Abstract
Nondestructive testing is useful for maintenance of structures. Recently, nonlinear ultrasonic testing with subharmonic becomes attractive method of detecting the closed crack. However, the mechanism of subharmonic generation by the closed crack is not clear yet. This study investigates propagation of inclined incident ultrasonic waves through the closed crack and creates the two-dimensional model with nonlinearity. In our experiment, the closed crack was modeled as contact area of two aluminum specimens compressed. Four conditions were prepared by a combination of two incidence angle (30-degrees and 60-degrees) and of two compression force (3kN and 6kN). In each condition, after first finding a natural frequency from its frequency response, we analyzed received signals obtained under the excitation frequency twice the natural frequency, using the wavelet transformation. From the frequency response, not only the peaks of signals but also the natural frequencies were under the influence of the incident angle and the compression force. Moreover, from the analysis of received signals, 1/2-subharmonic generated if the incident angle was 30-degree and the compression force was 3kN, though 1/2-subharmonic did not generate in other conditions. According to these results, we introduced a two-dimensional model with a nonlinear spring normal to the contact area and with a nonlinear spring and a damper horizontal to the contact area. Specially, the nonlinearities of the spring in the horizontal direction are only odd powers. In conclusion, this two-dimensional modeling can be essential to understand mechanism of subharmonic generation at the closed crack under inclined incidence of ultrasonic waves.
