Apparent area of contact

The coefficient of friction /x between two solids is defined as F/W, where F denotes the frictional force and W is the load or force normal to the surfaces, as illustrated in Fig. XII-1. There is a very simple law concerning the coefficient of friction /x, which is amazingly well obeyed. This law, known as Amontons law, states that /x is independent of the apparent area of contact it means that, as shown in the figure, with the same load W the frictional forces will be the same for a small sliding block as for a laige one. A corollary is that /x is independent of load. Thus if IVi = W2, then Fi = F2. 

The basic law of friction has been known for some time. Amontons was, in fact, preceded by Leonardo da Vinci, whose notebook illustrates with sketches that the coefficient of friction is independent of the apparent area of contact (see Refs. 2 and 3). It is only relatively recently, however, that the probably correct explanation has become generally accepted. 

The force of friction is independent of the apparent area of contact. 

A traditional explanation of solid friction, which is mainly employed in engineering sciences, is based on plastic deformation.12 Typical surfaces are rough on microscopic length scales, as indicated in Figure 3. As a result, intimate mechanical contact between macroscopic solids occurs only at isolated points, typically at a small fraction of the apparent area of contact. 

The apparent area of contact between two surfaces is much larger than the actual area over which they touch, even if the surfaces appear smooth. The frictional force is proportional to the real contact area, so anything that changes the real contact area will change the force measured. 

Bowden and Tabor (7) suggested a physical explanation for the observed laws of friction. They determined that the true area of contact is but a small fraction of the apparent area of contact, because the surfaces of even the most highly polished material show irregularities appreciably larger than atomic dimensions called in the literature asperities, as shown in Fig. 4.3. Thus, with increasing normal load, more asperities come in contact and the average area of contact grows, as shown in Fig. 4.4... 

This discussion assumes uniform pressure distribution over the whole apparent area of contact. In the case of elastic contact between non-conformal surfaces, the contact pressure varies over the apparent contact area in accordance with a Herzian pressure distribution. For an elastic contact between a spherical surface and a flat surface the relationship becomes ... 

Frictional forces do not depend on an apparent area of contact, but rather the true area of contact between the opposing asperities (Fig. 2). 

A third central issue concerns the relationship between friction and the normal force or load L that pushes the two objects together. The macroscopic laws of friction found in textbooks were first published by the French engineer Amontons about 300 years ago [14], albeit the first recorded studies go back even further to the Italian genius da Vinci. Both found that the friction Fj between two solid bodies is (i) independent of the (apparent) area of contact and (ii) proportional to L. These laws can be summarized in the equation... 

When the ball is loaded against a hard, smooth flat surface with sufficient normal stress, it will be deformed, both elastically and plastically, and the apparent area of contact will be A. But though the surface of the ball and the flat may seem macroscopically smooth (e.g. to at least 10 nm), on the microscopic scale only asperities will actually be in contact. Moreover, if the adsorbed film of atmospheric constituents is not displaced from the surface, the area of true contact will be even smaller than that predicted from asperity contact. 

It is an observed fact that a constant rate of volume-wear, unaffected by progressive change in the apparent area of contact during the course of wear, is one of the consistently characteristic types of wear behavior. For Eqn 13-21 to be a variant of Eqn 13-20 requires that the area factor remains constant. One way to realize this is by means of the plastic deformation model of the real contact area of asperities, in which case the expression equivalent to Eqn 13-21 is... 

On a microscopic level no solid surface is smooth, and when one surface is placed on another, the contact between the two occurs only at high spots (asperities) and these take up the load. Bowden and Tabor [43] showed that the real area of contact is much smaller than the apparent area of contact. Usually, the load distribution on each asperity is such that it deforms plastically and adhesion takes place. If the load L is increased, the contact area increases, and for many situations A is proportional to L. This explains why the frictional force is independent of apparent area and proportional to L. 

Due to roughness effects, adherence of metals at moderate temperature and pressure is difficult to analyze. When roughnesses undergo plastic deformation, the true area of contact is proportional to the applied load P, and the adherence force F is often proportional to the load (hence the definition of an adhesion coefficient a = F/P), and independent of the apparent area of contact. These two "Laws of adhesion (41) are similar to Amonton s laws of friction. As shown by Gilbreath (42) the adhesion coefficient is very sensitive to adsorption. More precise experiments by Buckley (43,44) on single crystals in ultrahigh vacuum have shown that the adherence force does not increase linearly with the load, and that the position of the knees depends on the adsorption as if the effectively applied load depended on adsorption. 

Even a surface that appears to be flat on a millimeter scale may in fact be rough with micrometer scale asperities on it. Friction and the resulting energy dissipation are thus due to the interaction between the asperities of the different surfaces when they touch each other. It is the real contact area that affects the friction opposing the action of motion and the real area of contact may be therefore a few orders of magnitude smaller than the apparent area of contact. A brief summary on the development of theoretical models for friction is given by Meyer and co-workers (8). 

Microfriction in many cases is lower than macrofriction (65,74). This phenomenon is suggested to be due to a reduction in real area of contact and the degree of wear arises from increased hardness and modulus of elasticity with micro/nanoscratch. In addition, the small apparent area of contact reduces the number of particles trapped at the interface, and thus minimizes the ploughing contribution to the friction force (73,74). 

The real area of contact (A ) Is related to the apparent area of contact (aJ through the relationship... 

Atomic force microscope observations show that shear faulting occurs within the atomically smooth planes of the mica platelets and that friction is likely to occur under conditions in which the real and apparent area of contact coincide. 

Can the observed behaviour on the macroscopic and microstructural scales be reconciled with what we know about frictional sliding under these conditions To answer this question, we turn to other reported work with mica in which the real and apparent areas of contact coincide. Johnson reports that experiments with an atomic friction microscope (AFM), on mica in which the contact dimension is 2 to 10 nm, indicate a frictional shear stress of 1 GPa. Other measurements performed with a surface force apparatus (SFA), in which the contact dimension is in the order... 

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