Issue 37

N. Zuhair Faruq, Frattura ed Integrità Strutturale, 37 (2016) 382-394; DOI: 10.3221/IGF-ESIS.37.49

  t

 

 







Var

(5)

2.

a

q

The variance of shear strain can be determined directly by using the simple form of Eq. 6, [15]:

  t

T

 

 



Var

d C d [ ]

(6)



q

According to Fig 5c, for specific values of angles φ , θ and α, the terms d and [C] in Eq. 6 can be simply defined with the following definition:

 1 sin( )sin(2 )cos( ) sin( )sin(2 )cos( ) 2 1 sin( )sin(2 )cos( ) sin( )sin(2 )sin( ) 2 1 sin( )sin(2 ) 2 1 sin( )sin(2 )sin(2 ) cos( )cos(2 )sin( ) 2 sin( )cos( )co                                  s(2 ) cos( )sin( )cos( ) sin( )sin( )cos(2 ) cos( )cos( )cos( )              2 2

             

             

d d d d d d

1        

 

2 3 4 5 6

       

d

     

x V C C C C C C V C C C C C C V C C C C C C C V C C C C C C V C C C C C C V , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,                      x y x z x xy x xz x yz x y y y z y xy y xz y yz x z y z z z xy z xz z yz x xy y xy z xy xy xy xz xy yz x xz y xz z xz xy xz xz xz yz x yz y yz z yz xy yz xy yz yz

 

(7)

Figure 5 : Orientation of the Critical Plane [1].

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