Issue34

L. Marsavina et alii, Frattura ed Integrità Strutturale, 34 (2015) 387-396; DOI: 10.3221/IGF-ESIS.34.43

with  the shear modulus,  for plane strain,   for plane stress, and  is the Poisson's ratio. Based on SED criterion the crack initiation angle and the relation between K I , K II and K Ic are presented in Tab. 3.

Condition

Mathematical formulation





2

 sin 2cos 1 

   

 K

Crack initiation angle

I

(6)





 

 

2

2

 cos (2cos

 

  





 sin 6cos 1 

   

K K

K

2

1) 2sin

0

I II

II

   1 1 cos











2

 c





 c



 2sin 2cos

 c

  



K

K K

cos

1





, Ic F K K K , I II

 



I

c

I II

 2 1

(7)



  1 1 cos

 







 K K  2

2 Ic

   

 

 1 cos 3cos 1 

 c

 c

c

II

Table 2 : The SED criterion.

Condition

Mathematical formulation

 

   



     2

1





 

2

 sin 10 sin cos K   2 2

 6 sin cos 8 K  







K K

cos

  

 



I

I II

II



1







2

2





cos

3

 

   



    (3cos 

1





 

2

  2 1)

2

2



 

 4 sin cos





 8 sin cos I II





K K K

K

9 5cos

  

 



I

II



1









3

2





cos

3

Crack initiation angle

              

             

(9)

 



1

     



 

 

   

   

   

   

   

    

     

    

  

1

1

1

1

  1

   











ln

    

2

  

      

 

 



1





1



1

 

1

1

 

















 

 

2

  2 1

2

2



 8 sin cos I II





 

K K K

K

3cos

9 5cos

I

II



0





2

2





cos

3

 c

 c



   

1

2

 

 

1









4





, Ic F K K K , I II

 c

2

 c

 3 cos

(10)

 

 

1















 

 

2

 K K K 2 8

2

 K K 2

2 Ic

 c

 sin cos

 c

 c



 1 3cos

 

9 5cos

I

I II

c

II

Table 3 : The Gmax criterion.

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