Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-26T15:33:43.507Z Has data issue: false hasContentIssue false
  • English
  • Français

Surface flaw distributions in brittle materials and Hertzian fracture

Published online by Cambridge University Press:  03 March 2011

P.D. Warren ,
D.A. Hills  and
S.G. Roberts
P.D. Warren
Affiliation:
Department of Materials, Oxford University, Parks Road, Oxford OXI 3PH, England
D.A. Hills
Affiliation:
Department of Engineering Science, Oxford University, Oxford OXI 3PJ, England
S.G. Roberts
Affiliation:
Department of Materials, Oxford University, Parks Road, Oxford OXI 3PH, England
Get access

Abstract

Refined mode I and mode II stress intensity factors for short cracks perpendicular to a free surface driven by a Hertzian indenter have been calculated for the case where the sphere and substrate are made of the same material. Computer simulations of Hertzian indentation tests for a variety of random surface flaw distributions show that the ring crack is expected to form outside the contact radius in all cases and that for spheres of small radii, the fracture load is expected to be proportional to the sphere radius (Auerbach's law). Reconstruction of the surface flaw distribution using the “searched area” concept is described. A useful analytical approximation for the stress intensity factors is also presented.

Type
Articles
Information
Journal of Materials Research , Volume 9 , Issue 12 , December 1994 , pp. 3194 - 3202
Copyright
Copyright © Materials Research Society 1994

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1Zeng, K., Breder, K., Rowcliffe, D. J., and Herrstrom, C., J. Mater. Sci. 27, 3789 (1992).CrossRefGoogle Scholar
2Zeng, K., Breder, K., and Rowcliffe, D. J., Acta Metall. Mater. 40, 2595 (1992).CrossRefGoogle Scholar
3Zeng, K., Breder, K., and Rowcliffe, D. J., Acta Metall. Mater. 40, 2601 (1992).CrossRefGoogle Scholar
4Argon, A. S., Proc. R. Soc. London A250, 482 (1959).Google Scholar
5Oh, H. L. and Finnie, I. J., J. Mech. Phys. Solids 15, 401 (1967).CrossRefGoogle Scholar
6Matthews, J. R., McClintock, F. A., and Shack, W. J., J. Am. Ceram. Soc. 59, 305 (1976).CrossRefGoogle Scholar
7Wilshaw, T. R., J. Phys. D: Appl. Phys. 4, 1567 (1971).CrossRefGoogle Scholar
8Hertz, H., Zeitschrift fiir die Reine und Angewandte Mathematik 92, 156–171 (1881); English translation in Miscellaneous Papers, translated by Jones, D. E. and Schott, G. A. (Macmillan, London, U.K., 1896), pp. 146–162.Google Scholar
9Spence, D. A., J. Elasticity 5, 297 (1975).CrossRefGoogle Scholar
10Timoshenko, S. P. and Goodier, J. N., Theory of Elasticity, 3rd ed. (McGraw-Hill, New York, 1951), pp. 409–414.Google Scholar
11Huber, M. T., Ann. Phys. 14, 153 (1904).CrossRefGoogle Scholar
12Frank, F. C. and Lawn, B. R., Proc. R. Soc. London A229, 291 (1967).Google Scholar
13Warren, R., Acta Metall. 26, 1759 (1978).CrossRefGoogle Scholar
14Mouginot, R. and Maugis, D., J. Mater. Sci. 20, 4354 (1985).CrossRefGoogle Scholar
15Finnie, I., Dolev, D., and Khatibloo, M., J. Eng. Mat. Tech. 103, 183 (1981).CrossRefGoogle Scholar
16Nowell, D. and Hills, D. A., J. Strain Anal. 22, 177 (1987).CrossRefGoogle Scholar
17Auerbach, F., Ann. Phys. Chem. 43, 61 (1891).CrossRefGoogle Scholar