Issue 44

X.-P. Zhou et alii, Frattura ed Integrità Strutturale, 44 (2018) 64-81; DOI: 10.3221/IGF-ESIS.44.06

When Eq.(32) is expressed by the short-term uniaxial compressive strength  c

, Eq.(32) can be rewritten as

   

   

 c

s

f

(0)

3





iu



  

  



m n

1 3

2

3

iu f t

0 ( )

(33)

2

2

   

   

   

   

 c

 c

 c

s

f

s

f

s

f

(0)

(0)

(0)

iu

iu

iu

  



  







m n

0

1 3

2

3

iu f t

iu f t

iu f t

0 ( )

0 ( )

0 ( )

where  c

is the short-term uniaxial compressive strength.

C OMPARISON WITH THE EXPERIMENTAL RESULTS

T

he Lode stress angle is defined as follows:

 

  

  

 2 (



)

     0 30

0 30 )

3

1 2

  arctan



(

(34)









3(

)

1 2

 expressed by the first invariant 1

I of stress tensor and the second invariant of deviatoric stress

The stress tensor ij

tensor J 2

can be written as follows:

         I I 1 1 3

2 3

      

     







sin(

)



              1 2

2

 sin( ) 

(35)

J

3

2

3

    I 1

2 3

3







sin(

)



3

  

Micromechanics-based three-dimensional long-term strength criterion (32) can be expressed by the first invariant I 1 of stress tensor and the second invariant of deviatoric stress tensor J 2 , the following expression can be obtained         q f pq f F f f q pq f p q f f p ' ' ' 1 4 3 ' 2 ' 2 ' 2 ' 2 3 5 7 6 0 (36) where

4 cos

 





 3 2



2

'

 

 



 3 2 cos n



 m n







f

sin







1

3 4 1 3

f        f





2

'



 m n



cos



2















 n m n 



'

 2 3                m m n n m mn n n 3 6 2 2 6 2 2 2   



 







s

cos 2

3 2 2

sin 2





cl

3

2 3



 m n s 





 3 2



'

 

 

              f 7 '       s f f f 4 ' 5 6 2 ' 1 3 





 m n







n

3

2

cos

sin





cl

2



 m n s

 c

l





 3 2



2

 

 

 3 4 cos n



 m n



 c



si

n





l



2 2



m n

s

cl

75