Davim J.P. Tribology for Engineers: A Practical Guide

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Another assumption of this model is that wear occurs

where surface asperities touch, so the true area of contact is

the sum of all the individual asperity contact areas. For each

individual asperity contact, the maximum contact area for

an asperity of radius a, is

Wear takes place when a fragment of material detaches

from an asperity during contact. In this wear model, the

volume of this fragment is presumed to be proportional to

the cube of the contact dimension a, therefore the volume of

this wear fragment can be approximated as 2/3

, for a

sliding distance of 2a.

However, only a fraction

of the contacts generate volume

loss. The wear volume per unit of sliding distance is

[(2/3

)/2a] =

(



A/3) [2.13]

The wear rate is the total volume loss

Q =

/3 = [



(



A)] [2.14]

for the real area of contact between the two surfaces.

The Archard model considers that the deformation of the

asperity contacts is predominantly plastic. This leads to the real

contact area A being proportional to the load and described as

A = W/H [2.15]

where W = applied normal load; H = hardness of the material

that suffers volume loss.

By deﬁ ning the adimensional wear coefﬁ cient K as

/3, the

ﬁ nal equation results:

Q = KW/H [2.16]

Dry wear coefﬁ cient values are usually between 10

–2

and

–7

. The Archard equation is expressed as

Q = kW [2.17]

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Friction and wear

where k is K/H, and is called the dimensional wear coefﬁ cient

or just wear coefﬁ cient expressed in units of mm

(Nm)

–1

The wear coefﬁ cient compares the severity of the wear

damage, but is not sufﬁ cient to account for the mechanisms

which produce wear in each case.

In practice, wear coefﬁ cients can vary dramatically as the

sliding conditions change. Transient wear rates occur during

the initial or running-in period, while the sliding surfaces evolve

towards their steady-state sliding conditions. For most sliding

systems, no single wear mechanism operates, rather several

mechanisms are present, but their relative importance changes

as the sliding conditions change, with wear rate abruptly

changing when different wear mechanisms predominate. Many

variables inﬂ uence the wear damage processes of metals. Wear

maps have been represented to show how wear rates change

with sliding conditions using dimensionless variables; the

normalized contact pressure has been deﬁ ned as the loading

force divided by the nominal contact area and the hardness of

the softer material; and the normalized velocity, the sliding

velocity, divided by the velocity of heat ﬂ ow.

2.2.2 Fretting wear

Fretting is deﬁ ned as contact between surfaces subjected to

reciprocating motion of low amplitude, while reciprocating

wear occurs at much higher amplitudes. Surface degradation

usually occurs when the amplitude of the displacement is within

the range from 1 to 100

m, giving rise to fretting damage.

Fretting wear involves various wear mechanisms such as

adhesion, abrasion, oxidation and fatigue. At least two

mechanisms occur simultaneously depending on operation

parameters. Fretting wear produces oxidized wear debris and

the wear coefﬁ cient increases rapidly with increasing amplitude.

One of the main characteristics of reciprocating wear is that

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the wear coefﬁ cients are approximately constant for constant

sliding distance and do not depend on sliding amplitude. The

amplitude value for the transition between fretting and

reciprocating is not easily deﬁ ned as it depends on each set of

experimental conditions and materials (Chen, 2001).

2.2.3 Wear mechanisms

Plastic deformation dominates when metals slide at low

speed. The general requirement for plastic deformation is

that the mechanical stresses generated by the adhesive,

loading and frictional forces exceed the yield stress of one or

both of the sliding materials. Plastic deformation leads to

different surface damage forms:

■

Adhesion. Adhesive forces combined with plastic ﬂ ow pull

out wear particles from the tips of the asperities.

■

Delamination. Plastic ﬂ ow nucleates and promotes the

growth of subsurface cracks that propagate parallel to the

surface, before extending out to the free surface to form

platelet-like wear particles.

■

Surface cracks. For brittle materials, the high tensile

stresses generated by the traction within the contact region

lead to surface fractures and cracks.

■

Fatigue. Cyclic variations of stresses from repeated sliding

or rolling contact results in fatigue failure in the near-

surface region.

■

Mechanical milling and nanostructuring. A mechanically

mixed layer is formed and the composition of wear debris

is a mixture of constituents from the two sliding surfaces.

For unlubricated ductile materials, the grains near the

surface and the wear debris can be reﬁ ned down to the

nanometer level.

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Friction and wear

■

Seizure. Under extremely high contact pressures, the real

area of contact approaches the nominal area leading to

seizure of the moving parts followed by severe wear when

they move again.

Adhesive wear

The concept of adhesive wear is based on the notion that

adhesion occurs between asperities when they touch,

followed by plastic shearing of the tips of the softer asperities

which then adhere to the opposing surface, and ﬁ nally

separate as wear debris particles (Fig. 2.8). Adhesive wear

can be described by the Archard model. A high surface

energy should result in a high adhesive wear rate, as adhesive

forces are higher for high surface energy. Since surface energy

depends on the chemical composition of the surface, wear

rates from this adhesive mechanism should be very sensitive

to the presence of contamination layers or lubricant ﬁ lm.

Milling of materials is believed to be one of the causes

of tribological surface ﬁ lm formation in sliding contacts.

Besides the transfer and loss of material (Rigney, 2000),

adhesive wear usually involves the following processes:

adsorption of surface layers, i.e. moisture; sub-surface plastic

deformation; microstructural and phase transformations;

and surface ﬁ lm formation.

Model for adhesion, transference of material

and plastic deformation of wear debris

Figure 2.8

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After the process of adhesion, transfer and plastic

deformation, wear debris particles produced by adhesive

wear show a ﬂ at rounded morphology (Williams, 2005), as

can be observed in Fig. 2.9. Wear scars on the sliding surface

show plastically deformed material on the edges of the track

(Fig. 2.10 and Fig. 2.11).

Figure 2.10 shows a three-dimensional surface topography

proﬁ le of a wear scar showing accumulation of plastically

SEM micrograph of an adhesive wear debris

particle showing the ﬂ at rounded morphology

Figure 2.9

Three-dimensional surface topography proﬁ le of

a dry wear scar

Figure 2.10

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deformed material at the edges and the initiation of cracks

perpendicular to the sliding direction. This wear mechanism

produces an increase of the average roughness (R

) inside the

wear track with respect to the initial roughness outside the

track.

The line-scan of the cross section of the wear track shown

in Fig. 2.11 allows to determine the loss of material by

measuring the area of material removed from the track

surface (A

) and the plastically deformed material (A

+ A

The ﬁ nal amount of material lost by wear (A

) will be

= [ A

– (A

+ A

)] [2.18]

For metals sliding in air, adhesive wear can be reduced by the

presence of a monolayer of boundary lubricant which not

only reduces the surface energy but also resists displacement

by the contacting asperities, thus preventing the direct

contact between the metals.

Wear maps

Lim and Ashby (1987) developed a wear map for steel sliding

against steel under a pin-on-disk conﬁ guration (Fig. 2.12).

The map establishes the pressure-velocity regions where

different wear mechanisms prevail and under relatively low

pressures and velocities, material removal by delamination

takes place. Mild oxidational wear occurs when oxidation

due to frictional heating is relatively low, but under severe

Line-scan of the cross-section of a wear scar

Figure 2.11

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oxidational wear, wear particles are removed exclusively

from the oxide layers. Melt wear occurs when ﬂ ash

temperatures reach the melting point. This map for steel was

the precedent for other wear maps such as that developed by

Adachi et al. (1997) for ceramic materials (Fig. 2.13).

In the case of ceramics, a quantitative model for the

transition from mild to severe wear was developed from

experimental data of ceramics sliding against themselves

under the pin-on-disc conﬁ guration.

Abrasive wear

In abrasive wear, the rubbing of hard particles or hard

asperities against a surface removes or displaces the material

Load-velocity wear map for steel–steel under

pin-on-disc conﬁ guration

Figure 2.12

Adapted from Lim and Ashby (1987).

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from that surface (Hokkirigawa and Kato, 1988). For

abrasive wear to occur these particles, or one of the contacting

surfaces, needs to be considerably harder than the surface

being abraded (at least 1.3 times harder). The abrasive wear

process leads to a characteristic surface topography of long

grooves running in the sliding direction. The two general

types of abrasive wear are:

■

Two-body abrasion: Wear is caused by the hard protrusions

of one surface on the other. Cutting tools produce two-

body abrasive wear (Fig. 2.14).

■

Three-body abrasion: Wear is caused by hard particles that

slide between two sliding surfaces. This includes abrasion

by wear debris generated by other wear mechanisms.

A simple way to model the abrasive wear (Siniawski et al.,

2006) of an asperity in a two-body process or the corner

of a grit particle in a three-body process is to consider a cone

of a hard material gouging a groove into a softer material

Wear map for Al

Figure 2.13

Adapted from Adachi et al., 1997

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(Fig. 2.15). If the depth of the groove is x and the slope of the

side of the cone is tan

(Fig. 2.15), the volume V of material

displaced when the asperity slides a distance d is given by

V = dx

tan

= dx

cot

[2.19]

where 2

is the cone angle of the indenter.

Abrasive wear mechanisms by a sharp indenter

Figure 2.14

Abrasive wear by a cone-shaped asperity

Figure 2.15

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Since only the front half of the asperity applies a load W

over an area

/2, then

W =

cot

[2.20]

where H is the hardness of the softer material. From the

above equations, the wear rate for abrasive wear (Q

) will be

= V/d

= 2tan

H [2.21]

and the coefﬁ cient of abrasive wear (K

) would be 2/

(tan

In contrast with the wear track proﬁ le seen in Fig. 2.11,

abrasive wear produces parallel grooves inside the wear

track (Fig. 2.16) without plastic deformation, and the

morphology of wear debris particles (Williams, 2005)

produced by abrasion (Fig. 2.17) is similar to that of the

chips removed by machining operations. In most cases,

however, a combination of adhesive and abrasive mechanisms

is found due to the abrasion produced by the wear debris

trapped in the interface between the sliding solids.

Scratch tests were developed to measure the resistance to

abrasive wear of coatings. In the case of viscoelastic materials

such as polymers (Brostow et al., 2002; Dasari et al., 2009),

Abrasive wear scar proﬁ le obtained by contact

proﬁ lometry, showing abrasion grooves inside

the scar and the absence of plastic deformation

at the edges

Figure 2.16

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