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On some two-dimensional cracks in linear isotropic elasticity

Published online by Cambridge University Press:  09 April 2009

D. L. Clements
D. L. Clements
Affiliation:
Department of Applied Mathematics, University of Western Ontario, London, Canada
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In this paper the method of conformal transformation is used to consider a class of crack problem in linear isotropic elasticity. The conformal transformation used is the Joukowski transformation so that in general the crack profile is an aerofoil. This is a useful profile to consider since as well as providing information about the general aerofoil crack it includes as special cases the circular arc crack, the straight line crack and, as will be shown, can also be used to obtain similar results to those obtained by Bowie (1956) for the crack originating at the boundary of a circular hole. Thus by varying the parameters in the one elastic solution it is possible to obtain the elastic solution for a number of crack profiles. An examination of the stresses at the crack tip is made since this gives useful information about the direction of crack extension and also gives information necessary for the application of the fracture criterion which is derived in section 6. Some particular crack profiles are considered in detail in section 7.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 19 , Issue 1 , February 1975 , pp. 21 - 34
Copyright
Copyright © Australian Mathematical Society 1975

References

Bowie, O. L. (1956), ‘Analysis of an infinite plate containing radial cracks originating at the boundary of an internal circular hole’, J. Math. and Phys. 25, 60–71.CrossRefGoogle Scholar
Green, A. E. and Zerna, W. (1957), Theoretical elasticity (O.U.P. 1st edition, 1954), Chapter 8.Google Scholar
Griffith, A. A. (1921), ‘The phenomenon of rupture and flow in solids’, Phil. Trans. Roy. Soc. A221, 163–198.Google Scholar
Irwin, G. R. (1958), ‘Fracture’, Handbüch der Physik 6, 551–590.Google Scholar
Sih, G. C. and Erdogan, F. (1963), ‘On the crackextension in plates under plane loading and transverse shear’, J. Basic Engineering 85, 519–527.Google Scholar
Sih, G. C., Paris, P. C. and Erdogan, F. (1962),‘Crack-tip stress intensity factors for plane extension and plate bending problems’, J. Appl. Mech. 29, 306–312.CrossRefGoogle Scholar