Issue 33

M. Cova et alii, Frattura ed Integrità Strutturale, 33 (2015) 390-396; DOI: 10.3221/IGF-ESIS.33.43

(14)



, n a , n m b     

, , ,2 4 

n a eq





1 2

1 2

  

  

  

  

 

 

 

 

T

T





, n n 





n

n

max

V

V

V

V

1

2

1

2

1 2

1 2

 

  

  

  

  

T

T

T



n n 

n n 

b n 

n

S

V

V

1

2

2 

2 

2 

2 

b

b

b

b

1

1

1

1

  

  

  

  

  

  

  

  

  

  

  

  

T

T











n

b

, n n

b

n

max

V

V

S

V

V

S

1

2

1

2

And the maximum value, by changing the direction n, is:         , ,2 4 , , max 1 1 max a eq n n a eq b b eigvl b               

(15)

2 

2 

b

b

1

1

  

  

  

  

  

  

  





eigvl

b

,

 

 

V

V

S

V

V

S

1

2

1

2

2

2

However, the relative amplitude between the extremes at t 2

and t 4

is only one of the possible critical amplitudes; the other . These two combination are similar to that and t 4

and t 2

and, finally, between t 1

possibilities are the differences between t 1

investigated in the single pulsating loading case. Then the relative equivalent amplitudes are:         , , ,1 2 1 1 1 1 max , 2 2 n a eq V S V S b b eigvl b eigvl b                             

(16)

1

1

 b eigvl

 b eigvl

  

    

 

  ,

 

  

  

  

  

max

b

b









(17)

2

2

V

S

V

S

41, , ,

 eqan

2

2

The researched equivalent amplitude is, finally, the maximum of each computed amplitude; hence the maximum eigenvalue of the suggested six tensors:                                                              1 1 ; 2 1 ; 2 1 ; 2 1 2 1 ; 2 1 2 1 max 1 1 2 1 2 1 , , S V S V S V V S V V eqan b eigvl b eigvl b b eigvl b b eigvl b b b eigvl b b b eigvl                (18)

        

        

 

  ;

 

  ;

b

b

2

2

V

S

V

S

2

2

Figure 3 : Stress distribution at minimum et maximum of fatigue loading.

394