The authors constructed a novel apparatus based on subharmonic ultrasound for the accurate imaging of closed cracks. Linear and nonlinear responses not only from the tip but also from other parts of cracks were observed in fundamental and subharmonic images, which were changed with varying closure stress. The subharmonic images always gave an accurate length of partially closed cracks, in contrast to the fundamental images in which the crack length was underestimated. Significant similarities in generation and resonance phenomena of subharmonic waves, acoustic emission, and the vibration of microbubbles are discussed.

We developed a novel imaging method, subharmonic phased array for crack evaluation (SPACE) based on subharmonic waves and a phased array algorithm, to measure closed-crack depth in the thickness direction. This implementation of SPACE used a LiNbO3 single-crystal transmitter to generate the intense ultrasound required for subharmonic generation and a phased array sensor as a receiver for focusing using delay laws. We applied SPACE to closed fatigue and stress corrosion cracks and found that the measurement error of SPACE in measuring crack depths was approximately 1 mm, while that in the conventional method was 20 mm in an extreme case. To establish the basis of SPACE, we propose the concept of localized subharmonic resonances (LSRs) and explain SPACE images as accumulations of LSRs. As an example of LSR, the Rayleigh-mode resonance of a crack is described. The similarities and differences between subharmonic waves at closed cracks and at microbubbles are also discussed.

Cracks in solids can be detected by ultrasound if they are open. However, their detection is not easy when they are closed with a closure stress, and thus it is a fundamental problem in ultrasonic testing. Subharmonics with half the input frequency is potentially useful in the detection and evaluation of such cracks, although quantitative analysis has not been established. In this work, we develop analytical and numerical theories accounting for the crack parameters, such as closure stress and crack surface conditions, for the first time. We proved their validity by comparison with experiments on a well-defined fatigue crack in aluminum alloy, finding reasonable agreements. Based on these theories, it will be possible to estimate important parameters of partially closed cracks by fitting measured waveforms to theoretical predictions, which solves the fundamental problem in ultrasonic testing of cracks.

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We formed a stress corrosion crack (SCC) more than 10 mm deep to simulate those generated in atomic power plants. We precisely imaged the formed SCC by a novel imaging method, namely, the subharmonic phased array for crack evaluation (SPACE), and found that it had complex branches. Subsequently, we cut the specimen for the optical observation of the cross sections, and discussed the origin of the SCC extension on the basis of the optical microscopic observation of the cross sections. To examine the open and closed parts of crack in the optical images, we superposed the crack extracted from the optical images onto the SPACE images. We compared the optically and SPACE-measured crack depths, and demonstrated that SPACE is useful in reducing the underestimation of closed-crack depths.