applied fracture mechanics

Fracture Mechanics Based Models of Structural and Contact FatigueFracture Mechanics Based Models of Structural and Contact Fatigue 2917311−P(N)0.750.50.2501E7 1E8 1E9 1E10NFigure 14. Pitting probability 1 − P(N) calculated for the basic set of parameters (solid curve) and forthe same set of parameters and changed profile of residual stress q 0 (dashed curve) in such a way that atpoints where q 0 is compressive its magnitude is unchanged and at points where q 0 is tensile itsmagnitude is doubled (after Kudish [17]). Reprinted with permission from the STLE.parameters, just one parameter from the basic set of parameters will be varied at a time andgraphs of the pitting probability 1 − P(N) for these sets of parameters (basic and modified)will be compared. Figure 12 shows that as the initial values of the mean μ of crack half-lengthsand crack standard deviation σ increase contact fatigue life N decreases. Similarly, contactfatigue life decreases as the magnitude of the tensile residual stress and/or friction coefficientincrease (see Fig. 4 and 13). The results show that the fatigue life does not change when themagnitude of the compressive residual stress is increased/decreased by 20% of its base valuewhile the tensile portion of the residual stress distribution remains the same. Obviously, thatis in agreement with the fact that tensile stresses control fatigue. Moreover, the fatigue damageoccurs in the region with the resultant tensile stresses close to the boundary between tensileand compressive residual stresses. However, when the compressive residual stress becomessmall enough the acting frictional stress may supersede it and create new regions with tensilestresses that potentially may cause acceleration of fatigue failure.μ [μm] σ [μm] N 15.9 [cycles]49.41 7.61 2.5 · 10 873.13 11.26 1.0 · 10 898.42 15.16 5.0 · 10 7147.11 22.66 2.0 · 10 7244.25 37.62 6.0 · 10 6Table 1. Relationship between the tapered bearing fatigue life N 15.9 and the initial inclusion size meanand standard deviation (after Kudish [17]). Reprinted with permission from the STLE.Let us consider an example of the further validation of the new contact fatigue model fortapered roller bearings based on a series of approximate calculations of fatigue life. The