applied sciences Article Determination of Local Stresses and Strains within the Notch Strain Approach: The Efficient and Accurate Calculation of Notch Root Strains Using Finite Element Analysis Lukas Masendorf * , Ralf Burghardt , Michael Wächter and Alfons Esderts   Citation: Masendorf, L.; Burghardt, R.; Wächter, M.; Esderts, A. Determination of Local Stresses and Strains within the Notch Strain Approach: The Efficient and Accurate Calculation of Notch Root Strains Using Finite Element Analysis. Appl. Sci. 2021, 11, 11656. https://doi.org/ 10.3390/app112411656 Academic Editor: Theodore Matikas Received: 29 October 2021 Accepted: 1 December 2021 Published: 8 December 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Institute for Plant Engineering and Fatigue Analyses, Clausthal University of Technology, Leibnizstraße 32, 38678 Clausthal-Zellerfeld, Germany; ralf.burghardt@tu-clausthal.de (R.B.); michael.waechter@tu-clausthal.de (M.W.); alfons.esderts@tu-clausthal.de (A.E.) * Correspondence: lukas.masendorf@tu-clausthal.de Abstract: For the service life estimation of metallic components under cyclic loading according to strain-based approaches, a simulation of the elastic-plastic stress–strain path at the point of interest is necessary. An efficient method for determining this stress–strain path is the use of the load–notch- strain curve, as this is also implemented within the FKM guideline nonlinear. The load–notch-strain curve describes the relationship between the load on the component and the local elastic-plastic strain. On the one hand, this can be estimated from loads or theoretical elastic stresses by using notch root approximations. On the other hand, this can be determined in a finite element analysis based on the elastic-plastic material behaviour. This contribution describes how this latter option is carried out in general and how it can be optimised in such a way that the FEA requires significantly less calculation time. To show the benefit of this optimisation, a comparative calculation on an exemplary geometry is carried out. Keywords: service life estimation; load–notch-strain curve; notch strain approach; finite element analysis 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 [1–5]. These differ primarily in the procedures used to determine the local stresses and strains; e.g., the notch root approximations [6–16], 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 [17–24]. 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 calcula- tion 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 “Rechnerischer Festigkeitsnachweis für Maschinenbauteile Appl. Sci. 2021, 11, 11656. https://doi.org/10.3390/app112411656 https://www.mdpi.com/journal/applsci