Sliding contact theory

Figure 5 Typical velocity relationship of kinetic friction for a sliding contact in which friction is from adsorbed layers confined between two incommensurate walls. The kinetic friction F is normalized by the static friction Fs. At extremely small velocities v, the confined layer is close to thermal equilibrium and, consequently, F is linear in v, as to be expected from linear response theory. In an intermediate velocity regime, the velocity dependence of F is logarithmic. Instabilities or pops of the atoms can be thermally activated. At large velocities, the surface moves too quickly for thermal effects to play a role. Time-temperature superposition could be applied. All data were scaled to one reference temperature. Reprinted with permission from Ref. 25. 

Assume that the normal pressure and displacements are not affected by the existence of the tangential traction and resulting displacements. Hence, the normal pressure and contact area can be determined by the Hertzian theory. For the sliding contact of spheres, substituting Eq. (2.69) into Eq. (2.77) gives rise to the tangential traction as... 

Another theory of the reason for increased friction in the presence of moisture was proposed by Gao et al . They found that in a humid environment molybdenum disulphide films were more readily thinned by sliding contact, due to increased ease of interlamellar slip. They suggested that adsorption of water softened the films, and that resulting increased deformation by plowing in sliding contact led to a poorly oriented film and thus to increased friction. However, they considered that this was a short-term reversible effect which was not in conflict with theories of chemical breakdown. Gao et al also poiinted out the possibility that an increase In friction is caused by capillary pressure effects of moisture at asperity contacts. 

The sliding contact used here is composed of a sphere on a plane. Under normal loading, the solids are reversibly deformed (purely elastic and isotropic behaviour of the substrates). Thanks to Hertzian theory, the contact area is determined to be circular with a radius equal to a (Figure 2.29). The calculation of the distance between the ball and the flat where the crown appears would lead to a better understanding of the formation mechanism of the crown. The formula of the deformation of the ball determined by Cameron gives the distance between the pin and flat at a given distance (r) [54] ... 

Theory of Sliding Contact. Based on Hertzian contact model, Hamilton and Goodman (11), which was later elaborated by Hamilton (12), presented the scratch process as a combination of an indentation process and a sliding process. Figure 3 shows the schematic of the scratch process in this model. At the contact surface, where z = 0,... 

Examination of the coefflcient of friction of polymeric systems in the same manner as for metallic systems shows the functional differences. The primary difference between the two sliding systems is that even for polymeric systems that undergo initial plastic deformation, there will be a significant portion of the real area of contact that is in elastic contact. For elastomeric sliding systems virtually all of the real area of contact is loaded elastically. Thus, for the sake of discussion, assume that the contact is a sphere-on-flat configuration with completely elastic loading. One case where this occurs is for a soft elastomer on a hard, nominally flat counterface. In this situation, the real contact area is given by Hertzian contact theory radius calculation as... 

In an attempt to determine the applicability of JKR and DMT theories, Lee [91] measured the no-load contact radius of crosslinked silicone rubber spheres in contact with a glass slide as a function of their radii of curvature (R) and elastic moduli (K). In these experiments, Lee found that a thin layer of silicone gel transferred onto the glass slide. From a plot of versus R, using Eq. 13 of the JKR theory, Lee determined that the work of adhesion was about 70 7 mJ/m". a value in clo.se agreement with that determined by Johnson and coworkers 6 using Eqs. 11 and 16. 

Carpick, R.W., Enachescu, M., Ogletree, D.F. and Salmeron, M., Making, breaking, and sliding of nanometer-scale contacts. In Beltz, G.E., Selinger, R.L.B., Kim, K.-S. and Marder, M.P., (Eds.), Fracture and Ductile vs. Brittle Behavior-Theory, Modeling and Experiment. Materials Research Society, Warrendale, PA, 1999, pp. 93-103. 

Until recently, the theory did not allow the configuration of the positive state to be described, due to entry/exit DNAs interpenetration upon application of the positive constraint to the loop. A recent development [63] takes the DNA impenetrability into account and deals with the resulting DNA self-contacts, which were allowed to slide freely, following the needs of the energy minimization process. 

Friction is independent of the surface area, of speed (except when the objects are resting), and of temperature. This is in theory. However, in the real world, the contact area does matter. Furthermore, in the case of polymers, in general, and composite materials, in particular, the actual contact area is difficult to determine dne to deformations of the plastic. In reality, applied force, test temperature, sliding rate, and duration of the test, all are important. 

The continuum theory of interfacial rubbing temperature described in the preceding section requires perfect contact of the two bodies over the entire nominal rubbing area but we know that true contact of real surfaces is at the asperities. If the continuum treatment is to have any relevance for real rubbing temperatures, it must be an acceptable approximation to what actually occurs physically. One such possibility, advocated by Archard [3] as applicable for closely spaced asperities and slow sliding speeds, is to treat the aggregate true area of the asperity contacts as the equivalent area of a single contact. 

We note that Higbie s penetration theory (HI5), with contact time assumed as that required by the drop to traverse a distance of one diameter (W6), gives an expression identical with Eq. (18). Although potential-flow theory, unlike the penetration theory, takes interfacial acceleration into account, the two are actually physically identical, both being based on diffusion into an element of fluid sliding over the constant-temperature interface. 

If potential flow and constant surface temperature are assumed, an equation analogous to Eq. (18) is obtained for the internal Nusselt number. Note, however, that the reference velocity in the internal Peclet number is the drop velocity. Similar results will be obtained from the penetration theory, according to which the film is assumed infinite with respect to the depth of heat penetration during the short contact time of a fluid element sliding over the interface. Licht and Pansing (L13) report West s equation, based on the transient film concept, for the case of mass transfer through the combined film resistance. In terms of the overall heat-transfer resistance, l/U (= l//jj + I/he) and if the contact time is that required for the drop to traverse a distance equal to its diameter. West s equations yield... 

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