###### Abstract  
The fatigue strength of structural components is strongly affected by notches and imperfections. Both can be treated similarly, as local notch fatigue strength methods can also be applied to interior defects. Even though [PERSON]'s \(\surd\)area approach is commonly used in the threshold-based fatigue design of single imperfections, advanced concepts such as the Theory of Critical Distances (TCD), Notch Stress Intensity Factors (N-SIF), or Elastic Strain Energy Density (ESED) methods provide additional insight into the local fatigue strength distribution of irregularly shaped defects under varying uniaxial load vectors. The latter methods are based on the evaluation of the elastic stress field in the vicinity of the notch for each single load vector. Thus, this work provides numerically efficient methods to assess the local fatigue strength by means of TCD, N-SIF, and ESED, targeting the minimization of the required load case count, optimization of stress field evaluation data points, and utilization of multi-processing. Furthermore, the Peak Stress Method (PSM) is adapted for large opening angles, as in the case of globular defects. In detail, two numerical strategies are devised and comprehensively evaluated, either using a sub-case-based stress evaluation of the defect vicinity with an unchanged mesh pattern and varying load vector on the exterior model region with optimized load angle stepping or by the invocation of stress and strain tensor transformation equations to derive load angle-dependent result superposition while leaving the initial mesh unaltered. Both methods provide numerically efficient fatigue post-processing, as the mesh in the evaluated defect region is retained for varying load vectors. The key functions of the fatigue strength assessment, such as the evaluation of appropriate planar notch radius and determination of notch opening angle for the discretized imperfections, are presented. Although the presented numerical methods apply to planar simulation studies, the basic methodology can be easily expanded toward spatial fatigue assessment. t 202313220223132202313202  
V-notch is representative of the fatigue limit. In notched component design, the fatigue stress limit is often evaluated at a characteristic distance from the notch tip, according to the Theory of Critical Distances (TCD) [14; 15]. As the stress distribution in sharp V-notched parts is singular, the dimensioning by notch stress intensity factors (N-SIF) depends on the opening angle. Thus, a unified fatigue assessment for different notch angles is possible, either by means of the peak stress method (PSM) as a rapid fatigue assessment tool [16; 17] or by averaging the elastic strain energy density (ESED) within a certain control volume [18; 19; 20; 21; 22]. In summary, for linear-elastic stress field evaluation of a notched (or imperfect) component under uniaxial loading, the TCD, N-SIF, and ESED methods can all be used. Global approaches, such as [PERSON]'s method [23; 24; 25] for single imperfections or the extension towards extreme value statistics [26; 27; 28; 29], account for fatigue strength by evaluation of the projected defect area of the representative defect but do not take the effect of orientation on the global load vector into account. The basic principles of the TCD, N-SIF, and ESED methods, as local fatigue design approaches, are briefly reviewed in the following. First, the Theory of Critical Distances (TCD) [14; 15] is a local fatigue assessment tool requiring only the evaluation of the stress field at a dedicated point away from the notch tip [30; 31]. In the case of the Point Method, the stress is evaluated at a distance of \(a_{0}/2\) from the notch tip. The El Haddad-Smith-Topper parameter \(a_{0}\)[32] is material-dependent and indicates its supporting effect. The evaluated fatigue strength was originally threshold-based [33; 34], while a recent extension toward finite life fatigue assessment has been introduced in [35; 36; 37], and exemplified for macroscopic imperfections in [38].