PSI - Issue 33

Victor Rizov et al. / Procedia Structural Integrity 33 (2021) 416–427 Author name / Structural Integrity Procedia 00 (2019) 000–000

418

3

2 E 



.

(3)



1 t t 

0 

UN 

At

the stress is decreased from

to

. The strain-time relationship is obtained by applying the

principle of superposition. The result is

1 1

  

 

       UN 

  

  





 

 













t t

t

  

1

1

1





e

e











0 

1 0

.

(4)

1

E

E





1

Fig. 1. Inhomogeneous viscoelastic beam with a longitudinal crack.

It should be mentioned that (4) is valid when

1 t t 

.

(5)

The material is continuously inhomogeneous in both thickness and length directions of the beam. The distributions of , and along the thickness of the beam are written as

1 E

2 E



          

     

      3       3

2 h z h



 1 sin 

 E E UP 1 1

,

(6)

2

          

     

2 h z h



 1 sin 

 E E UP 2 2

,

(7)

2