PSI - Issue 28

5

Mohamed Khodjet Kesba et al. / Procedia Structural Integrity 28 (2020) 864–872 KHODJET KESBA Mohamed / Structural Integrity Procedia 00 (2019) 000–000

868

02 C p C C  

,

(21)

C q C 

11

22 00

22

Provided that

. Consequently the solutions are of the form:

2

4 q p 

(22)

cos

sin

1 A ch

2 A sh















With  2



a sh a ch a a sh a a           2 sin 2 cos sin        a sh a ch a a sh a a           2 sin 2 cos sin        



(23)

A



1



2



(24)

A



2

And

sin 4 1

cos 4 1

4 1 2  q





;

(25)

;

 q 

 q 

 arctg 

2

2

p

The reduced stiffness E x can be expressed in the following form :

(26)

1

E



x

E

t l t

1 ( ) g l

E

 

1



0

x

0

E

0 0 0

Where

is expressed as:

( ) 0 g l

2

sinh(2 ) sin(2 ) cos(2 ) cosh(2 ) 0 0 l l l l       



(27)

( ) 0

g l



2

2









0

0

3. Results and discussion 3.1 Reduction of longitudinal Young’s modulus for [0 m / β n ] s

In this section we will validate the results of the present program without taking into account the hygrothermal effect on the material properties. The results are compared with experimental data for glass/epoxy laminate (Katerelos et al. (2008)). The material properties of the chosen composite as well as their geometrical characteristics are summarized in Table 1.

Table 1. Mechanical properties of glass/epoxy composite laminas Constituent E 1 (GPa) E 2 (GPa) G 12 (GPa)

υ 12 0.3

13 43

4.69 4.69 8.76

0° layer 90° layer 45° layer

43 13

0.09 0.42

13.36

13.36

Fig. 2 and 3 show a comparison of results obtained by the analytical models and experimental data for [0/45] s glass/epoxy laminate and with two different thickness. We note that the transverse crack is in the 45° ply. The progressive shear model seems the closer to the experimental data compared to parabolic analysis and variational model (Fig. 2). On the other side, by increasing the thickness of the 45° cracked layer (Fig. 3) , the variational analysis is closer to the experimental which gives an advantage to this method to represent the behavior of the [0 m /β n ] s composite laminate under transverse cracking and delamination effect.