Analysis of the elastic punch-substrate contact under fretting: Monotonic and cyclic loading of the punch

The object of this paper is to analyze the elastic behaviour of a 2-D contact problem between a right-angled flat punch and a semi-infinite substrate, subjected to a constant normal compressive load and a cyclic shear load using a finite element code. The knowledge of the stress and strain fields produced close to the corners of the punch under different loading conditions as a function of the friction coefficient will allow insight to be gained into the fretting fatigue problem associated to this cyclic loading. In order to better understand the behaviour and analyze the possibility of using fracture mechanics approaches to study the stress field close to the punch corners, two different models have been compared to each other: one without continuity solution between the punch and the substrate and the other with a couple of contact surfaces between them. Using the continuous model, a particularization of the general analytic solutions of Williams has been proposed. The complete stress field around the corners of the punch for this model has been obtained for any values of the punch size, normal and shear loads. Some general guides for understanding and systematizing the punch-substrate behaviour have been extracted from the above solution and that of a sliding wedge, provided by the literature, which enable a systematic numerical analysis of the problem. Further on, a more detailed study of the slip between punch and substrate, as well as of the stress field, has been accomplished using finite element analysis guided by the previous semi-analytical results. The study has been completed for the whole load process: compressive normal load, monotonic shear load, and cyclic shear load.