Vol. 6, No. 9-10, 2011

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ISSN: 1559-3959
Wave scattering from a rectangular crack in an anisotropic cladding

Per-Åke Jansson

Vol. 6 (2011), No. 9-10, 1267–1282
Abstract
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Ultrasonic testing of a thick elastic plate with a crack in an anisotropic cladding is modeled analytically for a fully three-dimensional case. The model includes an ultrasonic transmitter and a receiver as well as wave scattering from a rectangular crack. The effect of a corrugated interface between the base component and the cladding is also taken into account. To solve the scattering problem the null field approach is employed to determine a Green’s tensor for the same structure without a crack and the source point located in the cladding. Utilizing the Green’s tensor an integral representation for the displacement field in the same structure with a crack and an incident field generated by an ultrasonic transducer may be derived. It is then straightforward to derive a hypersingular integral equation for the crack opening displacement, which can be used to determine the change in signal response due to the crack by Auld’s reciprocity argument. Numerical results are given for a variety of cases illustrating the effects of size, position, and orientation of the crack and the properties of the corrugated interface.

Keywords
ultrasound, crack, anisotropy, cladding
Milestones
Received: 21 September 2010
Revised: 15 February 2011
Accepted: 20 March 2011
Published: 15 January 2012
Authors
Per-Åke Jansson
Department of Applied Mechanics
Chalmers University of Technology
SE-412 96 Gothenburg
Sweden