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

870

7

2 z D C z   2

t C





(30)



Fig. 4. Desorption phase

With the initial conditions: C=C init for -h/2 < z < h/2 and t = 0 C=0 for z=-h/2 ; z= h/2 and t >0 The initial conditions being uniform and the boundary conditions are constants, the unidimensional solution of Fick equation can be expressed as (Benkhedda et al. (2008), Khodjet kesba et al. (2016)):





  

     

  

2 2

 2 1 ( 1) n n 

(2 1)

C

n

z

D n

t

 



 

   0 n

  

  

(31)

 ( , ) 4

cos 2 1

exp

C z t

ini

k

z





k

2

h

h



The loss of stiffness in the laminate as of crack density is evaluated compared to the initial stiffness of the same uncracked laminate and for the same environmental case. We note that this initial stiffness of the uncracked laminate is function of temperature. Consequently, Equations (3) and (26) become:                   0 12 0 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 i xy i x i x i         (32)

   

  

0( ) 0 i

12 21

11 0

yy



E E

1

(33)

( )

x i



E E

t l t 

1 ( ) g l ( ) 0 i

0

( ) i



1



( )

x i

0( ) 0 0 i

The index (i) represents the considered case of the environmental conditions. The longitudinal Young’s modulus degradation is represented in off-axis [0/β 3 ] s cracked laminate exposed to hygrothermal conditions with a parabolic variation of longitudinal displacement in both 0° and β° layers (transverse cracks are in β° layers). Transient and non-uniform moisture concentration has been selected to represent the effect of temperature and moisture in the cracked off-axis composite laminates for desorption case. Three sets of environmental conditions are considered. Top=22°C for environmental case 1, Top=60°C for environmental case 2 and Top=120°C for environmental case 3. The time chosen for simulation is taken equal to t sat =4222h with t sat is the moisture saturation for T300/5208. The characteristics of fibre and matrix of graphite/epoxy (T300/5208) laminate are exposed in Table 2.

Table 2. Fiber and matrix characteristics of graphite/epoxy material (T300/5208) (Tsai 1988). Efx (GPa) E fy (GPa) ν fx E m (GPa) ν m G m (GPa) G fx (GPa) V f 259 18.69 0.25 3.4 0.35 1.26 19.69 0.7