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Fig.5.1. Contact scheme of rubbing bodies A and B: N - normal load; T - tangential force; F is the friction force.
pre-shift
In accordance with the existence of friction of rest and friction of motion, the force of friction of rest and the force of friction of motion are distinguished, which quantify these processes. The change in the friction force during the transition from rest to the movement of contacting bodies as one body moves relative to another is illustrated in Fig.5.2. When starting a motionless body from a place, the movement is preceded by a stage of preliminary displacement .

Fig.5.2. The change in friction force depending on the amount of displacement x .
Pre-displacement is a relative micro-displacement of two solid bodies ranging from a state of rest to the start of relative motion.
Developed as the microdisplacement increases, the incomplete static friction force F _np increases until the full friction force F _{p is reached} , the excess of which leads to the beginning of the macrodisplacement, i.e. the static friction is abruptly replaced by the friction of motion F _d and the continuous movement of one body relative to the other begins. It has an initially elastic character, i.e. termination of the shear force T (see Fig. 1) leads to a return to the equilibrium position.
The total static friction force developed during microdisplacement for non-lubricated bodies F _p is almost always higher than the motion friction force F _d .
Amonton's laws for sliding friction
When considering the process of sliding friction, as a first approximation, the regularities experimentally established by Amonton (1699) are used, known in the literature as Amonton's laws.
1. The friction force F is proportional to the force N, which compresses the rubbing bodies in the direction normal to the friction surface (The friction surface is the nominal surface of a solid body, along which the interaction of solid bodies occurs during external friction)
F = fN. (5.2)
The proportionality factor f in this equation is called the coefficient of friction. In other words, the coefficient of friction is the ratio of the friction force of two bodies to the normal force pressing these bodies against each other. The coefficient of friction is the most important comparative characteristic, which makes it possible to compare the friction of various bodies under different conditions, regardless of the load on the friction unit.
2. The force of friction does not depend on the nominal contact area of rubbing solids.
In the process of development of tribotechnics, it was found that the scope of Amonton's laws is limited. Thus, the independence of the friction coefficient from the load, which follows from the above equation, is violated in the region of very small and fairly large loads. Amonton's law is also violated for very rigid bodies (diamond) and very elastic bodies (rubber). The coefficient of friction of these materials decreases with increasing load. The nominal contact area of rubbing bodies can affect the magnitude of the friction force for materials with viscoelastic properties, as well as in cases where it affects the flow of the medium into the tribocontact.
Mechanism of external friction
In the general case, the coefficient of friction depends on a large number of factors (the stress-strain state of the friction contact, the mechanical and physico-chemical properties of the surface layer of the contacting bodies, the environment, including the lubricant, the design features of the interface, the mode of operation of the friction unit, etc. .) and is determined mainly by the interaction of the surface layers of solids involved in tribological contact with each other and by the interaction of the working surfaces of solids with the medium, including the lubricant.
The interaction of solid bodies in the process of friction develops in microvolumes formed in the zone of contact of these bodies. According to I.V. Kragelsky, frictional bonds arise at the points of contact (i.e., contact spots that form and exist only with the combined action of normal and tangential forces in frictional contact), forming a kind of “third body”. This third body includes the modified material of both contacting bodies, endowed with its own chemical composition, stress state and structure. I.V. Kragelsky, when analyzing the tribological process, distinguishes three stages:

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  friction bond formation;
  
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  the existence of a frictional connection due to changes occurring on the friction surfaces (the direction of these changes is determined by the Le Chatelier-Brown principle) as a result of these interactions;
  
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  violation of frictional bonds, leading to the destruction of surfaces.
  

In the event that the breakage of frictional bonds occurs inside the "third body", external friction takes place . In this case, such a ratio of the strength properties of the “third body” and the properties of the material of rubbing bodies in the volume should be observed, at which the shear strength increases as the distance from the surface deep into the base material (formulated by I.V. Kragelsky rule of a positive gradient of mechanical properties in depth, characterized by ratio dτ _cr /dτ>0). In this case, not only the ratio of shear strengths in the thinnest surface layer (“third body”) and in the volume of bodies is important, but also the geometric characteristics of the tribological contact (dimensionless depth of the deformation zone). This ratio is called the external friction threshold . For a spherical model of irregularities, this relation has the form:
(5.3)
where h is the depth of penetration of a single roughness into a deformable body, r is the radius of this roughness, τ is the shear strength of the friction bond; σ _τ - yield strength of the deformable material.
If this ratio is violated, there is a transition from external to internal friction, characterized by intensification of the destruction of the surface layers of the contacting bodies.
The distribution of localization areas of external and internal friction is illustrated in Fig.5.3.