2D SH modelling of ultrasonic testing for cracks near a non-planar surface

A model of 2D SH ultrasonic nondestructive testing for interior strip-like cracks near a non-planar back surface in a thick-walled elastic solid is presented. The model employs a Green's function to reformulate the 2D antiplane wave scattering problem as two coupled boundary integral equations (BIE): a displacement BIE for the back surface displacement and a hypersingular traction BIE for the crack opening displacement (COD). The integral equations are solved by performing a boundary element discretization of the back surface and expanding the COD in a series of Chebyshev functions which incorporate the correct behaviour at the crack edges. The transmitting ultrasonic probe is modelled by prescribing the traction underneath it, enabling the consequent calculation of the incident field. An electromechanical reciprocity relation is used to model the action of the receiving probe. A few numerical examples which illustrate the influence of the non-planar back surface are given.