The Fretting Contact of Coated Bodies. Part II – The Stress State

Abstract

The service life of contacting coated machine elements is ultimately determined by the distribution of stresses in the coating and in the substrate. By assuming the elastic bodies as elastic half-spaces, the contact stress computation entails the calculation of convolutions expressing the superposition of effects of unit point loads acting on the boundary. The fundamental solutions of stresses and displacements in multilayered materials have only been calculated in the frequency domain, and are known as the frequency response functions. An additional difficulty arises in the stress calculation, related to frequency response function valuation in the origin of the frequency domain, where a singularity is usually encountered. This case of un-determination is circumvented in this paper by substituting the required value with the mean value of the frequency response function over a vicinity centered in origin. The latter approach is endorsed by the fact that the frequency response function is singular, but numerically integrable in the aforementioned vicinity. The latter technique is validated by comparison with results obtained for the sliding contact, and then applied to derive the elastic stresses arising during a fretting loop in the coating and in the substrate. The stresses due to shear tractions are superimposed to those induced by contact pressure. The calculation is performed in layers of constant depth, and the algorithmic complexity is optimized by using state-of-the-art techniques for discrete convolution computation. The equivalent stress is discontinuous across interface between the two layers, and the location and intensity of the maximum von Mises stress is determined by the frictional coefficient and by the mismatch between the Young moduli of the coating and the substrate. The results obtained with the newly proposed numerical technique may extend the understanding of the fretting contact of coated materials and assist the design of improved coating configurations.