13th International Conference on Fracture June 16–21, 2013, Beijing, China -10- 5. Conclusion A combined experimental and Crossland multiaxail fatigue approach is developed to rationalise the crack nucleation risk induced by plain fretting and fretting fatigue loadings. It shows that due to the very stress grading imposed by the contact stressing, a local “hot spot” fatigue stress analysis is not suitable. The application of the critical distance approach based on the Taylor’s formalism improves the prediction but still display high dispersion. Finally, the non local “weight function” approach provides very consistent and stable predictions. This analysis shows that the “k” factor defining weight function is highly dependent on the ℓ length scale variable over which the hydrostatic stress gradient is computed. We show a variation of the k factor versus the ℓ length variable. Finally, we confirm that the stability of this approach according that the related R² correlation factor remains high and constant (i.e. above 0.85) over the whole studied ℓ length (i.e. up to 200µm). This stability regarding the spatial stress resolution suggests that, this approach could efficiently be transposed in coarse industrial FEM contact meshing to achieve pertinent fretting cracking predictions. References [1] R.B. Waterhouse, Fretting Fatigue, Applied Science publishers, 1981. [2] M.P. Szolwinski, T.N. Farris, Mechanics of fretting crack formation. Wear 1996;198:93-107. [3] S. Fouvry, Ph. Kapsa, F. Sidoroff, L. Vincent, Identification of the characteristic length scale for fatigue cracking in fretting contacts. J. Phys. IV France 1998; 8: 159-166. [4] J.A. Araújo, D. Nowell, The effect of rapidly varying contact stress fields on fretting fatigue. International Journal of Fatigue 2002; 24 (7): 763-775. [5] S. Fouvry, K. Kubiak, Development of a fretting–fatigue mapping concept: The effect of material properties and surface treatments, Wear, 267(2009) 2186–2199 [6] IV. Papadopoulos. Int J Fatigue 2001;23:839–49. [7] R. Amargier, S. Fouvry, L. Chambon, C. Schwob, C. Poupon, , Int. J of Fatigue,2010, 32 (12) : 1904-1912. [8] L.J. Fellows, D. Nowell, DA. Hills, On the initiation of fretting fatigue cracks. Wear 1997;205:120–9. [9] KL. Johnson, Contact Mechanics, Cambridge University Press,1985. [10]H. Proudhon, S. Fouvry, J.-Y. Buffière, A fretting crack initiation prediction taking into account the surface roughness and the crack nucleation process volume. International Journal of Fatigue,2005; 27(5):569-579. [11] D. Nowell, D.A. Hills,Mechanics of fretting fatigue tests, Int. Jnl. Mech. Sci., 1987, 29, 5: 355-365 [12] B. Crossland, Proceeding of the Inter. Conf. On Fatigue of Metals, Inst. of Mechanical Engineers, London, 1956, pp. 138-149. [13]D. Taylor D. Analysis of fatigue failures in components using the theory of critical distances. Engng Fail Anal 2005;12:906–14.
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