PSI - Issue 41

Victor Rizov et al. / Procedia Structural Integrity 41 (2022) 134–144 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

137

4

2 E  are the stresses in the springs with modules of

1 E  and

1   is the strain in the linear dashpot,

where

elasticity, 2 E , respectively. The stresses in the linear springs and the linear dashpot are expressed as functions of strains by applying the Hooke’s law 1 E and

1 E E  E  2 E

 



,

(8) (9)

E

1

1



,

E

2

2

    .



(10)

1 1 

1 

9 0.04 10    v rad/sec 3 , curve 2 – at

9 0.07 10    v rad/sec 3

Fig. 3. Variation of the strain energy release rate with time (curve 1 – at

9 0.10 10    v rad/sec 3 ).

and curve 3 – at

By combining of (2), (5) – (10), one obtains 3 2 1 1 1 t          ,

(11)

where

1   E E   1

2

,

(12)

1

2  E v 

2 

.

(13)

1 

The solution of equation (11) is found as   Ht Qt At R e t       2 3 1 1 1    ,

(14)

1 2    A

,

(15)