Issue 38

D. Marhabi et alii, Frattura ed Integrità Strutturale, 38 (2016) 36-46; DOI: 10.3221/IGF-ESIS.38.05

1

*

C ( ) 



ds

W M W C S C S C * ( ( ) ( )) * ( ) ( )  

(1c)

D Uniax



At the endurance limit, this quantity

is supposed to be constant. If we note

as being its value at the

C ( ) 

endurance limit for any uniaxial stress our criterion is:

D C Uniax 

(1d)

( ) 





Postulate: The quantity  is an intrinsic size in the material (noted

) thus it does not depend on the loading type.

Uniax

We can identify their energy to satisfy the equation:

Uniax Te Pb Rb d W W W W W ,     Rb

(2a)

D Uniax Te  

     



(2b)

Rb

Pb

Rb d ,

Uniaxial Energy Associated to critical stress By reference to an homogenous fully reversed uniaxial stress and the energy analyses by Palin-Luc, Lasserre and Banvillet (Eqs. 1a and 1c). The authors deduce the influencing critical stress value corresponding to σ* in the fatigue initiation crack:

*

2

2











2

(3)

Eq

Eq Te ,

Eq Rb ,

D Uniax

From (Eqs. 1a and 1c) and value at the endurance limit for (Eq. 3) it easy to prove that * Uniax



W is given by (4b);

can

be calculated by (4c).

        

(4a)

*

2 ) ( 

2

a (4 )









2(

)

, 1 

, 1 

Eq

Te 

Rb

2 ) ( 

2



2(

)

, 1 

, 1 

Te

Rb

*

b (4 )

(4b)



W

Uniax

E

4

2 ) ( 

2





(

)

, 1 

, 1 

Rb

Te

D Uniax

c (4 )





(4c)

E

4

E NERGY UNDER DISSYMMETRICAL ROTATING BENDING

T

he service stress (Fig. 1 (5a) (b)) on a straight section by a cylindrical specimen: y r t t Rb d m Rb Rb R R ( ) sin , ,       

(5a)

The energy density given to each elementary under dissymmetrical rotating bending is:

m Rb r E R E R 2 2 2 , 4 4                Rb y

2



(5b)

W

Rb d ,

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