PSI - Issue 33

10

Victor Rizov et al. / Procedia Structural Integrity 33 (2021) 402–415 Author name / Structural Integrity Procedia 00 (2019) 000–000

411

   

n t

   

2 1

2 1







2 2

e v t UN i 2 

1

u

E v t pri UN 

n E E 







.

(31)

0

1

UN

i

i

pri

i

DRH v  and

DUN v  , which are involved in (14) and (29) are found in the following way.

The speeds,

5 10 0.0066   

Fig. 7. The strain energy release rate in non-dimensional form plotted against 31 q (curve 1 – at

 v

rad / sec , curve 2 – at

5 10 0.0132   

5 0.02 10   

 v

 v

rad / sec and curve 3 – at

rad / sec ).

First, one equation is written by using the fact that the bending moments in the cross-sections of the right-hand delamination crack arm and the un-cracked beam portion are equal          RH i UN i i n i A i n i A UNi i z dA z dA 1 ( ) 1 ( ) 2 1   . (32)

t v DRH  and

t v DUN  in (6). After

DRH  and DUN  with

Further one equation is worked-out by replacing of

substituting of stresses, DUN v  by using the MatLab computer program. It should be mentioned that equations (32) and (6) can be used to determine DRH v  and DUN v  at various values of the time. By substituting of (22), (23) and (26) in (22), one obtains the following solution to the strain energy release rate: i  and UNi  , in (32), equations (32) and (6) are solved with respect to DRH v  and

    RH i n i 1 ( )

    RH i n i 1 ( )

h 1

  

  

G

u dA RH 0

u dA i RH 0





.

(33)

i

A

A

i

i