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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that neglecting the hot-dip galvanization leads to an overestimation of the fatigue life. In addition, a comparison of the variable slope parameters shows that the higher notch sharpness in the presence of hot-dip galvanizing is not represented when S f = 1 . 00 is applied, see Table 4. In contrast, the use of a strain factor S f > 1 . 00 leads to a better description of the variable slope. This also reduces the large overestimations of the fatigue life, as can be seen when comparing the ∆ σ c , 50% values in Table 4 and is also shown in Figure 7 (b), (d). Hence, the results indicate that the approach proposed by Eichsta¨dt (2019) is capable of covering the e ff ect of hot-dip galvanizations on the fatigue strength of bolting assemblies.

4.4. Consideration of threads rolled after heat treatment

The positive e ff ect of threads rolled after heat treatment on the fatigue strength mainly results from induced first order residual compressive stresses σ res , Wiegand et al. (2007). A comparison of the microstructure at the thread root of the bolts M2-M56-b-sv and M2-M56-b-sg can be seen in Figure 8 (a) and (b). Unglaub (2019) performed measurements of axial residual stresses in threads of hot-dip galvanized HV bolting assemblies of property class 10.9 and nominal diameter M36 using neutron di ff ractometry and found maximum values of up to σ res = − 250 N / mm 2 at a depth of approx. 1 mm below the thread surface. He also reports results from Stephens et al. (2005), who found axial residual compressive stresses of up to σ res = − 500 N / mm 2 using x-ray di ff ractometry.

Fig. 8: (a) Microstructure at thread root for bolt M2-M56-b-sv; (b) Microstructure at thread root for bolt M2-M56-b-sg; (c) Calculated overall service life N tot for di ff erent compressive residual stresses and comparison with mean experimental results; (d) Comparison of fatigue life calculations with di ff erent compressive residual stresses σ res for series M2-M56-b-sg.

In the notch-strain approach, a common method for including residual stresses into the calculation is the so-called thin surface layer model acc. to Seeger and Heuler (1984), which modifies the relation of nominal stress S and local strain ε by adding residual strains ε res . For more details, see for example Eichsta¨dt (2019). In the following, the thin surface layer model is used to re-evaluate the calculation results for series M2-M56-b-sg shown in Table 3. For this purpose, di ff erent residual strains ε res and resulting residual stresses σ res are introduced into the calculation model. The results are shown in Figure 8 (c). As can be seen, for lower residual stresses, the calculation results don’t change, since still the whole hystersis is used in the calculation of P J . However, at increasing residual stresses, the results shift towards higher calculated service lifes N tot since parts of the hystersis are no longer considered damaging in the calculation of P J . For all analyzed stress levels, the mean experimental results are approx. met at a residual compressive stress of σ res = − 600 N / mm 2 , which lies above the values documented in literature but is still in a comparable order of magnitude. Therefore, Figure 8 (d) and Table 5 show the comparison of the calculation results without the consideration of residual compressive stresses and with a value of σ res = − 600 N / mm 2 . It can be seen, that the shift in the results is only caused by the crack initiation lifes N ini , which is plausible since the input parameters of the fracture mechanics calculation are the same for both calculations. All in all, the results of the parameter study show the general potential of the thin surface layer model to incor porate the positive e ff ect of residual compressive stresses into the notch-strain approach. However, for more realisitc calculations, actual values for σ res are required for the investigated bolting assembly.