Modelling adhesive contact problems involving a layered elastic solid and cylindrical indenter using Lennard Jones potential

• We present an iterative algorithm that solves for the displacement and sub-surface stresses induced within a layered elastic solid adhering to a rigid cylindrical indenter under lightly loaded conditions.
• We use the Lennard–Jones potential to model the adhesive force acting between the indenter and solid whilst the effects of surface adhesion are characterised using Tabor’s parameter.
• The shear modulus and thickness of the coating have a significant effect on material behaviour with harder coatings experiencing significantly larger tensile stresses but smaller surface displacement than softer coatings.

This paper presents an iterative algorithm that solves for the displacement and sub-surface stresses induced within a layered elastic solid adhering to a rigid cylindrical indenter under lightly loaded conditions. The solid is assumed to comprise a functionally graded coating of finite thickness bonded to a homogeneous substrate of infinite extent and is assumed to be in a state of plane strain which allows a two-dimensional analysis to be performed. The Lennard–Jones potential is used to model the adhesive force acting between the indenter and solid whilst the effects of surface adhesion are characterised using Tabor’s parameter.A selection of numerical results for the adhesive contact problem are presented which indicate that the maximum pressure and induced sub-surface stresses increase dramatically as Tabor’s parameter increases. It is also found that the shear modulus and thickness of the coating have a significant effect on material behaviour with harder coatings experiencing significantly larger tensile stresses but smaller surface displacement than softer coatings. The present investigation allows us to deduce that at smaller scales, surface adhesion can be instrumental in causing wear or potential material failure if coatings are improperly designed.