PSI - Issue 13

B. Boukert et al. / Procedia Structural Integrity 13 (2018) 174–180 B.Boukert et al/ Structural Integrity Procedia 00 (2018) 000–000

177

4

Table 1.Temperature ∆ T & concentration ∆ C profile shape

N°

REF

Mech-Transverse load

f1(z,T) T 0 +ZT 1 2T 0 (z/h)

f2(z,C) C 0 +ZC 1 2C 0 (z/h)

1 2 3 4 5 6 7 8 9

MTC2 MTC3 MTC4 MTC5 MTC6

Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes

T 0 (1/2+z/h)

C 0 (1/2+z/h)

T 0 (1-4z

2 /h 2 )

C

0 (1-4z

2 /h 2 )

T 0 +T 1 (2z/h)+T 2 (4z

2 /h 2 )

C 0 +C 1 (2z/h)+ C 2 (4z

2 /h 2 )

MTCF1 MTCF2 MTCF3 MTCF4 MTCF5

T 0 +ZT 1 2T 0 (z/h)

Lois de Fick Lois de Fick Lois de Fick Lois de Fick Lois de Fick

T 0 (1/2+z/h)

T 0 (1-4z

2 /h 2 )

10

T 0 +T 1 (2z/h)+T 2 (4z

2 /h 2 )

The same equations 8-10 are used for the hygroscopic part using expansions coefficient to calculate N Ci mn ,M Ci mn ,P Ci mn . 3. Numerical results & discussion In this section we simulate the behavior of a T300 / 5208 cross ply laminates [0°/90°/90°/0°] , thickness equal to 1 mm, a/h = 4 and a/b = 1, 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. The Stress state is shown in the figures 1-12, where:

2

2

2

( , , )( a b z

a

( , , )( a b z

a

a

),

),

(0, 0, )( z

)

SIG

SIG

SIG













xx

xx

yy

yy

xy

xy

7

7

2 2

2 2

. .

E h



. . .10 E h

. . .10 E h





L L

L L

L L

2

2

2 b

a

2 a

a

(0, , )( z

),

( , 0, )( z

)

SIG

SIG









xz

xz

yz

yz

3

3

. . .10 E h

. . .10 E h





L L

L L

Table 2. Simulation conditions. N° REF

Mechanical loading

Environnement

∆T

∆C

T 0 =10°C , T 1 =15°C T 0 =15°C , T 1 =20°C T 0 =20°C , T 1 =25°C

C 0 =0.01 , C 1 =0.02 C 0 =0.02 , C 1 =0.03 C 0 =0.03 , C 1 =0.04

ENV 1 ENV 2 ENV 3 ENV 1 ENV 2 ENV 3 ENV 1 ENV 2 ENV 3 ENV 1 ENV 2 ENV 3 ENV 1 ENV 2 ENV 3 ENV 1 ENV 2 ENV 3

1

MTC2

q 0 =100

2 3 4

MTC3 MTC4 MTC5

T 0 =10°C T 0 =15°C T 0 =20°C

C 0 =0.01 C 0 =0.02 C 0 =0.03

q 0 =100

T 0 =10°C , T 1 =15°C , T 2 =20°C T 0 =20°C , T 1 =25°C , T 2 =30°C T 0 =30°C , T 1 =35°C , T 2 =40°C

C 0 =0.01 , C 1 =0.02 , C 2 =0.03 C 0 =0.03 , C 1 =0.04 , C 2 =0.05 C 0 =0.05 , C 1 =0.06 , C 2 =0.07

5

MTC6

q 0 =100

T 0 =10°C , T 1 =15°C T 0 =15°C , T 1 =20°C T 0 =20°C , T 1 =25°C

Lois de Fick (HR=40%,t=200H) Lois de Fick (HR=50%,t=200H) Lois de Fick (HR=60%,t=200H) Lois de Fick (HR=40%,t=200H) Lois de Fick (HR=50%,t=200H) Lois de Fick (HR=60%,t=200H) Lois de Fick (HR=40%,t=200H) Lois de Fick (HR=50%,t=200H) Lois de Fick (HR=60%,t=200H)

6

MTCF1

q 0 =100

7 8 9

MTCF2 MTCF3 MTCF4

T 0 =10°C T 0 =15°C T 0 =20°C

q 0 =100

T 0 =10°C , T 1 =15°C , T 2 =20°C T 0 =20°C , T 1 =25°C , T 2 =30°C T 0 =30°C , T 1 =35°C , T 2 =40°C

10

MTCF5

q 0 =100

Figure 1-12 represent simulations on the behavior of cross ply laminates under different loading types presented in table 1 in 03 different environments in terms of temperature and humidity (Table 2), the purpose of this simulation is to see the influence of the environment (Temperature and humidity simultaneously) on the behavior of the laminate, For this reason, the simulations are changing from less aggressive environment to more aggressive, M1 purely mechanical loading with a sinusoidal force, MT1 thermomechanical with linear temperature change, MTC2 hygrothermomecanical,