Contact mechanics vs Amonton’s law in friction – experimental and computational study

Xin He,1 Zhong Liu,2 Lei Chen,3 Q. Jane Wang,2,3 and Seong H. Kim1,3

1. Department of Chemical Engineering and Materials Research Institute, Pennsylvania State University, University Park, PA, USA

2. Department of Mechanical Engineering, Northwestern University, Evanston, IL, USA

3. Tribology Research Institute, Southwest Jiaotong University, Chengdu, Sichuan Province, China

Abstract
This presentation will discuss what governs the interfacial friction in the absence of wear. In the nanoscale, various contact mechanics models have been successfully used to describe the friction responses in terms of contact areas with a proportionality constant term called shear strength. In these contact mechanics models, friction force typically varies in proportion to the 2/3 power of the total load. However, in the macroscopic scale, friction force is observed to be linearly proportional to the applied load; this is called Amonton’s law. If we put the Hertzian contact mechanics equation the Amonton’s law equal, then the shear strength of the macroscopic contact would vary in proportion to the 1/3 power of the applied load. What does it physically mean? Is it simply because of changes in real contact area between non-ideally-flat surfaces? Or due to some other physical factors? In order to address this question, we conducted careful experimental studies using the surfaces with certain degrees of roughness and measured friction responses in the vapor phase lubrication condition which can prevent wear of the surfaces. The absence of wear (material removal) allows the experimental data to be compared with computational calculation results. The comparison of experimental and computational results provide deeper insights that could not be obtained otherwise.