Microscopic points of contact

The net area of this intimate contact is called the real area of contact Areai. It is assumed that plastic flow occurs at most microscopic points of contact, so that the normal, local pressures correspond to the hardness aj, of the softer of the two materials that are in contact. The (maximum) shear pressure is given by the yield strength cry of the same material. The net load L and the net shear force Fs follow by integrating aj, and cry over the real area of contact Areai. That is, L = cs, Arca and Fs = ayAreai. Hence, the plastic deformation scenario results in the following (static) friction coefficient ... 

Consider a 3-dimensional, corrugated solid placed on a smooth substrate as a simplified model for a mechanical contact, which is a subtle case (Section III. C.5). The macroscopic contact will then consist of individual junctions where asperities from the corrugated solid touch the substrate. A microscopic point of contact p then carries a normal load Ip, and a shear force fp will be exerted from the substrate to the asperity and vice versa. These random forces fp will try to deform both solids. For the sake of simplicity, let us only consider elastic deformations in the top solid. Asperities in intimate contact with the substrate will be subject to a competition between the (elastic) coupling to the top solid and the interaction with the substrate. If the elastic stress exceeds the local critical shear stress c,p of junction p, the contact will break and asperity p will find a new mechanical equilibrium position. In order for (5 to exceed Uep, the area A = tiL- over which the random forces accumulate must be sufficiently laige. The value of L where this condition is satisfied is called the elastic... 

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