PSI - Issue 75

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

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for each test series based on an approach adapted from Dowling (1979). The final crack size a end , mean was measured on the fracture surfaces of the respective tested bolting assemblies and averaged individually for every load level. N prop = a end , mean a ini 1 C · ∆ K m da (6) The results of the calculations acc. to the notch-strain approach and fracture mechanics are summarized in Table 3 and are further discussed in the following sections. The calculation of crack initiation life and crack propagation life described in the previous section is used to assess the fatigue strength of the two bolting assemblies M1-M12-b-sv and M2-M56-b-sv, which represent the most basic of the tested assemblies and also span over a wide nominal diameter range. The results are shown in Figure 6 (a), (b). It can be seen that the calculations give results with reasonable agreement taking into account the approximated material properties used, which indicates that the notch-strain approach is capable of covering di ff erent nominal diameters. It can be assumed that calculations using real cyclic material data will further improve the calculation results. 4.2. Consideration of size e ff ects

Fig. 6: (a) Comparison of calculated results and test data for series M1-M12-b-sv; (b) Comparison of calculated results and test data for series M2-M56-b-sv; (c) Calculated stress concentration factors; (d) Calculated direct stress ranges for crack initiation lifes N ini = 2 · 10 6 . However, statements on the size e ff ect require data for additional nominal diameters, which can be experimentally challenging, especially for the diameter range > M56. In addition, test material of the same batch in di ff erent nominal diameters is rarely available, so that e ff ects from changed material properties are superimposed. A major strength of the notch-strain approach is the possibility of synthetically extending the experimentally investigated parameter range. This allows, for example, individual influencing parameters to be investigated separately with regard to their e ff ects on the fatigue strength. The geometric size e ff ect is taken into account directly in the FE model used to determine the local stresses and strains. The stress-mechanical size e ff ect can be included, for example, by multiplying the P-life curve with the notch sensitivity factor according to Siebel and Stieler (1955) or FKM-Guideline (2020). Eichsta¨dt (2019) investigated HV bolting assemblies in the nominal diameter range of M36 to M72 and found that better results are achieved in this range if the Siebel / Stieler notch sensitivity factor is neglected. This is consistent with his finding that the notch sensitivity factor determined according to FKM is consistently close to one. Due to these findings, only the e ff ect of the bolt geometry is investigated here. For this purpose, linear-elastic 2D FE models are used to determine the SCF in the first load-bearing thread for HV bolting assemblies of nominal diameters M30, M36, M48, M56, M64 and M72, see Fig. 6 (c). Based on these results, the local stresses and strains are determined using the approximation method according to Neuber (1961) to reduce the computation e ff ort compared to the elastic-plastic FE calculations from section 4.1, since direct stress ranges are then determined iteratively for a crack initiation life of N ini = 2 · 10 6 stress cycles. The material parameters of the M2-M56 series given in Table 2 are applied across all nominal diameters to avoid superimposed influences. The results of this calculations are shown in Fig. 6 (d). For comparison, the stress ranges obtained by applying di ff erent size exponents on the basis of the calculation result for the nominal diameter M30 are shown.