A hybrid Semi-Analytical Finite Element (SAFE) and standard finite element procedure is adopted to locally detect and characterize an outer surface breaking, axisymmetric notch in an otherwise infinitely long steel pipe. Numerical simulations demonstrate that interactions between incident, dispersive ultrasonic guided waves and the notch change a radial displacement's temporal history and introduce singularities in the previously unblemished pipe's Frequency Response Function (FRF). The new singularities indicate the presence of a nearby notch. Furthermore, the frequency differences between the singularities of the unblemished and blemished pipes are shown to reflect the axisymmetric notch's dimensions. The conceptually straightforward but computationally expensive extension to nonaxisymmetric notches is also suggested.
Stoyko, Darryl K., Popplewell, Neil, and Shah, Arvind H., “Using Singularities to Detect and Describe a Notch in a Pipe,” Proceedings of the Thirty-Ninth Annual Review of Progress in Quantitative Nondestructive Evaluation (QNDE), July 15-20, 2012, Denver, Colorado.