PSI - Issue 33

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

424

9

l



 3 1 

M

x l



1

,

(34)



2

l

where

l 2 3 1

l 1    l x

(35)

and





2    l l

2 3 M B B 

x

,

(36)

1

3

where

2( l x l     2 1 l l 3 1

)

.

(37)

0.5  F 

1.0  F 



Fig. 6. The strain energy release rate in non-dimensional form plotted against

(curve 1 – at

, curve 2 – at

and

2.0  F 

curve 3 – at

).

The strain energy release rate calculated by (31) matches exactly that obtained by (20). This fact proves the correctness of the fracture analysis in loading phase. The strain energy release rate in the phase of unloading after decreasing of the stress from to is derived first by applying (20). For this purpose, the time-dependent strain energy density in the lower crack arm is written as 0  UN 

2 1

u

01 

.   UN

(38)

By substituting of (4) in (38), one obtains