## 1 Introduction  
The assessment of fatigue strength is one of the most important aspects in the design of safety-related components. As an alternative or as a supplement to experimental strength assessments, analytical assessments can be performed. Various calculation approaches exist for this purpose; these can be distinguished into stress- and strain-based concepts [1, 2]. The latter, which are also called local strain approaches or the notch strain concept, assume elastic-plastic material behaviour in the component, and use the local stresses and strains calculated as basic load quantities. The notch strain concept, also known as the local strain approach, can be found in many variants throughout the literature [1, 2, 3, 4, 5]. These differ primarily in the procedures used to determine the local stresses and strains; e.g., the notch root approximations [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16], and in the so-called load parameters (also known as mean stress parameters or damage parameters) used to evaluate the damage of individual stress-strain hystereses [17, 18, 19, 20, 21, 22, 23, 24]. Both can have a significant influence on the calculation result of a component's fatigue life. In addition, the calculation procedures used for the notch strain approach--regardless of how it is expressed--can only be applied with the help of computational algorithms, since, for example, numerical solution procedures need to be used. Therefore, the calculation result also depends to a certain extent on the user-specific implementation of these calculation algorithms. In order to use local strain approaches for a reliable analytical component assessment, the above-mentioned diversity of variants and dependency of the calculation result on the implementation tend to be disadvantages. Calculation results are not comparable. To overcome this weakness, the \"Recherischer Festtigkeitsnachweis fur Maschinenbauteileunter expliziter Erfassung nichtlinearen Werkstoffverformungsverhaltens\" (Analytical strength assessment for components under explicit consideration of nonlinear material behaviour [25]) guideline was developed in Germany. In this guideline, the above-mentioned diversity of variants in the calculation algorithms is reduced to two variants with different levels of complexity. Both variants are also described in such detail that the deviations in the calculation results of different users are reduced to a minimum. In addition, the calculation algorithm is provided with a safety factor concept that allows the assessment of component fatigue lives for low probabilities of failure. The described guideline was developed by the German research association \"Forschungskuratorium Maschinenbau\" (FKM), and subsequently will be referred to as the \"FKM guideline nonlinear\". As the guideline is only available in the German language at present, the calculation model for the fatigue strength assessment will be briefly explained below. More detailed information can be found in [25; 26]. The FKM guideline nonlinear allows two different calculation procedures for fatigue strength assessment that differ in their estimation of the local stresses and strains and the load parameter used. * On the one hand, the local elastic-plastic stresses and strains can be estimated using the notch root approximation according to [PERSON] [27] with the extension according to [PERSON] and [PERSON] [28]. For each closed hysteresis detected from the local stress-strain paths estimated in this way, a load parameter \(\mathrm{P_{RAM}}\) is calculated using Equation (1): \[ \begin{array}{ll}\mathrm{P_{RAM}}=\sqrt{(\sigma_{a}+k\cdot\sigma_{m})\cdot \epsilon_{a}\cdot E}&\text{if }(\sigma_{a}+k\cdot\sigma_{m})\ \geq\ 0\\ \mathrm{P_{RAM}}=0&\text{if }(\sigma_{a}+k\cdot\sigma_{m})<\ 0\end{array} \] (1) where \(\sigma_{a}\) is the stress amplitude, \(\sigma_{m}\) is the mean stress, \(\epsilon_{a}\) is the strain amplitude of the detected hysteresis, E is [PERSON]'s modulus, and k is a correction factor that takes into account the mean stress sensitivity of the material.