Effects of inclined incidence on ultrasonic testing of a closed crack

Detection and sizing of a closed crack are difficult by the conventional ultrasonic testing, because ultrasonic waves propagate through a closed crack. Recently, the nonlinear ultrasonic testing using superharmonics and/or subharmonics is regarded as a remarkable method of detecting a closed crack. However, the mechanism of subharmonics generation by a closed crack is not clear yet. In this study, we investigated propagation of inclined incident ultrasonic waves through a closed crack and introduced a two-dimensional model with reference of a one-dimensional model which we had introduced in our previous study (Kurihara, et al, 2011). In our experiments, after first finding natural frequencies from frequency response curves, we analyzed received signals obtained under the excitation frequencies twice the natural frequencies, using the Wavelet transformation. From the experimental results, subharmonics generation as well as the natural frequencies were influenced by the incident angles and the compression forces. Considering these results, we introduced a two-dimensional model with nonlinear springs. This model gives us numerical results corresponding with the experimental ones. Consequently, this two-dimensional model can be essential to understand the mechanism of subharmonics generation at a closed crack under inclined incidence of ultrasonic waves.