The effect of autocorrelation length on the real area of contact and friction behavior of rough surfaces

Autocorrelation length (ACL) is a surface roughness parameter that provides spatial information of surface topography that is not included in amplitude parameters such as root-mean-square roughness. This paper presents a relationship between ACL and the friction behavior of a rough surface. The influence of ACL on the peak distribution of a profile is studied based on Whitehouse and Archard's classical analysis [ Whitehouse and Archard Proc. R. Soc. London, Ser. A 316 , 97 ( 1970 ) ] and their results are extended to compare profiles from different surfaces. The probability density function of peaks and the mean peak height of a profile are given as functions of its ACL. These results are used to estimate the number of contact points when a rough surface comes into contact with a flat surface, and it is shown that the larger the ACL of the rough surface, the less the number of contact points. Based on Hertzian contact mechanics, it is shown that the real area of contact increases with increasing of number of contact points. Since adhesive friction force is proportional to the real area of contact, this suggests that the adhesive friction behavior of a surface will be inversely proportional to its ACL. Results from microscale friction experiments on polished and etched silicon surfaces are presented to verify the analysis.