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

1320

2

Khalij et al. (2015), Xu et al. (2018), Meng et al. (2020), and Wang et al. (2022) reported the natural frequencies of materials owing to the presence of cracks. This causes a change in the vibration of materials, even under the same vibration conditions. However, the degree of change in vibration depends not only on the size of the crack but also on the vibration frequency. Therefore, we introduced a simple index to estimate the degree of change in vibration at different vibration frequencies and proposed a method for predicting the crack size based on the change in vibration. The validity of the method was verified by comparing the crack size predicted by the method with the measured crack size. 2. Methods 2.1 Bending vibration test Ti-6Al-4V was used as the specimen. Fig. 1 shows the shapes and dimensions of the specimens used for the bending vibration test. Tables 1 and 2 list the chemical composition and mechanical properties of Ti-6Al-4V, respectively. The specimens were electropolished via mechanical polishing using a waterproof abrasive paper. Bending vibration tests were conducted using low-noise compact vibration testing equipment (IMV Corp., m 030/MA1). As shown in Fig. 2, the specimen was fixed to the vibration table using a bolt, and the vibration table vibrated sinusoidally in the z -direction. In this study, the vibration frequency ( f v ) was set to a constant value near the first resonance frequency at approximately 23 Hz. To observe the crack initiation and propagation, the test was interrupted at specified intervals, and replicas of the surface, back, and side surfaces of the notch part were obtained. The crack length ( c ) and depth ( a ) were measured based on optical microscopy images of the replicas. In this study, the total crack area ( S ) was calculated by assuming the crack shape to be an ellipse, as expressed in Eq. (1):

# $

!

!

! = = " "

,

(1)

%

" "

"

where i denotes the number of cracks in the notch. The i values of the specimens vibrated at 21.4 Hz, 25.0 Hz, and 25.3 Hz, which are described later, were 2, 2, and 4, respectively. In addition, to observe the vibration of the specimen during the test, a high-speed video camera (Shimadzu Corp., HPV-1) was used to capture images in the y -direction at a shooting speed of 2 ms at approximately the same time that the replicas were obtained. The bending displacement amplitude ( d a ) was measured based on the image showing the largest bending displacement in one cycle, as shown in Fig. 3.

Fig. 1. Shape and dimensions of the specimens.

Table 1. Chemical composition of Ti-6Al-4V (mass%).

Al

V

O

Fe

C

N

H

Ti

6.0

4.0

0.11

0.15

0.02

0.006

0.005

Bal.

Table 2. Mechanical properties of Ti-6Al-4V.

0.2% proof stress, s 0.2 [MPa]

Tensile strength, s B [MPa]

Elongation [%]

893

977

11.6