Second harmonic reflection and transmission from primary S0 mode Lamb wave interacting with a localized microscale damage in a plate: A numerical perspective

Nonlinear Lamb Wave Micro-Crack Direction Identification in Plates with Mixed-Frequency Technique

This paper investigates the direction identification of micro-cracks with nonlinear components generated by Lamb wave with frequency-mixing technique. Three-dimensional finite element simulations were carried out to investigate the interaction mechanism between Lamb wave signals and micro-cracks. Upon re-visiting the conventional Lamb wave excitation signal with two kinds of fundamental frequencies (f1 and f2), it was found to be possible to generate new types of frequencies (f1 ± f2) at the sideband if nonlinear sources existed in the plate. A pulse inversion method was used to extract the sideband frequency for nonlinear ultrasonic detection. By arranging piezoelectric chip arrays around the micro-crack, the acoustic nonlinearity parameter β related to the fundamental frequency and the sideband frequency for different micro-crack directions was calibrated. It was shown that β varied for different crack directions, which provides useful information about the scattering features of the nonlinear Lamb wave interacting with the micro-crack to characterize its directivity. Moreover, the scattering degree defined with the relative nonlinear parameter β′ of the micro-crack in different directions was investigated in detail by changing the size of the micro-crack. The outcomes showed that the forward scattering signal of the crack had a greater amplitude, whereas the backscattering signal had a smaller amplitude compared with the scattering signals in other directions from micro-cracks. In addition, the signal scattering degree in the forward direction from micro-cracks increased with the increasing micro-crack length, but decreased with increasing crack width. Furthermore, for the buried crack, the forward scattering degree of Lamb wave from micro-crack decreased as crack was buried deeper in plate. In summary, the findings of this study can help to further advance the use of nonlinear Lamb wave with the frequency-mixing technique for identifying the direction of micro-cracks.