PSI - Issue 13

M. Khodjet-kesba et al. / Procedia Structural Integrity 13 (2018) 181–186 KHODJET KESBA Mohamed/ Structural Integrity Procedia 00 (2018) 000–000

182

2

of transverse cracking is generally schematized by the models which make the analysis of the shear transfer between fiber and matrix with the assumption that the mechanical loading is transferred between the layers. The shear-lag model was used to predict the effect of transverse cracks on the mechanical properties degradation of transient hygrothermal aged angle-ply [θ m /90 n ] s composite laminates. The obtained results show a good agreement comparing with experimental data (Joffe et al. 2001) for different angle-ply laminate and without taking into account the hygrothermal effect. On the other hand, the angle-ply laminates is initially exposed to the hygrothermal aging submitted to transient and non-uniform moisture concentration distribution for absorption case. The obtained results illustrate well the dependence of the elastic properties degradation on fibre angle orientation, cracks density and transient hygrothermal conditions for absorption case. 2. Theoretical analysis Transverse matrix cracking is a common damage mode in angle-ply laminates under uniaxial tension. It is assumed that the 90 ° ply has developed continuous intralaminar cracks in fiber direction which extend from edge to edge in z direction. The angle-ply laminate is characterized by 2.t 90 the width of 90° ply, t θ the width of θ °ply and the spacing between two cracks is 2.l 0 (Fig. 1)

Fig. 1. Transverse cracked angle-ply laminate and geometric model.

For ideally equally distributed crack spacing in 90° layers for symmetric and balanced laminates, the stiffness and Poisson ratio degradation model (Adda et al. 2008) was used to show that the crack spacing reduces the extensional mechanical properties of the specific angle-ply composite laminates according to:

    0 0

E

1

and

(1)

1

c R l a R l  



 

x



xy

  0



E

1

a R l 



0

1



0

x

xy

0 1 ;

0       0 90 l l t 

Where

is the noramalized crack density and a , c are known functions, dependent on elastic

 

2 l

properties and geometry of the θ° and 90° layer : 0 12 90 12 90 90 12 21 90 11 1 1 1 xy xy xy x yy S t S t E t a E S t S t                                 

(2)

0

   

       

   





1 1

11 12 S S S S  xy

 

12    

E t

xy

yy

90 90

(3)

c





yy S t 

90 11 S t 



12 21

xy



x E  and 90 E are the Young’s moduli of θ° and 90° layers respectively and 0 xy v is the Poisson’s ration of the undamaged laminate. The   0 R l is a function if the ideal crack spacing, which influences the elastic constant reduction rate and has different forms according to the Poisson’s ratio analysis model adopted as the shear lag model. In this