Real area of contact

Thus, under conditions of plastic defonnation the real area of contact is proportional to the nonnal force. If the shear force during sliding is proportional to that area, one has the condition that the shear force is proportional to the nonnal force, thus leading to the definition of a coefficient of friction. 

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... 

Yield pressurep of the asperities is about three times the tensile yield strength for many materials. The real area of contact is frequently a minute fraction of the total area. With a typical bearing contact stress of 3 MPa and a bron2e bearing asperity yield pressure of 500 MPa, for instance, less than 1.0% of the nominal area would involve asperity contact. 

So it follows that, if two surfaces are placed in contact, no matter how carefully they have been machined and polished, they will contact only at the occasional points where one set of asperities meets the other. It is rather like turning Austria upside down and putting it on top of Switzerland. The load pressing the surfaces together is supported solely by the contacting asperities. The real area of contact, a, is very small and because of this the stress P/a (load/area) on each asperity is very large. 

Obviously, if we double P we double the real area of contact, a. 

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 ... 

When rubber is brought into contact with another surface it deforms elastically and the real area of contact will increase with increasing normal load and, hence, the coefficient of friction will decrease with increasing normal load. It is also apparent that the real contact area is dependent on the surface geometry of the test piece. It is, hence, desirable to measure the friction of rubber over the range of normal forces of interest and to test with the surface geometry to be used in service, which may mean using the product or part of it as the test piece. 

The nature of the interaction between two surfaces is determined by the real area of contact, especially by the size of the real area. With a simple limit analysis assuming ideally plastic deformation, we can try to calculate a minimum value for Ar. If the surfaces that are placed in contact are rough, but not excessively rough, a typical junction will be induced as shown in Figure 2.4. Then the interface will be in a state of triaxial constraint. Thus the value of the real area of contact, Ar, is given by ... 

Here we discuss the properties of solids that are to be polished during CMP. Surface properties are important for CMP because they are related to the real area of contact, friction, wear, and tribochemical interactions between surfaces of wafers, slurry particles, and polishing pads. Upon contact, there are four structural elements involved in the wear mechanisms. They are, as shown in Figure 2.5,4 surface films that are present < 1 pm from the surface, near-surface structure occurring between 1 and 150 pm from the surface, subsurface structure that occurs between 50 and 1000 pm from the surface,... 

The simple asperity area mechanism of Section 8.1 for friction can be brought under a common umbrella with the extended mechanism developed in the foregoing portion of this section. In the simple mechanism, the real area of contact is fixed by the relation y = 4/p the tangential... 

Going back to the system represented by Eqn 9-2, the total real area of contact is... 

The derivation of Eqns 13-29 implies that we know how to sum up the total wear volume and the total contact area. The format of Eqn 13-30 stems from Archard s analysis of the surface model described in Chapter 12, Section 12.2.1, where the relation between real area of contact and load as given by Eqn 12-9 reduces to A = W/P for the case of plastic deformation of asperities. Other relations between real area of contact and load and other models for the formation of wear particles will give other expressions for wear, as discussed by Archard [6]. The quantity Z, which we have termed the effectivity factor, is designated as a... 

The geometric nominal area and the real area of contact are here taken to be identical. 

An evaluation of actual contact areas in hardness measurements clearly indicates the relevance of microscopic studies of mechanical properties. From the known values of //, we can compute the real area of contact between the solid and the indenter at various loads. These are shown in Table 8.3. The real contact area is a very small fraction of the geometric area, especially at smaller loads. The real area of contact... 

TABLE 8.3. Real Area of Contact at Different Loads for Four Metals of Different Hardness... 

On a microscopic level no solid surface is smooth, and when one surface is placed on another, the contact between the two occurs only at high spots (asperities) and these take up the load. Bowden and Tabor [43] showed that the real area of contact is much smaller than the apparent area of contact. Usually, the load distribution on each asperity is such that it deforms plastically and adhesion takes place. If the load L is increased, the contact area increases, and for many situations A is proportional to L. This explains why the frictional force is independent of apparent area and proportional to L. 

If plastic deformation occurs at the asperities the real area of contact (4/ ) is proportional to the load, L, so AT is proportional to v and. The equation also shows that the thermal conductivities of both surfaces are important. 

This point of view leads to the conclusion that to get A andB to make a stronger joint we need to increase their real area of contact. This means that one or both of the materials must be made to conform better to the surface roughness of the other. This implies, in a practical sense, that one of the materials should be fluid when placed in contact with the other. However, that one of the materials be liquid is a necessary, but may not be a sufficient, condition for if the liquid makes a... 

---