PSI - Issue 76

Jürgen Bär et al. / Procedia Structural Integrity 76 (2026) 27–34

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Table 2. Parameter used in the three models to estimate the KT diagram. Steel N Steel V Unit Δ K th,LC 14,82 12,27 MPa√m   e 690,6 878,5 MPa Y 0,728 0,728 Y Murakami 0,65 0,65 d 8,6 6,4 µm

The resulting KT diagrams obtained with these models for the two steels are shown in Fig. 2a and b, respectively. For Steel N, Chapetti's model shows in the middle range an increase of the fatigue limit ∆ σ th with the defect size a that cannot be explained physically and is therefore a mathematical inconsistency of the model. The two KT diagrams clearly show that the three models differ in the technically relevant area, emphasizing the importance of an experimental validation.

(b)

(a)

700 800

600 700 800 900 1000

600

500

500

400

Steel V, R=-1  e

Steel N, R=-1  e  th,LC  th,a,EH

400

 th,LC  th,EH  th,Chapetti  th,d,Chapetti

300

300 stress range [MPa]

stress range [MPa]

 th,Chapetti  th,d,Chapetti

200

200

0,001

0,01

0,1

1

10

0,001

0,01

0,1

1

10

a [mm]

a [mm]

Fig. 2. KT diagram of (a) Steel N and (b) Steel V calculated with the experimentally determined parameters and the equations (1)-(5).

3. Experimental validation of the Kitagawa-Takahashi Diagram 3.1. Requirements and solutions

Fatigue tests with notched samples are required for experimental validation of the KT diagram. The notches must be as sharp as possible and should be fabricated without influencing the surrounding material. When notches are produced by Electrical Discharge Machining (EDM), the surrounding material remains practically unaffected, but the notches are only moderately sharp, with a notch radius of approx. 40 µm, as shown in Fig. 3a. In contrast, the production of notches using an engraving laser results in very sharp notches with a notch radius of less than 3 µm (Fig. 3b). Metallographic examinations have shown that the heat-affected zone is less than 2 µm thick. In addition, the notches can be produced in a fraction of the time compared to EDM.