Ultrasonic 2D SH crack detection in a layered anisotropic plate

The 2-D scattering problem of an internal crack in a layered anisotropic pl ate is considered in this paper. In the model, two ultrasonic SH probes are attached on the upper surface of the plate and the incoming displacement f ield is generated by one of the probes and the other probe is acting as a r eceiver. The transmitting and the receiving probe may be the same. The prob lem is solved by deriving the Green function for the layered plate and then using the integral representation for the total field to obtain an integra l equation for the crack opening displacement. The integral equation is sol ved by expanding the crack opening displacement (COD) in Chebyshev function s. A crucial part of the method is the expansion of the Green function in a free space part, expressed in the crack coordinate system, and a reflectio n part, expressed in the plate coordinate system. The electrical signal res ponse is calculated by an electromechanical reciprocity relation. Numerical examples are given for a transversally isotropic graphite-epoxy plate, whe re the symmetry axes are mutually perpendicular in the layers. The results are presented as A-scans, i.e. the electrical response as a function of tim e.