Modelling of ultrasonic scattering from a crack in a pipe

Licentiate thesis, 2015

This thesis considers elastic wave scattering in an infinitely long cylindrical pipe with an infinitely long internal axial crack. The method used in this thesis is called a hypersingular integral equation method since it starts with an integral representation and by using the Green's tensor of the pipe it can be manipulated to a hypersingular equation for the crack-opening displacement (COD). The singularity arises from the singularity in the free space part of the Green's tensor. To regularize the equation the COD is expanded in Chebyshev functions and then the integral equation is projected on the same Chebyshev functions. An SV probe in the shape of a rectangle on the outer surface of the cylinder is modelled by a traction boundary condition on the effective probe area. A reciprocal argument is used to calculate the signal response in the receiving probe due to the crack. To illustrate the method the signal response is calculated for a few cases when the probe is moved in the circumferential direction, thus creating a C-scan.