Issue 38

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

The energy value corresponding to σ* for fatigue initiation crack is represented by:

2

2

2

2 ) ( 

2

2

y *    

r *        







2(

)



, 1 

, 1 

m Rb ,

Te

Rb

*

*

Rb









W

(5c)

W

E R E R 4 4    

Uniax

Rb,d

E

4

The Iso-energy (Eq. 5c) is an ellipse on the cross-section of the specimen (Fig. 1).

Eq. 5a

Eq. 5c

*W ( Eq. 5c ).

Figure 1 : Dissymmetrical rotating bending ( Eq. 5a ) and line Iso-energy

The large half axis a * and the small half axis b *

defined by (Eq. 5c) are the ellipse axes:

2

2

2

b       R * a R   *



2 



Te Rb Rb m Rb , 1 2 2 ,    

, 1 

    

(6a)

2

2 ) ( 

2





2(

)

, 1 

, 1 

Te

Rb

    

(6b)

2



Rb

Over-Energy under Dissymmetrical Rotating Bending (D.R.B) in the Ellipse Axes This part is dedicated to analyze the over-energy expressed in the ellipse support is:

W ds



2

2

I

*

Rb d ,







2

*

S

ce









, 1 

, 1 

Te

Rb



(7a)

WUniax

*

b a                    R R * * 

E

4

S

RB d ,

2 1 



R

The member term I ce is given by:





Rb d W y r d dr I I y , ( , )  

I

Rb d W y r d dr y , ( , )





(7b)

Sc

Se

ce

c e

S c

and S e

are respectively the circular and the elliptical section (Fig. 1 (5c))

The Integral transformation in elliptical section gives

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