Analytical modeling of contact acoustic nonlinearity of guided waves and its application to evaluating severity of fatigue damage

Targeting quantitative estimate of fatigue damage, a dedicated analytical model was developed based on the modal decomposition method and the variational principle. The model well interprets the contact acoustic nonlinearity induced by a “breathing” crack in a two-dimensional scenario, and the nonlinear characteristics of guided ultrasonic waves (GUWs) (e.g., reflection, transmission, mode conversion and high-order generation) when GUWs traversing the crack. Based on the model, a second-order reflection index was defined. Using the index, a fatigue damage evaluation framework was established, showing demonstrated capacity of estimating the severity of fatigue damage in a quantitative manner. The approach, in principle, does not entail a benchmarking process against baseline signals pre-acquired from pristine counterparts. The results obtained using the analytical modeling were compared with those from finite element simulation, showing good coincidence. Limitations of the model were also discussed.