PSI - Issue 79

D. Marhabi et al. / Procedia Structural Integrity 79 (2026) 34–52

43

The experimental test of [10] suggested the endurance limit 2 2 1 1 2(1 ) Rb To       

(11.c)

The triaxiality degree The triaxiality on the endurance limit of metals is known experimentally. We choose the proposition of De Leiris [11] to define the degree of triaxiality. The triaxiality degree variable is used the parameters: m m m Rb W dT W  for the Average component and a a a Rb W dT W  the alternating component. The authors observed separately the evolution of dynamic and average energy, which lead to priming, as a function of the degree of triaxiality. On this basis, the authors postulate that the influence of triaxiality can be translated by two empirical functions [11] and [12]         ( ( )) 1 1 ( ( ), ) 1 ln 1 1 1 ( ( )) 1 1 ( ( ), ) 1 ln 1 1 1 1 a a a a a a Rb m m m m m m Rb W dT Rb To F dT Rb To dT e dT W W dT Rb To G dT Rb To dT e dT W e                                      We will be led to establish a bound of the sum of the empirical functions of energies separated from the dynamic and mean contribution. The global functions is written: ( ( ), ( ), ) ( ( ), ) ( ( ), ) a m a m HdT Rb To dT Rb To F dT Rb To G dT Rb To          (12.b) Triaxiality Factor Value and the Multiaxial Energy ( * W  Rb To ,   Rb To ) The evaluation of the factor β is based on two tests [23]: alternating torsion τ = 178 MPa and alternating rotating bending σ = 243 MPa. The calculation of the triaxiality factor by the material is given by the following equation:   2 1 1 2 3 1 ln 1 1 0 3 Rb To e                              . Solving this equation gives β = 2.07 with ν = 0.3 (12.a)

Representation of the Empirical Function The Major to calculate is represent by the empirical function whatever the two triaxiality effects:

( a HdT Rb To dT Rb To F dT Rb    ( ), ( ( ( ), ) a m

), ) 

(13a)

, ) 



( R dT dT ,

a m

where









 

  

1

1



(13b)



1 ln 1 





( ( ), ) 

F dT Rb

dT e

1

a

a

dT  



1

a