13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- a threshold crack length after 106 cycles. The following methodology is applied: After each fretting test, the plane specimen is cut along the median axis of the fretting scar. Cross section observations are performed to determine the projected crack length (bp) along the normal of the surface. The polishing process is then repeated twice so that the crack measurement is performed on 6 different planes located along the median axis of the fretting scar. From these six measurements, the maximum projected crack length (bpmax) is determined. This crack analysis is generalized to various tangential force amplitudes in order to plot the evolution of bpmax versus the applied tangential force amplitude (Fig. 3b). Finally, the threshold crack nucleation is determined by extrapolating the tangential force amplitude related to a bpth = 10 µm projected crack length. This strategy was systematically applied for all the studied conditions. The corresponding * CN Q values are compiled in table 2. The expertise shows that the incipient crack nucleation is systematically observed at the trailing contact borders. Note that under established partial slip conditions, the surface wear is negligible and the contact geometry assumed unchanged during the fretting tests. 4. Contact stress analysis 4.1. Fretting Fatigue Stress field computation The contact stress analysis of studied plain fretting and fretting fatigue experiments is performed by applying an analytical formulation which consists to combine the Mindlin’s analytical description of partial slip contact (Fig. 4a) [9] with an adequate application of the McEven formalism’s [9]. P Q X=x/a Z=z/a +1 ‐1 p(X) surface pressure field q(X) p0 sliding zones ‐c/a c/a sticked zone surface shear field (unloading :-Q*) q(X) surface shear field (loading :+Q*) (a) -1 +1 a e -1 0 +1 +Q* ( ) q X sliding zones ( ) p X trailing edge (Loading) tangential force a e0 -Q* ( ) q X ( ) p X (Unloading) Compression c a 2 / c a 2 / aσ − aσ + Tension X=x/a X=x/a tangential force (b) Figure 4. Pressure and Shear surface profiles under partial slip conditions a) plain fretting – b) fretting fatigue The McEven formalism allows us to establish the stress state below the surface related to elliptical surface pressure or shear profiles. By summing the contribution of various elliptical shear distributions, the partial slip loading path can be determined. Note that the offset or eccentricity “e” of the stick zone, which induced by the fatigue strain deformation of the fatigue specimen, is considered by applying the Nowel’s formalism [11] (Fig. 4b). This approach is justified if the
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