PSI - Issue 33

A.F.M.V. Silva et al. / Procedia Structural Integrity 33 (2021) 138–148 Silva et al. / Structural Integrity Procedia 00 (2019) 000–000

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issues that can explain the lower experimental P m are imperfections in the joints’ fabrication, load cell accuracy, and possible misalignments in the testing machine or elastic deformation on some of its components. On the other hand, in the CZM model validation, it is considered that the adherends are perfect aligned, the adhesive is uniformly distributed in the joint, t A is constant and all materials are completely homogeneous. On the other hand, the experimental  P m values are significantly higher than the numerical ones, which can be due to errors introduced by integration of the accelerometer’s data, leading to an inflated value. The difference is 82.7% for the tested adhesive. Following this validation, it can be concluded that the adopted numerical technique has good predictive capabilities, and a fully numerical study on the strength tubular adhesive joints with the same adhesive will follow, beginning with the stress analysis.

16

3.6

16

13.61

11.75

12

2.7

12

8

1.8

8

P [kN]

 P m [mm]

P m [kN]

1.56

0.9

4

4

0.27

0

0

0

Experimental

Numerical

0

0.5

1

1.5

2

2.5

 [mm]

Pm dPm 

a)

b)

Experimental

Numerical

Fig. 5. P -  curve (a) and P m and  P m (b) comparison: experimental and CZM data.

3.2. Stress analysis In the numerical study of tubular joints,  y and  xy stresses in the adhesive were studied in the adhesive layer, since these are the relevant ones for the applied load. To enable the direct comparison between different L O , the length in the x -axis is normalized by L O , i.e., 0≤ x / L O ≤1 is considered. Additionally, both  y and  xy stresses are normalized by  avg , which represents the average  xy along the bond length for the respective joint geometry. Thus, the peak values in the stress plots correspond to a measure of the stress gradients along the adhesive line, rather than absolute values.

4

4

3

3

2

2

 xy / τ avg

 xy / τ avg

1

1

0

0

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 1 mm 2 mm 3 mm 4 mm

a)

b)

10 mm

15 mm

20 mm

Fig. 6.  xy /  avg stresses in the adhesive layer as a function of L O (a) and t SE (b).

The τ xy stress distributions as a function of L O for the tubular joints bonded with the Araldite ® AV138 are presented in Fig. 6 (a). According to the common knowledge in these joints,  xy stresses peak at both overlap ends, with lighter loads being transferred at the inner overlap region. Furthermore, no symmetry exists in the τ xy stress distributions, with the overlap end at x / L O =0 having higher peak stress due to the higher axial deformation in the inner tube, given its smaller section area compared to the outer tube (Barbosa et al. 2018). It is also visible that L O increases the overall