Amontons

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. 

Although friction between objects is a matter of everyday experience, it is curious that Amontons law, although of fairly good general validity, seems... 

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. 

This is Amontons law as stated in the opening paragraphs of this chapter. 

An interesting and very practical application of Amontons law occurs in the calculation of the minimum speed of a vehicle from the length of its skid marks. 

If p is taken to be a constant during a skid, application of Amontons law leads to a very simple relationship between the initial velocity of the vehicle and the length of the skid mark. The initial kinetic energy is mv fl, and this is to be entirely dissipated by the braking action, which amounts to a force F applied over the skid distance d. By Amontons law. 

Thus if Amontons law is obeyed, the initial velocity is determined entirely by the coefficient of friction and the length of the skid marks. The mass of the vehicle is not involved, neither is the size or width of the tire treads, nor how hard the brakes were applied, so long as the application is sufficient to maintain skidding. 

Substances in this category include Krypton, sodium chloride, and diamond, as examples, and it is not surprising that differences in detail as to frictional behavior do occur. The softer solids tend to obey Amontons law with /i values in the normal range of 0.5-1.0, provided they are not too near their melting points. Ionic crystals, such as sodium chloride, tend to show irreversible surface damage, in the form of cracks, owing to their brittleness, but still tend to obey Amontons law. This suggests that the area of contact is mainly determined by plastic flow rather than by elastic deformation. 

TWo limiting conditions exist where lubrication is used. In the first case, the oil film is thick enough so that the surface regions are essentially independent of each other, and the coefficient of friction depends on the hydrodynamic properties, especially the viscosity, of the oil. Amontons law is not involved in this situation, nor is the specific nature of the solid surfaces. 

Carpick et al [M] used AFM, with a Pt-coated tip on a mica substrate in ultraliigh vacuum, to show that if the defonnation of the substrate and the tip-substrate adhesion are taken into account (the so-called JKR model [175] of elastic adliesive contact), then the frictional force is indeed proportional to the contact area between tip and sample. Flowever, under these smgle-asperity conditions, Amontons law does not hold, since the statistical effect of more asperities coming into play no longer occurs, and the contact area is not simply proportional to the applied load. 

The often-cited Amontons law [101. 102] describes friction in tenns of a friction coefiBcient, which is, a priori, a material constant, independent of contact area or dynamic parameters, such as sliding velocity, temperature or load. We know today that all of these parameters can have a significant influence on the magnitude of the measured friction force, especially in thin-film and boundary-lubricated systems. 

Berman A, Drummond C and Israelaohvili J N 1998 Amontons law at the moleoular level Tribal. Lett. 4 95-101... 

Amontons G 1699 De la resistenoe oause dans les maohines Memdres de I AcademIe Royale A 275-82... 

Combining the two previous relations for contact area and friction force gives Amonton s law ... 

Scientific studies of friction can be traced back to several hundreds years ago when the pioneers, Leonardo da Vinci (1452-1519), Amontons (1699), and Coulomb (1785), established the law of friction that "friction is proportional to the normal load and independent of the nominal area of contact, which are still being taught today in schools. Since then, scientists and engineers have been trying to answer two fundamental questions where friction comes from and why it exhibits such a behavior as described above. Impressive progress has been made but the mystery of friction has not been resolved yet. In an attempt to interpret the origin of... 

The model proposed by Bowden and Tabor has been regarded as the most successful one for presenting a simple and logical theory capable of explaining the Amontons friction law. However, suspicions concerning the two fundamental assumptions in the model were gradually aroused over past years. Friction has been attributed, in Bowden and Tabor s model, to the adhesion between asperities in contact and torn-off of the adhesive junctions when the shear stress exceeds a critical value. This implies that plastic flow and surface destruction may occur at the moment of slip, and that friction is dominated by the shear strength of the adhesive conjunctions, which is material dependent. 

More recently, arguments for the origin of Amontons s law have arisen that are based on experimental studies demonstrating that the shear stress as varies with the local pressure P according to Eq. [4]... 

Numerous simulations of boundary lubricants have shown that cto is indeed small, even at pressures close to the yield strengths of solids.14,21 Thus, it seems that Amontons s law should hold in a wide range of cases. However, exceptions are observed when adhesive interactions are strong, which leads to large values of cto. 

Microscopic Theory of Amontons s Laws for Static Friction. 

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