Issue 74

P. Zuliani et alii, Fracture and Structural Integrity, 74 (2025) 385-414; DOI: 10.3221/IGF-ESIS.74.24

3 π

/2 ∞ π ∫ ∫ ∫ π −

L

( ) L

(

)

2

σ

, , σ θ ϕ θ θ ϕ sin r r dr d d

=

(23)

AV

1

3 0

L

2

/2 0

4) Predict the number of cycles to failure (N prediction ) using the S-N curves of the smooth specimens.

1

0 AV A σ     

B

0

= 

prediction N

(24)

5) Verify if the predicted N predicted for the notched specimens is equal to N assumption . If this step is verified, the iteration process is ended; otherwise, the value of N assumption is changed and the steps from 2 to 5 are repeated. In Fig. 26 the flowchart of the process is reported.

Figure 26: Flowchart of the Stress Gradient Method defined by Shen et al.[29].

According to the Authors, this method can be applied with success to the INCONEL 718 alloy because the data are concerned within ±3 life factors using their approach. To evaluate the precision of their method, Shen et al. [29] also tried to apply the classical approaches of the TCD introduced by Susmel in the HCF regime [35] . Mechanical Property Method (MPM), Fatigue Testing Method (FTM) and K t method (KTM). The comparison shows that the SGM of Shen et al. is more precise than the other methods. However, the applicability of their for other materials has not been verified. Finally, Gao et al. [11] proposed a modification of the Theory of Critical Distance (mTCD). Their idea is to use the Line Method to calibrate the critical distance ( TCD LM l ) distance at 10 6 cycles by comparing the smooth and notched fatigue strengths. This calibration was already proposed in a previous work in the HCF regime [36]. Then, the following steps are to be followed: 1) Use the S-N curve of the smooth specimens to compute the nominal stress of the notched specimens ( smooth nom σ ) corresponding to a selected number of cycle to failure (N f ). 2) Consider a certain value of the nominal stress of the notched specimen ( nom σ notched ) and compute the average stress ( σ eff ) using the Line Method.

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