PSI - Issue 75

Fritz Wegener et al. / Procedia Structural Integrity 75 (2025) 363–374 Wegener et al. / Structural Integrity Procedia 00 (2025) 000–000

369

7

Fig. 5: (a) Sections of nominal stress loading paths used in the FE calculations; (b) Local strains at thread root resulting from nominal stress; (c) Local stress at the thread root determined from the local strains based on the cyclic stress-strain relationship; (d) Local loading path at thread root.

To determine the crack initiation life, the P J -value calculated for the respective stress-strain-hysteresis is compared to the P J -life curve, which is derived from the strain-life curve based on an iterative procedure described by Haibach (2006). The P J -life curves for the investigated materials are shown in Figure 4 (d).

Table 3: Results for crack initiation life N ini , crack-propagation life N prop and overall service life N tot and comparison to experimental data.

P J

a ini

N ini

a end , mean

N prop

N tot

N exp , mean

∆ N rel

σ

∆

Series

[N / mm²] [N / mm²] [mm]

[-]

[mm]

[-]

[-]

[-]

[%]

33,174 1.6 102,873 1.9

225 170 140 280 170 120 200 150 100 250 200 150 200 150 100

5.0 2.8 1.9 8.1 2.9 1.5 4.3 2.4 1.0 6.8 4.3 2.4 4.3 2.4 1.1

45,064 78,238 72,135 98,466 201,339 131,210

+ 8

M1-M12-b-sv

0.070

+ 53 + 26

253,105 2.2 169,196 422,301 321,955

13,245 2.1

27,098 40,343 46,686 -14

M2-M12-hdg-sv

0.070

85,084 2.5 103,241 188,325 146,044 435,479 3.1 262,704 698,183 386,759

+ 28 + 81

40,235 6.7

47,781 88,016 106,631 -17

M2-M56-b-sv

0.175

121,883 8.1 108,264 230,147 298,787 -23 830,781 11.3 336,015 1,166,796 1,157,554 + 1

18,675 9.5 40,235 9.3

29,335 48,010 123,373 -61 52,522 92,757 234,536 -60

M2-M56-b-sg

0.175

121,883 10.2 113,938 235,821 580,416 -59

40,235 6.1 121,883 5.8

46,281 86,516 70,795 96,671 218,554 133,709

+ 24 + 64

M2-M56-hdg-sv

0.175

830,781 7.3 305,094 1,135,875 414,785

+ 183

To compare the calculation results with the results of the experimental fatigue tests in the finite life of the S-N curve, the further crack propagation life is calculated using fracture mechanics. For this purpose, the crack propagation law acc. to Paris and Erdogan (1963) is used, see Equation 6. The necessary material constants are taken from FKM Guideline (2018) for 42CrMo4 as C = 2 · 10 − 8 and m = 2 . 63 in accordance with Eichsta¨dt (2019). The stress intensity factor is calculated following FKM-Guideline (2018) using the round bar model under constant tension with a circumferential surface crack. The initial crack size a ini for the integration of the Paris law is determined individually