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

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distribution, the minimum macro-load, P

, would be N times Eq. (3.17), where N is the

number of asperities in contact.

A similar approach can be used to develop expressions regarding the formation of

loose adhesive wear fragments (53). The expression for the minimum junction size for a

loose fragment is

2  10

ð3:18Þ

The expression for the minimum asperity load is

p  10

ð3:19Þ

is the interfacial energy between the two surfaces and p is the hardness of the softer of

the two materials. The concept behind these relationships is that when junction separation

occurs the stored elastic energy in a bonded fragme nt will cause that fragment to break off,

if the elastic energy is greater than the interface energy.

The combined concepts of a minimum load for transfer to occur and K being

affected by load are illustrated and supported by the data shown in Figs. 3.13 and 3.14

for unlubricated sliding between noble metal specimens. Figure 3.13 shows how K varies with

load for unlubricated sliding between gold specimens. There are two stable regions for K,

one below 5 g and the other above 30 g. These two transition points are close to the mini-

mum loads for transfer and loose fragments to occur, respectively. Values of 1 and 25 g are

estimated for these, using the simple models described (54). The data suggest that adhesive

wear can only be characterized by a stable K value after the mean junction load exceeds

the junction load required for the formation of a loose particle. At the same time the data

support the concept that K becomes 0 at sufﬁciently low loads. The fact that in the graph K

does not go to 0 and appears to stabilize below 5 g is attributed to the existence of other

wear mechanisms. The appearance of wear scars for load under the minimum load for

transfer indicates that the wear mechanism is some form of deformation. An example

of such a wear scar is shown in Fig. 3.14. Note the absence of features suggestive of

transfer.

Since a higher plasticity index implies a higher mean junction load, a coroll ary to the

requirement for a minimum load for transfer is that the probability for transfer would tend

Figure 3.12 Model for the formation of a hemispherical adhesive wear fragment.

to be higher with higher values of the index. Consequently, roughness conditions that

increase the plasticity index would also tend to increase K.

Transfer is rarely observed in nominal rolling and impact situations. When it is

observed in such situations, traction and slip at the interface are generally present

(55,56). Also, a greater degree of transfer and adhesion is observed when interfaces

are pulled apart after they have been subjected to shear than when they have not

(55–57). It is generally concluded from these observations that the probability for transfer

Figure 3.13 Variation in K of Eq. (3.7) as a function of load for unlubricated, Au–Au sliding.

(From Ref. 53.)

Figure 3.14 Wear scar on silver, below the minimum load required for transfer. (From Ref. 53,

reprinted with permission from John Wiley and Sons, Inc.)

is much lower when junctions are pulled apart than when sheared. As a consequence,

adhesive wear is primarily considered to be a sliding wear mechanism. K is typically

assume to be 0 for pure rolling and normal impact. In rolling and impact situations, it

is generally assumed that any adhesive wear is the result of tangential motion, which

may be present.

In summary, the model for adhesive wear indicates that the major factor involved is

the probability factor, K, which varies over several orders of magnitude. This factor is

inﬂuenced by a wide variety of parameters, that may be grouped as follows: material pair

compatibility, surface energies, lubrication, as well as the nature of asperity contact and

load distributions. Also, adhesive wear is most probable in sliding wear situations but

may occur in rolling and impact situations when there is slip and traction between the

surfaces.

3.3. SINGLE-CYCL E DEFORMATION MECHANISMS

Single-cycle deformation mechanisms are deformation mechanisms that produce plastic

deformation, permanent displacement, or removal of material in a single engagement.

These processes result from the penetration of a softer body by a harder body. Common

forms of this type of mechanism for sliding are plowing, wedge formation, cutting, and

microcracking, which are illustrated in Fig. 3.15. Physical examples of three of these

mechanisms, plowing, wedge formation and cutting, are shown in Fig. 3.16. An exampl e

of microcracking would be the fracturing that occurs when an ice pick is dragged across a

piece of ice. The same generic mechanisms of plastic deformation an d cracking are also

possible for pure rolling and normal impact. In ro lling and impact situations, cutting is

also possible when there is some sliding or tangential motion involved. The micrographs

shown in Fig. 3.17 provide additional examples of the damage resulting from these types

of single-cycle deformation mechanisms. Single-cycle deformation mechanisms are the

dominant mechanisms in abrasive and erosive wear situations, when the particles are

harder than the wearing surface.

It has been found that for sliding situations in which single-cycle deformation

mechanisms dominate, the wear can be described by the following equation, which is

the same form as that for adhesion [see Eq. (3.7)]. However, while the forms are the same,

the coefﬁcients are affected by different parameters

V ¼

ð3:20Þ

For single-cycle deformation mechanism, the following model provides a basis for this

empirical relationship.

The model assumes that the junctions between the two surfaces can be represented

by an array of hard conical indenters of different sharpness plastically indenting and

penetrating a softer surface. As relative sliding occurs the cones produce wear grooves

in the softer surface, whose individual volumes are the cross-sectional area of the indenta-

tion times the distance of sliding. The situation for a single cone is shown in Fig. 3.18.

Since penetration hardness, p, is load divided by projected contact area, the load on

an individual cone, P

,ispa

, where a

is contact area for the individual cone. Only the

leading surface of the cone is in contact. As a result, the projected contact area of a cone

is pr

=2. This results in the following for P

¼ p

ð3:21Þ

By consideration of the geometry of the contact, it can be shown that the cross-sectional

area of the indentation is r

tan y

. The wear volume, dV

, produced in a sliding distance,

dx, by a single cone, is therefore given by

¼ r

tan y

dx ð3:22Þ

Combining wi th Eq. (3.21), integrating and summing over the array, the following

expression is obtained total amount of wear, V, occurring for a sliding distance of x

V ¼

i¼1

tan y

()

x ð3:23Þ

It is possible to convert this form to one using the total load, P, by using an effective value

for tan y

, tan Y. This is deﬁned by the following equatio n:

P tan Y ¼

i¼1

tan y

ð3:24Þ

Using this effective value, the equation for V can be written as

V ¼

2 tan Y

Px ð3:25Þ

Combing the constants with tan Y, Eq. (3.20) is obtained.

Figure 3.15 Four single-cycle deformation mechanisms. (From Ref. 142, reprinted with permission

from ASM International.)

In Table 3.5, values of K for different values of Y are given. The equivalent included

cone angle an d surface roughness condition, as well as the range for some silicon carbide

abrasive papers, are also given in this table (58). These suggest that the nominal range for

K in typical situations is between 10

2

and 1. Empirical data from situations where this

form of wear is known to dominate indicate a narrower but similar range, 210

2

210

1

(59).

Empirical data also show that K is also affected by material properties and wear

mechanism. Conceptually, these effects can be taken into account by modifying the

relationship between indentation size and groove size. To account for these affects, it

is assumed that a proportionality relationship exists between the area of the groove

and the area of the indention, rather than being equal. This modiﬁes the expression for

tan Y to the following:

P tan Y ¼ e

i¼1

tan y

ð3:26Þ

In this expression, e is the ratio of the groove area to the indentation area, which can be

affected by material properties, such as ductility, toughness, and elasticity, and vary with

the mechanism. As a result, K, which is proportional to e, would also be inﬂuenced by these.

Figure 3.16 Changes in single-cycle deformation wear morphology as a function of increasing

load. ‘‘A’’, plowing, ‘‘B’’, wedge formation; ‘‘C’’, cutting. Load increases from A to C. (From

Ref. 62, reprinted with permission from ASME.)

K values tend to be higher for microcracking and cutting then for plowing and wedge

formation as a result of this effect. With microcracking cracks propagate beyond the

indention, which results in material being removed beyond the indentation. Studies have

indicated that the cracked area may be up to 10 the indentation area (60). Consequently,

for microcracking, e would be greater than 1, and could be as large as 10. For plowing,

wedge formation, and cutting, e would be less than or equal to 1, because of elastic

Figure 3.17 Examples of wear scar morphology on metal surfaces, resulting from various single-

cycle deformation mechanisms during sliding contact. ‘‘A’’–‘‘D’’, ‘‘F’’, and ‘‘G’’ are from three-

body abrasive wear situations. ‘‘E’’ is a wear scar resulting from a single sliding stroke between a

hard ball and a softer ﬂat. (‘‘A’’ from Ref. 152, ‘‘B’’ from Ref. 148, ‘‘C’’ & ‘‘D’’ from Ref. 65,

‘‘E’’ from Ref. 67, ‘‘F’’ & ‘‘G’’ from Ref. 64. ‘‘A’’, ‘‘B’’, ‘‘C’’, ‘‘D’’, ‘‘F’’, and ‘‘G’’ reprinted with

permission from ASME. ‘‘E’’ reprinted with permission from Elsevier Sequoia S.A.)

recovery. Any elastic recovery, which occurs, will result in the groove area being smaller

than the indentation area. As a result, e would be less than 1 and would become smaller

with larger degrees of recovery. With cutting, there is less recovery than with wedge

formation and plowing. Therefore, e would tend to be larger for cutting than either of

the two plastic deformation mechanisms. The difference between plowing and cutting is

illustrated in Fig. 3.19. In this ﬁgure, the area of the groove produced by a stylus in a softer

material is plotted as a function of attack angle. A transition from plowing and wedge

formation to cutting occurs at a critical attack angle, a

. In the cutting region, the groove

areas are larger and more sensitive to angle than in the plowing region.

Since deformation characteristic, such as ductility, toughness, and elasticity, tend to

be different with diff erent classes of materials, K can be different for different classes

of materials. K tends to be higher for brittle materials and lower for tougher and ductile

Figure 3.18 Model for single-cycle deformation wear.

Table 3.5 K Values for Different Cone Angles

Y (



) Cone angle (



) KR

(mm) Abrasive papers

0 180 0

0.1 179.8 0.001

0.7 179 0.008 0.01

1 178 0.01 0.1

5 170 0.06 1

10 160 0.1 # 600

20 140 0.2

30 120 0.4 10

45 90 0.6 # 100

60 60 1.1 100

75 30 2.4

80 20 3.6

85 10 7.3

materials. Such an effect on K is shown in Fig. 3.20. In this ﬁgure, wear rate for three

classes of materials is plotted as a function of hardness. For each class, the behavior with

hardness is that given by Eq. (3.20). However, the value for K is different for each class. The

large difference between carbon and the other two classes of materials is primarily related

to the poorer ductility of carbon. With carbons microcracking typically occurs, resulting in

additional material loss, while it does not with the metals or plastics. The smaller difference

between plastics and metals is a result of the difference between cutting and plowing. It has

Figure 3.19 The effect of attack angle on chip formation for a hard stylus sliding against a softer

metal surface. (From Ref. 176, reprinted with permission from Elsevier Sequoia S.A.)

Figure 3.20 The effect of hardness on the abrasive wear rate of different classes of materials. The

data are for two-body abrasion, using 100 mm SiC paper. (From Ref. 58.)

been shown that the following relationship exists between the coefﬁcient of friction, m, and

the angle at which the transition from plowing to cutting takes place, a

(61–65):

tanð90



 a

Þ

1  m

ð3:27Þ

Examination of this equation shows that lowering friction reduces the critical angle. Since

the coefﬁcient of friction with plastics is generally lower than with metals, cutting, which is

more severe, is a more likely mechanism for plastics than for metals.

Because of this relationship between the critical angle for cutting and friction, K can

also be affected by lubrication. Values of K tend to be a factor of two to ﬁve times higher

when lubrication is involved [(66); see Table 3.8]. There is also another possible explana-

tion or contributing factor for the increase in K with lubrication. In addition to its effect

on the critical attack angle, lubrication can also increase single-cycle deformation wear by

its effect on debris accumulation. When wear debris is trapped between or coat surfaces, it

tends to provide separation, reducing the amount of contact with and penetration by par-

ticles or asperities, as is illustrated in Fig. 3.21. Lubrication tends to remove debris and

prevent the buildup, which would result in more contact with the abrasives or asperities.

Single-cycle deformation mechanisms are not limited to asperities and particle con-

tacts. These mechanisms can also occur on a macro-scale and be associated with the gross

geometry of the contacting bodies (57,67–69). A necessary condition for these mechanisms

to occur is that the asperity, particle, or counterface be harder than the wearing surface.

This is illustrated by the sharp decrease in abrasive wear that occurs when the surface

becomes harder than the abrasive, as shown in Fig. 3.22. Consequently, making the sur-

face harder than the counterface or abrasives can eliminate these mechanisms.

As stated initially in this section, single-cycle deformation mechanisms can occur in

rolling and impact situations, as well as in sliding situations. These mechanisms follow the

same general trend as for sliding, as illustrated by the following equation for solid particle

erosion: [(70); see Sec. 3.8]

V ¼ K

ð3:28Þ

In this equation, M is the total mass of the particles producing the wear and v is particle

speed. K

is similar to K. It is a function of particle proﬁle, that is, sharpness, and material

properties and mechanism affect its value in the same manner as with K. It is also affected

by incident angle, because of changes in mechanisms (see Sec. 3.8).

Some major trends for single-cycle deformation wear mechanisms are: (1) they only

occur when the surface is softer than the counterface or particle, (2) wear volume is inver-

sely proportional to hardness, and (3) plastic deformation or ductile mechanisms are

milder than cracking or cutting. There is a fourth trend related to elasticity. Except for

the difference in elasticity between elastomers and other classes of materials, K is generally

not affected by differences in elasticity. K values with elastomers tend to be 0 or much

lower than with other materials for plowing and wedge formation as a result of their abil-

ity to recovery from very large strains. This difference in elasticity is usually not a signiﬁ-

cant factor with cutting and K values are unaffected for this mechanism (58).

Except in abrasive situations and some sliding situations involving soft materials and

very rough surfaces, that is, ﬁle-like surfaces, single-cycle wear mechanisms tend to become

less signiﬁcant as wear progresses. This is generally attributed to changes that take place as

a result of wear and the emergence of other mechanisms. Typical changes that contribute

to the reduction of single-cycle wear are reduction in the average junction stress and asso-

ciated penetration, as described in Sec. 3.2 on adhesion, increased conformity of surfaces,

and as well as strain-hardening with some materials. An example of this reduction in sig-

niﬁcance is shown in Fig. 3.23 for the case of lubricated sliding wear of Cu. As can be seen

in the ﬁgure, striations, indicative of plowing, are the dominant feature initially. As sliding

continues, these features become less pronounced and features indicative of repeated-cycle

deformation mechanism appear and become the dominant ones.

Figure 3.21 ‘‘A’’ shows the wear behavior of several polymers sliding against SiC-coated abrasive

paper. The decrease in wear rate with number of cycles is attributed to the accumulation of polymer

wear debris on the surface of the paper. The effect of this on the contact situation is illustrated in

‘‘B’’. The polymer ﬁlm tends to protect the surface from contact with the abrasive particles. (From

Ref. 156, reprinted with permission from Elsevier Science Publishers.)