On the modelling of ultrasonic testing using boundary integral equation methods

Doctoral thesis, 2011

Ultrasonic nondestructive testing has important applications in, for example, the nuclear power and aerospace industries, where it is used to inspect safety-critical parts for flaws. For safe and reliable testing, mathematical models of the ultrasonic measurement systems are invaluable tools. In this thesis such measurement models are developed for the ultrasonic testing for defects located near non-planar surfaces. The applications in mind are the testing of nuclear power plant components such as thick-walled pipes with diameter transitions, pipe connections, etc. The models use solution methods based on frequency domain boundary integral equation methods, with a focus on analytical approaches for the defects and regularized boundary element methods for the non-planar surfaces. A major benefit of the solution methods is the ability to provide accurate results both for low, intermediate and high frequencies. The solution methods are incorporated into a framework of transmitting probe models based on prescribing the traction underneath the probe and receiving probe models based on electromechanical reciprocity. Time traces are obtained by applying inverse temporal Fourier transforms, and it is also shown how calibration and effects of material damping can be included in the models.