A possible mechanism causing subharmonics in ultrasonic testing of a closedcrack

Nowadays nondestructive testing is noted due to the need of maintenance instructures, such as nuclear energy plants and aircrafts. However, detection andsizing of a closed crack are difficult by the conventional ultrasonic testing,because ultrasonic waves penetrate the contact area of the closed crack. Nownonlinear ultrasonic testing is attracting attention. Though there have beenexperimental reports on superharmonics or subharmonics and some theoreticalresearches accounting the superharmonics, so far there have yet been few reportsthat clarify the mechanism causing the subharmonics. Generation ofsuperharmonics at a closed crack was theoretically explained by modeling thecontact of the crack surfaces as a nonlinear spring. This modeling is based onthe fact that, when the gap between the crack surfaces decreases, the contactpressure increases nonlinearly due to the asperity of the crack surfaces. Inthis study a closed crack was regarded as a nonlinear spring with up to thethird order terms, and nonlinear analysis and numerical simulation were carriedout. In experiment, two aluminum specimens strongly pressed were used in placeof a metal block with a closed crack. Numerical simulation predicts generationof the subharmonics. They can appear if the input frequency close to twice thenatural frequency. Conditions for the subharmonics can also be foundanalytically with respect to the input frequency and the input amplitude.Subharmonics were also confirmed by experiment. In conclusion, a possiblemechanism causing the subharmonics at a closed crack was explained by regardinga closed crack as a nonlinear spring with up to the third order terms.