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It is interesting to note, that if these two asymptotic formulae had been obtained earlier, they might have brought an end to the discussion raised between Dupuit and Morin in the nineteenth century concerning the dependence of the friction force on the radius of the roller. Ishlinsky's formulae support both suggestions. More complicated and also more realistic models of viscoelastic bodies are based on the mechanics of solids. The methods of solution of some contact problems for viscoelastic solids have been presented in May, Morris and AtackLee and RadokHunter, Morland,Galin and ShmatkovaTingBraat and Kalkeretc.

Some problems for inelastic solids concerning normal, sliding, and rolling contact and impact are discussed by Johnson The analysis of the contact problem solutions taking into ati radeon 3223300 inelastic properties of solids and friction allows the establishment of the dependence of the contact characteristics on the mechanical properties of bodies and the contact conditions.

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It also makes possible to determine the conditions that allow us to use the simplified models. Some rolling and sliding contact problems for viscoelastic bodies are also presented in Chapter 3. The solutions of these problems are used to calculate the mechanical component of friction force and to analyze its dependence ati radeon 3223300 the sliding velocity. Since specific surface properties of contacting bodies considerably influence the stress distribution near the contact region and the friction force, the solution of contact problems for bodies with elastic parameters which vary with depth is of great interest for tribology. A review of early works devoted to investigation of contact problems for inhomogeneous elastic bodies may be found in Galin b and Gladwell Most of ati radeon 3223300 works are concerned with the special forms of the functions describing the dependence of elastic moduli the Young modulus and the Poisson ratio on the depth.

Different kinds of coatings and surface modification are widely used in friction components to decrease friction, to increase the wear resistance and to prevent seizure between contacting surfaces. The lifetime of coatings and their tribological characteristics friction coefficient, wear resistance, etc.

Contact Mechanics in Tribology

It is important for tribologists to choose the optimal mechanical and geometrical characteristics of coatings for any particular type ati radeon 3223300 junctions. Contact mechanics of layered bodies can help to solve this problem.

Ati radeon 3223300 researches in this field are reviewed in monographs by Nikishin and Shapiro, Vorovich, Aleksandrov and BabeshkoAleksandrov and Mhitaryan They give solutions of plane and axisymmetric contact problems for an elastic layer bonded to or lying without friction on an elastic or rigid foundation. Considerable attention has been focussed recently on the production of thin coatings, the thickness of which is commensurable with the typical size and distance between asperities.

This initiated the investigation of contact problems for layered ati radeon 3223300 with rough surfaces. Problems of this kind are considered in detail in Chapter 4. The effect of the boundary conditions at the interface between the coating and the substrate is also analyzed in that chapter. This analysis elucidates the influence of the interface adhesion on the internal stresses and the fracture of coating.


Chapter 4 also includes contact problems for viscoelastic layered elastic bodies. Solving these problems for rolling or sliding elastic indenter with smooth or rough surface is very important for studying the dependence of the friction force on the speed for junctions operating in the boundary lubrication condition or in the presence of solid lubricants. What is the influence of a thin viscoelastic layer on the stress distribution in the lubricated contact of two elastic rollers? This question is also discussed in Chapter 4 where the model of lubricated contact includes equations from hydrodynamics, viscoelasticity and elasticity. This model allows us to analyze the dependence of the friction coefficient on speed for variable mechanical and geometrical characteristics of the surface layer.

Investigation of the contact ati radeon 3223300 taking into account friction, microstructure, presence of surface layers and an intermediate medium ati radeon 3223300 us to determine contact and internal stresses in a thin subsurface layer, where the cracks initiate.

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Such analysis becomes a basis for prediction of the surface fracture process wear in friction interaction. The methods and models of fracture mechanics are most commonly used to model the fracture of surface layer in friction process. However, modelling of fracture in tribology has specific features. First, ati radeon 3223300 predict the type of wear, we must know both bulk and surface strength characteristics of materials. Secondly, detachment of one wear particle from the surface does not mean the failure of the junction; the ati radeon 3223300 of wear particles detached from the surface during the life of junction may be considerable.

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The surface fracture process changes surface properties the shape of the surface and its microgeometry, mechanical properties, damage characteristics, etc. The variable surface properties influence, in turn, the wear process. Some problems of contact fracture mechanics are discussed in monographs by MarchenkoWaterhauseKolesnikov and MorozovHills and Nowelland Mencik and in papers by Miller, Keer and Cheng ati radeon 3223300, Hattori et al. The models of delamination of the surface layer and wear particle detachment in friction of rough surfaces are presented in Chapter 5. They are based on the theory of ati radeon 3223300 damage accumulation in cyclic loading.


Wear of surfaces leads to the continuous irreversible changes of the ati radeon 3223300 macroshape in time. Consideration of these changes requires new contact problem formulations and solution methods.

All contact characteristics pressure distribution, shape variation, size and position of contact region, approach of bodies are unknown functions of time in ati radeon 3223300 case. Calculation of the wear process for different junctions is a necessary condition for design of long-life machines. The first formulation of the wear contact problem suggested by Pronikov see also Pronikov, did not take into account the deformation of contacting bodies; the contact conditions included only the irreversible surface displacements due to wear. The contact problem for elastic bodies taking into account the surface shape variations during the wear process was formulated by Korovchinsky In this work the displacements of the surface due to wear are supposed to be commensurable with the elastic displacements.

At any instant of time, the shape of the surface is determined by wear at each point, ati radeon 3223300 simultaneously influences the contact pressure.ATI RADEON DRIVER - Try to setup your display adapter with a standard VGA driver before.

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