7Wear Mechanisms

7.1 Introduction 7.2 Change of Wear Volume and Wear Surface Roughness

with Sliding Distance7.3 Ranges of Wear Rates and Varieties of Wear Surfaces7.4 Descriptive Key Terms7.5 Survey of Wear Mechanisms

Adhesive Wear • Abrasive Wear • Fatigue Wear • Corrosive Wear • Mechanical Wear of Ceramics under Elastic Contact

7.6 Concluding Remarks

7.1 Introduction

Wear has been recognized as meaning the phenomenon of material removal from a surface due tointeraction 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, wearcontrol 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 conditionsand 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 selectionof materials are the keys to controlling wear. As one way to meet these requirements, wear maps havebeen proposed for prediction of wear modes and wear rates (Lim and Ashby, 1987; Hokkirigawa andKato, 1988). A wear map is considered one of the best descriptions of tribological conditions and is usefulin 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 wearrate, varieties of wear modes, and wear mechanisms is essential.

Wear is the result of material removal by physical separation due to microfracture, by chemicaldissolution, 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 reasonsthat include changes in surface material properties and dynamic surface responses caused by frictionalheating, chemical film formation, and wear.

Wear mechanisms are described by considering complex changes during friction. In general, wear doesnot take place through a single wear mechanism, so understanding each wear mechanism in each modeof wear becomes important.

Our present understanding of the mechanisms of the four representative wear types is described inthe following sections.

Koji KatoTohoku University

Koshi AdachiTohoku University

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 char-acterizing wear.

Three representative types of wear volume curves are shown schematically in Figure 7.1. Type I showsa constant wear rate throughout the whole process. Type II shows the transition from an initially highwear 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 amountof sliding before catastrophic wear is the period at which crack initiation takes place and depends on theinitial surface finish, material properties, and frictional conditions.

On the other hand, three representative types of roughness curves on wear surfaces are shown inFigure 7.2. Type I shows the case of steady wear, where the surface roughness does not change from theinitial value. Type II shows the case of steady wear, where surface roughness increases to a certain valueand stays there. Type III illustrates initial running-in and steady wear, where surface roughness decreasesdrastically 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 degreeof wear is described by wear rate, specific wear rate, or wear coefficient. Wear rate is defined as wear

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.

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 definedas 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 lubri-cation 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 distri-bution in the range of 10–15 to 10–1 mm3/Nm by the differences in lubrication states. Figure 7.4 showsthe distributions of specific wear rates and friction coefficients measured in unlubricated sliding of fourkinds 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 wearcan 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 ofdynamic parameters, environmental parameters, and material parameters.

FIGURE 7.3 Distribution of specific wear rate of metallic materials in sliding contact under different lubricationconditions. (Data from Archard, 1953; Bhansali, 1980; Hirst, 1957; Hokkirigawa, 1997; Holm, 1946; Lancaster, 1978;Rabinowicz, 1980).

FIGURE 7.4 Distribution of specific wear rates and friction coefficients of ceramics in unlubricated sliding againstthemselves.

7.4 Descriptive Key Terms

There are many terms used to describe wear, and they are not always well differentiated. This sometimesmakes understanding wear mechanisms confusing and difficult. Further effort must be given to achievegreater clarity in our approach to the analysis of wear mechanisms.

In this section, descriptive key words of wear and their interrelations are summarized. This summaryis 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,

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.

unidirectional sliding, unidirectional rolling, reciprocal sliding, reciprocal rolling, and rolling with slipare 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, orslurry 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, apparentand real contact conditions at the contact interface are introduced without particularizing about thesecontact configurations. Severity of contact, such as elastic contact or plastic contact, is the simplest andmost direct way to think about wear mechanisms, and is a tribosystem response determined by dynamicparameters, material parameters, and atmospheric parameters.

The following four wear modes are generally recognized as fundamental and major ones (Burwell,1957/58):

1. Adhesive wear2. Abrasive wear3. Fatigue wear4. Corrosive wear

Adhesive wear and abrasive wear are wear modes generated under plastic contact. In the case of plasticcontact between similar materials, the contact interface has adhesive bonding strength. When fracture issupposed to be essentially brought about as the result of strong adhesion at the contact interface, theresultant 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 hardermaterial penetrates to the softer one. When the fracture is supposed to be brought about in the mannerof micro-cutting by the indented material, the resultant wear is called abrasive wear, recognizing theinterlocking contact configuration necessary for cutting, again without particularizing about adhesiveforces and fracture mode.

FIGURE 7.6 Descriptive key words of wear and their interrelations.

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 isaccelerated. When the tribochemical reaction in the corrosive media is supposed to be brought about bymaterial removal, the resultant wear is called corrosive wear. In air, the most dominant corrosive mediumis 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 deformationand fracture are generated by mechanically induced strains and stresses. Therefore, this type of wear isgenerally described as mechanical wear.

The material removal in corrosive wear is governed by the growth of chemical reaction film or itschisolution on wear surface, where chemical reactions are highly activated and accelerated by frictionaldeformation, 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, wherefrictional heating and partial high temperature govern the process.

The macroscopic classifications in terms of mechanical, chemical, and thermal wear are useful to acomprehensive understanding of wear because almost all models of wear are included in these threetypes. The descriptions of wear by different definitions are summarized in Figure 7.6 to show the relativerelations.

7.5 Survey of Wear Mechanisms

As the traditionally accepted representative wear modes, the four wear modes shown in Figure 7.7 areconsidered, 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 strengthto resist relative sliding, large plastic deformation caused by dislocation is introduced in the contactregion 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.

crack is initiated and is propagated in the combined fracture mode of tensile and shearing. When thecrack reaches the contact interface, a wear particle is formed and adhesive transfer is completed. Thistype of wear, which occurs when there is enough adhesive bonding at the contact interface, is calledadhesive 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 contactpoint is formed after the disappearance of the former one, the total number of contacts n stays constantduring sliding. By supposing a circular contact area of radius a, the possible volume of wear particlesgenerated after sliding the distance of 2a is assumed as the half sphere volume described by 2πa3/3. Basedon these assumptions, the possible wear volume V for n contact points after sliding the distance L isgiven by:

(7.1)

Since the normal contact pressure with plastic deformation is almost equal to the hardness value Hof the wearing material, the total real contact area for n contact points nπa2 is expressed by:

(7.2)

By substituting Equation 7.2 into Equation 7.1, possible wear volume V under normal load W aftersliding distance L is given by:

(7.3)

Equation 7.3 shows that the adhesive wear volume is proportional to the normal load and the slidingdistance, and is inversely proportional to the hardness of the wearing material. Considering the relation-ship 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 (Kayabaand 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 comefrom 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:

(7.4)

where Kad is called the wear coefficient for adhesive wear. It is a principal value for a friction pair todescribe its wear rate. The physical meaning of Kad is the wear volume fraction at the plastic contactzone, and it is strongly affected by the material properties and the geometry of the zone in compressionand 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 awear coefficient Kad is not a constant value but is a possible value in the range of adhesive wear rate.

V n aL

a= ⋅ π ⋅2

3 23

n aW

Hπ =2

VWL

H= ⋅1

3

V KWL

Had= ⋅

7.5.1.2 Adhesive Wear Mode

Tangential shear under compression at the contact interface of strong adhesive bonding generates slipsalong slip planes in the contact region. As a result of the slips, flake-like shear tongues are formed, asshown in Figure 7.8a, and are followed by a crack initiation and propagation in the combined fracturemode of tensile and shear in the leading region of the contact. The large plastic deformation in thecontact region sometimes forms a wedge-like shape, which is followed by crack initiation and propagationin the combined fracture mode of tensile and shear in the trailing region of the contact, as shown inFigure 7.8b.

Fractographic analysis of the fracture surfaces of wear particles of Figure 7.8a and b indicates that thelarger part of the fracture surface of the flake-like wear particle shows the fracture mode of compressionand shear, and that all parts of the fracture surface of the wedge-like wear particle in Figure 7.8b showsa tensile and shear fracture mode. Both wear modes which produce flake-like and wedge-like wearparticles are basic ones in adhesive wear.

In the adhesive wear process, transfer and retransfer from one surface to the mating surface take placein many cases. As a result, relatively large wear particles composed of two surfaces are formed. This isanother basic part of the adhesive wear mechanism (Sasada, 1979).

In the successive process of repeated sliding, these wear particles leave the contact interface as freeparticles 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

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.)

the contact interface is at first parallel to the sliding direction, the interface rotates and becomes inclinedand 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 modeof 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, ploughingtakes place in sliding. As a result of ploughing, a certain volume of surface material is removed and anabrasive 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 flatsurface and forms a groove on it by ploughing. When wearing material has a ductile property, a ribbon-like, 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 differencesare 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 groovesare generally found on the wear surface after sliding. The peak and the valley coincide well with themating surfaces, as shown in Figure 7.10. This result means that the hard abrasive asperities are formedon the mating surface because of, for example, work hardening, phase transitions, and third-bodyformation at the contact interface during repeated sliding contact. Therefore, abrasive wear is recognizedas a more representative wear mode of ductile material in repeated sliding.

7.5.2.1.1 Estimation of Abrasive Wear VolumeThe first point to understand in the abrasive wear mechanism is the estimation of wear volume fromwhich wear particles can be generated. Here, we assume a simplified contact model in which the abrasivehas a conical shape with an angle θ, and the indentation depth of the abrasive is d, as shown in Figure 7.11.

FIGURE 7.9 Abrasive wear of ductile material, which is dominated by plastic deformation (a) and one of brittlefracture, which is dominated by brittle fracture (b). (From Evans, A.G. and Marshall, D.B. (1981), Wear mechanismin ceramics, in Fundamentals of Friction and Wear of Materials, Rigney, D.A. (Ed.), ASM, 439. With permission.)

Based on this assumption model, the possible wear volume V, which is ploughed by harder asperitiesafter sliding a distance of L, is given by:

(7.5)

Since the normal contact pressure under plastic contact can be assumed to be equal to the hardness valueH of the wearing material, real contact area of π(dtanθ)2/2 is expressed by:

(7.6)

By substituting Equation 7.6 into Equation 7.5, possible wear volume V under normal load W and aftersliding distance L is given by:

(7.7)

Equation 7.7 gives the wear volume for the case of ideally plastic abrasive grooving in microcuttingshown 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 itsinitial size in Figure 7.12b, and no wear particles are generated in Figure 7.12c. It means that wear volumein 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 amodifier, and the wear volume is described by:

(7.8)

FIGURE 7.10 The cross-sectional profiles of two mating wear surfaces of 0.45% carbon steel after pin-on-ringsliding.

FIGURE 7.11 Typical model of abrasive wear by a conical indentor.

V d L= ⋅ ⋅2 tan θ

1

2

2π ⋅( ) =d

W

Hv

tanθ

VWL

Hv

=π⋅

⋅2

tanθ

V KWL

Hab= ⋅

Equation 7.8 shows that the abrasive wear volume is proportional to the normal load and the slidingdistance, and it is inversely proportional to the hardness of the wearing material. In fact, abrasive wearresistance 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 valuefor a friction pair in describing its wear rate. The physical meaning of Kab is the wear volume fractionagainst the nominal groove volume zone, and it depends on the ductility of wearing material, shearstrength 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 datathat wear coefficient Kab is not a constant value in abrasive wear. By comparing Kab with Kad in adhesive

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. (FromHokkirigawa, K. and Kato, K. (1988), An experimental and theoretical investigation of ploughing, cutting and wedgeformation 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.)

wear, it is clear that abrasive wear gives a relatively large wear coefficient. That is why abrasive wear isrecognized as severe wear.

Abrasive grooving by the hard and sharp asperity is possible only when the asperity is not flattenedor 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 AsperityThe 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 rabove the critical value rc1, wear volume of mating material decreases, and finally almost no wear isobserved when r is close to a critical value rc2 (1 to 1.4; Rabinowicz, 1983). This relation is shownschematically 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 anasperity is given in Figure 7.15 (Kayaba et al., 1983) between the hardness ratio r and the critical asperitytip angle θc. The parameter f in Figure 7.15b is the ratio of the shear strength of the interface to the shearstrength of the softer material, and Figure 7.15a shows the relation at f = 0. Plastic grooving by the asperityis possible when its tip angle θ is larger than the critical value θc, and this value changes depending onthe 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 hardnessratio r is very close to unity theoretically. This is evidence of the high possibility of groove formation atthe sliding interface between similar ductile materials.

7.5.2.1.3 Abrasive Wear ModeAs mentioned above, abrasive wear takes three different modes: microcutting, wedge forming, andploughing, 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 thiswear mode. In the wedge-forming mode, a wedge-like wear particle is formed at the tip of the groovingasperity as shown in Figure 7.12b and stays there working as a kind of built-up wedge to continuegrooving. Sliding takes place at the bottom of the wedge where adhesive transfer of a thin layer from theunderlying counterface continues to grow the wedge slowly. This wear mode appears as a combined effectof 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

FIGURE 7.14 Schematic diagram of effect of hardness ratio on wear rate of abraded material against abrasive.

generated by a single pass of sliding and only a shallow groove is formed. Repeated sliding and accumu-lation 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 slipline field theory (Challen and Oxley, 1979). Theoretical predictions agree well with experimental resultsof 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:

(7.9)

where R is the pin tip radius, H the hardness of the wearing material, and W the load. The parameter fin Figure 7.16 has the same meaning as that in Figure 7.15. Theoretical solid lines are drawn accordingto the theory (Challen and Oxley, 1979) by substituting the relationship of Dp = 0.8 (1 – cosθ)/sinθ whereθ is the attack angle.

In all these three abrasive wear modes, grooves are formed as the result of wear particle generationand 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 unitsliding distance observed above the initial surface level on both sides of the groove, (∆Vg — ∆Vr) givesthe wear volume at one groove in one pass of sliding. With these descriptions, the concept of degree ofwear β at one groove is introduced, as shown in Figure 7.17 and is given as follows:

(7.10)

where β = 1 corresponds to the state of ideal material removal without forming ridges, and β = 0 meansthe ideal ploughing of no material removal.

FIGURE 7.15 Relationship between the critical tip angle θc and the hardness ratio r where the normalized shearstrength 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. Withpermission.)

D RH

W

H

WRp = π − π

−2 2

12

β =−∆ ∆

∆V V

Vg r

g

The degree of wear β defined in this way is a function of the hardness H of the wearing material andthe degree of penetration Dp as shown in Figure 7.18 (Hokkirigawa and Kato, 1989) for heat treatedsteels. This β is related to the abrasive wear coefficient Kab mentioned above at one groove as follows:

(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 theindentor.

FIGURE 7.16 Abrasive wear mode diagram: abrasive wear modes of ductile material as a function of degree ofpenetration Dp and normalized shear strength f at the contact interface. Solid lines are theoretically induced withmodified two-dimensional model. (From Hokkirigawa, K. and Kato, K. (1988), An experimental and theoretical inves-tigation 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 volumeand ∆Vr: two side ridges’ volume of two sides.

KV H

Wabg= β

∆

The parameter β and ∆Vg are given from the result of a pyramidal scratch test as (Zum Gahr, 1987):

(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 thegroove. εs in Equation 7.12 is given by:

(7.13)

where E is the Young’s modulus of the wearing material, µ is the friction coefficient, θ is the angle of thepyramid, and R is the tip radius of the pyramid:

(7.14)

By introducing Equations 7.12, 7.13, and 7.14 into Equation 7.11, the wear coefficient Kab is expressedtheoretically in terms of material parameters, geometrical parameters, and frictional conditions of loadand friction coefficient. If the expression for volumetric is introduced by defining the inverse of wearrate (sliding distance/wear volume), it is given by (β∆Vg)–1. The comparisons of experimental andtheoretical values of the volumetric wear resistance show good agreement, as shown in Figure 7.19 (ZumGahr, 1987).

The expressions of Equations 7.9 through 7.14 and Figures 7.15 through 7.19 are all for simple abrasivescratching. But in practical abrasive contact, there are many abrasive contact points at the same time,

FIGURE 7.18 Degree of wear β as a function of degree of penetration Dp observed with heat-treated steel of differenthardness H (kgf/mm2). (From Hokkirigawa, K. and Kato, K. (1989), Theoretical estimation of abrasive wear resistancebased on microscopic wear mechanism, in Proc. Int. Conf. on Wear of Materials, ASME, pp. 1-8. With permission.)

β εε

= − −

1 2 0

1 3

exp lnH

Hs

c

ε

θ

s

W E

HR=

+ µ( )

21 10

26

1 3 2 3 21 2

2 3ln

tan

∆VW

H

HR

Wg = + µ( ) +

π−

1

51 10

2

22

121 2 2

tan

tan

θ

θ

and each of them is at a different state of deformation and wear. Therefore, it becomes necessary tointroduce a model for the distribution of contact geometry, contact load, and the resultant abrasive wearmode.

If we know the distribution of Dp at multiple abrasive contacts of a surface, the total wear rate of thesurface can be introduced by summarizing all the values of β at all contact points. Figure 7.20 (Hok-kirigawa and Kato, 1989) shows the experimental data and theoretical solid and broken lines obtainedin 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 generateddue to mainly brittle fractures caused by initiation and propagation of cracks, such as the median and

FIGURE 7.19 Theoretical abrasive wear resistance vs. experimental abrasive wear resistance measured on differentmaterials by using a diamond scratch of attack angle θ = 90° and tip radius r = 8 mm under load W = 2N. (FromZum 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 experimentallyand estimated theoretically. (From Hokkirigawa, K. and Kato, K. (1989), Theoretical estimation of abrasive wear resistancebased on microscopic wear mechanism, in Proc. Int. Conf. on Wear of Materials, ASME, pp. 1-8. With permission.)

lateral cracks shown in Figure 7.10b. Therefore, wear rate of the brittle material is strongly dependenton fracture toughness. Figure 7.21 (Fischer et al., 1989) shows the effect of fracture toughness on thewear rate of zirconium oxide under abrasive contact. It is clear that fracture toughness is an importantparameter 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 (Evansand Marshall, 1981). It is assumed that a wear particle is generated by lateral crack propagation which

FIGURE 7.21 Relationship between abrasive wear resistance and fracture toughness of yttria-doped zirconiumoxide. (From Fischer, T.E., Anderson, M.P., and Jahanmir, S. (1989), Influence of fracture toughness on the wearresistance of yttria-doped zirconium oxide, J. Am. Ceram. Soc., 72, 2, 252-257. With permission.)

FIGURE 7.22 Abrasive wear model for brittle material.

reaches to the surface. If the crack is propagated by the residual stress, crack length c is defined by thefunction of normal load W, fracture toughness Kc, hardness H, and Young’s modulus E as follows:

(7.15)

where α1 depends on the shape of the abrasive and is determined by calibration on a material with well-characterized fracture properties.

The depth b of lateral fracture is estimated by the radius of plastic contact zone, and is given by:

(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:

(7.17)

where L is the sliding distance and α3 is a material-dependent constant determined by calibration on amaterial with well-characterized fracture properties.

Another analysis (Evans and Wilshaw, 1976) on a similar model with different assumptions gives aslightly different equation of abrasive wear volume of brittle materials as follows:

(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 inFigure 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 wearparticles. There are other cases of wear where a certain number of repeated contacts are essential for thegeneration of wear particles. Wear generated after such contact cycles is called fatigue wear. When thenumber 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 ishigh-cycle fatigue fracture in the contact region. The critical number of rolling cycles Nf for the generationof wear particles by spalling or flaking is given experimentally as follows (Lundberg and Palmgren, 1952):

(7.19)

cW

K H

E

Hc

=

α1

5 8

1 2 1 8

3 5

bE

H

W

H=

α2

2 5 1 2

VW

K H

E

HL

c

=

α3

9 8

1 2 5 8

4 5

VW

K HL

c

= α4

5 4

3 4 1 2

NWf n

∝ 1

where W is the normal load and n is a constant which depends on the shape of the rolling element. Inthe 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 thatspalling 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 contactregion, local yield is generated in the contact region because of the existence of microdefects in thematerial. A single crystal has slip planes for preferential sliding under shear stress. A polycrystal has grainboundaries, inclusions, and vacancies. Because of these inhomogeneities, the local stress in the contact

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.)

region exceeds the yield stress of the material even when the theoretical stress for the homogeneousmaterial does not exceed the yield stress (Dufrane and Glaeser, 1976).

There is a state where a plastically deformed region appears beneath the interface without reachingthe 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 µmbeneath the surface, and the value of maximum hardness increases with an increase in the number ofrolling 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 strainaround some stress concentration points, and cracks are generated after reaching a certain number offrictional cycles. The mechanism of crack initiation and propagation in such a situation is that of fatiguefracture, which is a kind of rate process controlled by the inhomogeneity of the microstructure of amaterial.

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 wearis easily observed as the ploughing mode shown in Figure 7.12c (Hokkirigawa and Kato, 1988). In thismode, a wear particle is not generated by a single pass of sliding and only a shallow, conformable grooveis 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 isexpected 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 flowwear particles of steel under boundary lubrication. It is seen that a thin surface layer protrudes in the

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 rollingcontact, Technology Report, Tohoku Univ., 41, 1, 21-46.)

direction of sliding, and grows as the number of sliding cycles increases. Figure 7.27 shows the amountof 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. Con-forming between two sliding surfaces occurs by this gradual surface plastic flow and wear in metallictriboelements. This phenomenon is representative of low fatigue wear under plastic contact.

FIGURE 7.26 Flow wear process for steel during repeated sliding in boundary lubrication. (From Akagaki, T. andKato, 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 slidingconditions. (From Akagaki, T. and Kato, K. (1988), Simulation of flow wear in boundary lubrication using Vickersindentation method, STLE, Trib. Trans., 31, 3, 311-316. With permission.)

If we suppose that the plastically deformed layer is detached as wear particles by low-cycle fatiguefailure, Nf would be given by the modified Coffin–Manson relationship:

(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 relation-ship of Equation 7.20, the specific wear rate ws defined by wear volume/load/distance is described byChallen et al. (1986) as follows:

(7.21)

where rp is the ratio of plastic to total work of sliding and k is the average shear flow stress of the wearingmaterial. By introducing the relation of k = H(Hardness)/(3 × 31/2) into Equation 7.21, the fatigue wearcoefficient Kf, defined in the same way as Kad and Kab mentioned above, can be expressed as:

(7.22)

The three parameters of ∆γs, rp, and µ are functions of the attack angle α (= π/2 – θ), where θ is definedin Figure 7.11, and the normalized shear strength f. The parameter f has the same meaning as inFigures 7.15 and 7.16; it is the ratio of shear strength τ at the contact interface to the shear flow stress kof the wearing material, i.e., f = τ/k. From Figure 7.28 (Challen et al., 1986), which shows the calculatedvalues of Kf by changing the values of θ and f, it can be seen that Kf is predicted to vary in the rangefrom 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 aresult of deformation and wear in the groove surface layer. Better conformity between asperity and groovesurfaces is attained where the contact pressure is decreased and elastic strains have to be considered. Ifthe maximum Hertzian contact pressure is above the critical value of the elastic shakedown limit in anelastic–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 whichcomprises a reversing (fatigue) component ∆εa acts parallel to the surface. If it were acting alone, thenumber Nf of cycles to surface failure would be given by the Coffin–Manson relationship as follows:

(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 inratcheting is given by Johnson (1994) and Kapoor and Johnson (1994) as:

(7.24)

where ∆γr is the ratcheting shear strain per cycle. In this ratcheting region, however, it is not quite clearwhether ultimate failure would be caused by fatigue or by ductile fracture. It would be reasonable to

NC

fs

s

D

=

∆γ

wr

kCsp

sD

sD

=µ

−∆γ1

K w Hr

Cf sp

Ds

D= =

× µ−

3 31 2

1∆γ

NC

fa

=

22

∆ε

NC

rr

=

∆γ

suppose that each fatigue wear mode described by Equation 7.20, 7.23, or 7.24 has the possibility of beingthe prevailing wear mode depending upon the contact condition, and two or three of them may coexistin some cases. Careful experimental observation (Black et al., 1996) gives the value of D = 1.67, whichsuggests 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 thesurface mainly by chemical or electrochemical interactions. If these reaction products adhere strongly tothe surface and behave like the bulk material, the wear mechanism should be almost the same as that ofthe bulk material. In many cases, however, such reaction products behave very differently from the bulkmaterial. Therefore, wear is quite different from that of the bulk material, and is dominated by thereaction products formed by the interaction of solid materials with the corrosive environment. This kindof 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 wearrate of the reaction layers and, as a result, of the bulk material. Therefore, models of the reaction layergrowth 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 oxidativereaction between steel and normal atmospheric air and assuming the film removal model where an oxidefilm of steel is supposed to detach from the surface at a certain critical thickness, corrosive wear coefficientKc defined in the same way as Kad and Kab has been expressed by Quinn (1987) as:

(7.25)

FIGURE 7.28 Variation of wear coefficient Kf in sliding friction assuming a low-cycle fatigue wear mechanism withattack 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.)

KdA

v

Q

R Tcg

= −

ξ ρ2 2

exp

where A is the Arrhenius constant, Q the activation energy, Rg the gas constant, T the absolute temper-ature, ρ the density of oxide, v the sliding velocity, and L the distance along which a wearing contact ismade.

It is generally assumed that activation energy does not vary substantially between static and slidingconditions. Making this assumption, the experimental wear results for oxidation of steels give a value ofthe 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 staticcondition. This seems to be supported by another experimental result where the thickness of oxidativewear 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 becomesimportant.

Furthermore, the real temperature at the real contact interface is important in the determination ofthe wear rate, because the reaction rate required to form a chemical product is strongly affected by thetemperature induced by friction.

On the other hand, if the reaction rate is not high enough to grow an oxide film to the critical thicknesswithin a cycle of sliding, oxidative wear of the steel may not occur. Even in this case, the reaction ratealso 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 fromthe surface by rubbing, and it dissolves in water (Fischer and Tomizawa, 1985). If the reaction rate ishigh, a lot of silicon nitride hydroxide can be formed and worn away quickly. The reaction rate determinesthe wear rate in this case.

If it is assumed that friction heating also accelerates chemical reaction at the contact interface, thewear coefficient Kc of nonoxidative ceramics sliding against themselves is explained by Kitaoka et al.(1997) as:

(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 mechanismis difficult to understand without first understanding the process of the formation of the reaction layerfrom the viewpoint of the combined effect of mechanical activation and chemical reaction, namely, fromthe 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 fatiguewear even under elastic contact. It is the wear governed by the microscopic brittle fracture at surfacemicrocracks under nominal elastic contact. This is the representative wear mechanism of ceramics whenspecific 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 thepropagation of a predominant surface crack in brittle manner. Such crack propagation can be enhancedby the tensile stress induced by friction under elastic contact.

Based on the linear elastic fracture mechanics model, the critical condition for the crack propagationis expressed by the following equation:

(7.27)

KA

v

Q

R Tcc

g

= −

ρ

exp

B d Kcσmax π ≥

where σmax is the maximum tensile stress at the crack tip, d preexistent crack length, Kc fracture toughnessof the wearing material, and B constant.

Sliding generates the friction force which introduces the shear stress at the contact interface in additionto the compressing stress. As the result, the maximum tensile stress σmax is induced at the trailing edgeof the contact, which is expressed by the following equation (Hamilton, 1983) in the case of the Hertziancontact:

(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:

(7.29)

Substituting Equation 7.29 into Equation 7.27, the critical condition for surface crack propagation isgiven by the parameter Sc,m defined as follows:

(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 contactwhen Sc,m exceeds the threshold value Cm.

FIGURE 7.29 Wear model of brittle material, in which wear particles are generated by propagation of preexistentcrack under elastic sliding contact: (a) sliding contact under elastic contact; (b) application of tensile stress to cracktip; (c) propagation of crack; and (d) generation of wear particle.

µ p

Hertzian Contact

(a)

Tensile stress

(b)

(c)

(d)

σ ν νmax max= − + + πµ

P1 2

3

4

8

σmax

max=+ µ( )P 1 10

6

SP d

KCc m

Cm,

max=+ µ( )

≥1 10

On the other hand, sliding generates heat pulses by friction heating, which in turn generates thermalstrain at the contact. The thermal stress σmax induced at a crack tip as a tensile stress σmax is given by thefollowing equation:

(7.31)

where E is Young’s modulus, α the coefficient of thermal expansion, ν Poisson’s ratio, and ∆T thetemperature difference due to the heat pulse.

If temperature difference ∆T is assumed to be proportional to the flash temperature, the criticalcondition for crack propagation is given by the parameter Sc,t defined as follows:

(7.32)

where γ is the heat partition ratio, µ the friction coefficient, ∆Ts the thermal shock resistance, v the slidingvelocity, 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 againstKc. Wear particles are generated by brittle fracture induced by tensile stress under elastic contact whenSc,t exceeds the threshold value Ct.

With these two parameters of Sc,m and Sc,t describing the severity of contact, the region for surfacecrack propagation is separated from the region of no crack propagation on the wear map shown inFigure 7.30 (Adachi et al., 1997).

The state of wear in the region of crack propagation is generally called severe wear, and that in theregion of no crack propagation is generally called mild wear. Experimental specific wear rate in the severewear 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 wearregions in Figure 7.30 are 6 and 4.0 × 10–2, respectively.

FIGURE 7.30 Wear map of ceramics, which shows the possible region of brittle fracture dominated wear underelastic 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.)

σ ανmax =

−E

T1

∆

ST

vWH

k cCc t

st, = µ ≥γ

ρ∆

Al2O3

Mild Severe

Wear modeMaterial

ZrO2

SiC

0

5

10

15

20

10-3 10-2 10-1 100

Ceramicsagainst themselves

γ µTs

vWHVkρc

Sc,t (= )

(1+

10µ)

Pm

ax

KIC

dS

c,m

(=

)

Crack propagationwithout

Mild wear

Severe wear

Crack propagationwith

7.6 Concluding Remarks

Wear types of adhesive, abrasive, fatigue, and tribochemical wear are introduced and their wear mecha-nisms are explained with wear models in this chapter. In practical wear of triboelements, some of thesewear types are involved at the same time, and major wear type changes in some cases from one to anotherduring 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 inrelation to system parameters.

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