a a (a) Transgranular, Material A, R=−1 45 60 75 90 10 1 10 2 10 3 Angle of intrusion, α (deg) Depth of intrusion, d (nm) σ a=110MPa σ a=115MPa Crack Slip band (b) Transgranular, Material B, R=−1 (c) Transgranular, Material A, R=0 45 60 75 90 10 2 10 3 Angle of intrusion, α (deg) Depth of intrusion , d (nm) σ a=110 MPa σ a=115 MPa Crack Grain boundary (d) Intergranular, Material B, R=−1 Figure 6: Fatigue crack initiation condition. before the crack initiation, and solid marks show data after the crack initiation. The solid-lines in Fig. 6 show the relationship given from Eq. (1) for the value of s = 380 nm. For the transgranular crackings, which are shown in Fig. 6, data before the crack initiation fall below the solid lines, and data after the crack initiation locate above the solid lines. It indicates that there was a critical value of accumulated slip-distance, s. The critical value of s was 380 nm, independent of the stress amplitude, the mean stress, and the grain-size. When the accumulated slip distance of an intrusion in a slip-band grew up to the critical value, a cracks was initiated from the intrusion. These results indicate that the transgranular crack initiation is controlled by the damage accumulation due to the dislocation substructures rather than the stress concentration induced by the intrusion. As shown in Fig. 6 (d), the grain boundary depth at the intergranular crack initiation was not a unique function of the grain boundary angle relative to the stress axis. Other mechanism for the intergranular crack initiation should be considered, which may include the incompatibilities of deformation between two adjacent grains. Since the critical value of slip distance at crack initiationwas independent of mechanical and metallurgical conditions, the effects of these parameters on the fatigue crack initiation life should be attributed to their effect on the growth rate of slip distance. Therefore, the effects of the intrusion angle and the slip line length on the growth rate of the intrusion depth were examined. As shown in Figs 7 and 8, the rate was controlled not only by the intrusion angle and the slip-line length. It was affected by many factors, for example, constraint of deformation from adjacent grains. However, it is easy to predict when the depth reaches the critical value
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