Contact areas

The contact fatigue creates independent part of the fatigue tests. As consequence of triaxial state of stress and flexible plastic state in contact area occurrence comes to very considerable scattering of experimental data. From this reason it is necessary to test statistic meaningful number of samples. 

Fig. xn-2. Comparison of actual contact areas for (a) metal-on-metal and (b) plastic-on-metal. (From Ref. 2.)... 

Normally, then, the actual contact area is determined by the yield pressure, so that... 

Deduce from Fig. XII-5, using the data for Hs, how the contact area appears to be varying with load, and plot A versus IV. 

Derive Eq. XII-18. In an experiment using hexadecane and crossed mica cylinders, the circular flat contact area is about 10 cm in diameter and the two surfaces oscillate back and forth to the extent of 1 % of their diameter per second. The separation distance is 10 A and the yield pressure of the glue-backed mica is 0.1 kg/mm. ... 

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. 

Modelling of the tme contact area between surfaces requires consideration of the defonnation that occurs at the peaks of asperities as they come into contact with mating surfaces. Purely elastic contact between two solids was first described by H Hertz [7], The Hertzian contact area (A ) between a sphere of radius r and a flat surface compressed under nonnal force N is given by... 

In reality most solids in contact under macroscopic loads undergo irreversible plastic defonnation. This is caused by the fact that at high nonnal forces the stresses in the bulk of the solid below the contact points exceed the yield stress. Under these conditions the contact area expands until the integrated pressure across the contact area is equal to the nonnal force. Since the pressure is equal to the yield strength of the material cr, the plastic contact area is given by... 

Detennining the contact area between two rough surfaces is much more difficult than the sphere-on-flat problem and depends upon the moriDhology of the surfaces [9]. One can show, for instance, that for certain distributions of asperity heights the contact can be completely elastic. However, for realistic moriDhologies and macroscopic nonnal forces, the contact region includes areas of both plastic and elastic contact with plastic contact dominating. 

The separation of two surfaces in contact is resisted by adhesive forces. As the nonnal force is decreased, the contact regions pass from conditions of compressive to tensile stress. As revealed by JKR theory, surface tension alone is sufficient to ensure that there is a finite contact area between the two at zero nonnal force. One contribution to adhesion is the work that must be done to increase surface area during separation. If the surfaces have undergone plastic defonnation, the contact area will be even greater at zero nonnal force than predicted by JKR theory. In reality, continued plastic defonnation can occur during separation and also contributes to adhesive work. 

In both of these pieces of apparatus, isothermal operation and optimum membrane area are obtained. Good temperature control is essential not only to provide a value for T in the equations, but also because the capillary attached to a larger reservoir behaves like a thermometer, with the column height varying with temperature fluctuations. The contact area must be maximized to speed up an otherwise slow equilibration process. Various practical strategies for presetting the osmometer to an approximate n value have been developed, and these also accelerate the equilibration process. 

Figure 2.1 served as the basis for our initial analysis of viscosity, and we return to this representation now with the stipulation that the volume of fluid sandwiched between the two plates is a unit of volume. This unit is defined by a unit of contact area with the walls and a unit of separation between the two walls. Next we consider a shearing force acting on this cube of fluid to induce a unit velocity gradient. According to Eq. (2.6), the rate of energy dissipation per unit volume from viscous forces dW/dt is proportional to the square of the velocity gradient, with t]q (pure liquid, subscript 0) the factor of proportionality ... 

The model describing interaction between two bodies, one of which is a deformed solid and the other is a rigid one, we call a contact problem. After the deformation, the rigid body (called also punch or obstacle) remains invariable, and the solid must not penetrate into the punch. Meanwhile, it is assumed that the contact area (i.e. the set where the boundary of the deformed solid coincides with the obstacle surface) is unknown a priori. This condition is physically acceptable and is called a nonpenetration condition. We intend to give a mathematical description of nonpenetration conditions to diversified models of solids for contact and crack problems. Indeed, as one will see, the nonpenetration of crack surfaces is similar to contact problems. In this subsection, the contact problems for two-dimensional problems characterizing constraints imposed inside a domain are considered. 

Most effective differentiation of the receptor between substrates will occur when multiple interactions are involved in the recognition process. The more binding regions (contact area) present, the stronger and more selective will be the recognition (17). This is the case for receptor molecules that contain intramolecular cavities, clefts or pockets into which the substrate may fit (Fig. 1). 

The driving force in diffusion involves differences in the concentration of the diffusing substance. The molecular diffusion of a gas into a hquid is dependent on the characteristics of the gas and the hquid, the temperature of the hquid, the concentration deficit, the gas to hquid contact area, and the period of contact. Diffusion may be expressed by Pick s law (13,14) ... 

The rate of mass transfer (qv) depends on the interfacial contact area and on the rate of mass transfer per unit interfacial area, ie, the mass flux. The mass flux very close to the Hquid—Hquid interface is determined by molecular diffusion in accordance with Pick s first law ... 

Interfacial Contact Area and Approach to Equilibrium. Experimental extraction cells such as the original Lewis stirred cell (52) are often operated with a flat Hquid—Hquid interface the area of which can easily be measured. In the single-drop apparatus, a regular sequence of drops of known diameter is released through the continuous phase (42). These units are useful for the direct calculation of the mass flux N and hence the mass-transfer coefficient for a given system. 

In industrial equipment, however, it is usually necessary to create a dispersion of drops in order to achieve a large specific interfacial area, a, defined as the interfacial contact area per unit volume of two-phase dispersion. Thus the mass-transfer rate obtainable per unit volume is given as... 

In order to maintain a definite contact area, soHd supports for the solvent membrane can be introduced (85). Those typically consist of hydrophobic polymeric films having pore sizes between 0.02 and 1 p.m. Figure 9c illustrates a hoUow fiber membrane where the feed solution flows around the fiber, the solvent—extractant phase is supported on the fiber wall, and the strip solution flows within the fiber. Supported membranes can also be used in conventional extraction where the supported phase is continuously fed and removed. This technique is known as dispersion-free solvent extraction (86,87). The level of research interest in membrane extraction is reflected by the fact that the 1990 International Solvent Extraction Conference (20) featured over 50 papers on this area, mainly as appHed to metals extraction. Pilot-scale studies of treatment of metal waste streams by Hquid membrane extraction have been reported (88). The developments in membrane technology have been reviewed (89). Despite the research interest and potential, membranes have yet to be appHed at an industrial production scale (90). 

Ultrasonic Welding. Ultrasonic welding has been appHed to Tefzel with weld strength up to 80% of the strength of the base resin. Typical conditions include a contact pressure of 172 kPa (25 psi) and 1—2 s cycle time. The two basic designs, the shear and butt joints, employ a small initial contact area to concentrate and direct the high frequency vibrational energy. 

Dry Sliding. When two surfaces mb, the real area of contact involves only sufficient asperities of the softer material so that their yield pressure balances the total load (3). As the initial load W increases, the real contact area illustrated in Figure 1 increases proportionately according to the relation... 

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

Of course, the above appHes when staying within a given tread design and at equivalent tread stiffness. Tire designs that allow water to be channeled out of the tread mbber/road contact area are significantly superior to those that do not, even when more contact area is available. Tread element stiffness plays an important role in traction capabiUties as softer treads have less column stiffness and reduce tread void areas, ie, there is more mbber on the road but this is offset if water channeling is significantly reduced. 

For dry traction more contact is desired and the stopping distance is directiy related, ie, the more contact area the shorter the stopping distance. A softer, more pHable compound conforms to the road surface topography. Too soft a compound (low mechanical strength) abrades more easily and can therefore acts as a roUer and not allow sufficient contact area to be maintained. This is not readily encountered in nominal tires and conditions but has been encountered in cases of extremely high torque conditions for very fast acceleration and sudden stops. 

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