PSI - Issue 68

Lukas Dominik Geisel et al. / Procedia Structural Integrity 68 (2025) 1273–1279 L. D. Geisel and S. Marzi / Structural Integrity Procedia 00 (2024) 000–000

1274

2

l s

l

F ,δ

h

H

a

L

2 L

(a) Schematic side-view depiction

F / 2

F / 2

l s

l

EI ,κµ A

2 EI , 2 κµ A

x

φ 1

φ 2

φ 3

φ 4

z

a

2 L

(b) Beam theoretical idealisation

Fig. 1: Schematic depictions of the 4-OSLB setup

(2024). This reliance on just strain measurements yields a potential alternative for cases in which the classical mea surement methods come up short. To test this potential, previously obtained and published experimental data of the 4-OSLB test (see Geisel and Marzi (2024)) is re-evaluated using this new method.

2. Theoretical background

Consider the 4-OSLB setup shown in Fig. 1. Traction-separation laws (TSL) that characterize the mode III fracture behaviour of structural adhesives can be obtained for this setup if a cohesive zone is assumed to exist ahead of the crack tip and single-mode loading is present. The cohesive stresses and the CTOD are in that case related to the ERR by J ( w CTOD ) = w CTOD 0 τ coh ( w COD )d w COD , (1) as was shown by Rice (1968). Traction-separation laws can therefore be obtained by di ff erentiation of J w.r.t. w CTOD . The external J -integral (computed via surface integration) for this particular setup is thought to be obtainable by measuring the angles φ 1 , φ 2 , φ 3 and φ 4 as well as the load-line force F according to

F 2 h

( φ 1 − φ 2 − φ 3 + φ 4 ) .

(2)

J ext ( F ) =

If this specimen is considered from a beam theoretical standpoint (see Fig. 1), the alternative evaluation method proposed by Aydin and Marzi (2024) can be used. This method requires only backface strain measurements (i.e., ε ( F , x , z = H / 2) = ˜ ε ( F , x )) along the entire length of the fracture process zone since both the ERR and the COD can be calculated with the help of some beam theoretical considerations.