PSI - Issue 77

C.F.F. Gomes et al. / Procedia Structural Integrity 77 (2026) 95–102 Gomes et al. / Structural Integrity Procedia 00 (2026) 000–000

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underestimating P m due to using a triangular CZM law. For this adhesive, differences of 18.4% for L O =20 mm and 14.3% for L O =40 mm were observed. Given that the observed discrepancies remain within an acceptable range, the numerical model is considered appropriate for the subsequent studies.

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Exp AV138 Exp 2015 Exp 7752 Num AV138

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P m [kN]

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Num 2015 Num 7752

0

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L O [mm]

Fig.3. CZM validation results by P m comparison.

3.2. Damage analysis The damage in an adhesive joint can be analyzed using the stiffness degradation (SDEG) variable in Abaqus ® (Fig. 4). Thus, it is possible to study damage propagation within the adhesive and understand its degradation during different loading phases. The SDEG variable is plotted at P m . This variable ranges from 0, the moment before damage occurs (the elastic zone) to 1, when the material’s strength is cancelled, resulting in rupture. Values between 0 and 1 correspond to the cohesive law softening zone. The ΔSDEG variable is calculated as the difference between the SDEG damage peaks at x / L O =0 and x / L O =1, relative to the higher damage at x/ L O =0.

1

1

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0.6

SDEG

SDEG

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x / L O CFRP AW 6082-T651 aluminum DIN 55Si7 steel

x / L O

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b)

20 mm

40 mm

10 mm

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SDEG

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x / L O Araldite® AV138 Araldite® 2015 SikaForce® 7752

c)

Fig. 4. SDEG in the adhesive layer at P m for different a) L O , b) adherend materials, and c) adhesives.

The L O effect was studied using CFRP joints bonded with the 2015, considering L O =10, 20, and 40 mm (Fig. 4 a). The results showed a more uniform damage distribution for L O =10 and 20 mm, due to lower σ y and τ xy peak stresses. However, the undamaged length of the L O =40 mm joint was the smallest, covering only 14% of its total L O , compared to 17% for L O =20 mm and 35% for L O =10 mm. The main cause of this behavior was the increasing τ xy stress gradient, which is responsible for the fracture process and increases with L O , reducing the undamaged area. The maximum