The Fretting Contact of Coated Bodies. Part I – Contact Parameters

Abstract

In case of a mismatch between the elastic properties of the contacting bodies, the solution of the fretting contact can only be achieved numerically due to the connection between the contact pressure and the shear tractions. The numerical treatment of the contact processes employs an iterative strategy, and therefore requires the computation of the displacement response of the elastic body, assumed as an elastic half-space, subjected to general loadings. Unlike the case of homogeneous bodies with known Green’s functions, a closed-form expression of the response of layered semi-infinite solids to unit point loads has only been attained in the frequency domain. The latter formulas are used in this paper to assess the displacement due to arbitrary normal and shear surface tractions, thus empowering the application of a trial-and-error approach in finding the parameters of a fretting contact: the contact area, the slip and the stick regions, and the distributions of pressure and shear tractions. The contact parameters are assessed in a nested loop strategy, involving three levels of iterations. The inner level, based on the conjugate gradient method for linear systems of equations, finds the pressure when solving the contact problem along the normal direction, disconnected from any tangential effects, or the shear tractions when considering the contact equations in the tangential direction, disconnected from the pressure influence. The middle level stabilizes the pressure with respect to the shear tractions, thus assuring that the global instantaneous contact solution is achieved. The outer level manages the reproduction of the loading history in a fretting loop, by load incrementation. The proposed strategy proves itself as a robust tool for the prediction of the fretting contact process involving coatings.