PSI - Issue 42

Markus Winklberger et al. / Procedia Structural Integrity 42 (2022) 578–587 M. Winklberger et al. / Structural Integrity Procedia 00 (2019) 000–000

584

7

· 10 2

10 2

− 2 − 4 − 6 − 8 − 10 · Frequency shift ∆ f FE i , c [Hz]

i = Hz / mm 2 FE 1 = − 50 . 00

f FE i , pristine = kHz λ FE f FE 1 , pristine = 56 . 2 fit λ

i = Hz / mm 2 FE 1 = − 28 . 65 = − 55 . 13 = − 14 . 32 FE 2 FE 3

f FE i , pristine = kHz λ FE f FE 1 , pristine = 49 . 6 fit λ

− 10 − 12 − 14

f FE 2 , pristine = 82 . 3 f FE 3 , pristine = 82 . 7

f FE 2 , pristine = 51 . 1 f FE 3 , pristine = 77 . 8 f FE 4 , pristine = 97 . 0 f FE 5 , pristine = 98 . 6 f FE 6 , pristine = 112 . 5 f FE 7 , pristine = 113 . 9 f FE 8 , pristine = 115 . 7 f FE 9 , pristine = 129 . 2

FE 2 FE 3 FE 4 FE 5 FE 6 FE 7 FE 8 FE 9

fit λ fit λ fit λ fit λ fit λ fit λ fit λ fit λ

= − 115 . 97 = − 77 . 49 = − 92 . 13 = − 118 . 34 = − 12 . 97 = − 101 . 95 = − 31 . 90 = − 58 . 45

fit λ fit λ

f FE 4 , pristine = 102 . 9 fit λ FE 4 f FE 5 , pristine = 154 . 0 fit λ FE 5 f FE 6 , pristine = 154 . 8 fit λ FE 6 f FE 7 , pristine = 155 . 7 fit λ FE 7 f FE 8 , pristine = 178 . 7 fit λ FE 8

− 2 − 4 − 6 − 8 Frequency shift ∆ f FE i , c [Hz]

= − 102 . 83 = − 34 . 16 = − 51 . 38 = − 43 . 29 = − 67 . 95

f FE 10 , pristine = 159 . 7 fit λ FE f FE 11 , pristine = 233 . 3 fit λ FE f FE 12 , pristine = 235 . 2 fit λ FE

10 = − 155 . 43 11 = − 124 . 23 12 = − 54 . 90

0 0 . 5 1 1 . 5 2 2 . 5 3 0

0 0 . 5 1 1 . 5 2 2 . 5 3 0

Crack length a c [mm]

Crack length a c [mm]

b)

a)

Fig. 5. Identified trajectories including parameters λ FE i

of their closest fits for a) straight lug and b) tapered lug.

and for the tapered lug eight quadratic trajectories are found. A comparison of Fig. 4 and Fig. 5 for straight and tapered lug reveals that quadratic trajectories are not necessarily found around all of the ten identified largest σ 1 peaks (e.g., for the highlighted peak at approximately 70 kHz none was found). Moreover, in some frequency ranges more than one quadratic trajectory could be identified (e.g. for the highlighted peak at approximately 113 kHz for the straight lug and at approximately 155 kHz for the tapered lug). These circumstances are not problematic as long as a statistically relevant number of quadratic trajectories is identified in the process. Otherwise, the number of highest peaks (ten in this study) and thus the number of investigated 5 kHz bands must be increased.

3.2. Monitoring crack growth in straight and tapered lugs

The next step after the model-based identification of crack sensitive resonance frequencies in the conductance spectra is the baseline measurement of the structure (measurement no. 1). The experimental setup and the specimen position of the baseline measurement for the straight lug is depicted in Fig. 6a (setup and specimen position are comparable for the tapered lug baseline measurement).

d) Meas. No. 4

a) Meas. No. 1

c) Meas. No. 3

b) Meas. No. 2

flat (180 ◦ )

flat

standing

lateral

Fig. 6. Straight lug pristine measurements a) No. 1 in flat, b) No. 2 in lateral, c) No. 3 in standing, and d) No. 4 in flat (180 ◦ ) specimen position. Necked and tapered lug specimens shown are subsequently measured in similar positions, which is not depicted here.

For the current investigations with straight and tapered lugs three additional measurements of the pristine structures are performed (measurement no. 2 – 4). For each of these preceding measurements only the positions of the lugs were changed marginally, as depicted in Fig. 6b to Fig. 6d. This procedure should simulate a crack initiation period, where no crack is present and the measured spectrum is only altered by, e.g, environmental influences or measurement noise.