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Some basic properties of penny-shaped cracks

Published online by Cambridge University Press:  26 February 2010

A. F. Emery  and
F. W. Smith
A. F. Emery
Affiliation:
Department of Mechanical Engineering, University of Washington, Seattle, Washington.
F. W. Smith
Affiliation:
Department of Mechanical Engineering, Colorado State University, Fort Collins, Colorado.
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Abstract

The problem of a penny-shaped crack which is totally embedded in an isotropic material is treated by the theory of linear elasticity. It is shown that for a prescribed crack surface displacement due to compressive stresses on the surface, stress singularities of order higher than the usual inverse square root are possible. It is also demonstrated that for all physically admissible crack surface stresses the singularity can only be of the inverse square root order and that the shape of the crack tip must be elliptical.

Type
Research Article
Information
Mathematika , Volume 13 , Issue 2 , December 1966 , pp. 172 - 180
Copyright
Copyright © University College London 1966

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References

1. Sneddon, I. N. and , D. S. Berry, “Classical theory of elasticity”, Handbuch Der Physik, VI. Elastizität und Plastizät.Google Scholar
2. Deutsch, E., “Axially symmetric crack problem for an infinite elastic medium with transverse isotropy (displacement presented)”, Archiwum Mechaniki Stosowanej, 16 (1964).Google Scholar
3. Irwin, G. R., “Crack extension force for a part-through crack in a plate”, ASME Paper 62-WA-13. 1962.Google Scholar
4. Smith, F. W., Kobayashi, A. S., and Emery, A. F., “Stress intensity factors for pennyshaped cracks, Part I: Infinite solid”, submitted to ASME, Journal of Applied Mechanics.Google Scholar