PSI - Issue 51

Victor Rizov et al. / Procedia Structural Integrity 51 (2023) 206–212 V. Rizov / Structural Integrity Procedia 00 (2022) 000–000

208

3



  t



i      1 1 0 i g e

E E

,

(1)

D D

i

i

i D E 0

i g and i  are parameters. The modulus of elasticity increases with time at

is the modulus initial value,

where

0  i g . At

0 1    i g the modulus of elasticity decreases with time.

Fig. 2. Viscoelastic model. The relation between stress, strain and time for the model in Fig. 2 under a constant applied strain,  , is derived as

H i E 

i i E g  0 D

i i E g  0 D

  

t     i  e 





 

t



i 

1

E E g 

E

g  

e









H  

,

,

(2)

i

i

i

0

0

i

D

i

D

i





 

 

i

i

i

i

i

i

i

i

i  . The TDSERR, G , is obtained by applying the formula (Rizov (2021)) i  

where

hda dU

G 

,

(3)

where U is TDSE, da is an elementary increase of delamination. The time-dependent SE is found as

3 2 1 U U U U    ,

(4)

3 U are TDSE in the right-hand and left-hand delamination arms and in beam portion,

1 U ,

2 U and

where

l a x   4 , respectively. The TDSE cumulated in the right-hand delamination arm is (Fig. 3)

2 h

y

1 i        1 1 i 1 1 y i n i

U a 

01 1 1 u dy dz i

,

(5)

1

2 h