PSI - Issue 68
Lea Aydin et al. / Procedia Structural Integrity 68 (2025) 1280–1286 L. Aydin and S. Marzi / Structural Integrity Procedia 00 (2024) 000–000
1281
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tests to be able to evaluate them statistically. The new method introduced here uses a test setup that potentially makes it possible to obtain more results with significantly fewer tests. This means that it is no longer just a TSL at the initial crack tip that is obtained, but rather a TSL over the entire length of the beam at each measurement time. In this case, around 1000 TSLs per test were obtained. This method also further simplifies the detection of cracks and inhomogeneities in the adhesive. Lastly, it was also possible to track the crack length throughout the test, making it possible to use di ff erent methods of material characterization that require this parameter.
2. Theoretical background
2.1. Evaluation method for TSLs
The mode I test setup for the J-Integral method is shown in Fig. 1 (left). This method usually requires a measure of the forces F applied to the sample, the associated rotations ϕ 1 and ϕ 2 as well as the crack opening displacement w CTOD at the initial crack tip (CTOD). The latter value is often obtained using a digital image correlation (DIC) system. With that and the width of the adhesive layer b the (external) J-Integral J ext and eventually the peel stress σ ext can be calculated through
F ( ϕ 1 + ϕ 2 ) b
d J ext d w CTOD
J ext =
σ ext ( w CTOD ) =
(1)
→
.
Fig. 1. Schematic description of the setups used. Left: ’external’ measurement at the crack tip. Right: measurement with optical fiber sensor.
The attached optical fiber sensor (OFS) along the outer faces of the beam gives the strain
∂ 2 ∂ x 2
h 4
ε ( x , t ) = −
w COD ( x , t )
(2)
with a discretization of 0.65 mm throughout the duration of the test. Here, h is the height of one beam or one adherent, respectively. Making use of the connection of the strain ε and the curvature w II with w COD = 2 w and w being the deflection in Eq. (2) and a Euler-Bernoulli beam theory approach getting the moment M ( x ) = − EIw II ( x ) it gives the J-Integral J OFS and the peel stress σ OFS
b
w COD
2 → σ OFS ( w COD ) =
∂ 2 ∂ x 2
d d w COD
EI
J OFS ( w COD )
(3)
J OFS ( w COD ) =
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