Effect of Structural Parameters on the Relative Contact Area for Ideal, Anisotropic, and Correlated Random Roughness

Abstract

The relative contact area between an initially flat, adhesion-and frictionless, linearly elastic body and a variety of rough, rigid counterbodies is studied using Green's function molecular dynamics. The indenter's height profiles range from ideal random roughness through roughness with a moderate amount of correlation to periodically repeated, single-asperity indenters having perfect phase coherence. At small reduced pressures, p * ≡ p/(E * ḡ) ≪ 1, sufficiently large systems are consistent with a linear a c = κ p * relation. Here p is the pressure, E * is the contact modulus,ḡ the root-mean-square height gradient, and κ a unitless proportionality coefficient. However, the parameterḡ must be evaluated over the real contact area for the linear relation to hold if the random roughness is correlated or the interfacial dimension reduced. No single unitless structural parameter-including the Nayak parameter-correlates in a significant fashion with κ.

Modeling the surface topography dependence of friction, adhesion, and contact compliance

“…Specifically, for frictionless elastic surfaces, it predicts contact area to obey where is the contact modulus of the solid (when both bodies are deformable, their inverse contact moduli add, as in a series coupling of springs), E is the Young’s modulus, the Poisson’s ratio of the elastic material, and is the (combined) root-mean-square (rms) height gradient of the surfaces. Although the theory was originally derived for ideal random roughness (see Equation 5 ), it makes astonishingly accurate predictions on the relative contact area if is averaged only over the true contact area, 24 even in the limiting case of single-asperity contacts, which are the polar opposite to ideal random roughness.…”

Elastic Contacts of Randomly Rough Indenters with Thin Sheets, Membranes Under Tension, Half Spaces, and Beyond

“…While Persson's theory predicts the deviations from full contact at large p * reasonably well for all studied systems, agreement for a r (p * ) at small p * is less satisfactory: for 0.5 ≤ n ≤ 2 , logarithmic corrections to a linear a r (p * ) = n p * dependence are required, while an entirely different power law is observed for n = 3 . The need for the logarithmic corrections might disappear or at least be strongly suppressed in the thermodynamic limit, in particular for n = 1 [52]. However, the contact is spread out over many small patches for n = 2 , Thus, finite-size corrections to Persson's theory conducted similarly as those for the interfacial stiffness of semi-infinite elastomers [30] would not apply to the contactarea calculation of the n = 2 elastomer.…”

“…The generalization is that the stress variance is evaluated over the true contact rather than over the entire randomly rough surface. This modification is not only successful for said single indenters but also for randomly rough indenters not satisfying the random-phase approximation in contact with a regular semi-infinite, elastic counterface [52]. Thus, assuming a r = erf(p∕ c ) to hold, it needs to be understood how the true-contact-area stress variance 2 c deviates from the full-surface stress variance 2 .…”

Significance of Elastic Coupling for Stresses and Leakage in Frictional Contacts

“…1(a)), assuming steady-state conditions and Amontons' microscopic friction. Although some of the issues raised here have already been addressed in line contacts [22][23][24], load-area and other relations do not generalize from line to areal contacts, neither in simple indenter geometries [25] nor in randomly rough contacts [26,27], so that the effect of roughness on the friction coefficient can differ between the two cases. More importantly, the analysis of how coupling affects leakage cannot be addressed in line contacts, since they automatically seal in the lateral (sliding) direction, while they are open in the transverse direction.…”