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A note on the problem of the penny-shaped crack

Published online by Cambridge University Press:  24 October 2008

Ian N. Sneddon
Ian N. Sneddon
Affiliation:
University of Glasgow
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Extract

1. The problem of determining the distribution of stress in the neighbourhood of a penny-shaped crack defined in terms of cylindrical coordinates (ρ, φ, z) by 0 ≤ ρ ≤ α, z = 0, has been considered by Sneddon ((2)) and Sack ((1)). In the latter paper the solution is derived only in the case in which the stress field is due to the application of constant pressure to the faces of the crack. In the former paper the analysis given applies to an axisymmetric distribution of pressure p(ρ) applied to both the upper and lower face of the penny-shaped cavity, but the calculation of the stress intensity factor

and of the energy W required to open up the crack is a complicated matter even in the case in which p(ρ) is a constant.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 61 , Issue 2 , April 1965 , pp. 609 - 611
Copyright
Copyright © Cambridge Philosophical Society 1965

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References

REFERENCES

(1)Sack, R. A.Extension of Griffith's theory of rupture to three dimensions. Proc. Phys. Soc. 58 (1946), 729.Google Scholar
(2)Sneddon, I. N.The distribution of stress in the neighbourhood of a crack in an elastic solid. Proc. Roy. Soc. Ser. A, 187 (1946), 229.Google Scholar
(3)Sneddon, I. N.The elementary solution of dual integral equations. Proc. Glasgow Math. Ass. 4 (1960), 108.Google Scholar
(4)Sneddon, I. N.Fourier transforms (McGraw-Hill; New York, 1951).Google Scholar
(5)Titchmarsh, E. C.Introduction to the theory of Fourier integrals (Oxford, 1937).Google Scholar