13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Application of a non local fatigue stress gradient- weigth function approach to predict the crack nucleation risk induced by Fretting Fatigue Siegfried Fouvry*, Bruno Berthel LTDS, Ecole Centrale Lyon, 69134 Ecully, France * Corresponding author: siegfried.fouvry@ec-lyon.fr Abstract Fretting-Fatigue problems are very complex to address due to the multiaxiality and the very sharp stress gradients imposed below the interfaces. Hence, multiaxail and non local fatigue approach must be considered. An experimental cylinder/plane fretting fatigue and plain fretting analysis a 35 Ni Cr Mo 16 low alloyed steel at 106 cycles has been performed to investigate the incipient crack nucleation response for various stress gradient conditions. Imposing elastic stress conditions, the Crossland’s approach is applied to predict the crack nucleation risk. This analysis confirms that a local stress analysis at the “hot spot” stress located at surface trailing contact border is not suitable. The non local “critical distance” approach which considers the stress loading path at a fixed distance from the “hot spot” improves the prediction but still induce a large discrepancy. Finally, the best predictions are achieved using an alternative non local “weight function” approach where the crack nucleation risk computed at the “hot spot” is weighted by a function expressed as as a linear decreasing expression of the hydrostatic stress gradient operating around the “hot spot” location. The stability of this approach regarding the contact stress field resolution and related application for FEM application is discussed. Keywords Fretting Fatigue crack nucleation, Stress gradient, Non local fatigue approach, Crossland 1. Introduction Fretting is a small amplitude oscillatory movement, which may occur between contacting surfaces that are subjected to vibration or cyclic stress. Combined with cyclic bulk fatigue loading, the so-called fretting-fatigue loading can induce catastrophic cracking phenomena which critically reduce the endurance of assemblies [1]. Fretting Fatigue loading can be characterized by the superposition of a heterogeneous cyclic stress gradient related to the contact loading, and a quasi-homogeneous fatigue bulk loading (Fig. 1). The crack nucleation phenomenon is commonly addressed by transposing conventional multi-axial fatigue criteria [2] taking into account or not the stress gradient effects [3, 4]. Indeed, as illustrated in Figure 2, the fretting stressing conditions are characterized by very severe stress gradients which could be one order of magnitude higher than common notch fatigue stress configurations. Non local fatigue approaches are therefore required to predict the cracking risk. Stress averaging approaches [3, 5], or equivalent critical distance methods [4] which consist to consider the stress state at a “critical distance” from the stress “hot spot” are commonly applied to capture the stress gradient effect. However, these approaches, which consider a fixed length scale value are limited when large stress gradient fluctuations are operating. To palliate such limitation, an alternative strategy which consists to weight the prediction given at the “hot spot” location using a linear decreasing function expressed as a function of the gradient of the hydrostatic stress around the hot spot stress location is considered. Introduced by Papadopoulos [6], this approach was simplified by Amargier et al. to predict plain fretting crack nucleation conditions
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