Contact elasticity factor

The second factor contains the influence of the contact region with its different properties related to the matrix material this influence is expressed by the ratio of the two moduli. The term also contains the pressure dependence of the velocity controlled by a strong pressure dependence of the contact elasticity (modulus Me). 

Fig. 20. The JKR represenUilion of loading experimental and modified data for a viscoelastic adhesive contact. Each set of points corresponds to a compression step in which the load P and contact radius a decreases and increases with time, respectively. LHS refers to the term on the left hand side of Eq. 61. It represents the equivalent of r/ in elastic JKR plot after being weighed by the viscoelastic factor (38. ...

The mechanical properties of a material play an important role in powder flow and compaction by influencing particle-particle interaction and cohesion, that is to say, by influencing the true area of contact between particles. For example, Hertz [26] demonstrated that both the size and shape of the zone of contact followed simply from the elastic properties of a material. Clearly then, the true area of contact is affected by elastic properties. From the laws of elasticity, one can predict the area of contact between two elastic bodies. More recent work has demonstrated, however, that additional factors must be taken... 

In addition to electric charge between particles other factors are in some cases operative in preventing actual contact, thus the medium may be strongly adsorbed by the surface, and the thin film may not readily be displaced on collision of the two neutral particles, in other cases a tough elastic film may be formed, possessing definite mechanical strength and necessitating a violent impact to ensure rupture. 

In general these factors determine cost, mechanical and visco-elastic properties, resistance to degrading environments and influences, processing characteristics of the compound, and special requirements such as flame resistance, oil resistance, low temperature flexibility, chemical resistance wear and abrasion resistance and non-toxicity requirements for application in contact with foodstuff, etc. 

Note that the preceding equation is for ideal cases, in which the particles are monodis-persed, spherical, and totally elastic, and the contact surface is clean. In practice, the particles are usually nonspherical and polydispersed the collision could have involved some heat loss, plastic deformation, or even breakup and the contact surface may have impurities or contaminants. In these cases, a correction factor tj is introduced to account for the effects of these nonideal factors. The applicable form of the electric current through the ball probe is, thus, given by... 

Contact during and after CMP is between a wafer and a polymer as a pad or brush thus the nature of the contact is predominantly elastic. As we saw in Section 2.1, the ratio of the elastic modulus E and the hardness H determines the extent of the plasticity in the contact region as well as the surface topography. For metals, E/H is typically 100 or greater, whereas for many of the softer polymers (low P s), E/H is only about 10. Thus the contact between metals and polymers is almost completely elastic except against very rough surfaces. Another factor that affects the friction of polymers is the strong time dependence of their mechanical properties most polymers are viscoelastic and also show a marked increase of flow stress with strain rate. 

In functioning machinery the contacting parts repeatedly rub one another many times. The interaction of two surfaces on reiterated contact will in part depend on the condition in which the previous iteration left them. Under ordinary circumstances, with the machinery operating satisfactorily, each iteration is much like the one before and an analysis of steady-state wear or friction can be made on the basis of one cycle of surface interaction. Generally in such cases, but not necessarily always, asperity deformation is elastic rather than plastic. Whether an adhesive junction forms depends on the condition of the asperity surface. If the materials f>e.n. 4e are easily adhesive but the surfaces are covered by a film which inhibits adhesion, then to initiate adhesion obviously the film must first be removed, broken up or penetrated. The subsequent course of adhesive contact will then be governed by such factors as the size of the contact, the shape of the asperity, the impressed load, the strength of the material, etc., in accordance with the fundamental modes of behavior. 

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