Nonlinear aspects of “breathing” crack-disturbed plate waves: 3-D analytical modeling with experimental validation

Abstract Previously, a two-dimensional (2-D) analytical model for interpreting the modulation mechanism of a “breathing” crack on guided ultrasonic waves (GUWs) is developed [1]. Based on the theory of wave propagation in three-dimensional (3-D) waveguides and using an elastodynamic analysis, the 2-D model is extended to a 3-D regime, to shed light on the nonlinear aspects of GUWs disturbed by cracks with “breathing” traits. With the model, generation of contact acoustic nonlinearity (CAN) embodied in GUWs, subjected to the key parameters of a “breathing” crack (e.g., crack length), is scrutinized quantitatively. On this basis, a nonlinearity index is defined to link crack parameters to the quantity of extracted CAN. In virtue of the index, initiation of an undersized fatigue crack in a 3-D waveguide can be delineated at its embryonic stage, and, in particular, the crack severity can be quantitatively depicted. This facilitates prognosis of imminent failure of the monitored structure. Experimental validation is performed in which a hairline fatigue crack is evaluated, and the results well corroborate the crack parameters predicted by the 3-D analytical model.