PSI - Issue 68

Ihssane Kididane et al. / Procedia Structural Integrity 68 (2025) 358–364 Ihssane Kididane et al. / Structural Integrity Procedia 00 (2024) 000–000

361

4

additively decompose the total external J -integral into contributions from the individual single fracture modes,

1 2 w 1 2 w

( F 2 + F 3 ) ( θ 2 − θ 3 ) , and ( F 2 − F 3 ) ( θ 2 + θ 3 ) + 1 w

J I =

(2)

( F 1 θ 1 − F 4 θ 4 ) .

J II =

(3)

Based on this mode-decomposition from external boundary conditions, which is based on assumptions from linear elastic fracture mechanics (LEFM), the mode-mixity φ is defined,

1 J II J I

φ : = tan −

(4)

.

Based on the assumptions of beam theory, an equivalent crack length a eq can be calculated from the symmetrical portion (DCB part) of the load,

3 δ 2 2( θ 2 − θ 3 ) .

a eq =

(5)

A possible estimate of a eq from the asymmetrical (ENF) part is considered less accurate and is therefore not pursued further here. The equivalent crack length obtained from Eq. 5 corresponds to the corrected crack length from the corrected beam theory (CBT). As recently shown by Geisel and Marzi (2024), such an equivalent crack length is expected to deviate from the actual crack length by a constant o ff set, so that the crack propagation is the same for both. Eqs. 1 to 5 are also applicable to SLB tests (Ji et al., 2012) where they further simplify due to F 2 = 0. However, in order to calculate J I , J II , φ and a eq the rotation θ 3 has to be known, but this quantity was not measured in the SLB tests presented in this work. Instead, the analytical value of φ ≈ 41 ◦ (Hong and Yoon, 1990) was used to compare SLB to CMMB test results.

3. Results

3.1. CMMB and SLB - comparison to a reference from literature

The CMMB test methodology was compared with reference measurements from the literature published by Ji et al. (2012) for the same adhesive and layer thicknesses in the same range. Therefore, CMMB tests were performed in δ 2 − √ J II -control (Kididane et al., 2024) at constant φ = 41 ◦ , which is the mode-mixity in SLB tests. Additionally, CMMB tests were performed in SLB configuration as described above. Fig. 3 compares the measurements to refer ences from the literature. It turns out that the obtained maximum values of the J -integral - with a large variance in the measured adhesive layer thicknesses - are significantly below the references except for a single experiment (Fig. 3, left). On the other hand, the results of the CMMB and SLB tests carried out in this work are in excellent agree ment. As Ji et al. (2012) reported cohesive fracture surfaces of ”typical shear failure mode”, the fracture patterns of two selected samples are illustrated in Fig. 3, right. In all tests with lower fracture energy compared to the reference, adhesive failure was observed in the interface between the substrate and the adhesive layer. However, in the only experiment consistent with the reference, the failure mode appears to be dominated by cohesive fracture. Recall that Ji et al. (2012) used steel substrates, while the beams in this work were made of aluminum, which apparently a ff ects adhesion and fracture behavior. As a consequence, the obtained fracture energies can not be directly compared to the ones from literature due to the di ff erent fracture behavior. Although the obtained values should be treated as properties