The two-dimensional fretting contact with a bulk stress. Part I – Similar elastic materials

Abstract

Minute relative motions along the interface of contacting machine elements, brought about by cyclic tangential loading, lead to failure of many mechanical components from fretting fatigue. From the point of view of applied mechanics, the understanding of the fretting fatigue rely on the modelling of contact problems with partial slip. The experimental simulation of fretting fatigue often implies cylindrical pads in contact with a flat specimen, leading to a plane strain contact scenario requiring the solution of the two-dimensional contact problem. The numerical solution for the latter problem is achieved in this paper for similar elastic materials by employing the technique of influence functions, derived from fundamental half-plane solutions of point forces acting on the boundary. The contact model is first divided into two parts with solutions more easily to obtain. The linear systems with the normal and shear tractions as unknowns are solved with the conjugate gradient method, which can be applied for symmetric and positive definite system matrices. The most time-consuming operations are the convolutions products assessing the displacements induced by the contact tractions. A method based on the fast Fourier transform is applied for increased computational speed without sacrificing accuracy. The proposed algorithm was benchmarked by reproducing the solution of the classic two-dimensional Cattaneo-Mindlin problem. In practical situations, other loadings besides the contact itself may induce bulk stresses within one or both of the contacting bodies. New results are obtained by introducing a bulk stress, thus replicating the conditions from fretting fatigue experiments. The advanced numerical program for the two-dimensional contact with partial slip proves itself as an efficient tool for the understanding of the fretting fatigue by numerical modelling and simulation.