Friction elastic deformation

Where one or both of the contacting surfaces becomes permanently deformed during sliding, the energy required to produce the deformation represents an additional component of the friction force. For engineering surfaces the amount of permanent deformation which can be tolerated is very limited so that the deformation friction is small in comparison with the adhesive friction. Elastic deformation only makes a significant contribution to the total friction when there is a high level of hysteresis in the elastic recovery, such as in vehicle tyres, and this is not normally a consideration when molybdenum disulphide is used. For practical purposes it can therefore be assumed that adhesive friction is the only type of friction which needs to be considered. 

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. 

Elastohydrodynamic Lubrication (EHL). Lubrication needs in many machines ate minimized by carrying the load on concentrated contacts in ball and toUet beatings, gear teeth, cams, and some friction drives. With the load concentrated on a small elastically deformed area, these EHL contacts ate commonly characterized by a very thin separating hydrodynamic oil film which supports local stresses that tax the fatigue strength of the strongest steels. 

As reviewed thermoplastics (TPs) being viscoelastic materials respond to induced stress by two mechanisms viscous flow and elastic deformation. Viscous flow ultimately dissipates the applied mechanical energy as frictional heat and results in permanent material deformation. Elastic deformation stores the applied mechanical energy as completely recoverable material deformation. The extent to which one or the other of these mechanisms dominates the overall response of the material is determined by the temperature and by the duration and magnitude of the stress or strain. The higher the temperature, the most freedom of movement of the individual plastic molecules that comprise the... 

The indentation process is driven by the applied load, and resisted by two principal factors the resistance of the specimen to plastic deformation (and elastic deformation) plus the frictional resistance at the indenter/specimen interface. The ratio of these resistances changes with the size of the indentation because the plastic resistance is proportional to the volume of the indentation, while the frictional resistance is proportional to the surface area of the indentation. Therefore, the ratio varies as the reciprocal indentation size. This interpretation has been tested and found to be valid by Bystrzycki and Varin (1993). 

With a strong interfacial bond, when a fiber fractures, the high stresses in the matrix near the broken ends are relieved by the formation of a short radial crack in the resin. There is no interfacial debonding and corresponding friction at a sheared interface, but rather, the load is transferred to the fiber by elastic deformation of the resin. The lack of adhesive failure in this case is responsible for the relatively low emission observed. 

Knowledge of the sample pressure is essential in all high-pressure experiments. It is vital for determinations of equations of state, for comparisons with other experimental studies and for comparisons with theoretical calculations. Unfortunately, one cannot determine the sample pressure directly from the applied force on the anvils and their cross-sectional area, as losses due to friction and elastic deformation cannot be accurately accounted for. While an absolute pressure scale can be obtained from the volume and compressibility, by integration of the bulk modulus [109], the most commonly-employed methods to determine pressures in crystallographic experiments are to use a luminescent pressure sensor, or the known equation of state of a calibrant placed into the sample chamber with the sample. W.B. Holzapfel has recently reviewed both fluorescence and calibrant data with the aim of realising a practical pressure scale to 300 GPa [138]. 

How can the actual contact surface be measured One possibility is to measure the electrical resistance between two conductors and calculate the contact area from the measured resistance and the specific resistivity of the materials. Another possibility is to use an IR sensitive microscope to measure hot spots of a transparent solid that is in contact with a hot surface. With these methods it was found that the friction force is, in fact, proportional to the actual contact area. This implies that the true contact area must increase linearly with load. To illustrate how this is possible, we consider two extreme cases. In the first case, purely elastic deformation is considered. In the second case, we assume plastic deformation of the microcontacts. 

During a collision, the colliding solids undergo both elastic and inelastic (or plastic) deformations. These deformations are caused by the changes of stresses and strains, which depend on the material properties of the solids and the applied external forces. Theories on the elastic deformations of two elastic bodies in contact are introduced in the literature utilizing Hertzian theory for frictionless contact and Mindlin s approach for frictional contact. As for inelastic deformations, few theories have been developed and the available ones are usually based on elastic contact theories. Hence, an introduction to the theories on elastic contact of solids is essential. 

Slip Region The slip region, as the name implies, is characterized by material slipping onto the roll surface with a corresponding elastic deformation of the particles. Frictional forces on the roll surface impart a forward motion to the bulk material and cause it to flow further into the region between the rollers. 

To accomplish the above, the design of a ram extrusion press must provide a relatively long extrusion channel. However, there are physical limits to this parameter because friction and drive power as well as overall stressing of the equipment increase with channel length. Briquettes may retain a certain elastic deformation which, if suddenly released, will damage or destroy the product. Therefore, in most applications, a gradual release is provided in the channel prior to product discharge. 

Figure 1. Schematic representation of various possible friction mechanisms (a) Geometric interlocking of asperities with typical angle 0, (b) elastic deformation (stretched dashed bonds) to interlock atoms and/or macroscopic peaks, resulting in multiple metastable states, (c) defect pinning (circles), (d) pinning by an intervening layer of weakly bound material, (e) plastic deformation or plowing, and (f) material mixing or cold welding.

Elastic deformations within the solid can also produce static friction between surfaces that would not otherwise interlock. Figure lb illustrates a system where the spacing between peaks on the top surface is stretched to conform to the bottom surface. This could occur at the scale of either macroscopic asperities [21] (Section Vll) or individual surface atoms (Section 111). The elastic energy required to displace each peak into an opposing valley must be compensated by the gain in potential energy due to interactions between the surfaces. This... 

Miiser [25] examined yield of much larger tips modeled as incommensurate Lennard-Jones solids. The tips deformed elastically until the normal stress became comparable to the ideal yield stress and then deformed plastically. No static friction was observed between elastically deformed surfaces, while plastic deformation always led to pinning. Sliding led to mixing of the two materials like that found in larger two-dimensional simulations of copper discussed in Section IV.E. 

The molecular model is confined to the case of weak adhesion (5 < 0) to ensure homogeneous contact [48, 65]. In this case, two sources contribute to the frictional stress of a gel elastic deformation of an adsorbing polymer chain Cei and the lubrication of the hydrated layer of the polymer network ffvis, which can be represented as follows (Fig. 12) ... 

The hysteresis loss mechanism of friction is based on the fact that in real life recovery of a material from elastic deformation on removal of the stressing load is never perfect. The energy lost by this effect can be treated as a frictional loss. The hysteresis loss mechanism is of major importance in explaining rolling friction. Details of the rolling friction process are complex the second volume of the monograph by Bowden and Tabor [23] devotes an entire chapter to various aspects of rolling. 

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