PSI - Issue 79

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

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experimental test, they have used the threshold stress σ * under tension load. The first part is a reminder for readers about the prediction of non-damaging stresses contributing to the new criterion in the second part. At the Sevilla conference in 2016, we have established an over-energy [2] according to the threshold stress under rotating bending and expressed in the ellipse axes ( * a , * b ). An Asymptotic approach transformed an over-energy in biquadratic function, which predicts the unknown threshold stress σ *. This Assessment has been modified in order to express optimal numerical stress values (See Table 1). The data of the fatigue tests for the rotating bending realized on the steel 30NCD16 are used. The analyse of biquadratic function and numerical work focuses on the prediction of threshold stress σ *. It’s localized near a small crack, which does not propagate. These threshold stresses σ * are lower than the endurance limit σ -1 . The stress was modified by taking into account the effect of nominal stress based on the maximum energy Mises criteria. Hence, the small crack and shear stress reproduces well the Kitagawa Plot trend. We show also that this Kitagawa plot is significantly bounded by the Bazant Low. The second part is intending to validate the new fatigue criterion. We presented a fatigue criterion under rotating bending and torsion, which depends on the shear stress lower than the endurance limit. The previous expression of an over-energy and the triaxiality function suggested by De Leiris are formulated scientific principle. The damage factor depending on shear stress requires beforehand the choice of an equivalent tensile through some experimental tests. The analysis of the influence of fatigue defects uses both global and critical plane approaches to multiaxial fatigue. We have been able to define the field of numerical application using seven criteria. The data tests of Gough refer to the experimental fatigue for material S65A steel We have tried to bring together both the most famous and the recent criterion, and to divide them into two families: 1- The damage to the material by fatigue at a point of the mechanical component is imposed by the most Stressed material plane passing through this point. The sliding of crystallographic planes generates the interatomic shear. Among these approaches criteria, we are interested in the McDarmid 2, the Dang Van 2 and Robert. 2- The advantage of the Global Approach Criteria is the study computation time is almost instantaneous. In this category, we have: Sines, Kakuno-Kawada and Froustey-Lasserre. We have been defining the field of application using last criteria [13-20] and our own criterion to verify the test results under rotating bending and torsion. The quality of this study is to inform the reader on the steps of analyzing fatigue resistance with the smalls cracks in order to prove the applicability of threshold stress methods. 2. ENERGY FOR ANY UNIAXIAL WHEN FATIGUE IS RESULTING SMALL CRACK As proposed by Banvillet, Palin-Luc, Lasserre [1] and [3]to predict the effect on the fatigue under the uniaxial load. From fully reversed fatigue, t hese authors show that the threshold stress σ * contribute to micro-damage under tension load Te  . In this study the material remains elastic at the macroscopic scale (even if there is some local plasticity at the mesoscopic scale). For a given elementary area of material Banvillet & all used the strain work density: 3 3  Also, to bring into consideration the effect caused by the threshold stress on small cracks. A* is the area influencing fatigue small crack. It’s defined by equation (1b) around each damage in point C * *( ) ( , ) ( ) ( ) A C Px y around C so that WP W C         (1.b) The authors postulate that the part of W exceeding W* is the damaging part of the elastic-plastic energy density. On the area A*, the energy ( ) C  allows short cracks around the point C is: 1 1 j 1 W ( , ) M t ( , ) ij  ij i T M t dt T        (1.a)

1

*

  

  





( ) C W M W C ds  ( ) ( )

( ) C

(1.c)



* ( ) A

A C

*

Postulate: The quantity  is an intrinsic size in the material (noted that Uniax  ) thus it does not depend on the loading (tensile or rotating bending).The authors [1] can identify their energy to satisfy the equation: Uniax Te Rb      (1.d)