Comprehensive model for scale effects in friction due to adhesion and two- and three-body deformation (plowing)
Introduction
Micro- and nanoscale measurements of tribological properties, which became possible due to the development of the surface force apparatus (SFA), atomic force microscope (AFM), and friction force microscope (FFM) demonstrate scale dependence of adhesion, friction, and wear as well as mechanical properties including hardness [1], [2], [3], [4]. Advances of micro/nanoelectromechanical systems (MEMS/NEMS) technology in the past decade make understanding of scale effects in adhesion, friction, and wear especially important, since surface to volume ratio grows with miniaturization and surface phenomena dominate.
Bhushan and Kulkarni [5] measured friction of Si3N4 tip versus Si, SiO2, and natural diamond using an AFM, Fig. 1. They reported that for low loads the coefficient of friction is independent of load and increases with increasing load after a certain load. It is noted that the critical value of loads for Si and SiO2 corresponds to stresses equal to their hardness values, which suggests that transition to plasticity plays a role in this effect. The friction values at higher loads for Si and SiO2 approach to that of macroscale values. The data in Table 1 for a Si3N4 tip versus HOPG graphite, natural diamond, and Si(1 0 0), indicate that the coefficient of nanoscale friction is smaller than that at the macroscale [2], [3], [6]. As a further evidence of scale dependence, Table 2 shows the adhesive force and coefficient of friction measured for Si(1 0 0), DLC, Z-DOL, and HDT on micro- and macroscales [7], [8]. It is clearly observed that friction values are scale-dependent. The values on the nanoscale are about an order of magnitude lower than those on the microscale.
There can be the following four and possibly more differences in the operating conditions responsible for the differences in the friction value on the nanoscale to micro/macroscale. First, the contact stresses at AFM conditions, in spite of small tip radii, generally do not exceed the sample hardness that minimizes plastic deformation. Average contact stresses in macrocontacts are generally lower than that in AFM contacts, however, a large number of asperities come into contact and some nanoscale and tall asperities go through some plastic deformation. Second, when measured for the small contact areas and very low loads used in nanoscale studies, indentation hardness is higher than at the macroscale [1], [9], [10]. Lack of plastic deformation and improved mechanical properties reduce the degree of wear and friction. Third, the small apparent area of contact reduces the number of particles trapped at the interface, and thus minimizes the third-body plowing contribution to the friction force [1], [3]. As a fourth and final difference, it has been reported by Bhushan and Sundararajan [11] (also see [3]) that coefficient of friction increases due to an increase in meniscus contribution with an increase in the AFM tip radius. AFM data are taken with a sharp tip, whereas asperities coming in contact in macroscale tests range from nanoasperities to much larger asperities which may be responsible for larger values of friction force on macroscale.
When two bodies come into contact, the contact takes place only on high asperities or summits, and the real area of contact is a small fraction of the apparent area of contact (Fig. 2). During sliding, friction is contributed by adhesion and deformation (plowing) at asperity summits in contact. However, as a result of plowing, wear debris of various sizes are generated, and they, along with contaminant particles, constitute a so-called “third body”. In the three-body model, the contact takes place on high asperities and particles. Number of particles participating in the contact depends on statistical distribution of particles size and on probability for a particle of given size to be trapped at the interface between the bodies. A quantitative theory of scale effects should consider these contributions, which involves treatment of the strain-gradient plasticity, dislocation-assisted sliding, surface roughness, and contamination of the interface by particles. However, conventional theories of contact and friction lack characteristic length parameters, which would be responsible for scale effects.
Scale effect on adhesional friction has recently been studied by Hurtado and Kim [12], Bhushan and Nosonovsky [13] and Adams et al. [14]. Hurtado and Kim considered dislocation-assisted friction mechanism, which involves numerous parameters, and they did not propose a simple scaling rule. Adams et al. further extended their model for multiple-asperity elastic contact. Bhushan and Nosonovsky developed a model for adhesional friction based on strain-gradient plasticity and dislocation-assisted sliding. The present paper considers scale effect on two- and three-body deformation and develops a comprehensive model. Various statistical size distributions of wear and contamination particles are presented and discussed in Section 2 of the paper. A scale-dependent model of friction, which involves adhesion, and two- and three-body deformation, is presented in Section 3. Results are discussed in Section 4.
Section snippets
Statistical models
Particle size analysis is an important field for different areas of engineering, environmental, and biomedical studies. In general, size distribution of particles depends on how the particles were formed and sorted. Several statistical distributions, which govern distribution of random variables including particle size, have been suggested (Fig. 3) [15], [16], [17], [18], [19]. Statistical distributions commonly used are either the probability density (or frequency) function (pdf), p(z), or
Friction model
According to the adhesion and deformation model of friction [3], the coefficient of dry friction μ can be presented as a sum of adhesion component μa and deformation (plowing) component μd. The later, in the presence of particles, is a sum of asperity summits deformation component μds and particles deformation component μdp, so that the total coefficient of friction iswhere W is the normal load, F is the friction force, Ar, Ads, Adp are the real
Modeling results
The scale dependence of adhesional friction in single-asperity contact is presented in Fig. 6(a). In the case of single-asperity elastic contact, the coefficient of friction increases with decreasing scale (contact diameter), because of an increase in the adhesion strength, according to Eq. (21). In the case of single-asperity plastic contact, the coefficient of friction can increase or decrease with decreasing scale, because of an increased hardness or increase in adhesional strength. The
Conclusions
A comprehensive model, which explains scale effects on friction, has been presented. During sliding, adhesion and deformation contribute to the friction force. The deformation contribution, in turn, is considered as a sum of the two-body (deformation of summits) and three-body (particles) components. Each of these three components of the friction force depends on the relevant real area of contact and relevant shear strength during sliding. The relevant scaling length is the nominal contact
Acknowledgements
The project was supported as part of the Nanotechnology Initiative of the National Institute of Standards and Technology, Materials Science and Engineering Laboratory in conjunction with Nanotribology Research Program (Contract No. NANB1D0071).
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2022, Journal of Materials Processing TechnologyCitation Excerpt :They reported that the coefficient of friction between sliding surfaces is due to the various combined effects of an asperity deformation component, a component from plowing by wear particles and hard surface asperities and a component from adhesion between the flat surfaces. Bhushan and Nosonovsky (2004) considered scale (size) effects in dry friction from macro to nano scale. They considered strain-gradient plasticity, dislocation-assisted sliding, surface roughness, and contamination of the interface by particles as scale effects.