Issue 34

Y. Sumi, Frattura ed Integrità Strutturale, 34 (2015) 43-59; DOI: 10.3221/IGF-ESIS.34.04

can be calculated by using Eq.(7), and the stress intensity factors at the extended crack tip in an infinite plane can be obtained as

  

 

3 8

3 2

9 4

9 8

2

1 9 2 8   

5 4

  

 

  

  

( ) 

2

2

1/2

2

1   









1  

3   k 















K

k

k

k

k

T h 

b

b

2

I

I

II

II

I

I

II

II



(9)



11 2

27 32

3 2

  

 

2

3/2







( k h O h 







T

),

I



2

 

    

1/2       

7 8

1 2

3 4

2

21 2

1 27 2 8   

 

  

  

  

  

( ) 

2 

2 

k   







II b k  

1   



  

1  

K

k

k

T

II k h 

2

II

II

I

I

I





8

(10)

 



3

63 2

5 2

  

 

  

  

2

3/2

 





b  

 



( k h O h 

T

2

).

I

II



4 4

32

 

As far as the terms obtained by Wu [9], and Amestoy and Leblond [10] are concerned, Eq. (9) represents the exact second order asymptotic behavior of the Mode-I stress intensity factor, while the second order terms in Eq. (10) are approximate. Although being small, this slight numerical difference may arise from the interaction of stress singularities between the kinked corner and the crack tip. Stress Intensity Factors for a Finite Body Since the leading terms of the far-field stress and displacement are of the order of the crack extension length h [7], the finite body corrections of the stress intensity factors at the kinked and curved crack tip are given by



3 8

1 8

11      

 



  

 

   

I f K

( )

2 

2

k k k  



II k k k    I

1      

1   

I

II

12





(11)

3 2

3 2









3/2



k k k  



( k k k h O h   





),

I

II

21

II

I

22



7 8

5 8

21      

 



  

 

  

II f K

( )

2

2

1      

k k k  

1   

II k k k    I





I

II

22





(12)

1 2

1 2











3/2



k k k  



( k k k h O h   





),

I

II

11

II

I

12

11 k ,

21 k and

12 k ,

22 k correspond to the stress intensity factors of Mode-I and Mode-II for the Mode-I and Mode-

where

II fundamental fields [19], respectively, [5, 6,7]. The stress intensity factors K I are accordingly obtained by the sum of Eqs. (9) and (11), and the sum of Eqs. (10) and (12) given by, and K II

, at the kinked and curved crack tip

( ) f K K K O h     ( ) (

3/2

),

(13)

I

I

I

( ) f K K K O h     ( ) (

3/2

).

(14)

II

II

II

If we only retain the first order terms with respect to  (  1

) , the solution is simplified as

b

3 2

9 4

5

  

 

  

1/2

 



I      3 b





II k k k 

I K k 

k

II k h

I

II

II

I 11

2 4

(15)

3 2

3 2



  

  

  



3/2



( k k k k k k k k h O h       

),

  

I

12

21

II 12

II

11

22

45