PSI - Issue 54

I.R.S. Araújo et al. / Procedia Structural Integrity 54 (2024) 406–413 Araújo et al. / Structural Integrity Procedia 00 (2019) 000 – 000

410

5

each of the two resulting sub-elements consists of real nodes (those corresponding to the cracked portion) and phantom nodes (those no longer belonging to the respective part of the original element). These two elements exhibit fully independent displacement fields and replace the original one. From this point onward, each pair of real/phantom nodes in the cracked element can separate following an appropriate cohesive law until failure. At this stage, the real and phantom nodes are free to move without constraints, effectively simulating crack growth. A softening XFEM law is considered, employing an energetic failure power law criterion of a specific type

I G G G G       + =         II IC IIC

(3)

1,

where G I and G II represent the current fracture energies in tension and shear, respectively. The analysis in this work focused on the QUADS initiation criterion and a linear damage law with a power parameter of  =1. 3. Results 3.1. Experimental results Fig. 4 presents the experimental P m average values and their respective standard deviation (STDV) as a function of   for the three evaluated adhesives. From data analysis, a similar strength evolution with  is noticeable among them. P m of all adhesives is found for  =3.43 o , while for the other angles P m diminish and the lowest reduction was attained between  =3.43 o and  =10 o . Comparing all adhesives, the AV138 stands out, with higher P m for  =3.43 o by 35.6 and 120.0% when compared with the 2015 and the 7752, respectively.

40

30

20

P m [kN]

10

0

0

10

20

30

40

50

α [º]

AV138

2015

7752

Fig. 4. Experimental P m average results and STDV as function of  for the three adhesives.

Table 2 shows the average experimental P m , STDV, and coefficients of variation (CoV). The CoV was higher for the joints with  =45 o bonded with the 2015 and AV138, of 17.43 and 11.03%, respectively, which may result from specimens’ manufacture or issues associated with testing procedures. The 7752 presented higher deviations with the scarf architectures of  =15 o ,  =20 o and  =30 o . All remaining values are acceptable.

Table 2. P m average values, STDV, and CoV for scarf joints bonded with the different adhesives.

3.43

10

15

20

30

45

 [ o ]

AV138 STDV [N] CoV [%] 2015 STDV [N] CoV [%] 7752 STDV [N] CoV [%]

29700 1500 21903 1600 13500 510.90 5.05 7.30

10648 346.63 7509 772.04 10.28 4677 195.40 3.26

7926 642.49 4858 141.92 3132 286.25 8.11 2.92

5715 310.02 3567 205.56 2378 229.38 5.42 5.76

4480 150.89 2832 101.03 1543 167.86 10.88 3.37 3.57

3325 366.66 11.03 1868 325.56 17.43 1142 63.51

3.78

4.18

9.14

9.65

5.56