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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Of these parameters, surface condition and external shape are themselves subject to variations in manufacturing processes and tool condition, such as the degree of cutting-edge wear, for example. Furthermore, surface condition causes scatter not only due to surface topography, but also due to residual stresses present in the surface as well as boundary-layer strengths (Adenstedt, 2001; Liu, 2000). Scatter related to external shape is caused by deviations in diameters and radii (Adenstedt, 2001; Liu, 2000; Schijve, 1994). Material condition causes scatter due to variations in chemical composition and heat treatment (Adenstedt, 2001; Hück, 1992). In all cases, the results of scattering are different material properties or strengths due to deviating microstructures. In addition, it is assumed that a varying fatigue behavior is also inherent to the structure at microscopic level (Adenstedt, 2001; Liu, 2000). Fatigue scattering due to grain orientation and microstructural inhomogeneities of the material will not be considered in this paper. The aforementioned scatter-influencing parameters can not only vary between production, material and heat-treatment batches, but can also vary within batches. 3. Local strength approach Local strength approaches are commonly used to predict fatigue strength (e.g., Rennert et al., 2020). Therefore, a calculation approach is derived from existing local strength approaches with the aim of including the parameters that influence fatigue strength and their scatter. For this purpose, the procedure of the derived local strength approach required for the strength verification is described below based on Fig. 1.

Material condition

Extern. shape

Loadtype + , + , + ,

Surface condition

Surfacefactor

Localelasticnotchstresses

Residual stresses

Local hardness

Local fatigue limit

, , ,

Support factor

Fictitious stress state

,

Local strengthverification ,

Strengthhypothesis (SIH)

Fig. 1. Local strength approach.

Based on the influence parameters of external shape and stress type, the local elastic notch stresses of a shaft can be determined. These are calculated using finite element analysis (FEA) at the notch surface, for example. They can be expressed in an x – y coordinate system as a plane stress state with the components , and . The time histories of the stress components must be synchronous under external loading. As exemplified for the stress component ( ) in equation (1), the stress component has an amplitude and a mean stress , due to the external load. ( ) = , + (1) In order to be able to take the influence of surface condition on fatigue strength into account, a partial concept is used (Kleemann and Zenner, 2006). The surface topography is described using a surface factor (Liu, 2000) and the residual stresses at the component surface are included in the local stress state as mean stresses by means of a strength