“God made the bulk; surfaces were invented by the devil”, a Nobel prize winning physicist Wolfgang Ernst Pauli said. In tribology, as in many other sciences, surface features (asperities, roughness) play an important role. In many cases, the surface roughness dramatically alters the friction, contact area, wear, etc. and the quotation from the famous scientist truly apply. In other cases, surfaces can be regarded as ideally smooth without significant errors.
The real contact area (typically much smaller than the apparent) is responsible for the amount of friction developed in the contact and therefore is of high interest in tribology. The surface roughness significantly affects the behavior of the contact area as a function of load. Hertz theory, established more than a century ago, states that contact area is proportional to the applied load non-linearly: . Numerical simulation results showed, on the other hand, that in presence of the surface roughness, in many cases there is a linear dependence: .
Recently, researchers from Karlsruhe Institute of Technology and Johns Hopkins University performed large scale molecular dynamic simulations to reveal the dependance of the contact area on normal load for a sphere with imposed fractal roughness. They varied the radii of curvature of the sphere from 30nm to 30 and normal load across 10 orders of magnitude.
Based on the results, the researchers distinguished three regions of various functional dependence of the contact area on load. At the loads higher than the critical load (the equation for its calculation was provided in the article), the macroscopic Hertz theory was found to be accurate. The theory holds, since the deformation of the surfaces is much larger than the roughness scale and the surface come into full contact. At very low loads, the contact is fully determined by the first asperity in contact. In this case, the Hertz theory is valid again, if applied locally on the asperity level. Transition from this region to the intermediate (multi-asperity) can be also estimated with the same equation with only changing the macroscopic radius to the asperity radius. In the intermediate region, the linear relation holds due to multi-asperity contact. Besides, the researchers included the influence of adhesion, which becomes important at nanoscale and adjusted the corresponding scaling equations.
A good agreement of the proposed equations with molecular dynamic simulations was observed. These simple equations can be used to distinguish the contact regimes to describe experimental results (as Atomic Force Microscope data) and employ corresponding contact models.
The details of the research can be found in the original article: Lars Pastewka, Mark O. Robbins, ontact area of rough spheres: Large scale simulations and simple scaling laws; Appl. Phys. Lett. 108, 221601 (2016); http://dx.doi.org/10.1063/1.4950802.
Credit for image: Edited with permissions from Appl. Phys. Lett. 108, 221601 (2016); http://dx.doi.org/10.1063/1.4950802.
Founder of TriboNet, Editor, PhD (Tribology), Tribology Scientist at ASML, The Netherlands. Expertise in lubrication, friction, wear and contact mechanics with emphasis on modeling. Creator of Tribology Simulator.