## 2 Properties of Fine Granular Area
### Characteristics of the FGA
#### 2.2.1 Characteristics Observed on the Fracture Surface  
As described above a characteristic morphology was observed on the fracture surface directly around the crack-initiating defect, like non-metallic inclusions, for failure in the VHCF-regime. This characteristic microstructural feature was designated \"optically dark area\" by [PERSON] et al. [9], \"granular bright facet\" by [PERSON] et al. [10], \"rough granular area\" by [PERSON] et al. [11], or \"fine granular area\" by [PERSON] et al. [12] depending on the observation method used to analyze the fracture surface. While [PERSON] et al. and [PERSON] et al. used light microscopy and observed a dark area, or a granular bright facet depending on the light settings, [PERSON] et al. and [PERSON] et al. used SEM and described the area as rough granular or fine granular area. However, all those designations describe the identical fracture area that differs from the classical fish-eye structure, which is a common feature around the crack-initiating inclusion on fatigue fracture surfaces. Early attempts at explanations of this new characteristic feature FGA were based on the roughness of the fracture surface; it was shown that the roughness within the FGA is significantly larger than in the surrounding fish-eye [23] and that the roughness increases with increasing the distance from the crack initiation site [86]. Furthermore, the average area of convex particles observed in the FGA were determined and correlated with the average size of carbides, which led to the development of the FGA-formation model based on dispersive decohesion of spherical carbide described in Section 3.2. To gain further insight into the underlying mechanism, the size of the crack-initiating inclusion as well as of the FGA and the fish-eye were investigated in more detail. To describe the crack propagation around inclusions the \(\sqrt{area}-\) Model [34, 87] developed by [PERSON] is now well established. It uses the projected area perpendicular to the applied load to describe the stress-increasing effect of a defect by transformation into an equivalent crack for the calculation of the stress intensity factor (SIF). FGA-formation is observed for inclusions with a SIF \(\Delta\mathrm{K_{Inc}}\) smaller than the threshold value for long crack propagation \(\Delta\mathrm{K_{th}}\)[15, 62, 88] and the SIF around an inclusion decrease with increasing lifetime due to the reduced applied stress (white and grey symbols in Figure 2) [56, 70]. However if the maximum stress intensity factor \(\rm K_{max,FGA}\) at the border between the FGA and the fish-eye is determined in analogy to the \(\sqrt{area}\) - Model by [PERSON], using the entire area of the FGA including the non-metallic inclusion, their values match their respective threshold values for long crack propagation of high-strength steels for the respective stress ratio \(\rm R=-1\) of \(\rm K_{max,th}\approx\) 4-5 \(\rm MPam^{1/2}\)[8, 10, 15, 89, 90]. FGA-formation is only observed if the SIF \(\rm K_{max}\) of the crack-initiating defect is below the threshold for long crack propagation. If the area of the FGA is used to calculate the resulting SIF at the border between the FGA and the fish-eye (blue symbols in Figure 2), it reaches or exceeds the threshold for long crack propagation \(\rm K_{max,th}\)[91, 92]. Similar results were obtained by [PERSON] et al. [56] who reported that the value of the SIF of inner inclusions leads to failure without FGA are 4-5 \(\rm MPam^{1/2}\) and are similar to those of surface defects corresponding to the threshold value for crack propagation, while the SIF values for inclusions with FGA-formation are significantly lower at 2.5-3.3 \(\rm MPam^{1/2}\). In analogy [PERSON] et al. [39] reported that for Ti-6 Al-4V the values of the SIF at the border of the RA also corresponds to the threshold for crack propagation in vacuum.