PSI - Issue 28

Victor Rizov et al. / Procedia Structural Integrity 28 (2020) 1212–1225 Author name / Structural Integrity Procedia 00 (2019) 000–000

1220

9

Finally, by substituting of (29), (30) and (36) in (28), one derives

R 3     0

  u RdR R 02 0 4

1

   ,

G 

u RdxdR 01

(39)

R

3

where 01 u , 02 u and 4 R are obtained at x a  . The integration in (39) is performed by using the MatLab computer program.

Fig. 3. The strain energy release rate in non-dimensional form presented in a function of the non-dimensional time by using the linear viscoelastic model shown in Fig. 2a (curve 1 – at / 1.2 2 1  R R , curve 2 – at / 1.5 2 1  R R and curve 3 – at / 1.8 2 1  R R ). The solution to the strain energy release rate (39) is verified by considering the balance of the energy. For this purpose, by assuming a small increase, a  , of the crack length, the balance of the energy is written as



a T U   

a Gl a crf   

,

(40)

where T is the torsion moment. From (40), the strain energy release rate is derived as

1 

a U





G T 



.

(41)

l

a l





crf

crf

By using the integrals of Maxwell-Mohr, one obtains