Figure 2: Experimental results for 1 mm thick specimens and unfretted baseline conditions. Figure 3: Experimental results for 4 mm thick specimens and unfretted baseline conditions. 0 100 200 300 400 500 600 700 0 200 400 600 800 1000 R = 0.1; CR = 3.2 mm R = 0.5; CR = 3.2 mm R = 0.1; CR = 0.4 mm R = 0.5; CR = 0.4 mm Short Pad Model Haigh Stress (MPa) Ave. Clamping Stress (MPa) R=0.1; CR = 3.2 mm R=0.5; CR = 3.2 mm R=0.1; CR = 0.4 mm R=0.5; CR = 0.4 mm Long Pad Model The next results presented are the K solutions plotted as a function of depth into the specimen (Figs. 4 through 6) for the deformed edge of contact (DEC) location and two adjacent locations 20 µm on either side of the DEC. In Figures 4, 5, and 6, y=0 corresponds to the surface of the specimen in contact with the pad. Each plot also includes the axial stress σx, illustrating the extent of the gradients into the specimen thickness for the corresponding K curve. The K values peak at the DEC, as do the stresses on the specimen surface. Other cases (not shown) for locations farther beyond the DEC indicated K values decaying proportional to the stress field. However, K distribution trends at the DEC show a continuous increase in K with crack length, and point to crack propagation to failure and not crack arrest, as reported for other geometries [5]. In comparing the various cases modeled here, we first address the cases where µ is taken as 0.3, a value which represents an average of values corresponding to gross slip over the entire pad length [1]. Data for the 1 mm thick specimen and short pad case are shown in Figure 5; data for the 4 mm thick specimen and long pad are shown in Figure 6. The values of maximum σx, shown in Table 1, vary from ~500 MPa for the 4 mm thick long pad case (Fig. 5) to ~1300 MPa for the 1 mm thick short pad case (Fig. 4). Since K depends strongly on the stress field, the calculated K values are higher for the case with the higher stresses, namely the 1 mm thick specimen and short pad case. Variations of stress gradients into the depth from one case to another are not too great and have little effect on the nature of the variation of K with crack length. The experimental results for these two cases indicate nearly identical fatigue limits (Figs. 2 and 3). One would expect similar peak stresses and stress intensity factors in cases reflecting similar fatigue limits for the same fatigue life. As reported previously [1], differences in applied shear stress and average applied clamping stress at the contact for these two cases do not adequately explain the marked differences in the stresses from the numerical simulations. One possible explanation lies in the value of µ used in the analyses. Work by other researchers has indicated pronounced changes in µ over time under fretting fatigue conditions [14, 15], and as our previous work indicated, overall fretting fatigue behavior is extremely sensitive to µ. Another observation from the previous work [1] was that the maximum relative displacement (see Table 1) at the edge of contact was considerably different for the two cases studied. This observation, coupled with the observation that increasing the value of µ resulting in increasing values of σx, lead to consideration of increasing µ for the case of the 4 mm thick specimen, which showed both lower stresses and higher relative displacements. While there is no physical basis for this assumption, the concept of higher µ for higher slip displacements is not totally without merit. It is also of interest to note that an early fretting parameter [10] contained the product of the stress and relative displacement. Perhaps the theory proposed here has the same
RkJQdWJsaXNoZXIy MjM0NDE=