PSI - Issue 41

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

120

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purpose, the contour of integration, Q , is used. The solution of the J -integral is found as

3 2 1 Q Q Q J J J J    . The J -integral in section,

(31)

1 Q , of the integration contour is written as ds x p v x p u yi xi              ,   

z

i    1 1 1 i n 

  

i cos 01

J

u



(32)

Q

1

1

i



z

1

i

where

1 cos    ,

(33)

x i p i y p

   ,

(34) (35)

i

0 

,

1 ds dz  ,

(36)

x u

 

  .

(37)

Fig. 3. Variation of the non-dimensional strain energy release rate with non-dimensional time (curve 1 – for statically undetermined beam and curve 2 – for statically determinate beam).

2 Q , of the integration contour the J -integral is (Fig. 2) ds x p v x p u u i z yi xi i i n n                   2 1 1 cos 02  ,

In section,

  

  

J



(38)

Q

2

1

i

z

2

i

where

1 cos    ,

(39)