## 1 Introduction  
Modern production technologies focus on the economic and sustainable design of components in mass-production. This often yields complex-shaped components and high local load factors of corresponding cross-sections. Due to their high-load-bearing capabilities at moderate costs, cast steel alloys are widely utilized in lightweight design [1; 2; 3; 4]. The degree of complexity in geometric shape severely affects process parameters such as the local solidification rate, which provokes the formation of manufacturing process-based imperfections during the solidification of cast steel components [5]. As the size of respective defect structures often reaches dimensions of several millimetres, the local acting stress field is altered significantly, resulting in severely limited fatigue strength of defect-afflicted cast steel components [6; 7; 8; 9; 10; 11]. In order to assure the operationally durable design of imperfections components, the commonly utilized engineering guideline FKM (Forschungskuratorium Maschinenbau) proposes safety factors, that depend on the utilized methods of non-destructive testing during the quality control of cast steel components [12]. However, the application of such general safety factors often results in a highly conservative design of mechanical structures, leading to overweight components, which represent a contradiction to modern lightweight design efforts. Hence, the application of local fatigue assessment methods which consider the complex geometric shape of spatial imperfections is beneficial. [PERSON]'s theory of critical distances (TCD) depicts a widely utilized methodology to assess the fatigue strength of components affected by a stress concentrator, such as a notch [13]. Regarding the therein formulated point method, the concept states that the linear-elastic stress at a certain distance from the notch apex equals the fatigue strength of the plain material \(\Delta\sigma_{0}\), if the component is dimensioned against threshold condition \(\Delta K_{th,lc}\) in terms of fatigue crack initiation. The critical distance between the evaluation point and the notch root is proportional to the material intrinsic length \(a_{0}\), also known as the El-Haddad length [14], which is given by Equation (1). \[a_{0}=\frac{1}{\pi}\left(\frac{\Delta K_{th,lc}}{\Delta\sigma_{0}}\right)^{2} \tag{1}\]  
The TCD is comprehensively applied and validated for static and dynamic analysis of notched components [15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25]. More recently, the methodology was applied to predict the fatigue strength of cast steel components affected by bulk imperfections based on two-dimensional radiographs [26]. The strain energy density (SED) concept constitutes another local fatigue assessment methodology, which facilitates a uniform assessment of arbitrary geometrical configurations subjected to varying loading conditions. The methodology states that fatigue strength of a component is controlled by the strain energy density averaged over the control volume \(\Omega\), which represents a finite volume in the vicinity of the assessed stress concentrator, such as a blunt V-notch. Figure 1 depicts a blunt V-notch which is characterized by the notch opening angle \(2\alpha\), the notch root radius \(\rho\) and the notch depth. The position of its centre is defined by the parameter \(r_{0}\), which depends both on \(2\alpha\) and \(\rho\)[27]. The size of the control volume determines the aggregated amount of strain energy considered for fatigue assessment and is described by the material dependent control radius \(R_{c}\). Hence, the evaluation of an appropriate control radius plays a decisive role for energy-based fatigue assessment. [PERSON] et al. [28] presented an analytical solution for the determination of \(R_{c}\) applicable for cracks and V-notches. Equation (2) can be utilized for the evaluation of \(R_{c}\), invoking the material threshold and endurance limit [28].