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

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Wear scar morphology, similar to the stage three morphology observed with the Cu

single crystal, and cracks have been observed in many sliding systems (23,25,76,77,85–87).

While this is the case, the nature of the crack systems is frequently different. The micro-

graphs in Figs. 3.27 and 3.31 serve to illustrate these points. Many of the topological fea-

tures of the wear scars shown in these two ﬁgures are similar to those associated with

Figure 3.32 The morphology of the three stages of sliding fatigue wear observed in Cu. The initial

stage is shown in ‘‘A’’. The intermediate stage is shown in ‘‘B’’ and the ﬁnal, in ‘‘C’’.’’D’’, which is a

TEM of a region below the surface of the wear scar, shows the subsurface cracks found in the ﬁnal

stage. (From Ref. 20, reprinted with permission from Elsevier Sequoia S.A.)

stages three Cu wear. However, it is apparent that the crack systems in each of these three

cases are different. In Fig. 3.27, the cracks are near and parallel to the surface. This mode

was termed delamination wear and was described in terms of dislocation behavior (25,77).

In Fig. 3.31, cracks form at the base of extruded wedges or lips. This mode is sometimes

referred to as extrusion wear (87). In Fig. 3.32d, it can be seen that in low stress sliding

wear of Cu, the cracks had a more random orientation and extended well below the

surface.

Figure 3.32 (continued )

The crack systems found in sliding are generally different from those found under

rolling and impact conditions. Figure 3.30 shows some examples of the crack systems for

impact. The wear scar topography also varies with the situation, as can be seen by compar-

ing the micrographs in Figs. 3.24, 3.27, 3.31 and 3.32. For impact and rolling, features sug-

gestive of sliding are not evident. Also, in the case of rolling, the features tend to be coarser

or larger than typically found in sliding situations. The variation in crack systems and pa t-

terns can be related to the response of materials to different stress systems.

Because of this strong inﬂuence of stress on fatigue wear, it is worthwhile to consider

the nature of the stress syst ems associated with different contact situations, prior to dis-

cussing formulations for fatigue wear. Conceptually, the stress system occurring in a wear

contact can be separated into two parts. One part may be termed the macro-stress system

and is related to the overall geometry or shape of the contacting members, that is, the

features that relate to the apparent area of contact. The second part is the micro-stress sys-

tem and this is governed by local geometry associated with the asperities. This concept is

illustrated graphically in Fig. 3.34.

For the macro-system, there are two general types of contact situations which are

illustrated in Fig. 3.35. One is a conforming situation, such as a ﬂat against a ﬂat or

a sphere in a socket of the same radius. The second is a nonconforming contact situation,

such as a sphere against a plane, two cylinders in contact , or sphere in a socket of a large r

radius. For the conforming situation, the pressure distribution across the surface is

uniform and the stress level is highest on the surface, decreasing with distance from the

surface. For the nonconforming case, the situation is quite different. Hertz contact theory

shows that in this case the pressure is greatest in the middle of the contact and that the

maximum shear stress is below the surface at a dista nce of approximately a third of the

radius of the apparent contact area (83). It also has a value of approximately one-third

of the maximum contact pressure. In this case, signiﬁcant stress can occur well below

Figure 3.33 The number of cycles required to produce the second stage in the fatigue wear of Cu

as a function of shear stress. (From Ref. 20.)

the surface, up to depths comparable to contact dimens ions. The comparative nature of

these two contact situations is illustrated in Fig. 3.36.

When shear or traction is applied to the interface, the macro-stress system is modi-

ﬁed. The modiﬁcation is most signiﬁcant at or near the surface since the shear decays

rapidly as a function of depth (88). With m as the coefﬁcient of friction and q(x)asthe

pressure distribution, mq(x) is the traction across the contact. For the case of a conforming

contact, the maximum shear stress is on the surface and can be shown to be approximately

(0.25 þ m

)

1=2

, where q

is the contact pressure. For the nonconforming case, the max-

imum shear stress can occur either on the surface or beneath the surface, depending on the

Figure 3.34 General nature of the stress ﬁeld in contact situation, illustrating the relative effects

of contact geometry and asperities on stress.

Figure 3.35 Examples of conforming and nonconforming contacts. ‘‘A’’, a cylinder in a groove of

matching radius, ‘‘B’’, a ﬂat on a ﬂat, and ‘‘C’’, a sphere in a spherical seat of matching radius, are

examples of conforming contacts. ‘‘D’’, a cylinder in a hole of larger radius, ‘‘E’’, parallel cylinders,

and ‘‘F’’, a sphere on a ﬂat, are examples of nonconforming contacts.

value of m. For nonconforming contacts, the maximum shear stress on the surface is

approximately mq

, where q

is the maximum pressure. This is also the maximum shear

stress if m is greater than 0.3. If m is less than 0.3, it would be below the surface and

approximately 0.3q

. A consequence of this is that for a nonconforming contact situation,

lubrication cannot only modify the stress level but also the stress distribution, as illu-

strated by the ch ange in the location of maximum stress.

The pressure distribution associated with the macro-system can effect the load dis-

tribution across the asperities, as illustrated in Fig. 3.37. Since the pressure distributions

are different for conforming and nonconforming contact, the micro-stress systems for

these two general types of contact will also be different. For nonconforming contacts,

asperities in the center of the contact region will tend to be loaded higher than asperities

near the edges of the contact region. For conforming contacts, the loading will be more

uniform.

While asperities have curvature, the micro-stress ﬁelds can be of two types. If the

asperity is plastically deformed, the stre ss ﬁeld will have the characteristics of a conform-

ing contact. If elastically deformed, the stress ﬁeld will have the characteristics of a non-

conforming contact.

When considering stress in wearing contacts, a further aspect has to be recognized.

This is that wear generally changes the micro- and macro-geometrical features of the sur-

faces in contact. As a result, there can be changes in the two stress systems associated with

the contact. The magnitude of the stresses can change as a result of changes in the real and

apparent areas of contact, as well as the stress distribution. As discussed in Sec. 3.2, wear

Figure 3.36 Comparison of the stress ﬁelds associated with conforming and nonconforming

contacts.

also tends to reduce the plasticity index, implying that asperity deformations become more

elastic with wear (37). Wear will also cause an initial nonconforming contact to become a

conforming contact, changing the nature of the macro-stress system and increasing the

apparent area of contact, as illustrated in Fig. 3.38.

Different feat ures of the wear can be related to these two stress systems. For exam-

ple, grooving and striations in the direction of sliding can be related to the micro-stress.

Also, the general nature of the cracks and crack system can be related to these stress sys-

tems. The effect of the macro-stress system on crack formation, illustrated in Fig. 3.39, is

an example of this. Also, differences between the wear scars, which are shown in Figs. 3.24,

3.27 and 3.30–3.32, can be related to the stre ss conditions of the tests. In the examples

of sliding that are shown in Figs. 3.27 and 3.31 the contacts were conforming, that

is, ﬂat-against-ﬂat. They were also unlubricated and as a result the coefﬁcient of fric-

tion, m, was high. In these cases, the signiﬁcant stress would be conﬁn ed to a small region

near the surface, essentially at the asperity level and the micro-st ress system would be the

predominate system. In these cases near-surface cracking is found, as well as surface fea-

tures related to asperity contact. In the rolling contacts, the macro-geometry was noncon-

forming and there was negligible friction and traction. The initial geometry in the

experiments with Cu was also nonconforming and the tests were performed with lubrica-

tion, which resulted in a low value for m. In this case, the nonconforming nature of the

contact would remain until the end of the incubation period. At this point, material loss

would resul t in a change to a conforming contact. In these two situations, signiﬁcant stres-

ses would occur well beyond that near-surface region and the macro-stress would be sig-

niﬁcant. For the sliding wear of Cu, as shown in those ﬁgures, the micro-stress system

would become more signiﬁcant beyond the incubation period, since the geometry would

then become conforming. Also, the average stress level would decrease as a result of

increasing contact area. For impact the contacts were initially nonconforming and

approach conformity with wear. In these situations, wear behavior is related to the

Figure 3.37 Effects of the macro-contact stress distribution on asperity load distribution.

macro-stress system and signiﬁcant stresses occur well below the surface (75). In these

three cases, rolling, impact and low-stress sliding, sub-surface cracking is found and

damage related to asperity contact is not evident, except for the initial stages of sliding

wear.

The main features of several of the models proposed for fatigue wear after the incu-

bation period can be illustrated by the consideration of an idealized and simple model.

Assume that the sliding system can be approximated by a smoot h, ﬂat surface of area,

, sliding against a ﬂat, rough surface, which has by an exponential distribution of aspe-

rities of different heights and a tip radius of b. Further, assume that the wear is conﬁned to

the smooth ﬂat surface. This situation is shown in Fig. 3.40. The key assumption in these

models is that the formation of a fatigu e wear particle can be described by Wohler’s equa-

tion for fatigue (89), namely,



ð3:31Þ

In this equation, N

is the number of cycles to failure at a stress level of S and S

is the

stress level required to pro duce failure in a single stress cycle. Both t and S

are material

dependent.

On the macro-scale, the contact situation considered is a conforming one. Hence, the

principal stre ss system will be associated with the asperity contact conditions. In a fatigue

wear situation, any init ial plastic loading conditions would modify asperi ty geometry so

that the material would respond elastically in subsequent load cycles. Consequently, it

is generally assumed for fatigue wear that the asperity contacts can be described by elastic

contact theory. In the assumed situation, the asperity contacts can be approximated by a

sphere pressed against a ﬂat surface, a situation that is covered by Hertzian contact theory

(83). The principal equations governing this situation are:

¼ 0:58P

01=3

2=3

2=3

ð3:32Þ

¼ 0:91P

01=3

1=3

1=3

ð3:33Þ



1  v



1  v



ð3:34Þ

Figure 3.38 The changing nature of the contact situation that occurs in the case of a hard steel

sphere sliding against a soft copper ﬂat.

where q

is the maximum contact pressure at the asperity contact, a

, the radius of the con-

tact spot, P

, the load on the asperity, and E’s and n ’s, the Young’s modulus and Poisson’s

ratio for the two materials in contact. Assuming that the load is uniformily distributed

Figure 3.39 Examples of the inﬂuence of the nature of the stress system on crack formation. (From

Ref. 63.)

over the asperities,

ð3:35Þ

where P is the load between the two surfaces and F is the number of asperities per unit

area in contact a t load P.

While shear stress is frequently related to fatigue behavior, some studies have indi-

cated that, in the case of wear, it can be correlated with the maximum tensile stress, which

occurs at the leading edge of the contact area (90). This is not signiﬁcant in the develop-

ment of the model since both are proportional to the maximum contact pressure. The

maximum shear stress is either mq

or 0.31q

with the former occurring at the interface

and the latter at a distance of approximately 0.3a

below the asperity tip. The maximum

tensile stress is approximately 0.5mq

. All of these cases can be covered by the following

relationship:

S ¼ Gq

ð3:36Þ

In this form, G can be viewed as an empirical ly determined coefﬁcient, which is material

dependent. Ultimately, a zone of the surface will experience enough loading cycles so that

a free particle will form. Assuming that the dimensions of this particle can be approxi-

mated by the dimensions of the region of signiﬁcant stress under the contact, the volume

of the fragment may be estimated. This may be approximated as a spherical shell of dia-

meter 2a

and depth 0.3a

. In that case it can be shown that the volume of the wear frag-

ment, v

, is given by

0:36P



ð3:37Þ

For a sliding distance of L the number of stress cycles the surface will experience is given

by LF

1=2

. The number of times a wear fragment will form during this amount of sli ding is,

therefore, LF

1=2

and the total volume, V, that is lost is given by

V ¼

3=2

ð3:38Þ

Using the relationships developed for ﬂat rough surfaces, it can be shown that for an expo-

nential distribution of asperity heights with a standard deviation of s, F is given by the

Figure 3.40 Contact situation between a smooth surface and a rough surface, used in the develop-

ment of a fatigue wear model. It is assumed that the rough surface can be characterized by an asper-

ity distribution of different heights but the same tip radius.