PSI - Issue 51

R.B.P. Barros et al. / Procedia Structural Integrity 51 (2023) 17–23 R.B.P. Barros et al. / Structural Integrity Procedia 00 (2022) 000–000

20 4

2.3.4. Gustafson el al. method In the work of Gustafson et al. (1989), the authors carry out non-linear modelling of a composite CLS specimen by Beam Theories. The bending moment applied to the joint is calculated, leading to G T of delamination to be calculated 2

1 0 c F b e e             1 1 

G

(4)



.

T

2

E

Mode partitioning ( G I and G II ) requiring using other tools (e.g., FEM). 2.3.5. Azazi el al. method According to Azari et al. (2009), an adhesive layer can be characterized for G T by the CLS geometry by 2 2 2 2 2 2 cu2 cu2 cu1 cu1 cu0 cu0 T 2 2 1 1 0 0 2 2 2 2 2 2 F M F M F F G Ee D Ee D Ee D                               . (5) The subscripts 1, 2 and 0 respect to the lower adherend, upper adherend and combination, respectively. F cu i and M cu i are, by this order the, unit-width force and bending moment of the adherends at the crack tip cross-sections (the subscripts i can take values of 1, 2 and 0). D i is the flexural stiffness by unit width of adherend i . 2.3.6. da Silva el al. method The method of da Silva et al. (2011) takes advantage of the Grady (1992) formulation to calculate G T and suggests the following expression for mode partitioning

G

1 II



(6)

tan

;

.

T I G G G  





II

G

I

3. Results 3.1. P-  and R curves

The P -  curves are given in Fig. 2. The AV138 data (Fig. 2 a) reveals a nearly linear curve with minor loss of linearity prior to crack onset, at P ≈12 kN, due to a short fracture process zone. The 2015 specimens (Fig. 2 b) give rise to a more pronounced non-linear region after P ≈10 kN, caused by the large fracture process zone.

20

40

15

30

10

20

P [N]

P [N]

10

5

0

0

0.0

1.0

2.0

3.0

4.0

5.0

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

δ [mm]

δ [mm]

a)

b)

Fig. 2. P -  curves for the AV138 (a) and 2015 (b) adhesives (four specimens tested for each adhesive).

R -curve analysis followed, but G I and G II could only be calculated by the theories of Grady, Kinloch, and da Silva et al. Moreover, since G I and G II from da Silva et al. derive from Grady's G T , this method is not considered in the G T analysis. Fig. 3 presents G T for selected specimens considering the AV138 (a) and 2015 (b) adhesives. The da Silva