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The Initiation and Propagation of Hertzian Ring Cracks

  • I. Finnie
  • S. Vaidyanathan
Part of the Fracture Mechanics of Ceramics book series (FMOC, volume 1)

Abstract

After a brief review of the literature it is concluded that the Wei bull probabalistic treatment of brittle strength explains, very adequately, the condition under which Hertzian ring cracks initiate on glass surfaces. The case of cracking produced by a flat cylindrical punch is also considered and is compared with that due to a sphere. It is shown that ring cracking data obtained with a punch, or less conveniently with a sphere, may be used to deduce the parameters of the Weibull strength distribution.

Once a ring crack is formed in a brittle solid, its subsequent propagation under increasing load should, in principle, be predictable from the procedures of linear elastic fracture mechanics. Some observations are reported on crack trajectories which together with a finite element solution for the stress field enable the fracture toughness of glass to be estimated. A comparison is made of this approach and an approximate solution in the literature based on an energy method.

Keywords

Fracture Toughness Linear Elastic Fracture Mechanic Fracture Load Spherical Indenter Weibull Parameter 
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.

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References

  1. 1.
    H. Hertz “Collected Works” (Leipzig Barth 1882 ) Vol. 1, p. 174Google Scholar
  2. 2.
    F. Auerbach, Annln Physik and Chemie, 43, 61, (1891)CrossRefGoogle Scholar
  3. 3.
    W. Weibull, Ingvetenskakad Handl. (Stockholm) Nos 149, 151, 153, (1939)Google Scholar
  4. 4.
    H. L. Oh, I. Finnie, J. Mech. Phys. Solid, 15, 401, (1967)CrossRefGoogle Scholar
  5. 5.
    H. L. Oh, I. Finnie, Int. J. Fract. Mech., 6 287, (1970)Google Scholar
  6. 6.
    K. P. L. Oh, I. Finnie, Int. J. Fract. Mech., 6, 333, (1970)Google Scholar
  7. 7.
    J. P. A. Tillet, Proc. Phys. Soc., B69, 47, 1956.CrossRefGoogle Scholar
  8. 8.
    F. C. Roesler, Proc. Phys. Soc., B69, 55, (1956)CrossRefGoogle Scholar
  9. 9.
    O. L. Anderson, In “Fracture” (edited by B. L. Averbach, D. K. Felbeck, G. T. Hahn and D. A. Thomas) MIT press 1959Google Scholar
  10. 10.
    F. C. Frank, B. R. Lawn, Proc. Roy. Soc. (London) 299A, 291, (1967)Google Scholar
  11. 11.
    G. I. Barenblatt, In Advances in Applied Mechanics (H. L. Dryden and T. von Karman editors) 79 55, 1962.Google Scholar
  12. 12.
    T. R. Wilshaw, J. Physics D: Appl. Phys., 4, 1567, (1971)CrossRefGoogle Scholar
  13. 13.
    B. Hamilton, H. Rawson, J. Mech. Phys. Solids, 18 9 127 (1970)CrossRefGoogle Scholar
  14. 14.
    Y. M. Tsai, H. Kolsky, J. Mech. Phys. Solids, 15, 29, (1967)CrossRefGoogle Scholar
  15. 15.
    J. W. Harding, I. N. Sneddon, Proc. Cambridge Phil. Soc. 41, 16, (1945)Google Scholar
  16. 16.
    E. Y. Robinson, I. Finnie, Proc. 1969 Colloque de Geotechnique, Toulouse, Franoe (pub. by INSA Toulouse )Google Scholar
  17. 17.
    K. P. L. Oh, “On the Statistical Nature of Brittle Fracture”, Ph.D. thesis in Mechanical Eng., University of California (Berkeley) 1970Google Scholar
  18. 18.
    F. C. Roesler, Proc. Phys. Soc., 69B, 981, (1956)Google Scholar
  19. 19.
    F. Erdogan, G. C. Sih, Trans. ASME, J. Basic Eng., 85D, 519, (1963)Google Scholar
  20. 20.
    B. Cotterell, Int. J. Fract. Mech. 1, 96, (1965)Google Scholar
  21. 21.
    J. F. Kalthoff, Int. J. Fract. Mech., 7, 478, (1971).Google Scholar
  22. 22.
    A. Saith, “On the Stability and Arrest of Cracks”, Ph.D. thesis in Mechanical Eng., University of California (Berkeley ) 1973Google Scholar
  23. 23.
    K. R. Linger, D. G. Holloway, Phil. Mag., 18, 1269, (1968)CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1974

Authors and Affiliations

  • I. Finnie
    • 1
  • S. Vaidyanathan
    • 1
  1. 1.Department of Mechanical EngineeringUniversity of California at BerkeleyUSA

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