This document summarizes an investigation into adhesional friction and adhesive wear laws for micromechanical surface contact. It incorporates adhesion theory into a multiasperity contact model to derive equations for static coefficient of friction and real contact area that support existing friction laws. A new proposed adhesive wear law is derived from the relationship between dimensionless real contact area and dimensionless wear volume. This is then compared to the existing Archard adhesive wear law. Key aspects of Johnson-Kendall-Roberts (JKR) adhesion model and multiasperity contact models are also summarized.
International Journal of Computational Engineering Research(IJCER)ijceronline
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
International Journal of Computational Engineering Research(IJCER)ijceronline
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
Interrelation of Friction-Wear and Mechanism of Energy Dissipation for MEMS A...ijceronline
Adhesion is a predominating force in Micro electro mechanical System (MEMS) due to high surface to volume ratio. In the present study of MEMS surfaces contact, adhesional friction force and adhesive wear volume have been computed numerically and new interrelation in between the wear and friction is developed after, finding their ratio. Also, mechanism of energy dissipation has been summarized on the basis of Arrhenius theory of mechanochemical reaction under working condition of MEMS devices.
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
When a ductile material with a crack is loaded in
tension, the deformation energy builds up around the crack tip
and it is understood that at a certain critical condition voids are
formed ahead of the crack tip. The crack extension occurs by
coalescence of voids with the crack tip. The “characteristic
distance” (Lc) defined as the distance b/w the crack tip & the void
responsible for eventual coalescence with the crack tip. Nucleation
of these voids is generally associated with the presence of second
phase particles or grain boundaries in the vicinity of the crack tip.
Although approximate, Lc assumes a special significance since it
links the fracture toughness to the microscopic mechanism
considered responsible for ductile fracture. The knowledge of the
“characteristic distance” is also crucial for designing the size of
mesh in the finite element simulations of material crack growth
using damage mechanics principles. There is not much work
(experimental as well as numerical) available in the literature
related to the dependency of “characteristic distance” on the
fracture specimen geometry. The present research work is an
attempt to understand numerically, the geometry dependency of
“characteristic distance” using three-dimensional FEM analysis.
The variation of “characteristic distance” parameter due to the
change of temperature across the fracture specimen thickness was
also studied. The work also studied the variation of “characteristic
distance”, due to the change in fracture specimen thickness.
Finally, the ASTM requirement of fracture specimen thickness
criteria is evaluated for the “characteristic distance” fracture
parameter. “Characteristic distance” is found to vary across the
fracture specimen thickness. It is dependent on fracture specimen
thickness and it converges after a specified thickness of fracture
specimen. “Characteristic distance” value is also dependent on the
temperature of ductile material. In Armco iron material, it is
found to decrease with the increase in temperature.
To ensure good adhesion between a 200 nm thick silicon dioxide layer and a 4.5 μm thick hardcoat polymeric coating, a better understanding of mechanisms of adhesion at this interface is needed. To reach this purpose, focus is placed on two axes: characterizing mechanical properties of materials composing the system and in parallel, finding an applicable and effective method to quantify adhesion. Small dimension of SiO2 thin film makes it challenging to accurately characterize it. Hence the use of both nano-indentation and AFM to attempt assessment of SiO2 thin film elastic modulus Ef; taking into account limitations and uncertainty associated with each technique. Elastic modulus of SiO2 thin film determined by nano-indentation is roughly 50 GPa on a wafer substrate and 15 GPa on a lens substrate. As for AFM, modulus measured is approximately 56 GPa on a wafer substrate and 22 GPa on a lens substrate. This highlights significant influence of substrate for both techniques. Impact on mechanical properties between SiO2 thin films under different intrinsic stresses was also investigated. Results suggest that higher density of SiO2 thin film leads to higher elastic modulus.
To quantify adhesion, micro-tensile and micro-compression tests were performed. Micro-tensile experiments give ultimate shear strengths of hardcoat-substrate interface ranging from 9 to 14 MPa. Values of energy release rates of SiO2 / Hardcoat, range from 0.1 J/m² to 0.5 J/m², depending on moduli values found on wafer or lens substrate.
Magnetic Properties and Interactions of Nanostructured CoCrTa Thin FilmsIOSR Journals
Magnetic properties of CoCrTa alloy thin films were studied as function of the deposition pressure. Films deposited at low deposition pressure showed low coercivity and high loop squareness ratio. At relatively higher deposition pressurean increase in the samples’ coercivity, and decrease in both the magnetic loop squareness ratio, andthe strength of the exchange interaction amongst the grains of the films were recorded. The observations indicate the films to have properties quite suited for recording media application as well as magnetic memory devices.
Effects of bending on a flexible metamaterial absorberjournalBEEI
This paper presents a study of bending a metamaterial based absorber. The study of bending is important for textile material since it can be easily crumpled. The basic absorber that is simulated for the study is an annulled circle as the top patch, and metal ground plane that sandwich a textile-based substrate. The center frequency for the absorber is 10.525 GHz. The type of bending is divided into two parts, which is convex bending and concave bending. Through series of simulations, the effects of the bending on the absorptivity and the shifting of the resonant frequency is observed. Also, the study on the change of incident and polarization angle is also included to support the basis of flexible metamaterial absorber affected by the bending.
Adhesion is linked with surface forces like capillary pressure and is thus detrimental at the
nanoscale where body forces are negligible. It can lead to instant failure during fabrication and
operation but it can also lead to overtime failure because of induced friction and wear. However,
when it is possible, coating a device with hydrophobic materials reduces drastically that mechanism.
Understanding how adhesion works is crucial to design new systems and to enable new
technologies. Two models (JKR and DMT) are studied in this paper and model adhesion in different
cases. Photolithography and particularly the release step must be carefully designed to prevent
contamination and stiction. Materials must be chosen and designed wisely to prevent adhesion
failure during operation but lubricants can be used to reduce its impact as well as the impact of
friction and wear.
MSEC2013- Interface delamination of diamond-coated carbide tools considering ...The University of Alabama
Interface delamination is the major failure mode of diamond-coated carbide tools in machining. On the other hand, coating cracking is possibly accompanied during a tribological process that induces the delamination phenomenon. However, such an influence between the two failure behaviors has not been investigated in a quantitative way to better understand and design diamond coating tools.
In this study, a three-dimensional (3D) indentation model combining cohesive interactions and extended finite element method (XFEM) was developed to investigate the diamond-coating, carbide-substrate interface behavior with the incorporation of coating cracking. The cohesive interaction was based on a cohesive zone model (CZM) with a bilinear traction-separation law. XFEM was applied to the coating domain to model cracking in the diamond coating with a damage criterion of the maximum principal stress. Deposition stresses were also included to investigate their effect on the coating delamination and fractures. The model was implemented in finite element (FE) codes to analyze the cone crack in brittle coatings, as well as the interface delamination of diamond coated carbide tools. The XFEM model was validated by the indentation testing data from literature in crack initiation and propagation in brittle materials. FE results from the indentation on diamond-coated tools show that the interface delamination size and loading force become smaller when coating fractures are incorporated in the model, and the deposition stresses will increase the initial crack radius and the critical load for delamination in diamond coatings.
Research on Contact Characteristics between Bump End Effector and WaferIJRES Journal
In the IC industry, commonly used methods are wafer clamping friction transmission type and vacuum suction. Combining science and theological contact theory,the contact friction transmission characteristics when using the bump and transmission actuator wafer, the wafer and the end actuators. Starting from the material properties of the wafer by ANSYS simulation analysis in contact with the wafer bump deformation due to its own gravity, and verify that it meets the requirements of small deformation wafer transfer. Compute and solve the friction contact with the wafer bump bristles between.
Analysis of Conditions in Boundary Lubrications Using Bearing MaterialsIJMER
In order to clearly establish the tribological potential of these alloys as bearing materials, the tribological parameters of the RAR Zn-Al alloys are compared to parameters of the CuPb15Sn8 lead-tin bronze, as a widely applied conventional bearing material. Existing Bearing of connecting rod is manufactured by using non ferrous materials like Gunmetal, Phosphor Bronze etc.. This paper describes the tribological behavior analysis for the conventional materials i.e. Brass and Gunmetal as well as New non metallic material Cast Nylon. Friction and Wear are the most important parameters to decide the
performance of any bearing. In this paper attempt is made to check major tribological parameters for three material and try to suggest better new material compared to conventional existing material. It could help us to minimize the problem of handling materials like Lead , Tin, Zinc etc.After Test on wear machine. Our experimental results are accessing efficient processing in bearing conditions in semantic data representation of extracted related data materials
Interrelation of Friction-Wear and Mechanism of Energy Dissipation for MEMS A...ijceronline
Adhesion is a predominating force in Micro electro mechanical System (MEMS) due to high surface to volume ratio. In the present study of MEMS surfaces contact, adhesional friction force and adhesive wear volume have been computed numerically and new interrelation in between the wear and friction is developed after, finding their ratio. Also, mechanism of energy dissipation has been summarized on the basis of Arrhenius theory of mechanochemical reaction under working condition of MEMS devices.
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
When a ductile material with a crack is loaded in
tension, the deformation energy builds up around the crack tip
and it is understood that at a certain critical condition voids are
formed ahead of the crack tip. The crack extension occurs by
coalescence of voids with the crack tip. The “characteristic
distance” (Lc) defined as the distance b/w the crack tip & the void
responsible for eventual coalescence with the crack tip. Nucleation
of these voids is generally associated with the presence of second
phase particles or grain boundaries in the vicinity of the crack tip.
Although approximate, Lc assumes a special significance since it
links the fracture toughness to the microscopic mechanism
considered responsible for ductile fracture. The knowledge of the
“characteristic distance” is also crucial for designing the size of
mesh in the finite element simulations of material crack growth
using damage mechanics principles. There is not much work
(experimental as well as numerical) available in the literature
related to the dependency of “characteristic distance” on the
fracture specimen geometry. The present research work is an
attempt to understand numerically, the geometry dependency of
“characteristic distance” using three-dimensional FEM analysis.
The variation of “characteristic distance” parameter due to the
change of temperature across the fracture specimen thickness was
also studied. The work also studied the variation of “characteristic
distance”, due to the change in fracture specimen thickness.
Finally, the ASTM requirement of fracture specimen thickness
criteria is evaluated for the “characteristic distance” fracture
parameter. “Characteristic distance” is found to vary across the
fracture specimen thickness. It is dependent on fracture specimen
thickness and it converges after a specified thickness of fracture
specimen. “Characteristic distance” value is also dependent on the
temperature of ductile material. In Armco iron material, it is
found to decrease with the increase in temperature.
To ensure good adhesion between a 200 nm thick silicon dioxide layer and a 4.5 μm thick hardcoat polymeric coating, a better understanding of mechanisms of adhesion at this interface is needed. To reach this purpose, focus is placed on two axes: characterizing mechanical properties of materials composing the system and in parallel, finding an applicable and effective method to quantify adhesion. Small dimension of SiO2 thin film makes it challenging to accurately characterize it. Hence the use of both nano-indentation and AFM to attempt assessment of SiO2 thin film elastic modulus Ef; taking into account limitations and uncertainty associated with each technique. Elastic modulus of SiO2 thin film determined by nano-indentation is roughly 50 GPa on a wafer substrate and 15 GPa on a lens substrate. As for AFM, modulus measured is approximately 56 GPa on a wafer substrate and 22 GPa on a lens substrate. This highlights significant influence of substrate for both techniques. Impact on mechanical properties between SiO2 thin films under different intrinsic stresses was also investigated. Results suggest that higher density of SiO2 thin film leads to higher elastic modulus.
To quantify adhesion, micro-tensile and micro-compression tests were performed. Micro-tensile experiments give ultimate shear strengths of hardcoat-substrate interface ranging from 9 to 14 MPa. Values of energy release rates of SiO2 / Hardcoat, range from 0.1 J/m² to 0.5 J/m², depending on moduli values found on wafer or lens substrate.
Magnetic Properties and Interactions of Nanostructured CoCrTa Thin FilmsIOSR Journals
Magnetic properties of CoCrTa alloy thin films were studied as function of the deposition pressure. Films deposited at low deposition pressure showed low coercivity and high loop squareness ratio. At relatively higher deposition pressurean increase in the samples’ coercivity, and decrease in both the magnetic loop squareness ratio, andthe strength of the exchange interaction amongst the grains of the films were recorded. The observations indicate the films to have properties quite suited for recording media application as well as magnetic memory devices.
Effects of bending on a flexible metamaterial absorberjournalBEEI
This paper presents a study of bending a metamaterial based absorber. The study of bending is important for textile material since it can be easily crumpled. The basic absorber that is simulated for the study is an annulled circle as the top patch, and metal ground plane that sandwich a textile-based substrate. The center frequency for the absorber is 10.525 GHz. The type of bending is divided into two parts, which is convex bending and concave bending. Through series of simulations, the effects of the bending on the absorptivity and the shifting of the resonant frequency is observed. Also, the study on the change of incident and polarization angle is also included to support the basis of flexible metamaterial absorber affected by the bending.
Adhesion is linked with surface forces like capillary pressure and is thus detrimental at the
nanoscale where body forces are negligible. It can lead to instant failure during fabrication and
operation but it can also lead to overtime failure because of induced friction and wear. However,
when it is possible, coating a device with hydrophobic materials reduces drastically that mechanism.
Understanding how adhesion works is crucial to design new systems and to enable new
technologies. Two models (JKR and DMT) are studied in this paper and model adhesion in different
cases. Photolithography and particularly the release step must be carefully designed to prevent
contamination and stiction. Materials must be chosen and designed wisely to prevent adhesion
failure during operation but lubricants can be used to reduce its impact as well as the impact of
friction and wear.
MSEC2013- Interface delamination of diamond-coated carbide tools considering ...The University of Alabama
Interface delamination is the major failure mode of diamond-coated carbide tools in machining. On the other hand, coating cracking is possibly accompanied during a tribological process that induces the delamination phenomenon. However, such an influence between the two failure behaviors has not been investigated in a quantitative way to better understand and design diamond coating tools.
In this study, a three-dimensional (3D) indentation model combining cohesive interactions and extended finite element method (XFEM) was developed to investigate the diamond-coating, carbide-substrate interface behavior with the incorporation of coating cracking. The cohesive interaction was based on a cohesive zone model (CZM) with a bilinear traction-separation law. XFEM was applied to the coating domain to model cracking in the diamond coating with a damage criterion of the maximum principal stress. Deposition stresses were also included to investigate their effect on the coating delamination and fractures. The model was implemented in finite element (FE) codes to analyze the cone crack in brittle coatings, as well as the interface delamination of diamond coated carbide tools. The XFEM model was validated by the indentation testing data from literature in crack initiation and propagation in brittle materials. FE results from the indentation on diamond-coated tools show that the interface delamination size and loading force become smaller when coating fractures are incorporated in the model, and the deposition stresses will increase the initial crack radius and the critical load for delamination in diamond coatings.
Research on Contact Characteristics between Bump End Effector and WaferIJRES Journal
In the IC industry, commonly used methods are wafer clamping friction transmission type and vacuum suction. Combining science and theological contact theory,the contact friction transmission characteristics when using the bump and transmission actuator wafer, the wafer and the end actuators. Starting from the material properties of the wafer by ANSYS simulation analysis in contact with the wafer bump deformation due to its own gravity, and verify that it meets the requirements of small deformation wafer transfer. Compute and solve the friction contact with the wafer bump bristles between.
Analysis of Conditions in Boundary Lubrications Using Bearing MaterialsIJMER
In order to clearly establish the tribological potential of these alloys as bearing materials, the tribological parameters of the RAR Zn-Al alloys are compared to parameters of the CuPb15Sn8 lead-tin bronze, as a widely applied conventional bearing material. Existing Bearing of connecting rod is manufactured by using non ferrous materials like Gunmetal, Phosphor Bronze etc.. This paper describes the tribological behavior analysis for the conventional materials i.e. Brass and Gunmetal as well as New non metallic material Cast Nylon. Friction and Wear are the most important parameters to decide the
performance of any bearing. In this paper attempt is made to check major tribological parameters for three material and try to suggest better new material compared to conventional existing material. It could help us to minimize the problem of handling materials like Lead , Tin, Zinc etc.After Test on wear machine. Our experimental results are accessing efficient processing in bearing conditions in semantic data representation of extracted related data materials
1. Biswajit Bera / International Journal of Engineering Research and Applications (IJERA)
ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 5, September- October 2012, pp.404-411
Adhesional Friction Law and Adhesive Wear Law of
Micromechanical Surface Contact
Biswajit Bera*
*(Department of Mechanical Engineering, National Institute of Technology Durgapur, India)
ABSTRACT
The paper describes the investigation on Ka 3
power of load P a 2 P 2/ 3 .To avoid
adhesional friction law and adhesive wear law of
micromechanical surface contact. Adhesion
R
the violation of the theory, Bowden and Tabor
theory of loading force and friction force is
simply, mentioned that all asperities should deform
incorporated in multiasperity contact to find out
plastically and real area of contact is linearly
static coefficient of friction which supports
Amontons's law of friction. New adhesive wear proportion to load P a 2 H a 2 P . Though
law is developed from almost linear relationship the theory is well accepted, still there is a question
of dimensionless real area of contact and why real area of contact is linearly proportional to
dimensionless adhesive wear volume, and it is load in so many tribosystem where plastic
compared with existing Archard's adhesive wear deformation does not occur.
law. This is investigated in adhesive MEMS surface
contact considering adhesion model of elastic solid.
Keywords - Real area of contact, Adhesional However, there are two type of adhesion model of
loading force, Adhesional friction force, elastic solid; one is JKR adhesion model [3] which
Coefficient of friction, Adhesive wear law considers adhesion force within contact area of
elastics solid sphere and another is DMT adhesion
1. Introduction model [4] which considers adhesive force out side of
Friction could be defined as the force of contact area of elastic solid sphere. First of all,
resistance that occurs when one body moves Chang et al. [5] have developed multiasperity
tangentially over another body. In the 15th century adhesion model of metallic rough surface contact
da Vinci discovered a law about dry sliding friction, based on DMT adhesion model. Thereafter,
which was rediscovered by Amontons about 200 Roychowdhury and Gosh [6] have considered JKR
years later. Friction laws were stated by French adhesion model for study of adhesive rough surface
engineer Guillaume Amontons [1] in 1699 from the contact but have evaluated external Hertzian load in
conclusions of his experimental work which are presence of adhesion, though which could be
given as follows: evaluated directly. However, adhesion component of
JKR model is not considered for evaluation of
a) The friction force linearly proportional to adhesion of multiasperity rough surface contact. The
the normal load between the two bodies in adhesive component of JKR adhesion model is
contact. considered for present study of adhesive MEMS
b) The friction force is independent of the surface contact. Actually, Johnson et al. [3] has
apparent area of contact between the two extended Hertz model considering adhesion of solid
bodies. elastic sphere based on energy method. Thereafter,
on the basis of same method, Savkoor and Briggs [7]
Thereafter, microscopic analysis of friction process has extended JKR adhesion model and developed
was described by Bowden and Tabor [2] in 1931. adhesional friction model of elastic solid sphere
The theory was based on following two statements: under tangential loading. The SB adhesional friction
model is considered for finding adhesional friction of
a) The friction force is dependent on real area MEMS surface contact.
of contact between two bodies.
b) The friction force is dependent on shearing On the other hand, due to rapid growth of
strength of adhesive bond formed between micro-machine, it has become important to study the
two bodies at tip of asperities. wear phenomena in the nano-scale under ultra low
loading condition. Archard's adhesive wear law [11]
The adhesional friction theory of Bowden and Tabor is essentially based on the classical concept of
is appeared to be inconsistent with Hertz theory of adhesion of metallic surface as proposed by Bowden
deformation of contacting elastic asperities, which and Tabor [2]. The fundamental idea is that the
predicts that the contact area should vary as 2/3 welded junctions are formed at the pick of the
404 | P a g e
2. Biswajit Bera / International Journal of Engineering Research and Applications (IJERA)
ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 5, September- October 2012, pp.404-411
asperities due to localized high adhesion and the
Ta
4
2 RF 3 R
2
subsequent shearing of the junctions from weaker
material causing adhesive wear. Similar idea is
G
K
0
implemented to find new adhesive wear law
considering adhesion component of JKR adhesion
4
2KR 3 R
1.5 1.5 2
(3)
model [3]. Thereafter, it is compared with existing GK
Archard's adhesive wear law.
where 1 2 1 1 2
2. Single asperity contact G G1 G2
2.1 Single asperity real area of contact
JKR adhesion theory has modified Hertz 2.4 Single asperity adhesive wear volume
theory of spherical contact. It predicts a contact
radius at light loads greater than the calculated Hertz If wear particle is in the shape of hemispherical and
radius. As asperity tip is considered spherical, the is cut off from tip of the asperity, wear volume is
adhesion model of single asperity contact could be 2
extended to multiasperity of rough surface contact. Va a 3
3
So, real contact area of single asperity is 2 R
F0 3 R 6 RF0 (3 R ) 2
2
R 3 3 K
A a F0 3 R 6 RF0 (3 R ) 2
K
Substituating F K (R) , we get
1.5
Substituting F K (R) , we get
1.5 0
R
a
R
2 1.5 1.5 3 R 2 6 R 3.5 1.5 9 2 2 R 4 (4)
2 Va R
3 R 2 6 R 3.5 1.5 9 2 2 R 4 3 3
K K K2
A a R 1.5 1.5 (1)
K K K2 3. Multiasperity contact
First of all, Greenwood and Williamson
2.2 Single asperity adhesional loading force [8] developed statistical multyasperity contact model
of rough surface under very low loading condition
According to JKR adhesion model, the expression and it was assumed that asperities are deformed
of adhesional loading force for each asperity contact elastically according Hertz theory. Same model is
is modified here in adhesive rough surface contact and
it is based on following assumptions:
Fa F0 3 R 6 RF0 (3 R ) 2
i. The rough surface is isotropic.
ii. Asperities are spherical near their summits.
KR 0.5 1.5 3R 6KR1.5 1.5 (3R) 2 (2)
iii. All asperity summits have the same radius
R but their heights vary randomly.
where 1 3 1 1 1 2
2
2 iv. Asperities are far apart and there is no
K 4 1 E E2 interaction between them.
v. Asperities are deform elastically according
and E1 , E2 , 1 and 2 are Young’s modulus and to JKR adhesion theory
poisson’s ratios of the contacting surfaces vi. There is no bulk deformation. Only, the
respectively, asperities deform during contact.
Flat plane
where surface energy of both surfaces, 1 2 12
2.3 Single asperity adhesional friction force
δ
Savkoor and Briggs theory has found adhesional Z
friction of spherical contact under tangential loading. d
As asperity tip is considered spherical, the
adhesional friction model of single asperity contact
could be extended to multiasperity of rough surface Mean
contact. According to the Savkoor and Briggs
model, the expression of adhesional friction force for Rough surface
each asperity contact is
Fig. 1 Rough surfaces contact
405 | P a g e
3. Biswajit Bera / International Journal of Engineering Research and Applications (IJERA)
ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 5, September- October 2012, pp.404-411
Multiasperity contact of adhesive rough surface has R
0.5
shown in Fig.1. According to, GW model, two rough (R) 3(R)
K
surface contact could be considered equivalently, F
*
()d
0.5 2
contact between rough surface and smooth rigid 0
6(R) 2 R 1.5 9 2 (R) 2
surface. Let z and d represents the asperity height
K K
and separation of the surfaces respectively,
measured from the reference plane defined by the
mean of the asperity height. δ denotes deformation
of asperity by flat surface. Number of asperity 0 R 00.5 3A 0 B0
1 h 2
contact is exp d
2 0.5 1.5
0 6A 0 B0 R 0 9 2 A 0 B 0 2
2 2
2
N c N ( z )dz (5)
d
where dimensionless surface roughness parameter,
where N is total number of asperity and (z ) is the A 0 R and dimensionless surface energy
Gaussian asperity height distribution function. parameter, B0
K
3.1 Multiasperity real area of contact
3.3 Multiasperity adhesional friction force
n
So, from eq (1) and (5), real area of contact for
multiasperity contact is So, , from eqn (3) and (5), total adhesional friction
force for multiasperity contact is
A N A a ( z )dz T N c Ta
d
2 KR
2
N 3 R (z)dz
4
3 R 2 6 R 3.5 1.5 9 2 2 R 4 3
1.5 1.5 2
N R 1.5 1.5
d K
K
K2
(z)dz
d
G
K
Dividing both side by apparent area of contact An Dividing both side by AnK
0.5 2
R
T
4
*
2(R) 2
3 (R)
1.5 2 2
()d
1.5 1.5 R
G K
0.5
(R) 3 (R)
1.5 1.5 2.5
K K
0
K
A* ()d
R R
0.5 2
0
6 4 ( R) 3 1.5 9 5 (R) 3
K K
h 2
2A 0 B0 R 0 0.5 1.5 3 2 A 0 B0
4 1
2 2 2
exp d
1.5 A1.5 .5 3 2.5 A1.5 B R 0.5
1
1 h 2
0
GK 2
2
0 0 0 0
exp d
0 6 A 0 B0 R 0 9 A 0 B0 R 0 2
4 3 0.5 1.5 5 3 2 2
3.4 Multiasperity adhesive wear volume
3.2 Multiasperity adhesional loading force
So, from eqn (4) and (5), adhesive wear volume for
So, , from eqn (2) and (5), adhesional loading force multiasperity contact is
for multiasperity contact is
V N c Va
F Nc Fa
N Va (z)dz
N KR 0.5 1.5 3 R 6 KR 1.5 1.5 (3 R ) 2 (z)dz d
d
2 6 R 3.5 1.5 9 2 2 R 4
Dividing both side by AnK
3 R 2
N R 1.5 1.5 (z)dz
d
3
K K K2
Dividing both side by A n
406 | P a g e
4. Biswajit Bera / International Journal of Engineering Research and Applications (IJERA)
ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 5, September- October 2012, pp.404-411
ROUGH SMOOT H
0.5
R 1.5 R INT ERMEDIAT E SUPER SMOOT H
(R) 3(R)
2 K 0.003
ADHESIONAL LOADING FORCE (F* )
V
*
()d
3 0 2
R 1.5 R
1.5 2
6(R) 2
9 (R)
2 2
0.002
K K
0.002
0.001
2 A 0 R 0 3A 0 B0 R 0 1 h 2
0.5 1.5
exp d 0.001
3 0 6A 0 B0 R 0 9 A 0 B0 R 0 2
2 1.5 1.5 2 2 2 2
2
0.000
4. Results and Discussion 4 3 2 1 0 -1
Tayebi and Polycarpou [9] have done MEAN SEPARAT ION (h)
extensive study on polysilicon MEMS surfaces and
four different MEMS surface pairs. Similarly, Fig.3 Adhesional loading force
tribological properties of the MEMS surfaces are
being considered for present study as input data as Johnson et. al. first mentioned that
shown in table 1 [Appendix A].The material deformation of spherical contact would be greater
properties of MEMS surface samples are modulus of than the deformation predicted by Hertzian spherical
elasticity, K =4/3E = 112 GPa, modulus of rigidity, G contact. It is mentioned that only attractive adhesive
= 18.42 GPa hardness, H = 12.5 GPa, and poisions force acts within Hertzian contact area and it
ratio, ν1 = ν2 = 0.22 increases deformation of sphere resulting higher
contact area. From Fig.2, dimensionless real area of
4.1 Investigation on adhesional friction law contact increases with decrement of dimensionless
mean separation exponentially. It is found that
ROUGH SMOOT H
maximum real areas of contact for the all cases of
INT ERMEDIAT E SUPER SMOOT H
MEMS surfaces increase as smoothness of MEMS
0.90 surfaces increase. Dimensionless real area of contact
0.80 for super smooth MEMS surface is very high almost
REAL AREA OF CONTACT (A * )
0.70 near to the apparent area of contact due to presence
of strong attractive adhesive force. On the other
0.60
hand, real area of contact is very small for the rough
0.50
MEMS surface contact. Fig.3 depicts variation of
0.40 dimensionless adhesional loading force with
0.30 dimensionless mean separation. From the loading
0.20 expression of JKR adhesion model, it is found there
0.10
is two component of force; one is Hertzian
deformation force (i.e. external force) and another is
0.00
adhesive force. Fig.3 shows that adhesional loading
4 3 2 1 0 -1
forces are also increases with decrement of
MEAN SEPARAT ION (h) dimensionless mean separation exponentially. As
smoothness of MEMS surfaces increases,
Fig.2 Real area of contact deformation force decreases but adhesive force
increases. So, deformation force and adhesive force
are inversely proportional according to consideration
of roughness as well as smoothness and there should
be a reference MEMS surface where both the force
should be minimum such a way that total force
should be small [10]. This is happening for smooth
MEMS surface. Now, adhesional loading force for
rough and intermediate MEMS is much more than
that of smooth MEMS surface due to mainly
Hertzian deformation force. Similarly, adhesional
loading force of super smooth MEMS surface is
much more than that of smooth MEMS surface due
to mainly high adhesive force.
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ROUGH SMOOT H ROUGH SMOOT H
INT ERMEDIAT E SUPER SMOOT H INT ERMEDIAT E SUPER SMOOT H
AREA COEFFICIENT OF FRICTION (T * /A* )
0.08 0.02
AREA COEFFICIENT OF LOAD (F * /A* )
0.07 0.01
0.06 0.01
0.05 0.01
0.04 0.01
0.03 0.01
0.02 0.00
0.01 0.00
0.00 0.00
4 3 2 1 0 -1 4 3 2 1 0 -1
MEAN SEPARAT ION (h) MEAN SEPARAT ION (h)
Fig.4 Area coefficient of load
Fig.6 Area coefficient of friction
Fig.4 shows area coefficient of load verses
dimensionless mean separation. This coefficient is From Fig.5, adhesional friction force
considered to understand the relationship in between increases with decrement of dimensionless mean
real area of contact and loading force. Generally, it separation exponentially. It is found that maximum
is assumed that real area of contact and load are adhesional friction force for the all MEMS surfaces
linearly proportional as mentioned by Bowden and increases as smoothness of MEMS surface increases.
Tabor considering plastic deformation of asperity. Adhesional friction force for super smooth MEMS
For mean separation smaller than 1, area coefficient surface is very high due to presence of strong
for all four cases are comparatively small and are of attractive adhesive force. On the other hand,
the slightly descending with same magnitude. adhesional friction force is very small for the rough
However, as mean separation larger than 2, MEMS surface contact.
deviation in the coefficient among the four cases
becomes increasing prominent and it maintain Fig.6 shows area coefficient of friction
almost different constant value with mean verses dimensionless mean separation and it follows
separation. The separation in between 2 and 1, there the similar nature of curve as shown for area
is transition of the coefficient from higher different coefficient of the loading force. Similarly, It shows
value to lower descending constant value. So, from non linear relationship in between real area of
the discussion, it is found that it do not support the contact and friction force.
linear relationship in between real area of contact
and the loading force ROUGH SMOOT H
INT ERMEDIAT E SUPER SMOOT H
ROUGH SMOOT H
COEFFICIENT OF FRICTION (T * /F* )
0.50
INT ERMEDIAT E SUPERSMOOT H
0.45
ADHESIONAL FRICTION FORCE (T )
0.0008
*
0.40
0.0007 0.35
0.30
0.0006
0.25
0.0005 0.20
0.0004 0.15
0.10
0.0003
0.05
0.0002 0.00
0.0001 4 3 2 1 0 -1
0.0000 MEAN SEPARAT ION (h)
4 3 2 1 0 -1
MEAN SEPARAT ION (h) Fig.7 Coefficient of friction
Fig.5 Adhesional friction force Fig.7 displays variation of coefficient of friction
with mean separation. It is found that static
coefficient of friction is almost constant except for
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Vol. 2, Issue 5, September- October 2012, pp.404-411
the super smooth MEMS surface. So, the Amontons
law of static friction is validated for adhesive ROUGH SMOOT H
micromechanical surface contact. Only for the INT ERMEDIAT E SUPER SMOOT H
supersmooth MEMS surface contact, coefficient of 160.00
AREA COEFFICIENT OF WEAR (V * /A* )
static friction suddenly drops at close contact though
140.00
nature of curve of adhesional loading force and
adhesional friction force for supersmooth MEMS 120.00
surface is same. 100.00
80.00
4.2 Investigation on adhesive wear law
60.00
ROUGH SMOOT H
40.00
INT ERMEDIAT E SUPER SMOOT H
20.00
100.00
90.00 0.00
ADHESIVE WEAR VOLUME (V )
*
80.00 4 3 2 1 0 -1
70.00 MEAN SEPARAT ION (h)
60.00
50.00 Fig.9 Area coefficient of wear
40.00
*
30.00 So, Area coefficient of wear V V K
A
* adh
20.00 A
10.00
V K adh A
0.00
4 3 2 1 0 -1
Where real area of surface contact, A P according
MEAN SEPARAT ION (h)
H
to Bowden and Tabor theory
Fig.8 Adhesive wear volume
P
Fig.8 depicts variation of adhesive wear V K adh
H
volume with mean separation. It is found that
maximum adhesive wear volume for the all cases of Where V= Wear volume, Kadh = adhesive
MEMS surfaces increase as smoothness of MEMS wear coefficient (i.e. area coefficient of wear), P =
surfaces increase. So, super smooth MEMS surface normal load, H = soft material hardness, σ = rms
produces maximum adhesive wear volume whereas roughness of surface.
rough MEMS surface produces very low adhesive
wear volume. According to new adhesive wear law,
adhesive wear coefficient increases with increment
Fig.9 shows area coefficient of wear verses of MEMS surface contact. And Kadh = 0.25 for rough
dimensionless mean separation. This coefficient is surface, Kadh = 5 for smooth surface, Kadh = 30 for
considered to understand the relationship in between intermediate surface, and Kadh = 120 for super
real area of contact and wear volume. From the smooth surface.
nature of curves, it is found that dimensionless
adhesive wear volume is almost linearly proportional .
with dimensionless real area of contact. So area Now, wear rate, v v × no. of pass per revolution
coefficient of wear is almost constant. × RPS
v n p RPS
Generally, Pin on Disk tester are commonly used to
measure wear rate. If circular cross sectional pin of
diameter, d is placed on disk at diameter, D,
no. of pass per revolution, np
Total area crossed Dd D
4
d 2 / 4 d
Cross sec tional area of pin
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Vol. 2, Issue 5, September- October 2012, pp.404-411
However, in comparison of new adhesive wear law References
with Archard's law of adhesive wear, the new law is [1] G Amontons, Histoire de l'Académie
much more appropriate from the point view of Royale des Sciences avec les Mémoires de
volume concept. In case of well accepted Archard's Mathématique et de Physique (1699)
law of adhesive wear, sliding distance is on the plane
of real area of contact and so, how does [2] F P Bowden and D Tabor, The Friction and
multiplication of both the two parameter produce Lubrication of Solids (Oxford University
volume whereas in case of new law of adhesive Press, New York 1950)
wear, r.m.s. roughness perpendicular to the plane of
real area of contact which produces volume removal [3] K L Jhonson, K Kendall, and A D Roberts,
in the form of adhesive wear. Surface energy and the contact of elastic
solids, Proc. R. Soc. Lond., A 324, 1971,
5. Conclusions 301-313
The study is the theoretical investigation on
existing static friction coefficient and adhesive wear [4] B V Derjaguin, V M Muller, and YU P
law. From the study of micromechanical contact of Toporov, Effect of contact deformation on
MEMS surfaces, following conclusions could be the adhesion of particles, J. Coll. and Inter.
drawn: Sc., 53, 1975, 314-326
a) When micro-rough surfaces are come in
contact due to application of external force, [5] W R Chang, I Etsion, and D B Bogy,
spherical tip of the contacting asperities Adhesion model for metallic rough
form adhesive bond followed by JKR surfaces, Journal of Tribology, 110, 1988,
adhesion theory. 50-56
b) As smoothness of surfaces increase, it [6] S K Roy Chowdhury and P Ghosh,
produces much more strong adhesive bond Adhesion and adhesional friction at the
at the tip of the contacting asperities. contact between solids, Wear, 174, 1994, 9-
19
c) Real area of contact increases with
adhesional loading force nonlinearly which [7] A R Savkoor and G A D Briggs, The effect
is generally, considered linearly of tangential force on the contact of elastic
proportional as stated by Bowden and solids in adhesion Proc. R. Soc. Lond., A
Tabor. 356, 1977, 103-114
d) Similarly, real area of contact and static [8] J A Greenwood, and J B P Williamson,
adhesional friction force are also Contact of nominally flat surfaces. Proc. R.
nonlinearly proportional. Soc. Lond., A 295, 1966, 300-319
e) Static coefficient of friction is almost [9] N Tayebi and A A Polycarpou, Adhesion
constant for micromechanical surface and contact modeling and experiments in
contact which is theoretical evidence of microelectromechanical systems including
Amonton's law of friction. roughness effects, Microsyst. Technol., 12,
2006, 854-869
f) Justified new adhesive wear law is
developed where adhesive wear volume is [10] B Bera, Adhesion and adhesional friction of
equal to multiplication of real area of micromechanical surface contact. Journal
contact and rms roughness. Coefficient of of Engineering and Applied Sciences, 6,
adhesive wear increases as smoothness of 2011, 104-108
surface increase.
[11] J F Archard, Contact and rubbing of flat
g) Finally, though above study is done for surfaces. Journal of Applied Physics, 24,
micro-rough surface contact of MEMS but 1953, 981-988
it could be applicable for macroscopic
study of tribo-system as interface is always
microscopic.
Acknowledgements
I would humbly thank to Prof. B Halder, NIT
Durgapur, India whose inspiration and support have
made the work successful.
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ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 5, September- October 2012, pp.404-411
APPENDIX A
Table.1 Input data
Combined Rough Smooth Intermidiate Super Smooth
MEMS
Surfaces
η (m-2) 14.7.1012 11.1. 1012 17.1012 26.1012
R (m) 0.116.10-6 0.45.10-6 1.7.10-6 26.10-6
σ (m) 15.8.10-9 6.8.10-9 1.4.10-9 0.42.10-9
γ (N/m) 0.5 0.5 0.5 0.5
K (N/m2) 112.109 112.109 112.109 112.109
G (N/m2) 18.42.109 18.42.109 18.42.109 18.42.109
A0 27.10-3 34.10-3 41.10-3 53.10-3
B0 2.825.10--4 6.565.10--4 31.887.10--4 74.405.10—4
R0 7.342 66.176 1214.285 5600.000
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