A possible mechanism causing subharmonics in ultrasonic testing of a closed crack

Nowadays nondestructive testing is noted due to the need of maintenance in structures, such as nuclear energy plants and aircrafts. However, detection and sizing of a closed crack are difficult by the conventional ultrasonic testing, because ultrasonic waves penetrate the contact area of the closed crack. Now nonlinear ultrasonic testing is attracting attention. Though there have been experimental reports on superharmonics or subharmonics and some theoretical researches accounting the superharmonics, so far there have yet been few reports that clarify the mechanism causing the subharmonics. Generation of superharmonics at a closed crack was theoretically explained by modeling the contact of the crack surfaces as a nonlinear spring. This modeling is based on the fact that, when the gap between the crack surfaces decreases, the contact pressure increases nonlinearly due to the asperity of the crack surfaces. In this study a closed crack was regarded as a nonlinear spring with up to the third order terms, and nonlinear analysis and numerical simulation were carried out. In experiment, two aluminum specimens strongly pressed were used in place of a metal block with a closed crack. Numerical simulation predicts generation of the subharmonics. They can appear if the input frequency close to twice the natural frequency. Conditions for the subharmonics can also be found analytically with respect to the input frequency and the input amplitude. Subharmonics were also confirmed by experiment. In conclusion, a possible mechanism causing the subharmonics at a closed crack was explained by regarding a closed crack as a nonlinear spring with up to the third order terms.