An efficient method for solving three-dimensional fretting contact problems involving multilayered or functionally graded materials

Three-dimensional fretting contacts involving multilayered or functionally graded materials are commonly seen in mechanical systems. The analyses of surface fatigue and contact failure require the knowledge of pressure, shear tractions, and stresses. This paper presents a novel method for analyzing the fretting contacts of these materials. The frictional contact equations are divided into two portions, one containing the unknown contact pressure and the other the shear tractions, solved by using the conjugate gradient method with boundary conditions enforced during the iteration. Displacements and stresses caused by the contact pressure and shear tractions are calculated through the use of the influence coefficients and by means of the fast Fourier transform. The influence coefficients are obtained from the analytical frequency response functions derived by the authors, which are the frequency-domain responses of a multilayered surface system to a unit concentrated normal or tangential force. Functionally graded coatings are modeled with multiple sufficiently thin layers; and the minimum number needed to simulate a functionally graded material is numerically determined. This modeling approach is applied to simulate the fretting contact involving multilayered materials and functionally graded coatings and to unfold the dependence of the tangential load-displacement relationship on the degree of material dissimilarity.