PSI - Issue 68

Junji Sakamoto et al. / Procedia Structural Integrity 68 (2025) 1319–1323 Junji Sakamoto et al. / Structural Integrity Procedia 00 (2025) 000–000

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Fig. 2. Experimental setup of the bending vibration test.

Fig. 3. Example of measuring d a .

2.2 Predicting crack area The S was predicted by monitoring the d a of the specimen under vibration using basic data that were obtained in advance. The basic data obtained are described in Section 2.2.1, and this is followed by the crack area prediction method in Section 2.2.2. 2.2.1 Basic data Fig. 4 shows the changes in the d a and S of the two specimens. First, the d a changes significantly for both specimens starting at approximately 40,000 cycles. Considering the change in the crack area, d a changes as S increases. This change in d a is attributable to the decrease in the first resonance frequency due to cracks in the specimen. Therefore, it is assumed that the degree of change in d a at f v = 21.4 Hz and 25.0 Hz depends approximately on the slope of the tangent line at f v = 21.4 Hz and 25.0 Hz in the relationship between f v and d a shown in Fig. 5, respectively. The specific values of the tangent slopes at f v = 21.4 Hz and 25.0 Hz are 35.0 and -30.8. Whether the values are positive or negative determines whether the vibration amplitude increases or decreases with an increasing crack area. Fig. 6 shows the relationship between the change in the bending displacement amplitude ( D d a ) and the product of the total crack area and tangent slope ( S ·d d a /d f v ). The figure shows a straight line approximated by the least-squares method form the results of the two specimens. The approximate straight line is expressed by Eq. (2):

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Fig. 4. Changes of the bending displacement amplitude and total area of cracks.