Molecular probes reveal deviations from Amontons\u2019 law in multi-asperity frictional contacts

B Weber,T Suhina,T Junge,A M Brouwer,D Bonn,L Pastewka

doi:10.1038/s41467-018-02981-y

Abstract

Amontons’ law defines the friction coefficient as the ratio between friction force and normal force, and assumes that both these forces depend linearly on the real contact area between the two sliding surfaces. However, experimental testing of frictional contact models has proven difficult, because few in situ experiments are able to resolve this real contact area. Here, we present a contact detection method with molecular-level sensitivity. We find that while the friction force is proportional to the real contact area, the real contact area does not increase linearly with normal force. Contact simulations show that this is due to both elastic interactions between asperities on the surface and contact plasticity of the asperities. We reproduce the contact area and fine details of the measured contact geometry by including plastic hardening into the simulations. These new insights will pave the way for a quantitative microscopic understanding of contact mechanics and tribology.

Highlights

Amontons’ law defines the friction coefficient as the ratio between friction force and normal force, and assumes that both these forces depend linearly on the real contact area between the two sliding surfaces
Through atomic force microscopy (AFM) and contact simulations, we show that there is not much contact structure below this length scale (Supplementary Figs. 4 and 9)
In summary, the first determination, with molecular resolution perpendicular to the plane, of the real contact area in a frictional contact shows that the static friction is directly proportional to the real contact area

Summary

Introduction

Amontons’ law defines the friction coefficient as the ratio between friction force and normal force, and assumes that both these forces depend linearly on the real contact area between the two sliding surfaces. All frictional theories aim to understand how frictional dissipation emerges from the details of contacts between two sliding surfaces Experimental testing of such contact theories for rough interfaces is crucial, but has proven very challenging. Using pressure-sensitive fluorescent molecules, we visualize the entire area of real contact that defines the roughsphere-on-flat glass interface We directly compare this experimental visualization of the real contact area to rough-on-flat contact simulations in which various deformation mechanisms can be included or left out. Through this comparison we find that neighboring roughness extremities are not deformed independent of each other, but rather transmit strain to one another through the underlying bulk material. We find that the static friction force is proportional to the real contact area resulting in the breakage of Amontons’law

Methods

Results

Conclusion