On the tractive rolling nanocontact of an exponentially graded coating-substrate structure

Abstract

This paper studies the tractive rolling nanocontact occurring between an exponentially graded coating-substrate structure and a circular rigid indenter. Employing the framework of Steigmann–Ogden surface elasticity, it models the surface effects inherent in the nanocontact of graded coatings. The contact area is assumed to comprise a central stick zone bounded by two distinct slip zones. Central to the investigation is the utilization of the nonclassical Flamant solution, which serves as the foundational framework for deriving integral equations governing the continuity of both vertical and tangential displacement gradients. Utilizing Gauss–Chebyshev quadratures, the paper discretizes and collocates these integral equations, along with the force equilibrium conditions and shear traction smooth condition at the leading side stick/slip transition point. An iterative algorithm is then developed to tackle the resultant algebraic system, particularly concerning the discretized contact pressure and friction traction. The paper rigorously validates its proposed solution method and numerical algorithm against existing literature results, showcasing their accuracy and reliability. Moreover, it conducts extensive parametric studies to unravel the effects of various parameters, such as surface material properties, coefficient of friction, inhomogeneity index, and thickness of the exponentially graded coating. These analyses uncover the significant role of surface effects in shaping contact pressure, frictional traction, stresses, subsidence distributions, and stick–slip zones. Notably, the inclusion of surface effects is found to reduce maximum stress and subsidence while inducing a shift of the stick region towards the rolling direction. The parametric exploration of graded coating properties also offers insights into tailoring nanocontact responses for gradient nanostructures.