PSI - Issue 79

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

42

Bazant curve for ( γ = 8 ) Bazant curve for ( γ = 1,25 ) Small Crack under Shear stress for 30NCD16 Steel

Fatigue limit line (658 Mpa) Long crack threshold line a0 : Initial crack in the specimen

1000

Stress σ n and shear stress (MPa)

Fatigue small crack growth

Mesoplasticity

Crack Length a

100

1,00E-06

1,00E-05

1,00E-04

1,00E-03

Figure 5: Small Crack effect for 30NCD16 steel under Shear stress

The small crack a 0 length below which the LEFM analyses considered is the first point where the Bazant curve ( γ = 8) detaches from the endurance line. The initiation crack length predicted (Fig.5) is a 0 = 4.E-5 m. The small crack (10a) and shear stress mini (Table 1) reproduces well the Kitagawa variation plot trend (Fig. 5). We show also that the curve predicted by (Eq. 10a) is significantly bounded by the Bazant’s Low (Eq. 10b) for γ = 1,25 and γ = 8. Our studies have shown that the shear stresses (Fig. 4) on a log-log scale are represented linearly. However, the same shear stress data σ * presented between the Bazant curves ( γ = 1,25 and γ = 8) evolve in semi quadratic behavior. The research did by Newman and his colleagues [5] have only shown the small crack effect to exist below 0.1mm. Furthermore, their work has also shown that the small crack effect is not significant in all materials. However, the small crack effect has been shown by some studies to be as large as 0.3 mm [12]. 7. ENERGY NEW CRITERION OF NON-DAMAGING STRESS The fatigue behavior of a metallic material depends on several parameters, such as the nature of the loading (tension, torsion or rotating bending), the presence of defects induced by the manufacturing process. These defects all contribute to modifying the fatigue behavior according to the size position (internal in material or on the surface). Over-Energy of Rotating Bending or Torsion and The endurance limit This study shows the alternated load of rotating bending on a specimen test is:   , , ( ) sin m Rb a Rb Rb r t t R        By reference to an homogenous reversed pure rotating bending or torsion, the energy is suggested by [12].   1 ( ) 2 * Rb * * * 2 1 W -W 2 1 ) ( Rb Rb E S ds S r R                     (11.a)

r       R

* 2

2 (1





1

)







(

)

(11.b)

and

To

To

E

The postulate of identical energies (11a) and (11b) leads to the expression: 2 

2

 

 

2(1 )

Rb

To