Analytical insight into “breathing” crack-induced acoustic nonlinearity with an application to quantitative evaluation of contact cracks

To characterize fatigue cracks, in the undersized stage in particular, preferably in a quantitative and precise manner, a two-dimensional (2D) analytical model is developed for interpreting the modulation mechanism of a “breathing” crack on guided ultrasonic waves (GUWs). In conjunction with a modal decomposition method and a variational principle-based algorithm, the model is capable of analytically depicting the propagating and evanescent waves induced owing to the interaction of probing GUWs with a “breathing” crack, and further extracting linear and nonlinear wave features (e.g., reflection, transmission, mode conversion and contact acoustic nonlinearity (CAN)). With the model, a quantitative correlation between CAN embodied in acquired GUWs and crack parameters (e.g., location and severity) is obtained, whereby a set of damage indices is proposed via which the severity of the crack can be evaluated quantitatively. The evaluation, in principle, does not entail a benchmarking process against baseline signals. As validation, the results obtained from the analytical model are compared with those from finite element simulation, showing good consistency. This has demonstrated accuracy of the developed analytical model in interpreting contact crack-induced CAN, and spotlighted its application to quantitative evaluation of fatigue damage.