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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hypothesis. The total influence of the surface condition results from the multiplicative combination of surface topography and residual-stress influences. Residual stresses can be interpreted as axial and tangential residual stress components , and , of the local biaxial residual stress state in the form of normal mean stresses. These can be superposed on the mean stress of the external load. For the superposition, the sums of the mean- and residual-stress components can be formed component by component. This superposition is exemplified for the mean stress component in equation (2) by the summation of the mean stress component , and the residual stress component , . = , + , (2) The surface factor makes it possible to characterize the surface topography and the microstructure of the material. It is based on considerations of the multiple notches (Liu, 2000) present in technical surfaces, particularly as grooves resulting from turning processes. Here, the surface groove form factor , can be described according to equation (3) for normal stresses. The equation for the surface shape number , for shear stresses can be taken from the literature (Liu, 2000). The multiple grooves of a surface are described in terms of the parameters of depth , radius , groove width and the distance between two adjacent surface grooves. , = 1 + (2 − ) ∙ √ (3) As explained in detail in the literature (Liu, 2000), an analogy can be made between a half-disk with a crack in a semi-elliptical boundary notch and a surface groove with a crack of the size of the intrinsic fatigue crack size 0 . From this, the surface factor for normal stress , follows according to equation (4). The surface factor for shear stress , is obtained analogously. , = 1 1 + [( , − 1) −2,5 + (√1 + 0 − 1) −2,5 ] −0,4 (4) The intrinsic fatigue crack size 0 can be described by the fatigue threshold ∆ , ℎ , the fatigue limit and the crack geometry factor according to equation (5). 0 = 1 ( ∆ , ℎ 2 ∙ ∙ ) 2 (5) According to the literature (Liu, 2000), the support factor required in the local strength approach results from equation (6) as the product of the mechanical deformation support factor , fracture mechanical support factor and statistical support factor . = ∙ ∙ (6) The mechanical deformation support factor can be obtained from the literature (Rennert et al., 2020). It includes Young’s modulus , the plastic strain limit amplitude , , at the fatigue limit and the strain-hardening exponent ′ . The fracture mechanical support factor is calculated according to the literature (Götz, 2012). It contains the related stress gradient ∗ , which must be determined for the stress components, as well as the intrinsic fatigue crack size 0 . The statistical support factor, which is also included in the mechanical deformation and fracture mechanical support factor in addition to equation (6), is set to = 1 . The reason for this is that the statistical size effect represented by the statistical support factor is already implicit in the probabilistic method that will be developed. With the help of the support factor and the surface factors, a local fictitious stress state is determined similar to the procedure in the literature (Liu, 2000). This consists of cyclic and static stress components. Based on the local fictitious stress state determined, an equivalent stress amplitude , can be calculated according to equation (7) when applying the shear stress intensity hypothesis (SIH) (Liu, 2000). , = √ ∙ 2 + ∙ 2 + ∙ 2 + ∙ (7)