Upload
qiaunus
View
115
Download
2
Embed Size (px)
Citation preview
UNIVERSITY OF MANCHESTER
School of Mechanical, Aerospace & Civil Engineering
MACE 20037
Plastics: Design, Materials & Manufacture
Laboratory Report
Report on an Experiment to Investigate the
Stress & Time Dependence of the Creep of Polypropylene
Prepared by:
Shuhaib Maudarbaccus
Second Year Mechanical Engineering
Experiment performed on: February 8, 2011
Report Submitted on: February 22, 2011
(ii)
Table of Contents
Abstract ..................................................................................................................................... 1
Introduction .............................................................................................................................. 1
Theory .................................................................................................................................... 1
Experimental Procedure ......................................................................................................... 3
Apparatus & Equipment ......................................................................................................... 3
Procedure ................................................................................................................................ 3
Experimental Results ............................................................................................................... 4
Calculation of the conversion factors ..................................................................................... 4
Results from isochronous test ................................................................................................ 5
Results from isometric tests ................................................................................................... 6
Interpolation of two more creep curves .................................................................................. 7
Discussions ................................................................................................................................ 9
Analysis of the link between theory and experimental results ............................................... 9
Possible sources of experimental errors ................................................................................. 9
Conclusions ............................................................................................................................. 10
Appendix I – Experimental Data .......................................................................................... 11
References ............................................................................................................................... 11
Bibliography ........................................................................................................................... 11
List of Figures
Figure 1: The ICI Creep Machine .............................................................................................. 5
Figure 2: Lever arrangement of creep machine ......................................................................... 5
Figure 3: Mirror arrangement of extensometer .......................................................................... 6
Figure 4: Isochronous stress-strain graph at 30s ....................................................................... 8
Figure 4: .................................................................................................................................... 8
Figure 4: .................................................................................................................................... 8
Figure 4: .................................................................................................................................... 8
List of Tables
Table 1: ..................................................................................................................................... 3
Table 2: ..................................................................................................................................... 3
Table 3: ..................................................................................................................................... 4
Table 4: ..................................................................................................................................... 7
Table 5: ..................................................................................................................................... 8
1
Abstract
The experiment was carried out to investigate the stress and time dependence of the creep of
polypropylene at room temperature. Appropriate tests, namely isochronous and isometric tests, were
performed to generate data required to analyse those dependencies. Isochronous stress-strain graphs
and isometric curves (creep curves) were also produced. Conclusions reached were that firstly, the
strain at a particular time was higher for a larger stress but the proportional relationship as suggested in
theory was less obvious and secondly, the creep rate decreased significantly within a very short time to
support the idea of back stress building up to oppose the applied stress and slow down the creep. A
number of possible sources of errors have also been identified, accounting for the scattering in the
plots produced. The change in room temperature was also identified as a source of error but its effect
on the results was less obvious than that of other sources identified. Further investigation into the
effect of temperature on creep is therefore required to support results from this experiment.
Introduction
In this experiment, the creep variations of polypropylene with stress and time have been investigated.
To determine those variations, creep specimens of polypropylene were subject to 2 types of tests,
namely isochronous and isometric tests.
The isochronous test involved finding the strain of a specimen after 30 seconds under a range of
stresses. The resulting data was then used to plot an isochronous stress-strain curve from which the
30s-creep-modulus of the polypropylene specimen could be estimated.
The isometric test involved observing the change in strain with time under a constant stress and then
plotting the strain against a logarithmic time scale to obtain a creep curve. The test was then
repeated under another applied stress to be able to produce a second creep curve.
It has to be noted that the creep curves had to be forced to agree with the isochronous stress-strain
curve at 30s and the corresponding stress by determining correction factors and using them to correct
the data from the isometric test. The corrected data was then used to plot new creep curves and also to
interpolate two more creep curves at different stresses. The findings from those two tests, their
implications and possible experimental errors have been explained in the Discussions section. The
background theory and main concepts needed for the experiment have also been outlined in the
subsection below.
Theory
Polypropylene, being a polymer, is made up of long chains of covalently bonded carbon atoms. These
chains are tangled together and are held by secondary forces like Van der Waal forces which can be
compared to weak cross-links at regions of entanglement (1). The presence of those secondary forces
causes polymers to exhibit glass transition which occurs at a temperature known as the glass transition
temperature, TG. At temperatures well below TG, polymers can be very stiff but as the temperature
increases, the polymer molecules “gain enough thermal energy to begin sliding past one another” (2).
Therefore, under the application of stress, the polymer undergoes an instantaneous strain according to
Hooke‟s Law accompanied by an increase in strain as polymer chains slide past one another,
2
overcoming the secondary forces between them (1). This change in strain is termed creep and is a
property of polymeric solids known as viscoelasticity.
Creep experiments to investigate time and stress dependence of strains have revealed the linear
relationship between strain and stress at an arbitrary time after application of the stress, which in turn
led to the definition of the creep compliance at time t, (3). However, this property,
termed linear viscoelastic creep, is only observed at low stresses (sufficiently low to cause strains
below 0.005) (3).
In this experiment, strains observed were less than 0.005 and based on the previous fact, a straight line
passing through the origin could be fitted in the isochronous stress-strain plots as shown later in the
report. This allowed the creep modulus for a specific time to be calculated for the polypropylene
specimen.
On the other hand, various models have been made to describe creep and one of them is the Zener
Model which leads to the following equation for strain of a material at time, t, and under stress, σ:
where and represent spring constants and represents viscosity of the system of springs and
dashpot used to model creep (4). Clearly, the above equation reveals the non-linear relationship
between strain and time and creep curves, plots of strain-log t under constant stress, will therefore also
be non-linear. Although the exact relationship is not known, exponential curves have been fitted
through the strain-log t plots from the isometric tests as they provide a very good agreement with the
plots.
Finally, another factor which had to be considered was the room temperature at which the experiment
was performed. In fact, unlike metals, polymers undergo significant creep at room temperature. The
higher the temperature is above the TG of the polymer, the greater the viscoelastic behaviour. The
creep specimen used in this experiment was polypropylene, which has a TG of around -10°C (5) and
the room temperature was around 20°C. Therefore, any changes in temperature during the experiment
would need to be taken into consideration when analysing the results from the creep tests performed.
3
Experimental Procedure
Apparatus & Equipment
An ICI Creep Machine, shown in Fig. 1, was provided to
carry out the investigation. This machine features an
extensometer with a set of three mirrors, one of which is
fixed while the other two rotate by an amount proportional
to the extension of the specimen being tested. The mirror
system deflects a light beam from a slit and the image of a
hairline then appears on a curved scale (labelled A in Fig. 1).
The displacement of this light spot (hairline image) can be
simply read off the scale which is accurate to 1mm, and then
used to calculate the strain in the specimen. The creep
machine also uses an electromagnetic loading system
(labelled B on Fig. 1) to allow the load to be released
quickly and start timing at the same time. A damper is also
required to ensure that the load is applied without shock and
overshoot.
A vernier calliper, accurate to 0.1mm, was also provided to measure the thickness and width of three
creep specimens to be used during the experiment while timing was done using a stopwatch accurate to
1 second.
Procedure
Before starting the experiment, the thickness and width of three creep specimens were measured using
the vernier calliper and an average value for both dimensions determined.
The loading bearings were fitted onto each end of one of the specimens. The specimen was then
mounted onto the extensometer using a jig to ensure the knife edges of the extensometer were 80mm
apart. The specimen could then be placed into the creep machine and was allowed to creep under the
pre-load for about 5 minutes, following which the „fixed‟ mirror of the extensometer was rotated so
that the light spot was approximately on the zero line. This was done to remove any errors in extension
induced by the weight of the loading mechanism (excluding the hanger) and which would otherwise be
carried forward into the measurements taken.
The first part of the experiment was the isochronous test. This involved applying a load to the
specimen and recording the displacement of the light spot just before the load was applied and 30s
later. The test was done with loads ranging from 5N to 45N, in steps of 5N and between each loading
cycle, the specimen was allowed to „recover‟ for 2 minutes so that the displacement of the light spot
could return close to the zero line before the next cycle could be started. The measurements have been
used to plot an isochronous stress-strain curve in the next section.
B
A
Figure 1: The ICI Creep Machine
4
For the second part, an isometric test was carried out. Another specimen was loaded into the creep
machine following the same steps as outlined earlier and again the specimen was left to creep under
the pre-load for 5 minutes. A load of 40N was set into the machine and timing started as it was
released. Readings of the displacement of the light spot were taken at 10s intervals for the first 2
minutes, then at 30s intervals for the next 3 minutes and finally at 1 minute intervals till the last
reading at 900s. The same experiment was carried out with a load of 20N by another group of students
from whom a second set of measurements was obtained. The data collected has been used to plot two
creep curves which can be found in the next section.
Experimental Results
Calculation of the conversion factors
To simplify the calculation of stress and strain under the different load and time conditions, conversion
factors relating the stress and the strain to the corresponding independent variable can be determined
and then used to evaluate all the stress and strain values. The conversion factors are each defined by
the equations and , where F refers to the weight of the sets of loads used, including
the hanger, and X is the displacement of the light spot along the curved scale. The conversion factors
thus depend on the dimensions and arrangement of the creep machine and the extensometer.
The schematic in Fig. 2 shows the lever arrangement
translating the load F to the force T applied on the
specimen. It is known that the ratio is 5:1 and by
equating the moments at the pivot to 0, T can expressed
in terms of F as follows:
It is also known that , where A is the cross-
sectional area of the specimen and that .
Equating the two expressions above and using :
To find the second conversion factor, the rotation of the mirrors attached
to the rollers of the extensometer and the displacement of the light
spot, X (refer to Fig. 3), need to considered. Fig. A1 in Appendix I
shows that the rollers rotate through a distance for an
overall extension of . If the angle through which they
both rotate is , and is the radius of the rollers, then:
a b
F
T
Specimen
Figure 2: Lever arrangement
of creep machine
Figure 3: Mirror arrangement
of extensometer (6)
5
Also, the rotation of the mirrors deflects the light beam through an angular displacement of . A light
beam incident on a mirror which rotates by an angle and which would deflect the beam through
has been shown in Fig. A2 in Appendix I. With an additional mirror rotated through , the beam
would therefore be deflected through a total angle of 4 . The displacement X which can be read off
from the curved scale is related to by , where R is the radius through which the light spot
moves along the curved scale. Finally, from the definition of strain, it is known that .
From the measurements of the thickness and the width of 3 specimens, the average thickness and
width were found to be 3.31mm and 4.99mm respectively. The area A is therefore 16.52mm2. Also
known are the values , and . Replacing the above values in the
expression for the conversion factors, the following is obtained:
Results from isochronous test
Table 1: Data from isochronous test with strain and stress values
F / N Xi / mm Xf / mm X / mm ε[30s] σ / MPa
5 0.0 2.0 2.0 1.56E-04 1.51 10 0.0 6.5 6.5 5.08E-04 3.03 15 0.5 13.0 12.5 9.77E-04 4.54 20 1.0 22.5 21.5 1.68E-03 6.05 25 1.0 34.0 33.0 2.58E-03 7.56 30 1.5 44.0 42.5 3.32E-03 9.08 35 1.5 49.0 47.5 3.71E-03 10.59 40 1.5 53.0 51.5 4.02E-03 12.10 45 1.5 56.0 54.5 4.26E-03 13.61
An isochronous stress-strain graph has been
plotted in Fig. 4. Assuming linear viscoelastic
creep as outlined in the Theory section, a line
passing through the origin can be fitted through
the points plotted using the least-squares analysis.
This analysis leads to the equation
for the best-fit line.
Since the modulus of a material is determined by
taking the ratio of stress to strain, in this case, the
30s-creep-modulus is therefore the gradient of
the line of best-fit and is equal to:
σ = 3037.7ε
0
2
4
6
8
10
12
14
0.0
00
0.0
01
0.0
02
0.0
03
0.0
04
0.0
05
Str
ess
, σ
/ M
Pa
Strain at 30s, ε[30s]
Figure 4: Isochronous stress-strain graph
at 30s
The measurements made
during the isochronous test
have been tabulated in Table 1
to the right. X is the difference
between Xf and Xi and the
strain and stress values for
each set of readings have been
calculated using the previously
calculated conversion factors.
6
Results from isometric tests
t / s X / mm
lg (t/s) Strain, ε
F = 20N F = 40N F = 20N F = 40N
0 0.0 0.0
0.00E-00 0.00E-00 10 17.5 50.0 1.00 1.37E-03 3.91E-03 20 18.5 51.0 1.30 1.45E-03 3.98E-03 30 19.0 51.0 1.48 1.48E-03 3.98E-03 40 19.5 51.5 1.60 1.52E-03 4.02E-03 50 20.0 52.0 1.70 1.56E-03 4.06E-03 60 20.0 52.0 1.78 1.56E-03 4.06E-03 70
52.5 1.85
4.10E-03
80
52.5 1.90
4.10E-03 90 20.5 53.0 1.95 1.60E-03 4.14E-03
100
53.0 2.00
4.14E-03 110
53.5 2.04
4.18E-03
120 21.0 53.5 2.08 1.64E-03 4.18E-03 150 21.5 54.0 2.18 1.68E-03 4.22E-03 180 21.5 54.0 2.26 1.68E-03 4.22E-03 210 22.0 54.5 2.32 1.72E-03 4.26E-03 240 22.0 55.0 2.38 1.72E-03 4.30E-03 270 22.5 55.0 2.43 1.76E-03 4.30E-03 300 22.5 55.0 2.48 1.76E-03 4.30E-03 360 22.5 55.5 2.56 1.76E-03 4.34E-03 420
56.0 2.62
4.38E-03
480 23.0 56.0 2.68 1.80E-03 4.38E-03 540
56.5 2.73
4.41E-03
600 23.0 56.5 2.78 1.80E-03 4.41E-03 660
56.5 2.82
4.41E-03
720 23.5 57.0 2.86 1.84E-03 4.45E-03 780
57.0 2.89
4.45E-03
840 24.5 57.0 2.92 1.91E-03 4.45E-03 900
57.0 2.95
4.45E-03
960 25.0
2.98 1.95E-03
ε = 0.0012e0.1645*lg(t)
0.0013
0.0014
0.0015
0.0016
0.0017
0.0018
0.0019
0.002
1 1.5 2 2.5 3
Str
ain
, ε
lg (t/s)
ε = 0.0036e0.0739*lg(t)
0.0038
0.0039
0.004
0.0041
0.0042
0.0043
0.0044
0.0045
1 1.5 2 2.5 3
Str
ain
, ε
lg (t/s)
Table 2 shows the readings from
the isometric tests carried out
with loads of 20N and 40N. It
also contains values of lg (t) for
the values of t at which readings
were taken, except for t = 0s for
which lg (t) is undefined. The
strain values tabulated have been
calculated using the conversion
factor Kε and the displacement X.
The empty cells under the
displacement and strain columns
indicate that no reading was
taking at the corresponding value
of time, t.
The data from Table 2 has been
used to plot two graphs of strain-
log t, also known as creep curves,
for the two applied loads of 20N
and 40N. The corresponding
stresses for these applied loads
can be calculated using the
conversion factor, Kσ, and are
equal to 6.05MPa and 12.11MPa
respectively. Exponential curves
have been used to fit the plots as
shown in Fig. 5 and Fig. 6, as
seen in the Theory section.
Table 2: Data from isometric tests with strain values
Figure 5: Creep curve for F=20N
(σ=6.05 MPa) Figure 6: Creep curve for F=40N
(σ=12.11 MPa)
7
Interpolation of two more creep curves
Due to the variations in the properties of the specimens used in the isochronous and isometric tests and
errors like differences in cross-sectional areas of specimens, the strains from the creep curves at t=30s
do not agree with the strains from the isochronous stress-strain curve for the same applied loads. To
resolve this problem and reduce errors carried into the interpolated creep curves, the two existing creep
curves have been corrected using two correction factors. For this purpose, the equation of the best-fit
line for the isochronous graph has been used to find the strains at stresses of 6.05MPa and 12.11MPa.
The conversion factors have then been calculated by taking the ratio of the strains from the
isochronous curve to that from the isometric tests. The strain values used and the correction factors
have been tabulated in Table 3 below.
F / N σ / MPa ε from isochronous
curve ε from
isometric tests Correction
Factor 20 6.05 0.001993 0.001484 1.34271 40 12.11 0.003986 0.003984 1.00045
t / s lg (t/s) Original Strains Corrected Strains Interpolated Strains
F = 20N F = 40N F = 20N F = 40N F = 30N F = 35N
0
0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 10 1.00 1.37E-03 3.91E-03 1.84E-03 3.91E-03 2.87E-03 3.39E-03 20 1.30 1.45E-03 3.98E-03 1.94E-03 3.99E-03 2.96E-03 3.47E-03 30 1.48 1.48E-03 3.98E-03 1.99E-03 3.99E-03 2.99E-03 3.49E-03 40 1.60 1.52E-03 4.02E-03 2.05E-03 4.03E-03 3.04E-03 3.53E-03 50 1.70 1.56E-03 4.06E-03 2.10E-03 4.06E-03 3.08E-03 3.57E-03 60 1.78 1.56E-03 4.06E-03 2.10E-03 4.06E-03 3.08E-03 3.57E-03 70 1.85 4.10E-03 4.10E-03 80 1.90 4.10E-03 4.10E-03 90 1.95 1.60E-03 4.14E-03 2.15E-03 4.14E-03 3.15E-03 3.64E-03
100 2.00 4.14E-03 4.14E-03 110 2.04 4.18E-03 4.18E-03 120 2.08 1.64E-03 4.18E-03 2.20E-03 4.18E-03 3.19E-03 3.69E-03 150 2.18 1.68E-03 4.22E-03 2.26E-03 4.22E-03 3.24E-03 3.73E-03 180 2.26 1.68E-03 4.22E-03 2.26E-03 4.22E-03 3.24E-03 3.73E-03 210 2.32 1.72E-03 4.26E-03 2.31E-03 4.26E-03 3.28E-03 3.77E-03 240 2.38 1.72E-03 4.30E-03 2.31E-03 4.30E-03 3.30E-03 3.80E-03 270 2.43 1.76E-03 4.30E-03 2.36E-03 4.30E-03 3.33E-03 3.81E-03 300 2.48 1.76E-03 4.30E-03 2.36E-03 4.30E-03 3.33E-03 3.81E-03 360 2.56 1.76E-03 4.34E-03 2.36E-03 4.34E-03 3.35E-03 3.84E-03 420 2.62 4.38E-03 4.38E-03 480 2.68 1.80E-03 4.38E-03 2.41E-03 4.38E-03 3.39E-03 3.89E-03 540 2.73 4.41E-03 4.42E-03 600 2.78 1.80E-03 4.41E-03 2.41E-03 4.42E-03 3.41E-03 3.92E-03 660 2.82 4.41E-03 4.42E-03 720 2.86 1.84E-03 4.45E-03 2.47E-03 4.46E-03 3.46E-03 3.96E-03 780 2.89 4.45E-03 4.46E-03 840 2.92 1.91E-03 4.45E-03 2.57E-03 4.46E-03 3.51E-03 3.98E-03 900 2.95 4.45E-03 4.46E-03 960 2.98 1.95E-03 2.62E-03
Table 3: Strain values from the tests & the correction factors
Table 4: Corrected and interpolated strains values
8
Table 4 above shows the corrected strain values under 20N and 40N loads and interpolated values of
strains under stresses of 9.08MPa, equivalent to F=30N, and 10.60MPa, equivalent to F=35N. The
corrected strain values were obtained by multiplying the raw data by the appropriate correction factors
while the interpolated values were determined through linear interpolation between the strain values
for F=20N and F=40N using the equation below for each set of readings. The subscripts denote the
force applied, F, and „i‟ needs to be replaced by 30 or 35 to give the strains for F=30N or F=35N.
The assumption made when interpolating was that the specimen had been tested within the linear
viscoelastic region. This means that strain should vary proportionally with stress at any specified time
within the time-frame used and that the ratio of stress to strain should correspond to the creep modulus
at that same time (or the inverse of the compliance, J, at that specified time). This would therefore also
comply with the isochronous stress-strain curve in Fig. 4. The data from Table 4 was then plotted and
an exponential curve fitted through each set of points to generate the four creep curves in Fig. 7 below.
0.0015
0.002
0.0025
0.003
0.0035
0.004
0.0045
1 1.5 2 2.5 3
Str
ain
, ε
lg (t/s)
F = 40N
σ = 12.11MPa F = 35N
σ = 10.60MPa
(interpolated)
F = 30N
σ = 9.08MPa
(interpolated)
F = 20N
σ = 6.05MPa
Figure 7: Two experimental and two interpolated creep curves
9
Discussions
Analysis of the link between theory and experimental results
For the first part of the experiment, results from the isochronous test were used to plot an isochronous
stress-strain curve in Fig. 4. The plots appeared to follow a smooth curve but theory suggested that for
strains less than 0.005, the creep can be taken to be in the linear viscoelastic region such that a straight line
can be fitted through the plots. Doing so reveals scattering of the plots on both sides of the best-fit line,
indicating that the measurements could have been prone to random errors. As far as the significance of the
graph in Fig. 4 is concerned, it shows that the strain at a particular time, in this case 30s, definitely varies
with the applied stress. However, the proportionality between them is less obvious due to the scattering of
the points and therefore had to be assumed by fitting a best-fit line.
Unlike for the isochronous test, for the isometric one, the variation of strain with lg (t) is not exactly
known, although it is known that the variation is non-linear, as seen in the Theory section. For this reason,
the best option was to fit an exponential curve which clearly agreed with the plots as seen in Fig. 5 & 6 and
again, the scattering of the points can be justified by the presence of experimental random errors. Possible
errors which could have affected the experiment have been listed in the next subsection. The first
observation made by comparing the creep curves in Fig. 5, 6 & 7 is that the strain is higher at higher
stresses, which is line with the deduction from the isochronous test. The second observation is that a rather
straight line on a strain-log t scale implies that the strain rate is very high for short lengths of time but then
reduces significantly as the time scale increases. This idea agrees with the concept of back stress which
builds up with time to oppose the applied stress and therefore reduce the creep rate (3). At some point, the
back stress equals the applied stress such that the net stress is then zero and the polymer ceases to creep.
Regarding the interpolation of two more creep curves, some corrections had to be made to the original
creep curves before proceeding. In fact, since the isochronous curve was constrained by having to pass
through the origin, it was easier to force the isometric plots to agree with the isochronous curve rather that
the other way round. This ensured that the concept of compliance, , in the region assumed to be linear
viscoelastic, was respected since, for corresponding stresses, the points along the isochronous curve and the
isometric plots at t=30s corresponded to the same points and had to agree as closely as possible. In other
words, if a vertical line is drawn at in Fig. 7 and the points at which the line intersects with the
creep curves are plotted on a stress-strain scale, the resulting straight line should closely match with that in
Fig. 4. Therefore, the main assumption made for the interpolation was that the creep observed during the
test was always linear viscoelastic. This can be proved by repeating either the isochronous test for different
values of time or the isometric test at different stresses and comparing the results with the graphs in Fig. 7
or Fig. 4 respectively.
Possible sources of experimental errors
The main source of errors dealt with recording the measurements of displacement X. In fact, the scale is
accurate to 1mm and measurements could only be made to the nearest 0.5mm by estimation and the fact
that the light spot was around 1mm thick made it more difficult to estimate the readings. Performing the
experiment with a thinner slit and taking the readings in a darker environment would have reduced the risk
uncertainties in the measurements.
10
Similarly, the use of the stopwatch might have introduced errors but its impact would have been more
noticeable at the start of the tests, when creep rate was quite high. One way to reduce errors in this case
would be to perform the experiment under the same conditions and then average the results.
The experiment involved the use of 3 creep specimens and an average cross-sectional area for the 3
specimens was determined before the experiment. However, to improve accuracy of the results, average
cross-sectional area of the specimen used for each test should be determined and recorded and then used to
evaluate the stresses applied in each test separately, although this would make the calculations longer.
Another source of errors would be concerned with the weights used as the applied force, F. Firstly, it has to
be noted that the mass of the hanger is around 0.47kg but for simplicity it was considered to be 0.5kg. The
weights used were also quite rusty, such that their mass could have been a little lower that stated. Besides,
the gravitational constant, g, was approximated as 10m/s2 to simplify the calculation of the force, F, but
since this force is actually multiplied by 5 due to the lever system, any error in F would also be increased
by a factor of 5. While this would not affect the shape of the creep curves, it would however affect that of
the isochronous stress-strain curve and consequently the value of the 30s-creep-modulus. A possible
improvement would be to determine the mass of the loads used and use g=9.81m/s2 but this would
inevitably require more time and would make calculations of F longer.
Finally, it has to be pointed out that this experiment investigated creep as a function of time and stress but it
is also known, as seen in the Theory section, that creep depends on ambient temperature as well. Since the
temperature dependence was not being investigated, this meant that temperature had to be maintained
constant throughout the experiment. However, this was not the case and the temperature rose from around
19°C to around 22°C during the course of the experiment. While this seemed to be a very small change, its
effect on the creep of the specimen could have been more important. This can only be confirmed by further
investigation on the effect of temperature on creep and if it is found that the changes in creep and creep
rates around 20°C is negligible, the temperature factor could be ignored. Otherwise, the experiment should
be repeated under controlled conditions or the room temperature should be noted at the beginning and at
the end of the different tests performed and then a correction factor be used, based on the effect of
temperature on creep, to correct the measurements and account for the temperature change.
Conclusions
The first conclusion from the experiment was that the strain of the polypropylene clearly increased with
increase in stress but it was less clear whether the relationship was proportional. Secondly, the creep rate of
the polymer visibly decreased with time, supporting the idea of back stress opposing the appied stress.
The results from the experiments have shown some degree of scattering, as discussed earlier. Considering
the possible sources of errors outlined previously, this scattering can be clearly justified and therefore, the
graphs produced using the results should be used with some degree of tolerance.
However, their reliability can be further assessed and hence increased by doing the same tests under
different time and stress conditions and then verifying the agreement between the isochronous and the
creep curves. Correction factors can be determined as before and the closer they are to unity, the more
reliable the results are. Doing the experiment again with the improvements suggested earlier would also
lead to more accurate results and might also reveal other sources of errors which have been overlooked.
11
Appendix I – Roller & Mirror Arrangements of Extensometer
References
1. Methven, J. Topic 1: Bonding & Structure. s.l. : University of Manchester, 2011. lecture notes for
the module Plastics: DMM - MACE 20037.
2. Robello, D. R. Chem 421: Introduction to Polymer Chemistry. Polymer Properties and MW.
[Online] 2002. [Cited: 21 February 2011.]
http://chem.chem.rochester.edu/~chem421/propsmw.htm#tg.
3. N. G. McCrum, C. P. Buckley, C. B. Bucknall. Principles of Polymer Engineering. 2nd Edition.
New York : Oxford University Press, 1997. pp. 117-120.
4. Methven, J. Topic 2: Polymer Viscoelasticity. s.l. : University of Manchester, 2011. lecture notes
for the module Plastics: DMM - MACE 20037.
5. Scott, C. E. PolymerProcessing.com. Polypropylene. [Online] 2001. [Cited: 21 February 2011.]
http://www.polymerprocessing.com/polymers/PP.html.
6. Methven, J. Engineering Manufacturing & Materials Laboratory. s.l. : University of Manchester,
2011. laboratory sheets.
Bibliography
M. F. Ashby, D. R. H. Jones. Engineering Materials 1. 2nd Edition. Oxford : Butterworth-
Heinemann, 1997. pp 61-62, 193-194.
Figure A1: Schematic view of
extensometer showing the 2 rollers (6)
p is the angle through which the reflected light
beam rotates as mirror rotates by angle Θ.
Figure A2: Angle of deflection of a light beam
incident on a mirror rotated by angle (6)