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Abstract. Interest in using the higher harmonic generation of ultrasonic guided wave modes for nondestructive evaluation continues to grow tremendously as the understanding of nonlinear guided wave propagation has enabled further analysis. The combination of the attractive properties of guided waves with the attractive properties of higher harmonic generation provides a very unique potential for characterization of incipient damage, particularly in plate and shell structures. Guided waves can propagate relatively long distances, provide access to hidden structural components, have various displacement polarizations, and provide many opportunities for mode conversions due to their multimode character. Moreover, higher harmonic generation is sensitive to changing aspects of the microstructures such as to the dislocation density, precipitates, inclusions, and voids. We review the recent advances in the theory of nonlinear guided waves, as well as the numerical simulations and experiments that demonstrate their utility. 1 Introduction Nonlinear ultrasonic nondestructive evaluation uses interrogation signals at frequencies other than the excitation frequency to detect changes in structural integrity and characterize degradation of materials. Nonlinear ultrasonic methodologies provide improved sensitivity to damage and the ability to identify incipient damage relative to linear methods. In general, linear ultrasonic methods provide good sensitivity to macroscale damage such as long fatigue cracks. However, in many cases, once damage appears at the macroscale, the remaining life is short, severely limiting maintenance decisions. Thus, characterization of incipient damage could facilitate a paradigm shift in operations of structural systems from schedule-based to condition-based maintenance that would ultimately enhance safety and reduce life cycle costs. Nonlinear ultrasonics is a broad discipline 1,2 which encompasses many specialized techniques reliant upon nonlinear material behavior to detect and/or characterize incipient damage. Some of these include nonlinear resonant ultrasound spectroscopy, 3 nonlinear elastic wave spectroscopy, 4-6 and second-harmonic generation.

Fatigue crack growth in plate structures is monitored with ultrasonic guided waves generated from piezoelectric transducers. Cracks initiate in the vicinity of fastener holes due to cyclic in-plane loading. Ultrasonic guided waves that are partially obstructed by the fastener holes are investigated. Since fatigue crack growth increases the obstruction, these waves are effective for monitoring fatigue crack growth in a pitch-catch mode. The transmission coefficient (TC), which is defined essentially as the current-to-baseline amplitude ratio, and the transmission coefficient ratio (TCR), which is based on amplitude ratios from a single wave, are signal features used for crack characterization. The TCR is well suited for structural health monitoring. The excellent agreement between experimental results and finite element analysis of wave propagation corroborates the experiments. A sparse array of transducers is shown to effectively monitor a multifastener joint. The approach using obstructed ultrasonic guided waves has strong potential for prognostics-based structural health management due to the linear relationship between crack size and the TC.

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The characteristics of Lamb waves, which are multimodal and dispersive, provide both challenges and opportunities for structural health monitoring (SHM). Methods for nondestructive testing with Lamb waves are well established. For example, mode content can be determined by moving a sensor to different positions and then transforming the spatial-temporal data into the wavenumber-frequency domain. This mode content information is very useful because at every frequency each mode has a unique wavestructure, which is largely responsible for its sensitivity to material damage. Furthermore, mode conversion occurs when the waves interact with damage, making mode content an excellent damage detection feature. However, in SHM, the transducers are typically at fixed locations and are immovable. Here, an affixed polyvinylidene fluoride (PVDF) multielement sensor is shown to provide these same capabilities. The PVDF sensor is bonded directly to the waveguide surface, conforms to curved surfaces, has low mass, low profile, low cost, and minimal influence on passing Lamb waves. While the mode receivability is dictated by the sensor being located on the surface of the waveguide, both symmetric and antisymmetric modes can be detected and group velocities measured.

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