PSI - Issue 79

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

41

Behavior of Smalls cracks growth In 1976, Kitagawa [6] presented a schematic comparison between stress range and crack length a, on a log-log scale. In this study, we approximate the crack size for any nominal stress with a pure rotating bending. The fatigue small crack is defined by the normal stress � is: 2 5 * 3 1.77 th n K a          The fatigue limit ratios have frequently been discussed based on the maximum energy Mises criteria *   . The process small crack is controlled by the shear stress *  and the following equation holds with   

3 5

n



on the basis of our data (Table 1) is: 2

   

   



K

5

th

(10.a)



a

* 3 1.77*

2 *2

m   

The experimental stress factor range of the 30NCD16 steel is Δ K th = 6 MPa  m. From the energy curve of every rotating bending load (Fig.2) we hold roots values. Besides, we associate these results with the fatigue crack as expressed by (10a). We have schematic representations:

Figure 4:The Logaritmic scale represented by small crack size and shear stress of 30NCD16 steel

In this curve a 1 defines the smallest crack length and a 2 defines the crack size at which small crack effects is on LEFM analysis. This work has been shown to deviate from two lines between smallest crack lengths labeled a 1 and small crack a 2 . Consequently, the result of over-energy approach should recognize the Kitagawa’s schematic representation between small crack length and threshold stress in material under service conditions. Bazant’s Law and Shear stress Small Crack [2] In this part, we approximate the small crack size for various stress σ * under nominal stress and expressed by Bazant’s law [7]. If threshold stress cannot lead to long crack growth prediction, the method used is Bazant’s law for cracked material is : 1 0 2 5 ( ) *( ) 1 ( ) 3 n th K a a a a                 (10.b) According to Tanaka [8] and Livieri [9], most of experimental data is situated between two corresponding curves in γ = 1.25 and γ = 8. The shear stress for 30NCD16 steel have average values between 4.3 MPa  m and 6 MPa  m. In our analyses we use K th  = 6 MPa  m and 0.1 a th mm  . The representation of (Eq 10a, 10b) gives: