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In the ultrasonic detection using nonlinear Lamb wave, only the cumulative second-harmonic Lamb wave is useful for the nondestructive evaluation of plate-like structures. One of the conditions for cumulative second-harmonic Lamb wave generation is phase velocity matching between the primary and the secondary wave. However, in most cases, the phase velocities are approximate matching. In this paper, we theoretically analyzed and discussed the cumulative effect of second-harmonic Lamb wave. The theoretical results show that, when the phase velocities of the primary and the secondary Lamb waves are approximate matching, there is still a cumulative effect in the secondary wave within a specific distance, which is referred as accumulation distance. Based on the accumulation distance, an excitation window is proposed as the basis for mode selection and excitation condition determination of nonlinear Lamb wave. It is considered that, in the case of approximate phase velocity matching, the mode pair with larger excitation window could generate second-harmonic Lamb wave easier than the other mode pairs. Then, the excitation windows of different Lamb wave mode pairs are calculated and compared theoretically. In order to verify the validity of the excitation window as the basis for mode selection, the ranges of two mode pairs’ primary Lamb wave that could generate cumulative second-harmonic Lamb wave are measured and compared in a specific plate. In the experiment, the primary and the secondary Lamb waves around a longitudinal mode pair and a crossing mode pair are excited and measured using wedge piezoelectric transducers. In the measurement, the second-harmonic Lamb wave is generated by the primary wave in different frequency and phase velocity ranges, and then the ranges of the primary Lamb wave are confirmed in the phase velocity dispersion curves, using the time-frequency analysis. The experimental result shows that, the primary wave range of the longitudinal mode pair is larger than that of the crossing mode pair, which means that the selected longitudinal mode pair could generate second-harmonic Lamb wave easier than another one. The experimental result is in accordance with the comparing result of the excitation windows. The theoretical and experimental results show that, the excitation window could be an indicator for mode selection and excitation condition determination of cumulative second-harmonic Lamb wave generation, and it can be used in the field of ultrasonic detection using nonlinear Lamb wave.

Non-collinear wave mixing recently has been proposed to detect and localize micro-damage in materials. It is proved sensitive to the interaction angle α of the incident waves. In this work, the relationship between the acoustic nonlinearity parameter χ and the α is studied by numerical simulations and experimental measurements based on the nonlinear interaction of two shear waves. A single-peak change in the normalized acoustic nonlinearity parameter χ ′ of the mixing wave versus the incident angle is observed from numerical simulations and then is verified by experiments. The results show a -6 dB decrease of χ ′ corresponds to a deviation of about 4° in the incident angle. Meanwhile, the detection and localization of plastic deformation is also conducted on an aluminum alloy based on the scanning of non-collinear wave mixing, in which the distribution of the acoustic nonlinearity is similar to that of the plastic strain.

The detection of the nonlinear Lamb wave using a PVDF comb transducer is described in this research. The construction features of the PVDF comb transducer is firstly described. Then, the harmonic-frequency characteristic of PVDF comb transducer as the receiver in the nonlinear Lamb wave inspection is qualitatively investigated by the output-vector addition method. The theoretical result shows that, when the wavelength of the fundamental Lamb wave is equal to the PVDF comb transducer's finger spacing, the transducer can receive the fundamental wave. When the frequency of the higher-harmonic Lamb wave is integral multiple of the frequency of the fundamental one, the PVDF comb transducer can also receive the higher-harmonic Lamb wave. In order to verify the harmonic-frequency characteristic of the PVDF comb transducer, we conducted an experiment based on the cumulative effect of the nonlinear Lamb wave. That is, the value of the relative nonlinearity parameter will grow higher when the propagation distance increases. In order to receive the fundamental and second-harmonic Lamb waves, a PVDF comb transducer with special finger spacing was made and pasted on an aluminum plate surface. The desired Lamb-wave mode was generated by a wedge transducer. It had been observed that the value of relative nonlinearity parameter increased with the wave propagation distance. That means that the PVDF comb transducer had received both the fundamental and the second-harmonic Lamb waves. Both the theoretical and experimental results show that, because of the PVDF comb transducer's simultaneous response to the fundamental and second-harmonic signals, the nonlinear Lamb wave can be detected using a PVDF comb transducer.

This paper presents physical and experimental studies of the static component of Lamb waves (SCLWs) induced by partially closed cracks. The generation mechanism of SCLWs was investigated according to the nonlinear interaction between Lamb waves and partially closed cracks with various lengths, widths and orientation angles in finite element simulations. It was found that the SCLWs are more sensitive to the crack length, width and orientation angle as compared with the second harmonic Lamb waves. Fatigue crack evolution was further experimentally detected in aluminum alloy plates using SCLWs. Consistent with the simulation results, the acoustic nonlinearity parameter increases monotonically with increasing fatigue crack length. We show that the SCLWs are sensitive to partially closed cracks and can serve as a potential method to quantitatively evaluate the evolution of partially closed crack in metal plates. The findings of this study pave the way for the detection of partially closed crack using SCLWs in the field of nondestructive evaluation and structural health monitoring.

This paper experimentally investigates the early stage damage caused by the surface corrosion in thin plates based on two nonlinear Lamb wave methods, which are the low-frequency S0 mode Lamb wave method and one-way S0-A0 Lamb mixing wave method. The experimental results show that the significant second/third harmonics and the resonant waves from these methods can be caused by the surface corrosion damage. Meanwhile, it is found that the normalized acoustic nonlinearity parameters in these methods increase monotonically with the number of corrosion times before the generation of the distinct cavities. Moreover, the position and the length of the surface corrosion region can be characterized by the resonant waves from one-way S0-A0 Lamb mixing wave method. This study reveals that the low-frequency S0 mode Lamb wave method and one-way S0-A0 Lamb mixing wave method are feasible to evaluate early stage damage caused by the surface corrosion.

This paper investigates an experimental technique for evaluating early stage material damage in an aluminum plate using quasi-static component of Lamb waves, which is a simpler version of the nonlinear Lamb wave measurement technique. Different levels of material nonlinearities were induced by local plastic bending. A pair of piezoelectric ceramics transducers (PZTs) were used to excite and detect the fundamental Lamb waves and quasi-static component, respectively. The quasi-static component was extracted from received signals through signal processing with a low-pass filter. The effectiveness of PZT was validated through laser inspection. The results show that the measured acoustic nonlinearity parameter (ANP) monotonically increases with bending time before the generation of macro-cracks, and Fast Fourier Transform (FFT) is a good and efficient choice to demonstrate the intensity of the quasi-static component. Compared with the established framework of the second harmonic generation technique, this study reveals that the quasi-static component method is a more powerful technique in evaluating early stage local plastic damage.

Low efficiency of energy transition is generally considered to be the only weakness of electromagnetic ultrasonic transducers (EMATs). Electromagnetic acoustic resonance (EMAR) technique has been successfully used to overcome this disadvantage with a combination of the EMATs with the ultrasonic resonant method. In this paper, a nonlinear EMAR technique has been proposed to evaluate the thermal damage of metallic materials, which combines the feature of EMAR with the merit of higher harmonic generation that provides an effective indicator to material damage. The use of contactless EMATs can isolate the material nonlinearity and maintain the coupling condition consistently on measurements of higher harmonics generated. EMAR provides high enough signal magnitude for higher harmonic generated. An experimental scheme is proposed and applied to assess the thermal damage in aluminum and nickel plates. In addition, conventional EMAR techniques based on the measure of shear wave velocity and attenuation within a certain frequency range, are also carried out for the specimens. The experimental results show a monotonic relationship between the normalized amplitude of higher harmonic generated and the artificial thermal loading time, while no stable trends are observed by conventional linear EMAR approaches. The results in this paper indicate that nonlinear EMAR technique proposed can be used to assess the thermal damage in both nonferromagnetic and ferromagnetic materials, with improved reliability and sensitivity over linear one.

The thermal degradation in ferritic Cr–Ni alloy steel plates is measured using the nonlinear effect of Lamb wave propagation. Experiments were carried out to introduce controlled levels of thermal damage to determine the nonlinear response of Lamb waves. A “mountain-shape” change in the normalized acoustic nonlinearity of Lamb wave versus the level of thermal degradation in the specimens has been observed. The variation in the measured acoustic nonlinearity reveals, based on metallographic studies, that the normalized acoustic nonlinearity increases due to the second phase precipitates in the early stage and it decreases as a combined result of dislocation change and micro-void initiation in the material. The results show a potential application of the nonlinear Lamb waves for the quantitative assessment of thermal damage in metallic plates or pipes.

This research has developed an approach for studying second-harmonic generation of generalized Lamb waves (GLWs) in layered planar structures. On the basis of a modal analysis approach and second-order perturbation treatment, an effective theoretical model has been established. The material non-linearity can result in second-harmonic generation by primary GLWs propagating in layered structures, and the non-linearity is treated as a second-order perturbation of the elastic response of primary GLW propagation. There are second-order bulk and surface/interface driving sources in layered planar structures when primary GLWs propagate. These driving sources can be thought of as the forcing functions of a series of double frequency GLWs (DFGLWs) in terms of the approach of modal expansion analysis of guided waves. The total second-harmonic displacement fields consist of a series of DFGLWs in the stress-free layered structures. Thus, the complicated problem of second-harmonic generation of GLWs can be determined exactly within the second-order perturbation regime. Despite the strongly dispersive nature of primary GLWs in layered planar structures, it is found that the second harmonics of primary GLWs can grow with propagation distance along layered structures when the phase velocities of the DFGLWs are equal to those of the primary GLWs. Also, the formal solution of the second harmonics of the primary GLWs are presented. Numerical simulations were performed to understand the physical process of second-harmonic generation by primary GLW propagation in layered structures. The potential application of the present results to practical inspections of layered structures is discussed.