PSI - Issue 3

5

Jilali Nattaj et al. / Procedia Structural Integrity 3 (2017) 579–587 Jilali NATTAJ/ Structural Integrity Procedia 00 (2017) 000–000

583

 

* 0 3.2 e   

0

K

gives



f

*

e

0 u     

From then, the coefficient φ is evaluated to be equal to 0.4, σ u to 558 MPa and * e  to almost 70 MPa The expressions of the rate of variation of the nondimentional endurance limit γ e as a function of n i .

1 d dn K    e





b

(9)

   



e

i

a

The instantaneous value σ e is connected to the instantaneous static resistance σ ur of the material as follows,

0 e      ur u

8

(10)

( )

such as:

8

a         u 

0 e  

*

1  if i n = 0 and

if i n = N f



e

The integration of equation (6) give rise to the equation presenting the calculation of cycle’s number for the fatigue curve (σ – N f ) as shown below:

 

      

1 1 

1

(11)

N k

 

 



f

a b

8

1







u         

  



with b and k a are constants of the materials. Our approach consists in determining these two constants, using the experimental results in order to be able to predict and trace the curve (σ-N f ). To do this, we took 2 points sufficiently spaced among the three constraints used in the experiment (282 And 352 MPa in our case) and we found:

K a = 3.7 10

6 Cycles,

b = 2.03

4.3. Determination of α k The Wohler curve N°1, determined by the unified theory approach as well as the relationship (11), gives the following values:

N

f

k  = 1.56

For Δσ = 248 MPa:

= 3146,8.10 -6 and

N

0

f