Normal incident excitation of leaky Lamb waves for crack detection in pipe walls

Abstract

A mathematical model is presented that describes the interaction of guided waves, or leaky Lamb waves, with a notch in a plate to emulate a crack in a pipe wall. The model is based on sensitivity kernel theory from the field of seismology, which accounts for a finite scatterer in the wave path between a transmitter and a receiver. The crack detection method and model setup are directly based on the setup developed by the former company Halfwave, who investigated the use of normally incident transducers in a pitch-catch setup to excite leaky Lamb waves in gas pipelines to detect cracks. Since crack sensitivity may be dependent on multiple measurement setup parameters, the sensitivity kernel model can perform computationally efficient parameter sweeps to optimize the setup. In addition, since a crack detection method must provide a reliable crack size to pipeline operators, the model can potentially be used in inverse tomographic imaging methods. The input to the sensitivity kernel model is the field variables within a plate when no notch is present. To optimize computational efficiency, the field variables are derived using the angular spectrum method (ASM), which accounts for a transmitter, diffraction effects, transmission and reflection effects of the plate, and a separation distance between the transmitter and plate. The results of the field variables within a plate without a notch are validated against the finite element method software COMSOL, though the ASM model is highly computationally efficient in comparison. By implementing the ASM descriptions of the field variables in the sensitivity kernel theory, we investigated the notch sensitivity of the Lamb modes labeled S1, S2, and A3 for a normally incident pitch-catch setup of a water-immersed plate. The measurements and calculations of the sensitivity kernel were compared and showed the best agreement for the frequencies of the S2 mode. The same mode frequency components also showed the highest notch sensitivity and a high leaky component when there was no notch present. By varying the model parameters, it is also shown that notch sensitivity is dependent on frequency within a Lamb mode frequency range and the separation distance between plate and transmitter. Considering the generality of the presented sensitivity kernel theory, it is possible to convert the model to the case with angled transducers and the case where the setup is immersed in gas instead of fluid. Comments of the generality and applicability of the sensitivity kernel in other setups are given towards the end of this thesis, accompanied by preliminary results. If the sensitivity kernel modeling method is adapted and validated against other measurement setups and environments, it might be highly valuable in industrial applications for efficient parameter sweep simulations and thus optimization of setups and ultrasonic defect detection methods.