In this paper, characterization of the orientation of a microcrack is quantitatively investigated using the directivity of second harmonic radiated by the secondary sound source (SSS) induced by the nonlinear interaction between an incident ultrasonic transverse wave (UTW) and a microcrack. To this end, a two-dimensional finite element (FE) model is established based on the bilinear stress-strain constitutive relation. Under the modulation of contact acoustic nonlinearity (CAN) to the incident UTW impinging on the microcrack examined, the microcrack itself is treated as a SSS radiating the second harmonic. Thus, the directivity of the second harmonic radiated by the SSS is inherently related to the microcrack itself, including its orientation. Furthermore, the effects of the stiffness difference between the compressive and tensile phases in the bilinear stress-strain model, and the UTW driving frequency, as well as the radius of the sensing circle on the SSS directivity are discussed. The FE results show that the directivity pattern of the second harmonic radiated by the SSS is closely associated with the microcrack orientation, through which the microcrack orientation can be characterized without requiring a baseline signal. It is also found that the SSS directivity varies sensitively with the driving frequency of the incident UTW, while it is insensitive to the stiffness difference between the compressive and tensile phases in the bilinear stress-strain model and the radius of the sensing circle. The results obtained here demonstrate that the orientation of a microcrack can be characterized using the directivity of the SSS induced by the interaction between the incident UTW and the microcrack.
Keywords: bilinear stress–strain model; directivity; microcrack orientation; secondary sound source; ultrasonic transverse wave.