Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-25T14:48:00.407Z Has data issue: false hasContentIssue false
  • English
  • Français

A circular disc containing a radial edge crack opened by a constant internal pressure

Published online by Cambridge University Press:  24 October 2008

R. D. Gregory
R. D. Gregory
Affiliation:
University of Manchester
Get access Rights & Permissions [Opens in a new window]

Abstract

A circular disc of radius a, made of homogeneous, isotropic, linearly elastic material, contains a radial edge crack of length b(0 < b < 2a). The disc is in equilibrium in a state of generalized plane stress caused by loading the faces of the crack by a constant internal pressure. The problem of determining the resulting stress field throughout the disc is solved analytically in closed form. The principal results are that the stress concentration factor at the crack tip, the total strain energy W, and the opening U at the mouth of the crack, are given exactly by

where A is a constant whose value correct to 6 significant figures is

and , W0, U0 are normalising factors defined in section 6.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 81 , Issue 3 , May 1977 , pp. 497 - 521
Copyright
Copyright © Cambridge Philosophical Society 1977

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

(1)Benthem, J. P. and Koiter, W. T. Asymptotic approximations to crack problems. Chapter 3 of (9).Google Scholar
(2)Cardew, G. E. and Howard, I. C.An edge crack in an elastic strip and related problems in fracture mechanics and viscous flow. Int. J. Engng Sci. 14 (1976), 403–414.CrossRefGoogle Scholar
(3)Coker, E. G. and Filon, L. N. G.A treatise on photoelasticity, 2nd ed. (Cambridge University Press, 1957).Google Scholar
(4)Gurtin, M. E. The linear theory of elasticity. Handbuch der Physik 6a/3 (Springer-Verlag, 1972).Google Scholar
(5)Jeffery, G. B.Plane stress and plane strain in bi-polar co-ordinates. Phil. Trans. Roy. Soc. A 221 (1921), 265–293.Google Scholar
(6)Keer, L. M. and Freedman, J. M.Tensile strip with edge cracks. Int. J. Engng Sci. 11 (1973), 1265–1275.CrossRefGoogle Scholar
(7)Knowles, J. K. and Pucik, T. A.Uniqueness for plane crack problems in linear elastostatics. J. of Elast. 3 (1973), 155–160.CrossRefGoogle Scholar
(8)Noble, B.Methods based on the Wiener-Hopf technique (Pergamon Press, 1958).Google Scholar
(9)Sih, G. C. (Ed.) Methods of analysis and solutions of crack problems (Noordhoff, 1973).CrossRefGoogle Scholar
(10)Sneddon, I. N.Fourier transforms (McGraw-Hill, 1951).Google Scholar
(11)Sneddon, I. N. and Das, S. C.The stress intensity factor at the tip of an edge crack in an elastic half-plane. Int. J. Engng Sci. 9 (1971), 25–36.CrossRefGoogle Scholar
(12)Sokolnikoff, I. S.Mathematical theory of elasticity (McGraw-Hill, 1956).Google Scholar
(13)Stallybrass, M. P.A crack perpendicular to an elastic half-plane, Int. J. Engng Sci. 8 (1970), 351–362.CrossRefGoogle Scholar
(14)Tweed, J. and Rooke, D. P.The stress intensity factor of an edge crack in a finite elastic disc. Int. J. Engng Sci. 11 (1973), 65–73.CrossRefGoogle Scholar
(15)Williams, M. L.On the stress distribution at the base of a stationary crack. J. Appl. Mech. (Trans. A.S.M.E., Ser. E) 24 (1957), 109–114.CrossRefGoogle Scholar