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Holmberg2007-FrictionWearCoatedSurfaces.pdf
Available online at www.sciencedirect.com
Surface & Coatings Technology 202 (2007) 1034 – 1049
www.elsevier.com/locate/surfcoat
Friction and wear of coated surfaces — scales, modelling and
simulation of tribomechanisms
Kenneth Holmberg a,⁎, Helena Ronkainen a , Anssi Laukkanen a , Kim Wallin b
a
VTT Technical Research Centre of Finland, Finland
b
Academy of Finland, Finland
Available online 21 August 2007
Abstract
Coating a surface with a thin layer changes the surface material properties and is an important tool for controlling friction and wear. The
tribological mechanisms, scale effects and parameters influencing the friction and wear of coated surfaces are discussed. The basic friction and
wear mechanisms can be reduced to: friction by adhesion, ploughing and hysteresis and wear by adhesion, abrasion and fatigue combined with
material fracture. The tribochemical and surface physical effects and surface fatigue taking place before material fracture are treated here as pure
surface material modification mechanisms. Scale effects in a tribological contact are illustrated by explaining typical surface roughness related
tribological mechanisms for diamond and DLC coated surfaces. For diamond coatings asperity interlocking effects are important for rough
surfaces, graphitisation is a dominating mechanism for smooth engineering surfaces and hydrogenising of dangling bonds may be crucial for
physically smooth surfaces. For DLC coated surfaces, surface graphitisation is important with rougher surfaces; building up transfer layers and
graphitisation is crucial for smooth engineering surfaces and hydrogenising of dangling bonds can explain superlubricity for physically smooth
surfaces. An analysis of dominating surface parameters such as elastic, plastic and fracture behaviour of the top surface, the coating, the coating/
substrate interface and the substrate in addition to the coating thickness forms the basis for surface modelling. A stress intensity factor analysis of
crack growth shows the importance of considering both modes I, II and III loading, crack spacing and location of crack, while crack orientation,
location in crack field as well as load biaxiality have minor influences. It is shown how surface 3D FEM modelling generates stress and strain
values at the nano level, within bond layers at coating/substrate interfaces and around cracks and forms the basis for better understanding the
origin of wear.
© 2007 Elsevier B.V. All rights reserved.
Keywords: Tribology; Coatings; Modelling; Scale effects; Diamond; Diamond-like carbon (DLC)
1. Introduction
Energy saving, environmental, economic and safety aspects in
our society all emphasise the importance of controlling friction
and wear in machinery and devices. Lubrication with oil is the
most common way to control friction and wear. However, the use
of liquid lubricants is often not so desirable for environmental
reasons, problems with keeping it in the contact zone, ageing,
circulating, storing, contamination etc. Surface engineering,
where the surface properties of the moving contacts are changed
⁎ Corresponding author. VTT Technical Research Centre of Finland, P.O. Box
1000, 02044 VTT, Finland. Tel.: +358 20 7225370; fax: +358 20 7227077.
E-mail address: [email protected] (K. Holmberg).
0257-8972/$ - see front matter © 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.surfcoat.2007.07.105
in a favourable way by deposition or surface treatment now offers
another efficient way of controlling friction and wear.
The development of the vacuum deposition techniques,
chemical vapour deposition (CVD) and physical vapour
deposition (PVD), has been of major impact, since they make
it possible to deposit a thin layer of only a few micrometers (or
down to nanometer thickness) on the surfaces of most
engineering materials. The geometrical change is minimal and
the surface layer may have properties covering an extremely
wide range, from hard diamond and ceramic coatings to very
soft polymeric or lamella-structured films [1].
In the 1980s hard ceramic TiN, TiC and Al203 coatings were
commercially introduced as surface layers on tools in the
production industry, and wear rates were decreased by one to
two orders of magnitude or more. In the 1990s very low friction
K. Holmberg et al. / Surface & Coatings Technology 202 (2007) 1034–1049
diamond, diamond-like carbon (DLC) and MoS2 surface layers
were investigated and some of them were introduced commercially. Their friction and wear properties were again one to two
orders of magnitude lower than for earlier solutions and they
were suitable for components in engines and devices requiring
both low friction and low wear. In the 2000s much development
work has been focussed on modifying the structures of the thin
coatings in a controlled way. This includes the development of
different multi-component and nanostructured coatings such as
layered coatings, gradient coatings, doped coatings, nanocomposite coatings etc. This development has been reviewed
recently by several authors [2–8].
These advanced surface engineering technologies make it
possible to tailor the surfaces and their properties with great
precision even to molecular and atomic levels (Fig. 1). However, there is one problem. It is easy to specify for some
application that a certain level of low friction and low wear is
needed but we have still no good generic tools to specify the
surface properties that may result in the required tribological
behaviour. The problem is to specify the optimal surface
parameters like coating thickness, surface roughness, coating
material and its structure resulting in a certain hardness,
elasticity, residual stress and fracture toughness of the coating,
bond layers and substrate. There is much empirically-based
experience on how to choose a suitable coating for a specific
purpose but still no systematic tool for this. Much of the surface
engineering development work is still based on a trial and error
approach. Only a few parameter interactions have been
theoretically modelled, to a limited extent [1,9–17].
In this article we present our systematic approach to
modelling and simulation of surface properties for tribological
purposes. We first discuss the basic tribological mechanisms
involved, indicate the importance of scale effects and illustrate it
by a discussion on scale effects for diamond and DLC coated
surfaces, discuss the parameters influencing friction and wear of
coated surfaces in micro level contacts and finally show how
deformations, stresses and strains can be modelled by advanced
three dimensional finite element method (3D FEM) and form a
1035
basis for surface fracture analysis. The aim is to proceed in the
direction of systematic surface design for tribological
applications.
2. Basic friction and wear mechanisms
There are a number of classifications of friction and wear
mechanisms published [18–21]. Two basic friction mechanisms, adhesive friction and ploughing, are normally mentioned.
The variety of classification suggestions is much larger for wear.
In the early days wear was typically classified based on its
appearance on the surface after the contact event. Examples of
such appearance based classes are scoring, scuffing, pitting,
gouging, spalling, fretting and galling. Some of these classes are
more or less related to certain applications, such as gear
contacts. The classifications used have recently been based
more on the fundamental mechanisms of material removal due
to the increased knowledge of the fundamental wear processes.
The most widely used classifications are: adhesive wear,
abrasive wear, fatigue wear and tribochemical wear [1,21].
We believe that the classification of basic friction and wear
mechanisms can be developed even one step further and suggest
the classification shown in Fig. 2. Friction is the motion
resisting force at a certain moment in the process of motion
between the two surfaces in contact. This may be due to:
1) adhesion, that is breaking the adhesive bonds between the
two surfaces,
2) ploughing, that is resistance originating from elastic and
possibly plastic deformation when a harder countersurface
moves through a softer or more elastic surface and
3) hysteresis, that is resistance originating form continuous
elastic deformation within one of the surfaces in motion.
In the basic friction mechanisms no material removal is
involved. Some debris in the contact zone would make the
contact mechanisms much more complicated but still the basic
mechanisms for motion resistance are those mentioned above.
Fig. 1. The advanced surface coating deposition techniques offer large possibilities to modify and tailor the top surface mechanical and chemical properties that govern
the friction and wear behaviour in industrial applications.
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K. Holmberg et al. / Surface & Coatings Technology 202 (2007) 1034–1049
Fig. 2. The basic friction and wear mechanisms are related to adhesion, ploughing and hysteresis. In the case of wear these contact mechanisms result in material
fracture, detachment and removal.
Wear is the process of detachment of material from one
surface. It is different from friction in the sense that it is not
taking place at a certain moment but during a time period when
the surfaces are in moving contact. The detachment of material
may be due to:
1) adhesion + fracture, that is the adhesive lifting or shearing
force is causing such high tension and shear stresses in the
surface that they exceed the material strength and a crack is
formed, resulting in crack growth and material detachment — a wear debris has been formed,
2) abrasion + fracture, that is a hard countersurface moves
through a softer surface and deforms it to the extent that such
high mainly shear stresses are formed that they exceed the
material strength and a crack is formed, resulting in crack
growth, fracture and material detachment — a wear debris
has been formed,
3) fatigue + fracture, that is compressive loading of the surface
deforms it to the extent that such high, mainly shear, stresses
are formed that they exceed the material strength and a crack
is formed, resulting in crack growth and material detachment — a wear debris has been formed. The crack growth
process may take place during a number of loading cycles.
By definition wear always includes material removal.
Normally fracture is a term describing bulk failure of brittle
materials. Here the term is understood more widely as a process
starting from loss of cohesion between bond structures in the
material, continuing as crack propagation and resulting in debris
being liberated from the surface.
The above classification of the basic wear mechanisms is
focussing on how the material removal takes place. For this
reason tribochemical wear is not included. The chemical
processes that take place on a surface are certainly important
but they are not mechanisms that cause material removal. They
are chemical reactions that cause surface material modification,
either improvement or degradation, and changes in, e.g., the
plastic and elastic properties and fracture resistance of the top
surface. The changed surface properties will either increase or
decrease the strength of the material and its resistance to
cracking and material removal. However, the basic mechanisms
of material removal in so-called tribochemical wear are still one
of the three mentioned above.
Actually the fatigue wear as it is normally considered can be
divided into two phases. In the first phase is only material
modification taking place without any material removal. During
continuous loading of the surface the close to surface material
properties are slowly changed. The second phase, that is the
wear or material removal phase, starts when the changed
material cannot any more withstand the loading and a crack is
created, it grows, material is liberated and debris is formed.
It is interesting to note that the friction hysteresis mechanism
is based on elastic material deformation and thus it is in a sense
similar to the ploughing mechanisms, only the geometry is
different. The same goes for the fatigue and fracture wear
mechanism that is based on material deformation by compression and shear and is in that sense similar to the abrasion
mechanism. So the next step would perhaps be to consider only
two basic friction and wear mechanisms. For friction it would
be adhesive friction and elastic and plastic deformation
controlled friction. For wear it would be adhesive wear and
plastic deformation and fracture controlled wear. The surface
material modification processes, surface chemistry and fatigue,
would be considered separately as non wear processes.
3. Scales in tribology
It is important to understand the basic mechanisms especially
when trying to model and predict friction and wear in different
contact situations. At the same time it is also important to
remember that very seldom do they appear in a contact situation
purely as such. Normally the basic mechanisms are combined in a
very complex way due to a more complicated contact geometry,
involving roughness and debris, due to inhomogeneous surface
materials with changing properties and due to variations in
loading and sliding conditions. The main parameters influencing
K. Holmberg et al. / Surface & Coatings Technology 202 (2007) 1034–1049
1037
Fig. 3. The tribological contact process is determined by a number of geometry, material and energy related parameters, including changes that can be described on e.g.
macro- micro- and nano-level and results in friction, wear and changed contact conditions.
the tribological process are illustrated in Fig. 3. During the sliding
contact some of the parameters will change, surface layers are
formed, strain hardening takes place, local temperature rises
causing softening, etc. and after one sliding event we may have a
new set of parameters controlling the friction and wear.
It is often useful to study the tribological phenomena on
different size levels. Fig. 4 shows typical contact conditions that
occur on a macro level when a hard sphere is sliding on a flat
surface deposited with a thin coating [22]. Even if the number of
influencing parameters is large the situation is still not hopeless
to control. In each contact situation there is typically a limited
number of some five to ten parameters that dominate the friction
and wear behaviour. If we can identify them and understand
their interactions then we are well on the road to predicting and
controlling both friction and wear. Dominating parameters in
the contact situations shown in Fig. 4 are the coating/substrate
hardness relationship (hard on soft or soft on hard), coating
thickness, surface roughness and debris in the contact. These are
very important parameters since in a typical PVD or CVD
coated contact coating thickness, surface roughness and wear
debris are all in the size range of some few micrometers and thus
their interrelationship is crucial.
The whole picture is becoming even more complicated since we
have friction and wear related phenomena appearing on different
Fig. 4. Main parameters influencing the friction in a macro-contact with thin coated surfaces are the hardness of the coating and the substrate, the coating thickness, the
surface roughness and debris in the contact zone. These parameters result in several different contact conditions, each of which can be modelled by a set of dominating
parameters and interaction mechanisms.
1038
K. Holmberg et al. / Surface & Coatings Technology 202 (2007) 1034–1049
Fig. 5. The tribological process has been studied on machinery level, component level, contact level, asperity level and molecular level.
size levels. In some cases we have shearing taking place on a nano
level due to molecular or atomic interactions. In other cases we talk
about cracks appearing at asperity collisions on a microlevel. Or
when observing the prevention of contacts by elasto-hydrodynamic lubrication we calculate the pressure and lubricant film
thickness on a macrolevel. Forces and vibrations are observed on
component level while the efficiency and lifetime is estimated on
machinery level. These length scales of tribology that represent
different approaches to identify and understand characteristic
tribology related phenomena are illustrated in Fig. 5 [23].
Here we can talk about tribology on five different length
scale levels:
Nanotribology or molecular tribology includes phenomena
related to the interaction between molecules and atoms, such as
the effects of van der Waals forces and related interatomic
phenomena, determined by the crystal and bonding structures of
materials.
Microtribology or asperity tribology relates to aspects
typically taking place at the peaks of the surface topography.
Phenomena such as adhesion between asperities, fracture, elastic
and plastic deformation, debris formation, surface layer
formation and topography changes are all important at this scale.
Macrotribology or contact tribology relates to aspects often
covering the whole contact zone, such as the longer-range
stresses present within contacting bodies. Combined loading
response is important particularly in highly-loaded applications
like gears, bearing elements and rollers. Macro-level stresses
influence observable wear mechanisms such as scuffing,
scoring and pitting.
Component tribology or decitribology is related to defining
and measuring typical parameters originating from the interaction of components, and which define their performance, such
as torque, forces, vibrations, clearance and alignment.
Machinery tribology or unitribology describes the performance-related phenomena for a system of components
assembled in a machine or a piece of equipment. The parameters
of interest are performance, efficiency, reliability and lifetime
estimation.
4. Friction and wear mechanisms of diamond and DLC
coated surfaces
Detailed investigations in the 1990s and 2000s carried out in
many laboratories world wide have shown that extremely low
friction and wear can be measured for sliding contacts with one
or both surfaces covered by a thin diamond or DLC coating
(Table 1). In the most favourable cases the wear has been
undetectable and the friction coefficient has been even below
0.001, which is called super lubricity [24–28]. The mechanisms
Table 1
Friction coefficients values and wear rates from the literature for diamond,
diamond-like carbon and doped DLC coatings [29]
Property
Diamond
coatings
Hydrogen free Hydrogenated
DLC
DLC
Modified/
doped DLC
Structure
CVD
diamond
a-C
ta-C
a-C:H
ta-C:H
Atomic
structure
Hydrogen
content
μ in vacuum
μ in dry N2
μ in dry air
5–15%
μ in humid air
15–95% RH
μ in water
μ in oil
k in vacuum
k in dry N2
k in dry air
5–15%
k in humid air
15–95%
k in water
k in oil
sp3
sp2 and sp3
sp2 and sp3
a-C:Me
a-C:H:Me
a-C:H:x
Me = W,Ti….
x = Si,O,N,F,
B…
sp2 and sp3
–
N1%
10–50%
0.02–1
0.03
0.08–0.1
0.3–0.8
0.6–0.7
0.6
0.007–0.05
0.001–0.15
0.025–0.22
0.03
0.007
0.03
0.03–0.15
0.05–0.23
0.02–0.5
0.03–0.4
0.002–0.08
0.07–0.1
0.03
60–400
0.01–0.7
0.06
0.01–0.06
0.0001–400
0.01–1
0.1–1
0.0001–1
–
–
0.002–0.2
0.15
(0.1)
1–1000
0.1–0.2
1–5
0.0001
0.00001–0.1
0.01–0.4
The wear rate k is given in 10− 6 mm3/N·m units.
K. Holmberg et al. / Surface & Coatings Technology 202 (2007) 1034–1049
1039
The contact mechanism is dominated by asperity interlocking, asperity breaking and asperity ploughing.
- Diamond coatings sliding in air, water or oil (Fig. 6b) with
micro scale smooth topography, Ra =0.01–0.1 μm, have a
friction coefficient of μ =0.001–0.1 and a wear rate k =0.0001–
0.1 · 10− 6 mm3/N m with the lowest μ and k values measured in
water. A graphite film of the thickness h= 100–200 nm is
formed on the contacting surfaces. The contact mechanism is
shear within sp2 hybridised graphitic basal planes, formed by
transformation from sp3 by sliding asperities at high local
temperature and pressure.
- Diamond coatings sliding in air at T b 600 °C and nonvacuum (Fig. 6c) nano scale molecularly smooth topography, Ra = 1–30 nm, have a friction coefficient that is
μ = 0.03–0.15 and a wear rate of k = 0.01–5 · 10− 6 mm3/N
m. The contact mechanism is shear between two flat layers
of single hydrogen atoms at dangling bonds. Only weak van
der Waals bonds between the atoms are present and no
strong chemical bonding is involved.
Corresponding contact conditions at the macro, micro and
nano scales are shown in Fig. 7 for diamond-like carbon coatings.
Fig. 6. Different tribological contact mechanisms determining friction and wear
for diamond coated surfaces described on (a) macro scale with engineering
surfaces, (b) on micro scale with smooth engineering surfaces and (c) on
nanoscale with physically smooth surfaces.
resulting in these conditions were first not very clear to
researchers. Some mechanisms have been proposed, such as the
dangling bond mechanism, surface graphitisation and transfer
layer formation. All three of these have been convincingly
shown to work both experimentally and theoretically. However,
in the literature these mechanisms are often mixed and it is not
clearly understood which mechanism is dominating in which
conditions.
We believe that it is easier to understand the governing
friction and wear mechanisms by analysing the tribological
contact condition at different length scales. We call the levels
macro, micro and nano scale and they are closely linked to the
roughness of the surfaces in contact. On a macro scale we look
at what we would call typical engineering surfaces with a
surface roughness in the range of Ra = 0.1–1 μm. On a micro
scale the surfaces are what we would call smooth engineering
surfaces with a roughness in the range of Ra = 0.01–0.1 μm.
And on nano scale the surfaces are physically smooth with a
roughness in the range of Ra = 1–30 nm. In addition to the
surface roughness the surrounding environment is another
important parameter that we consider.
- Diamond coatings sliding in air or vacuum (Fig. 6a) at a
macro scale may have a very rough, sometimes pyramid
shaped, topography, Ra = 0.1–1 μm; the friction coefficient is
μ = 0.1–0.7 and the wear rate k = 0.1–100 · 10− 6 mm3/N m.
Fig. 7. Different tribological contact mechanisms determining friction and wear
for diamond-like carbon coated surfaces described on (a) macro scale, (b) micro
scale and (c) nano scale.
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K. Holmberg et al. / Surface & Coatings Technology 202 (2007) 1034–1049
The data given above originate from a number of
experimental studies listed in Table I. The mechanisms referred
to are summarised from the most recent literature [1–3,6,27–
29]. The parameter representing the hydrogen content
in DLC coatings has not been included in the presentation
above in order to more clearly illustrate the scale effect. The
hydrogen effect has been analysed and discussed in detail
elsewhere [29].
tool for tribological modelling at the nano scale [30–33]. In the
following we will focus on showing how FEM modelling helps
us understand the interactions in a tribological contact with thin
coatings on the micro scale level.
Based on the analysis of the basic friction and wear
mechanisms discussed above in Section 2 we will first analyse
different contact situations and indicate the tribologically
dominating parameters that should be the focus in a modelling
study.
The friction and wear is governed by the shear taking place
at the top surface and in the deformed surface layer, and by
the elastic, plastic and fracture behaviour both at the top surface
and in the deformed surface layer. A thin coating is typically
a part of this deformed surface layer. In addition surface
degradation may take place due to tribochemical and fatigue
processes that influence on the surface strength to withstand
loaded conditions. Thus the crucial material parameters are the
elastic modulus, the hardness or shear strength and the fracture
toughness on the top surface, in the coating, at the coating/
substrate interface and in the substrate under the coating, as
shown in Fig. 8. In this presentation hardness, H, is used as a
symbol representing the resistance to plastic deformation due
to its common use (even if referring to the elastic–plastic
constitutive response of the material would be the correct
expression).
In this presentation we limit ourselves to the conditions of a
sphere sliding over a flat coated surface, ideally smooth
surfaces, homogenous materials and no contamination or wear
debris involved. The influence of these parameters in a coated
contact has been discussed elsewhere [1,6].
Adhesive friction is dominated by the shear taking place in
the surface top layer or the shear in between the two interacting
surfaces (see Fig. 2). Surface chemistry, reaction and transfer
layers and structural parameters, like hydrogen content for DLC
coatings, are important. The coefficient of friction
5. Dominating surface parameters in a coating contact
la ¼ f ð s u Þ
- DLC coatings sliding in air, water or oil (Fig. 7a) at a macro
scale with a rough topography, Ra = 0.1–1 μm, have a
friction coefficient μ = 0.01–0.6 and a wear rate k = 0.0001–
1 · 10− 6 mm3/N m. The contact mechanism is graphitisation
of the top surfaces with shear within sp2 graphitic basal
planes resulting in low shear resistance. In some cases the
surface roughness may inhibit graphitisation resulting in
high friction and wear.
- DLC coatings sliding in air against a steel or ceramic
countersurface (Fig. 7b) with micro scale smooth topography,
Ra = 0.01–0.1 μm, have a friction coefficient μ = 0.05–0.3
and a wear rate k = 0.0001–10 · 10− 6 mm3/N m. The contact
mechanism is first smoothening of the countersurface by
building up a transfer layer containing typically Al, C, Cr,
and Fe. The transfer layer thickness is h = 100–200 nm.
Graphitisation occurs on both the DLC top surface and the
countersurface transfer layer. Shear takes place within the
sp2 graphitic basal planes.
- DLC coatings sliding in dry nitrogen (Fig. 7c) with nano
scale molecularly smooth topography, Ra = 1–30 nm, have a
friction coefficient that is μ = 0.001–0.15 and a wear rate of
k = 0.00001–0.1 · 10− 6 mm3/N m. The contact mechanism is
shear between two flat, highly hydrogenated layers of single
hydrogen atoms at dangling bonds. A positive atomic dipole
charge of the hydrogen atoms out from the surface at both
surfaces gives rise to repulsive forces.
Complete modelling of a tribological contact is a most
complex task. This is on one hand due to the large number of
influencing parameters, related to contact geometry, material
properties and energy input, and on the other hand, due to the
number of interactions taking place simultaneously on different scales with a variation of up to ten orders of magnitude
both in terms of size and time, as illustrated in Fig. 5. The
picture gets even more complex when we introduce coatings on
the surfaces. Still it is possible to get very useful results from
tribological modelling by not trying to be too generic and
instead focussing on a specific contact case and specific
contact phenomena related to limited contact conditions.
Advanced finite element method (FEM) techniques offer
today a very good tool for tribological modelling of the mechanical behaviour, including deformations, stresses and strains, of
a tribological contact both on macro and micro scales [9–17].
Molecular dynamic simulation (MDS) has developed rapidly
over the last decade boosted by the increased computer power
and software development. It has turned out to be a very useful
ð1Þ
Ploughing friction is dominated by the elastic and plastic
behaviour of the coating and the substrate. Structural properties,
multilayer, gradient, modified and doped structures and structural
parameters, like sp2/sp3-ratio for DLC coatings, are important. The
Fig. 8. Symbols used for material parameters in a coated surface.
K. Holmberg et al. / Surface & Coatings Technology 202 (2007) 1034–1049
1041
Fig. 10. Abrasive wear is characterised by a hard asperity (a) or debris (b) that
deforms the countersurface in a ductile or brittle way resulting in fracture,
cracking and debris generation.
each location as shown in Fig. 9 b–e. Due to the depth of the
debris detachment the result is
-
top layer fragments dominated by Ku (Fig. 9b),
coating fragments dominated by Kc (Fig. 9c),
coating delamination dominated by Ki (Fig. 9d) or
substrate and coating debris dominated by Ks (Fig. 9c).
Fig. 9. Two surfaces attach to each other by adhesion (a) and the movement of
the top surface results in an adhesive force, Fa, that tries to detach material over
an area, A, from one of the surfaces. The detachment may take place (b) at the
top surface, (c) within the coating, (d) at the coating/substrate interface and (e) in
the substrate.
Abrasive wear is dominated by geometrical collision of the
two moving surfaces resulting in high stresses, material shear
and fracture, and debris formation. The collisions may be due to
hard asperity or debris ploughing or asperity collisions, as
shown in Fig. 10. The wear rate
capacity of the coating/substrate system to withstand deformation is
frequently called load carrying capacity. The coefficient of friction
k ¼ Vabr =wd s ¼ f ðKc ; Ki ; Ks ; Hc ; Hi ; Hs ; hÞ
lp ¼ f ðEc ; Hc ; Es ; Hs ; hÞ
ð2Þ
Hysteresis friction is mainly dominated by the elastic
properties of the substrate but also to some extent by the elastic
properties of the coating. The coefficient of friction
lh ¼ f ðEs ; Ec ; hÞ
Due to the depth of the debris detachment the result is
- coating fragments dominated by Kc,
- coating delamination dominated by Ki or
- substrate and coating debris dominated by Ks.
ð3Þ
Adhesive wear is dominated by the fracture behaviour in the
surface top layer, in the coating, at the coating/substrate interface
and in the substrate. With fracture we understand here the property
of the material to resist cracking, intrinsic detachment and
breaking to parts. The adhesive force, Fa, from the counterface
tries to tear off part of the surface material over the contact area A
(Fig. 9a). When surface roughness is included A will decrease and
the adhesive wear typically decrease. The wear rate
k ¼ Vadh =wd s ¼ f ðKu ; Kc ; Ki ; Ks Þ
ð5Þ
Fatigue wear is a result of material degradation where the
strength of the material decreases to a level so that it cannot any
more withstand the repeated loading. The result is fracture,
cracking, and debris formation (Fig. 11). It is dominated by the
ð4Þ
where Vadh is the volume of adhesive wear, w is the load and s is
the sliding distance.
The breaking of the material may take place at different
locations in the surface depending on the material strength at
Fig. 11. Fatigue wear is characterised by repeated loading of the coated surface
resulting in cracking at the surface in the coating, at the interface or in the
substrate, followed by fracture, material detachment and debris generation.
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K. Holmberg et al. / Surface & Coatings Technology 202 (2007) 1034–1049
elastic and fracture properties of the coating, the coating/substrate
interface and the substrate. The loading may be rolling or sliding.
The wear rate
k ¼ Vfat =wd s ¼ f ðKu ; Kc ; Ki ; Ks ; Ec ; Ei ; Es ; hÞ
ð6Þ
Due to the depth of the debris detachment the result is
-
top layer fragments dominated by Ku,
coating fragments dominated by Kc,
coating delamination dominated by Ki or
substrate and coating debris dominated by Ks.
Surface modification is here considered separately from the
pure wear mechanisms since it alone will not result in material
liberation. Still it is very important to consider in a wear process
since it often precedes the wear event and may be the reason for
wear to start. Typical surface modification mechanisms are
chemical reactions taking place at the surface and material
fatigue from repeated loading.
Chemical reactions and sometimes even physical structural
modifications, such as oxidation of metallic coatings, graphitisation of DLC and crystallographic re-orientation of MoS2
coatings, take place mainly at the top surface and influence the
shear, τu, and fracture, Ku, properties and thus the adhesive
friction and adhesive wear. Sometimes also the whole coating
structure and the coating/substrate interface may be affected.
Fatigue is a result of repeated compressional loading on the
material that weakens the molecular structure by including
cumulative damage to a level that it cannot take the loading any
more. The maximum compressional stress peaks are normally
under the coating in the substrate because the coating layer is
very thin. Thus the substrate elastic properties, Es, and fracture
toughness, Ks, are crucial. If the stress peaks are high also closer
to the surface, the elastic and fracture properties of both the
coating and the coating/substrate interface, Ec, Kc, Ei and Ki,
may also be important.
6. Modelling the surface loading conditions, stresses and
strains
6.1. The contact geometry
In our work the tribosystem of a sphere sliding on a coated
flat surface with increasing normal load was chosen for the
study. This corresponds to the contact of the diamond tip sliding
against the coating in a scratch tester and thus there is much
empirical information available to compare with. The method is
widely used today by the coating industry and coating
development laboratories, as well as in research for evaluating
the tribological properties of coatings. The scratch test is
generally accepted as a good and efficient method for the
quality assessment of a coated surface [34]. In the scratch test
procedure the diamond stylus has a Rockwell C geometry with a
120° cone and a 200 μm radius spherical tip. The scratch test
procedure is described in the European Standard prEN 1071-3
[35].
6.2. Contact mechanisms, deformations and stress generation
The material loading and response conditions in a scratch
tester have been divided into three phases by Holmberg [36] to
illustrate the contact and deformation mechanisms involved.
Phase one represents the ploughing of a stylus in the substrate
material. The substrate material is deformed by elastic and
plastic deformation and a groove is formed. Phase two represents the bending and drawing of the coating like a sheet
on top of the substrate surface. The upper surface of the
coating rubs against the stylus front surface and the force
required for pulling the coating is equal to the frictional force
on the coating against the stylus front surface. The bending
movements cause stresses and stress release in the coating.
Phase three represents pulling the coating from one point on
the surface when fixed over the substrate. The increasing
pulling force results in cracks at the place of maximum tensile
stress.
The sliding spherical diamond tip deforms the surface both
plastically and elastically as schematically shown in Fig. 12. At
the initial stage a small spherical indent is formed and the plastic
material flow pushes up the material around the indent in a torus
formed shape. As the tip moves forward a groove with increasing
depth is formed. Under the tip there is both plastic and elastic
deformation while in the surface behind the tip only the plastic
part prevails. Another torus shape is formed in front of the tip.
The stress field in the coated surface is formed as a result of
the following four effects:
1) Friction force. The friction force between the sliding tip and
the surface results in compressional stresses from the
pushing force in front of the tip and tensional stresses from
the pulling force behind the tip.
2) Geometry changes. The elastic and plastic deformations are
spherical indent, groove and torus shaped. They result in
bending of the coating as shown in Fig. 12. The stresses are
both compressional and tensional.
3) Bulk plasticity concentration. The spherical indentation
pattern causes the substrate to deform plastically, reaching
its peak value at an angle of about 45° from the plane of
symmetry in the plane of the coating. This can be identified
with local tensile stress minima and maxima of deformation
between the tensile stress peaks around the indenter (at
locations of 0 and 90°, respectively).
4) Residual stresses. It is very common especially for thin
ceramic coatings that they, due to the deposition process,
contain even very considerable compressional residual
stresses. These are typically of the order of 0.5–3 GPa but
values even as high as 10 GPa may appear [1,37,38].
When the diamond stylus is drawn over the surface with an
increasing normal load, a very complex and dynamic stress field
is formed with stress concentrations at changing locations. For
e.g. a TiN or DLC coated steel surface it typically results in a
coating fracture and spalling pattern. The formation of cracks in
the groove of a scratch tester has been shown by several authors
[35,39–43]. They can typically be described as a) angular
K. Holmberg et al. / Surface & Coatings Technology 202 (2007) 1034–1049
1043
Fig. 12. The stress field in a coated surface resulting from a sliding sphere is a result of four loading effects: friction force, geometrical deformations, bulk plasticity
concentration and residual stresses. Illustration (a) shows the loading effects with exaggerated dimensions and deformations and (b) with correct dimension
interrelationships.
cracks, b) parallel cracks, c) transverse semi-circular cracks, d)
coating chipping, e) coating spalling, and f) coating breakthrough. Methods for the determination of mechanical properties
of coatings and contact stresses have been reported [44,45].
6.3. Modelling the contact by three dimensional finite element
method
A three dimensional finite element model has earlier been
reported and was now further developed for calculating the
stresses and strains in the coated surface and for identifying
the stress concentrations where the first cracks of the coated
surface are expected to occur [9–11,17]. The scratch test
experiment was discretised using the inherent symmetry of
the geometry and introducing a finite element mesh where
mesh sizing is of the order of the coating thickness (Fig. 13).
After analysing the convergence behaviour of the boundary
value problem and assessing whether suitable accuracy of
contact-related field variables can be attained, a suitable
mesh density around the contact area was found to be
25 nm–8 μm. Bilinear hybrid elements were used in Abaqus
6.6-3, 6.2-1 and Warp3D 15.3 finite element software. The
volume of the finite element slit taken to describe the scratch
test configuration was 12 × 4 × 2 mm 3 (length, width,
thickness). The substrate deformation behaviour was characterised as elastic–plastic with isotropic hardening, while
the coating was modelled to behave in a linear–elastic
manner. The sliding spherical diamond tip was modelled as
completely rigid.
The kinetic formulation was presented applying a finite
strain deformation description. The contact event was
modelled by describing two contact zones, commonly
referred to as the master and slave surfaces, where the
master surface is the one having greater rigidity. During the
progress of the experiment the relative positions of the master
and slave surfaces define the contact event. The contact
formulation was of the finite sliding type due to large local
deformations and the distance the tip travels during the
experiment. The contact was presented as a ‘hard contact’
between smooth surfaces, i.e. tractions are transferred at the
instant of contact but not before. Computational initial
oscillations were treated with viscous damping. A velocityindependent Coulombian friction model was used to
characterise related surface interactions, and the surfacehardening effect due to plastic deformation of the substrate
Fig. 13. Schematic illustration of the three dimensional finite element mesh. The
mesh sizing is in the range of 0.025–100 μm and the number of mesh degrees of
freedom is about 500.000.
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K. Holmberg et al. / Surface & Coatings Technology 202 (2007) 1034–1049
included in the model. The basic model is in detail described
in [10].
The results are inferred and analysed primarily with
respect to the first principal stress. Generally, studies in the
current field apply the von Mises equivalent stress to
characterise deformation and failure events. However, the
von Mises stress has its greatest potential in understanding
and modelling deformation-related events, such as the
plasticity of metals, and is not usually associated with the
brittle type of failure. It can be argued, and has often been
presented [46] that local unstable cracking is more dependent
on the prevailing tensile stress state than the practically nonexistent state of deformation, and that deformation-related
parameters and invariants do not comply with the physical
appearance of fracture. Most local approach models for such
failure micromechanisms rely on the first principal stress.
Since the current work is related to cracking of a brittle layer
incapable of exhibiting much more than elastic deformation
all the way to final rupture, it can be expected that the use of
the first principal stress as a fundamental stress component to
explain the physical fracture patterns will bring about the
most success.
Compared to real scratch tester contact conditions, the
following limitations have been set for the sake of simplicity:
- Compressive residual stresses normally occurring in ceramic
thin coatings are not included in the simulation cases
reported here. They have been introduced into the model and
results with residual stresses have been reported separately
[17,47].
- The stress relaxation effect of previously generated cracks on
the stress distribution is not included in the present
simulations.
- The surfaces in the model are ideally smooth, which means
that surface roughness effects are not considered.
- The materials are considered to be fully homogenous and
free from contaminants, pinholes and such defects often
occurring in thin ceramic coatings.
7. Simulation of surface stresses and strains
7.1. Simulated contact conditions
The above described contact conditions and sliding process
have been simulated by the computer model. The following
parameters were used in the calculations of the stress and strain
distributions:
Scratch test parameters: sliding distance 10 mm, load
increases linearly from 5 N pre-load and 0.5 μm indentation
depth before sliding starts to 50 N and 3 μm indentation depth at
10 mm sliding distance, and the sliding velocity is not included
in the model, i.e. the model is time independent.
Sliding stylus (Rockwell C): radius of the spherical tip
200 μm, the material is diamond, Young's modulus 1140 GPa,
hardness 80 GPa, Poisson's ratio 0.07, and the roughness is
ideally smooth.
Coating: thickness 2 μm, the material is titanium nitride
(TiN) deposited by PVD, Young's modulus 300 GPa, hardness
25 GPa, Poisson's ratio 0.22, and the roughness is ideally
smooth.
Bond layer: thickness 500 nm, hard ceramic layer with a
Young's modulus of 500 GPa and Poisson's ratio 0.22.
Substrate: the geometry is an ideally smooth plate, the
material is High Speed Steel, Young's modulus 200 GPa,
hardness 7.5 GPa, Poisson's ratio 0.29, the yield strength is
estimated from ultimate bending strength to 4100 MPa, and the
strain hardening coefficient is 20.
Friction: The values for the coefficient of friction were
measured from samples corresponding to the above material
combination. In the simulations a constant value 0.08 was used
for the coefficient of friction due to friction from interfacial
shear which excludes the ploughing component of friction.
7.2. First principal stresses of a TiN coated steel surface with
hard bond layer
One typical simulated stress distribution is shown in Fig. 14.
The figure is a topographical stress-field map where each colour
corresponds to a certain stress level range at the surface and at
the intersection shown in the figure. The observation direction is
similar to that in Fig. 12 but the spherical tip is invisible in order
to display the stresses. The border of the corresponding contact
area of the coated plate and the sphere is close to the green to
yellow colour transition half circle where the stresses are close
to zero.
The smoothly changing stress field shows a considerable
compressional stress under the diamond tip, indicated by green
and blue colours, and the variations in the tensile stresses
around the contact zone, indicated by the orange and red
colours. The maximum compressional stresses under the tip are
about 5200 MPa and the compressional stresses ranges about
40 μm down below the surface. It can also well be seen that
there is a thin range of high tensile stresses within the bond layer
right under the loaded tip. These tensile stresses are about
3000 MPa just under the tip. A circular region of high tensile
stresses is seen as a red belt around the contact zone. It has its
maximum value at some distance behind the back of the contact
zone at the location of the formed groove edge. Here it reaches a
level of about 3300 MPa. This is the place where the first cracks
normally occur in scratch test experiments with similar coated
surfaces. Behind the contact zone there is a tail of high residual
tensile stresses on the surface in the groove area having values
of about 2500 MPa.
Fig. 15 shows a close up of the part of Fig. 14 just at the back
end of the contact zone by the symmetry plane. It shows both
the distribution of the rapid stress change in this region and the
very high tensile stresses in the bond layer just behind the
contact zone, being as high as 5150 MPa.
7.3. Strain in a TiN coated steel surface with hard bond layer
The strain distribution for the same contact conditions as in
Fig. 14 is shown in Fig. 16. The dark red region directly under
K. Holmberg et al. / Surface & Coatings Technology 202 (2007) 1034–1049
1045
Fig. 14. Topographical stress-field maps showing first principal stresses on the coating and at the symmetry plane intersection of the steel sample coated with a 2 μm
thick TiN coating (E = 300 GPa), a 500 nm hard interface layer (E = 500 GPa) and loaded by a sliding spherical diamond tip. Sliding direction is from left to right. The
values on the colour scale are given as MPa. The stress field at 15 N load and 2.1 mm of sliding is shown.
the loading tip shows large strain due to both elastic and plastic
deformation and it reaches about 40 μm down under the surface.
The red tail behind the contact region shows the residual plastic
strain just under the groove and it reaches about 20 μm down
under the groove surface.
7.4. First principal stresses of a TiN coated steel surface with
interface crack
Cracks at the surface will have a considerable influence on the
formed stress fields. The lateral cracks generated at the interface
Fig. 15. Close up of the region just behind the back of the contact zone at the interface plane in Fig. 14.
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K. Holmberg et al. / Surface & Coatings Technology 202 (2007) 1034–1049
Fig. 16. Topographical strain-field maps showing equivalent strain on the coating and at the symmetry plane intersection of the steel sample coated with a 2 μm thick
TiN coating (E = 300 GPa), a 500 nm hard interface layer (E = 500 GPa) and loaded by a sliding spherical diamond tip. Sliding direction is from left to right. The values
on the colour scale represent the equivalent strain at 15 N load and 2.1 mm of sliding.
between the coating and the substrate are of special interest since
they indicate the break down of the coating/substrate adhesion.
The growth of these lateral cracks result in the formation of larger
detached coating flakes and coating delamination from the
surface. Fig. 17 shows the stress pattern and the high stresses
formed by the ends of one short lateral crack at the interface.
Fig. 17. Topographical stress-field maps showing first principal stresses at the symmetry plane intersection of the steel sample coated with a 2 μm thick TiN coating
(E = 300 GPa), having a 1 μm long lateral crack at the coating/substrate interface and loaded by a sliding spherical diamond tip. Sliding direction is from left to right.
The values on the colour scale represent relative stress at 10 N load and 1.2 mm sliding.
K. Holmberg et al. / Surface & Coatings Technology 202 (2007) 1034–1049
1047
Fig. 18. Crack growth parameters studied and used terminology.
7.5. Crack propagation in a TiN coated steel surface
II and III (in-plane and out-of-plane shear). The results are
presented using the equivalent SIF concept, i.e.
The crack propagation has been studied by Boundary Element
Method (BEM) by [17] based on analysis of the simulated stresses
in the coated surface. The parameters influencing on crack
propagation studied can be summarised as (Fig. 18):
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
KE ¼ KI2 þ KII2 þ ð1 þ mÞKIII
1)
2)
3)
4)
loading modes, (I, II, III).
orientation of the crack, (θ = 0, 20°, 45°)
density of the crack field, crack spacing (ρ =5, 10, 30 μm and ∞)
location of the crack in the crack field, (centrecrack,
centrecrack + 1 etc., edgecrack)
5) location of the crack on the scratch groove (middle cracks,
side cracks)
6) tensile load biaxiality in loading mode I, (β = 0, 0.5, 1)
Observe that the crack spacing ρ = ∞ = infinite corresponds to
one single crack and ρ = 0 to an infinite number of cracks
approaching each other.
The results of the BEM analysis are summarised in Fig. 19.
BEM analysis results for single crack cases with different crack
angles are presented for uniaxial tension and for loading modes
ð7Þ
The crack angle is defined such that cracks oriented at an
angle of 0 degrees are perpendicular to the applied uniaxial
tension. All results were presented over a normalized crack front
parameter, s, and given normalized with the value of stress
intensity factor (SIF) at the deepest point of the single crack case
under uniaxial tension. It was shown that crack oriented from the
perpendicular plane towards tension exhibit a somewhat smaller
equivalent crack driving force, the differences being of the order
of 15% for crack tilted 20° and 30% for crack tilted 45°.
Different loading mode effects to crack driving force are
indicated, mode II component is being somewhat pronounced
over the mode III. The effects of biaxial loading are of the order
∞
∞
of 5–10% with biaxiality ratios (β) of 1 and 0.5, β = σ22
/σ11
,
where the stress components are applied at model boundary.
The effects of crack field density on straight cracks with
uniaxial tension are depicted. A single uniaxial tension crack
Fig. 19. The effect of different crack growth parameters on normalized stress intensity factor (SIF).
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K. Holmberg et al. / Surface & Coatings Technology 202 (2007) 1034–1049
case is provided for reference. Two effects are noted, first how
crack density introduces a differing driving force to variable
density crack fields and second, how center and edge cracks
exhibit a somewhat different driving force dependant on crack
density. For crack fields with a lower density the crack driving
force is higher in comparison to dense crack cases and separate
cracks are relatively independent of each other, i.e. different
cracks have nearly identical crack driving forces. It was noted,
that the crack density is an extremely important parameter in
evaluating the SIF values, the effects being more than meaningful.
Crack location, i.e. whether edge or center cracks are
concerned, has similar effects as with straight cracks under
unidirectional tension. Loading biaxiality had no remarkable
effect on straight scratch bottom cracks, but the differences
become noticeable when angular cracks are concerned. The
differences for the ρ = 5 μm crack field are at their maximum of
the order of 35%, the biaxiality effects affect edge and center
crack field cracks much in the same fashion and of the same order
of magnitude. Biaxial loading is seen to have a similar effect as
with the middle crack fields, the overall difference between the
single transversal middle crack being of the order of 40–60%.
Different density crack fields are seen to produce relatively field
density insensitive results, whilst differing quite a bit from the
single crack solution, the difference being of the order of 80%.
8. Conclusions
The article discusses the basic friction and wear mechanisms,
scale effects and parameters influencing the friction and wear of
surfaces coated with thin films. This forms the basis for surface
optimisation by modelling, stress simulation and surface fracture
calculations.
It is shown that the basic friction and wear mechanisms can
be reduced to friction by adhesion, ploughing and hysteresis and
wear by adhesion, abrasion and fatigue combined with material
fracture. The tribochemical and surface physical effects and
surface fatigue taking place before material fracture are treated
as pure surface material modification mechanisms.
The scale effects in a tribological contact are illustrated by
explaining typical surface roughness related tribological
mechanisms for diamond and DLC coated surfaces. For
diamond coatings asperity interlocking effects are important
for rough surfaces, graphitisation dominates for smooth
engineering surfaces and hydrogenisation of dangling bonds
may be crucial for physically smooth surfaces. For DLC coated
surfaces surface graphitisation is important with rougher
surfaces, building up transfer layers and graphitisation is crucial
for smooth engineering surfaces and hydrogenising of dangling
bonds can explain superlubricity for physically smooth
surfaces.
An analysis of dominating surface parameters such as elastic,
plastic and fracture behaviour of the top surface, the coating, the
coating/substrate interface and the substrate in addition to the
coating thickness forms the basis for surface modelling. The
dominating parameters depending on the governing basic wear
mechanisms have been identified. Stress simulations locate high
tensile stresses on the top surface behind a sliding spherical tip
and high residual tensile stresses in the coating covering the
deformed groove. Hard interlayers between the coating and
substrate generate extremely high tensile stresses and the
formation of stress concentrations at crack ends for cracks at the
coating/substrate interface are shown.
A stress intensity factor analysis of crack growth shows the
importance of considering all modes I, II and III stresses, crack
spacing and location of crack in the scratch groove, while crack
orientation, location in crack field as well as load biaxiality have
minor influences.
The study shows how surface 3D FEM modelling generates
stress and strain values at nano level, at coating/substrate
interfaces and around cracks and forms a basis for understanding
the origin of wear. Micro and nano scale modelling, simulation
and fracture calculations are very useful tools for a systematic
approach to finding optimal surface and coating parameters and
for successful surface design for a specific application.
Acknowledgements
The authors want to acknowledge the following colleagues
for the interesting and valuable discussions in relation to the
work: Allan Matthews, Sheffield University, UK; Philippe
Kapsa, Ecole Central de Lyon, France; Henry Haefke and Imad
Ahmed, CSEM, Switzerland; Ali Erdemir, Argonne National
Laboratory, USA; Koij Kato, Tohoku University, Japan; and
Kaj Pischow and Rosa Aimo, Savcor Coatings.
The financial support of TEKES the Finnish Technology
Agency; Taiho Kogyo Tribology Research Foundation, Japan;
Savcor Coatings, Finland; and the VTT Technical Research
Centre of Finland is gratefully acknowledged.
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