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Computational Materials Science 25 (2002) 54–60
Numerical simulation of wear-mechanism maps
A. Cantizano
, A. Carnicero a, G. Zavarise
Instituto de Investigaci
on Tecnol
ogica (IIT), Universidad Pontificia Comillas de Madrid. C/Alberto Aguilera, 23, 28015, Madrid, Spain
Dipartimento di Ingegneria Strutturale e Geotecnica, Politecnico di Torino, C.so Duca degli Abruzzi, 24, 10129 Torino, Italy
Wear-mechanism maps for different materials, actually steel on steel, are being modeled with FEM. A microthermomechanical approach has been used in order to model accurately the macroscopic phenomena of wear. A plastic law for
the normal micromechanical contact of asperities has been implemented in FEAP and a slight modification, based on
experimental results, is proposed. For the three mechanisms modeled, good correlation between the numerical results of
wear and those found in literature has been obtained for a pin-on-disk configuration. The flash temperatures reached in
the contact interface have been also studied and fair good agreement with literature is achieved.
Ó 2002 Elsevier Science B.V. All rights reserved.
PACS: 46.30.P; 73.40.J; 02.60
Keywords: Wear model; Contact; Friction; Metal-to-metal; Micromechanics; Finite elements
1. Introduction
Wear is an inevitable phenomenon generated
whenever two rough surfaces slide. It is a very
complicated process due to the many variables
that play an important role and therefore, different
approaches have been used in order to find useful
equations that could describe the regimes of wear,
as can be seen in [7].
A model of the wear phenomena depends on
the thermo-mechanical characteristics of the two
surfaces sliding. Thus, an accurate model for
contact based on the real geometry of the surfaces
is needed. These models have been developed
either using a theoretical analysis of microscopi-
Corresponding author.
cally rough surfaces as in [4] or in [3], or can be
based on experimental data as is proposed in [10].
There are many different ways of representing
the wear data, usually as a tabulation of the wear
rates of the dominant regimes considered. However, these presentations can be considered restrictive because they usually cover a relatively
narrow range of sliding conditions related to the
mechanical system which is being studied. A much
more complete analysis can be found in the wearmechanism maps proposed and developed by [5],
where a wider range of sliding conditions can be
included, showing how the mechanisms interface
under the possible various operating situations.
Thus, the dominant mechanism for any specific
condition can be investigated.
The process of wear has been widely modeled using the finite elements method, although
these approaches have studied only one wear
0927-0256/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved.
PII: S 0 9 2 7 - 0 2 5 6 ( 0 2 ) 0 0 2 4 9 - 5
A. Cantizano et al. / Computational Materials Science 25 (2002) 54–60
nominal area of contact
Arrhenius constant for oxidation
real area of contact
constant used in the model for mildoxidational wear
normal load
F~, Fnorm normalized load ðF~ ¼ F =AHo Þ
seizure load
hardness of sliding surface
room-temperature hardness
thermal conductivity of oxide
normal pressure
activation energy for oxidation
molar gas constant
bulk temperature
flash temperature
melting temperature of oxide
volume lost per unit area of surface
W~ , Wnorm normalized wear rate ðW~ ¼ W =AÞ
critical thickness of oxide film
mechanism. With the finite element developed
here, different wear mechanisms are implemented
so that depending on the operating conditions––
normal force and sliding velocity––the predominant wear process is activated following the
wear-mechanism map proposed in [5].
The treatment of the contact surfaces have
never taken into account the thermo-microscopical
behavior of a real surface when modeling wear
with finite elements. In the present paper, the micromechanical contact law allow a more realistic
simulation of what is actually happening in the
contact interface during the wearing out process.
The flash temperatures achieved in the contact
interface when two surfaces slide highly influence
the wear rates. The heat generated at the surfaces
enters through the true contact area which is a
function of the radius of asperity that is considered
constant for any loading condition, as is explained
[5]. In their other work, [2], the calculation of the
flash temperatures is improved because they depend
on a radius of a contact-junction which can be
made up of many unit contacting asperities for
c1 , c2
v~, vnorm
thermal diffusivity
experimental constants
current mean plane distance
volume fraction of molten material removed during sliding
Archard’s dimensionless wear coefficient
equivalent linear diffusion distance for
flash heating
mean absolute asperity slope
rate of heat input per unit area
radius of an asperity
radius of a contact-junction
radius of the pin
sliding velocity
normalized velocity ð~
v ¼ vro =aÞ
heat distribution coefficient
coefficient of friction
RMS surface roughness
that load. The micromechanical law used here allows a good approach to the flash temperature
calculation, where the radius of asperity depends
on the load and much better results are obtained
when comparing with the improved method proposed in [2].
The model implemented assumes a constant
statistical characterization of the contacting surfaces. The wear achieved in every pass of the pin
over the disk is considered to regenerate the
roughness of the pin. This approximation is necessary because the wear-mechanism map that is
modeled does not study the wear-rate transitions
related to the mechanisms [6], and is accurate enough to obtain good results for a steady-state wear
2. Modeling
The importance in modeling, accurately, wearmechanism maps for any pair of materials using
the finite elements method is the ability to obtain
A. Cantizano et al. / Computational Materials Science 25 (2002) 54–60
precisely the amount of material worn out for any
sliding situation and for any geometry of a mechanical system. In this way, a complete precise
study of the different types of wear acting on every
part of the mechanical system can be done.
A law for the normal microscopical contact is
required in order to reproduce the real behavior of
the contact interface between two rough surfaces.
In the present work, a plastic law for the behavior
of the asperities in contact, based on a statistical
characterization of the surfaces, has been implemented. Also a slight modification, based on experimental results, has been proposed.
With the characteristics of the mechanical system defined, the procedure followed by the finite
element in order to calculate the material worn out
is described in Fig. 1.
The normal contact force obtained from the law
mentioned above is introduced in the classic constitutive law of friction in order to verify the sliding condition. The tangential contact force is,
therefore, calculated and also the heat generation
due to friction, with which the bulk temperature
achieved can be obtained. Then, the flash temperatures are calculated taking into account the
radius of the contacting asperities under deformation. With these magnitudes, the thermomechanical behavior at a microscopic scale is
completely defined. Thus, according to the normal
force and the sliding velocity, a predominant wear
mechanism is activated following the wear-mechanism maps developed in [5], and the volume of
material worn out calculated.
2.1. Micromechanical contact law
All surfaces are rough, as was said in [9]. The
shape and distribution of the asperities depend on
the method of production of the surfaces. The
basic hypothesis of the model consider the asperities to be randomly distributed over the apparent
contact area and having a Gaussian distribution of
the asperity heights. As a result of the deformation, there is a number of circular contact spots
with a determined radius.
Following the work initiated by [3], an implicit
expression (Eq. (1)) for the contact hardness and
the applied pressure, considering plastic behavior
of the asperities––Eq. (3), n ¼ 1––was proposed in
c "
2 ) #c2
P 4 106 r 2
H c1
In [8], a useful explicit expression (Eq. (2)) was
found, by approximating the inverse of the complementary error function of Eq. (1) in the range
of values where the difference between both expressions is negligible ð6 108 < P =H < 4 103 Þ.
#1=ð1þ0:0711c2 Þ
c1 1617646:152r
Eq. (2) is used in [12,13] in order to find an important correlation between the current mean
plane distance and the apparent mechanical pressure which is required for the numerical implementation in finite elements.
Finally, taking into account the mechanical relationship based on experiments, [10] presented the
following relationship between the true ðAr Þ and
the nominal area of contact ðAÞ,
Fig. 1. Flow-chart for the simulation of wear.
A. Cantizano et al. / Computational Materials Science 25 (2002) 54–60
A more general expression of the correlation between the current mean plane distance and the
apparent mechanical pressure, as a function of n, is
2 1þ0:0711nc2
1617646:152r 2 exp d ð1:363rÞ2
P ¼ c1
5:589ð1þ0:0711nc2 Þ=n
2.2. Friction
The classical law of friction, but where the coefficient of friction depends on the sliding velocity,
as in [5],
l ¼ 0:78 0:13 log10 ð~
W~ ¼ kA F~
In the first two mechanisms described above, the
value of the real area of contact is critical, Eq. (7),
and determines the flash temperatures reached in
the contact interface, Eq. (6), and thus the volume
of the material that has been worn out. These three
important mechanisms of wear, for a steel on steel
contact pair are widely described in [5].
The transition between these three regimes
mainly depends on the sliding velocity for most of
the operating conditions. The influence of the
normal force applied has to be taken into account
only for quite high normal forces or extremely low.
has been implemented. A modification of Eq. (5) is
proposed in [2], which takes into account the local
melting of the asperities at high velocities but is
not considered in this work.
2.3. Mechanisms of wear
When steel surfaces slide at speeds above 1 m/s,
the flash temperatures reached cause oxidation
and therefore, the wear debris consists mainly
of iron oxides. At low velocities, the oxide film
formed on the sliding surface is cold and brittle.
The splitting off of this film is called mild-oxidational wear. The normalized amount of material
removed W~ is defined as
C Ao r o
Qo F~
W~ ¼
exp Zc a
RTf v~
At higher velocities (v > 10 m/s), the oxide film
formed is thicker and more continuous, hotter and
more plastic, which implies a change in the wear
process. This is called severe-oxidational wear and
can be calculated as
Kox ðTmox Tb Þ
W ¼
aq ð7Þ
When the sliding velocities are very small (v < 0:1
m/s), the surface heating can be considered negligible. Then the frictional force deforms the metal
surface and causes the removal of slivers of metal
from both surfaces. In this case, the wear rate
follows the well-known Archard’s law [1]:
3. Results and discussion
Three different mechanisms of wear have been
simulated with a pin-on-disk configuration, as
shown in [2], with an enhanced version of the finite
element program FEAP developed by R.L. Taylor
and J.C. Simo and documented in [14] (Fig. 2).
The radius of the pin ðro Þ is chosen to be 1.5 mm
and its length of 9 mm ð6ro Þ, and these values allow us to compare the numerical results with those
obtained in [5]. The operating conditions simulated are:
Mildoxidational wear
7.1 10
14.1 103
5.0 103
1.6 103
5.0 103
1.5 103
1.65 102
1.65 102
1.65 102
1.65 102
3.3 102
3.3 102
Severeoxidational wear
7.1 103
15.6 103
8.7 103
2.1 103
14.7 103
1.65 104
1.65 104
1.65 104
8.24 104
8.24 104
Delamination wear
7.1 103
14.2 103
5.0 103
1.5 103
5.0 103
1.65 101
1.65 101
1.65 101
1.65 101
A. Cantizano et al. / Computational Materials Science 25 (2002) 54–60
Fig. 2. Model of a pin-on-disk configuration in sliding conditions.
The results are presented to show the ability of
the contact element for predicting accurate values
of wear for several conditions of operation and its
possible application for real problems (Fig. 3).
Several numerical simulations have been made in
order to obtain normalized wear rates ðW~ Þ, for
different values of normalized applied force ðF~Þ
and normalized sliding velocity ð~
vÞ. In Fig. 3 the
normalized wear rates can be seen for the three
mechanisms of wear implemented.
The severe oxidational wear ð~
v > 104 Þ and also
the delamination mechanism of wear ð~
v < 10Þ are
well predicted by the numerical results. The
Fig. 3. Normalized wear rates for three mechanisms: severe
oxidational, mild oxidational and delamination wear.
mechanism of mild-oxidational wear presents a
worse correlation and it is mainly due to the difference in the flash temperatures calculated. These
temperatures highly depend on the radius of asperity ðra Þ that was considered a constant of 105
m in the calculations made in [5]. But here, the
radius of asperity was allowed to increase as the
load was applied. In order to obtain a value of ra
approximate to the constant given above, after
loading, different microscopical characterizations
of the surfaces have been chosen for the several
values of F~ to guarantee the same value of ra for
every test. This artificial characterization of the
surfaces might be a reason for the discrepancy
found, although with a constitutive law that allows
the deformation of the asperities in the contact
interface a much more realistic behavior of the
contact should be achieved.
In [2], the calculation of the flash temperatures
is improved and a radius of a contact-junction ðrj Þ
is also taken into account (Eqs. (9)–(11)). The
micromechanical law is able to obtain flash temperatures quite similar in this case, specially for
n ¼ 5=6, as is shown in Fig. 4.
The real area of contact, in [2], is expressed as
Ar ¼ Nj prj2
and the following mechanical relationship is defined,
Fig. 4. Flash temperatures for the mild-oxidational mechanism
of wear.
A. Cantizano et al. / Computational Materials Science 25 (2002) 54–60
Ar F
A Fs
where Fs is the load when seizure occurs
Fs ¼
Ho A
ð1 þ 12l2 Þ
and for which the real area of contact equals the
nominal area.
For the range of velocity considered Eq. (5) and
the load applied, Eq. (10) is much more similar to
Eq. (3), specially when n ¼ 5=6, than the classical
plastic relationship used in [5],
A Ho
The value of rj is fairly well predicted by the actual
radius of asperity, after loading, calculated with
the microscopical law for every F~, which is slightly
higher than the constant ra . The flash temperatures, obtained as in [2], for the mechanism of
mild-oxidation wear are represented in Fig. 4.
As can be seen in Fig. 4, better results for
the flash temperatures are obtained when n ¼ 5=6
than for n ¼ 1, but only for the sliding conditions
4. Conclusions
A new way of modeling steady-state wear has
been proposed based on a micromechanical law
for the normal contact that takes into account a
statistical characterization of the rugosity of the
surfaces that slide together. This realistic treatment
of the surface allows the calculation of the flash
temperatures achieved in the contact interface,
that play a very important role in the wear rates.
Other micromechanical laws can be treated in the
same way in order to obtain accurately these
Three mechanisms of wear have been modeled
using the finite elements method, with a pin-ondisk configuration. The numerical results predict
quite well the mechanisms except for the mild
oxidational, where the flash temperatures calculated differ. An improved formulation for the flash
temperatures was tested and a much better agree-
ment with the values obtained with the model, was
A finite element with a whole wear-mechanism
map can be build and be used for the study of any
geometry and operating condition of a mechanical
system where different mechanisms of wear can
interface at the same time. Also an elastic law of
micromechanical contact can be implemented to
take into account the elastic steady state for situations with repeated sliding conditions.
The authors wish to acknowledge the interest
and the support of Prof. Franco Bonollo from the
Universita di Padova at Vicenza during the study
of the wear-mechanism maps.
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