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The edge-cracked circular disc under symmetric pin-loading

Published online by Cambridge University Press:  24 October 2008

R. D. Gregory
R. D. Gregory
Affiliation:
University of Manchester†
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Extract

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 under various loadings, which are motivated by the fact that this geometry is to become a standard test specimen configuration in the fracture testing of materials.

The first cases considered are those in which the disc is loaded by either (i) opposing point forces P normal to the crack, or (ii) opposing point couples M, in each case acting at the crack mouth. The problem of determining the resulting stress field throughout the disc is solved analytically in closed form in each case, and the respective stress intensity factors are given exactly by

where K+(0), K+(i) are constants whose values are

K+(0) = 0.966528…,

K+(i) = 0.355715…,

correct to 6 decimal places.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 85 , Issue 3 , May 1979 , pp. 523 - 538
Copyright
Copyright © Cambridge Philosophical Society 1979

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References

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