PSI - Issue 28

8

Victor Rizov et al. / Procedia Structural Integrity 28 (2020) 1226–1236 Author name / Structural Integrity Procedia 00 (2019) 000–000

1233

2 1

1

2   

1

n in



u B

D



,

(31)

0

in

in

1

n



2 1

1

2   B  uc

1

n uc



u

D



.

(32)

0

uc

1

n



1 2 / R R ratio (curve 1 – at /

0.25 0  D B , curve 2

Fig. 3. The strain energy release rate in non-dimensional form presented as a function of

/ 0.50 0  D B and curve 3 – at /

0.75 0  D B ).

– at

By substituting of  and U in (29), one derives

B R 2

2 1 2 2 R R R R ft et          

2

  

  

1

    R



1

n



D

RdR

G T 







2

1

n



1

1

B R 1

B R 2

2

2

  

  

  

  

1

1

  





 

 0

 RdR D n in 1 

 RdR D n uc 1 







in

uc

.

(33)

2

1

2

1

n

n





0

The integration in (33) is carried-out by the MatLab computer program. It should be mentioned that the strain energy release rate obtained by (33) is exact match of that found by (27). This fact is a verification of the longitudinal fracture analysis of the inhomogeneous non-linear elastic rod with internal crack loaded in torsion developed in the present paper.