The two-dimensional fretting contact with a bulk stress. Part II – Loading history and dissimilar elastic materials

Abstract

The contact model for similarly elastic materials advanced in the companion paper is enhanced to account for the more general case of contacting bodies with different elastic properties. The latter contact model, involving dissimilarly elastic bodies under partial slip, is particularly difficult to solve due to the mutual interaction between the normal and the shear tractions. As opposed to the contact of similar elastic materials, pressure is affected by the shear tractions and vice versa. Therefore, the contact submodels in the normal and in the tangential direction are not independent. The connection can only be overcome in an iterative manner, by adding a new external loop to the contact algorithm, in which the solutions of the systems in the normal and in the tangential directions are mutually adjusted by successively solving both systems until convergence is reached. Moreover, with friction being a dissipative process, any state depends upon the process path, i.e., on all previous states attained during the loading history. The contact model is solved as a series of quasi-static states that are expected to replicate the loading path. Two levels of iterations are added to the model of similarly elastic materials, described in the companion paper, to account for the dissimilarity in the elastic properties. The contact process is reproduced on a prolonged loading history, consisting in the first fretting loops. The distributions of contact tractions are obtained using a technique for the fast computation of convolutions involving the fast Fourier transform. The conducted simulations prove the method robustness and its application in the modelling of the fretting processes.