A novel approach to predict fretting fatigue crack initiation
Résumé
Fretting-fatigue occurs in engineering assemblies subjected to vibration loads. Micro-slip, between the contacting bodies, leads to surface damage, and then crack initiation. Local approaches used to predict the fatigue life based on the stresses at the hot spots are over-conservative for fretting-fatigue because they do not account for the possibility of crack arrest due to a strong stress gradient from the surface to the bulk. Moreover, the crack initiation threshold is not unique in terms of local quantities and shows a strong dependency to the geometry. And even if the use of the critical distance theory helps to predict crack arrest, the capability to transfer results from laboratory to real structure is not guaranteed due to the impact of the gradient on the critical distance. A novel approach was proposed by Montebello overcoming the limitation presented above. In a local reference frame attached to the contact edge, the kinematic field is described by a sum of products of non-local intensity factors (analogous to LEFM) which represent the degrees of freedom and shape functions which are defined once for all for any contact problem between bodies. Additional nonlocal intensity factor making it possible to characterize the extent of the partial slip zone. The use of the new linear non-local quantities makes it possible to define a unique threshold for fretting-fatigue crack initiation. Moreover, the transition between gross-slip and partial slip conditions can be predicted directly by a “Coulomb-like” relation between the intensity factors. The extension of this approach in 3D allows to take into account out-of-plane loading and consequently to study the influence of the loading path for non-proportional tangential loadings. Simulation shows (Figure 1), that different loading paths with the same loading amplitude in terms of intensity factors produce a very different response in terms of partial slip. Both the sliding direction and its intensity are path dependent. In addition, the linear intensity factors can be determined as a function of the boundary conditions, using coarse mesh FE analysis and allow to predict through an incremental formulation with internal variables. With regard to the crack initiation and life prediction this approach makes it possible to formulate a non-local damage criterion when variable non-proportional loading conditions are encountered in fretting-fatigue.