Bayer R.G. Mechanical Wear Fundamentals and Testing, Revised and Expanded

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More than one type of mechanism can be present in a wear situation. Typically, one

can ﬁnd in the examination of a wear scar features indicative of different mechanisms, as

illustrated by the micrographs shown in Fig. 3.5. When more than one mechanism is pre-

sent, they can interact serially to form a more complex wear process, as illustrated by the

fretting situation discussed previously in this section. They can also act in a parallel or

simultaneous fashion, with each contributing to the total wear. While this is the case, most

situations can usually be characterized in terms of one controlling or dominant mechan-

ism. There are some situations, however, where this cannot be done and it is necessary

to consider the contributions of each (10,32–34).

There is another approach to classifying wear mechanism that can also be useful

(35). In this classiﬁcation, wear mechanisms are divided into cohesive wear and inter facial

wear categories. Under cohesive wear are those wear mechanisms which occur primarily in

the relatively large volumes adjacent to the interface. Interfacial wear, on the other hand,

includes those mechanisms related to the interface alone. Both types of deformation

mechanisms would be included in the former, while adhesion, triboﬁlm, and oxidation

mechanisms in the latter. Thermal could be of eithe r type, depending on the depth of

the heat-affected zone. This alternate classiﬁcation focuses on the signiﬁcance of the

energy densities involved in the two regions, that is, in the thin layers at the interface

and in the larger regions adjacent to it. A corollary to this classiﬁcation is that bulk prop-

erties and responses are generally major aspects in the mechanisms included in the cohe-

sive category, while surface properties and phenomena are key in the interfacial category.

While this classiﬁcation is not particularly useful in grouping physical mechanisms, it is

useful for identifying aspec ts that must be considered in the treatment of wear and offers

the opportunity for some insigh t into what are controlling factors in certain wear situa-

tions, that is surface vs. bulk phenomena.

The classiﬁcation of basic wear into the eight categories shown in Table 3.1 is not

necessarily a complete or rigorous classiﬁcation. However, it does provide a useful

basis for an effective engineering understanding of wear, particularly as it relates to

design.

3.2. ADHESIVE MECHANISMS

Before adhesive mechanisms are discussed some general concepts regarding the nature of

the contact between two surfaces and the behavior of inter-atomic forces need to be con-

sidered. The ﬁrst aspect that will be considered is the area of contact.

In engineering, the macro-geometry or contour of the bodies in contact is often used

to determine contact area. This is usually done by geometrical projection or by models,

which are based on the elastic or plastic deformation. For example, the Hertz contact the-

ory is frequently used not only to determine stress levels in the contact but the size of the

contact region as well (10,36). In these approaches, the surfaces are generally assumed to

be smooth. Actual surfaces, on the other hand, always exhibit some degree of roughness

and as a result the actual contact situation is different from that implied by these macro-

methods. Figure 3.6 illustrates the actual situation. What this illustrates is that actual physi-

cal contact occurs at localized spots within the area that is deﬁned by the macro-geometry.

These points at which the actual contact occurs are referred to as junctions. The sum of the

individual contact areas of these junctions is called the real area of contact. The area of

contact that is determined through the macro-considerations is called the apparent area

of contact. As will be seen, fundamental physical models regarding wear generally are

developed in terms of real area considerations, while engineering formulations and models

generally are related to the apparent area of contact.

The roughness characteristics of the surface have a signiﬁcant inﬂuence on the num-

ber of junctions formed, as well as on the ratio of the real area of contact to the apparent

area of contact. The degree to which one surface penetrates the other, which is a function

of the normal force pressing the bodies together, can also inﬂuence both these aspects.

Figure 3.7 shows how the real area of contact changes, assuming one surface to be ﬂat and

smooth, as load and penetration is increased. The real area in this illustration increases

not only because the cross-sectional area of an asperity increases with penetration but

also because the number of asperities encountered increases with penetration.

The size and number of these junctions and their relationship to the apparent area of

contact have been investigated by both theoretical and experimental means (37–40).

Because of the potential range of the pa rameters involved, a wide variety of contact con-

ditions is possible; however, some generalization may be made. One is that the real area of

contact is generally much less than the appa rent area. The ratio might be as small as 10

4

in practical situations (41). A similar generalization can be made regarding individual

junctions. It has been estimat ed that the diameter of typical junctions is in the range of

1–100 mm (42). The larger value would most likely occur for a very rough surface and high

loads. Diameters of the order of 10 mm would be more likely in more typical contact situa-

tions. While on the basis of stability, it can be argued that there must be at least three junc-

tions involved, the number general ly is larger. Estimates based on the yield point of

materials and juncti on size generally indicate that the number ranges from the order of

Figure 3.6 Apparent and real area of contact. Contact occurs are discrete locations, called

junctions.

10 to the order of 10

, with 10 to 10

being more likely (43) . The deformation properties of

the materials involved and the loading conditions on the junctions also inﬂuence the real

area of contact . Junction growth as a result of applied shear, that is, friction, also occurs.

The deformation at the junction can be plastic as well as elastic. Just how much of

each occurs depends on the number of junctions and their size, as well as the properties of

the materials involved. While it is not impossible to have only elastic deformation on all

the junctions, this is generally not the case. Models, assuming typical surface pr oﬁles, indi-

cate that some junctions would generally be plastically deformed (37,38). This tends to be

conﬁrmed by the topography found in the initial stages of wear. Some evidence of local

plastic deformation can usually be found on these.

The con tact between rough surfaces and the effect of shear have been modeled and

equations for the real area of contact have been developed (37,38,44,45). A summary of

the eq uations for the real area of contact obtained from these models is given in

Table 3.3. If the plasticity index, a measure of the state of stress at the junctions, is

less than 0.6, all the junctions are elastically deformed; if greater than 1, all are plasti-

cally deformed. For intermediate values, there are some junctions in both states. It can

be seen from the equation for the plasticity index that increa sed hardness, lower mod-

ulus, more unifor m and rounder asperities reduce the degree of plastic deform ation in

the real area of contact. For typical unworn surfaces, the plasticity index is generally

closer to 1 than 0.6. However, roughness features tend to change with wear and as a

result the index changes with wear, often becoming smaller (37). Because of these

changes in roughness and the change in apparent area of co ntact that is often the result

of wear, the ratio of real to apparent areas of contact, the number of junctions formed,

and the size of the junctions typically change wi th wear as well.

In summ ary, the most signiﬁcant points to be recognized about the contact between

two bodies is that actual contact occurs at individual sites within an apparent area of con-

tact and that the real area is generally only a fraction of the apparent area. The features

observed in most micrographs of wear scars produc ed under sliding conditions support

this view of the contact between two surfaces, as well as the generalizations regarding

the ratio of real and apparent areas, junction size and number, and the plasticity index.

It is important to understand the nature of the interaction that occurs at these junc-

tions on both an asperi ty and an atomic level. At the asperity level, the focus is on the type

Figure 3.7 The effect of increased load on the real area of contact. h is the penetration of a rough,

hard, surface into a smooth, ﬂat, soft surface at a low load; H, at a higher load. Both the number

and size of the junctions increase with increasing penetration.

of deformation that occurs at these junctions. To understand the interacti ons on an atomic

level, it is necessary to consider the nature of inter-atomic forces. The behavior of the force

between two atoms is illustrated in Fig. 3.8. For large separations between the atoms there

is a weak attractive force. At separations comparable to inter-atomic spacing the attractive

force increases rapidly. With still smaller separations, the attractive force begins to

decrease an d ultimately the force changes to a repulsive one. Arrays of atoms also exhibit

the same general behavior, which is shown in Fig. 3.9 for the case of an Al crystal and a Zn

crystal (46). In this ﬁgure, A shows the variation in the potential energy of such a contact

as a function of the separation of the two crystals. This is the more common way of

describing the interactions. A negative potential energy indicates bonding. The slope of

the curve is force; a negative slope indicates a repulsive force and a positive slope indicates

an attractive force. B shows the corresponding variation in force with separation.

Table 3.3 Equations for the Real Area of Contact

Plasticity index

c ¼



For elastic contact, c < 0.6

For plastic contact, c > 1.0

Mixed, 0.6 < c < 1.0

Elastic contact



3:2P

ðÞ

1=2

Plastic contact

Effect of shear

¼ A

1 þam



1=2

Symbols

c, plasticity index

, real area of contact without friction

, real area of contact with friction

p, hardness of softer material

P, load

, composite elastic modulus

1v

ðÞ

1v

ðÞ



1

E, elastic modulus

n, Poisson’s ratio

, composite standard deviation of asperity peak heights

þ s



1=2

s, standard deviation of asperity peak heights

, composite mean radius of curvature of asperity tips



1

r, radius of curvature of asperity tips

m, coefﬁcient of friction

a, empirical constant (approximately 12)

Since junctions form as a result of two surfaces being pressed together, the nature of

inter-atomic forces indicates that bonding occurs at these juncti ons. It also means that

over some portion of the real area of contact the atoms of the two surfaces must have gone

past the point of maximum bonding. This is the only way the forces can be balanced. This

implies that some adhesive forces or bonds must be overcome to separate the two surfaces

at these sites. This atomic view of the contact situation at the junctions provides the foun-

dation for the co ncept of adhesive wear.

Consider the diagram shown in Fig. 3.10. This depicts the situation at a junction at

which bonding has occurred. As the two surfaces move relative to one another, rupture of

the junction will eventually occur. If the rupture occurs along Path 2, which is the original

interface, no material will be lost from either surface, though some plastic deform ation

may have occurred. If, on the other hand, the rupture oc curs along some other path, illu-

strated by Path 1 in the ﬁgu re, the upper surface would have lost material. The removal of

material from a surface in this manner is called adhesive wear.

Scanning electron microscope (SEM) and electron dispersive x-ray (EDX) micro-

graphs, illustrati ng the adhesive wear process, are shown in Fig. 3.11. These micrographs

show the sequence of events associated with a simulated asperity moving across a smooth

ﬂat surface. In this case, a small rounded iron stylus simulates the asperity. In the lower

right of A, the results of asperity engagement and junction formation are evident. Initially

the junction formed by this asperity appears to rupture at the original interface, leaving

only a plastically deformed groove in the wake of its motion. Som e deformation of the

asperity is likely as well during this period. At some point, failure no longer occurs at

the original interface but at some depth within the asperity, leaving a portion of the asper-

ity adhering to the ﬂat surface. This is the event indicated in the middle by the adhered

wear fragment. B shows that as sliding continued, the same series of events repeated

(upper left in the EDX) but with the asperity now modiﬁed both by plastic deformation

and adhesive wear.

There is a mathematical model for adhesive wear that has been found to be in good

agreement with experimental observations (47). It has been used extensively in describing

Figure 3.8 General nature of the force between atoms as a function of separation.

adhesive wear behavior. This formulation can be developed as follows. Assume that the

real area of contact is composed of n circular junctions of diameter d. Further, assume that

if an adhesive wear fragment is formed, it will be hemispherical shaped with a diameter d.

The total real area of contact, A

, is then

npd

ð3:1Þ

An assumption frequently used in tri bology is that all the junctions are plastically

deformed. In which case A

is also given by the following equation from Table 3.3

ð3:2Þ

Figure 3.9 ‘‘A’’ shows the variation in adhesive energy between A1 and Zn surfaces as a function

of separation (from Ref. 46). ‘‘B’’ illustrates the corresponding variation in the force between the two

surfaces.

where P is the normal force pressing the two surface together and p is the penetration

hardness of the softer material. Combining these equations, the following is obtained

for n:

n ¼

ppd

ð3:3Þ

Now, if the distance of sliding over which any given junction is operative is approximately

d, then in a unit distance of sliding each junction must be replaced by another (1=d) times.

Therefore, the total number of junctions occurring in a unit distance, N,is

N ¼

ppd

ð3:4Þ

If K is the probability that the rupture of any given junction will result in adhesive wear,

the number of junctions producing adhesive wear in a unit sliding distance, M , is given by

M ¼ KN ¼

ppd

ð3:5Þ

Since the volume of an adhesive wear fragment is pd

=12, the volumetric wear rate, dV=dx,

where V is the volume of wear and x the distance of sliding, is

ð3:6Þ

Integrating and combining the following relationship is obtained for adhesive wear:

V ¼

Px ð3:7Þ

Figure 3.10 The lower diagram illustrates possible separation paths at a junction. Separation along

Path 1 does not result in loss of material. Separation along Path 2 results in rupture and loss of

material, as indicated in the upper diagrams.

This equation was ﬁrst developed by Archard (47) and because of that it is frequently

referred to as Archard’s equation.

A key point in the development of this equation is that K is a probability and there-

fore it cannot be greater than unity. Experimental data are consistent with that. This can

be seen in Table 3.4, which gives values for K inferred from sliding wear data for a range of

conditions. Such data generally provide an upper-bound estimate of K, since in many cases

other wear mechanisms are present, contributing to the wear and possibly even dominat-

ing the situation. However, K values in the range of 10

4

or higher have been documented

for wear situations in which adhesion has dominated (48). This being the case, these data

also do indicate that in most situations K is likely quite small, particularly in practical

Figure 3.11 Example of adhesive wear process. ‘‘A’’ shows the wear scar produced by an iron pin

sliding across the ﬂat surface of a nickel disk. ‘‘B’’ is an EDX map for iron on the disk surface,

conﬁrming transfer of material from the pin to the disk. (From Ref. 175, reprinted with per-

mission from ASME.)

situations. It also indicates that the range of K values possible is very large. The values

indicate that the probability of a junction wearing by adhesion can range from one in

ten to less than one in a million. As a point of reference, a value of K of 10

5

and often

much less is required for acceptable wear behavior in applications. This being the case, the

large range possible for K makes it an extremely important parameter in controlling this

type of wear mechanism. From an engineering point of view, this means selecting design

parameters so that high values of K are avoided, i.e., the probability of adhesion is low.

One factor that can affect K is the relative strength of the junction interfaces to the

strength of the asperities that make up the junctions. The weaker the adhesion at the inter-

faces is, the less likely adhesive wear will occur. Consequently , choosing conditions, which

inhibit adhesion over those, that promote adhesion reduce K and adhesive wear.

Interface adhesion can be affected by the similarity of the two materials in contact.

The more similar they are, the stronger the adhesion. As a result, dissimilar pairs should

have lower values of K than more simila r or identical pairs. In addition to composition,

such aspects as lattice parameters and mutual solubility characteristics, can also be factors

in determining the degree of similarity (49–52). Another factor affecting interface adhesion

is surface energy. Lower surface energies result in lower adhesion. Therefore, since poly-

mers and ceramics generally have lower surface energies than metals, K values would

generally be lower for situations involving these materials than between metals. Also,

the presence of oxides, lubricants and contaminates on metal surfaces reduce surface

energy and result in lowering of K values.

The data in Table 3.4 illustrate some of these trends . Clean, unlubricated, and similar

metal pairs generally have high values for K. Lubricated conditions give the lowest values

and conditions involving ceramics and polymers have intermediate values associated with

them.

As is shown in the following, there is a minimum asperity load required for transfer

to take place and a minimum asperity load for the transferred fragment to remain

attached. K, which is the average probability for transfer, will be changed as the percen-

tage of junctions with loads below the critical value for transfer changes, since the prob-

ability for failure at these junctions is 0. Consequently, K can also be affected by the

distribution of load across the junctions. The percentage of these junctions would tend

to be higher as load is decreased, since the average pressure on the junctions decreases with

decreasing load (38). A simple model can illustrate the requirement for a minimum asper-

ity load for transfer (53).

Table 3.4 K Values for Adhesive Wear

Combination K

Selfmated metals

Dry 2 10

4

– 0.2

Lubricated 9 10

7

–910

4

Non-self-mated metals

Dry 6 10

4

–210

3

Lubricated 9 10

8

–310

4

Plastics on metals

Dry 3 10

7

–810

5

Lubricated 1 10

6

–510

6

Consider a circular junction of diameter d and the formation of hemispherical wear

fragment of diameter d, as illustrated in Fig. 3.12. For such an ideal situation, the adhesive

wear process can be reduced to the following criteria. For adhesive wear to take place, the

elastic energy stored in the volume of the potential fragment, E

, must be equal to or

greater than the energy associated with the new surfaces, E

. Mathematically,

 E

ð3:8Þ

Assuming that the tip of the asperity has been plastically deformed, the stored elastic

energy per unit volume is

ð3:9Þ

where s

is the yield point and Y is Young’s mo dulus. Since the vo lume of the hemisphe-

rical region is pd

=12,

24Y

ð3:10Þ

Noting that two hemispherical surfaces are formed and assuming that the material on both

sides is the same,

¼ pd

G ð3:11Þ

where G is the surface energy. Com bining, the minimum junction diameter, d

, required for

an adhesive wear fragment to be formed is

24GY

ð3:12Þ

If P

is the load supported by that asperity,

ppd

ð3:13Þ

Combining these two equations and utilizing the following the empirical relationships

(53):

¼ 3  10

3

Y ð3:14Þ

ð3:15Þ

G ¼

1=3

ð3:16Þ

where b is a constant for different classes of materials, it can then be shown that the mini-

mum asperity load for adhesive wear to take place is inversely proportional to the surface

energy, namely,

4:5  10

ð3:17Þ

Since the sum of the asperity loads must equal the applied macro-load, P, a similar

relationship should also exist at the macro-level. For the simple case of a uniform asperity