PSI - Issue 47

Hachimi Taoufik et al. / Procedia Structural Integrity 47 (2023) 711 – 722 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

716

6

The C3D8R mesh was applied according to the geometry and material deposition. The interaction between layers is called Tie interaction, defined as encountered interaction. The simulation was carried out to simulate the mechanical behavior of the simple edge notched tension with two layers and compare those results with the experimental test. 2.5. Stress intensity factor: The best fracture mechanics method applies to crack propagation laws based on various stress intensity parameters. The stress intensity variables appropriately define the stress field near the crack's tip and give the basic details of the crack's propagation in elastic fracture analysis Najat et al. (2022) . The two primary methods for determining the stress intensity parameters are the extrapolation method close to the fracture tip and the technique that employs the energy generated during crack propagation. In this investigation, the fracture tip displacement fields have been extrapolated. Based on fig. 6, The correlation of the stress intensity factor with the I-mode displacement fields (1), (2).

Fig. 6. Definition of the coordinate system around the crack tip.

2 2 I K r G

(

)

1

+ =

u

k

+

(1)

2



2 2 I K r G

(

)

1

− =−

u

k

+

(2)

2



E

I K Is the Stress intensity factor for mode-I and

.

G

=

3 4 k v = − (for a plane deformation) and

With

( 2 1

)

v

+

Where r is the distance to the crack tip. Thus, the stress intensity factor for mode-I can be obtained from the displacements of the crack opening,

2 2 m U u u + − = −

) 2 2 [ ] m r v 

E U

K

=

(3)

(

I

8 1

−

The empirical formula based on linear elastic fracture mechanics related to the stress intensity factor in the case of SENT geometry shown in Fig. 2b is given by Vu‐Khanh et al. (1985) :

a       w

K

a f

 

=

(4)

I

With: σ : Maximum tensile stress; a: Length of the crack; w: Width of the test specimen, and a f w       factor depending on the structure's geometry. In our case, this factor is expressed by: 2 3 4 a a a a a f 1.12 0.231 10.55 21.72 30.39 w w w w w           = − + − +                    

It is a correction

(5)