Elastic wave scattering by a rectangular crack near a non-planar back surface

A 3D model of non-destructive ultrasonic testing for cracks near a non-planar back surface is presented. The scattering by an interior rectangular crack in a thick-walled component with a back surface of general geometry is considered. The 3D wave scattering problem is solved using boundary integral equation methods (BIEMs): the boundary element method (BEM) for the back surface displacement is combined with an analytical technique for the hypersingular traction boundary integral equation for the crack opening displacement. The solution method generates many unknowns, but by applying a threshold criterion a sparse approximation of the system matrix is obtained such that a fast sparse solver may be used. The computations are accelerated further using the stationary phase approximation for the computation of probe field integrals. The action of ultrasonic probes in transmission and reception, calibration by side-drilled holes and effects of material damping are taken into account in the model, and a few numerical examples illustrate the influence of the back surface geometry.