PSI - Issue 28

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

866

3

Fig. 1. Transverse cracked off-axis [0/β] s composite laminate and geometric model

Strain- stress equations are giving in the following form : a) In the 0° layer:

     

     

0 S S S S S S S S S S S S S S S S S S 0 0 0 0 0 yz xz yy xy xy xx       yy xy xy xx

0

         

    

    

    

0

0

z       z

  

xz

x

x

(1)

0 0 y

0

0 0 y



yz

0

zz

z

b) In the β° layer:

     

     



    

    

    





  

xz

x

x

(2)









y

yz

y







xz

yz

zz

z

Where S ij is the compliance matrix for off-axis composite laminate. We obtain the modified expression of the longitudinal Young’s modulus of the off-axis laminate due to transverse cracks:                   0 12 0 90 0 0 0 12 0 1 2 1 1 1 1 1 s t s t s t s t R a a E t E t E E xy xy xy x x        (3) The model developed by Berthelot (1997) is used. This latter is modified by introducing the stress perturbation function: (4) x a         11 0 90 12 21 0 0 yy

   

) cosh( ) cosh( a 

) tanh( 2 a 

( )

d x

R a





a



Where, is the shear-lag parameter:

0 0 t E E t t E t E     (

)

(5)

2

G





0

0



The coefficient depends on used assumptions about the longitudinal displacement and shear stress distribution a) In the case of the assumption of a parabolic variation of longitudinal displacement in both 0° and 90° layers, the coefficient is done by : G G

 t G G 3 

(6)

The shear modulus G of the elementary cell:

(7)



G

G



xz

( ) 

' t f t f t 



G G

1 3 

xz

0

( ) 

xz

3 2





By replacing the function  

in the (7), the shear modulus for parabolic

0  t t t 2 2 t t z f z z       2 t 0 0 2 

2

