Wear 269 (2010) 435–442 Contents lists available at ScienceDirect Wear journal homepage: www.elsevier.com/locate/wear On the scale dependence of coefficient of friction in unlubricated sliding contacts S. Achanta a,b,∗ , J.-P. Celis a a Dept MTM, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium b Falex Tribology NV, Wingepark 23B, B-3110 Rotselaar, Belgium article info Article history: Received 25 January 2010 Received in revised form 24 April 2010 Accepted 28 April 2010 Available online 15 June 2010 Keywords: Friction Scale effects Amontons’ law Surface roughness Coefficient of friction Tribosystem abstract Friction at different force, length, and time scales is of great interest in tribology. The mechanical, chemical, and physical (atomic) interactions, each operating at their own force and length scale, make friction a highly scale dependent event. This work is an attempt to trace important mechanisms of friction on commonly used engineering materials over a normal force scale ranging from nN up to N, and thereby altering the contact size from nm 2 up to mm 2 . The relevance of existing theories on friction is verified on different engineering surfaces taking into account mechanical (hard/hard, hard/soft), chemical, and physical aspects of the sliding surfaces. The applicability of Amontons’ law is experimentally investigated. For rough surfaces it was found that the existence of a constant coefficient of friction over a wide force and length scales is only a special case. For a hard/hard tribosystem (like DLC/Si 3 N 4 ), a linear dependence of friction on normal force was observed, whereas a non-linear relationship was more evident on hydrophilic surfaces and hard/soft couples. Irrespective of the material system considered, the dependence of friction on normal force can be altered by modifying the surface roughness or texture of the material couple. In all, changes in the force and length scales bring about significant changes in the governing mechanisms of friction. The experimental findings were in good agreement with recent elasto-plastic and fractal contact mechanical theories on friction. © 2010 Elsevier B.V. All rights reserved. 1. Introduction A good understanding of tribological processes at different force and length scales is essential for improving efficiency in many applications. There is a gamut of engineering materials like metals, ceramics, polymers, and composite materials, used in applications like automotive parts, machinery components, and microelectron- ics where friction and wear challenge both efficiency and reliability. Friction is being investigated for centuries and Coulomb-Amontons’ law stating that friction force = ·applied force, is a well known empirical expression and the slope , known as the ‘coefficient of friction’, is commonly used as a measure of friction between two contacting surfaces undergoing a relative motion [1]. Over the last few decades, theoretical, experimental, and computational inves- tigations were done to gather an understanding of friction, and specifically on the wide acceptability of Amontons’ law [2–7]. The classic definition of friction force is shear strength times the true contact area between the surfaces [2]. Tabor and Bowden observed a linear dependence between the applied normal force and the true contact area [2] for plastic load conditions through ∗ Corresponding author at: Falex Tribology NV, Wingepark 23B, B-3110 Rotselaar, Belgium. Tel.: +32 16405128. E-mail address: sachanta@falexint.com (S. Achanta). electrical conductivity measurements. The linearity between the applied load and true contact area was also validated for rough elastic contacts with a normal distribution of asperities [3]. On the contrary, at nanoscale a non-linear dependence of friction on the applied normal force was reported by Carpick and Salmeron [8] who tested a platinum tip sliding against mica during LFM measure- ments, and by Ruths et al. [9] who tested silicon and gold surfaces. In other studies, it was experimentally shown that the linear or non- linear dependence of friction on normal force is largely linked to the chemical nature of the sliding solids [6,10]. Berman and Drum- mond [10] reported on the validity of Amontons’ law in the case of two non-adherent atomically smooth mica surfaces. Ruths [11] obtained a similar coefficient of friction on non-adherent mono- layer coated surfaces at nano- and macroscale irrespective of force and length scales with more than 6 orders of magnitude difference in contact radii, contact pressure, and loads. Friction arises from the shear strength,, between the contacts. The shear strength, between two adhering junctions varies linearly proportional with the applied contact pressure, P, as  =  0 + ˇP, with  0 the inherent shear strength, and ˇ a constant related to the material couple [2]. This relationship was proven to be valid for material systems like MoS 2 tested against different counter- bodies, and mica surfaces sliding against each other under elastic contact conditions [12]. If the surfaces are chemically inert then, the inherent shear strength,  0 , is small (P still being large), and the 0043-1648/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.wear.2010.04.029