Sliding Friction

Friction is usually introduced and studied at an early stage during courses on classical mechanics and general physics. Thus one may think that friction is a simple and well understood subject. However, nothing could be more wrong. The two fundamental forces of Nature which manifest themselves on a macroscopic length scale are the electromagnetic and the gravitational forces. On a subatomic level other force fields come into play and contribute to the interaction between the fundamental particles of Nature, namely the quarks and leptons. However, only the electromagnetic forces are of direct relevance to the mechanical and friction properties of solids which is our concern in this book.

Tribology is the science and technology of interacting solid surfaces in relative motion. The word tribology is based upon the Greek word tribos, meaning rubbing. The topics covered by this word are in the main ancient and well-known and include the study of lubricants, lubrication, friction, wear, and bearings. Since surface interactions dictate or control the functioning of practically every device developed by man to enhance the quality of life, tribology has been of central importance for thousands of years, even if this has not always been generally recognized.

Practically all sliding friction devices have an interface where the friction force is generated, a finite sliding mass M, and some elastic properties usually represented by a spring k _s as in Fig. 3.1. The spring does not need to be an external spring but could represent the overall elastic properties of the sliding device. In most sliding friction experiments the free end of the spring moves with a constant velocity v _s , but sometimes it varies with time. The force in the spring as a function of time is the basic quantity registered in most of these experiments. It is important to note that, due to inertia, during acceleration the spring force is not equal to the friction force acting on the block.

Most surfaces of solids are rough, at least on a microscopic scale. Most engineering surfaces are covered by asperities having slopes in the range 5°–10°. Unlubricated metal surfaces encountered in an industrial environment will, in general, be covered by a whole series of surface films, as shown in Fig. 4.1. Working outwards from the metal interior, we first encounter an oxide layer, produced by reaction of oxygen from the air with the metal; this is present on all metals except gold. Next will come an adsorbed layer derived from the atmosphere, the main constitutes of this layer being water and oxygen molecules. Outermost, there will usually be grease or oil films. Note also that the metal just below the oxide layer is in general harder than that in the bulk (it is “work hardened”).

The friction force equals the shear stress integrated over the area ΔA of real contact. Because of surface roughness, the area of real contact is usually much smaller than the apparent area of contact. In this section we discuss the physical processes which determine the area of real contact and present some experimental methods which have been used to estimate ΔA. In most practical applications, the diameter of the contact areas (junctions) are on the order of ~ 10 urn. However, the present drive towards microsystems, e.g., micromotors, has generated a great interest in the nature of nanoscale junctions. The physical processes which determine the formation and behavior of nanoscale junctions are quite different from those of microscale junctions. We consider first microscale junctions and then nanoscale junctions.

A lubricant is used to lower the friction and reduce the wear between two sliding solid bodies. Here we consider only liquid lubricants although some solids, e.g., graphite and molybdenum disulfide, are also used as lubricants. As pointed out before, almost all surfaces are normally covered by a layer of grease, which may have a similar influence on the sliding friction as an added lubricant.

In this chapter we consider the sliding of adsorbate layers on surfaces. This problem is of great interest in its own right but is also directly relevant for several sliding friction problems, as illustrated by the following two examples.

It is very hard experimentally to directly probe the nature of the rapid processes which occur at a sliding interface. But some information can be inferred indirectly by performing sliding friction measurements on well-defined systems, and registering the macroscopic (e.g., center-of-mass) motion of the block as a function of time. For lubricated surfaces, such measurements have been performed during the past few years, using the Surface Forces Apparatus (Chap. 3) [9.1–5]. These studies usually use mica surfaces which can be produced atomically smooth (without a single step) over macroscopic areas. A spring is connected to the mica block and the “free” end of the spring is moved with some velocity v _s , which typically is kept constant but sometimes is allowed to change in time. The force in the spring is registered as a function of time and is the basic quantity measured in most of these friction studies. It is obvious that the time dependence of the spring force (and its dependence on v _s ) contains information about the nature of the processes occurring at the sliding interface, but this information is very indirect.

The study in Chap. 9 assumed that the lateral corrugation of the adsorbate-substrate interaction potential was so weak that the adsorbate layer could fluidize as a result of the shear force stemming from the external force acting on the block. For this case we have argued that the kinetic frictional force at low sliding velocities is likely to involve the formation and fluidization of solid structures. But in many cases the corrugation of the adsorbate-substrate potential energy surface is so strong that no fluidization of the adsorbate layer can occur. This often seems to be the case when fatty acids are used as boundary lubricants: the polar heads of fatty acid molecules bind strongly to specific sites on many metal oxides and the sliding occurs now between the inert hydrocarbon tails as indicated schematically in Fig. 2.5. In Sect. 10.1 we discuss some simple models which illustrate the fundamental origin of the friction force when no fluidization can occur. As will be shown below, if the corrugated substrate potential is large enough compared with the local elasticity, an elastic instability will occur, which will result in a kinetic friction force which remains finite as the sliding velocity v → 0 (we assume zero temperature, so that no thermally activated creep motion occurs). In Sect. 10.2 the elastic coherence length ξ is introduced and calculated for a semi-infinite elastic solid exposed to a random surface stress.

In this section we consider creep and other slow (thermally induced) relaxation processes which occur at low sliding velocity [11.1]. We first argue that the lubrication film at low sliding velocities has a granular structure, with pinned adsorbate domains accompanied by elastic stress domains in the block and substrate. At zero temperature, the stress domains form a “critical” state, with a continuous distribution P(σ) of local surface stresses σ extending to the critical stress σ _a, necessary for fluidization of the pinned adsorbate structure. During sliding adsorbate domains will fluidize and re-freeze. During the time for which an adsorbate domain remains in a fluidized state, the local elastic stresses built up in the elastic bodies during “stick” will be released, partly by emission of elastic wave pulses (sound waves) and partly by shearing the lubrication fluid. The role of temperature-activated processes (relaxation and creep) will be studied and correlated with experimental observations. In particular, the model explains in a natural manner the logarithmic time dependence observed for various relaxation processes; this time dependence follows from the existence of a sharp step-like cut-off at σ = σ _a in the distribution P(σ) of surface stresses.

Consider the sliding of a block on a substrate under boundary lubrication conditions. To the block is connected a spring (force constant k _s ) and the free end of the spring is moving with the velocity v _s . Depending on the parameter values (k _s , v _s ) the motion of the block may be either steady or of stick-slip nature. In this chapter we discuss the nature of the (k _s , v _s ) phase diagram, i.e., the regions in the (k _s , v _s )-plane where the motion is steady and oscillatory are determined and the nature of the transition between the two types of sliding behavior is discussed.

In Chap. 12 we studied sliding dynamics for lubricated surfaces. We have emphasized several times that most “real” surfaces are lubricated, e.g., by a layer of grease, even if no lubrication fluid has been intentionally added to the system. Nevertheless, in some cases the increase of the static friction force with the time of stationary contact, due to the processes discussed in Chap. 12, may be negligible; we will refer to these systems as exhibiting “dry” friction. Dry friction may prevail for many surfaces lubricated by fatty acids; because of the high local pressures which occur in the contact areas between, e.g., two steel surfaces, the relaxation time for interdiffusion and other rearrangement processes may be very long (Sects. 7.2,6) so that a negligible increase in the static friction force may occur during a typical stick-time period, in which case the static friction nearly equals the kinetic friction, as indeed observed in many cases (Table 7.5). But even in the case of “dry” friction, the static friction force may increase with time due to an increase in the area of real contact which occurs in many real systems for the reasons discussed in Chap. 5 and below. For hydrophilic materials, the formation of capillary bridges will also result in an increase of the static friction force with the time of stationary contact; see Sect. 7.5.

In this section we discuss in detail a few sliding systems, some of which are usually not included in books on tribology. The aim is to illustrate the general theoretical concepts and results obtained in the earlier part of this book, and to show how different physical phenomena are governed by similar physical principles. In addition, each of the topics treated below is itself of great intrinsic interest.

The topic of sliding friction has experienced a major burst of activity since 1987, much of which has developed quite independently and spontaneously. It is likely that the next few years will result in a deeper understanding of the fundamentals of sliding friction and also a general realization that many different physical phenomena, which in the past have been studied independently of each other in different disciplines, such as earthquake dynamics and the sliding of flux line systems, are closely related and perhaps should be studied together. Such a unification may not only lead to a cross fertilization of ideas, but also represents one of the goals of theoretical physics.