Scattering of the fundamental torsional mode at an axial crack in a pipe

A quantitative study of the interaction of the $T(0,1)$ torsional mode with an axial defect in a pipe is presented. The results are obtained from finite element simulations and experiments. The influence of the crack axial extent, depth, excitation frequency, and pipe circumference on the scattering is examined. It is found that the reflection from a defect consists of a series of the wave pulses with gradually decaying amplitudes. Such behavior is caused by the shear waves diffracting from the crack and then repeatedly interacting with the crack due to circumferential propagation. Time-domain reflection coefficient analysis demonstrates that the trend of the reflection strength for different crack lengths, pipe diameters, and frequencies from a through-thickness crack satisfies a simple normalization. The results show that the reflection coefficient initially increases with the crack length at all frequencies but finally reaches an oscillating regime. Also, at a given frequency and crack length the reflection decreases with the increase in pipe circumference. An additional scattering study of the shear wave $SH0$ mode at a part-thickness notch in a plate shows that the reflection coefficient, when plotted against depth of the notch, increases with both frequency and notch depth.