Sliding frictional contact between a rigid punch and a laterally graded elastic medium

Abstract

a b s t r a c tAnalytical and computational methods are developed for contact mechanics analysis of functionally graded materials (FGMs) that possess elastic gradation in the lateral direction. In the analytical formulation, the problem of a laterally graded half-plane in sliding frictional contact with a rigid punch of an arbitrary profile is considered. The governing partial differential equations and the boundary conditions of the problem are satisfied through the use of Fourier transformation. The problem is then reduced to a singular integral equation of the second kind which is solved numerically by using an expansion-collocation technique. Computational studies of the sliding contact problems of laterally graded materials are conducted by means of the finite element method. In the finite element analyses, the laterally graded half-plane is discretized by quadratic finite elements for which the material parameters are specified at the centroids. Flat and triangular punch profiles are considered in the parametric analyses. The comparisons of the results generated by the analytical technique to those computed by the finite element method demonstrate the high level of accuracy attained by both methods. The presented numerical results illustrate the influences of the lateral nonhomogeneity and the coefficient of friction on the contact stresses.

Frictional contact of a rigid punch on an arbitrarily oriented gradient half-plane

“…Solutions to the contact model of a rigid punch on a laterally graded half-plane can be found based on the present model. Taking the orientation angle θ = π 2 and the same material parameters as those in Dag et al [30] (note that a opposite coordinate has been chosen in the present paper) yields excellent agreement as shown in Fig. 3.…”

“…In all the above-mentioned studies, graded properties of materials are assumed to vary along the thickness direction, which is perpendicular to the contact interface; few works consider FGMs with gradient in lateral directions [30]. However, materials with gradient properties in an arbitrarily oriented direction have been intentionally or unintentionally used, for example sands, soils and rocks [1].…”

Performance Analysis of Functionally Graded Coatings in Contact with Cylindrical Rollers

“…FEM modeling of sliding contact on laterally graded substrates is investigated with exact verification by Dag et al [27] and continued by Adibnazari et al [28,29] in microand macroscales for frictional sliding. The mathematical modeling of rolling contact problems leads to a system of two coupled Cauchy singular integral equations were done recent years by Guler et al [3,30,31].…”

Contact behaviors of a rigid punch and a homogeneous half-space coated with a graded layer

“…With the evolution of graded materials being extended to a coating layer with finite thickness, notable contributions have been made by Erdogan and his co-workers [3,8,9,[25][26][27]. Guler and Erdogan [9] proposed a model that the shear modulus of the coating varies with depth according to an exponential law μ(y) = μ 2 e δy , (0 ≤ y ≤ h, δ = log(μ 1 /μ 2 )/ h), where μ(y), μ 2 are the shear modulus of the coating and substrate, respectively, δ is a constant characterizing the material inhomogeneity, and h denotes the thickness of the coating.…”