PSI - Issue 42

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

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M. Winklberger et al. / Structural Integrity Procedia 00 (2019) 000–000

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FEM SL: S maxPrincipal detected peaks 10 largest peaks

σ 1 [MPa]

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Frequency f [kHz]

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FEM TL: S maxPrincipal detected peaks 10 largest peaks

σ 1 [MPa]

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Frequency f [kHz]

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Fig. 4. Simulated stress spectra of pristine structures in the range of 50 kHz – 250 kHz for a) straight lug, b) tapered lug (for the σ 1 spectrum of the necked lug, see (Winklberger et al., 2021a)).

using the model-based identified crack sensitivities λ FE i

for each i th trajectory T M

i and associated measured frequency

shifts ∆ f M i , c . In the present investigation the estimated mean crack length for each measurement c is calculated by averaging a M i , c over all trajectories i .

3. Results and discussions

The results for straight and tapered lugs are presented in the order of the method overview in Fig. 3. For the discussion of measurement results of the necked lug see Winklberger et al. (2021a).

3.1. Model-based crack identification for straight and tapered lugs

Using the numerical models of straight and tapered lugs presented in Fig. 2, the model-based crack identification starts by analyzing the mean major principal stress σ 1 spectra of pristine structures. The simulation is proceeded within a wide frequency range of 50 kHz – 250 kHz and a low frequency resolution of 250 Hz. The resulting stress spectra in the areas of expected crack initiation are depicted in Fig. 4. All resonance frequency peaks detected by the peak finding algorithm signal.find peaks (included in the Python 3.8 package scipy ) are marked with blue crosses in Fig. 4. As described above, the largest peaks in each σ 1 spectrum are assumed to be most sensitive to a crack in the investigated region. In this study, the ten largest peaks in each spectrum are selected for further investigation, which are highlighted with red dots in Fig. 4. In 5 kHz bands around these resonance frequencies FE simulations (applying the same model as for the major principal stress spectra simulation) with a higher frequency resolution of 31 . 25 Hz are performed to investigate the conductance G ( ω ) spectra for pristine and cracked lugs (the length of the introduced seam is enlarged by 0 . 5 mm until a maximum crack length of 3 . 0 mm is reached). For each of these spectra the resonance peaks are identified and numerous trajectories T FE k are tracked, each starting at the peak frequency f FE k , pristine of the pristine model and ending at the peak frequency f FE k , c of the model with the largest crack. Quadratic resonance frequency peak trajectories T FE i are identified by finding the best fit to the function in Equ. (3) and evaluating the quality of fit with the CCD metric. Trajectories with CCD < 0 . 03 are chosen as crack indicators. Identified crack sensitive trajectories T FE i for all lug types are plotted in Fig. 5. For each of the trajectories T FE i the pristine resonance frequency f FE i , pristine as well as the parameter λ FE i are provided in the legend of each graph. For the straight lug twelve