PSI - Issue 68

Lea Aydin et al. / Procedia Structural Integrity 68 (2025) 1280–1286

1284

L. Aydin and S. Marzi / Structural Integrity Procedia 00 (2024) 000–000

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4.2. Evaluation of ERR

Using the first part of both Eq. (1) and Eq. (3) and the corresponding w COD we were able to compare the ERRs as shown in Fig. 5. The grey data represent the many positions and time steps we got from the OFS. The red line is their mean value and the transparent red background is the standard deviation. The bold black line is the result of the DIC. Especially in the region close to the origin and the plateau of roughly 2 kJ / mm 2 at the end fit well with the mean value of the OFS. However, the constant slope in the beginning makes it hard to evaluate the cohesive sti ff ness in the TSL later on. Moreover, to manage this problem seeing the clear existence of the fracture process zone in the strain or curvature results from the OFS an elastic foundation approach, also used by Sun and Blackman (2021) as well as Shokrieh and Heidari-Rarani (2011) and Cabello et al. (2017) seemed suitable. This method was investigated by many other authors like Jumel et al. (2011) and Wang and Zhang (2009) before and has been shown to deliver good results, especially for a thin adhesive layer, and was discussed in Subsec. 2.2.

Fig. 5. Comparison of ERR from external measurement and OFS

4.3. Evaluation of TSLs

In Fig. 6 the results of the TSLs are shown. The black curve represents the results of the ERR and in grey those of the stress from Eq. (1) and Eq. (3), respectively. The blue line has a constant slope with the value of the cohesive sti ff ness k s and purple gives the maximum COD w max COD with the corresponding standard deviation. A criterion was necessary for w max COD , as the curves converge very slowly towards the abscissa. Hence we chose 5% of the maximum stress as the cut-o ff condition. The results were divided into two intervals to verify whether the results may di ff er at the initiation and propagation of the crack. It can be seen that the curves vary slightly in the maximum stress, but this may also be a product of the scattering of the data. As a whole, we can assume that this e ff ect is negligible. Moreover, the data here also agree well with the externally measured data. The results are listed in Tab. 1.

Table 1. Cohesive sti ff ness and maximum COD values Interval

cohesive sti ff ness k s / N / mm 3

max. COD w max COD 0.1130 ± 0.0201 0.1399 ± 0.0227

/ mm

crack initiation crack propagation

4066.03 ± 1533.77 4688.14 ± 1357.44