Viscoelastic response of polymeric solids in sliding contacts

Part III: Applications and analysis

Padmanabhan Krishnan
Viscoelastic response of hybrid polymeric
dental composites in sliding contacts and
applications
Abstract: The viscoelastic response of polymeric solids to sliding contact conditions
is observed and analyzed with respect to the sliding speed, material composition,
and geometry. It was discovered that polymeric solids produced their own distinct
viscoelastic signatures that cause resonance at certain sliding speeds which can be
explained with resonance conditions for electromagnetic waves. The observed vis-
colelastic phenomenon is characterized with respect to the relaxation and recovery
times for rigid polymeric solids. It is confirmatory as a demonstration of proof of
existence of viscoelasticity and self-organization in these materials under sliding con-
tact conditions. Viscoelastic observations are also made on the aged specimens in
sliding contact.
Keywords: Viscoelasticity, polymer, hybrid composites, surfaces, sliding contact,
ageing, stress waves
1 Introduction
Polymer-based composites with ceramic fillers are being increasingly used in dental
applications as they combine the requirements for strength, fatigue, toughness,
and bio-compatibility with enamel and wear resistance. The surface integrity and
long-term wear performance of these materials is a key issue in deciding their suit-
ability for dental applications. Pin on disc (POD) sliding wear testing of dental re-
storative materials (amalgam, ceramics, polymers, and composites) is a widely
accepted practice to generate data and evaluate the contact wear performance of
these materials prior to other wear test methods approved for use in dentistry. Dur-
ing the POD sliding wear of polymeric composites at loads ranging from a moderate
contact load of 5 N to a load of 15 N corresponding to the occlusal forces on the
molars, the choice of low sliding speeds of 2–5 mm/s was seen to produce some
interesting and periodic distortions in the friction force trace that can be mistaken
Padmanabhan Krishnan, School of Mechanical Engineering, Vellore Institute of Technology,
Vellore 632014, India, e-mail: padmanabhan.k@vit.ac.in
Acknowledgement: The author thanks VIT management and the School of Mechanical Engineering
colleagues for the wonderful support and encouragement.
https://doi.org/10.1515/9783110724684-003

for machine-related vibrations to begin with and considered undesirable in the
measurement of frictional force and estimation of the coefficient of friction. This
new disruptive discovery was later proven to be viscoelastic in nature as the ma-
chine vibrational frequencies were higher by an order or more. The discovery of
such a viscoelastic response would lead to many important applications later.
2 Viscoelastic models and the phenomena
In plastic materials, prolonged exposure to stress may cause noticeable and irre-
versible deformation which must be taken into consideration when designing parts
for structural and bio-medical applications. The susceptibility to permanently de-
form under load or a relaxation mechanism under stress can be measured in creep
and stress relaxation experiments, respectively [1–4]. In the simplest case, the re-
laxation mechanism under a constant strain can be described with the help of one-
dimensional Maxwell model which consists of a spring and dashpot in series.
According to the model shown in Figure 1, an instantaneous strain causes only the
elastic spring to initially deform, while the viscous dashpot slowly and gradually re-
laxes and allows the spring to slowly return to the original condition. Thus, for times
much shorter than the relaxation time, the Maxwell element behaves essentially like
a spring, whereas for times much longer than the relaxation time, it behaves like a
dashpot [5].
Figure 1: The Voigt and Maxwell viscoelastic models.
44 Padmanabhan Krishnan

An ideal linear elastic material does not experience any relaxation process. This
material can also be described with the Voigt model which consists of a spring paral-
lel to a dash pot. In this arrangement, no relaxation takes place because the visco-
elastic flow is restricted by the spring element. The viscoelastic behavior of real
polymeric materials is much more complicated, that is, these materials neither
fully relax nor are they ideally elastic. To accurately describe their relaxation be-
havior, Maxwell and Voigt elements have to be combined with more complex ar-
rangements. Zener arrangements and models are also exhibited by polymers that
show a linear viscoelastic behavior which explains the creep and stress relaxation
phenomena [6]. Zener models normally consist of Maxwell Kelvin–Voigt models
in series or parallel arrangements. Burger materials are examples of a set of poly-
mers obeying the viscoelastic models with the Maxwell material and Kelvin mate-
rial in series [6].
To study this strange phenomenon in sliding contacts further, parameters like
geometry (human enamel pin on polymeric disc or an alumina ball with a wider
contact area on disc) and material microstructure of the pin as well as the disc
{polymer-ceramic filler, ceramic filler-polymer-binder, and ceramic-(glassy)ceramic
composites} were considered, and combinations of geometry and material systems
were tried out to study the phenomenon further in a quantitative and methodical
manner. The wear behavior of these materials was also studied using a POD appara-
tus and the results, presented.
3 Experimental procedures
The two composites used in this study were
Hybrid Composite 1: A methacrylic ester matrix with silanated barium alumina sil-
ica glass and silicon dioxide microfillers by 70 wt% with an average particle size of
1 μm.
Hybrid Composite 2: A hybrid ceramic composite (enamel and dentin) with 92 wt%
of fine glass (0.1–10 μm, average 2 μm, and microfiller < 0.1 μm). The resin being
bis–glassy methacrylate (bis–GMA) and triethylene glycol methacrylate (TEGMA).
Composite restorative discs of approximately 15 mm diameter and 3 mm thickness
were prepared by light curing the samples between glass plates with inner Mylar™
film sheets (a thermoplastic-added polyester) and circular (polytetrafluoroethylene)
dams of 3 mm thickness in order to obtain uniformly cured discs. The curing was for
a time period between 60 and 120 s using a xenon light source with a strobe mode
(Dentacolor XS, Heraeus Kulzer) based on manufacturer’s recommendations for indi-
vidual pastes of raw materials in tubes. The fabricated discs were dry-polished using
grit 600 abrasive paper which is the normal grit size used for restorative finishes and
Viscoelastic response of hybrid polymeric dental composites 45

finished with “Texmet” cloth to a maximum surface roughness of Rmax ~ 2.5 to 3.5 μm
and an average roughness of Ra = 0.257 µm. Another set of discs were dry-polished to
a surface roughness of Rmax ~ 0.9–1.5 μm using grit 1200 and “velvet” cloth to obtain
a surface smoother than the average particle size down to about an Ra of 0.15 µm.
Acetone was used in minimum quantities to clean the surfaces that were dried and
then electric-blower-dried. Machined and polished human enamel pins from third
maxillary molars and pins of the polymeric materials that constitute the disc were
used, with a maximum possible tip roughness of 0.2 μm. Alumina balls (8.02 mm di-
ameter) with an average surface roughness Ra of 0.1 μm were also considered as pin
materials, but these were used as received. Needless to say, the contact area of the
balls with the disc can be expected to be higher than the pins but Hertzian likewise.
Thus, the counterfaces were defined. Sliding contact tests were conducted at 1–15
mm/s sliding speeds in a POD. A schematic sketch of the sinusoidal stress waves pro-
duced at different revolutions per minute (rpm) is presented in Figure 2.
This sketch also explains how viscoelastic signals lead to resonance when the wear
track perimeter and the wavelength of a single signal match under specific ratios. Fric-
tion force traces were obtained at various rpm. Some pins and discs were conditioned
Figure 2: A schematic sketch of the sinusoidal stress waves produced at different rpm.

in distilled water at room temperature up to absorption saturation to obtain consistent
wear data on distilled water-conditioned specimens and compare them with dry wear
data. This process required that specimens be stored for any time between 3 days and
2 weeks until the sample weight was steady correct to 0.1 mg. Certain select specimens
were aged for longer durations of up to 8 months and then wear-tested to evaluate the
long-term effects on wear of these composites. This replicates the oral environment.
The current investigation is a step further that reports a discovery that can aid
in characterizing the mechanical properties of polymers and their composites by
sliding contact tests and explains the phenomenon with examples. Ageing of the
samples has also been investigated.
4 Results and discussion
During the POD sliding wear of polymer-based composites using a CSEM tribometer
(Geneva, Switzerland) at a load range of 5–15 N corresponding to moderate chewing
to occlusal forces in the mouth, in dry and distilled water conditioned environment,
the choice of the conventionally adopted low sliding speeds of 0–15 mm/s was seen
to produce some interesting and periodic but secondary distortions, rendering the
measurement of friction force and hence the determination of coefficient of friction
unreliable. Such an observation and analysis seems to have missed the attention of
others who have reported the mean coefficient of friction and related wear data on
such composites under similar conditions. As the sliding speed is increased to
15 mm/s for wear track radii in the range of 4–5 mm, i.e. from ~ 10 rpm to 40 rpm
for the disc dimensions in this study, low speed periodic, localized wave packets
were observed as in Figures 3–6, if the material is a polymer or its composite viz.
Composites 1 and 2.
This was observed for any pin/ball geometry or material like its own counter-
face, enamel, or alumina. To negate any influence of smoothening effects due to
“wearing in,” the experiment was conducted by decreasing the sliding speed from
40 rpm to 10 rpm. Low speed distortions were still observed with the same ampli-
tude. Here, Series 1 refers to Composite 1 and Series 2 refers to Composite 2. It was
also seen that the amplitude of the wave like distortion was proportional to the
polymer matrix content in the disc material. For example, Composite 1 which con-
tains 30 wt% of methacrylic ester, a polymer, exhibited a higher amplitude of wave
like signature than Composite 2 which contains only 8 wt% of polymer, a blend of
bis-GMA/TEGMA (see Figure 2). The low rpm coefficient of friction varies by ~ ±10%
at maxima in case of Composite 1 against alumina ball in dry conditions. The same
composite exhibited an amplitude variation of up to ±75% at maxima with the
human enamel as the pin material in the same conditions. Composite 1 disc with
Composite 1 pin yielded wave packets similar in amplitude to those with the enamel

pin for the same geometry, except for a different range of friction force values. It
was seen that the effect of damping due to pin geometry played a significant role in
the magnitude of the amplitude of the wave packet for similar type of materials.
The human molar pin, being functionally gradient with a softer dentin inside and a
layer of enamel outside, produced resonance patterns with amplitude variations of
up to ±75% at maxima. Further, the maximum amplitude of friction force traces was
directly proportional to the normal load used in sliding contacts. Lower ranges of
friction force values correspond to lower loads of 10 and 5 N, respectively, for the
Figure 3: Coefficient of friction of Alumina Ball versus Composite 1 for dry sliding speeds of 40 rpm
to 10 rpm.
Figure 4: Coefficient of friction of Alumina Ball versus Composites 1 and 2 for dry sliding speeds of
10 rpm to 1 rpm.

set of materials used here. In general, the friction force trace for polymer compo-
sites is stable without oscillations only at ~ 35 rpm and above. This holds true in
dry as well as wet environments like distilled water. Needless to say, only 15 N tests
will be discussed henceforth for clarity and amplitude of signatures. When ceramic
discs like alumina or porcelain slide against a ceramic pin, there is no distortion at
any of the sliding speeds chosen as above. However, Composite 2 does show a wave
Figure 5: Friction force plots of Composites 1 and 2 versus Enamel Pin at 10–40 rpm in dry sliding
conditions.
Figure 6: A single wave train for the dry sliding of Alumina Ball versus Composite 1 at 10 rpm
indicating resonance.

packet like distortion with a much lesser amplitude than Composite 1 due to a
lower polymer binder content, for the same sliding speeds, thus confirming the vis-
coelastic influence of the polymer on the anomalous friction traces. This is evident
from Figures 4 and 5.
For composite 1 against alumina ball in dry conditions, when the speed of test-
ing was further lowered to 5 rpm, the wave train had an alternating strength of am-
plitude that resembled one with a carrier/modulator ratio of 5, what one exactly
comes across in wave transmission. When the rpm was reduced to 1, the wave train
pattern completely disappeared, and only a single waveform was seen to occur ex-
posing the linear viscoelastic response signal of the polymeric solid to the load ap-
plied (see Figure 7).
Schematically, this phenomenon is explained as shown in Figure 2, where the vibra-
tional resonance due to the sinusoidal viscoelastic stress wave propagation is shown
to arise from a 1:1 ratio between the viscoelastic wave length and the length of the
circumference of the wear track on the disc at 10 rpm. When the viscoelastic response
wavelength increases marginally at 5 and subsequently at 1 rpm, the resonance pat-
tern disappears completely as the single viscoelastic stress wave manifests out of the
packets due to a higher wavelength than the circumferential length. Since composites
with various surface roughness values at various stages of experimentation were em-
ployed in the study, it can be seen that the frictional force values are different along
the time axis due to “wearing in,” but the amplitude and wavelength are consistent
Figure 7: Coefficient of friction plots for dry sliding of Composite 1 vs. Alumina Ball showing a
single stress wave at 1 rpm.

with the material properties, load, and speed of testing as conditions. A viscoelasti-
cally distorting second phase is sometimes incorporated forming a frictionally differ-
ent surface layer that is prone to wear, which can easily be inferred when the force
traces transit. It is envisaged that each polymeric material or its composite produces
its own characteristic signal that is a signature whose wavelength and amplitude de-
pend on the normal load. The nature and contact area of the pin/ball affect the am-
plitude of the 10 rpm resonance patterns due to the difference in vibration modes,
but it has very little influence at 1 rpm due to the absence of the same. The sinusoidal
waves resemble the stress waves which propagate in linear viscoelastic solids obey-
ing a Maxwell or Zener/Burger parameter model under stretching. Since sliding wear
gives rise to tensile forces at the surface due to contact stretching and shear forces
with a strong gradient at a sub-surface plane, the same is manifested in the present
case. A five-parameter model for hygrothermally degraded polymer, explaining every
aspect of the observed phenomena for certain type of polymeric materials, is envis-
aged for future work. The viscoelastic response of a polymeric material against a sur-
face that distributes load in sliding contacts is the cause for such waveforms. The
present viscoelastic behavior is seen to be (a) consisting of dilational and shear
waves (see Figure 8), (b) producing subsurface shear waves, (c) a spring and dashpot
model-based manipulation, (d) a secondary and segmental in polymer relaxation,
and (e) a viscoelastic version similar to the Tomlinson and Frenkel–Kontorova atomic
frictional models presented in Figure 9 [7].
Dilatational Shear
u
u
P-waves S-waves
z
z
Vp Vs
Rayleigh wave
E,V,P
(a) (b)
(c)
Surface
Figure 8: A schematic drawing of dilational, shear,
and Raleigh waves generated in sliding contacts.

Self-organization can be adapted for the polymer molecular structures here,
where the substrate is presented as a periodic energy profile created by the mole-
cules, using the “m” or mass in the Tomlinson–Frenkel–Kontoraova model as a vis-
cous dashpot and “k” the spring constant in series. This is similar to the Maxwell
model where the dashpot and the spring are in series. The stress relaxation implies
that the stress is time-dependent and varying as the pin moves around the disc sur-
face in circles, causing the stress to increase and decrease due to instantaneous
contact. Further, the strain that is developed is instantaneous in a POD experiment
right under the pin at the interface and is almost negligible at the incipient or far
behind locations. Hence, the strain in this case is localized, and the viscoelastic re-
sponse models are also localized like a surf-riding situation. The developed stress
waves behave like a fatigue wave train. Surface Raleigh waves are generated as shown
in Figure 9 which can be used for in situ NDT (nondestructive testing) inspection.
Though there is self-organization, over a longer time, thermal and hygrother-
mal effects can relax the stress further, causing hygrothermo-mechanical fatigue. In
short, the rpm speed at the given radius/radii and the resulting sliding velocity was
comparable to the relaxation time, τ, of the polymeric solid for the conditions that
allow such a viscoelastic reaction to take place. Normally, the mechanical relaxa-
tion time (not volume) for a glassy polymer below its glass transition temperature
ranges from seconds to minutes [8–10], and the evaluation of relaxation time, τ, for
a polymer filled with inorganic particles, based on the relationships for a linear vis-
coelastic solid [8, 9], gives us a static frequency range of ω = 0.1–1 for tan δ = 0.001
to 0.1 as a dynamic mechanical analysis (DMA) test would prove for polymers. The
relationship ωτ = 1 gets us an approximate value of 1–10 s for the relaxation time
for these two polymer composites. Since there is time (t ≫ τ) for viscous reaction to
take place at a low rpm value of 1 (for radius of 4–5 mm), the time-dependent stress,
σt, drops and rises depending on the relaxation and recovery times. It is observed
that this is not a stick-slip behavior which manifests as a saw-tooth waveform in
the wear of materials but a sinusoidal stress wave as a result of viscoelasticity of
the polymeric material. When the rpm increases, the material behaves elastically
since the time for such a viscous reaction to take place is not available, as t ≪ τ. At
an intermediate 10 rpm speed, the resonance occurring due to the viscoelastic re-
sponse of the material was not noticed in the 8 month distilled water aged Compos-
ite 1 samples as the wavelength of the friction force trace was obviously longer due
to time-dependent viscoelasticity, and the ratio for resonance was not met with. It
leads us to believe that the viscoelastic response curve of an non-aged specimen at
m m m m m
k k k k
Figure 9: A schematic drawing of the Tomlinson
and Frenkel–Kontorova atomic friction model.

10 rpm is much shorter in order to obtain a wave train as shown in Figure 6, thereby
rendering support to the evidence that vibrational resonance due to viscoelastic re-
sponse of a polymer composite material to loading occurs when t = τ. The condition
for resonance, in order to obtain such a wave train, is very much similar to the Max-
well resonance condition for oscillation of fields as given in Feynman lectures [11]:
ω0 = 2.405 c=r
f g (1)
where ω0 is the resonant frequency, c the velocity, and r the radius of the wear track
that was discussed [9]. It is seen that the constant 2.405 can be interpreted as the
result of the path length of the wave train divided by the path length of the individual
viscoelastic signal, which is in fact the condition for resonance. The radius of the disc
can be substituted for r to obtain the condition for resonance. It is indeed interesting
to note the similarity between acousto-mechanical and electromagnetic resonance
conditions. The Maxwell resonant frequency in the present investigation, ω0, would
be less than 5 Hz in this case when we substitute for c and r. Here, the linear-
viscoelastic stress waves are in packets at certain speeds of sliding and represent the
viscoelastic and resonant stress wave propagation in the polymeric solid due to slid-
ing contact. As discussed earlier in Figure 2, the phenomenon of resonance originates
due to the coincidence of the viscoelastic signal wavelength with the perimeter of the
wear track, or in other words, one rpm.
The smooth attenuation of the friction force traces at rpm closer to 40 is a result
of an elastic behavior as discussed before. Further, dynamic damping can occur
when the material is both dissipative and dispersive [10] causing attenuation of the
friction force traces due to the dilational stress component reducing and the shear
stress component taking over. At higher loads and lower rpm, the attenuation
might be advanced. It is expected that the surface Raleigh waves generated due to
friction play a role in resonance at higher speeds and not in the viscoelastic re-
sponse at low rpm [12]. An acceptable level of treatise is presented on polymer tri-
bology by Sinha and Briscoe [13]. But this book does not deal with viscoelasticity or
the effect of aggressive environment on polymer tribology.
It is proposed to conduct monolithic unfilled polymer sliding contact tests in a lin-
ear reciprocating wear tester and confirm the precision and accuracy of the viscoelastic
signals, relaxation, and retardation times and resonance conditions which would lead
to the design and manufacture of viscoelastic testers that can correlate the viscoelastic
properties with the mechanical properties and predict the thermo-mechanical behavior
of polymers under controlled environment. At sub-zero temperatures, the threshold
transition from viscoelastic to elastic behavior can also be predicted in the presence of
a ductile to brittle transition. Viscoelastic response can also be appreciable when the
hygrothermal attack on restoratives and other polymer composites is appreciable. A
detailed account of the do’s and don’ts that involve the required specifications for
hygrothermal conditioning, postsaturation equilibration, and tribology of polymer
composites is presented in the investigations as done earlier [14, 15]. As viscoelasticity

is appreciable in the postsaturated and water-equilibrated polymers and restoratives,
these two references are considered significant. It is ascertained that it is not the ma-
chine natural frequency which falls between 50 and 1500 Hz as reported in literature
for similar machines [16], but a viscoelastic phenomenon whose relaxation times and
resonant frequencies with the POD geometry is much lower as evaluated here.
5 Erratum in existing literature and scope
Many publications have emerged in the last few decades that have either chosen to
ignore or just ignored the important aspect of viscoelastic interactions and mecha-
nisms in sliding contacts and wear of polymeric solids. Books, book chapters, and
research articles by tribology researchers have ended up measuring, assessing, and
evaluating wear, lubrication, and friction in polymeric solids without considering
the appreciable effects of viscoelasticity on these parameters [17–23]. As the friction
force traces in the low speed domain are significantly dependent on the viscoelastic
response of the material to sliding contact, any measurement of the friction force
traces that ignores these aspects without a regard for sensitivity is bound to be erro-
neous. Wear rates and wear volumes too depend on the material removed, and the
material just displaced out of the wear track due to viscoelasticity. Hence, their
measurement too is a suspect. Though viscoelasticity of polymers is a known phe-
nomenon, it has not been seriously considered by tribologists and machinists as a
significantly contributing subject in the evaluation of polymeric solids and their ap-
plications. The publications chosen here to highlight the issue are only an act of
serendipity and not choice. The real number is staggering and needs withdrawal or
revision of the data and the publications, if the conditions stated in this chapter are
encountered. The scope of viscoelasticity-based studies is very vast as polymeric
solids are known to be hygrothermally susceptible that renders them nonlinear – a
more complicated deviation from their linear viscoelasticity which is exhibited by
rigid polymers and their composites at normal pressures and room temperatures.
As nonlinear viscoelasticity demands the use of five-parameter models and similar
conformations in series or parallel, lot of scope exists in the study of these mecha-
nisms in the tribological modeling of such systems. The next section provides more
detail about the mechanisms and applications of this phenomena in tribology and
machining.

6 Applications of the viscoelasticity phenomena
in sliding contact
The following are some of the salient features and applications of the discovery of
the phenomenon of viscoelasticity in sliding contact mechanisms;
1. It provides a quick test method to assess the viscoelastic response of polymeric
solids to sliding contact mechanisms.
2. A correlation of the viscoelastic properties with the mechanical properties is
possible that would help in evaluating the mechanical properties of a polymeric
solid from a knowledge of its viscoelastic response.
3. It is proposed as a single test that would evaluate the quasi-static mechanical prop-
erties and the tribological properties with an acceptable level of approximation.
4. A linear reciprocating wear test apparatus with an associated specific software
would suffice to achieve this phenomenally easy way of evaluating the mechan-
ical properties of a solid polymer.
5. This method serves as an easy to perform substitute dynamic mechanical ana-
lyzer as the relaxation and retardation times can be evaluated with an approxi-
mate assessment of the storage and loss modulus.
6. It helps in a quick materials selection process for ductile and ductile–brittle
solid polymers with viscoelastic properties.
7. A detailed study of viscoelastic fatigue is possible as an outcome of this investi-
gation. A viscoelastic thermal or hygro-thermal cut off can be evaluated in a
tribological test where thermal or hygorthermal frictional softening effects
could be quantified and the design limits, set to a required level.
7 Summary and conclusions
This investigation on sliding contact friction of polymeric solids illustrates and ex-
plains the existence of viscoelastic response through analysis of the friction force
traces that result from contact sliding under loads. The factors influencing the char-
acterization of the viscoelastic and elastic properties of polymeric solids in sliding
contacts viz. the relaxation time, the viscous reaction due to ageing and condition
for resonance, are discussed. The Maxwell and other relevant models that seek to
explain this phenomenon are highlighted and explained. It is proposed to use this
phenomenon to evaluate the elastic and viscoelastic properties of virgin polymers
and filled polymers with various processing, testing, and environmental conditions
to aid in their complete hygrothermo-mechanical characterization through an un-
derstanding of sliding contact mechanics. The salient applications of the discovery
of viscoelastic phenomena in sliding contacts are also predicted.

References
[1] Drozdov, A. D., Viscoelastic Structures, Academic Press, New York, 1998.
[2] Findley, W. N., Lai, J. S., and Onaran, K., Creep and Relaxation of Nonlinear Viscoelastic
Materials, Dover, New York, 1989.
[3] Torskaya, E. V. and Stepanov, F. I., Effect of surface layers in sliding contact of Viscoelastic
Solids ( 3D Model of Material), Frontiers in Mechanical Engineering, 09 May 2019, doi:
https://doi.org/10.3389/fmech2019.00026.
[4] Carbone, G. and Bottiglione, F., Editorial: Adhesion, friction and lubrication of viscoelastic
materials, Lubricants, 2021, 9, 23.
[5] Roylance, D., Engineering viscoelasticity, MIT's Department of Materials Science and
Engineering, 2001.
[6] Krishnan, P., Rheology of epoxy/rubber blends, In: The Handbook of Epoxy Blends,
Parameswaranpillai, J., Ed., et.al., Springer, Switzerland, 2017, 185–210.
[7] Weiss, M. and Elmer, F. J., Dry friction in the Tomlinson-Kontoraova-Frenkel model: Static
properties, Physical Review B, 1996, 53, 7539.
[8] Matsuoka, S., Relaxation Phenomena in Polymers, Chapter 3: Glassy State, Hanser
Publishers, Munich, 1992, 80.
[9] Kolsky, H., Viscoelastic Waves, International Symposium on Stress Wave Propagation in
Materials, In: Davids, N., Ed., Interscience Publishers Inc, New York, 1960, 59.
[10] Perepechko, I. I., An Introduction to Polymer Physics, Mir Publishers, Moscow, 1981, 209.
[11] Feynman, R. P., Leighton, R. B., and Sands, M., The Feynman Lectures on Physics Vol:2,
Mainly Electromagnetism and Matter, Narosa, New Delhi, 1995, 1049.
[12] Nosonovsky, M. and Mortazavi, V., Friction-Induced Vibrations and Self-Organization
Mechanics and Non-Equilibrium Thermodynamics of Sliding Contact, CRC Press, FL, USA,
2014.
[13] Sinha, S. K. and Briscoe, B. J., Polymer Tribology, Imperial college Press, London, 2009.
[14] Padmanabhan, K., Comments on standards on restoratives, Indian Journal of Dental
Research, 2009, 20(4), 514.
[15] Padmanabhan, K., The need to revise standards on dental restoratives – a commentary,
Current Science, 25 August 2006, 91(4), 418.
[16] Bergantin, R., Maru, M. M., Farias, M. C. M., and Padovese, L. R., Dynamic signal analyses in
dry sliding wear tests, Journal of the Brazilian Society of Mechanical Sciences and
Engineering, Sept 2003, 25(3), doi: https://doi.org/10.1590/S1678-58782003000300011.
[17] Menezes, P. L., Nosonovsky, M., Ingole, S. P., Kailas, S. V., and Lovell, M. R., Tribology for
Scientists and Engineers, Springer, 2013, 295–340.
[18] Nak-Ho, S. and Suh, N. P., Effect of fiber orientation on friction and wear of fiber reinforced
polymeric composites, Wear, 1979, 53(1), 129–141.
[19] Vižintin, J., Kalin, M., Jahanmir, S., and Dohda, K., Tribology of Mechanical Systems:
A Guide to Present and Future Technologies, American Society of Mechanical Engineers,
USA, 2004.
[20] Nagarajan, V. S., Hockey, B. J., Jahanmir, S., and Thompson, V. P., Contact wear mechanisms
of a dental composite with high filler content, Journal of Materials Science, 2000, 35(2),
487–496.
[21] Lee, J. H., Xu, G. H., and Liang, H., Experimental and numerical analysis of friction and wear
behavior of polycarbonate, Wear, 2001, 251(1–12), 1541–1556.

[22] Moreau, J. L., Weir, M. D., Giuseppetti, A. A., Chow, L. C., Antonucci, J. M., and Xu, H. H. K.,
Long-term mechanical durability of dental nanocomposites containing amorphous calcium
phosphate nanoparticles, Journal of Biomedical Materials Research. Part B, Applied
Biomaterials, April 2012, doi: https://doi.org/10.1002/jbm.b.32691.
[23] Rutherford, K. L., Trezona, R. I., Ramamurthy, A. C., and Hutchings, I. M., The abrasive and
erosive wear of polymeric paint films, Wear, 1997, 203–204, 325–334.

Viscoelastic response of polymeric solids in sliding contacts

Viscoelastic response of polymeric solids in sliding contacts

Recommended

Recommended

More Related Content

Similar to Viscoelastic response of polymeric solids in sliding contacts

Similar to Viscoelastic response of polymeric solids in sliding contacts (20)

Recently uploaded

Recently uploaded (20)

Viscoelastic response of polymeric solids in sliding contacts