An adhesion model for elastic-plastic fractal surfaces

Abstract

The strong adherence (stiction) of adjacent surfaces is a major design concern in microelectromechanical system. The present research concerns the elastic-plastic adhesion of a rough surface contacting with a rigid flat. Rough surface is characterized by fractal geometry using a two-variable Weierstrass-Mandelbrot function [The Fractal Geometry of Nature (Freeman, New York, 1982)]. The microcontact model of single asperity is established in terms of fractal parameters, and the plastic adhesion model is also developed with the Dugdale approximation to consider the adhesive interaction within and outside the contact area. Then according to the plastic flow criterion, the Maguis-Dugdale transition theory [Adhesion of Adhesion and Rapture of Elastic Solids (Springer-Verlag, New York, 2005)] and the plastic adhesion model are used to solve the elastic-plastic adhesive interaction for the two approaching surfaces by incorporating the fractal surface model. Simulations of the adherence force versus the approaching distance of surfaces are performed. The necessity of considering the plastic deformation in microsized interface adhesion is also validated by comparing the result of the presented model with that of the Morrow model [J. Tribol 127, 206 (2005)]. The influence of fractal parameters on adherence force shows that controlling the surface topography is a readily means to control the adherence force for the elastic-plastic adhesion of rough surfaces, which is due to the intermolecular adhesive interactions.