PSI - Issue 79

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

35

Nomenclature

Tensile mean stress and dynamic amplitude,

, , m Te Te  



Elastoplastic strain rate after material adaptation



* 

Threshold stress and their effect on physically small crack.

Endurance limit under fully alternate tensile

, 1 Te  

Endurance limit under fully alternate rotating bending and torsion load,

,





, 1 

, 1 

Rb

To

Equivalent stress under tensile loading,

2

2

2



, m Te     Te

, Eq Te

Elastic energy and over-energy on the area S* under tensile loading

, Te Te W 

Elastoplastic enery on area initiating small crack

* Te W

Rotating bending mean stress and dynamic amplitude,

, , m Rb Rb  

Equivalent stress under rotating bending,

2

2

2



, m Rb     Rb

, Eq Rb

Elastic energy and over-energy on the area S* under rotating bending

, W Rb Rb 

* a , * b

The large and small half axis of an ellipse

Equivalent threshold stress under Rotating bending loading,

*2

2

*2 Rb



, m Rb    

, Eq Rb

Biquadratic function of over-energy expressed by the threshold stress,

( E Eq  

*)

* * min max ,  

Threshold stress for small crack and long crack.

The crack size at which small crack effects is on LEFM analysis

a

Experimental stress factor of material

K th 

( ) * a 

Bazant’s Law for cracked material

Triaxiality degree for the average component Triaxiality degree for the alternating component.

m dT a dT

Triaxiality parameter



Empirical function of triaxiality under rotating bending and torsion Empirical function of triaxiality under rotating bending and torsion

( ) dT Rb To a F   ), ( ( ) dT Rb To G   ( ( , , ) ) H dT Rb To  ), (

The sum function of the triaxiality degree

*

The Multiaxial Energy under rotating bending and torsion



,

W

  Rb To Rb To

E 0

The damage Indicator of new criterion Statistical Performance by the criterion fatigue

* (1 ) I EM m  

1. INTRODUCTION Several families of defects can be encountered: cracks or scratches due to machining. These defects all contribute to modifying the fatigue behavior. The material constitutive behaviour is using linear isotropic pseudo-plasticity. The analytical and numerical study published on the threshold stress near the small crack by the authors [1]. In