PSI - Issue 41

A.E.S. Pinheiro et al. / Procedia Structural Integrity 41 (2022) 60–71 Pinheiro et al. / Structural Integrity Procedia 00 (2019) 000 – 000

70

11

50

0

20

30

40

 P m [%]

-50

-100

L O [mm]

N-H

P&C-MPSC P&C-MSSC

FEM-MPSC FEM-MSSC

GY

FEM-CZM

P&C-MPSC+MSSC FEM-MPSC+MSSC

Fig. 9.  P m between the predictions and experimental results for the 7752.

Table 7. Summary of  P m [%] for the 7752 and both L O . L O [mm] 20

40

N-H

-64.4 -69.0 -64.4 -69.0 -4.2 -52.3 -62.9 -62.9 -18.4

-72.6 -79.4 -72.6 -79.4 13.3 -64.1 -74.2 -74.2 -14.3

P&C-MPSC P&C-MSSC

P&C-MPSC+MSSC

GY

FEM-MPSC FEM-MSSC

FEM-MPSC+MSSC

FEM-CZM

The results depicted in Fig. 9 show that, for this adhesive, the GY approach provides the best results, while the CZM data is slightly below the experimental results. The continuum mechanics-based predictions, coupled either analytical or FEM stress predictions, undervalue the joint behavior, identically to former analyses. Table 7 shows that these under predictions range between -52.3% and -69.0% for L O =20 mm, and between -64.1% and -79.4% for L O =40 mm. Consistently with previous analyses, the models of Pugno and Carpinteri, and Nayeb-Hashemi et al. models are equal. Since this adhesive fails under GY conditions, due to its large ductility, the GY criterion works the best for this adhesive. Inclusively, a negative  P m was found for L O =20 mm (-4.2%), which can be originated by the tested adhesive being stronger than the average measurements from the bulk characterization tests. For L O =40 mm, the difference was 13.3%. The CZM technique failed to accurately reproduce the experimental behavior, with  P m =- 18.4% ( L O =20 mm) and -14.3% ( L O =40 mm), mostly due to imposing stress reduction in the CZM law, which is not the most adequate for highly ductile adhesives. 4. Conclusions This work was mainly based on an analytical analysis to tubular bonded joints, whose results were also compared to FEM and the respective P m predictions with GY and CZM. Initially,  y and  xy stress distributions were obtained by the analytical models. Only the model of Pugno and Carpinteri could predict  y stresses, but major deviations were found to the expected behavior. On the other hand, the two proposed models showed identical  xy stress plots along the bondline, and the approximation to the FEM was acceptable. Between adhesives, the AV138 provided the highest peak values due to its increased stiffness. P m was predicted by the analytical models coupled with continuum mechanics-based criteria, the GY criterion, and CZM. The CZM overall provided the best results for the three adhesives, although with under predictions for the most ductile adhesive (7752). The GY criterion over predicted P m for the brittle adhesive, but it presented closer values to reality for the ductile adhesive. The analytical methods significantly under predicted the real joint behavior, but these were not far from the respective FEM predictions for the same failure criterion when considering  xy stresses. Nonetheless, the selected criteria are not suitable for P m prediction, even for brittle adhesives.