PSI - Issue 72

C.F.F. Gomes et al. / Procedia Structural Integrity 72 (2025) 34–42

38

3. Results 3.1. Validation with experiments

The CZM approach is initially validated by comparing it with experimental data. The chosen tubular joint configuration includes an L O ranging from 20 to 40 mm, an outer diameter of 20 mm, and an adhesive thickness of 0.2 mm. The specimens were tested using a Shimadzu-Autograph AG-X tester (Shimadzu, Kyoto, Japan) equipped with a 100 kN load cell. The experimental maximum load ( P m ) was plotted against L O in Fig. 4, alongside numerical predictions. Both experimental and numerical analyses indicated cohesive failures of the adhesive.

50

40

30

P m [kN]

20

10

0

0

10

20

30

40

50

L O [mm]

Exp AV138 Num AV138

Exp 2015 Num 2015

Exp 7752 Num 7752

Fig. 4. Experimental and numerical P m results for validation. The AV138 showed minimal differences between experimental and numerical results, with deviations of 2.4% for L O =20 mm and 4.7% for L O =40 mm. Similarly, for the 2015, the deviation was 6.1% for L O =20 mm, decreasing to 2.9% for L O =40 mm. Conversely, the tubular joints using the 7752 exhibited moderately lower numerical P m . Despite the differences, of 18.4% for L O =20 mm and 14.3% for L O =40 mm, with experimental values consistently higher, the numerical values are considered acceptable for comparative study of parameters and geometries. 3.2. Stress analysis Stresses are normalized by the average  xy stress along L O ( τ avg ). The adhesive layer length is normalized, such that the x -axis is represented between 0 and 1, which makes it easier to compare all the joints analyzed. 3.2.1. Peel stress The results of adhesive joints with L O =20 mm and the 2015 on all adherends were compared (Fig. 5 a). The maximum value of σ y / τ avg =2.00 was observed at the overlap edges for the CFRP joints. Since the longitudinal modulus ( E 1 ) of CFRP is greater than the Young´s modulus ( E ) of aluminum it gives rise to higher σ y peak stresses. The second highest peak stress was recorded by aluminum, with a maximum of σ y / τ avg =1.98. Given that steel is the adherend with the highest E value, the expected strain gradient will be lower than that of the others ( σ y / τ avg =1.09).

4

4

3

3

2

2

 y /  avg

 y /  avg

1

1

0

0

-1

-1

0

0.2

0.4

0.6

0.8

1

0

0.2

0.4

0.6

0.8

1

x / L O

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

a)

b)

10 mm

20 mm

40 mm