PSI - Issue 75

Okan Yılmaz et al. / Procedia Structural Integrity 75 (2025) 435 –441 O. Yılmaz and D. Van Hoecke / Structural Integrity Procedia 00 (2025) 000–000

439

5

where d 1 and d 2 are the material constants and P RAM , Z is the cut-o ff point for the component Wo¨hler curve. In order to calculate this parameter, one first needs to determine P RAM , Z , WS , which is the cut-o ff point of the material Wo¨hler curve:

1 f RAM ·

b P , Z m ,

1 f RAM ·

P RAM , Z , WS =

a P , Z · f 2 . 5% · R

(5)

P RAM , Z =

where a P , Z and b P , Z are the material constants and f 2 . 5% is used to shift the curve for the probability of failure of 2 . 5%. The additional factors are taken into account with the combined multiplier f RAM that includes the factors of size, roughness, and partial safety:

γ M n P · K R , P

(6)

f RAM =

,

where γ M is the partial safety factor set in this study for non-redundant components having moderate consequences of failure, K R , P is the roughness factor calculated for R z = 21 µ m , the measured average roughness for the rolled surface, and n P is the statistical size factor. For further details on the calculation of the size factor, see Fiedler et al. (2019). K R , P = 1 − a R , P · log R z · log 2 R m R m , N , min b R , P , (7)

where a R , P , b R , P , and R m , N , min are material constants. Table 2 provides the list of constants used for steel material.

Table 2. The constants provided for steel material in Fiedler et al. (2019). a M b M a P , Z (MPa) b P , Z d 1 d 2

f 2 . 5%

a R , P

b R , P

R m , N , min (MPa)

γ M

0.35

-0.1

20

0.587

-0.302

-0.197

0.71

1.1

0.27

0.43

400

4. Test results and discussion

Test results are presented in the form of P RAM damage parameter vs. experimentally determined fatigue crack initiation life in Figure 4 for UHSS-A and UHSS-B. The results were also compared with the component curve for a probability of failure of 2 . 5%, which was calculated by using material properties and shifting factors. It was observed that for the slopes obtained for valid bending operations are steeper compared to the component curves for both grades. Hence, at lower forces, the estimation of fatigue crack initiation becomes less conservative. In addition, all test results were combined and experimental fatigue crack initiation cycles were compared with the calculations in Figure 5. A scatter band with a factor of two was added to define a design space with identifying unsafe and safe regions. Since the calculations do not take into account the surface defects, the premise is that the defective surface generated using a bending ratio of r / t = 0.5, which is below the bending limit should fall in the unsafe region as the calculations will overestimate the fatigue life. The di ff erence between an experimental result and calculation should be a function of the size of the initial defect, thus some additional scatter is expected. Remarkably, only with one exception, all of the defective surface data points fell in the unsafe region while relatively smooth surfaces were in the safe region. Hence, a useful separator was constructed and validated so the future test should reveal if a factor that is detrimental to fatigue is dominant in the tested material without the necessity of testing additional reference samples.