Issue 35

L. C. H. Ricardo et alii, Frattura ed Integrità Strutturale, 35 (2016) 456-471; DOI: 10.3221/IGF-ESIS.35.52

Barsom [19] and the contribution of this term is  p

=K/  (  ) for a sharp elliptic or hyperbolic notch with a crack-tip

radius,  . The above equations can now be used to obtain the principal stresses after the simplifying assumptions of negligible contributions of T rr and f(  ,r,  ) are assumed. Hence, the principal stresses, as derived from Eq. (5), become:





K

        

         



  

cos 1 sin 2  

2



r K

2

1    3 2      





1 4

  

  

cos 1 sin 



(6)

2

2



r

2

    





   

Plane Stress Plane Strain

21

0

This, in conjunction with the von Mises and Tresca yield criteria, gives the expressions for the plastic zone shape as follows: von Mises:   2 2 2 2 3 sin ( ) (1 2 ) 1 cos( ) K             Plane Strain



4  

2

   



ys

( ) 

r

(7)

p

2

K

3 1 sin ( ) cos( )

  

  

2









Plane Stress

2



4

2

ys

Tresca:

   

2

2             sin 2 2  

K

cos

2 

2     

ys

( ) 

r

(8)

p

2

2

2

2       

2       

K

  

  

    

1 2 sin   

cos

Plane Strain

2 

2

ys

2

2

2       

2       

K

  

  

2

1 sin 

cos

Plane Stress

2 

2



ys

 da dN K K K K           min max ( ) 1 m c C K

( ) m

C K da dN K K   

c

max

da C K

1 ) ( ) m m K  



(

max

dN

Table 1 : Empirical crack growth equations for constant amplitude loading [14].

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