Interaction of concentrated forces with crack tips: hypersingular stress fields, weight functions and caustics
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Date
1991-11-28
Authors
Ioakimidis, Nikolaos
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Abstract
Hypersingular stress fields near a crack tip (and the related singular displacement fields) constitute the basis of the weight function method and related methods for the determination of stress intensity factors. Here a natural and elementary interpretation of these fields is proposed, which assumes them created by the interaction of a pair of concentrated forces with the crack tip. Next, this approach is applied to the determination of the weight function for a single straight crack (on the basis of Betti's reciprocal work theorem). Afterwards, the asymptotic formulae for the hypersingular stress components near the crack tip are derived. Furthermore, the theoretical forms of the caustics due to hypersingular stress fields near a crack tip are found and displayed in some detail and some of their geometrical properties are derived. Generalized, hypersingular stress intensity factors are also introduced. The Westergaard complex stress function method (for plane isotropic elasticity crack problems) is used for the derivation of the present results.
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Keywords
Fracture mechanics, Cracks, Concentrated forces, Westergaard complex potential, Plane isotropic elasticity