7
Wear Mechanisms
7.1
7.2
Koji Kato
Tohoku University
7.3
7.4
7.5
Adhesive Wear • Abrasive Wear • Fatigue Wear • Corrosive
Wear • Mechanical Wear of Ceramics under Elastic Contact
Koshi Adachi
Tohoku University
7.1
Introduction
Change of Wear Volume and Wear Surface Roughness
with Sliding Distance
Ranges of Wear Rates and Varieties of Wear Surfaces
Descriptive Key Terms
Survey of Wear Mechanisms
7.6
Concluding Remarks
Introduction
Wear has been recognized as meaning the phenomenon of material removal from a surface due to
interaction with a mating surface. Almost all machines lose their durability and reliability due to wear,
and the possibilities of new advanced machines are reduced because of wear problems. Therefore, wear
control has become a strong need for the advanced and reliable technology of the future.
Wear rate changes drastically in the range of 10–15 to 10–1 mm3/Nm, depending on operating conditions
and material selections (Archard, 1953; Bhansali, 1980; Hirst, 1957; Hokkirigawa, 1997; Holm, 1946;
Lancaster, 1978; Rabinowicz, 1980). These results mean that design of operating conditions and selection
of materials are the keys to controlling wear. As one way to meet these requirements, wear maps have
been proposed for prediction of wear modes and wear rates (Lim and Ashby, 1987; Hokkirigawa and
Kato, 1988). A wear map is considered one of the best descriptions of tribological conditions and is useful
in selecting materials in a wide range of operating conditions.
In order to design tribosystems and select materials based on the wear map, an understanding of wear
rate, varieties of wear modes, and wear mechanisms is essential.
Wear is the result of material removal by physical separation due to microfracture, by chemical
dissolution, or by melting at the contact interface. Furthermore, there are several types of wear: adhesive,
abrasive, fatigue, and corrosive. The dominant wear mode may change from one to another for reasons
that include changes in surface material properties and dynamic surface responses caused by frictional
heating, chemical film formation, and wear.
Wear mechanisms are described by considering complex changes during friction. In general, wear does
not take place through a single wear mechanism, so understanding each wear mechanism in each mode
of wear becomes important.
Our present understanding of the mechanisms of the four representative wear types is described in
the following sections.
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FIGURE 7.1
Three representative types of wear curves in repeated contacts.
FIGURE 7.2
Three representative types of surface roughness changes in repeated contacts.
7.2
Change of Wear Volume and Wear Surface Roughness
with Sliding Distance
Wear volume, wear surface roughness, and wear particle shape give us important information in characterizing wear.
Three representative types of wear volume curves are shown schematically in Figure 7.1. Type I shows
a constant wear rate throughout the whole process. Type II shows the transition from an initially high
wear rate to steady wear at a low rate. This type of wear is quite often observed in metals (Chiou et al.,
1985). Type III shows catastrophic transition from initial wear of low wear rate to wear of a high rate,
such as fatigue fracture. This type of wear is often observed in ceramics (Cho et al., 1989). The amount
of sliding before catastrophic wear is the period at which crack initiation takes place and depends on the
initial surface finish, material properties, and frictional conditions.
On the other hand, three representative types of roughness curves on wear surfaces are shown in
Figure 7.2. Type I shows the case of steady wear, where the surface roughness does not change from the
initial value. Type II shows the case of steady wear, where surface roughness increases to a certain value
and stays there. Type III illustrates initial running-in and steady wear, where surface roughness decreases
drastically in the running-in process. It is typically observed in lapping and polishing for surface finishing.
7.3
Ranges of Wear Rates and Varieties of Wear Surfaces
In general, wear is evaluated by the amount of volume lost and the state of the wear surface. The degree
of wear is described by wear rate, specific wear rate, or wear coefficient. Wear rate is defined as wear
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FIGURE 7.3 Distribution of specific wear rate of metallic materials in sliding contact under different lubrication
conditions. (Data from Archard, 1953; Bhansali, 1980; Hirst, 1957; Hokkirigawa, 1997; Holm, 1946; Lancaster, 1978;
Rabinowicz, 1980).
FIGURE 7.4
themselves.
Distribution of specific wear rates and friction coefficients of ceramics in unlubricated sliding against
volume per unit distance, which corresponds to the slope of the wear volume curve shown in Figure 7.1.
Specific wear rate is defined as wear volume per unit distance and unit load. Wear coefficient is defined
as the product of specific wear rate and the hardness of the wearing material.
The distributions of specific wear rates of metallic materials in sliding contact under different lubrication conditions are summarized in Figure 7.3 (Archard, 1953; Bhansali, 1980; Hirst, 1957; Hokkirigawa,
1997; Holm, 1946; Lancaster, 1978; Rabinowicz, 1980). Observed specific wear rates show a wide distribution in the range of 10–15 to 10–1 mm3/Nm by the differences in lubrication states. Figure 7.4 shows
the distributions of specific wear rates and friction coefficients measured in unlubricated sliding of four
kinds of ceramics against themselves under different normal loads, sliding velocities, and temperatures.
The specific wear rates range from 10–9 to 10–2 mm3/Nm, depending on materials and friction conditions,
even in the case of contact between similar materials.
Figure 7.5 shows the varieties of wear surfaces of ceramics observed under different contact conditions.
Wear surfaces look quite different depending on materials and friction conditions. This means that wear
can change drastically when small changes in contact conditions are introduced into the tribosystem.
The results shown in Figures 7.3, 7.4, and 7.5 clearly illustrate the following remark about wear (Bayer,
1994):
“Wear is not a material property. It is a system response.”
Wear changes drastically even with a relatively small change in a tribosystem, which is composed of
dynamic parameters, environmental parameters, and material parameters.
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FIGURE 7.5 Variety of worn surface morphologies of three kinds of ceramics under different operating conditions.
The arrows indicate relative sliding directions of counterfaces.
7.4
Descriptive Key Terms
There are many terms used to describe wear, and they are not always well differentiated. This sometimes
makes understanding wear mechanisms confusing and difficult. Further effort must be given to achieve
greater clarity in our approach to the analysis of wear mechanisms.
In this section, descriptive key words of wear and their interrelations are summarized. This summary
is shown in Figure 7.6
Wear is sometimes investigated from the viewpoint of the types of contact interaction of solid surfaces.
There are many different contact configurations in practice. Normal or inclined compression and detachment,
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FIGURE 7.6
Descriptive key words of wear and their interrelations.
unidirectional sliding, unidirectional rolling, reciprocal sliding, reciprocal rolling, and rolling with slip
are all different contact configurations classified from the viewpoint of motion of contacting bodies.
Furthermore, free solid particles sometimes become unique substances, which attack interacting surfaces.
This is also a contact configuration.
Wear in these contact types is described as sliding wear, rolling wear, impact wear, fretting wear, or
slurry wear. These descriptions of wear are all technical and based on the appearance of the contact type.
They do not represent wear mechanisms in a scientific way.
In order to focus on the wear mechanisms from the viewpoint of contact configurations, apparent
and real contact conditions at the contact interface are introduced without particularizing about these
contact configurations. Severity of contact, such as elastic contact or plastic contact, is the simplest and
most direct way to think about wear mechanisms, and is a tribosystem response determined by dynamic
parameters, material parameters, and atmospheric parameters.
The following four wear modes are generally recognized as fundamental and major ones (Burwell,
1957/58):
1.
2.
3.
4.
Adhesive wear
Abrasive wear
Fatigue wear
Corrosive wear
Adhesive wear and abrasive wear are wear modes generated under plastic contact. In the case of plastic
contact between similar materials, the contact interface has adhesive bonding strength. When fracture is
supposed to be essentially brought about as the result of strong adhesion at the contact interface, the
resultant wear is called adhesive wear, without particularizing about the fracture mode.
In the case of plastic contact between hard and sharp material and relatively soft material, the harder
material penetrates to the softer one. When the fracture is supposed to be brought about in the manner
of micro-cutting by the indented material, the resultant wear is called abrasive wear, recognizing the
interlocking contact configuration necessary for cutting, again without particularizing about adhesive
forces and fracture mode.
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In the case of contact in the running-in state, fatigue fracture is generated after repeated friction cycles.
When surface failure is generated by fatigue, the resultant wear is called fatigue wear.
In the case of contact in corrosive media, the tribochemical reaction at the contact interface is
accelerated. When the tribochemical reaction in the corrosive media is supposed to be brought about by
material removal, the resultant wear is called corrosive wear. In air, the most dominant corrosive medium
is oxygen, and tribochemical wear of metals in air is generally called oxidative wear.
Fatigue wear and corrosive wear can be generated in both plastic and elastic contacts.
The material removal in adhesive, abrasive, or fatigue wear is governed by deformation and fracture
in the contact region, where fracture modes are fatigue, brittle, or ductile fracture. Such deformation
and fracture are generated by mechanically induced strains and stresses. Therefore, this type of wear is
generally described as mechanical wear.
The material removal in corrosive wear is governed by the growth of chemical reaction film or its
chisolution on wear surface, where chemical reactions are highly activated and accelerated by frictional
deformation, frictional heating, microfracture, and successive removal of reaction products.
This type of wear is generally described as chemical wear or tribochemical wear.
In some cases, material removal is governed by surface melting caused by frictional heating or by
surface cracking caused by thermal stress. These types of wear are described as thermal wear, where
frictional heating and partial high temperature govern the process.
The macroscopic classifications in terms of mechanical, chemical, and thermal wear are useful to a
comprehensive understanding of wear because almost all models of wear are included in these three
types. The descriptions of wear by different definitions are summarized in Figure 7.6 to show the relative
relations.
7.5
Survey of Wear Mechanisms
As the traditionally accepted representative wear modes, the four wear modes shown in Figure 7.7 are
considered, and the wear mechanisms based on those wear modes are explained in detail. In addition,
the wear mechanism based on mechanical wear of ceramics is explained.
7.5.1 Adhesive Wear
If the contact interface between two surfaces under plastic contact has enough adhesive bonding strength
to resist relative sliding, large plastic deformation caused by dislocation is introduced in the contact
region under compression and shearing. As a result of such large deformation in the contact region, a
FIGURE 7.7
Schematic images of four representative wear modes.
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crack is initiated and is propagated in the combined fracture mode of tensile and shearing. When the
crack reaches the contact interface, a wear particle is formed and adhesive transfer is completed. This
type of wear, which occurs when there is enough adhesive bonding at the contact interface, is called
adhesive wear.
7.5.1.1 Estimation of Adhesive Wear Volume
If it is assumed that the real contact is composed of n contact points of equal size and if a new contact
point is formed after the disappearance of the former one, the total number of contacts n stays constant
during sliding. By supposing a circular contact area of radius a, the possible volume of wear particles
generated after sliding the distance of 2a is assumed as the half sphere volume described by 2πa3/3. Based
on these assumptions, the possible wear volume V for n contact points after sliding the distance L is
given by:
L
2
V = n ⋅ πa 3 ⋅
3
2a
(7.1)
Since the normal contact pressure with plastic deformation is almost equal to the hardness value H
of the wearing material, the total real contact area for n contact points nπa2 is expressed by:
nπa 2 =
W
H
(7.2)
By substituting Equation 7.2 into Equation 7.1, possible wear volume V under normal load W after
sliding distance L is given by:
1 WL
V= ⋅
3 H
(7.3)
Equation 7.3 shows that the adhesive wear volume is proportional to the normal load and the sliding
distance, and is inversely proportional to the hardness of the wearing material. Considering the relationship of Equation 7.2, it is proportional to the total real contact area during sliding.
In practice, however, adhesive wear can occur through various modes, as shown in Figure 7.8 (Kayaba
and Kato, 1981), and the size of the wear particles does not simply correspond to the size of the contact.
Furthermore, a wear particle is not always generated only from the relatively soft material but can come
from both materials. The probability of wear particle generation at each contact point is also not equal.
It depends on the microscopic shape of the contact, microstructure of the material in the contact region,
microscopic surface contamination, and other disturbances in the surroundings.
In order to accommodate all these variables, a parameter Kad is introduced in Equation 7.3 as a modifier,
and the wear volume is described by:
V = K ad ⋅
WL
H
(7.4)
where Kad is called the wear coefficient for adhesive wear. It is a principal value for a friction pair to
describe its wear rate. The physical meaning of Kad is the wear volume fraction at the plastic contact
zone, and it is strongly affected by the material properties and the geometry of the zone in compression
and shearing.
In the adhesive wear of metals (Archard, 1953; Hirst, 1957), wear coefficient Kad varies between 10–7
and 10–2 depending on the operating conditions and material properties. It should be recognized that a
wear coefficient Kad is not a constant value but is a possible value in the range of adhesive wear rate.
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FIGURE 7.8 Schematic diagram of representative adhesive transfer process observed in the adhesive wear process;
adhesive transfer of a thin flake-like wear particle (a) and a wedge-like wear particle (b). (From Kayaba, T. and Kato,
K. (1981), The adhesive transfer of the slip-tongue and the wedge, ASLE Trans., 24, 2, 164-174. With permission.)
7.5.1.2 Adhesive Wear Mode
Tangential shear under compression at the contact interface of strong adhesive bonding generates slips
along slip planes in the contact region. As a result of the slips, flake-like shear tongues are formed, as
shown in Figure 7.8a, and are followed by a crack initiation and propagation in the combined fracture
mode of tensile and shear in the leading region of the contact. The large plastic deformation in the
contact region sometimes forms a wedge-like shape, which is followed by crack initiation and propagation
in the combined fracture mode of tensile and shear in the trailing region of the contact, as shown in
Figure 7.8b.
Fractographic analysis of the fracture surfaces of wear particles of Figure 7.8a and b indicates that the
larger part of the fracture surface of the flake-like wear particle shows the fracture mode of compression
and shear, and that all parts of the fracture surface of the wedge-like wear particle in Figure 7.8b shows
a tensile and shear fracture mode. Both wear modes which produce flake-like and wedge-like wear
particles are basic ones in adhesive wear.
In the adhesive wear process, transfer and retransfer from one surface to the mating surface take place
in many cases. As a result, relatively large wear particles composed of two surfaces are formed. This is
another basic part of the adhesive wear mechanism (Sasada, 1979).
In the successive process of repeated sliding, these wear particles leave the contact interface as free
particles or stay on either surface and form prows to scratch the counterface (Vingsbo and Hogmark,
1980; Chen and Rigney, 1985). Even if the contact is made between flat surfaces of similar materials and
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FIGURE 7.9 Abrasive wear of ductile material, which is dominated by plastic deformation (a) and one of brittle
fracture, which is dominated by brittle fracture (b). (From Evans, A.G. and Marshall, D.B. (1981), Wear mechanism
in ceramics, in Fundamentals of Friction and Wear of Materials, Rigney, D.A. (Ed.), ASM, 439. With permission.)
the contact interface is at first parallel to the sliding direction, the interface rotates and becomes inclined
and wavy as a result of the combined effect of normal and tangential forces in sliding (Cocks, 1962).
This is another aspect of deformation at a contact interface which explains why the adhesive wear mode
of Figure 7.8a or Figure 7.8b occurs commonly in practice.
7.5.2 Abrasive Wear
If the contact interface between two surfaces has interlocking of an inclined or curved contact, ploughing
takes place in sliding. As a result of ploughing, a certain volume of surface material is removed and an
abrasive groove is formed on the weaker surface. This type of wear is called abrasive wear.
Here, we assume a single contact point model where a hard, sharp abrasive is indented against the flat
surface and forms a groove on it by ploughing. When wearing material has a ductile property, a ribbonlike, long wear particle is generated by the mechanism of microcutting. In the case of brittle material,
however, a wear particle is generated by a crack propagation (Evans and Marshall, 1981). These differences
are summarized schematically in Figures 7.9a and b.
7.5.2.1 Abrasive Wear of Ductile Material
Even in the case of sliding contact between smooth surfaces of the same ductile material, parallel grooves
are generally found on the wear surface after sliding. The peak and the valley coincide well with the
mating surfaces, as shown in Figure 7.10. This result means that the hard abrasive asperities are formed
on the mating surface because of, for example, work hardening, phase transitions, and third-body
formation at the contact interface during repeated sliding contact. Therefore, abrasive wear is recognized
as a more representative wear mode of ductile material in repeated sliding.
7.5.2.1.1 Estimation of Abrasive Wear Volume
The first point to understand in the abrasive wear mechanism is the estimation of wear volume from
which wear particles can be generated. Here, we assume a simplified contact model in which the abrasive
has a conical shape with an angle θ, and the indentation depth of the abrasive is d, as shown in Figure 7.11.
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FIGURE 7.10
sliding.
The cross-sectional profiles of two mating wear surfaces of 0.45% carbon steel after pin-on-ring
FIGURE 7.11
Typical model of abrasive wear by a conical indentor.
Based on this assumption model, the possible wear volume V, which is ploughed by harder asperities
after sliding a distance of L, is given by:
V = d 2 ⋅ tan θ ⋅ L
(7.5)
Since the normal contact pressure under plastic contact can be assumed to be equal to the hardness value
H of the wearing material, real contact area of π(dtanθ)2/2 is expressed by:
(
)
2
1
W
π d ⋅ tanθ =
2
Hv
(7.6)
By substituting Equation 7.6 into Equation 7.5, possible wear volume V under normal load W and after
sliding distance L is given by:
V=
2
WL
⋅
π ⋅ tanθ H v
(7.7)
Equation 7.7 gives the wear volume for the case of ideally plastic abrasive grooving in microcutting
shown in Figure 7.12a. There are two other modes of wedge forming and ploughing in abrasive grooving,
as shown in Figures 7.12b and c (Hokkirigawa and Kato, 1988) where the wedge does not grow from its
initial size in Figure 7.12b, and no wear particles are generated in Figure 7.12c. It means that wear volume
in abrasive grooving is not always equal to the groove volume.
In order to accommodate all these meanings, a parameter Kab is introduced in Equation 7.7 as a
modifier, and the wear volume is described by:
V = K ab ⋅
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WL
H
(7.8)
FIGURE 7.12 Three different modes of abrasive wear observed by SEM: Cutting mode (a), steel pin on brass plate;
wedge-forming mode (b), steel pin on stainless steel plate; ploughing mode (c), steel pin on brass plate. (From
Hokkirigawa, K. and Kato, K. (1988), An experimental and theoretical investigation of ploughing, cutting and wedge
formation during abrasive wear, Tribology Int., 21, 1, 51-57. With permission.)
FIGURE 7.13 Effect of hardness on the relative wear resistance of pure metals. (From Khruschov, M.M. (1957),
Resistance of metals to wear by abrasion as related to hardness, Proc. Conf. Lubrication and Wear, Inst. Mech. Engr.,
655-659. With permission.)
Equation 7.8 shows that the abrasive wear volume is proportional to the normal load and the sliding
distance, and it is inversely proportional to the hardness of the wearing material. In fact, abrasive wear
resistance is linearly proportional to hardness of wearing metals, as shown in Figure 7.13 (Khruschov,
1957).
The proportional constant Kab is called the wear coefficient for abrasive wear. It is a principal value
for a friction pair in describing its wear rate. The physical meaning of Kab is the wear volume fraction
against the nominal groove volume zone, and it depends on the ductility of wearing material, shear
strength at the contact interface, and the shape of the abrasive asperity.
In the abrasive wear of metal (Rabinowicz, 1980), wear coefficient Kab varies between 10–4 and 10–1,
depending on the contact conditions and material parameters. It should be recognized from these data
that wear coefficient Kab is not a constant value in abrasive wear. By comparing Kab with Kad in adhesive
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FIGURE 7.14
Schematic diagram of effect of hardness ratio on wear rate of abraded material against abrasive.
wear, it is clear that abrasive wear gives a relatively large wear coefficient. That is why abrasive wear is
recognized as severe wear.
Abrasive grooving by the hard and sharp asperity is possible only when the asperity is not flattened
or fractured in sliding. Therefore, the abradability of the hard, sharp asperity must be evaluated.
7.5.2.1.2 Hardness Ratio and Shape of Abrasive Asperity
The hardness of the abrasive asperity is important in abrasive wear. Generally, when the hardness ratio r
(mating material hardness/abrasive hardness) stays below a certain critical value rc1 (0.5 to 0.8; Khruschov,
1974; Rabinowicz, 1983), abrasive wear clearly takes place. However, with the increase in hardness ratio r
above the critical value rc1, wear volume of mating material decreases, and finally almost no wear is
observed when r is close to a critical value rc2 (1 to 1.4; Rabinowicz, 1983). This relation is shown
schematically in Figure 7.14.
The results in Figure 7.14 require consideration as to the yield criterion of asperity in grooving action.
Theoretical analysis was made by the slip line field theory, and the critical condition for the yield of an
asperity is given in Figure 7.15 (Kayaba et al., 1983) between the hardness ratio r and the critical asperity
tip angle θc. The parameter f in Figure 7.15b is the ratio of the shear strength of the interface to the shear
strength of the softer material, and Figure 7.15a shows the relation at f = 0. Plastic grooving by the asperity
is possible when its tip angle θ is larger than the critical value θc, and this value changes depending on
the values of hardness ratio r of two surfaces and f, as shown in Figure 7.15b.
These figures show that the asperity with large θ can plough the mating surface even when the hardness
ratio r is very close to unity theoretically. This is evidence of the high possibility of groove formation at
the sliding interface between similar ductile materials.
7.5.2.1.3 Abrasive Wear Mode
As mentioned above, abrasive wear takes three different modes: microcutting, wedge forming, and
ploughing, as shown in Figure 7.12. Wear particles are formed differently depending on these three modes.
In the cutting mode, long and curled ribbon-like wear particles are formed. Low friction assists in this
wear mode. In the wedge-forming mode, a wedge-like wear particle is formed at the tip of the grooving
asperity as shown in Figure 7.12b and stays there working as a kind of built-up wedge to continue
grooving. Sliding takes place at the bottom of the wedge where adhesive transfer of a thin layer from the
underlying counterface continues to grow the wedge slowly. This wear mode appears as a combined effect
of adhesion at an inclined or curved contact interface and shear fracture at the bottom of the wedge.
High friction or strong adhesion assists in this wear mode. In the ploughing mode, a wear particle is not
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FIGURE 7.15 Relationship between the critical tip angle θc and the hardness ratio r where the normalized shear
strength f is zero in (a) and changes from zero to 1.0 in (b). (From Kayaba, T., Kato, K., and Hokkirigawa, K. (1983),
Theoretical analysis of the plastic yielding of a hard asperity sliding on a soft flat surface, Wear, 87, 151-161. With
permission.)
generated by a single pass of sliding and only a shallow groove is formed. Repeated sliding and accumulation of plastic flow at the surface is necessary for the generation of wear particles.
These three abrasive wear modes are theoretically predictable with two dimensional models of the slip
line field theory (Challen and Oxley, 1979). Theoretical predictions agree well with experimental results
of spherical pin-on-disk tests, which are shown in the abrasive wear mode diagram of Figure 7.16
(Hokkirigawa and Kato, 1988) by introducing the following parameter Dp for the degree of penetration:
Dp = R
 πH  2
πH
− 
 R −1
2W
 2W 
(7.9)
where R is the pin tip radius, H the hardness of the wearing material, and W the load. The parameter f
in Figure 7.16 has the same meaning as that in Figure 7.15. Theoretical solid lines are drawn according
to the theory (Challen and Oxley, 1979) by substituting the relationship of Dp = 0.8 (1 – cosθ)/sinθ where
θ is the attack angle.
In all these three abrasive wear modes, grooves are formed as the result of wear particle generation
and plastic flow of material to form ridges on both sides of a groove. If we introduce the groove volume
∆Vg per unit sliding distance observed below the initial surface level and the ridge volume ∆Vr per unit
sliding distance observed above the initial surface level on both sides of the groove, (∆Vg — ∆Vr) gives
the wear volume at one groove in one pass of sliding. With these descriptions, the concept of degree of
wear β at one groove is introduced, as shown in Figure 7.17 and is given as follows:
β=
∆Vg − ∆Vr
∆Vg
(7.10)
where β = 1 corresponds to the state of ideal material removal without forming ridges, and β = 0 means
the ideal ploughing of no material removal.
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FIGURE 7.16 Abrasive wear mode diagram: abrasive wear modes of ductile material as a function of degree of
penetration Dp and normalized shear strength f at the contact interface. Solid lines are theoretically induced with
modified two-dimensional model. (From Hokkirigawa, K. and Kato, K. (1988), An experimental and theoretical investigation of ploughing, cutting and wedge formation during abrasive wear, Tribology Int., 21, 1, 51-57. With permission.)
FIGURE 7.17 Schematic diagram of cross-sectional profile of groove formed after scratching. ∆Vg: groove volume
and ∆Vr: two side ridges’ volume of two sides.
The degree of wear β defined in this way is a function of the hardness H of the wearing material and
the degree of penetration Dp as shown in Figure 7.18 (Hokkirigawa and Kato, 1989) for heat treated
steels. This β is related to the abrasive wear coefficient Kab mentioned above at one groove as follows:
K ab = β
∆Vg H
W
(7.11)
It is clear in Equation 7.11 that β represents the fracture property of the wearing material and (∆VgH/W)
represents the deforming property of the wearing material under the effect of f and the shape of the
indentor.
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FIGURE 7.18 Degree of wear β as a function of degree of penetration Dp observed with heat-treated steel of different
hardness H (kgf/mm2). (From Hokkirigawa, K. and Kato, K. (1989), Theoretical estimation of abrasive wear resistance
based on microscopic wear mechanism, in Proc. Int. Conf. on Wear of Materials, ASME, pp. 1-8. With permission.)
The parameter β and ∆Vg are given from the result of a pyramidal scratch test as (Zum Gahr, 1987):
  H 1 3  ε  


β = 1 − exp −2 0  ln s  
 εc  
  H 

(7.12)
where H0 is the original hardness of the wearing material, H is the hardness after deformation by grooving,
εs is the strain on the groove surface, and εc is the strain above which material is removed from the
groove. εs in Equation 7.12 is given by:
 13 23
2
 W E 1 + 10µ
ε s = 2 ln 
6 HR2 3


(
)
12
θ
tan 
2



(7.13)
where E is the Young’s modulus of the wearing material, µ is the friction coefficient, θ is the angle of the
pyramid, and R is the tip radius of the pyramid:

W  1
∆Vg =  1 + 10µ 2
H 5

(
)
12

θ 
tan
π

HR 
2 − 1 
+



θ
2

W tan 
 
2
2
(7.14)
By introducing Equations 7.12, 7.13, and 7.14 into Equation 7.11, the wear coefficient Kab is expressed
theoretically in terms of material parameters, geometrical parameters, and frictional conditions of load
and friction coefficient. If the expression for volumetric is introduced by defining the inverse of wear
rate (sliding distance/wear volume), it is given by (β∆Vg)–1. The comparisons of experimental and
theoretical values of the volumetric wear resistance show good agreement, as shown in Figure 7.19 (Zum
Gahr, 1987).
The expressions of Equations 7.9 through 7.14 and Figures 7.15 through 7.19 are all for simple abrasive
scratching. But in practical abrasive contact, there are many abrasive contact points at the same time,
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FIGURE 7.19 Theoretical abrasive wear resistance vs. experimental abrasive wear resistance measured on different
materials by using a diamond scratch of attack angle θ = 90° and tip radius r = 8 mm under load W = 2N. (From
Zum Gahr, K.H. (1987), Microstructure and wear of materials, Tribology series, Elsevier, 132-148. With permission.)
FIGURE 7.20 Relationship between abrasive wear resistance and hardness of worn material observed experimentally
and estimated theoretically. (From Hokkirigawa, K. and Kato, K. (1989), Theoretical estimation of abrasive wear resistance
based on microscopic wear mechanism, in Proc. Int. Conf. on Wear of Materials, ASME, pp. 1-8. With permission.)
and each of them is at a different state of deformation and wear. Therefore, it becomes necessary to
introduce a model for the distribution of contact geometry, contact load, and the resultant abrasive wear
mode.
If we know the distribution of Dp at multiple abrasive contacts of a surface, the total wear rate of the
surface can be introduced by summarizing all the values of β at all contact points. Figure 7.20 (Hokkirigawa and Kato, 1989) shows the experimental data and theoretical solid and broken lines obtained
in this way. Good agreement of experimental data and theoretical lines is confirmed.
7.5.2.2 Abrasive Wear of Brittle Material
In the case of brittle material, which is indented and ploughed by the abrasive, a wear particle is generated
due to mainly brittle fractures caused by initiation and propagation of cracks, such as the median and
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FIGURE 7.21 Relationship between abrasive wear resistance and fracture toughness of yttria-doped zirconium
oxide. (From Fischer, T.E., Anderson, M.P., and Jahanmir, S. (1989), Influence of fracture toughness on the wear
resistance of yttria-doped zirconium oxide, J. Am. Ceram. Soc., 72, 2, 252-257. With permission.)
FIGURE 7.22
Abrasive wear model for brittle material.
lateral cracks shown in Figure 7.10b. Therefore, wear rate of the brittle material is strongly dependent
on fracture toughness. Figure 7.21 (Fischer et al., 1989) shows the effect of fracture toughness on the
wear rate of zirconium oxide under abrasive contact. It is clear that fracture toughness is an important
parameter to determine the abrasive wear rate of the brittle material.
Wear volume in scratching the brittle material is described by the model shown in Figure 7.22 (Evans
and Marshall, 1981). It is assumed that a wear particle is generated by lateral crack propagation which
© 2001 by CRC Press LLC
reaches to the surface. If the crack is propagated by the residual stress, crack length c is defined by the
function of normal load W, fracture toughness Kc, hardness H, and Young’s modulus E as follows:
c = α1
W5 8  E 
 
K c1 2 H 1 8  H 
35
(7.15)
where α1 depends on the shape of the abrasive and is determined by calibration on a material with wellcharacterized fracture properties.
The depth b of lateral fracture is estimated by the radius of plastic contact zone, and is given by:
E
b = α2  
H
2 5
W 
 
H
12
(7.16)
where α2 is a material-independent constant.
Based on these assumptions, the wear volume V in scratching of the brittle material with a hard asperity
is given by the following equation:
V = α3
W9 8  E 
 
K c1 2 H 5 8  H 
4 5
L
(7.17)
where L is the sliding distance and α3 is a material-dependent constant determined by calibration on a
material with well-characterized fracture properties.
Another analysis (Evans and Wilshaw, 1976) on a similar model with different assumptions gives a
slightly different equation of abrasive wear volume of brittle materials as follows:
V = α4
W5 4
L
K c3 4 H 1 2
(7.18)
where α4 is a constant.
It is clear from Equations 7.17 and 7.18 that abrasive wear rate depends strongly on both hardness
and toughness. Wear rate predicted by both equations agrees well with experimental data, as shown in
Figure 7.23 (Evans and Marshall, 1981) and Figure 7.24 (Buljan and Sarin, 1985).
7.5.3 Fatigue Wear
Repeated cycles of contact are not necessary in adhesive and abrasive wear for the generation of wear
particles. There are other cases of wear where a certain number of repeated contacts are essential for the
generation of wear particles. Wear generated after such contact cycles is called fatigue wear. When the
number of contact cycles is high, the high-cycle fatigue mechanism is expected to be the wear mechanism.
When it is low, the low-cycle fatigue mechanism is expected.
7.5.3.1 Fatigue Wear in Rolling and Sliding Contact under Elastic Contact
In the case of the elastic contact generally observed in rolling elements, the main wear mechanism is
high-cycle fatigue fracture in the contact region. The critical number of rolling cycles Nf for the generation
of wear particles by spalling or flaking is given experimentally as follows (Lundberg and Palmgren, 1952):
Nf ∝
© 2001 by CRC Press LLC
1
Wn
(7.19)
FIGURE 7.23 Correlation between abrasive wear resistance and (hardness)5/8 × (toughness)1/2. (From Evans, A.G.
and Marshall, D.B. (1981), Wear mechanism in ceramics, in Fundamentals of Friction and Wear of Materials, Rigney,
D.A. (Ed.), ASM, 439. With permission.)
FIGURE 7.24 Relationship between abrasive wear resistance and (toughness)3/4 × (hardness)1/2. (From Buljan, S.T.
and Sarin, V.K. (1985), The future of silicon nitride cutting tools, Carbide Tool J., May/June, 4-7. With permission.)
where W is the normal load and n is a constant which depends on the shape of the rolling element. In
the case of rolling bearings, the value of n is about 3.
This empirical law has been widely accepted in the design of rolling bearings. Its basic premise is that
spalling or flaking can be treated as statistical fracture phenomena following the modified theory (Weibull,
1930).
Although the apparent practical contact pressure is not so high as to introduce yield in the contact
region, local yield is generated in the contact region because of the existence of microdefects in the
material. A single crystal has slip planes for preferential sliding under shear stress. A polycrystal has grain
boundaries, inclusions, and vacancies. Because of these inhomogeneities, the local stress in the contact
© 2001 by CRC Press LLC
FIGURE 7.25 The change in the hardness distribution beneath the surface during the repeated rolling of steel
(0.45C, 0.27 Si, 0.85 Mn). (From Kayaba, T. and Suzuki, S. (1976), An investigation of surface damages by rolling
contact, Technology Report, Tohoku Univ., 41, 1, 21-46.)
region exceeds the yield stress of the material even when the theoretical stress for the homogeneous
material does not exceed the yield stress (Dufrane and Glaeser, 1976).
There is a state where a plastically deformed region appears beneath the interface without reaching
the surface. In this case, work hardening takes place in the yield region as a result of repeated contact.
This is shown in Figure 7.25 (Kayaba and Suzuki, 1976), where the hardness peak is located about 130 µm
beneath the surface, and the value of maximum hardness increases with an increase in the number of
rolling cycles. The maximum hardness value of about 400 kgf/mm2 is reached after about 2 × 106 cycles,
when pits start to appear on the surface.
Repeated friction under elastic or elastoplastic contact causes the accumulation of local plastic strain
around some stress concentration points, and cracks are generated after reaching a certain number of
frictional cycles. The mechanism of crack initiation and propagation in such a situation is that of fatigue
fracture, which is a kind of rate process controlled by the inhomogeneity of the microstructure of a
material.
7.5.3.2 Fatigue Wear in Sliding Contact under Plastic Contact
In the friction between metallic materials, conformity at the contact interface without catastrophic wear
is easily observed as the ploughing mode shown in Figure 7.12c (Hokkirigawa and Kato, 1988). In this
mode, a wear particle is not generated by a single pass of sliding and only a shallow, conformable groove
is formed. In the case of repeated contact of abrasive sliding at the same grooves, plastic burnishing
(ploughing mode in Figure 7.12c) becomes predominant. In this ploughing mode, fatigue fracture is
expected to take place after a critical number Nf of plastic strain cycles in the wave.
Figure 7.26 (Akagaki and Kato, 1987) shows the effect of repeated sliding on the growth of plastic flow
wear particles of steel under boundary lubrication. It is seen that a thin surface layer protrudes in the
© 2001 by CRC Press LLC
FIGURE 7.26 Flow wear process for steel during repeated sliding in boundary lubrication. (From Akagaki, T. and
Kato, K. (1987), Plastic flow process of surface layers in flow wear under boundary lubricated conditions, Wear, 117,
179-196. With permission.)
FIGURE 7.27 Amount of flow wear of the surface layer as a function of sliding cycles under the same sliding
conditions. (From Akagaki, T. and Kato, K. (1988), Simulation of flow wear in boundary lubrication using Vickers
indentation method, STLE, Trib. Trans., 31, 3, 311-316. With permission.)
direction of sliding, and grows as the number of sliding cycles increases. Figure 7.27 shows the amount
of plastic flow of the surface layer as a function of the sliding cycles for the two different contact pressures
(Akagaki and Kato, 1988). The flow rate observed is a few micrometers per 104 cycles of sliding. Conforming between two sliding surfaces occurs by this gradual surface plastic flow and wear in metallic
triboelements. This phenomenon is representative of low fatigue wear under plastic contact.
© 2001 by CRC Press LLC
If we suppose that the plastically deformed layer is detached as wear particles by low-cycle fatigue
failure, Nf would be given by the modified Coffin–Manson relationship:
 C 
Nf =  s 
 ∆γ s 
D
(7.20)
where Cs is the monotonic effective shear strain, ∆γs is the effective shear strain increment per wave pass,
and D is a constant usually taken as 2.
By considering the plastic work needed to produce unit volume of wear and introducing the relationship of Equation 7.20, the specific wear rate ws defined by wear volume/load/distance is described by
Challen et al. (1986) as follows:
ws =
rpµ
kC ∆γ 1s− D
D
s
(7.21)
where rp is the ratio of plastic to total work of sliding and k is the average shear flow stress of the wearing
material. By introducing the relation of k = H(Hardness)/(3 × 31/2) into Equation 7.21, the fatigue wear
coefficient Kf, defined in the same way as Kad and Kab mentioned above, can be expressed as:
K f = ws H =
3 × 31 2 rpµ
C D ∆γ 1s− D
(7.22)
The three parameters of ∆γs, rp, and µ are functions of the attack angle α (= π/2 – θ), where θ is defined
in Figure 7.11, and the normalized shear strength f. The parameter f has the same meaning as in
Figures 7.15 and 7.16; it is the ratio of shear strength τ at the contact interface to the shear flow stress k
of the wearing material, i.e., f = τ/k. From Figure 7.28 (Challen et al., 1986), which shows the calculated
values of Kf by changing the values of θ and f, it can be seen that Kf is predicted to vary in the range
from 10–6 to nearly 1 for α and f values ranging from 0.1° to 10° and from 0 to 0.99, respectively.
The contact between a hard asperity and a groove generally becomes milder in repeated sliding as a
result of deformation and wear in the groove surface layer. Better conformity between asperity and groove
surfaces is attained where the contact pressure is decreased and elastic strains have to be considered. If
the maximum Hertzian contact pressure is above the critical value of the elastic shakedown limit in an
elastic–plastic half-space of the wearing body, repeated plastic deformation takes place in the form of
“cyclic plasticity” or “ratcheting” (Johnson, 1994). In cyclic plasticity, a cycle of axial plastic strain which
comprises a reversing (fatigue) component ∆εa acts parallel to the surface. If it were acting alone, the
number Nf of cycles to surface failure would be given by the Coffin–Manson relationship as follows:
 2C 
Nf = 

 ∆ε a 
2
(7.23)
where C is the monotonic fracture strain.
In ratcheting, unidirectional plastic shear strain ∆γr per cycle acts and is accumulated until the total
strain reaches a critical value C where surface failure is generated. The number Nr of cycles to failure in
ratcheting is given by Johnson (1994) and Kapoor and Johnson (1994) as:
 C 
Nr = 

 ∆γ r 
(7.24)
where ∆γr is the ratcheting shear strain per cycle. In this ratcheting region, however, it is not quite clear
whether ultimate failure would be caused by fatigue or by ductile fracture. It would be reasonable to
© 2001 by CRC Press LLC
FIGURE 7.28 Variation of wear coefficient Kf in sliding friction assuming a low-cycle fatigue wear mechanism with
attack angle α and normalized shear strength f. (From Challen, J.M., Oxley, P.L.B., and Hockenhull, B.S. (1986),
Prediction of Archard’s wear coefficient for metallic sliding friction assuming a low cycle fatigue wear mechanism,
Wear, 111, 275-288. With permission.)
suppose that each fatigue wear mode described by Equation 7.20, 7.23, or 7.24 has the possibility of being
the prevailing wear mode depending upon the contact condition, and two or three of them may coexist
in some cases. Careful experimental observation (Black et al., 1996) gives the value of D = 1.67, which
suggests the possibility of a mixture of these two modes of fatigue wear.
7.5.4 Corrosive Wear
When sliding takes place, especially in corrosive liquids or gases, reaction products are formed on the
surface mainly by chemical or electrochemical interactions. If these reaction products adhere strongly to
the surface and behave like the bulk material, the wear mechanism should be almost the same as that of
the bulk material. In many cases, however, such reaction products behave very differently from the bulk
material. Therefore, wear is quite different from that of the bulk material, and is dominated by the
reaction products formed by the interaction of solid materials with the corrosive environment. This kind
of tribochemical wear accelerated by corrosive media is called corrosive wear.
In corrosive wear, tribochemical reaction produces a reaction layer on the surface. At the same time,
such layer is removed by friction. Therefore, relative growth rate and removal rate determine the wear
rate of the reaction layers and, as a result, of the bulk material. Therefore, models of the reaction layer
growth and those of the layer removal become very important.
7.5.4.1 Oxidative Wear of Metals
Oxidative wear is the most representative mode of corrosive wear of metals. Based on the oxidative
reaction between steel and normal atmospheric air and assuming the film removal model where an oxide
film of steel is supposed to detach from the surface at a certain critical thickness, corrosive wear coefficient
Kc defined in the same way as Kad and Kab has been expressed by Quinn (1987) as:
Kc =
© 2001 by CRC Press LLC
 Q 
dA
exp  −

2 2
ξρv
 RgT 
(7.25)
where A is the Arrhenius constant, Q the activation energy, Rg the gas constant, T the absolute temperature, ρ the density of oxide, v the sliding velocity, and L the distance along which a wearing contact is
made.
It is generally assumed that activation energy does not vary substantially between static and sliding
conditions. Making this assumption, the experimental wear results for oxidation of steels give a value of
the Arrhenius constant in Equation 7.25 which is 103 – 1010 times larger than one in static oxidation
(Quinn, 1987). This means that oxidation is much more rapid under sliding contact than in the static
condition. This seems to be supported by another experimental result where the thickness of oxidative
wear layers of steel and titanium are more than 500 times larger than those grown under static conditions
(Krause and Scholter, 1978). Therefore, estimation of real activation energy at the sliding surface becomes
important.
Furthermore, the real temperature at the real contact interface is important in the determination of
the wear rate, because the reaction rate required to form a chemical product is strongly affected by the
temperature induced by friction.
On the other hand, if the reaction rate is not high enough to grow an oxide film to the critical thickness
within a cycle of sliding, oxidative wear of the steel may not occur. Even in this case, the reaction rate
also determines the wear rate.
7.5.4.2 Oxidative Wear of Ceramics — Tribochemical Wear of Ceramics
The hydroxide of silicon nitride in water is very weakly bonded on the surface, is easily removed from
the surface by rubbing, and it dissolves in water (Fischer and Tomizawa, 1985). If the reaction rate is
high, a lot of silicon nitride hydroxide can be formed and worn away quickly. The reaction rate determines
the wear rate in this case.
If it is assumed that friction heating also accelerates chemical reaction at the contact interface, the
wear coefficient Kc of nonoxidative ceramics sliding against themselves is explained by Kitaoka et al.
(1997) as:
Kc =
 Q 
Ac
exp −

ρv
 RgT 
(7.26)
where Q is the activation energy, Rg the gas constant, T the reaction temperature, ρ the density of oxide,
and v the sliding velocity.
It is clear from both models (Quinn, 1967; Kitaoka et al., 1997), that the corrosive wear mechanism
is difficult to understand without first understanding the process of the formation of the reaction layer
from the viewpoint of the combined effect of mechanical activation and chemical reaction, namely, from
the viewpoint of tribochemistry.
7.5.5 Mechanical Wear of Ceramics under Elastic Contact
In the contact of ceramics, wear particles are generated mechanically without the mechanism of fatigue
wear even under elastic contact. It is the wear governed by the microscopic brittle fracture at surface
microcracks under nominal elastic contact. This is the representative wear mechanism of ceramics when
specific wear rate is larger than 10–6 mm3/Nm (Adachi et al., 1997).
Figure 7.29 shows a schematic diagram of the model, where a wear particle is generated by the
propagation of a predominant surface crack in brittle manner. Such crack propagation can be enhanced
by the tensile stress induced by friction under elastic contact.
Based on the linear elastic fracture mechanics model, the critical condition for the crack propagation
is expressed by the following equation:
Bσ max πd ≥ K c
© 2001 by CRC Press LLC
(7.27)
µp
Hertzian Contact
(a)
Tensile stress
(b)
(c)
(d)
FIGURE 7.29 Wear model of brittle material, in which wear particles are generated by propagation of preexistent
crack under elastic sliding contact: (a) sliding contact under elastic contact; (b) application of tensile stress to crack
tip; (c) propagation of crack; and (d) generation of wear particle.
where σmax is the maximum tensile stress at the crack tip, d preexistent crack length, Kc fracture toughness
of the wearing material, and B constant.
Sliding generates the friction force which introduces the shear stress at the contact interface in addition
to the compressing stress. As the result, the maximum tensile stress σmax is induced at the trailing edge
of the contact, which is expressed by the following equation (Hamilton, 1983) in the case of the Hertzian
contact:
 1 − 2ν 4 + ν 
σ max = Pmax 
+
πµ
8
 3

(7.28)
where Pmax is the maximum Hertzian contact pressure, ν Poisson’s ratio, and µ friction coefficient.
Assuming that the Poisson’s ratio is 0.25, Equation 7.28 is simplified as follows:
σ max =
(
Pmax 1 + 10µ
)
6
(7.29)
Substituting Equation 7.29 into Equation 7.27, the critical condition for surface crack propagation is
given by the parameter Sc,m defined as follows:
Sc , m =
(1 + 10µ)P
max
KC
d
≥ Cm
(7.30)
where Cm (= 6/(Bπ1/2)) is a constant.
Sc,m gives mechanical severity of contact from the viewpoint of contact stress and its concentration
against Kc. Wear particles are generated by brittle fracture induced by tensile stress under elastic contact
when Sc,m exceeds the threshold value Cm.
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On the other hand, sliding generates heat pulses by friction heating, which in turn generates thermal
strain at the contact. The thermal stress σmax induced at a crack tip as a tensile stress σmax is given by the
following equation:
σ max =
Eα
∆T
1− ν
(7.31)
where E is Young’s modulus, α the coefficient of thermal expansion, ν Poisson’s ratio, and ∆T the
temperature difference due to the heat pulse.
If temperature difference ∆T is assumed to be proportional to the flash temperature, the critical
condition for crack propagation is given by the parameter Sc,t defined as follows:
Sc , t =
γµ
∆Ts
vWH
≥ Ct
kρc
(7.32)
where γ is the heat partition ratio, µ the friction coefficient, ∆Ts the thermal shock resistance, v the sliding
velocity, W the normal load, H hardness, k thermal conductivity, ρ density, c specific heat, and Ct constant.
Sc,t gives thermal severity of contact from the viewpoint of thermal stress and its concentration against
Kc. Wear particles are generated by brittle fracture induced by tensile stress under elastic contact when
Sc,t exceeds the threshold value Ct.
With these two parameters of Sc,m and Sc,t describing the severity of contact, the region for surface
crack propagation is separated from the region of no crack propagation on the wear map shown in
Figure 7.30 (Adachi et al., 1997).
The state of wear in the region of crack propagation is generally called severe wear, and that in the
region of no crack propagation is generally called mild wear. Experimental specific wear rate in the severe
wear region varies from 10–6 to 10–2 mm3/Nm, and that in mild wear region from 10–9 to 10–6 mm3/Nm.
The experimental critical values of Sc,m and Sc,t at the boundaries between the severe and mild wear
regions in Figure 7.30 are 6 and 4.0 × 10–2, respectively.
Wear mode
Mild Severe
Material
Sc,m (=
(1+10µ) Pmax d
KIC
)
20
Ceramics
against themselves
Al2O3
15
10
ZrO2
SiC
Severe wear
with
Crack propagation
Mild wear
without
Crack propagation
5
0
10-3
10-2
Sc,t (=
10-1
γµ
Ts
vWHV
kρc
100
)
FIGURE 7.30 Wear map of ceramics, which shows the possible region of brittle fracture dominated wear under
elastic contact. The regions of mild wear and severe wear are clearly shown by the critical values of Sc,m and Sc,t .
(From Adachi, K., Kato, K., and Chen, N. (1997), Wear map of ceramics, Wear, 203-204, 291-301. With permission.)
© 2001 by CRC Press LLC
7.6
Concluding Remarks
Wear types of adhesive, abrasive, fatigue, and tribochemical wear are introduced and their wear mechanisms are explained with wear models in this chapter. In practical wear of triboelements, some of these
wear types are involved at the same time, and major wear type changes in some cases from one to another
during running as a result of wear itself.
On the other hand, wear is sensitive to the change of various system parameters such as mass, shape,
stiffness, material properties, and environment. Because of such multiparameter sensitivity of wear,
quantitative prediction of wear rate in practice is still far from reality.
It becomes important, therefore, to recognize the major wear type and its typical wear mechanism in
relation to system parameters.
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