## 2 Properties of Fine Granular Area
### Influences Regarding the Formation Process of FGA
#### 2.1.2 Influence of the Material and Purity  
As mentioned above usually a change from crack initiation at the surface to initiation at internal defects is observed in the VHCF-regime for high-strength steels. It was observed that surface defect initiation and internal defect initiation are competing processes [24; 25]. The transition of the initiation sites depends on the defects as well as the microstructure and the mechanical properties of the tested material [26]. For instance, for high-strength steels with ultra-fine-grained (UFG) microstructure FGA-formation is not observed even in the VHCF-regime [27]. Since inclusion failure dominates in VHCF-regime for high-strength materials, a reduction of the fatigue strength is observed with increasing risk volume, because of the increased probability of larger existing inclusions inside the specimen [28; 29]. The extrapolation of fatigue results in the VHCF-regime from specimens with small risk volumes (V\({}_{0}=3.4\) mm\({}^{3}\)[30] or V\({}_{0}=33\) mm\({}^{3}\)[31]) to results with a larger test volume (V\({}_{0}=260\) mm\({}^{3}\)[30] or V\({}_{0}=912\) mm\({}^{3}\)[31]) was successfully performed using a two-step procedure. In the first step, the maximum inclusion size for the increased testing volume was estimated and, depending on this, the VHCF fatigue strength was estimated in a second step [30; 31]. However, the extrapolation of results from small samples with a risk volume of V\({}_{0}=55\) mm\({}^{3}\) to samples with even larger risk volumes of V\({}_{0}=5000\) mm\({}^{3}\) is complicated by the fact that the size of defects could not be accurately predicted using largest extreme value distribution [32]. Therefore, ultrasonic testing on specimens with larger risk volume such as the Gaussian specimens proposed by [PERSON] et al. [33] provide a better estimate of the critical defects and therefore a better basis for component design [29; 31; 32]. For low- and medium-strength steels the fatigue strength correlates very well with the hardness, independently of the microstructure [34; 35; 36] and the transition from surface crack initiation to internal crack initiation is not observed, therefore surface crack initiation being the dominating fatigue mechanism [18; 37; 38]. For the case of titanium alloys, which are almost free of inclusions and cavities, this shift from surface-induced to internal crack initiation is observed nevertheless [39; 40; 41]. The fatigue behavior is dominated by crack initiation at \(\alpha\) grain boundaries or inside \(\alpha\) grains in bimodal microstructure as well as \(\alpha\)-\(\beta\) interfaces in basket-weave microstructure [41]. For the case of internal crack initiation, [PERSON] et al. [40] describe a rough area around the crack initiation site inside the fish-eye. This fracture surface area is referred to by [PERSON] et al. [39] as rough area (RA). The transition of fatigue crack initiation from surface defects to subsurface defects like inclusions to subsurface non-defect area or matrix is also described in martensitic-ferritic and martensitic-austenitic dual phase steels by [PERSON] [42] and is called \"subsurface non-defect crack origins (SNDFCO)\". The fatigue damage mechanisms are described to be either the formation of cracks in the softer phase due to intrusion and extrusion processes or crack initiation at the grain boundaries due to dislocation pile-up. Furthermore, the crack propagation inside the SNDFCO is stage I cracking influenced by the microstructure. Moreover, while the size of the SNDFCO varies, the stress intensity factor (SIF) at its border is observed to be constant and the value correlates with the fatigue threshold for long crack propagation of the examined material. Similar results are reported by [PERSON] et al. [43].