Understanding adhesive sliding nanocontact mechanics in an exponentially graded coating–substrate structure

The objective of this study is to investigate the frictionally adhesive nanocontact characteristics between a sliding rigid cylinder and an exponentially graded coating–substrate structure. Adhesive forces are modeled using the Maugis–Dugdale adhesive theory, while the Steigmann–Ogden surface mechanical theory describes the surface effects of the graded coating. Within the contact region, normal and tangential tractions adhere to the extended Amontons’ friction law. The governing equations and boundary conditions of the nanocontact problem are reformulated into Fredholm integral equations, which are solved numerically using Gauss–Jacobi quadratures and a self-designed iterative algorithm. Validation against existing literature results demonstrates the accuracy and reliability of the proposed solution method and numerical algorithm. Extensive parametric studies are conducted to investigate the effects of various parameters, including surface material properties, coefficient of friction, Tabor’s parameter, inhomogeneity index of the exponentially graded coating, and external loads. Results reveal that sliding friction significantly influences adhesive nanocontact, affecting nanocontact boundaries, contact traction distribution, and adhesive region boundaries. Additionally, surface effects play a crucial role, leading to smaller nanocontact length and maximum pressure but larger adhesive zone. Furthermore, the interplay between sliding friction, surface effects, and adhesion is underscored, emphasizing the importance of considering these factors in the analysis of sliding nanocontact problems involving graded materials. Ultimately, this work provides a comprehensive solution framework for addressing such complex nanocontact scenarios, offering insights valuable to the field of materials science and engineering.