## 4 Discussion
Also, the very slow crack propagation rate that is observed within the FGA is not explainable by short crack propagation and the observation of fine-grained areas ahead of the crack tip [88; 91] is inexplicable by this model. Also, the recent observation [104] that compressive loads that lead to FGA-formation during fatigue testing did not form an FGA during a compressive fatigue test on a pre-cracked specimen suggest that the repeated fracture surface contact is not the underlying mechanism of FGA-formation. The model based on cold welding-induced grain refinement first postulated by [PERSON] and [PERSON] [81] sharing similar explanations to the NCP model, for the formation only being observedin the VHCF-regime and for the diminishing tendency of FGA-formation with increasing stress ratio could explain the slow crack propagation rates observed because of a repeated cold-welding process. However, the different grain orientations detected by SAD would not be expected by a process of different crack paths and repeated cold welding of the previously generated fracture surfaces. Also, the vacuum dependence of the formation of FGA [81; 83; 84] can be explained by this model, however, the formation of FGA at surface cracks reported for cold rolled stainless steel [85] is in contradiction to the postulated formation mechanism based on cold welding. The model of Stage-I-like crack propagation with grain refinement in the crack wakes proposed by [PERSON] et al. [62] shares the strengths and weaknesses with the NCP model. While explaining the fine-grained layer and also explaining the FGA sensitivity to stress ratios, the low crack propagation rate as well as the observation of grain refinement in front of the crack tips are inexplicable by this model. The model of local grain refinement at the crack tip first proposed by [PERSON] et al. [15] and then extended by [PERSON] [91] is based on the propagation of long cracks due to rearrangement of dislocations and consequently grain refinement resulting in a locally reduced threshold. The rearrangement of dislocations followed by formation of dislocation cells [118] and the formation of small sub grains and low angle boundaries were observed in steels in the VHCF regime [119] caused by local plasticity [122]. A decrease in the threshold for long crack propagation and higher crack growth rates have been observed for fine grained steels [27; 123] and generally in fine-grained metals [124; 125]. Therefore, the formation of a fine-grained layer according to this model is not only explainable but is a necessary condition for VHCF failure. In addition, the correlation between the increasing thickness of the FGA with the plastic zone size for increasing crack length, as well as the gradient in regards to the increasing grain size along the crack path inside the FGA can be explained. The slow crack propagation rate can therefore be explained by the repeated process of grain refinement to reduce the threshold value for crack propagation locally within the refined microstructure and the subsequent need for grain refinement once the crack propagated to the original microstructure. The tendency of decreasing FGA-formation with increasing stress ratio can be explained by a decreasing threshold for crack propagation [58; 59], as well as the decreasing cyclic plastic zone size [126] that might result in the absence of dislocation cell formation and the resulting grain refinement. In analogy, the vacuum-like conditions that seem to be beneficial for FGA-formation can be explained by the increasing plastic zone size [78; 79] and the easier movement and interaction of dislocations under those conditions [80] resulting in beneficial conditions for rearrangement into dislocation cells with subsequent grain refinement. However, the reported formation of FGA-like morphologies due to cyclic loading with K\({}_{\text{max}}\) < K\({}_{\text{th}}\) on previously generated fracture surfaces reported by [PERSON] [61] is inexplicable with this model.