The reflection of the fundamental torsional mode from cracks and notches in pipes

A quantitative study of the reflection of the T(0,1) mode from defects in pipes in the frequency range 10-300 kHz has been carried out, finite element predictions being validated by experiments on selected cases. Both cracklike defects with zero axial extent and notches with varying axial extents have been considered. The results show that the reflection coefficient from axisymmetric cracks increases monotonically with depth at all frequencies and increases with frequency at any given depth. In the frequency range of interest there is no mode conversion at axisymmetric defects. With nonaxisymmetric cracks, the reflection coefficient is a roughly linear function of the circumferential extent of the defect at relatively high frequencies, the reflection coefficient at low circumferential extents falling below the linear prediction at lower frequencies. With nonaxisymmetric defects, mode conversion to the F(1,2) mode is generally seen, and at lower frequencies the F(1,3) mode is also produced. The depth and circumferential extent are the parameters controlling the reflection from cracks; when notches having finite axial extent, rather than cracks, are considered, interference between the reflections from the start and the end of the notch causes a periodic variation of the reflection coefficient as a function of the axial extent of the notch. The results have been explained in terms of the wave-number-defect size product, ka. Low frequency scattering behavior is seen when ka < 0.1, high frequency scattering characteristics being seen when ka > 1.