Two-dimensional contact problem for a coating-graded layer-substrate structure under a rigid cylindrical punch

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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  • Jie Yang
  • Liao-Liang Ke


Original languageEnglish
Pages (from-to)985-994
Journal / PublicationInternational Journal of Mechanical Sciences
Issue number6
Publication statusPublished - Jun 2008


The two-dimensional frictionless contact problem of a coating structure consisting of a surface coating, a functionally graded layer and a substrate under a rigid cylindrical punch is investigated in this paper. The coating and substrate are homogeneous materials with distinct physical properties, while the intermediate layer is inhomogeneous with its shear modulus changing arbitrarily along the thickness direction. To approximate the through-thickness variation, a piecewise linear multi-layer model is used and the graded layer is divided into a number of sub-layers whose shear modulus is assumed to vary linearly. Poisson's ratio, however, is taken as a constant within the structure for simplicity. By using the transfer matrix method and Fourier integral transform technique, the governing equations are reduced to a Cauchy singular integral equation which is numerically solved to determine the normal contact pressure, contact region, the through-thickness stress fields and longitudinal stress distributions at interfaces. A parametric study is conducted, showing that both normal contact pressure and stress fields in the structure are significantly influenced by the shear modulus ratio and the thickness ratio of the exponentially graded layer but are less sensitive to the gradient index of the graded layer whose shear modulus follows a power law variation. © 2008 Elsevier Ltd. All rights reserved.

Research Area(s)

  • Contact mechanics, Functionally graded materials, Linear multi-layer model, Stress analysis