PSI - Issue 41

T.F.C. Pereira et al. / Procedia Structural Integrity 41 (2022) 14–23 Pereira et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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A marked difference between the P -  curves of Fig. 4 (a) was found. The experimental  at failure was significantly higher than that of the CZM predictions (difference of 567.8%). However, it should be emphasized that the experimental  is influenced by the technique implemented by the impact test equipment. In fact,  is estimated by integrating accelerometer data, resulting in an offset of the experimental  to the expected behavior. On the other hand, the numerical P m over predicts the experimental data, which is assumed to be related to the perfect bonding assumption in the numerical simulations, theoretical and uniform t A , together with absence of flaws. Identically, fabrication variability also does not affect the CZM predictions. Fig. 4 (b) reports the P m and  P m differences. The numerical P m result is 15.8% higher than the test results, whose difference can be justified identically to the former description on  . Oppositely to P m , the experimental  P m over predict the CZM data by a large amount. For this adhesive, the found difference was 82.7%. Considering the obtained results, it is concluded that the impact CZM approach is accurate, and thus a numerical study on the CZM parameter analysis will follow in the next section. 3.2.1. Mode decoupling Regardless of the cohesive law used, the damage initiation criterion used in this work was the same for all laws, i.e., the quadratic nominal stress criterion (Campilho et al. 2013). Once the damage initiates, traction and shear can be either coupled or uncoupled during the damage propagation, which is achieved by turning to zero the non diagonal terms of the stiffness matrix (Abaqus® 2017). Consequently, the CZM models done here were evaluated with the coupled and uncoupled conditions. The comparison between both cases is shown in Fig. 5. In all cases, the coupled models provided a higher P m than their uncoupled counterparts, agreeing with previous work (Campilho et al. 2013). The differences for the four L O were 24.9%, 26.1%, 23.5%, and 25.1% for increasing L O . Hence, on average, the coupled models provide P m 25% higher than its uncoupled counterpart. Furthermore, previous research shows that coupled traction-shear leads to predicted P m closer to experimental values (Campilho et al. 2013). 3.2. Parameter analysis

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12

8

P m [kN]

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0

0

12.5

25

37.5

50

L O [mm]

Coupled

Uncoupled

Fig. 5 – P m vs. L O curves for the coupled and decoupled models.

3.2.2. CZM shape The CZM law shape is known to have influence in the static strength prediction of bonded joints, although satisfactory predictions are mostly found by the applications of laws that do not exactly correspond to the adhesive’s behavior (Zhang et al. 2018). In this work, the triangular, trapezoidal, and exponential decoupled formulations described in detail in the work of Rocha and Campilho (2018) were used to assess their influence under impact loads, whose effect is not widespread in the literature. Fig. 6 compares the mentioned CZM laws. Under impact, and in the case of brittle adhesives, the CZM law shape has a minor effect on P m . Compared to the commonly used triangular law, the largest relative differences were -3.7% for the exponential law ( L O =25 mm) and +4.4% for the trapezoidal law ( L O =12.5 mm). However, for ductile adhesives, a higher difference could be found due to the larger extent (i.e., allowed displacements) of the respective CZM laws, which increases the number of cohesive elements within the adhesive layer under softening whose stress transfer is miscalculated.