PSI - Issue 41

Victor Rizov et al. / Procedia Structural Integrity 41 (2022) 94–102 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

97

4

respectively. The time-dependent shear modulus,

* G , of the model in Fig. 2 is found as

  =

* G

.

(7)

Fig. 2. Viscoelastic model for treating the creep behaviour.

By using of (1) and (7), one obtains

1

−

G t

   

   

1

1 1

  

  

t

2 2 

−

G

e

=

+ + −

.

(8)

*

G

G

1 

1

2

2 G , 1  and 2  with

B G * , of layer 2 is determined by replacing of

1 G ,

The time-dependent shear modulus,

B G 1 , B 2  in formula (8). The strain energy release rate, G , for the delamination in Fig. 1 is found by applying the following dependence: (9) where U is the strain energy in the beam structure. The following formula is applied to calculate the strain energy: B G 2 , B 1  , h a G U   = ,

4 2 1 U U U U U = + + + , 3

(10)

where 1 U , 2 U , 3 U and 4 U are the strain energies cumulated in beam portion,

1 2 H H , in the left-hand and right

3 4 H H , respectively.

hand crack arms and in beam portion,

1 U , is determined as dx ,

The strain energy,

l

G I T D * 2

1  =

U

(11)

1

2

0

where 1 l is the length of beam portion, used to obtain this rigidity (Muskhelishvili (1996)): ( )  + + = 3 3 8 G I G b G b h B D          h 5 2 4       * 2 * 1 * 2

1 2 H H , G I D * is rigidity in torsion of the beam. The following formula is

( ) Q G ch jb G ch jb B 2 * 2 2 * +

( ) − 1

4

  

  = i 0

  

( ) ( ) Q G G ch jb ch jb B 2 1 2 * 2 * ) ( +

( ) ( ) − + 2 1

5

4

 −  

4

  

Q ch jb ch jb

h G G

  = i 0

  

  

  

  

−

* *

B

2



 ( Q j b b ch 1

)    − −  1 2

−

,

(12)