Contact analysis of elastic-plastic fractal surfaces

Abstract

Rough surfaces are characterized by fractal geometry using a modified two-variable Weierstrass–Mandelbrot function. The developed algorithm yields three-dimensional fractal surface topographies representative of engineering rough surfaces. This surface model is incorporated into an elastic-plastic contact mechanics analysis of two approaching rough surfaces. Closed form solutions for the elastic and plastic components of the total normal force and real contact area are derived in terms of fractal parameters, material properties, and mean surface separation distance. The effects of surface topography parameters and material properties on the total deformation force are investigated by comparing results from two- and three-dimensional contact analyses and elastic and elastic-perfectly plastic material behaviors. For normal contact of elastic-perfectly plastic silica surfaces and range of surface interference examined, the interfacial force is predominantly elastic and the real contact area is approximately one percent of the apparent contact area or less, depending on the mean interfacial distance. The analysis can be easily modified to account for anisotropic fractal surfaces and different material behaviors.

Cryogenic Performance of RF MEMS Switch Contacts

“…An accurate representation of the surface roughness is needed to generate meaningful predictions for contact area and resistance. A multiscale 3-D surface topography was generated for the switch contacts using a Weierstrass-Mandelbrot function paired with the fractal dimension and fractal roughness measurements from an atomic force microscope [14]- [16]. Modeling of the contact surfaces, when left in the closed position for extended periods of time, predicted the true contact area to reach a maximum of 7% of the total possible contact area [17].…”

Effects of surface structure deformation on static friction at fractal interfaces

“…These models and associated descriptors of roughness are inadequate for the interpretation of interfacial resistance to shear and indeed, under divergent conditions, increasing contact roughness may result in either higher or lower values of static friction (Persson, 2006(Persson, , 2007. Much of the complexity of surfaces arises from their fractal structures, with self-similar features present at ever-finer scales (Sammis & Biegel, 1989;Majumdar & Tien, 1990;Yan & Komvopoulos, 1998). Considering the fractal dimension of surfaces is of great importance in the simulation of granular materials (as shown in Fig.…”

Static friction between rigid fractal surfaces

“…In contrast, the WM surfaces are statistically self-affine, exhibiting different homothetic ratios in different directions with statistical variations. The surface simulation approach employed here yields structures with a highest-level wavelength to account for stochastic processes [31]. Our choice is justified by previous fractal analyses that have been performed on real surfaces such as in magnetic tapes, thin-film rigid disks, steel disks, plastic disks, and diamond films [54].…”

“…Following the Ausloos-Berman variants of the WM function, a realistic surface profile with stochastic highest-level features is generated by means of a formula suggested in previous papers [31,58,59],…”

“…Following these two proportionalities, the ubiquitous friction-load linearity of Amonton's law is observed. The original idea of Archard was later extended by several authors (Yang and Komvopoulus [31], Ciavarella et al [32], and Gao and Bower [33]), who introduced fractal models for the statistical description of the self-affinity of roughness. These models focused on the fractal properties of the contact areas and the number of contact spots, while the connection between surface roughness and actual friction has been explored only recently [12].…”