A 2D model of ultrasonic testing for cracks near a non-planar surface

2D P–SV elastic wave scattering by a crack near a non-planar surface is investigated. The solution method employed is based on a reformulation of the wave scattering problem as two coupled boundary integral equations (BIE): a traction BIE for the crack opening displacement (COD) and a displacement BIE for the back surface displacement. The two coupled integral equations are solved using a combination of the boundary element method (BEM) for the back surface and a series expansion of the COD in Chebyshev functions. To model an ultrasonic contact probe in transmission, the traction on the surface beneath the probe is prescribed. The action of the receiving ultrasonic probe is modelled using a reciprocity relation. A few numerical examples illustrating the influence of the back surface are given.