Figure 4: Intergranular fatigue crack initiation (σa =110 MPa, N=7.9×10 4, Material B). ' Figure 5: Slip-plane and directions relative to stress-axis and surface. Schmidt factor slip system. The depth of the grain boundary, d, also increased with the number of cycles, N, and the crack-initiation could be easily identified from the change of the slope of the logN−drelationship. DISCUSSION Condition for the transgranular crack initiation is analyzed through a geometrical model proposed by Tanaka and Nakai [7, 8] shown in Fig. 5, which explains the relation between the surface-step and the slip-direction, where the Cube ABCDEFGO indicates a small region of a specimen that is located adjacent to the surface, and Point H is an arbitrary point on the slip-plane. In the figure, Plane ABCD represents the specimen surface, Plane CKLM represents the slip-plane, and y-axis and Arrow QH represents the loading-direction. Line CK is the slip-trace at the specimen surface and Line ST is a line on the slip-plane and that is parallel to Line KC. Arrow HR is the slip-direction on the slip-plane, and Arrow HP is the normal of the slip-plane. The surface-step induced by the slip is d =s· sinβ · cosα , (1) where the value of s is the slip distance in the HR direction, the value of α is the angle between the normal to the surface and the trace of the slip-band on the plane that is perpendicular to the surface and parallel to the loading-axis, and the value of β is the angle between the slip-direction and the slip-traces on the surface (see Fig. 5). Cracks are considered to have been initiated from slip bands, which had slip system in the maximum resolved shear stress [7, 8]. These slip bands are what is called as ”persistent slip band (PSB)”. For QHR= PHQ= 45◦, the resolved shear stress along the slip-direction takes the maximum value, and the following relationship should be satisfied. cosβ =√2cosα. (2) For α=90◦, the value of β should be 90◦, which gives the maximum slip-step on the surface for a given slip distance. For α=45◦, the value of β shouldbe 0◦ and no slip-step is formed on the specimen surface. On slip-planes where the resolved shear stress takes the maximum value, the following equation should be satisfied. cot2 α+tan2 α =1. (3) The relation between dand s can be derived as a function of αby substituting Eqs. (2) and (3) into Eq. (1). Figure 6 shows the depth of intrusions for various numbers of cycles as a function of the intrusion angle relative to the stress-axis. In the figure, data from the same intrusion fall on the same angle. Open marks indicate data
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