Erratum: “Ultrasonic Evaluation of Closed Cracks Using Subharmonic Phased Array”

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.

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