A polymeric solid is seen to produce its own signatures in sliding contacts. This has immense applications. The viscoelastic phenomena and signatures are discussed with the relevant models.

1. Viscoelastic Response
of Polymeric Solids in
Sliding Contacts
Prof. Padmanabhan Krishnan
School of Mechanical Engineering
Director i/C,
Academic Staff College
Padmanabhan.k@vit.ac.in

2. Contents
Definition Problem
Statement
Methodology
Results Plots
Discussion and
Applications
References
A Discovery

5. Hygrothermal Viscoelasticity
 The linear viscoelasticity of a rigid polymer at room temperature slowly
transforms to a non-linear behaviour at higher temperatures near and
above the glass transition temperature due to a higher segmented chain
mobility . If hygrothermal attack and stresses are involved, the strain
would be higher at higher hygrothermal conditioning temperatures. As
plasticity would be higher at higher temperatures and moisture
conditioning percentages, the shift from linear to non-linear viscoelasticity
is inevitable. The shift from a dry Tg to a moisture conditioned wet Tg
which is lower, would accelerate plasticization and transform the polymer
in to a non-linear viscoelastic solid with more irrecoverable deformation.

6. Viscoelastic Models for Polymers

8. A five parameter Nonlinear Viscoelastic model

11. Retardation and Relaxation Times

12. Shear Modulus vs. Retardation times

13. Problem
Statement
It is observed that the polymeric
solids produce their own distinct
viscoelastic signatures that cause
resonance at certain sliding speeds.
This can be explained by the Maxwell
resonance conditions for
electromagnetic waves. The observed
viscoelastic phenomenon is
characterized with respect to the
relaxation, retardation and recovery
times for rigid polymeric solids.

14. Methodology
 Linear or Pin on Disc Wear Machines that can operate at very
slow Speeds/Velocities or RPMs, at sliding speeds of a few
millimeters per second, is required.
 The polymeric disc samples and the Ball/Pin for tribological
testing must be rounded and polished to less than 5 μm R max
to rule out mechanical stick slip and asperity interlocking
related phenomena.
 Can be tested at higher temperatures in hygrothermal
chambers to study viscoelastic functions.

15. Results and Discussion

16. A polymer Composite under Sliding

17. A Polymer Composite Under Sliding ( 10 to 1 RPM)

20. A clear viscoelastic Signal at very low sliding Speeds

21. About Retardation and Relaxation times
 In a linear viscoelastic polymeric solid, the retardation and relaxation times would be
closer but as a polymer exhibits more chain mobility or gets plasticized due to high
temperature and hygrothermal conditioning, the retardation times and the relaxation
times would differ appreciably. The polymer would relax more after the removal of the
load and the corresponding times would be more if strain or deformation is held
constant after the removal of stresses. As plasticization would lead to lower stress limits,
the retardation times would depend on the rate of loading but to reach the same stress
level of its linear viscoelastic form for initial loading conditions, the time taken would be
more. A non-linear viscoelastic solid plasticized by temperature and environment would
thus become non-linear and exhibit distorted sinusoidal signals.

22. Extraction of Data
 As loading is instantaneous at a particular point in a sliding
mode, a linear wear machine or a POD can be used to study
the pulsating force/stress waves. The stresses and strains,
retardation and relaxation times and associated wear data can
be computed using the linear or non-linear viscoelastic models
and the sliding contact traces. Each signature is typical of a
polymeric solid , the operational and environmental conditions.

23. A second order discovery based on
Viscoelasticity and Tribology !
A new Phenomenon !

24. Discussion of Results

27. Self Organization can be adapted for the polymer molecular
structures here, where the substrate is presented as a periodic
energy profile created by the molecules, using the ‘m’ or mass in
the Tomlinson-Frenkel-Kontoraova model as a viscous 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 surface in circles , causing the
stress to increase and decrease due to instantaneous contact.

28. Though there is self organization, over a longer time thermal and hygrothermal
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 relaxation time ( not volume) for a glassy polymer below its glass
transition temperature ranges from seconds to minutes and the evaluation of
relaxation time, τ, for a polymer filled with inorganic particles, based on the
relationships for a linear viscoelastic solid, gives us a static frequency range of
ω = 0.1 –1 for a tan δ = 0.001 to 0.1 as a DMA ( Dynamic Mechanical Analysis)
test would prove for polymers. The relationship τω = 1 gets us an approximate
value of 1 to 10 seconds for the retardation/relaxation time for these two polymer
composites.

29. Since there is time ( t >> τ ) for viscous reaction to
take place at a low rpm value of 1 ( for radius of 4 to
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
behaviour 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.

30. Vibrational resonance due to viscoelastic response 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 Maxwell
resonance condition for oscillation of fields as given in Feynman lectures ,
ωo = 2.405 {c/r} ------------ Equation
where ` ωo ‘ is the resonant frequency , `c’ the velocity and `r’ the radius of
the wear track that was discussed 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.

31. Salient Applications

32. 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 which is
like a signature.
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 properties and the tribological properties with an
acceptable level of approximation.

33. 4. A linear reciprocating wear test apparatus with an associated specific
software would suffice to achieve this phenomenally easy way of evaluating
the mechanical properties of a solid polymer .
5. This method serves as an easy to perform substitute Dynamic
Mechanical Analyzer (DMA) as the relaxation and retardation times can be
evaluated with an approximate 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
investigation. 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.

34. Book Chapter on Viscoelasticity

35. References
1. Aleksey Drozdov, A model for the non-liner
viscoelastic response in polymer at finite strains, 1998
2. Anna Ask, Andreas Menzel, Matti Ristinmaa, Electrostriction
in electro-viscoelastic polymers, 2012
3. B. Jasse and J.L Koenig, Orientation Measurements
in Polymers Using Vibrational Analysis, 2007
4. John M. Chalmers, Neil J. Everall, Qualitative and Quantitative
Analysis of Polymers by Vibrational Analysis, 2006
5. Michael Kapnistos, Viscoelastic
response of hyperstar polymers in the linear regime, 1999

36. References
6. Mohan D. Rao, Application of Viscoelastic damping for noise
control in automobiles, 2003
7. Neil J. Everall, Peter R. Griffiths, John M. Chalmers,
Vibrational Analysis of Polymers: Principles and Practices, 2007
8. Padmanabhan Krishnan, Viscoelastic Response of Hybrid
Polymeric Dental Composites in Sliding Contact and Applications,
De Gruyter Chapter, 2022.
9. Teng Cao, Yuan Mi, Xiaoniu Li, Gia Zhao, Viscoelastic
analytical model and design of polymer-based bimodal
piezoelectric motor, 2020

37. Thank you
and
Questions ?