PSI - Issue 33

R.V.F. Faria et al. / Procedia Structural Integrity 33 (2021) 673–684 Faria et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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adhesives with higher ductility lead to a gradual failure instead of abrupt, and detachment only after plasticization. The analysis between the bonded and hybrid joint (i.e., by adding a spot-weld over the adhesive layer) brings a significant advantage in P m (297.0%.) This marked difference is due to important role of the weld-nugget in the load transmission between adherends, taking place after the premature failure of the adhesive layer at x / L =0, while also existing surrounding adhesive to aid in the process. This hybrid joints’ enhanced performance can be explained by the fact that, after the failure of the adhesive layer between the joints’ loaded end and the vicinity of the weld nugget, the adhesive near the weld-nugget also has an effective role in the transmitted load between the adherends. 4.4. P m for different initiation criteria The XFEM is initially evaluated for different damage initiation criteria (both stress and strain based). For this first analysis, the propagation conditions were kept unchanged: linear stress softening up to failure and  =1. All data were compared with the experimental P m for assessment of the initiation criteria. For the MAXPE and MAXPS criteria, the maximum principal strains and stresses, respectively, are used to infer damage initiation and the direction of crack growth. As a result, the crack is forced to propagate perpendicularly to these quantities. As a result, it becomes numerically impossible to promote crack propagation in the adhesive layer through its length. To circumvent this limitation, the numerical P m is defined to the instant when cracking in the adhesive layer initiates. Oppositely to these criteria, the other ones allow crack growth to take place under mixed-mode conditions along the adhesive layer’s length, and the entire fracture behavior can be captured, starting from cracking onset to separation of the adherends. Under these conditions, P m is numerically assessed from the respective P -  curve. Fig. 7 shows P m (experimental and numerical) for the welded, bonded and hybrid joint. In this figure, the y axis of was cut, thus not showing P m for the QUADE, MAXE and MAXPE criteria (which highly overshoot the real results), to increase visibility for the other criteria. Table 3 provides the % P m errors between the XFEM data and experiments.

Fig. 7. Experimental/numerical P m comparison between all joint types - damage initiation criteria.

Table 3. Percentile P m errors between the XFEM data and experiments - damage initiation criteria.

Joint condition

QUADS

MAXS

MAXPS

QUADE

MAXE

MAXPE

Spot welded Bonded 2015 Hybrid 2015

2.7

4.9

-97.8

1106.7

1344.9

821.5

3.9

3.9

-68.9

107.6

107.7

56.8

1.1

2.8

-90.5

832.5

1006.2

611.6