PSI - Issue 41

Victor Rizov et al. / Procedia Structural Integrity 41 (2022) 94–102 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

98

5

where

) 

(

( ) ( ) +

1 * 5 2 1 i G ch jb sh jb 2

Q

= +

( ) ( )  2 1

* G ch jb sh jb B +

,

(13)

(

)

i  2 1 +

j

=

.

(14)

h

The strain energy in the left-hand crack arm is found as dx G I T U l a l * 1 2 1 2 2 2 1 1  + = ,

(15)

where 1 T is the torsion moment in the left-hand crack arm, 1 I is the moment of inertia of the cross-section of this crack arm. 1 I is calculated as (Muskhelishvili (1996))

5

4

3

1 ( )

4

( i th jb + 2 1

2 h

  = 1 i

  

  

  

I b h

  = −  1 3

.

(16)

)

1

5



Formula (15) is applied also to calculate the strain energy in the right-hand crack arm. For this purpose, 1 T , * G and 1 I are replaced with 2 T , B G * and 2 I where 2 T is the torsion moment of the this crack arm. The moment of inertia, 2 I , is determined by replacing of 1 b with 2 b in formula (16).

Fig. 3. The strain energy release rate displayed as a function of time.

3 4 H H , is calculated as

The strain energy in the beam portion,