Local frictional stress

The obtained solution also allows us to calculate some variables that are of practical interest. For example, the local frictional stress on the wall is... 

In this case, in contrast with (1.7.7), the local friction stress on the wall is given by... 

Another type of testing, that of electrostatic sensitivity, has been demonstrated in some cases to be more properly a delicate test of the ignitability of the material under localized thermal stress which correlates best to the friction sensitivity of the system under test rather than to electrostatic hazards. On the other hand, electrostatic tests done in the supposed atmosphere above a propellant mixer were reduced in absolute value by more than an order of magnitude when the ammonium perchlorate dust actually present was introduced in the test since this altered the potential path for spark discharge within the system. 

The conventional dimensionless measure of the local shear stress (the friction coefficient) is... 

Elastic and plastic deformations flatten the contact regions into micrometer-scale patches, which are many times larger than molecular scales. The static friction corresponds to an average yield stress within these contacts of ts - Fs/Areai, and a similar relation gives the local shear stress Tt corresponding to the kinetic friction. Experimental studies of a wide range of materials indicate that T rises linearly with the local pressure P [35 40] ... 

SO acts as a focus for stress concentration. During drying and in machine draws, local stresses are set up in the sheet. If the local friction between the filler particle and the fibre surface is large, then the fibre network locks until the drying stress exceeds the local failure stress. When local failure occurs the water meniscus between the fibres may be broken the fibre surfaces are then too far apart for hydrogen bonding to develop and reconsolidation of the bond is unlikely. 

If the filler particle is surrounded by mucilage such as cationic starch, the local friction between the filler particle and the fibre is reduced and slipping may occur under the action of localised drying stresses. When such slipping occurs, local stress concentrations are decreased and breaking of water menisci does not occur. Hence bonding and sheet consolidation can continue. 

The flowability of a particulate material is determined by its shear properties. When internal shear deformation is just about to occur, the local shear stress is called the shear strength. The shear strength is a function of the normal stress this functional relationship is referred to as the yield locus (YL). For a free-flowing material, the yield locus under fully mobilized friction conditions is... 

The tribological stress leads to the formation of poly(thio)phosphate tribofilms at all temperatures investigated, while in the non-contact areas only very thin thermal films were formed at 30 °C and 80°C. The contact pressure presumably leads to local frictional heating, which accelerates a chemical reaction of the adsorbed additives (see Fig. 13). Also, a purely tribochemical effect is likely at 30 °C, iron phosphate was found in the reaction layer, which is an indication that nascent iron, released because of wear, reacts with the phosphoryl groups and forms a component of the tribofilm. 

Figure 9 shows the lubricant film shear stress field, t(x), and local friction coefficient /j(x), calculated in at same point of the gear meshing line (point A) and for the same operating conditions. The global friction coefficient at point A (/UgA) is about 0.03. 

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. 

When forces are transmitted between tire and road the tire is deformed to some extent. It still adheres to the road in part of the contact area, but slides locally when the ratio of tangential stress to the local pressure exceeds the friction coefficient and wear occurs. It is this partial adhesion and sliding which on the one hand allows a control over the force transmission and on the other hand leads to wear of the tire. 

---