Issue 25

C. J. Christopher et alii, Frattura ed Integrità Strutturale, 25 (2013) 161-166; DOI: 10.3221/IGF-ESIS.25.23

1 2

1 2

1 2



5 1 2 2  





1 2

1

5

  

    











(A   

y 

4B 8E)r

cos

B

r cos

B

r sin 

sin

r

r

r

i

2 2

2

2

1 2

1 2









1 2

5

5

  



  

  









   





E

r ln(r ) cos

5cos

sin

5sin

O(r

)

2

2

2  

2

1 2

1 2

1 2



5 1 2 2  





1 2

1

5

  

  











 





x 

4B 8E)r

r c

(A

cos

B

os

B

r si

n

7sin

r

r

r

i

2 2

2

2

1 2

1 2









1 2

5

5

  

  



  

  









   



 

E

3cos

3sin

C O(r

r ln(r ) cos

sin

)

2

2

2  

2

(3)

1 2

1 2



5 1 2 2     





1 2

5

  

  

  





 







r

A sin

B

s

B r cos

3cos

in

xy

r

r

i

2

2

2

1 2

1 2





3

3

  

  













E

ln(r )cos

sin

O

(r

r sin

)

2

2

F K is defined from the asymptotic limit of y  as x 0   , along y 0  , i.e. towards the crack tip from the front along the crack line:

  

  

1 2





K lim 





(A 3B 8E)  

 

(4)

2 r(

2Er ln(r ))

F

y

r

r

2

r 0 

R K was obtained by evaluating x  in the limit as x 0   , along y 0  , i.e. towards the crack tip from behind along the crack flank:





 

R 0 2 r K lim    r

 

(2B E 

 



(5)

4

)

x

i

2

S K is derived from the asymptotic limit of xy  as x 0   , along y 0  , i.e. towards the crack tip from behind along the crack flank:



2 r  



 



A ) B 

K l

0 im 

(

(6)





S

xy

r

r

2

r

The +ve sign indicates y 0  , and a –ve sign that y 0  . The quantity II towards the crack tip from the front along the crack line:

K characterizes mode II loading, and is derived from the asymptotic limit of xy  as x 0   , along y 0  , i.e.

 

 

K lim 

 



2 B 

(7)

2 r

2

I

I

xy

i

r 0 

T-stress is the transverse stress which is added to x  as a constant term and is given by T C  

(8)

The new five-parameter model can be solved for displacement fields:

163