Numerical simulation of the elastic behavior of the automotive brake
disc in dry sliding contact with the pads
S. KERROUZ*1, T. TAMINE1, M. BOUCHETARA1
Department of Mechanical Engineering, Laboratory of Gaseous Fuel and Environment (LCGE)
University of Science and Technology of Oran Mohamed-Boudiaf
31000 Bir El Djir, El Mnaouar, Oran, P. O. B. 1505
ALGERIA
Abstract: - During braking and when the disk brought into contact with the brake pads which represent the
friction body, mechanical stresses are imposed at the contact zone. All physical parameters (temperature,
pressure speed and mechanical characteristics, and tribological conditions change over time), heat from friction
generated at the interface, and temperature may exceed the critical value. All these problems that allowed us to
do this study which concerns the numerical simulation by finite elements of a mechanical torque in dry sliding
contact with motor vehicle disk/brake pads at the moment of stop braking using the ANSYS calculation code
14.5 which is based on the finite element method with its friction contact management algorithms. This
behavior was analyzed in the transient case in terms of equivalent stresses and deformations (Von Mises) as a
function of the braking conditions ( the type of loading, the speed of rotation of a disk, the pressure force
applied to the brake pads, the coefficient of friction between the disk and the pads), and the thermal conditions
(the temperature of the disk, and the heat flux in the disk, and the heat exchange by convection over the entire
surface of the disk), the geometrical characteristics of the disk pads assembly and the position of the pads with
respect to the brake disk and the mechanical parameters assembly and the position of the pads with respect to
the brake disk and the mechanical parameters ( Young’s modulus, density, Poisson coefficient). This analysis
allows us to see the behavior of the disk and the pads in contact and to recognize these damages in order to find
the optimal technological solutions that will meet the needs of the engineer responsible for the design of the
braking system, in particular the disk-pads torque, and to improve this system and make it more reliable and for
an optimal and economical choice of the disk and pads well resist heat.
Key-Words: - dry sliding contact - friction - wear - disc – pads.
Received: December 19, 2021. Revised: November 4, 2022. Accepted: December 2, 2022. Published: December 31, 2022.
1 Introduction
IN the transportation field, today’s vehicles are
more powerful and faster. Therefore, braking
systems must ensure efficiency, reliability and
comfort with new technologies. The braking system,
which is a major safety component, is a very current
research topic for automotive engineers and
researchers. The phenomenon of friction between
two surfaces that slide on each other when there is
contact between two solids leads to a loss of
mechanical energy that is transformed into heat.
Moreover, friction and wear are independent
phenomena. It is indeed possible to design systems
with low wear and high friction (brakes) or high
wear and low friction (machining) [1], [2]. The
operation of the braking system to slow down or
stop the moving vehicle is based on the dissipation
of the kinetic energy of the vehicle into thermal
energy resulting from the disk-pad friction. The
brake is therefore a heat absorption system. Its
efficiency depends on the capacity of its
components to absorb and resist heat, and also on
the friction coefficient. In friction, [3] presented a
thermal study on sliding contacts with application to
braking. These authors used a numerical model and
an experimental device was developed on the
principle of three- body contact. The experimental
and numerical results obtained are coherent and
show the interest and the representativeness of a
model with three volumes, homogeneous and
continuous bodies. We can also mention the study
of [4], and more recently that of [5] on the thermal
behavior in brake discs. The study carried out by [4]
allowed to model numerically in 3D the thermal
WSEAS TRANSACTIONS on APPLIED and THEORETICAL MECHANICS
DOI: 10.37394/232011.2022.17.26
S. Kerrouz, T. Tamine, M. Bouchetara
E-ISSN: 2224-3429
215
Volume 17, 2022
behavior of the brake for a solid and ventilated disk.
The authors in [5] worked on the heat transfer from
the high temperature zone to the low temperature
zone by incorporating heat pipes on the surfaces of
ventilated brake discs. Experimental and numerical
results showed a decrease in the highest
temperatures and a greater uniformity of the
temperature during braking when heat pipes were
inserted on the surfaces of ventilated brake discs.
More recently, the same authors in [6] studied the
transient phenomenon of the temperature field on a
ventilated disk during its sudden braking phase.
The experimentation with thermocouples placed on
points on the surface of the disc allowed to verify
the numerical results and to draw the temperature
curves in the circumferential and radial direction of
the disc.
In the case of dry contact between the brake disc
and brake pads during braking, the work of [7],
based on numerical simulations, allowed
the determination of deformations and Von
Mises stresses as well as the distribution of
contact pressure in the brake pads for the case
of a solid disc and a ventilated disc.
The main objective of the present study is the
modeling and numerical simulation of the
thermoelastic behavior of the dry sliding contacts of
the brake disc-pad assembly in the presence of
friction between the two contacting solids. It is
important to underline the thermal influence on the
elastic behavior due to the dissipation of energy and
therefore heat produced at the contact area between
the disc and the pads. This influence has been taken
into account with the pressure exerted by the pads
on the disc during braking. The numerical
simulation was carried out by the element method
under the ANSYS Workbench code. The results
obtained in terms of equivalent deformations and
stresses (Von Mises) allowed to analyze the
influence of various parameters such as the
mechanical characteristics of the parts in contact,
the friction coefficient, the rotation speed of the
disc, the pressure applied on the pads while taking
into account the braking time.
1. Analysis of the elastic behavior of
the dry sliding contacts of the disk -
pad pair
In this study, a numerical approach is proposed for
the simulation of the static elastic behavior of the
disk-pad pair with dry sliding contactsas a function
of the mechanical boundary conditions. For this
purpose, the Ansys finite element code is used to
elaborate the geometrical model of the disk-pad pair
and the numerical model of the finite element
simulation. The computational code has algorithms
for handling frictional contacts based on Lagrange
multipliers or the penalty method [8]. The analysis
of the static elastic behavior of the disk-pad pair is
carried out as a function of the braking conditions
(type of loading, vehicle speed, number of braking
cycles) and of the geometric characteristics of the
disk-pad assembly as well as of the mechanical
parameters (Young’s modulus, density, the fish
coefficient and friction).
We will assume that the brake pads are bodies
made of friction materials, flexible while the disc is
ventilated with grooves and rigid. The contact
pressure and the rotation speed of the disc are
considered as input data for the numerical
simulation.
1.1. Vehicle specifications
From the vehicle data, the braking force on the tires
and the stopping time can be determined as a
function of the initial speed, the vehicle load and
the road profile (level or slope) as presented in
Table 1.
Table 1 shows the characteristics of the selected
vehicle.
Parameters
Designation Values
m
Vehicle mass (kg) 1700
V
0
Initial speed (m/s) 40
V
f
Vehicle speed at the
end of braking (m/s)
0
b
Vehicledeceleration
(m/s2)
-20
R
d
Brake disc radius (m) 0.144
A
d
Disc friction surface
(m2)
0.44772
A
p
Wafer surface (m2) 0.27085
μ
Coefficient of friction
disc - pads
0.2
R
p
Tire radius (m) 0.2516
t
s
Break time (s) 2
In the case of stopping braking, the kinetic energy of
the vehicle converted into thermal energy is equal
to:
WSEAS TRANSACTIONS on APPLIED and THEORETICAL MECHANICS
DOI: 10.37394/232011.2022.17.26
S. Kerrouz, T. Tamine, M. Bouchetara
E-ISSN: 2224-3429
216
Volume 17, 2022
(1.1)
Where M is the total mass of the vehicle, V0 the
initial speed.
To obtain the amount of heat dissipated by each of
the brake discs, we need to know the weight
distribution of the vehicle, expressed by the
coefficient β. Thus, the amount of heat dissipated by
each of the front brake discs will be [9]:

 (1.2)
We will take β equal to 30%. of the mass of the
vehicle.
The braking force applied to each front wheel is
equal to [9]:

 (1.3)
󰇡
󰇢
(1.4)
The braking force applied to each front wheel disc is
equal to:

󰇡
󰇣
󰇤
󰇢 (1.5)
The braking speed is equal to:
󰇛
󰇜 (1.6)
For the case of stopping braking, we have Vf =0.
The initial rotation speed of the disk is given by the
following relation:
(1.7)
The pressure exerted on the disc by the pads is
calculated accordingto [10]
 (1.8)
For the chosen vehicle, we have:Fd = 541.7[N], ωd
= 159tr/min, p = 1MPa.
To perform the digital simulation during the braking
phase, the following temporal conditions are
considered:
• Braking time = 4.5 [s]
• Step of the initial time = 0.25 [s]
• Minimum initial time step = 0.125 [s]
• Maximum initial time step = 0.5 [s]
1.2. Disc and pad materials
The materials commonly used for the manufac-ture
of discs are graphite cast irons. In this
study, high carbon gray cast iron FG25 was
chosen which has good con-ductivity, fairly
good mechanical strength
and low w ear
[11], [12]. For the linings, we opted for an
organic matrix material characterized by a good
friction coefficient (as high and constant as
possible, regardless of the variation in
temperature, contact pressure or disc rotation
speed) [13]. The pad holders are made of
mild steel; they sever to distribute the force
exerted by the hydraulic piston over the entire
surface of the pads in order
to guara
ntee the
largest and most homogeneous disk-pad contact
area possible. Table 2 summarizes the properties
of the organic matrix composite material for the
brake pads and the gray cast iron material for the
brake disc.
Table 2 Mechanical properties of gray cast
iron brake disc (a) and organic matrix composite
brake pads (b) [14].
Properties (a) (b)
Density (kg /m3) 7200 2500
Young's
modulus(Pa)
1.1E+11 3E+09
Poisson coefficient 0.28 0.25
Compressibility
modulus(Pa)
8.3333E+10 2E+09
Shear modulus (Pa) 4.2969E+10 1.2E+09
1.3. Disc and pad geometry models
Figure 1, Figure 2, Figure 3, and Figure 4 show
the geometric models of the disk and pads
developed using SolidWorks software.
WSEAS TRANSACTIONS on APPLIED and THEORETICAL MECHANICS
DOI: 10.37394/232011.2022.17.26
S. Kerrouz, T. Tamine, M. Bouchetara
E-ISSN: 2224-3429
217
Volume 17, 2022
Figure 1. Left view of the disc
Figure 2. Profile view of the disc
Figure 3. Left view of the brake pad
Figure 4. Profile view of the brake pad
1.4. Geometrical models of the disc and pad
pair
Figure 5, and Figure 6 respectively show the
brake model (disc – pads) and the different
pad position configurations that will be exported
to the ANSYS computer code for numerical
simulation.
Figure 5. (a) Right brake pads , (b) Left brake pads
Figure 6.(c) Brakepads at the bottom , (d) Brake pads
on top
1.5. Finite element mesh model of disc brake
components (disc, pads)
The finite element discretization of the disk
assembly and wafers was performed by
Ansys Workbench software. Figure 4 gives
respectively the volume mesh by default of the
disc and of the brake pad. The mesh of the break
pad for different knots are presented in Figure 7,
Figure 8 and Figure 9.
WSEAS TRANSACTIONS on APPLIED and THEORETICAL MECHANICS
DOI: 10.37394/232011.2022.17.26
S. Kerrouz, T. Tamine, M. Bouchetara
E-ISSN: 2224-3429
218
Volume 17, 2022
Figure 7. Mesh of a brake pad (Knots 829,
Items 1032)
Figure 8. Mesh models of the disc (Knots
27064, Items 16048)
Figure 9. (Grooved disc / pads) (Knots 30786 ,
Items 16558)
1.6. Boundary conditions
The boundary conditions applied to the disc-
pad torque are illustrated in Figure 10, Figure 11.
Figure 10. Left view of the boundary conditions and
the load applied to the grooved disc / brake
pad
Figure 11. Profile view of the boundary conditions
and the load applied to the grooved brake disc
/ pads
1.7. Thermal conditions applied to the torque
(brake disc / pads)
The study is assumed to be thermoelastic
considering the transient problem with the following
thermal conditions:
• The temperature of the disc is: T = 400C at time t
= 0 s,
• A flow of heat in the two contact areas between
the disc and the pads,
• Heat exchange by convection over the entire
surface of the disc.
2. Results and interpretations
2.1. Distribution of the equivalent elastic
strains as a function of the braking time for
the four positions
WSEAS TRANSACTIONS on APPLIED and THEORETICAL MECHANICS
DOI: 10.37394/232011.2022.17.26
S. Kerrouz, T. Tamine, M. Bouchetara
E-ISSN: 2224-3429
219
Volume 17, 2022
In this comparative study of the mechanical stresses,
we chose four configurations of the disc-pads pair
having a different position of the pads while
keeping the same boundary conditions. Figure
12, Figure 13, Figure 14, and Figure 15 give an
overview of the deformation zones on the disc
and the pads. It can be seen that the disc has
the lowest deformation due to its rigidity and
the hardness of the material used (gray cast iron).
Gray cast iron is most commonly used in brake
discs because it is more resistant to wear and heat.
While the deformations at the level of the pads are
more important because of the properties of the
material and their flexibility.
Figure 12. Right brake pads (max value = 0.01051)
Figure 13. Left brake pads (max value = 0, 01495)
Figure 14. Brake pads at the bottom (max value =
0.037395)
Figure 15. Brake pads on top (max value =0.03375)
2.1.1. Variation of the equivalent elastic strain in
the disc as a function of time for the four
configurations of the disc/brake pad pair
Figure 16 shows that regardless of the position
of the pads, the equivalent elastic strain increases
in a non-linear fashion with time. For cases
where the brake pads are placed at the bottom
and at the top, the equivalent elastic deformation
is the same. At the end of braking at t =
4.5s, the maximum equivalent elastic
deformation reaches 0.037 mm / mm at the outer
edges of the two linings. The time-dependent
deformation of the inserts placed on the right is
smaller than that of the inserts placed on the left.
At the end of braking, it is 0.01051mm / mm
for the case of the pads on the left and 0.01495
mm / mm for the pads on the right. This can be
explained through certain influencing factors such
as the phase and direction of attack of the pads,
the mounting positions, pollution of the friction
surface (metal encrustation on the friction
surface), the effect thermal (overheating of the
pads and the disc at the end of braking). All of
these factors lead to accelerated wear and
deformation of the pads.
WSEAS TRANSACTIONS on APPLIED and THEORETICAL MECHANICS
DOI: 10.37394/232011.2022.17.26
S. Kerrouz, T. Tamine, M. Bouchetara
E-ISSN: 2224-3429
220
Volume 17, 2022
Figure 16. Variation of the equivalent elastic strain in
the disc as a function of time
2.2 Equivalent stresses of Von Mises
Figure 17, Figure 18, Figure 19, and Figure 20
show the state of the equivalent Von Mises
stresses for the four configurations. In each of
the four variants, it can be seen that the equivalent
stresses are concentrated above all at the level of
the grooved surface of the contact zone between
the pad and the disc and decrease in the
direction of the bowl of the disc and the ventilation
fins. The maximum value obtained at the level of
the groove can cause cracks in the groove and
even its rupture.
From the results obtained, we note that for
the pads located at the top and bottom of the
disc the equivalent stresses are higher than those of
the pads placed to the right and left of the disc.
The stresses in the brake mounts are smaller than
that in the disc. It can be concluded that the
presence of the groove in the contact zone and
its position relative to the pads during contact
with the disc have an influence on the equivalent
stresses.
Figure 17. Right brake pads (σeqmax= 57,204MPa)
Figure 18. Left brake pads (σeqmax= 54,154MPa)
Figure 19. Brake pads at thebottom (σeq max
= 111,79MPa)
Figure 20. Brake pads on top (σeqmax = 133,96MPa)
2.2.1. Variation of the equivalent stress as a
function of time for the four configurations of the
disc / pad pair
The graph in Figure 21 shows that the
equivalent stress in the disk varies in a non-linear
fashion with time. For the pads located at the top
of the disc, the equivalent stress is greater than
that of the pads placed at the bottom of the disc.
At times t = 4.5 s, it is of the order of 133.96 MPa
for the pads located at the top of the disc and
111.79 MPa for the pads located at the bottom of
the disc.
In the case of the pads placed to the right and
to the left of the disc, the equivalent stresses are
almost identical, but less important than those
of the previous variants. At time t = 4.5s, it is of
the order of 57.204 MPa for the pads on the
right and 54.154MPa for the pads on the left. They
are half of the previous variants. Note that the
equivalent stress is greater in the grooved contact
zone between the disc and the pads than the other
parts of the disc.
WSEAS TRANSACTIONS on APPLIED and THEORETICAL MECHANICS
DOI: 10.37394/232011.2022.17.26
S. Kerrouz, T. Tamine, M. Bouchetara
E-ISSN: 2224-3429
221
Volume 17, 2022
Figure 21. Variation of the equivalent stress
as a function of time
2.3. Effect of the parameters on the
equivalent stresses of the disc-pad couples
This part of the study is devoted to the influence of
a certain number of parameters considered
significant, such as the speed of rotation of the disc,
the coefficient of friction, the pressure applied on
the brake pads and the choice of the material of the
disc on the Von Mises stress distribution in the disc
and pads when braking.
2.3.1. Influence of the rotational speed of the
brake disc
Figure 22, Figure 23, Figure 24, Figure 25, and
Figure 26 show the evolution of Von Mises
stresses in the disc-pad torque by increasing the
initial rotational speed of the brake disc.
These figures show that during the braking
phase, the equivalent stress increases significantly
with the increase in the initial rotational speed of the
disc, especially in the contact area and in the ends of
the pads. Conversely, it decreases in the direction of
the ventilation fins and the perforated bowl of the
disc.
Figure 22. ω =30 rd/s (σmax =25,384MPa)
Figure 23. ω=60rd/s(σmax=26,881MPa)
Figure 24. ω=90 rd/s(σmax=44,186MPa)
Figure 25. ω=120 rd/s(σmax=76,585MPa)
WSEAS TRANSACTIONS on APPLIED and THEORETICAL MECHANICS
DOI: 10.37394/232011.2022.17.26
S. Kerrouz, T. Tamine, M. Bouchetara
E-ISSN: 2224-3429
222
Volume 17, 2022
Figure 26. ω =159 rd/s(σmax=26,31Mpa)
Figure 26. Variation of the equivalent stress as a
function of the speed of rotation of the disc
2.3.2. Influence of the coefficient of friction
The influence of the coefficient of friction on the
equivalent stress of the disc-pad torque is shown
in Figure 27. We see that the equivalent
stress increases with the time of braking, but it
decreases slightly with the increase of the
coefficient of friction. The maximum value of the
stress is located at the level of the contact zone at
the end of braking.
The influence of the coefficient of friction on
the equivalent stress of the disc-pad torque is
shown in Figure 27. We see that the
equivalent stress increases with the time of
braking, but it decreases slightly with the
increase of the coefficient of friction. The
maximum value of the stress is located at the level
of the contact zone at the end of braking.
Figure 27. Variation of the equivalent Von-
Mises stress as a function of the friction
coefficient
2.3.3. Influence of the disc material
Table 3. Mechanical characteristics of the brake
discs (gray cast iron and stainless steel) [14], [15].
stainless steel
Grey cast
iron
7750
7200
1.93E+11
1.1E +11
0.31
0.28
1.693E+11
8.3333E+10
7.3664E+10
4.2969E+10
Figure 28 shows the evolution of the
equivalent stress for the two materials studied as a
function of time. We first notice that the maximum
value of the equivalent stress of the stainless steel
disc is higher than that of gray cast iron. The
difference in equivalent stress for these two
materials is all the greater with increasing time. At
the end of braking, this difference is of the order
of 39.14 MPa. As mentioned previously, although
the equivalent stress of the gray cast iron disc is
smaller than that of the stainless steel disc, the
gray cast iron disc is however distinguished by
very good resistance to corrosion and
deformation at hot. The mechanical characteristics
are presented in Table 3.
Figure 28. Von Mises stress as a function of time
for the two disc materials (stainless steel / gray cast
iron)
2.3.4. Influence of the pressure applied to the
brake pads
In the braking system, the pads press the disc and
generate friction during braking. Mechanical
loading is represented by the pressure of a hydraulic
piston applied to the pads.
The variation of the equivalent stresses under the
influence of the applied pressure is presented in
WSEAS TRANSACTIONS on APPLIED and THEORETICAL MECHANICS
DOI: 10.37394/232011.2022.17.26
S. Kerrouz, T. Tamine, M. Bouchetara
E-ISSN: 2224-3429
223
Volume 17, 2022
Figure 29. It is noted that the increase in the value
of pressure also has a role on the elastic behavior of
the couple disc / pads since the equivalent
stresses of Von Mises increases with the pressure
exerted.
Figure 29. Von Mises equivalent stress as a function
of the pressure applied to the brake pads.
3. General conclusion
1. The numerical analysis of the transient
thermoelastic behavior of the dry sliding contacts of
the disc-wafer pair was carried out using the
ANSYS 14.5 calculation code based on the finite
element method. We have been able to show the
influence of the position of the brake pads on the
disc and of certain significant braking parameters
such as the coefficient of friction, the choice of
material and the initial speed of rotation of the disc,
the pressure applied to the pads. Brake pressure, and
thermal conditions (disc temperature, heat flow
through the disc and heat exchange by convection
over the entire surface of the disc). The stresses and
strains of each configuration of the disc-pad couple
are expressed as a function of the braking time.
2. The comparative study of the four variants of
the disc-pad pair shows that the maximum stresses
are concentrated at the level of the grooved surface
of the disk (contact zone between the pad and the
disk), then they decrease in the direction of the base
of the bowl of the disk, and ventilation fins. The
pads located at the top and bottom of the disc give
greater stresses than those of the pads
placed to the right and left of the disc; this is due to
the position of the groove.
3. Numerical analysis of the thermoelastic
behavior of dry sliding contacts shows that the
coefficient of friction has a low influence on the
equivalent stress of a disc regardless of the braking
time. The equivalent stress decreases with the
increase in the coefficient of friction.
4. The results show that the stress field and the
strain field depend not only on the coefficient of
friction, but on other parameters such as; the initial
speed of rotation, the type of loading applied to the
pads (the pressure), the temperature of the disc, the
choice of the material of the disc as well as the
variation of the braking time.
5. The equivalent stress in the contact area
increases with increasing initial rotational speed of
the disc. The maximum equivalent stress that a
stainless steel disc can withstand is higher than that
of gray cast iron. Despite the fragility of gray cast
iron, the latter has a technological advantage such as
good resistance to corrosion and hot deformation.
6. The influence of the pressure also has a role on
the thermoelastic behavior of the dry sliding contact
between the disc and the pads.
References:
[1] Q. J, Wang, Y.W, Chung, Encyclopedia of
Tribology, Department of Materials
Science and Engineering and Center for
Surface Engineering and Tribology,
Springer, New York, NY, USA. LI Vol. 6,
4139, 2013
DOI: 10.1007/978-0-387-92897-5
[2] S. Wen, p. Huang, Principles of Tribology,
Tsinghua University Press, Wiley, 251 p,
2011
[3] H. Pelletier, C. Gauthier, R. Schirrer,
Influence of the friction coefficient on the
contact geometry during scratch onto
amorphous polymers, Elsevier Wear, Vol.
268, Issues 9–10, pp.1157–1169, 2010
DOI: 10.1016/j.wear.2010.01.003.
[4] J. Qifei, Li. Wang, Y. Shui, Thermal
analysis of ventilated brake disc based on
heat transfer enhancement of heat pipe,
International Journal of Thermal Sciences,
Vol. 155, 106356, 2020.
DOI: 10.1016/j.ijthermalsci.2020.106356.
[5] A. Belhocine , M. Bouchetara, Thermal
analysis of a solid brake disc, Applied
thermal Engineering, Vol.32, pp. 59-67,
2012.
DOI: 10.1016/j.applthermaleng.2011.08.029
[6] J. Qifei, L. Wang, Numerical and
experimental analysis of transient
temperature field of ventiled disc brake
under the condition of hard braking,
International Journal of Thermal Sciences,
Vol.122, pp. 115-123, 2017.
DOI:10.1016/J.IJTHERMALSCI.2017.08.0137.
WSEAS TRANSACTIONS on APPLIED and THEORETICAL MECHANICS
DOI: 10.37394/232011.2022.17.26
S. Kerrouz, T. Tamine, M. Bouchetara
E-ISSN: 2224-3429
224
Volume 17, 2022
[7] A. Belhocine, M. Bouchetara, Temperature
and Thermal Stresses of Vehicles Gray
Cast Brake, Journal of applied research
and technology, Vol. 11, pp. 674-682,
2013.
DOI:https://doi.org/10.1016/S1665-6423
(13)71575-X.
[8] B. MAGNAIN, Development of algorithms
and a computer code for the study of
impact and shock problems, Doctoral
thesis from the University of Evry –Val,
Essonne, French, P49, 2006
[9] J. M. Thomas, C. N. Steven, K. J. Ball, B
.C. Bredell, Thermal cracking in disc
brakes ,Department of Mechanical and
Industrial Engineering, university of
Illinois at Urbana –Champaign, 1206 West
Green Street, Urbana, IL 61802, USA,
journal of Engineering Failure Analysis,
Vol.9, pp.6-76, 2002
DOI: S1350-6307(00)00037-6.
[10] G. Oder, M. Reibenschuh, T. lerher, M.
ŠRAML, B. ŠAMEC, I. POTRČ, Thermal
and stress analysis of brake discs in railway
vehicles, Advanced Engineering, ISSN.
1846-5900, Vol. 3, 2009.
[11] H. Jang, K. Ko, S. J. Kim, R. H. Basch, J.
W. Fash , The effect of metal fibers on the
friction performance of automotive brake
friction materials, Wear, Vol. 256, pp. 406-
414,2004.
DOI:https://doi.org/10.1016/S0043-
1648(03)00445-9.
[12] M. Djafri, Numerical and experimental
study of the tribological behavior of sliding
contacts, Application to disc brakes,
doctoral thesis, University of Science and
Technology of Mohamed Boudiaf, Oran,
Algerian, 2014.
[13] J.M. Berthelot, Composite materials,
mechanical behavior and analysis of
structures, Springer New York, NY, XXV.
646, ISSN. 0941-5122, 1999
[14] S. Kerrouz, M. Bourdim, T,Tamine, M.
Bouchetara, Study of the Mechanical
Behavior of an Automobile Brake Disc,
Periodica Polytechnica Mechanical
Engineering, 2021.
https://doi.org/10.3311/PPme.15589
[15] S. Oller, Numerical Simulation of
Mechanical Behavior of Composite
Materials, CIMNE School of Civil
Engineering of the Technical University of
Catalonia, Barcelona, Spain, Series ISSN.
1877-7341, P XII. 220, 2014.
WSEAS TRANSACTIONS on APPLIED and THEORETICAL MECHANICS
DOI: 10.37394/232011.2022.17.26
S. Kerrouz, T. Tamine, M. Bouchetara
E-ISSN: 2224-3429
225
Volume 17, 2022
Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
The authors contributed in the present research, at
all stages from the formulation of the problem to
the final findings and solution.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for conducting this study.
Conflict of Interest
The authors have no conflict of interest to declare.
Creative Commons Attribution
License 4.0 (Attribution 4.0
International , CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en
_US