PSI - Issue 37

Sebastian Vetter et al. / Procedia Structural Integrity 37 (2022) 746–754 Sebastian Vetter / Structural Integrity Procedia 00 (2019) 000 – 000

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1. Introduction It is known that the fatigue strength of shafts is subject to scatter. Knowledge of the scatter or distribution of fatigue strength values is essential for producing shaft designs that avoid damage under cyclic loading. Since shafts are often used in machines at high rotational speeds, they undergo several millions of cycles even in short periods of time, which is why the HCF region is the focus of the following work. The scatter of fatigue-strength values is mainly influenced by material and manufacturing factors (Adenstedt, 2001; Hück, 1992; Liu, 2000; Schijve, 1994), and since it has not to date been possible to determine the scatter of fatigue strength by calculation, it is necessary to use data from literature or experimentally determined values. The determination of low-error experimental values of fatigue strength is extremely time consuming and cost intensive (Ellmer, 2019). Literature values for fatigue strength scatter in the HCF region are always based on experimentally determined values, and the use of such data is problematic due to their scarcity (Adenstedt, 2001; Hück et al., 1990; Vetter et al., 2019). Moreover, such data do not include all possible scattering influences for the shaft to be designed. Given these disadvantages of using literature values or experimentally determined values for fatigue-strength scatter, the aim of this paper is to develop a probabilistic method for calculating fatigue-strength scatter. Given that the fatigue strengths of shafts are usually described in terms of the nominal cross-section, fatigue strength is to be understood as the nominal fatigue strength in the following. Nomenclature , , , parameters of shear intensity hypothesis (SIH) constant parameter set of smallest area 0 intrinsic fatigue crack size variation coefficient area , Cartesian coordinates groove width ̅ mean value distance between grooves geometrical factor of a crack critical diameter , , plastic strain limit amplitude Young’s modulus Poisson’s ratio surface factor groove radius local hardness normal stress surface groove form factor stress state due to external load ∆ , ℎ fatigue threshold normal stress amplitude mean stress sensitivity factor , axial residual stress support factor , tangential residual stress facture mechanical support factor normal mean stress statistical support factor , normal mean stress due to external load mechanical deformation support factor , equivalent stress amplitude ′ strain hardening exponent local fatigue limit survival probability shear stress radius shear stress amplitude standard deviation , shear mean stress due to external load ℎ shaft shear mean stress nominal fatigue strength or stress shear fatigue limit groove depth ∗ related stress gradient 2. Parameters influencing fatigue-strength scatter In order to develop a probabilistic method for estimating fatigue-strength scatter, it is necessary to identify the parameters that influence scatter. According to literature sources (Adenstedt, 2001; Hück, 1992; Liu, 2000; Schijve, 1994), the surface condition, external shape and material condition in the HCF region can be identified as influencing parameters.