PSI - Issue 41

Victor Rizov et al. / Procedia Structural Integrity 41 (2022) 115–124 Author name / Structural Integrity Procedia 00 (2019) 00 – 000

121 7

xi p

iup    ,

(40) (41)

0 

i y p

,

2 ds dz  ,

(42)

x u

 

 

.

(43)

up

3 Q , the J -integral is found as

Finally, in section,

z

i    3 1 1 i n 

x p u xi  

x p v yi  

  

  

  

  

i cos 03

J

u

ds









,

(44)

Q

3

1

i



z

3

i

where

cos 1   ,

(45)

x i p





,

(46)

iun

0 

i y p

,

(47)

3 dz ds   ,

(48)

x u

 

 

.

(49)

un

11 12 /   ratio (curve 1 – at non-linear viscoelastic behaviour and

Fig. 4. Variation of the non-dimensional strain energy release rate with

curve 2 - at linear viscoelastic behaviour).

The J -integral is derived by substituting of (32), (38) and (44) in (31)

z

      i i n 1 1 i

  x p u xi

  x p v yi

  

    ds

  

  

1 1

i cos 01

J

u







z

1

i