On the competition between adhesive and surface effects in the nanocontact properties of an exponentially graded coating

This paper aims at investigating the adhesive nanocontact properties between a rigid cylindrical punch and an exponentially graded coating perfectly bonded with a homogeneous half-plane substrate. The interface of nanocontact is modeled with the Maugis–Dugdale adhesive contact model and the Steigmann–Ogden surface mechanical theory. Under plane strain assumption, governing equations and boundary conditions of the nanocontact problem are converted into triple integral equations. They are numerically solved for the determination of nanocontact length, pressure distribution and the application range of the adhesive zone, by the use of Gauss–Chebyshev quadrature, Gauss–Legendre quadrature and a self-designed iterative algorithm. The method of solution and numerical algorithm are first validated against literature results. Extensive parametric studies are then conducted with respect to the adhesive energy density, Tabor’s parameter, surface material constants and inhomogeneity index of the exponentially graded coating. Based on these results, the relationship between adhesive and surface effects can be identified as competitive. Both are of great importance in the determination of nanocontact behaviors of graded materials and structures. In addition, the Maugis–Dugdale adhesive contact model is found to converge to the Johnson–Kendall–Roberts model under large Tabor’s parameters. Large indenters, high adhesive energy densities, soft substrates and small adhesive cut-off distances are all helpful to the transition. The current work provides a generalized solution framework to the nanocontact problems of graded materials and structures in the simultaneous presence of adhesive and surface effects.