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

20

7

16

12

8

P m [kN]

4

0

0

12.5

25

37.5

50

L O [mm]

Triangular

Exponential

Trapezoidal

Fig. 6 – Numerical P m vs. L O curves as a function of the CZM law shape.

3.2.3. Damage initiation criterion Distinct types of crack damage criteria initiation were evaluated: quadratic stress (QUADS), maximum stress (MAXS), quadratic strain (QUADE) and maximum strain (MAXE). Equation (1) defines the QUADS criterion: 2 2

0 t     +         0 n s n n t t t

,

Eq. (1)

f

=

and the MAXS criterion is represented by Equation (2).

0 0 max , . n s n s t t t t         

f

=  Eq. (2) Strain-based criteria such as the MAXE and QUADE can also be employed to predict damage initiation in bonded joints. The QUADE criterion relies on a quadratic combination of strains (Equation 3) 2 2 Eq. (3) being ε n and ε s the current tensile and shear cohesive strains, respectively. The MAXE criterion is set on the maximum value of the following ratios (Equation 4) Eq. (4) Fig. 7 displays a comparison of the expected P m as a function of L O when applying each criterion, revealing that the QUADS and MAXS values are similar independently of L O . As previously concluded in Section 3.1, the QUADS criterion provides accurate results and can be considered as benchmark. On the other hand, the QUADE and MAXE criteria deviated to the expected behavior for all L O . The maximum P m deviation of the MAXS data, in relation to QUADS, occurs for L O =25 mm (-2.5%). However, this difference highly increases for the strain-based criteria, up to 109.9% for the QUADE criterion ( L O =12.5 mm) and 160.9% for the MAXE criterion ( L O =12.5 mm). These results show that damage initiation in bonded joints is clearly ruled by peak stresses rather than strains. 0 0       , n  s  n  n  f       = + 0     0 max =  , . n s n s f         

32

24

16

P m [kN]

8

0

0

12.5

25

37.5

50

L O [mm]

QUADS

MAXS

QUADE

MAXE

Fig. 7 – Numerical P m vs. L O curves as a function of the damage initiation criterion.