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V = kW x=H (21:5)

where V is the volume worn away, W is the normal load, x is the sliding distance, H is the hardness

of the surface being worn away, and k is a nondimensional wear coefficient dependent on the

materials in contact and their exact degree of cleanliness. The term k is usually interpreted as the

probability that a wear particle is formed at a given asperity encounter.

Equation (21.5) suggests that the probability of a wear-particle formation increases with an

increase in the real area of contact, Ar (Ar = W=H for plastic contacts), and the sliding distance.

For elastic contacts occurring in materials with a low modulus of elasticity and a very low surface

roughness Eq. (21.5) can be rewritten for elastic contacts (Bhushan's law of adhesive wear) as

[Bhushan, 1990]

V = k0

Wx=Ec (¾p=Rp)

1=2 (21:6)

where k0

is a nondimensional wear coefficient. According to this equation, elastic modulus and

surface roughness govern the volume of wear. We note that in an elastic contactæthough the

normal stresses remain compressive throughout the entire contactæstrong adhesion of some

contacts can lead to generation of wear particles. Repeated elastic contacts can also fail by

surface/subsurface fatigue. In addition, as the total number of contacts increases, the probability of

a few plastic contacts increases, and the plastic contacts are specially detrimental from the wear

standpoint.

Based on studies by Rabinowicz [1980], typical values of wear coefficients for metal on metal

and nonmetal on metal combinations that are unlubricated (clean) and in various lubricated

conditions are presented in Table 21.2. Wear coefficients and coefficients of friction for selected

material combinations are presented in Table 21.3 [Archard, 1980].

Table 21.2 Typical Values of Wear Coefficients for Metal on Metal and Nonmetal on Metal

Combinations

Metal on Metal

Condition Like Unlike* Nonmetal on Metal

Clean (unlubricated) 1500 ¢ 10¡6 15 to 500 ¢ 10¡6 1:5 ¢ 10¡6

Poorly lubricated 300 3 to 100 1.5

Average lubrication 30 0.3 to 10 0.3

Excellent lubrication 1 0.03 to 0.3 0.03

*The values depend on the metallurgical compatibility (degree of solid solubility when the two metals are melted

together). Increasing degree of incompatibility reduces wear, leading to higher value of the wear

coefficients.

© 1998 by CRC PRESS LLC

Microhardness

(kg/mm²)

Friction (k)

Mild steel Mild steel 186 0.62 7:0 ¢ 10¡3

60/40 leaded

brass

Tool steel 95 0.24 6:0 ¢ 10¡4

Ferritic stainless

steel

Tool steel 250 0.53 1:7 ¢ 10¡5

Stellite Tool steel 690 0.60 5:5 ¢ 10¡5

PTFE Tool steel 5 0.18 2:4 ¢ 10¡5

Polyethylene Tool steel 17 0.53 1:3 ¢ 10¡7

Tungsten carbide Tungsten carbide 1300 0.35 1:0 ¢ 10¡6

Source: Archard, J. F. 1980. Wear theory and mechanisms. In Wear Control Handbook, ed. M. B. Peterson and

W. O. Winer, pp. 35-80. ASME, New York.

Note: Load = 3.9 N; speed = 1.8 m/s. The stated value of the hardness is that of the softer (wearing) material in

each example.

Abrasive Wear

Abrasive wear occurs when a rough, hard surface slides on a softer surface and ploughs a series of

grooves in it. The surface can be ploughed (plastically deformed) without removal of material.

However, after the surface has been ploughed several times, material removal can occur by a

low-cycle fatigue mechanism. Abrasive wear is also sometimes called ploughing, scratching,

scoring, gouging, or cutting, depending on the degree of severity. There are two general situations

for this type of wear. In the first case the hard surface is the harder of two rubbing surfaces

(two-body abrasion), for example, in mechanical operations such as grinding, cutting, and

machining. In the second case the hard surface is a third body, generally a small particle of grit or

abrasive, caught between the two other surfaces and sufficiently harder that it is able to abrade

either one or both of the mating surfaces (three-body abrasion), for example, in lapping and

polishing. In many cases the wear mechanism at the start is adhesive, which generates wear debris

that gets trapped at the interface, resulting in a three-body abrasive wear.

To derive a simple quantitative expression for abrasive wear, we assume a conical asperity on

the hard surface (Fig. 21.7). Then the volume of wear removed is given as follows [Rabinowicz,

1965]:

V = kW x tan µ=H (21:7)

where tan µ is a weighted average of the tan µ values of all the individual cones and k is a factor

that includes the geometry of the asperities and the probability that a given asperity cuts (removes)

rather than ploughs. Thus, the roughness effect on the volume of wear is very

distinct.

Materials

Wearing Surface Counter Surface Vickers Coefficient of Wear Coefficient

Table 21.3 Coefficient of Friction and Wear Coefficients for Various Materials in the Unlubricated

Sliding

© 1998 by CRC PRESS LLC