Identification of a plane crack in an elastic body by invariant integrals

We consider the problem of plane crack identification in an elastic body from the results of static tests. We show that the crack plane, its volume under homogeneous normal loading, and the coordinates of the central point are uniquely determined from the results of three static tests by uniaxial te...

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Bibliographic Details
Published in:Mechanics of solids 2008-06, Vol.43 (3), p.437-452
Main Authors: Kaptsov, A. V., Shifrin, E. I.
Format: Article
Language:English
Subjects:
Classical Mechanics
Physics
Physics and Astronomy
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Summary:We consider the problem of plane crack identification in an elastic body from the results of static tests. We show that the crack plane, its volume under homogeneous normal loading, and the coordinates of the central point are uniquely determined from the results of three static tests by uniaxial tension in three mutually perpendicular directions. We obtain explicit formulas for these crack characteristics in terms of the corresponding invariant integrals, which can be calculated if the stresses and displacements are measured on the external boundary of the body in the experiments mentioned above. These formulas are exact for the problem about a crack in an infinite medium. If the elastic body boundedness is taken into account and it is assumed that the crack characteristic dimensions are small compared with the distance from the crack to the body boundary, then the obtained formulas can be considered as approximate ones.
ISSN:0025-6544
1934-7936
DOI:10.3103/S0025654408030151