###### Abstract
The plane strain state leads to a reduced control volume, thus favouring a conservative fatigue assessment. Under the plane strain condition, the range of the elastic strain energy density, averaged over the control volume \(\Omega\), can be expressed analytically for sharp notches [49]. The parameter \(e_{1}\) depends on the notch opening angle \(2\alpha\) and [PERSON]'s ratio \(\
u\). The radius of the control volume is given by the critical radius \(R_{c}\), which originates in the case of sharp notches at the notch tip. Equation (5) depicts only the contribution of Mode I.  
\[\Delta W=\frac{e_{1}}{E}\left[\frac{\Delta K_{I}^{V}}{R_{c}^{1-\lambda_{1}}} \right]^{2} \tag{5}\]  
The total elastic strain energy density can be related to the notch stress intensity factor, or in terms of the peak stress [50; 51; 52]. To account for the scale effect under non-linear material behavior, either plastic notch stress intensity factors [53; 54] or total strain energy density fatigue design utilizing both the elastic and plastic energy fractions [55; 56; 57] can be exploited. The cumulative value of the strain energy density can be linked to the number of cycles to failure [58; 59]. Thus, the crack initiation sites can be well-identified by strain energy density evaluation within a notched component [60; 61; 62]. Multi-axial loads can be taken into account by evaluating the energy density in critical planes [63; 64]. The aim of this work is to provide a methodology to set up numerical methods, realizable using commercially available finite element codes and user-defined scripting, which support the efficient evaluation of irregularly shaped defects under varying uniaxial tensile load vectors. At a glance, numerically efficient fatigue post-processing tools for planar meshes featuring a notched component are based on maintaining an unchanged mesh pattern within the notch vicinity, even for varying load vectors. Thus, local evaluation methods, such as interpolation of nodal stresses at TCD-specific points or calculation of element fractions within a certain control volume for ESED fatigue assessment, may be computed only once for several load cases. As only planar studies are considered in this work, the uniaxial tension load vector is rotated along half of the defect circumference. The applied load angle stepping, as well as the mesh-seed of the defect-afflicted model, determine the overall computation time. Key parameters affecting the calculated fatigue strength distribution, such as the global mesh-seed or control radius \(R_{c}\), are also identified and discussed. In general, if the chosen local fatigue concept is based only on the stress field, such as the case in the TCD or N-SIF fatigue assessment methods, stress transformation of the basic load steps for varying uniaxial load vectors is recommended in post-processing. Thereby, the nodal stress results are not simulated by means of finite element studies for each load vector but computed through post-processing transformation of the stress or strain tensor. If the fatigue design is to be based on ESED values, a sub-case-based approach is preferable, which allows for improved accuracy. This implies the splitting of the input model into a defect area with a circular border, which is glued to the rectangular bounding box. The latter bounding box component is rotated for each uniaxial load vector, but the interior part of the model is kept unchanged. Although an increased number of load case simulation runs is needed, the post-processing stage is simplified, as the additional transformations are omitted. Finally, the overall wall-time demand of the scripts dealing with curvature calculation, stress path evaluation, and control volume computation can be significantly improved through the utilization of multi-processing computation modules.