PSI - Issue 33

8

Victor Rizov et al. / Procedia Structural Integrity 33 (2021) 428–442 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

435

  

  

b 1

   .

b ( ) 1     A D

h h z

  

  

   

   

  u dA U A U 0 ( )



G

z

dA

u dA D 0







 



1



(24)

D n 1

2

U

n

2 2

1

n

D ( ) A

The integration in (24) is performed by the MatLab computer program. It should be noted that (24) is used to calculate the strain energy release rate at various values of the time. In this way, the evolution of the strain energy release rate with the time due to the stress relaxation is investigated.

LW E E /

/

0.5  UP   , curve 2 –

Fig. 5. The strain energy release rate in non-dimensional form plotted against

ratio (curve 1 – at

UP

LW

/

1.5  UP   and curve 3 – at

/

2.5  UP   ).

at

LW

LW

The strain energy release rate is obtained also by applying the compliance method in order to verify solution (24). According to the compliance method, the strain energy release rate is written as

2

da dC

G F 2 

,

(25)

b

where C is the compliance. For the beam in Fig. 1 the compliance is expressed as

F C u F  .

(26)

By substituting of (21), (22) and (26) in (25), one derives the following solution to the strain energy release rate: