On the adhesive nanocontact of a graded coating

Abstract

This paper analyzes the adhesive nanocontact properties between a rigid cylinder and an exponentially graded coating-substrate structure. While adhesion between the indenter and the graded coating is accommodated by Johnson–Kendall–Roberts adhesive model, surface effects are addressed by the full version of Steigmann–Ogden surface mechanical theory. In the presence of surface effects alone, the fundamental Flamant solution of the graded coating-substrate structure is determined first, with the aid of Fourier integral transforms. The displacement boundary condition under the rigid cylinder and the static equilibrium equation lead to dual Fredholm integral equations of the first kind. The adhesion is subsequently introduced in terms of the principle of minimum potential energy, by which both the adhesive nanocontact length and pressure are uniquely determined. In order to clarify the effects of adhesion and surface elasticity, parametric studies are carried out with respect to adhesive energy density, surface material constants, shear modulus gradation of the coating and indenter size. Surface effects tend to reduce contact length, maximum contact pressure and subsidence displacement. On the other hand, adhesion increases these three properties. Nonetheless, both effects result in higher pull-off forces. In general, the relation between adhesion and surface elasticity can be qualified as competitive. The current study systematically reveals the feature of adhesive nanocontact of a graded coating-substrate system in the presence of both adhesion and surface effects. It helps the community to extend adhesive nanocontact mechanics from homogeneous to graded materials and structures.