13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- For all the cases analyzed, the peak of the n-curve shifts away from the surface of the inner ring and, for cases shown in Figs. 5a and 5b, the peak values of n are smaller than the correspondent peaks for a material with uniform hardness. In other words, the rings with extra surface hardening have higher safety against fatigue failure. 3.2 Residual stresses In order to analyze the influence of pre-existing stresses in the bearing, two different residual stress distributions have been considered. The bearing with the assumed residual stress distribution, equilibrated by an elastic step calculation, is subsequently subjected to the stresses caused by the contact with the roller. The results obtained with the Dang Van criterion are then compared with the results obtained in the bearing free of residual stresses. Figure 7. Convention used for the principal stresses in the polar coordinate system. In Fig. 7 the convention used to name the residual stresses is clarified, while, in Figs. 8a and 8b, the residual stress distributions, in terms of principal stresses, are plotted versus the distance from the surface. Far away from the surface, the residual stresses are assumed to be constant and near zero. The results for the two different safe loci (Fig. 2) are shown in Fig. 9. The pre-existing stress states in the inner ring, in the case of the modified safe locus, have little effect, neither positive nor negative (Fig. 9a). The residual stresses, in fact, result in a simple shift along the σH axis in the Dang Van region (Fig. 2) but this does not change the distance from the limit curve since all the most critical material points are subjected to values of σH smaller than σA and therefore they are in the region where the limit value for max is constant and equal to A. If the original limit curve is used, instead, the residual stress distribution (a) from Fig. 8 results in a reduction of the maximum damage factor for the compressive residual stresses, but an increase of the maximum damage factor for tensile residual stresses (Fig. 9b). Figure 8. Residual stresses assumed in terms of principal stresses. Distribution (b) is obtained by multiplying (a) by -1.
RkJQdWJsaXNoZXIy MjM0NDE=