L. JOHNSON, J. ibid. 18 (1970) 115.CrossRefGoogle Scholar
  11. 11.
    M. C. SHAW and D. J. DESALVO, Trans. ASME 92 (1970) 469.Google Scholar
  12. 12.
    Idem., ibid. 92 (1970) 480.CrossRefGoogle Scholar
  13. 13.
    M. V. SWAIN and J. T. HAGAN, J. Phys. D 9 (1976) 2201.CrossRefGoogle Scholar
  14. 14.
    C. M. PERROTT, Wear 45 (1977) 293.CrossRefGoogle Scholar
  15. 15.
    S. S. CHIANG, D. B. MARSHALL and A. G. EVANS, J. Appl. Phys. 53 (1982) 298.CrossRefGoogle Scholar
  16. 16.
    Idem., ibid. 53 (1982) 312.CrossRefGoogle Scholar
  17. 17.
    K. L. JOHNSON, “Contact mechanics” (Cambridge University Press, Cambridge, 1985).CrossRefGoogle Scholar
  18. 18.
    D. G. GROSSMAN, J. Amer. Ceram. Soc. 55 (1972) 446.CrossRefGoogle Scholar
  19. 19.
    H. CAI, M. A. STEVENS KALCEFF and B. R. LAWN, J. Mater. Res. 9 (1994) 762.CrossRefGoogle Scholar
  20. 20.
    A. C. FISCHER-CRIPPS, J. Mater. Sci. (1996) in press.Google Scholar
  21. 21.
    M. BARQUINS and D. MAUGIS, J. Mec. Theori. Appl. 1 (1982) 331.Google Scholar
  22. 22.
    K. W. MAN, “Contact mechanics using boundary elements” (Computational Mechanics Publications, Southampton, Hants., 1994).Google Scholar
  23. 23.
    O. C. ZIENKIEWICZ and Y. K. CHEUNG, “The finite element method in structural and continuum mechanics” (McGraw-Hill, London, 1967).Google Scholar
  24. 24.
    S. R. WILLIAMS, “Hardness and hardness measurements” (American Society for Metals, Cleveland, OH, 1942).Google Scholar
  25. 25.
    C. HARDY, C. N. BARONET and G. V. TORDION, Int. J. Numer. Methods Engng 3 (1971) 451.CrossRefGoogle Scholar
  26. 26.
    P. S. FOLLANSBEE and G. B. SINCLAIR, Int. J. Solids Struct. 20 (1981) 81.CrossRefGoogle Scholar
  27. 27.
    R. HILL, B. STORAKERS and A. B. ZDUNEK, Proc. R. Soc. A 423 (1989) 301.CrossRefGoogle Scholar
  28. 28.
    K. KOMVOPOULOS, Trans. ASME 111 (1988) 477.CrossRefGoogle Scholar
  29. 29.
    Idem. ibid. 111 (1989) 430.CrossRefGoogle Scholar
  30. 30.
    A. C. FISCHER-CRIPPS and R. E. COLLINS, J. Mater. Sci. 29 (1994) 2216CrossRefGoogle Scholar

Copyright information

© Chapman and Hall 1997

Authors and Affiliations

  • G CARE
    • 1
  • A. C FISCHER-CRIPPS
    • 1
  1. 1.Department of Applied PhysicsUniversity of Technology SydneyBroadway, NSWAustralia

Personalised recommendations