The physics of friction and wear 233

11.4 The physics of friction and wear 233

a total area A r , as in Figure 11.5(b). The total load transmitted across the surface is

(11.6) where σ y is the yield strength. Thus, the real contact area is

F n ⫽ A ry σ

To see how small this is, return to the cube of Figure 11.1. Its mass is m ⫽ ρ a 3 , so the force needed to support it is F n

⫽ρga 3 ⫽ρgaA n ⫽A r σ y , where

A n ⫽a 2 is the nominal contact area and g is the acceleration due to gravity (9.81 m/s 2 ). Thus, the ratio of real to nominal contact areas is

ρ ga

Thus, a 100 mm cube of ordinary steel (density 7900 kg/m 3 , yield strength 200 MPa), weighing a hefty 7.9 kg, contacts any hard surface on which it rests over only 0.4 mm 2 . Now think of sliding one surface over the other. If the junctions weld together (as they do when surfaces are clean), it will need a shear stress F s equal to the shear yield strength k of the material to shear them or, if the materials differ, one that is equal to the shear strength of the softer material. Thus, for unlubricated sliding

or, since k ⬇ σ y /2,

(11.8) Dividing this by equation (11.6) gives

a value right in the middle of the spread in Figure 11.2.

So far we have spoken of sliding friction—F s is the force to maintain a steady rate of sliding. If surfaces are left in static contact, the junctions tend to grow

234 Chapter 11 Rub, slither and seize: friction and wear

by creep, and the bonding between them becomes stronger so that the force to start sliding is larger than that to maintain it. This means that the coefficient of friction to start sliding, called the static coefficient, µ s , is larger than that to sustain it, resulting in stick-slip behavior that can cause vibration in brakes, and is the way that the bow-hair causes a violin string to resonate.

Wear

We distinguish two sorts of sliding wear. In adhesive wear, characteristic of wear between the same or similar materials (copper on aluminum, for exam- ple), asperity tips, stuck together, shear off to give wear damage. In abrasive wear, characteristic of wear when one surface is much harder than the other (steel on plastic, say), the asperity tips of the harder material plough through the softer one, abrading it like sandpaper.

Figure 11.6 shows the way in which adhesion between surfaces causes wear fragments to be torn from the surface. To minimize the rate of wear we need to minimize the size of the fragments; that means minimizing the area of contact. Since A r ⫽F n /σ y , reducing the load or increasing σ y (that is, the surface hard- ness) reduces wear.

Figure 11.7 shows abrasive wear. The asperities of the harder surface slice off segments of the softer one, like grating cheese. More commonly the problem is

Adhesive junctions

Material transfer

New asperity contact

Plane of shear

Plane of shear

Wear particle

Figure 11.6 Adhesive wear: adhesion at the work-hardened junctions causes shear-off of