This paper presents a numerical study on nonlinear Lamb wave time reversing for fatigue crack detection. An analytical framework is initially presented, modeling Lamb wave generation, propagation, wave crack linear and nonlinear interaction, and reception. Subsequently, a 3D transient dynamic coupled-field finite element model is constructed to simulate the pitch-catch procedure in an aluminum plate using the commercial finite element software (ANSYS). The excitation frequency is carefully selected, where only single Lamb wave mode will be generated by the Piezoelectric Wafer Active Sensor (PWAS). The fatigue cracks are modelled nucleating from both sides of a rivet hole. In addition, contact dynamics are considered to capture the nonlinear interactions between guided waves and the fatigue cracks, which would induce Contact Acoustic Nonlinearity (CAN) into the guided waves. Then the conventional and virtual time reversal methods are realized by finite element simulation. Advanced signal processing techniques are used to extract the distinctive nonlinear features. Via the Fast Fourier Transform (FFT) and time-frequency spectral analysis, nonlinear superharmonic components are observed. The reconstructed signals attained from the conventional and virtual time reversal methods are compared and analyzed. Finally, various Damage Indices (DIs), based on the difference between the reconstructed signal and the excitation waveform as well as the amplitude ratio between the superharmonic and the fundamental frequency components are adopted to evaluate the fatigue crack severity. The DIs could provide quantitative diagnostic information for fatigue crack detection. This paper finishes with summary, concluding remarks, and suggestions for future work.

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