The influence of the statistical properties of self-affine surfaces in elastic contacts: A numerical investigation

Contact between representative rough surfaces

“…The rise in κ with decreasing λ l can be interpreted in terms of Persson theory [23,24]: reducing λ l is equivalent to decreasing magnification which rises κ. Note that our results for κ are not confined between the asymptotic limits of the BGT [5] κ BGT = √ 2π and Persson theories κ P = 8/π [23], as was generally observed by other authors [6,7,16, 10].…”

“…3, b): a higher H results in a smaller κ. This dependence of the results on the Hurst exponent corresponds to all up to date numerical investigations of the κ constant [6,7,16,10]. However, we argue that these results are strongly affected by non-representativity and an excessive roughness of exploited surfaces.…”

“…On the other hand, to the best of our knowledge, there are no consistent study on the influence of long cutoff wavelength λ l on the response of rough surfaces. Despite remarks made in [15] on the importance of λ l for mechanics of rough contact, in almost all investigations of the real-contact-area evolution [6,7,10,16] λ l was limited by the size of the specimen λ l = L. In this article we show that λ l plays a crucial role in numerically precise theory of rough contact, because it controls the representativity of the simulated system.…”

“…As in the latter models, the evolution of the contact area does not depend on the Hurst exponent. Numerical studies [6,7,10,16] demonstrated an approximately linear evolution of the contact area with load. But in contrast to the analytical models, κ was shown to depend on the Hurst exponent and to be confined between the asymptotic limits of the BGT [5] and Persson [23,24] theories.…”

Static friction between rigid fractal surfaces

“…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]. The fractal description we adopt here has been used in previous studies of friction where friction was related to the shear stress on the real contact area, with simplifications such as rough to flat contact or rigid to elastic-elastic or elastic-plastic contact [55][56][57]. Here we consider the rough to rough contact of simulated natural surfaces and neglect asperity deformation.…”