Time Temperature Superposition of Short Term Stress Relaxation

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Time Temperature Superposition of Short Term Stress Relaxation
TIME TEMPERATURE SUPERPOSITION OF SHORT TERM STRESS
RELAXATION BEHAVIOR TO UNDERSTAND RETENTION OF MATERIAL
MODULUS OVER TIME
Praful Soliya and Prasanta Mukhopadhyay, SABIC Research and Technology Private Ltd., Bangalore
562125, India
Abstract
under these conditions [3]. The results are presented in
this report.
Several engineering thermoplastics, because of their
higher mechanicals, thermal and dimensional stabilities,
are increasingly being considered for use as injection
molded components, in several industrial applications [1].
There are several load bearing applications, such as
springs, bearings, gears, valves etc., wherein during short
term, it could be subjected to constant strain under
varying temperature and humidity levels [2]. It is of
interest to have an understanding, if such materials during
end-use, has the ability to retain modulus over a short
period of time. Therefore, linear visco-elastic limit of the
material needs to be determined under the influence of
strain, temperature and moisture. To assess such
performance attributes of materials, short-term tensile
stress relaxation studies were conducted, using Universal
Tensile Instrument, under varying strain levels,
temperature and humidity in a 1-hour timescale. The study
revealed that the material retained linear visco-elastic
behavior in the range of 2% strain until 60°C and moisture
was found to have no impact. The relaxation modulus
measured from this experiment was also extended using a
master curve using Time-Temperature-Superposition
(TTS) up to 10 hours. Such an analytical technique could
be used for material screening by product developers.
Going forward, if there is need to assess the performance
of the material over a longer period (>10 hours), the
laboratory experimental duration can be proportionately
increased.
Experimental Method
Introduction
Polymeric resins have been evaluated for several load
bearing applications, such as springs, bearings, gears,
valves, etc. utilizing its high modulus, good creep
resistance and relaxation modulus performance. In these
applications, the molded part would be subjected to
constant strain during storage, under temperature and
humidity for extended period of time. Hence, it is
important to understand the polymer’s relaxation modulus
under these conditions. To evaluate the retention of
modulus at various strain levels, stress relaxation was
carried out.
Time temperature superposition (TTS) was used to
estimate the long-term performance and also to identify
time dependent linear range of viscoelastic performance
Engineering thermoplastic material was used for the study
(due to commercial reasons the grade nomenclature is not
disclosed). Tensile bars were molded for carrying out the
relaxation test. Stress relaxation tests were carried out
using ASTM – D638 on Type IV tensile bars using
displacement controlled Instron tabletop tester (Model
No.-5566), equipped with thermal chamber. The tests
were carried out at 23°C, 40°C, 50°C and 60°C. The
samples were prepared by exposing them to different
humidity levels starting with 0% RH (dried in oven or at
least 48hrs under vacuum), 50% RH and 100% RH using
humidity chamber (Instron Model 3119.405) with a
exposure time of 48 hours.
The samples were conditioned at the set temperature
for 1 hour to equilibrate before the measurements were
carried out using dual replicates, per condition, for a
period of 1 hour.
The strains during experiments were recorded using
extensometer (Instron – 2620 clip-on type) mounted on
the test samples and stresses were calculated based on
force readings from load cell from Instron.
Results and Discussions
Figure 1a-1d, shows the relaxation modulus
(G(t)) for strain varying from 1 to 4% at various humidity
levels. As can be seen for fixed strain levels, the
relaxation modulus does not vary much with change in
humidity levels at 23°C, ruling out the possibility of
plasticization effect of moisture at these conditions.
Figure
1a
SPE ANTEC™ Indianapolis 2016 / 1561
In figure 2, the data is summarized indicating relaxation
modulus as a function of time for varying strain levels and
humidity levels at 23°C. Error bars indicate the variation
of relaxation modulus with humidity levels. As can be
seen, higher strain results in lower modulus and also the
rate of modulus decrease is higher for higher strain values,
indicating rate of stress relaxation is higher. The
relaxation modulus for 1-2% strain indicates a linear
viscoelastic behavior. It was also found that the relaxation
modulus deviates significantly from linearity at 3% strain
and higher, pointing to the fact a non-linear behavior of
the material at such strain levels.
Figure
1b
Figure
2
Figure 2: Relaxation modulus as a function of time for
varying strain levels and humidity levels at 23°C
Figure
1c
Figure
1d
Similar trends for relaxation modulus is seen, when tests
are carried out at 40°C and 60°C as shown in Figure 3a-3d,
4, 5a-5d and 6, respectively. It was observed that with
increasing temperature, up until 60°C, the material does
retain it linear visco-elastic behavior, but only up to 2%
strain. The relaxation modulus deviates significantly from
linearity at 3% strain and higher, pointing to the fact a
non-linear behavior of the material at such strain levels. It
was also evident that the relaxation modulus did not vary
much with change in humidity levels, therefore indicating
no influence of moisture at such conditions.
Figure
3a
Figure 1a-1d: Relaxation modulus as function of different
strain and humidity levels.
SPE ANTEC™ Indianapolis 2016 / 1562
10
1%- Strain
Relaxation Modulus (Gpa)
40 oC
Figure
3b
2%-Strain
3%-Strain
4%-Strain
Figure
4
1
1
10
100
time (sec)
1000
10000
Figure 4. Relaxation modulus as a function of time for
varying strain levels and humidity levels at 40°C
Figure
Figure
3c
Figure
5a
Figure
5b
3d
Figure 3a-3d: Relaxation modulus as function of different
strain and humidity levels.
SPE ANTEC™ Indianapolis 2016 / 1563
Figure
6
Time Temperature Superposition (TTS) of
relaxation modulus
To extend the prediction range at 23°C from 1
hour, TTS was used and the shift factors were determined
using Arrhenius equation.
Figure
Figure 75d
Figure
5c
TTS was used to obtain the master curves for
stress relaxation. Relaxation modulus shift against time
(in log -time) is plotted in Fig 8. To generate master curve
the following steps were considered.
A material specimen was subjected to a constant
strain 1, 2, 3 and 4% at 23°C, 40°C and 60°C temperature
using UTM, and the variation of the stress of the specimen
is observed against the log (time). 23°C was selected as
reference temperature (TR). All the individual relaxation
curves corresponding to different temperature levels are
represented along the log (time) scale to superpose the
master curve.
Figure 5a-5d: Relaxation modulus as function of different
strain and humidity levels.
Figure 7 indicates that the shifting using 23°C as
reference temperature, for completely dry sample, is well
achieved. It is found that using 1 hour data the
extrapolation goes up to several days. However for all
practical purposes, considering that the experimental
duration was 1 hour, the relaxation modulus measured
from such experiment, should be extended using a master
curve using Time-Temperature-Superposition (TTS) up to
10 hours. Going forward, if there is need to assess the
performance of the material over a longer period (>10
hours), the laboratory experimental duration should be
proportionately increased.
10
1%-Strain
Relaxation Modulus (Gpa)
60 oC
2%-Strain
3%-Strain
4%-Strain
1
1
10
100
Time (sec)
1000
10000
Figure 6: Relaxation modulus as a function of time for
varying strain levels and humidity levels at 60°C
Figure 7: TTS of 0%RH data with 23°C as reference
temperature, for varying strain levels
SPE ANTEC™ Indianapolis 2016 / 1564
Conclusions
There are several load bearing applications, for
which linear visco-elastic limit of the material needs to be
determined under the influence of strain, temperature and
moisture to help design engineers to incorporate such
material data into FEM models for evaluating the part
performance.
The study revealed that the material retained
linear visco-elastic behavior in the range of 2% strain,
until 60°C and moisture was found to have no impact. The
relaxation modulus measured from such experiment, was
also extended using a master curve using TimeTemperature-Superposition (TTS) up to 10 hours. Such an
Analytical Technique could be used for material screening
by product developers. Going forward, if there is need to
assess the performance of the material over a longer
period (>10 hours), the laboratory experimental duration
can be proportionately increased.
References
1.
2.
3.
Engineering Plastics Handbook, McGraw Hill
Handbooks, James M Margolis.
Blends and Alloys of Engineering Thermoplastics,
Dr. H T van de Grampel
Selecting
Thermoplastics
for
Engineering
Applications, Second Edition Revised and Expanded,
Charles P Mcdermott and Aaron V Shenoy
Application of the Superposition Principle and
Theories of Mechanical Equation of State, Strain, and
Time Hardening to Creep of Plastics under Changing
Loads, William N. Findley1 and Gautam Khosla1, J.
Appl. Phys. 26, 821 (1955);
Introduction to Linear Viscoelasticity, John J. Aklonis
and William J. Macknight Wiley, 1983
SPE ANTEC™ Indianapolis 2016 / 1565

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