Tribology International 82 (2015) 423–430

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Tribology International
journal homepage: www.elsevier.com/locate/triboint

A model for single asperity perturbation on lubricated sliding contact

with DLC-coated solids
G. Pagnoux a,b,c,n, S. Fouvry b, M. Peigney c, B. Delattre a, G. Mermaz-Rollet a
a
PSA Peugeot Citroen, Route de Gisy, 78140 Velizy, France
b
LTDS, UMR CNRS 5513, Ecole Centrale de Lyon, 36 Avenue Guy de Collongue, BP163, 69131 Ecully, France
c
Univ. Paris-Est, Laboratoire Navier (Ecole des Ponts ParisTech, IFSTTAR, CNRS), F-77455 Marne-la-Vallee, France

art ic l e i nf o a b s t r a c t

Article history: In lubricated sliding contact systems with DLC coated solids, recent studies have shown that DLC
Received 25 September 2013 coatings are highly sensitive to asperities breaking through the lubricant film within the contact area.
Accepted 10 May 2014 Those asperities produce damages similar to those obtained from scratch tests, from where coating
Available online 20 May 2014
delamination can initiate and propagate. To better understand the link between scratches and coating
Keywords: delamination, endurance tests can then be performed on coating with controlled initial scratches. To
Single asperity contact ensure the scratches’ representativity with respect to the actual asperities’ contact condition, one has to
EHD lubrication estimate the load transmitted by such asperities as well as the induced perturbation on surface and
DLC coatings subsurface stresses. In this paper, a simplified numerical model corresponding to such problems is
Scratch map
presented. It is consistent with elasto-hydrodynamic (EHD) lubrication approximations and can be used
on coated or uncoated systems. As a simplified model, it can be run quickly on multiple configurations,
enabling the creation of representative scratch maps for the given lubricated contact conditions.
& 2014 Elsevier Ltd. All rights reserved.

1. Introduction were conducted on a cam–tappet system with coated tappets and it

has been experimentally observed that coating delamination initiates
Extreme low wear rates of Diamond-Like Carbon (DLC) [1] around scratch networks and propagates following scratch networks
coatings are one of the properties that make them particularly and substrate defects. However, the complex contact kinematic and
interesting for numerous applications, like automotive ones. This the multiple wear processes occurring during the experiment make
property is often observed during characterization tests in dry or it difficult to properly highlight the link between scratches and
lubricated contact under basic solicitations like fretting, and coating delamination, as in [9]. Hence, in such conditions, it would be
sliding, rolling–sliding. Many studies pointed out that DLC damage interesting to perform endurance tests on DLC coatings with initially
and wear processes depend on the atmosphere, on their thickness, scratched surfaces. Those scratches have to be representative of those
their microstructure (hydrogenated or not, doped or not, mono- or observed on the cam–tappet bench test. Therefore, it is necessary to
multi-layered) and on their interface quality with the substrate estimate the load transmitted by asperities as well as the induced
[2–5]. Nevertheless, few studies focus on the influence of com- perturbation on surface and subsurface stresses.
bined, variable or complex loadings on the coating lifetime. This load cannot be estimated by an analytical model such as
Recent ones have shown that under lubricated contact, DLC the classical Hertz or Johnson contact theory [10]. On the other
coatings are particularly sensitive to the stress perturbation due to hand, existing numerical models are either too complex and time
fragments or asperities breaking through the lubrication film into the expensive or based on inappropriate assumptions. For instance,
contact area. Under pure rolling conditions, hard particles from a Fujino et al. [11] developed a full EHD model for a sliding ball
highly contaminated lubricant cause more damage to DLC coated against a coated plane, using millions of tetrahedron elements. For
systems than to uncoated ones [6]. Under sliding conditions, it leads simplicity, He et al. [6] estimate the stress perturbation due to
to coating cracking or spallation [7] and asperities lead to damages particles by assuming a 2D plane strain model with no lubrication.
similar to those caused by scratch tests [8]. In this latter one, tests Haque et al. [7] estimate it with the Hertz formula, assuming a
linear coverage of the sand particles over the contact width.
The main purpose of the numerical model presented in this
n paper is to estimate the load transmitted by the asperity as well as
Corresponding author at: PSA Peugeot Citroen, Route de Gisy, 78140 Velizy,
France. the induced perturbation (in terms of stress or strain) with more
E-mail address: geoffrey.pagnoux@mpsa.com (G. Pagnoux). realistic assumptions than the existing simplified ones, regarding

http://dx.doi.org/10.1016/j.triboint.2014.05.009
0301-679X/& 2014 Elsevier Ltd. All rights reserved.
424 G. Pagnoux et al. / Tribology International 82 (2015) 423–430

our particular system. It is based on the asperity point load

mechanism [12] with a linearized normal lubricant behavior
around the EHD operating point. As a simplified model, it can be
run quickly on multiple configurations (by modifying the asperity
height, radius and position, the coating, substrate or lubricant
characteristics) and is workable in an industrial context. Outputs
can be used in several ways and will be discussed in the following
sections.

2. Experimental background

The contact kinematics of a cam–tappet system is a complex

combination of impact loading, rolling–sliding and sliding contact
under lubricated conditions, resulting in different solicitations on
the tappet surface. In the system considered here (Fig. 1), there is a Fig. 2. Focus on several scratch networks located outside a delaminated area. This
small gap between the cam and the tappet on almost 65% of the area itself exhibits multiple severe scratches.

cam rotation, and the cam is slightly off-centered compared to the

tappet axis. Then, for each cam rotation, the contact initiates, surface. Ongoing analysis of the lubricant and worn and unworn
moves and separates. The friction forces acting on the tappet cams should allow a better understanding of the asperity origin.
surface make it spin around its axis, leading to a theoretically Regardless of its source, it is necessary to assess the damage
axisymmetric cumulated wear. caused by such a defect on the coating lifetime and to validate its
Experiments were conducted on DLC coated tappet using a link with coating delamination with simplified experiments.
long-term component bench test with a standard lubricant. A Those latters ones will consist of pin-on-disk endurance tests
continuous low camshaft rotational speed was set, which is a with initially scratched coatings. Scratches therefore have to be
severe condition since it leads to the thinnest oil film thickness correctly defined in order to match the ones that can occur in the
(OFT) between the contacting parts. With such a low rotational complex system. They cannot be controlled using pre-tests with
speed, dynamic effects like impacts are negligible and the lubrica- a contaminated lubricant or a defined counterpart rugosity, as the
tion varies from mixed to EHD regime. scratch creation would be part of a highly random process.
Observations on worn coated surfaces revealed six character- Scratches can be created with a standard scratch tester where
istic facies and highlighted four wear mechanisms [8]. The worst it is set the normal load, the tip radius and the scratch length.
one, relative to coating delamination, was systematically found While the two last settings can be approximate thanks to observa-
to initiate around circular scratch networks (Fig. 2). A complete tions, the first one has to be calculated numerically with the
scenario bringing out all coupled wear mechanisms has been following model.
formulated, in which scratches and delamination are strongly
coupled. The bright area in Fig. 2 corresponds to tribochemical
wear. Its influence on coating delamination will be part of 3. Numerical model
another study.
Circular scratch networks may be created either by asperity The model is relevant for every EHD lubricated contact problem
existing on the initial cam surface or by hard particles (coming where a single asperity perturbates the overall contact stress field.
from a highly contaminated lubricant) incrusted into the cam This study is, however, restricted to line contact problems and
examples are obtained from cam–tappet configurations where
only the tappet is coated. All assumptions made on geometries,
material and lubricant behavior or calculations are discussed in
Section 5.

3.1. Geometric model

The unloaded and loaded geometric models are illustrated in

Fig. 3. It consists of two cylindrical parts Ω1 and Ω2 in contact,
separated by a thin OFT Ω3. Ω1 and Ω2 can be divided into two
regions: one for the substrate (Ωs1, Ωs2), the other for the coating
(Ωc1, Ωc2). Ω1 and Ω2 are geometrically defined by their initial
radius of curvature R1 and R2 (here, R2 ¼ 1) and coating thickness
h1 and h2 (here, h1 ¼ 0).
Under EHD lubricated contact, the OFT h3 ðxÞ is assumed to be
constant between  aC and aC and equal to the nominal OFT hL3
(see Section 3.3.2). Contacting surfaces and coating to substrate
interface are supposed to be perfectly smooth, i.e. with defects
negligible compared to the asperity characteristic dimensions. The
coating has a constant thickness and is perfectly bonded to the
substrate. A normal load FN is applied upon Ω1.
Without asperity, the problem could be associated with a 2D
plane strain problem. With an asperity in the contact, this 2D
plane strain assumption cannot be assumed anymore. The asperity
Fig. 1. Cam (c)–tappet (t) system. is represented by a spherical defect on Ω1 surface, high enough to
 G. Pagnoux et al. / Tribology International 82 (2015) 423–430 425

Table 1
Material and lubricant parameters.

Property Substrate Coating Lubricant

E (GPa) 210 105–420

ν 0.27 0.2
cf 0.1
μ0 (Pa s) 0.1
α (Pa  1) 1:5e  8

contact and a consistent normal lubricant behavior which require

two parameters: the lubricant atmospheric viscosity μ0 and its
pressure viscosity coefficient α (see Table 1). Further improvement
of this simplest material behavior is discussed in Section 5.

Fig. 3. Contact illustration without asperity. (a) Unloaded and (b) loaded.
3.3.2. Global lubricant behavior
Under EHD regime, the lubricant thickness hL3 can be evaluated
from approximated formulae which are either suited for point
or line contact, and which give either the minimum or the mean
OFT. Numerous studies have been performed and various formulae
have been identified, based on numerical results from full EHD
models or experimental observations. It can be highlighted here in
the studies of Ertel and Grubin, Dowson and Higginson, Hamrock
and Dowson or Moes and Venner [14], Rahnejat [15] or Haiqing
[16]. Basically, all those formulae use 3 main parameters with
a given coefficient and can be expressed as in Eq. (1). h~ is the
L
3
dimensionless film thickness, G the material parameter, U the
speed parameter and W the loading parameter. The loading
Fig. 4. Asperity illustration under loading.
parameter W depends inter alia on the load transmitted by the
lubricant FLN. Without any asperity in the contact, FLN is equal to FN:
break through the lubricant film Ω3 (Fig. 4). Its governing para- h~ 3 ¼ f l ðG; U; W; …Þ
L
where W ¼ f w ðF LN ; …Þ ð1Þ
L
meters are its height ha ðha 4 h3 Þ, its radius Ra and its position with
respect to the contact center xa . Among all the tested approximations on our considered
system, the Moes Venner formula is the one leading to the
thinnest OFT (Eq. (2), where h~ 3 ¼ h3 =R, G ¼ αEn , U ¼ ðμ0 V s Þ=ðEn RÞ,
L L
3.2. The point load mechanism L n
W ¼ F N =ðE RÞ, R ¼ 1=ðð1=R1 þ 1=R2 ÞÞ is the reduced radius of
The point load mechanism was firstly introduced by Alfredsson curvature, En ¼ 2=ðð1  ν21 Þ=E1 þ ð1  ν22 Þ=E2 Þ is the reduced elastic
et al. [13] and applied in [12] for rolling contact fatigue problems modulus, and Vs is the sliding speed). As a result, this formula has
on gear tooth. In this mechanism, the nominal stress field due to a been chosen as a conservative approximation:
two-dimensional loading is locally disturbed by the presence of
h~ 3 ¼ 1:56G0:55  U 0:7  W  0:125
L
ð2Þ
the axisymmetric asperity contact. As a disturbance, it is assumed
that its influence on the contact area is negligible. Assuming those approximations are also available for thin
Hence, with consistent material and lubricant behaviors, the coated solids (i.e. coatings which does not make the contact length
contact problem described in Section 3.1 can be solved numeri- and pressure differs too far from Hertz ones), the mechanical
cally with finite element method. The load transmitted by the principle considered here is the following: when an asperity
asperity can then be calculated by integrating the normal surface breaks through the lubricant film, it transmits a small part of
stress upon the asperity contact area. If the mesh is sufficiently the total loading, named F Na . As a result, the load transmitted
small around the asperity, a specific stress value can be evaluated by the lubricant FLN is reduced, thus modifying its thickness hL3. The
and associated with the asperity governing parameters in order to expression (2) can then be used in the present contact problem to
be used in a damage criterion. define the lubricant behavior as a loading FLN versus thickness hL3
behavior.
3.3. Material and lubricant behavior
3.3.3. Local lubricant behavior
3.3.1. Material behavior As it was previously introduced, the problem is designed to be
Coatings and substrate materials are defined as homogeneous, solved with the finite element method, meaning the lubricant, as
isotropic and purely elastic. The asperity is assumed to be part any part of the system, has to be discretized and meshed. This
of the as-machined surface, thus it has the same material (and requires to one identify a priori the actual contact width aC under
mechanical behavior) as its host. The lubricant film separating the loading. The global behavior described in Section 3.3.2 also has to
two contacting bodies ensures normal load transfer, but removes be redefined in terms of pressure versus closure behavior which
the tangential one. Hence, frictionless full film lubrication is can be directly used as normal behavior of lubricant elements,
s
assumed for the cylindrical contact. such as gasket elements in Abaqus .
As a result, the only required parameters needed to compute Therefore, the point of the model is to represent the lubricant
the contact problem are the elastic modulus E and the Poisson as a static interface with varying stiffness k(x), as illustrated in
ratio ν of each material, their friction coefficient cf under dry Fig. 5. Interface local stiffnesses are identified considering the
426 G. Pagnoux et al. / Tribology International 82 (2015) 423–430

Fig. 5. Interface representation.

Fig. 7. Comparison between ideal (- -) and chosen (–) lubricant behaviors. The
interface local stiffnesses correspond to the derivative of those curves.

ðsn ðxÞ A ½0; sn1 ðxÞ½Þ, the operating part ðsn ðxÞ A ½sn1 ðxÞ; sn2 ðxÞÞ, and
the overpressure part ðsn2 ðxÞ 4 sn2 ðxÞÞ. The operating part has to be
closely fitted to the ideal curves, while the two others can be
arbitrarily defined such as they are fully compatible with standard
Fig. 6. Normal stress as a function of the normal load. element behavior and avoid convergence difficulties. Here, the
behavior was chosen linear around the operating point. sn1 ðxÞ and
nominal normal stress and EHD approximations, with the follow- sn2 ðxÞ are defined as the boundaries above which the linear
ing inverse method. approximation deviates from more than 10% compared to the ideal
The nominal normal stress field along the contact sn ðxÞ as well behavior. The underpressure part has an exponential form, starting
as the contact width aC are obtained from a 2D dry contact analysis from ½0; 0 and having the same derivative as the operating part at
without asperity which approximates the actual EHD contact sn1 ðxÞ. The overpressure part is defined as horizontal (Fig. 7).
conditions closely. The initial lubricant thickness h3 ðxÞ is calculated The present simplified normal behavior of the interface
with respect to the initial part geometries, the EHD lubricant between the two bodies Ω1 and Ω2 is consistent in the sense
L
thickness hL3 and the asperity height ha, ensuring h3 ðxÞ 4 h3 and that negative closure gives zero pressure, like a loss of contact
that the asperity does not penetrate the opposite surface (Eq. (3), between the two bodies. With increasing closure, the normal
considering the geometry defined in Section 3.1): pressure evolves monotonously up to the operating point, with
L an evolution law close to an EHD behavior. Above the operating
h3 ðxÞ ¼ f h ðx; R1 ; R2 ; h3 ; Ra ; ha ; xa Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi point, an increasing closure leads to an increasing stress, up to a
¼ R1  R21 x2  ð  R2 þ R22  x2 Þ critical value. Upon this latter one, the interface can be seen as
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi fully damaged and cannot sustained more load. It can be noticed
L
þ maxð2h3 ; R3  R23  ðx  xa Þ2 Þ ð3Þ that an asperity in the contact will lead to a smaller closure than
the nominal one, so that the overpressure part of the behavior law
Thus, for each position x in the contact, the expected lubricant does not operate in the final equilibrium state.
closure under loading can be defined (Eq. (4), markers in Fig. 7):

cðxÞ ¼ h3 ðxÞ  h3
L
ð4Þ 3.4. FE model

Without asperity and setting aside the point load mechanism, a s

The problem was solved using Abaqus 6.10 software. Due to
perturbation in FLN induces a perturbation of the normal stress field symmetry, only half of the geometry was modelled and plane strain
sn ðxÞ (Eq. (5), Fig. 6. aH and pH refer to Hertz contact length and was enforced throughout the y-direction, i.e. at both y¼0 and
Hertz maximal pressure, respectively, under nominal loading): y ¼ ymax . Ω1 and Ω2 bodies were meshed using 4-node bilinear
sn ðxÞ ¼ f s ðx; F LN ; …Þ ð5Þ elements for 2D configurations, 8-node linear brick and 6-node linear
triangular prism elements for 3D configurations. For 2D and 3D
By combining the functions (2)–(5), the ideal pressure versus configurations, the interface Ω3 was meshed using 4-node plane
closure behavior can be calculated at each point x in the contact strain gasket elements and 8-node gasket elements, respectively.
area (Eq. (6), expressed for a given x): Several mesh refinements are defined, at the contact surfaces and
around the asperity (Figs. 8 and 9). A minimum of three elements
sn ðcÞ ¼ f s ○f w 1 ○f l 1 ðh3 cÞ ð6Þ
was used through the coating thickness. Surface-to-surface contact
With an asperity breaking through the lubrication film, the with finite sliding is defined between the asperity and the coating.
equilibrium state will slightly deviate from the operating points. The contact constraints were enforced using the augmented Lagrange
As a result, the only useful part of the curves is the one close method. As the lubricant normal behavior depends on its x coordi-
to the operating points. This enables us to discretize the final nate, it is calculated for each lubricant element considering its mean
behavior curves into three parts, namely the underpressure part coordinate and mean thickness.
 G. Pagnoux et al. / Tribology International 82 (2015) 423–430 427

Input Input
Input contact
geometry materials
conditions
and lubricant

F N , Vs
R1 , h1 , R2 , h2 E 1 , ν1 , E 2 , ν2 , c f

Mesh and
solution 2D
dry contact

Ra , ha , xa a c , σ n (x) μ0 , α

Solution global
and local lubri-
cant behavior

h3L, fσ

Mesh and solution

3D lubricated
contact with asperity

σ, ε

Post-
processing

Fig. 10. Global algorithm.

Fig. 8. Global mesh illustration. single point load was not found in the literature. Therefore, the
validation of the model is limited to basic comparisons with
simple contact conditions.

4.1.1. Hertz contact

Under the assumptions made in Section 3, a classical Hertz line
contact can be used as a reference configuration. The normal stress
field coming from Hertz formula, 2D and 3D lubricated contact
without coating and asperity is compared in Fig. 11.
Fluctuations can be seen around the contact boundaries due
to both interface averaged behavior and mesh effect. As expected,
Fig. 9. Focus on the asperity. the thinner the mesh, the closer the results to the Hertz ones.
Fluctuations are negligible and convergence is observed with at
least 30 elements in the contact in the x-direction (error of less
3.5. Global algorithm
than 0.5% on the maximal normal surface stress). Computations
were also performed with coated solids (including a coating with
The previous methodology can be summarized with the fol-
identical properties as the substrate), exhibiting equivalent results
lowing algorithm (Fig. 10). As a standard finite element model, the
between dry and lubricated contact.
present one does not require any heavy development (such as
multilevel methods) in order to be used and the calculus time
remains acceptable. In this study, for each cam–tappet configura- 4.1.2. Lubricant effect
tion, coating properties and asperity parameters, the calculus time The main purpose of this simplified model is to estimate the
s
was found to be between 200 s and 600 s, using an Intel CoreTM load transmitted by an asperity with better assumptions than
i7-2630QM CPU at 2.0 GHz with 16 GB RAM and a number of 3D existing simplified ones. Compared to non-lubricated models, the
elements varying from 5e4 to 10e4. stress perturbation as well as the calculated asperity load are
expected to be reduced. In the example used in Fig. 12, compared
to the non-lubricated contact, a 20% decrease of the maximal
4. Numerical analysis normal surface stress and a 50% decrease of the asperity load is
observed.
4.1. Validation of the model A convergence analysis was also performed to identify the limit
on the asperity mesh refinement above which the calculated load
To the authors' best knowledge, as it was previously men- does not evolve. It appears that the load can be accurately
tioned, there is no analytical solution for the full system consid- identified with only a few asperity nodes in contact, meaning that
ered here, regardless of the assumptions made. Similarly, a full the entire asperity can be meshed up to only ten nodes in the
EHD numerical model considering a line contact perturbated by a x-direction.
428 G. Pagnoux et al. / Tribology International 82 (2015) 423–430

4.2. Asperity stress perturbation Moreover, as it is suggested in Section 3.1, a static analysis with
no sliding is considered. Computations were made with a sliding
Scratch tests have been used for many years to assess coating- step and it has been observed that this latter one does not affect
to-substrate quality. The induced damage mechanism was high- the calculated asperity load by more than a few percent, thus it
lighted by Holmberg [17] and Bull [18], using both experimental can be neglected in the model. The resulting stress state is then
and numerical results and focusing on local stress fields and first closer to spherical indentation ones [19] than to scratch test ones.
crack location. It appears that the stress state around the moving Nevertheless, it can be shown that the stress perturbation is
indenter (around the asperity in our case) is very complex and large enough to create scratches (Fig. 12) by substrate plasticity
leads to different failure modes such as substrate plastic deforma- and coating fracture. It can be noticed that a bigger asperity is not
tion, bulk or through-thickness fracture and interfacial failure. As systematically associated with a more severe wear, as shown by
the critical stress associated with each failure mode is difficult to Woldman [20] and Haque [7], who suggested that the maximum
identify, scratch tests are usually regarded as semi-quantitative shear stress depth for huge asperity acts under the coating-to-
tests, resulting in critical loads upon which a well-defined failure substrate interface, thus providing overall negligible wear.
is observed. In the present study, scratches are calibrated with
respect to asperity loads and will be used as initial parameters for 4.3. Asperity load
endurance tests on DLC-coated samples. Hence, the present model
cannot be used to correlate failure modes with local critical Standard scratch tests usually use a Rockwell ‘C’ diamond
stresses, since the mesh density as well as the material behavior indenter with 200 μm hemispherical tip radius and a maximum
is not accurate enough to catch the actual complex stress state normal load varying in the range of several Newtons [21]. For sub-
around the asperity. micron coatings, nanoscratch is more suited and uses micrometric
tips and milli-Newton loads [22]. The question which arises is this:
are those adhesion tests representative of asperity loads acting on
a lubricated sliding contact?
The model described in Section 3 was used on multiple
configurations by varying the contact condition, the asperity
parameters and the coating thickness and mechanical properties.
As a result, the load transmitted by the asperity can be plotted as a
function of numerous variables.
Among them can be plotted the asperity load as a function of its
characteristic dimensions ha and Ra (Fig. 13 with xa ¼ 0 and fixed
cam–tappet and coating parameters). It can be noticed, for the given
contact and coating parameters, that the calculated normal loads
belong to a wide range, from mN to N, and that naturally, the bigger
the asperity, the higher the normal load. They are still comparable,
so compatible, with standard, micro- or nano-scratch tests.
On the other hand, it can be highlighted that the asperity
normal load has a strong dependency on the coating properties
(Fig. 14, Es and Ec referring to substrate and coating elastic
modulus, respectively). Whereas the overall contact is slightly
influenced by a thin coating, the asperity contact condition is not,
due to the fact that the coating thickness has the same dimension
order as the asperity. As a result, it can be noticed that the coating
can be designed with respect to a range of asperity probabilities, in
Fig. 11. Surface normal stress for Hertz configuration. order to optimize its lifetime.

Fig. 12. Lubricant effect on surface normal stress (a) and zoom (b).
 G. Pagnoux et al. / Tribology International 82 (2015) 423–430 429

Fig. 15. Scratch map.

The constant lubricant thickness assumption is the outcome of

the chosen lubricant behavior, which is based on analytical
Fig. 13. Asperity load as a function of asperity dimensions. approximations and which gives only the mean or the minimum
film thickness. On the other hand, compared to the stress values
due to asperities, the usual pressure spike in a lubricated contact
outlet as well as the lubrication perturbation around or behind the
asperity is negligible or, in all cases, does not seem to induce
damage as severe as the asperity does. Similarly, as it was not the
point of the present model, the purely elastic material behavior
can be extended with specific asperity material, coating residual
stress, substrate plasticity and so on to be more representative of
the actual material behavior and to have better asperity load
estimation. Under purely elastic behavior, this latter one can be
seen as an upper bound above which scratch tests become
irrelevant regarding the actual scratch conditions. By considering
an elastic-purely plastic behavior for the substrate, the upper loads
associated with the biggest asperities are lowered up to several
tenth of percents while the lower loads remains unchanged.
Despite this simplicity, there is a good correlation between the
numerical asperity contact length and the experimental scratch
width, both of them in the range ½1 μm–100 μm.
The main contribution of this model concerns the interface
normal behavior. A Comparison has been made using both the
ideal and the linearized behaviors in the operating part. Based on
the Hertz configuration, both behaviors converge to the same
Fig. 14. Asperity load as a function of coating properties. results with an increasing number of elements. However, the ideal
behavior is based itself on approximations and should not be
A scratch map consisting of fRa ; F Na g doublets can also be considered as the actual lubricant behavior. In addition, the linear
defined by varying every parameter in the range of the target approximation remains closer to Hertz results with a coarse mesh.
applications (Fig. 15). Regarding this scratch map, standard scratch The point load mechanism remains consistent while the
tests with 200 μm hemispherical tip are far from the actual asperity perturbation remains small. This can be quantified by
asperity conditions calculated here. The induced coating failure extracting the 2D stress field from the 3D configuration and
mode can then be different from those observed in cam–tappet comparing it with the one coming from the 2D configuration.
systems, as well as its link to coating delamination. For huge asperities, the point load mechanism as well as the
constant lubrication thickness cannot be considered anymore but
the present model remains consistent, as the lubricant effect will
5. Discussion become negligible compared to asperity ones.
The calculated normal load can be used as input data for
Several assumptions have been introduced in the model. another numerical model, like one dedicated to asperity contact
Geometrically, as-machined surfaces or incrusted particles have with sliding, designed to identify a critical stress correlated with
random angular shapes and heights. By considering them sphe- experimental coating failure.
rical, the associated stress perturbation is lowered. However,
observations on worn coated tappets attest the asperity failure
occurs after tens of scratches, meaning it has to be smooth and 6. Conclusion
small enough to avoid large concentration that which would break
it instantaneously. The spherical shape can then be seen as having Whereas DLC coatings usually exhibit extreme low wear rates,
an asperity steady state geometry during scratch network creation their lifetime can be highly degraded under lubricated sliding
and can be related to actual rugosity or particles measurement. contact where an asperity breaks through the lubricant film. The
430 G. Pagnoux et al. / Tribology International 82 (2015) 423–430

link between the induced damage and coating delamination needs [8] Pagnoux G, Fouvry S, Peigney M, Delattre B, Mermaz-Rollet G, Surface analysis
further studies, such as endurance tests on initially scratched of DLC coatings on cam–tappet systems. In: Proceedings of the ISDMM13,
Lyon, France, 2013.
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has been created using the point load mechanism and a lubricant polymeric nanocomposites, second ed. Oxford: Butterworth-Heinemann;
behavior based on EHD approximations. It is more representative 2013. p. 387–403 [Chapter 11].
[10] Johnson K. Contact mechanics. Cambridge, United Kingdom: Cambridge
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