PSI - Issue 3

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

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suggested a derivative expression rate of loss of the endurance limit of the material subjected to cyclic loading. The non-dimensional residual stress σ ur / σ u in function of the life fraction, β = N f /N f0 , is obtained as follows as presented by Bui-Quoc (1969):

        

      

σ

1

ur u

(1)

γ   

1

1 β

β



σ



k

γ



u          

γ γ γ

The damage D i has been defined by the equation (2):     1 D 1 er i e γ γ   

(2)

The parameter k is equal to 8 for steel as calculated by Rabbe & Amzallag. The damage is then expressed by the equation (3):

β

(3)

D



i

8           u

     

γ γ γ





1    β

β



1  

γ

 

2.2. Adopted approach A material subjected to fatigue phenomena under a loading Δσ, shows a cumulative instantaneous damage correlated by the life fraction parameter i  . Its reduction proportionally to the ultimate number of cycles N f0 is represented by the ratio (N f /N f0 ) and a constant "k" parameter, which is a characteristic of the material. The expression of the damage as a function of i  , α (function of N f /N f0 ) and m is given by the equation (4). The term in function of the nondimentional stresses γ in the equation (3) can be replaced by the parameter α k . The damage is expressed then by the equation (4):

        1 . k

(4)

D



i

where

8          

      

1 u γ γ γ γ

k α =

(5)

 

  