PSI - Issue 75

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

366

4

coe ffi cient σ ′ f , fatigue strength exponent b , fatigue ductility coe ffi cient ε ′ f and fatigue ductility exponent c , seeEqua tion 3.

+

σ a K ′

1 n ′

σ a E σ ′ f E

(2)

ε a = ε a , e + ε a , p =

(2 N ) b

+ ε ′ f (2 N ) c

(3)

ε a = ε a , e + ε a , p =

Since the required cyclic base material tests are very complex, many approaches have been developed in the past to estimate the cyclic material properties from the results of quasi-static tensile tests. A particularly popular approach is the so-called Uniform Material Law (UML) according to Ba¨umel and Seeger (1990), which estimates the parameters K ′ , n ′ , σ ′ f , b , ε ′ f and c based on Young’s modulus E and tensile strength R m , and is also used in the present investiga tions. However, previous investigations have shown that the quality of the results of the notch-strain calculation can generally be improved by determining the cyclic material properties as accurately as possible, see for example Marten (2009) and Eichsta¨dt (2019). Additionally, local stress-strain hystereses are determined at the failure-critical location, see Figure 2 (b). Analytical estimations such as those according to Neuber (1961) or Molski and Glinka (1981) on the basis of stress concentration factors (SCF), as well as comprehensive elastic-plastic finite element (FE) calculations can be used for this purpose. In this regard, studies by Eichsta¨dt (2019) show that axially symmetrical 2D models do not lead to a significant deterioration in the calculation results compared to a complete 3D model. The fatigue resistance is derived from the strain-life curve. As this is typically determined for an R-ratio of R ε = − 1, mean stress e ff ects must be taken into account seperately. For this reason, the strain-life curve is converted to a damage parameter curve using a suitable damage parameter, see Figure 2 (c). Depending on the parameter, other influences such as sequence e ff ects can also be taken into account in this way. Popular damage parameters are those according to Smith, Watson and Topper (1970) P SWT and according to Vormwald (1989) P J , see Equations 4 and 5. According to Eichsta¨dt (2019), the application of the P J parameter is preferable in the context of bolting assemblies. P SWT = ( σ a + σ m ) · ε a · E = σ o · ε a · E (4) P J = 1 . 24 · ∆ σ 2 ef f E + 1 . 02 √ n ′ · ∆ σ ef f · ∆ ε p , ef f (5) After also converting the local stress-strain hysteresis into an equivalent value of the damage parameter, the crack initiaion life N ini is determined by comparing this value to the damage parameter-life curve. To determine the overall service life N tot , the crack propagation life N prop has to be assessed using fracture mechanics, see Figure 2 (d). In this regard, the definition of the initial crack size as the starting point of the fracture mechanics calculation is challenging. The notch-strain approach gives no information about the initial crack size for the calculated crack initiation life. Therefore a definition by the user is necessary. Often, a constant crack size of 0.1 mm or 0.5 mm is specified, see Eichsta¨dt (2019) and Knobloch et al. (2024). However, there are also approaches for definition on a fracture mechanics basis. In this case, the crack size is defined as the size at which a transition between micro and macro crack growth occurs, see Knobloch et al. (2024). A corresponding approach is also used in the present investigations. An experimental basis for a validation of the notch-strain approach in its application to bolting assemblies is provided by fatigue tests on HV bolting assemblies of property class 10.9 in accordance with EN 14399-4 (2015-04), which are well established in steel structures. Two di ff erent manufacturers (M1, M2), two nominal diameters (M12, M56), two di ff erent surfaces (quenched and tempered black - b, hot-dip galvanized - hdg) and two di ff erent times of thread production (rolled before heat treatment - sv, rolled after heat treatment - sg) are considered in order to take into account the main parameters influencing the fatigue strength. For the nominal diameter M56, identical material batches were available for all the configurations investigated, so that the base material properties are not expected to influence the results. 3. Experimental fatigue assessment