Wear 263 (2007) 1315–1323
Friction in a coated surface deformed by a sliding sphere
Helena Ronkainen ∗ , Anssi Laukkanen, Kenneth Holmberg
VTT Technical Research Centre of Finland, P.O.Box 1000, FI-02044 VTT, Finland
Received 6 September 2006; received in revised form 31 January 2007; accepted 31 January 2007
Available online 16 May 2007
Abstract
Stress and strain modelling and stress field computer simulations are today an important tool for systematic approach and optimisation of
tribologically stressed coated contacts. Modelling illustrates and quantifies the dominating parameters resulting in crack initiation, crack growth
and failure of coated surfaces. Friction and its components, adhesive and ploughing friction, are necessary input parameters in stress modelling. In
Finite Element Method (FEM) modelling the ploughing component is integrated in the model while the adhesive component needs to be determined
as input value for stress simulations. This paper presents how adhesive friction is determined for the TiN (μa = 0.066) and DLC (μa = 0.047) coatings
from experimental friction measurements. The experimental value is used as an input value in the three dimensional finite element micro-model
that simulates the spherical tip sliding on a DLC coated flat substrate with increasing load similar to the conventional scratch test contact. Based
on the numerical contact analysis (FEM) similar friction evolution compared to the experimental friction in scratch testing was depicted. However,
the analytical approach resulted in a diverse solution.
© 2007 Elsevier B.V. All rights reserved.
Keywords: Friction; Adhesive; Ploughing; DLC; TiN; FEM modelling
1. Introduction
Thin surface coatings are today increasingly used for improving the tribological performance of advanced products. Coatings
are applied on tools and mechanical components in the production industry, on disc drives in the computer industry, on
precision instruments, on lenses in optical systems and on human
replacement organs. Coating deposition techniques offer a wide
variety of possibilities to tailor surfaces with advanced, functional coatings. The chemical vapour deposition (CVD) and
physical vapour deposition (PVD) techniques have made it possible to deposit thin coatings in a large temperature range from
about 1000 ◦ C down to room temperature. Coating materials
such as TiN, TiC, Al2 O3 and diamond-like carbon (DLC) and
their combinations with multilayer structures and doping agents
have been used with great success in numerous applications. In
many cases, the coatings have reduced the friction and wear of
components by one or two orders of magnitude. In has been
shown, that even super-low friction values down to 0.001 in dry
∗ Corresponding author at: VTT Technical Research Centre, P.O. Box 1000
(Metallimiehenkuja 6), FIN-02044 Espoo, Finland. Tel.: +358 20 722 4485/40
559 1499; fax: +358 20 722 7077.
E-mail address: [email protected] (H. Ronkainen).
0043-1648/$ – see front matter © 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.wear.2007.01.103
sliding can be reached with advanced DLC technology [1–5].
The deposition techniques of thin coatings and their tribological behaviour and applications have been described in several
publications [6–10].
The tribological contact between two stressed surfaces in
relative motion is a very complex system that is not easy to
understand nor simulate or predict. The system becomes even
more complex when coatings are introduced on the surfaces.
The tribocontact has been studied on a macrolevel, i.e. on the
component level, at microlevel, i.e. the surface asperity level,
and at nanolevel, i.e. the molecular level [7,11,12]. One problem is that there is a large range of different parameters used
to describe friction and wear behaviour in coated tribological
contacts, some of which are not generic parameters, but directly
related to experimental devices used. When modelling deformation and fracture of materials, it is crucial to use generic material
parameters that describe the basic material behaviour, such as
the Young’s modulus in elastic deformation, the yield strength
of material correlating with hardness in plastic deformation and
the fracture toughness for brittle failure [13,14].
Hard layers, such as TiN and DLC, can reduce the coefficient of friction of both lubricated and unlubricated surfaces by
minimising ploughing and plastic deformation in the substrate.
Komvopoulos et al. [15] carried out a two dimensional FEM
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H. Ronkainen et al. / Wear 263 (2007) 1315–1323
Table 1
The thickness, hardness and Young’s modulus of the coatings used in the tests
Coating
Deposition method
Coating thickness (␮m)
Hardness (GPa)
Young’s modulus (GPa)
TiN
DLC
Magnetron sputtering
PACVD
1.8
0.9
35 ± 10
5 ± 0.4
475 ± 90
39 ± 2
analysis of friction in sliding contacts with hard coatings, such
as TiN. They verified that the deformation mode at the asperity
contacts depends on the layer thickness, the interfacial friction,
the magnitude of the surface traction and the mechanical properties, such as Young’s modulus and hardness, of the hard layer
in relation to those of the substrate. With 3D FEM simulations
of a sphere on a coated flat with two values of the coefficient
of friction, μ = 0.1 and 0.25, Kral and Komvopoulos [16] found
that increasing friction has little effect on the residual groove
depth, with the exception of a slight decrease in groove depth
with sliding distance. The higher friction case exhibits larger
front and transverse pile-up regions, indicating that increasing
the coefficient of friction produces more deformation of the surface material in the sliding direction. The larger frontal pile-up
region may be responsible for the decrease in groove depth with
sliding distance, since a larger bow supports a larger fraction of
the normal load, resulting in a slightly shallower groove.
It has been shown by FEM modelling and simulation [17]
that the effect of the coefficient of friction on the deformation
behaviour of elastic-plastic layered surfaces is significant for
sliding contact and secondary for indentation loading. High friction loading promotes plasticity and intensifies the von Mises
and first principal stresses in both the layer and the substrate,
thus increasing the possibility for yielding and cracking in both
the coating and the substrate. In high-friction sliding, plasticity
in the substrate is affected predominately by the coefficient of
friction and secondarily by the residual stress in the coating. The
assessment of the situation is complicated by the “mixed” constitutive response of the system due to different materials within it,
i.e. typically the linear-elasticity of the coating layer and elastoplasticity of the substrate, and as such a single model build on a
single constitutive model may not be generally adequate.
In the 3D FEM modelling and simulations of friction, stresses
and deformations in the contact of a sphere sliding against a
coated surface the coefficient of friction values in the range 0.08
to 0.5 have been used [17–26]. The high values of 0.5 are used in
studies of the frictional heating effect while lower values in the
range of 0.08–0.26 correlate with the friction during the scratch
testing of a coated surface with a diamond stylus. However, there
is some confusion in the literature since all authors do not clearly
define if their coefficient of friction means the adhesive component, as used in modelling, or the total coefficient of friction, as
received in, e.g. scratch test measurements.
The scratch test has been widely used for the adhesion evaluation of thin films [27,28]. The tangential force measured during
scratching represents the friction force in scratching action. The
friction values measured in scratch testing differ according to
the coating type, environment and scratching parameters used,
but typical values reported vary in the range 0.1–0.2 for the
TiN coating on steel substrate [29] and 0.1 to 0.2 for the DLC
coatings on Ti–6Al–4V substrate [30].
In this study the experimental determination of the adhesive
friction component has been carried out. Based on the experimentally determined friction values numerical finite element
analysis has been carried out. The results of numerical analysis
will be compared to the results of analytical determination and
to the experimental friction results of scratch testing.
2. Experimental
The substrate material used was power metallurgical high
speed steel (HSS, Böhler S790 ISOMATRIX) with a Young’s
modulus of 214 GPa, Poisson’s ratio of 0.29 and the strain
hardening coefficient of 20. The Yield strength was estimated
from ultimate bending strength of 4100 MPa. The hardness was
8.3 GPa and the samples were polished to surface roughness Ra
0.01 ␮m prior to deposition. Two different coating types were
used in the study, namely commercial titanium nitride (TiN)
coating deposited by magnetron sputtering and diamond-like
carbon (DLC) coating prepared by plasma enhanced CVD process [31]. The details of the coatings are represented in Table 1.
Scratch tests were performed for the samples by the VTT
scratch tester by using a diamond stylus with a spherical tip of
a 200 ␮m radius (Rockwell C). The preload of 5 N was used
and the normal force was increased continuously from 5 to
50 N during scratching. The loading rate was about 50 N/min
(0.83 mm/s), sliding speed 10 mm/min (0.167 mm/s) and the
scratch length was 10 mm. During scratching the tangential force
representing the friction force was measured continuously. Also
separate multi-pass friction measurements were performed for
the coatings and for the uncoated HSS substrate by using the
scratch tester in the multi-pass mode performing reciprocating movement. In multi-pass testing a static normal load of 5
and 10 N were applied and the sliding speed was 10 mm/min
(0.167 mm/s). The distance of one sliding cycle was 5 mm and
the sliding was performed in the same track during the 10 sliding cycles. The friction was measured during multi-pass testing
continuously. After the tests the mean value of friction for each
sliding cycle was calculated and this value represented the friction during one sliding cycle. The tests were performed in normal
air at 50 ± 5% RH and 21 ± 2 ◦ C.
3. Experimental results
The friction trends measured in scratch testing for TiN and
DLC coated and the uncoated HSS samples are presented in
Fig. 1. The scratch tests are typically carried out at least three
times for one sample. The values in Fig. 1 represent the typ-
H. Ronkainen et al. / Wear 263 (2007) 1315–1323
1317
Fig. 1. The friction evolution in scratch testing of TiN coated, DLC coated and
uncoated HSS substrates as the normal load is increased from 5 to 50 N.
ical values measured for the coatings used in this study. The
friction values showed an increasing trend during scratching,
the friction coefficient typically changing from 0.08 to 0.14 for
the TiN and from 0.075 to 0.14 for the uncoated HSS sample.
For the DLC coating the friction coefficient increased steadily
from about 0.06 to 0.01 after which the friction fluctuated due
to delamination of the coating. The friction evolution was similar for the uncoated and TiN coated samples, but for the DLC
coated sample a clearly lower friction performance in scratch
testing was observed. This is in accordance with the low friction
of DLC coatings reviewed by several authors [31,32].
The friction evolution in multi-pass testing for the ten sliding
cycles is represented in Fig. 2 for the TiN coated, DLC coated
and uncoated samples. The tests were repeated three times and
based on the measured friction data, an average friction value
was determined for each cycle. The average values are represented for the normal load of 5 N (Fig. 2a) and for the normal
load of 10 N (Fig. 2b). The friction coefficient of the first sliding
cycle was considered to contain both adhesive and ploughing
friction. As the sliding occurred in the same track during the
repeated sliding cycles, it was assumed that the friction coefficient measured during the second sliding cycle represented
mainly the adhesive friction component. The drop between the
first and the second sliding cycles μ, was considered to be
equal to the ploughing component of friction, μp, as described
in the model of Bowen and Taber [33]
μ = μa + μp
(1)
The adhesive and ploughing components of friction determined with the above mentioned technique for the TiN and DLC
coated and the uncoated substrates are presented in Fig. 3. The
scatter bars represent the scatter of the measured data determined
for each value of friction separately. The adhesive friction was
the lowest for the DLC coated (0.047) and highest for the TiN
coated (0.066) substrate in tests carried out with 5 N normal load.
The values of adhesive friction measured with 10 N normal load
were similar, since the mean values were within the scatter limits of the results. The ploughing friction presented clearly lower
values compared to adhesive friction and increased as the normal load was increased from 5 to 10 N. The dimensions of the
wear scars were measured after the tests and the width of the
Fig. 2. The friction values measured in the multipass tests with (a) 5 N normal
load and (b) 10 N normal load for ten sliding cycles. Sliding speed was 10 mm/s
and sliding distance 5 mm/cycle.
wear scar changed from 0.032 to 0.049 mm and the depth of the
wear scar from 0.33 to 0.83 ␮m as the normal load was increased
from 5 to 10 N.
4. Numerical contact analyses and friction
Numerical FEM analyses were carried out in order to further
interpret the development of contact stresses during the sliding
contact, and as such evaluate the relative proportions of adhesive
and ploughing friction components. The analyses were carried
out using the ABAQUS and WARP3D software packages. The
FEM mesh is presented in Fig. 4. The model consists of a rectangular block of material and a spherical indenter of a scratch tester.
The finite space used to represent the material block under loading by a sliding indenter is of 14 mm × 1 mm × 1 mm size, the
diamond indenter having a radius of 200 ␮m. The dimensions are
specified such that the model is large enough to generate boundary condition independent results, i.e. it simulates a relatively
large slab of material undergoing loading via a contacting tip.
Boundary conditions are specified to facilitate such a situation.
The model is a half-symmetry model as apparent in Fig. 4. The
‘bottom’ boundary restraint, in the direction of the indentation,
is fixed, whilst all other sides, other than the plane of symmetry,
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H. Ronkainen et al. / Wear 263 (2007) 1315–1323
Fig. 3. (a) The adhesive component of friction coefficient and (b) ploughing
component of friction coefficient determined from the friction data collected in
multipass sliding tests.
have a continuity boundary condition specified for the respective
displacement components. Model size was deemed adequate on
the basis that the results near and in the region of contact are not
affected by a further increase in model dimensions, and during
the computation for example plasticity arising under the contact does not reach such a volume or magnitude that coupling
to model dimensions would present itself. The model is static in
nature and does not have time-dependent features. As a result,
the limiting conditions for its incrementation will arise from the
nonlinear behaviour of the substrate, nonlinearities of deformation, and nonlinearities associated with the contact procedure.
For computationally efficient analysis, adaptive incrementation
routines were applied specifying convergence criteria for relative
and absolute residual norms of force and displacement.
The model has approximately 650,000 degrees-of-freedom,
consisting of bilinear three-dimensional brick elements. Element sizes at and near the contacting region are of the size
of the coating thickness and below. The mesh has a gradient
structure, mesh density being highest near the initial point of
contact and getting scarcer from thereon in all principal coordinate axis directions (smallest elements having element side
lengths of the order of 0.25 ␮m, largest some tens of ␮ms). Element integration is carried out using reduced integration to avoid
Fig. 4. The numerical model consisting of a block of material and a scratching
indenter.
possible element locking. The material undergoing the test has
been specified to correspond to the DLC coated system with
a 1 ␮m coating and the underlying material being that of high
speed steel as presented in Section 2. The coating and indenter behave according to a linear-elastic material law following
a generalized Hookean model. The behavior of the substrate is
modelled as elastic-plastic following a piece-wise linear true
stress–strain curve. Isotropic strain hardening is used to model
the small, but still existent, hardening of the substrate. Finite
deformations are included within the analysis.
The contact analyses are carried out using Lagrangian formulation and finite sliding description of the contact itself. The finite
sliding refers to a scenario where the contact analysis behaves
similarly as a finite deformation analysis, and the process of
contact is dependent on the incremental solution of the contact
problem as a whole (for example changes in geometry arising
from contact are taken into account when computing the following state when the contact progresses according to the specified
loading conditions).The contact – penetration relationship that
is applied is of softened general type in order to provide generalized control of the process of contact, and dampen and soften
the “stiff” finite element solution to some degree. The softened
model which was applied in the presented results is a model
where the contact pressure is a linear function of the contactpenetration. The linear function naturally requires a slope, and
it was verified that the slope which was selected did not influence
H. Ronkainen et al. / Wear 263 (2007) 1315–1323
1319
Fig. 6. Comparison of the numerical and experimental results of friction evolution in scratch testing for the DLC coated steel substrate. The graphs contain both
the adhesive and ploughing friction. The adhesive friction values, μa = 0.047 and
μa = 0.1, are used as input values to the numerical model.
Fig. 5. The map showing the (a) contact pressure; (b) shear in direction 1 and (c)
shear in direction 3. The values are shown at the symmetry plane intersection of
the HSS sample coated with a 1 ␮m thick DLC coating and pressed by a sliding
spherical diamond tip. Sliding direction is from left to right. The values on the
colour scale are given as N(␮m)−2 . Stress field is shown after 2.5 mm sliding.
the results by carrying out analyses with differing slopes, differing contact-penetration “stiffnesses”, as well as probing the
characteristic stiffnesses of the finite element model by subjecting it to different nodal loading conditions and monitoring the
resulting displacements. Friction is modelled using a classical
Coulombian model.
The friction related results were computed based on the contact area, contact pressure and shear stress calculations. An
example of calculated results for DLC with coefficient of adhesive friction of 0.047 is presented in Fig. 5 at a sliding distance of
approximately 2.5 mm and a normal load of 16 N. The displacement of the maximum contact pressure, as well as the maximum
of the main shear component of the analysis is observed towards
the edge of the groove. The peak of contact stresses resides somewhat asymmetrically at the tail end of the contact and the highest
shear stresses occur in the direction of sliding.
Comparison of numerical and experimental results of friction
evolution containing both the adhesive and ploughing friction,
is presented in Fig. 6. The adhesive friction, μadh = 0.047, in
the analyses, being an input value to the numerical model, is
naturally identical. It can be seen that the development of the
ploughing component in the numerical approach is quite similar
in comparison to experimental friction evolution. The numerical
model beginning to drift from the experimental results, when the
sliding distance increases. For comparison an other numerical
model with different initial adhesive friction values (μa = 0.1)
is also presented in Fig. 6. It is noteworthy that in principal
both analyses, having the same boundary and initial conditions,
produce a similar ploughing response, the relative differences
between ploughing and adhesive components between the two
analyses being of the order of 20%.
5. Analytical determination of friction
According to Bowen and Tabor the measured friction force
can be divided into two components, namely adhesion and
ploughing
F = τA1 + pA2
(2)
where A1 is the projected contact area, A2 is the projected crosssection area of the scratch track, p is a material flow stress and τ
is an interfacial shear strength. Using this simple formula as the
basis, formulas describing the adhesive and ploughing components have been derived by e.g. Bull [34] and Malzbender and
de With [35]. Komvopoulos [36] used a formula, where parameters related to material properties of the contacting surfaces were
used. This formula was chosen for analytical calculations in this
study. The friction coefficient is described with the following
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H. Ronkainen et al. / Wear 263 (2007) 1315–1323
Fig. 7. A comparison between the semianalytical approach, numerical results
of friction and the experimental friction results for the DLC coating in scratch
testing. The semianalytical refers to the contact stresses from the numerical
model being used as input value in the analytical model.
Fig. 8. Prediction of adhesive friction for the DLC film from the total friction
using the analytical and semianalytical methodologies. The semianalytical refers
to the contact stresses from the numerical model being used as input value in
the analytical model. The experimental value represents the adhesive friction
determined for the DLC coating.
equation.
−1 2
h 2
h
h
−1
μ=
1− 1−
cos
1−
− 1−
π
r
r
r
⎤
1/2
h ⎦
h 2
Kn s
× 1− 1−
(3)
+
r
3
ks
r
ing trend for adhesive friction. It can be seen that the plastic
aspect, the ploughing component of friction, is modelled with
greater precision than the initial adhesive component of the multimaterial coating—substrate system as can be observed from
Figs. 7 and 8.
where h is the penetration depth, r is the radius of the tip, K is
the material strain constant, n is the strain hardening coefficient,
s is the shear stress at the interface and ks is the shear strength
of the ploughed surface.
A comparison between the analytical approach, numerical
results of friction and the experimental evolution of friction, is
presented in Fig. 7 for the case of DLC coating. The term semianalytical refers to a analytical model where the contact stresses
are received from the numerical model and used as input values
in the analytical model. The experimental, numerical and analytical results can be seen to produce tolerably similar ploughing
friction results, but the “semi-analytical” results have an initial
offset when the material parameters and geometry variables of
the current study are used.
For the semi-analytical model the following equation derived
from Eq. (3) was used
−1 2
h
h 2
h
μ=
cos−1 1 −
1− 1−
− 1−
π
r
r
r
⎤
1/2
2hs ⎦
h 2
(4)
+
× 1− 1−
r
pr
In scratch testing the evolution of friction measured was typical for the TiN and DLC coatings. DLC films had a lower
friction coefficient due to their advantageous tribological properties, whereas the TiN coatings had a similar friction performance
compared to uncoated sample. When the adhesive friction component was determined based on the results of multi-pass testing,
the adhesive friction turned out to be the main constituent of friction coefficient, being 0.066 for the TiN coating, 0.047 for the
DLC coating and about 0.060 for the uncoated HSS substrate.
The ploughing component increased from 0.011 to 0.017 for the
TiN coating, from 0.008 to 0.015 for the DLC coating and from
0.007 to 0.010 for the uncoated HSS substrate as the normal load
was increased from 5 to 10 N. Similar approach for determining
the adhesive friction has been used by von Stebut et al. [37]. The
value they determined for the adhesive friction as the diamond
stylus was sliding against TiN coating was 0.08, which is very
close to the value determined for TiN coating in this study. Von
Stebut et al. determined the ploughing component as the difference between the initial value and the stabilised values of friction
as diamond stylus was sliding against coated surface. In the
present study the ploughing components was determined as the
difference between the first and the second sliding cycle. However, the ploughing action was probably not completed during
the first sliding cycle, since the friction coefficient still decreased
for the DLC coated and uncoated substrates. For the TiN coated
sample similar effect was not observed, probably due to higher
hardness and stiffness of the coating. When the similar approach
to von Stebut et al. was applied for the present data, the plough-
Fig. 8 shows the experimental value of adhesive friction of
DLC film determined by using 5 N and 10 N normal loads and
the values calculated by using analytical and semi-analytical
equations. The “semi-analytical” approach predicts a decreas-
6. Discussion
H. Ronkainen et al. / Wear 263 (2007) 1315–1323
ing component value changed from 0.011 to 0.019 for the DLC
coating and from 0.0095 to 0.015 for the uncoated sample. These
values are very close to the values determined for the TiN coating, namely 0.011 to 0.017, which is in better agreement with the
actual determination of ploughing friction. In that case the adhesive friction would be lower for the DLC coated and uncoated
samples. Since the determination of friction components is not
unambiguous, the values determined need be treated as tentative.
The numerical results for contact pressure and shear stresses
are quite expected. One somewhat unusual difference is that the
contact pressure is larger outside the plane of symmetry than at
it. This is resulting from the shape of the groove and the rigidity
of the coating, i.e. the pressure at the plane of symmetry relaxes
to some extent since the coating is unable (being linear-elastic)
to comply with the shape of the diamond indenter and plasticity
of the substrate (due to compatibility limiting the deformation
of the system). The peak of contact pressure is somewhat behind
the region of contact, which is relatively symmetric in terms of
non-zero contact pressure. Since the movement is parallel to the
plane of symmetry, the frictional shear stresses are quite different
from each other with respect to magnitude. The shear stress in the
“1” – direction relates to the geometry of deformation (groove
edge in particular, and plane of symmetry), whilst direction “3”
primarily relates to the sliding itself and to the sliding direction,
explaining the large differences in the magnitude.
The comparison between experimental scratch test friction
results and those of numerical FEM simulation with a Coulombian model of friction proved quite satisfactory. Since the origin
of simulation is the adhesive friction, identical in both, the whole
question relates to the development of ploughing friction, primarily in the current problem arising from the elastic-plastic
deformation of the substrate. Other affecting parameters are
finite deformations, deformation of the coating, shape of the
indenter, etc., but overall within the problem the plasticity and
finite deformations (within sliding also) can be considered to be
the primary parameters. In experimental testing crack propagation in the coating and the coating detachment later along sliding
will influence the friction evolution. Experimental ploughing
friction develops nearly linearly with sliding distance, whilst
the numerical results have nearly an exponential, or monotonically rising, dependency after some sliding. This arises from
the increased plasticity in the numerical model once the limited hardening of the substrate, a high speed steel, runs out,
since the high speed steel is in practise almost a rigid plastic
material. In practise since in the FE model the coating cannot
crack, it experiences ever more ‘continuum’ deformation which
under monotonic loading leads to continued increase of stress
and strain. In reality cracks will be generated in the coating during scratching. The first cracks will appear after about 1.3 mm
of sliding in the DLC coating [38]. As the sliding proceeds to
3 mm, a dense crack field is generated in the coating covering the
scratch track. The formation of cracks in the coating will reduce
the strain and stress experienced by the system surface, which
will have a decreasing effect in friction. Similar effect has been
observed by Malzbender and de With [35], since they reported
the relaxation effect of cracking on the elastic stress field, which
resulted in reduction of friction.
1321
The numerical analyses were performed with various coefficients of adhesive friction, and a case with a coefficient of
friction of 0.1 was presented in Fig. 6. The contact pressures do
not rise, during the computed sliding distances to magnitudes
that the coupling back to ploughing friction due to increased
shearing of the contact area would be much visible. The difference in the magnitude of ploughing friction coefficient is
approximately 20% in this case. However, if the adhesive component of friction would be higher, e.g. 1.0, the effect would be
more pronounced leading to an earlier and steeper rising of the
ploughing friction component. In any event, since the ploughing is affected primarily by plasticity and nonlinear effects
within the contact interface and near vicinity, it is reasonable
to assume that the friction coefficient for ploughing will be a
function of the internal and state variables of the system. This
means that the ploughing friction is influenced practically by all
parameters involved, not only the geometrical parameters of the
contact.
One of the prime motivators of the current study was the
observation, that there are some problems in treating coated
systems, systems with nonlinear constitutive equations involving plasticity, either as linear-elastic or fully plastic. This was
substantiated by results given in Fig. 7. Since in the current case
there is no lubrication, the s/ks ratio of the analytical model is
high enough to result in friction results incompatible with experimental observations, and incompatible with the results attained
with numerical modelling, which are in decent agreement with
experimental observations. Considering how the system is modelled and how it responds, it is reasonable to presume that
the experimental results, on the basis of work cited in Section
3, are in between linear-elastic and plastic contacts. As such,
the system response (coating and substrate) is affected by the
elastic behaviour of the coating and the plasticity of the coating, both appearing simultaneously (as in a scratch test of the
current system), resulting in a mixed type of system affecting friction performance. This system cannot be understood
by simplifying it to either one of the constitutive responses,
but a more complex approach to understanding the frictional
behaviour is required, one that is difficult to approach in closed
form.
The results of Fig. 8 show that when the adhesive friction of
diamond against DLC sliding couple is predicted by analytical
approach, the difference to experimental results is in the range
20–80% depending on the s/ks value. In this study the range
0.1 < s/ks < 0.4 correlates to friction performance of diamond
against DLC sliding couple. These values are normally typical
for boundary lubricated conditions, as reported by Komvopoulos
[36]. The results demonstrate that the plastic aspects of friction
can be modelled to a better precision, i.e. the analytical and
numerical models are in better agreement with the ploughing
part of friction compared to adhesive friction. However, the system response within the current study was not within the reach of
simplified means of analysis, such as the analytical model of friction applied within the current work. Therefore, it was necessary
to use more advanced modelling approaches, like the numerical FEM solution, represented here, in order to get reasonable
friction modelling results.
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H. Ronkainen et al. / Wear 263 (2007) 1315–1323
7. Conclusions
Based on the experimental determination of friction components by scratch testing and combining the results with the
analytical determination and numerical finite element based
analyses the following conclusions can be made.
1. When the material parameters are included in the numerical model, as in the numerical FEM analyses, they have an
important influence on the evolution of friction. The most
dominating parameters are the plasticity of the substrate and
the substrate to coating Young’s modulus ratio.
2. The numerical 3D FEM analyses contain both elastic and
plastic deformation and therefore it gives more realistic friction results compared to analytical approach.
3. The numerical 3D FEM analyses give results closely related
to experimental values as long as the coating remains reasonably untouched. As soon as a dense crack field is generated
in the deformed coating, relaxation in the surface will occur
and the experimental values do not follow the theoretical
numerical results.
4. The analytical modelling of friction in a coated system used in
this study deviates from the experimental values significantly
in the range of 20 to 80%.
Acknowledgements
The authors want to acknowledge the following colleagues
for interesting and valuable discussions in relation to the work:
Philippe Kapsa, Ecole Central de Lyon, France; Henry Haefke
and Imad Ahmed, CSEM, Switzerland; Ali Erdemir, Argonne
National Laboratory, USA; Peter Barna, Hungarian Academy of
Science; Koij Kato, Tohoku University, Japan; and Kaj Pischow
and Rosa Aimo, Savcor Coatings. HEF in France and Ali
Erdemir at Argon National Laboratory in USA, are acknowledged for kindly providing the coatings for the research.
The financial support of TEKES the Finnish Funding
Agence for Technology and Innovation; Taiho Kogyo Tribology Research Foundation, Japan; Savcor Coatings, Finland; and
the VTT Technical Research Centre of Finland is gratefully
acknowledged.
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