## 1 Introduction  
The assessment of fatigue strength is one of the most important aspects in the design of safety-relevant components. As an alternative or a supplement to an experimental strength assessment, an analytical assessment can be performed. Various calculation approaches exist for this purpose, which can be distinguished into stress- and strain-based concepts [1, 2]. The latter, which are also called local strain approaches, assume elastic-plastic material behavior in the component and use the calculated local stresses and strains 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 variants 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 load 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 the component lifetime. In addition, the calculation procedures of 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. To be able to use local strain approaches for a reliable analytical component assessment, the abovementioned diversity of variants and the dependency of the calculation result on the implementation tend to be disadvantages. Calculation results are not comparable. To overcome this weakness, the guideline \"Rechnerischer Festigkeitsnachweis fur Maschinenbauteile unter expliziter Erfassung nichtlinearen Werkstoffverformungsverhaltens\" (Analytical strength assessment for components under explicit consideration of nonlinear material behaviour, [25]) has been developed in Germany. In this guideline, the abovementioned diversity of variants in the calculation algorithms has been reduced to two variants of different complexity. Both variants are also described in such detail that the deviations in the calculation results by 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 \"Forschungszuratorium Maschinenbau\" (FKM) and will be referred to as the FKM Guideline nonlinear in the following. As this guideline is only available in the German language so far, the calculation model for the fatigue strength assessment will be briefly explained in the following. More detailed information can be found in [25; 26]. The FKM Guideline nonlinear allows two different calculation procedures for fatigue strength assessment, which differ in the 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 \(\mathrm{P_{RAM}}\), Equation (1), is calculated. \[ \begin{array}{l}\mathrm{P_{RAM}}=\sqrt{(\sigma_{a}+k\cdot\sigma_{m})\cdot \varepsilon_{a}\cdot E}\quad\mathrm{if}\ (\sigma_{a}+k\cdot\sigma_{m})\ \geq\ 0\\ \mathrm{P_{RAM}}=0\quad\mathrm{if}\ (\sigma_{a}+k\cdot\sigma_{m})\ <\ 0\end{array} \] (1) Here, \(\sigma_{a}\) is the stress amplitude, \(\sigma_{m}\) is the mean stress and \(\varepsilon_{a}\) 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.