PSI - Issue 68

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

1282

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

3

through the OFS, whereas the derivation and usage of Eq. (3) was introduced by Suo et al. (1990) and further investi gated later on by Sørensen and Jacobsen (2003).

2.2. Definitions for cohesive sti ff ness k s

Now using the di ff erential equation of the Winkler elastic foundation approach

w IV

4 w

+ 4 λ

= 0

(4)

and the second derivative of its ansatz function

A λ 2

e λ x cos( λ x − ψ ) ,

w II ( x )

(5)

= −

as well as the cohesive sti ff ness being k s = 2 EI b λ 4 , using the fit of the elastic region. And with the double integral of the test data and the limits being the end of the beam x max as well as the current position x the w ( x ) and2 w = w COD is obtained, respectively, for the TSL.

Fig. 2. Example of measured curvature data with the fit function.

Regarding the applicability, the ansatz function was fitted to the experimental data only in regions where w II < 0as it is illustrated in Fig. 2. This procedure is based on the assumption that the adhesive layer performs linear-elastically in the compression region of the fracture process zone. Hence A acts as Amplitude and ϕ as phase angle and can be obtained as maximum value and the corresponding abscissa value.

3. Experimental setup

The sample comprises two beams with a length of 350 mm, a thickness of 10 mm, and a width of 15 mm. The adhesive layer has a thickness of 0.3 mm and a length of 200 mm. To be able to compare the energy release rate (ERR) of both methods, the experiment was set up so that both methods from Chap. 2.1 can be applied. This makes it possible to validate the new method with the already established one, at least at the initial crack. The setup consists of a load cell, two inclinometers attached near the load initiation point, a DIC aimed at the initial crack tip, and as mentioned the optical fiber sensor. The test was performed with a quasi-static, displacement-controlled rate of 0.5 mm / s.