ABSTRACT
We present an ultrasonic method of detecting cracks in pipelines based on using normally incident transducers in a pitch-catch setup, which can only excite Lamb modes of higher order than the fundamental modes A0 and S0 commonly used in crack detection applications. By excitation and measurements of the Lamb modes S1, S2, and A3, in a steel plate immersed in fluid with and without a notch (to emulate a crack), the performance of the modes towards crack detection is quantified by assessing whether it returns a high leaky component and whether the notch has a large impact on the leaky component. In order to narrow the scope of measurements necessary to investigate notch sensitivity for different system parameters, and to potentially optimize the system setup, we present a computationally efficient theoretical model based on angular spectrum method (ASM) and the theoretical sensitivity kernel formulation from the field of seismology that accounts for a scatterer in the wave path between the transmitter and receiver. The model is compared against measurements, which show that the frequency components of the S2 mode has both the largest leaky frequency component in the given setup and the largest sensitivity at a frequency close to the maximum leaky frequency such that a difference caused by the notch is easily measured. By using the measurements and the validation calculation as baseline reference, we calculate the expected S2 mode sensitivity and leaky components for larger plate thicknesses and larger standoffs, which exemplifies how the model can be applied in measurement system design and optimization.
ABSTRACT
An angular spectrum method (ASM) full-wave description of stress and energy density in a fluid-immersed plate for the optimization of leaky Lamb wave applications is presented. It models the case when leaky Lamb waves are generated by an external finite transmitter in the immersion fluid, and can calculate the associated stress, energy density, and other field variables within the plate. The normal component of the stress tensor and the energy density are compared against calculations in COMSOL with good agreement, but with some differences due to the two methods. The spatial field of the stress is analyzed using the angular spectrum (plane wave) representation of the stress, which is also used as a reference to exemplify the discrepancies between a pure plane wave approach in leaky Lamb wave applications and the spatial fields that accounts for diffraction and dispersion effects. Comments on the insight that the spatial fields within the plate may provide towards NDT/SHM applications are also given, along with a discussion on why the derivation and implementation of the ASM model is valuable when compared against a benchmarked, ready-to-use software such as COMSOL.
