Evolution of real contact area under shear and the value of static friction of soft materials
Résumé
The frictional properties of a rough contact interface are controlled by its area of real contact, the dynamical variations of which underlie our modern understanding of the ubiquitous rate-and-state friction law. In particular, the real contact area is proportional to the normal load, slowly increases at rest through aging, and drops at slip inception. Here, through direct measurements on various contacts involving elastomers or human fingertips, we show that the real contact area also decreases under shear, with reductions as large as 30%, starting well before macroscopic sliding. All data are captured by a single reduction law enabling excellent predictions of the static friction force. In elastomers, the area-reduction rate of individual contacts obeys a scaling law valid from micrometer-sized junctions in rough contacts to millimeter-sized smooth sphere/plane contacts. For the class of soft materials used here, our results should motivate first-order improvements of current contact mechanics models and prompt reinterpretation of the rate-and-state parameters. area of real contact | rough contact | elastomer | static friction | rate-and-state friction R ough solids in dry contact touch only at their highest asper-ities, so that real contact consists of a population of individual microjunctions (Fig. 1B), with a total area A R. A R is usually much smaller than the apparent contact area, A A , that one would expect for smooth surfaces. Since the seminal work of Bowden and Tabor (1), it is recognized that the frictional properties of such multicontact interfaces are actually controlled by A R rather than by A A. In particular, direct measurements of A R on transparent interfaces have been developed (2, 3) and repeatedly found proportional to the friction force, both for multicontacts (4-10) and for single contacts between smooth bodies (1, 11, 12), with the proportionality constant being the contact's frictional shear strength, σ. A R is a dynamic quantity with three major causes for variations. First, A R is roughly proportional to the normal load applied to multicontacts (5, 6, 10). This result, which provides an explanation for Amontons-Coulomb's law of friction (friction forces are proportional to the normal force), has been reproduced by many models of weakly adhesive rough contacts under purely normal load (1, 4, 13-16). In the case of independent elastic microjunctions, although each of them grows nonlinearly with normal load, proportionality arises statistically due to random-ness in the surface asperities' heights (13). Second, in static conditions , A R slowly increases, typically logarithmically, with the time spent in contact (5, 17). This phenomenon, so-called geometric aging (18), is interpreted as plastic (5, 19, 20) or viscoelas-tic (21) creep at the microjunctions, depending on the materials in contact, and is different from contact strengthening with time at constant contact area (18, 22), so-called structural aging. Third, at the onset of sliding of the interface, the population of already aged microjunctions gradually slips and is replaced by new, smaller microjunctions. Slip inception is thus accompanied by a drop of A R (5, 17), by up to a few tens of percent. This effect is often considered to be the origin of the difference between the peak (static) and steady sliding (kinematic) friction forces (18). Accounting for these three dependencies together has been a major success in the science of friction because it provides a consistent picture of the physical mechanisms underlying the ubiquitous state-and-rate friction law (5, 18, 20-31), which is obeyed by multicontacts in a variety of materials, from polymer glasses to rocks, through rubber and paper. However, a series of experimental observations reported here and there in the literature over recent decades suggest that the picture may not be fully comprehensive yet. These observations, made on smooth contacts, have repeatedly indicated that the area of apparent contact, A A , depends on the value of the tangential load, Q, applied to the interface. For instance, smooth metallic sphere/plane contacts typically grow as Q increases (1, 2), due to plastic deformations in the vicinity of the contact (1, 32). Conversely, A A decreases when smooth elastomer-based sphere/plane contacts as well as fingertip contacts are increasingly sheared (9, 33-38), presumably due to viscoelastic and/or adhesion effects (33, 36, 38-40). It is therefore tempting to hypothesize that not only smooth but also rough interfaces have a dependence of their contact area on the tangential load, Q. Such a dependence would directly affect the resistance to sliding of a rough contact, the way we use current contact and friction models to predict the static friction force, and the physical meaning of the parameters of the rate-and-state friction law. To test this hypothesis, we carried out experiments to monitor, in multicontacts involving elastomers or human fingertips, the evolution of A R when Q is increased from 0 to macroscopic sliding. Significance We investigate the origin of static friction, the threshold force at which a frictional interface starts to slide. For rough contacts involving rubber or human skin, we show that the real contact area, to which static friction is proportional, significantly decreases under increasing shear, well before the onset of sliding. For those soft materials, our results will impact how we use and interpret current contact mechanics and friction models.
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