PSI - Issue 41

Victor Rizov et al. / Procedia Structural Integrity 41 (2022) 125–133 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

131

7

R

R

R

1

2

2





0 



0 

U l a u RdR a u  ) 2 (   

2

2

l l a u RdR    

RdR



.

(28)

1

0

0

1

0

L L

L L

2 3

3 4

R

1

0 u , in the beam portion, 1 2 L L , and in the internal crack arm is found as

The strain energy density,

 u d   0 0

  .

(29)

2 3 0 L L u

3 4 0 L L u

. For this purpose,  is replaced

and

Formula (29) is used also to obtain the strain energy densities,

2 3 L L  and 3 4 L L  , respectively. By combining of (19), (27) and (28), one derives

with

R

R

R





1

  

   .

  

  

1

2

2





 0

L L

L L

u RdR

u RdR L L 2 3 0

u RdR L L 3 4 0

 G T









(30)

2 3 2 R R R 

3 4

0

R

1 0

1

2

2

R

1

The MatLab computer program is applied to carry-out integration in (30). The strain energy release rates determined by (26) and (30) are identical. This fact is verification of the analysis described in this paper. 3. Parametric investigation Results of a parametric investigation of the strain energy release rate are presented in this section of the paper.

/ 1 2  R R

0.3

/ 1 2  R R

0.4

1 p (curve 1 – at

Fig. 5. Evolution of the strain energy release rate with increase of

, curve 2 – at

and

/ 1 2  R R

0.5

).

curve 3 – at

0.350  l m,

0.005

0.015

0.100 1  l m,

0.7  i b ,

3  n ,

1  R

2  R

m,

m,

It is assumed that

0.7  i g and rad/sec. The evolution of the strain energy release rate with time can be observed in Fig. 3. It should be mentioned that 6 0.08 10     v