PSI - Issue 17

B.Boukert et al/ Structural Integrity Procedia 00 (2019) 000 – 000

4

B. Boukert et al. / Procedia Structural Integrity 17 (2019) 37–43

40

where N mn , M mn are given by equations 8-10:

1

1 k z k =   N z k +





     k k i Q 



Ti

Ti

Ti

3

, N M P ,

( ), T z T z z T z z dz    ( ) , ( )

=

(8)

mn

mn

mn

4 h

Ti

Ti

Ti

mn M M =

P

−

(9)

mn

mn

2

3

0 0   a b

4

i

i

mn T

T x

y dxdy

sin( ) sin( )  

=

(10)

ab

  =  









( , , ), T x y z C x y z   ( , , )

1( , ), 2( , ) sin( ) sin( ) f z T f z C x y  

(11)

n m

1 1

= =

The faces are exposed to relative humidity HR , the internal concentration is described by Fick equation with diffusivity D. 2 2 (2 1) 4 1 (2 1) , 1 sin exp 2 1 2 1 2 ( , ) ( , ) 2 C C j D t j z i z j C C j h h m i C z t C z t D z t z −  +  +    = − − = −  +   =         (12)

with :

C C à t i C C à t = =

0 0 et

z h

,

=

 

et z

z h

0

0, = =

,



m

A −       RT

(13)

D D =

0 exp

3. Numerical results & discussion

In this section, the behavior of a T300 / 5208 cross ply laminates [0 ° / 90 ° / 90 ° / 0 °] , thickness equal to 1mm , a / h = 4 and a / b = 1, was simulated. The simulations use the temperature and humidity distribution models shown in Table 1. Each temperature and humidity model is evaluated in several environments (see Table 2) in order to see the influence of temperature and humidity, the curves below represent the behavior.

Table 1 : T300 / 5208 Diffusion characteristics.

Diffusivity mm 2 /s D=132exp(-6750/T).

Max concentration

T300/5208

C m =0 .015HR