The scattering of the fundamental torsional mode from axi-symmetric defects with varying depth profile in pipes

Guided ultrasonic waves have been successfully applied to detect defects and corrosion in plates and pipes; however, defect sizing remains challenging due to the complex profiles of the defects encountered in practice. A study of the reflection of the fundamental torsional mode T(0,1) from an axi-symmetric defect with varying depth profile has been carried out via finite element modeling and experimental validation. Defects with gradually varying depth are represented by a series of tapered steps. It is revealed that, for both tapered up- and down-steps, the wave packet is reflected only at the start and end of the steps. The reflections from the start and end of the step have been predicted, and the frequency dependence of the overall reflection from the step has been studied. The study shows that the reflection coefficient varies as a function of the ratio of the average length of the tapered defect to the wavelength due to the interference between the waves reflected from the two ends of the defect. The reflection coefficient maxima decrease as the slope of the taper becomes more gradual, this effect being more pronounced when the ratio of the average defect length to the wavelength increases.