13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- show ratios between 0.57 and 0.8 [21]. Anyway, it is always possible to assume different values of σA, more or less conservative than the cut off shown in Fig 2. In the following sections, both the original safe locus and a new one with the mentioned cut-off will be used, and results will be compared. For w a value of 360 MPa has been imposed [24] and a ratio σw/w=√3. With this assumption the value of the constant αDV used in the calculations is approximately 0.23205. Figure 2. The Dang Van safe locus: the dashed line represents the alternative limit curve, for σH(t)<σA, here assumed equal to σw/3, as proposed in [20]. For a material point subjected, at time t, to σH(t) and max(t), the ratio between max(t) and the corresponding limit value for that σH(t) is here used to define the damage factor n(t). Points on the limit curve, then, result in a unit damage factor; points inside the safe region have damage factor smaller than one. As previously mentioned, two different safe loci are here used: one with a linear limit curve and another one with a bilinear limit curve. Consequently, a damage factor is here defined as n(t)= max(t) w-αDV σH(t) (17) if referred to the original Dang Van's safety region or nሺtሻ=ቐ max(t) w-αDV σH(t) if &σH>σA max(t) A &if σH≤σA (18) when the bilinear limit curve is used. As mentioned above, σA and A are chosen equal to σw/3 and σw/2, respectively. 3. Results and discussion The Dang Van criterion has been applied to the rolling contact problem and for the geometry described in section 2. The load history has been divided in an adequate number of steps and, for each time step, the value of the damage factor n(t) has been calculated, both with the original Dang Van limit curve and with the modified one. The maximum value in time n=maxt n(t) (19) is then chosen, as representative for that material point. If this n<1, the prediction is that initiation of fatigue failure will not occur in the material point. The representative points corresponding to the max value of the damage factor are plotted, in Fig. 3, in the Dang Van region, for all the integration points in the region analyzed. In Fig. 4 the maximum values of this factor n are plotted against the distance from the surface. Both safe regions, as described before, are used. As we can see, n reaches the highest value in a sub-surface region, about 0.20 mm below the surface : this is consistent with literature, where a lot of sub-surface initiated failures in bearings for windmill applications are reported.
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