A receding contact plane problem between a functionally graded layer and a homogeneous substrate

Abstract

In this paper, we consider the plane problem of a frictionless receding contact between an elastic functionally graded layer and a homogeneous half-space, when the two bodies are pressed together. The graded layer is modeled as a nonhomogeneous medium with an isotropic stress-strain law and over a certain segment of its top surface is subjected to normal tractions while the rest of this surface is free of tractions. Since the contact between the two bodies is assumed to be frictionless, then only compressive normal tractions can be transmitted in the contact area. Using integral transforms, the plane elasticity equations are converted analytically into a singular integral equation in which the unknowns are the contact pressure and the receding contact half-length. The global equilibrium condition of the layer is supplemented to solve the problem. The singular integral equation is solved numerically using Chebychev polynomials and an iterative scheme is employed to obtain the correct receding contact half-length that satisfies the global equilibrium condition. The main objective of the paper is to study the effect of the material nonhomogeneity parameter and the thickness of the graded layer on the contact pressure and on the length of the receding contact.

Thermoelastic instability of functionally graded materials in frictionless contact

“…They can reduce the magnitude of residual and thermal stresses, mitigate stress concentration and increase fracture toughness [1]. In the past few years, many experimental and numerical results have shown that controlling a material property gradient in FGMs could lead to a significant improvement in the resistance to the contact deformation and damage [2][3][4][5][6][7][8][9][10][11][12]. This potential application motivates the study of the contact mechanics of FGMs.…”

Numerical and Experimental Analysis of a Frictionless Receding Contact between Cylindrical Indenter, Layer and Substrate

“…The case of anisotropy was investigated in papers [15]- [17], with particular reference to the results in [16] and [17], where the layer was modelled as a functionally graded material (FGM). Ahn and Barber investigated the case of frictional contact [18] under cyclic loading, but they used a uniformly distributed pressure of constant width.…”

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

“…Dag and Erdogan [13], Choi and Paulino [14] tackled the contact problem between a sliding rigid punch and a graded substrate with a surface/interface crack. Receding contact between a functionally graded coating and a homogeneous substrate as well as the partial slip contact problem was investigated by El-Borgi et al [15,16]. Wang et al analyzed systematically the plane [17], axisymmetric [18] contact problems of FGMs with a linear multilayered model.…”