45th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit
2 - 5 August 2009, Denver, Colorado
AIAA 2009-5115
Tensile Tests of Paraffin Wax for Hybrid Rocket Fuel Grains
John D. DeSain*, Brian B. Brady, Kelly M. Metzler, Thomas J. Curtiss and Thomas V.
Albright
The Aerospace Corporation
2350 E. El. Segundo Blvd., El Segundo CA 90245-4691
Abstract: The tensile strength, elastic modulus and percent elongation of paraffin wax
doped with small concentrations of low density polyethylene (LDPE) where measured.
The centrifugal casting process was used to create paraffin wax / LDPE wax hybrid
rocket motors. Tensile tests were then performed on samples taken from these test
motors. Concentrations from 0 % to 4 % LDPE added to the paraffin wax were tested.
The tensile strength, and elastic modulus increased with increasing concentration of
LDPE. The results show that paraffin wax motors can be created that have a greater
elastic modulus and similar tensile strengths compared to current solid rocket motors
based on HTPB rubber motors. However the paraffin wax motors were found to be less
elastic than HTPB with a much lower percent elongation. Void formation, tiny bubbles
in the paraffin wax created during the casting process, were found to affect the tensile
properties measured.
Keywords: hybrid rockets, paraffin wax, tensile strength, Young’s modulus
* The Aerospace Corporation 2350 E. El. Segundo Blvd., El Segundo, CA 90245-4691
USA. M.S. 2-341 E-mail: [email protected]
LDPE = low density polyethylene wax
HTPB = hydroxyl-terminated polybutadiene
Introduction
Paraffin wax based hybrid rocket motors have the potential to replace current
solid rocket motors functionality as boost phase launch vehicle components. Wax based
hybrid rockets have several advantages to current solid rocket motors based on
HTPB/ammonium perchlorate. Wax based hybrid rocket motors are non-toxic, nonhazardous, shippable as freight cargo, potentially carbon neutral1 and they can be
throttled for thrust control or shut down in case of an on-pad anomaly and restarted on
demand. Since the fuel is non-explosive, the fuel can be fabricated on-site and thus can
save in both manufacturing and launch operation costs.2,3 One consideration for using
Copyright © 2009 by The Aerospace Corporation. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.
wax as a replacement material for current solid rocket motors is understanding the
material properties of wax in comparison to the current motors. This is particularly
important for solid rockets sense the fuel has no structural tank to hold it. The fuel
material is a solid material that must be stored and held together by the material
properties of the fuel grain itself. For large scale motors the tensile properties must be
known in order to understand how the fuel grain will respond during storage, assembly
and usage.
Current solid rocket motors use HTPB rubber as the binding material. The tensile
properties have been measured previously for these solid rocket motors.4-6 The material
properties of the rubber vary slightly from motor to motor due to variances in the
polymerization process that was used to create it. Also the average tensile strength and
elastic modulus of HTPB was observed to increase with the addition of additives
aluminum and ammonium perchlorate.4,6 The elastic modulus ranges from 3 MPa to 6
MPa depending on the mixture.4,5 The elastic modulus has previously been found to
increase with age of the rubber.5 The maximum tensile strength was found to be from
0.75 – 0.87 MPa.4 The strain at maximum tension was found to be around 27 %. Table
1 lists the material properties for several measurements of pure and doped paraffin wax.
Pure paraffin wax has a similar maximum tensile strength as HTPB rubber, but a much
smaller percent elongation. The paraffin wax material properties change slightly with the
melting point of the wax. As seen in table 1, the lower melting point paraffin wax has a
slightly larger maximum tensile strength than the high melting point wax and a slightly
larger percent elongation.
Paraffin wax hybrid rocket motors are usually made by pouring liquid paraffin
wax into a mold. The mold is subjected to a centrifugal force during the process of
solidifying the hot liquid wax. This centrifugal casting process is used to help avoid
cracking and void formation inside the solid paraffin wax as it cools.2 These voids are
formed because the liquid paraffin wax shrinks upon cooling by 15-25 % depending on
the grade of wax. This shrinking during the centrifugal casting process will form a
natural central port through the hybrid motor. Additives have previously been used in
these paraffin wax motors to modify the material properties.10 These additives are placed
in the paraffin wax while it is still liquid and thus go through the centrifugal casting
process. As seen on table 1 only a small addition (3 % by weight) of the additive (a
Eastman Kodak proprietary LDPE) was needed to nearly double the tensile strength and
increase the percent elongation. Wang et al. previously measured the Young’s modulus
was for paraffin wax (326 K melting point) to be 61.4 MPa.11 LDPE is the additive10 that
is commonly used to modify the material properties for paraffin wax hybrid motors.
LDPE material properties depend on the exact chain lengths involved in the material. In
general LDPEs have a melting point from 373 K – 393 K. LDPEs have a tensile strength
that is much larger than that of paraffin waxes (4-12.5 MPa). The LDPEs percent
elongation range from 90-800 % and the elastic modulus is typically around 1-0.1
GPa.12,13 Thus all the material properties of LDPEs are larger than paraffin waxes.
In this study the material properties of tensile strength, elastic modulus and
percent elongation were examined for paraffin wax and paraffin wax with LDPE wax
added. A paraffin wax rocket motor was made by the typical centrifugal casting process.
The dogbones used for the tension tests were then cut from these wax motors. Three
different formulations were tested pure paraffin, 2 % LDPE added to paraffin wax and 4
% LDPE added to paraffin wax.
Procedure
The paraffin wax formulations were heated to 363 K to melt the paraffin wax.
The LDPE wax was then added to the hot liquid paraffin wax. The wax sample
continued to be heated at 363 K for several hours. The sample was stirred until all the
LDPE wax flakes fully dissolved in the liquid paraffin wax. The casting mold used for
making the wax motors is shown in figure 1. The mold consisted of two aluminum end
caps and a phenolic tube ( 17.0 cm long with a inner diameter of 8.6 cm). To fill the
mold with the hot wax, two of the brass fittings were unscrewed. The hot wax was then
poured through a funnel into the rocket motor mold. The brass fittings were then
reattached to the mold. The mold was heated to 363 K for ~ 2 hrs to insure the wax
inside was all liquefied after the pouring. The mold was then placed into a centrifuge and
spun at 1500 rpms for several hours while the wax cooled to room temperature. The
temperature of the outside of the phenolic tube was monitored during the centrifugal
casting process. The aluminum caps were then removed from the mold and the wax
motor casting was removed from the phenolic casting tube. Figure 2 shows an end on
view of the wax rocket motor after casting.
The dogbone-shaped test samples used for
the tension tests where then machined out of the casted rocket motor. The dogbone
samples were glued to the holders using Miller-Stevens P907 Epoxy. The length of the
pull section was 5.08 cm, the cross sectional area was 1.21 cm2. Stronger wax samples
where modified to have smaller cross sectional areas of 0.60 cm2. Figure 3 shows an
example of a wax dogbone used in the tension tests.
The paraffin wax was previously tested for tensile strength and % elongation tests
in accordance with ASTM D 412 .7,14,15 The main instrument used in this experiment was
an Instron uniaxial testing machine. The specimen was held between two wedge grips,
each attached to a crosshead. The upper crosshead was fixed to the vertical columns and
remains stationary. The lower crosshead is connected to a screw and an electric motor,
which caused it to move up or down, at a prescribed speed selected by the user. The
experiment was set to run at two different elongation rates 5.08 mm min-1 or 50.8 cm
min-1.
The melting point of the paraffin wax-LDPE mixes were measured in a capillary
tube. The melting point was measured for 0, 2, 4, 10, 15, 20, 25 and 100 % LDPE in
paraffin wax. The paraffin wax does not have a pure melting point and melts over a small
range of temperatures.
The wax mixtures also do not have a pure melting point, but two
rough ranges of melting points. The wax mixtures first slush at around 333 K when the
paraffin wax matrix melts and then stay a slush until at higher temperatures the LDPE
finally melts. The density of the mixes was also measured. The wax was cut into small
pieces and weighed on an electronic scale. The pieces volume was then obtained by
volume displacement of methanol in a graduated cylinder.
The paraffin wax was purchased from Aldrich chemical company. It had a melting
point between 331-335 K. The LDPE wax was purchased from Paplin Products and had a
melting point between 372-376 K.
Results
Figure 4 shows a plot of the stress vs. strain on four pure paraffin wax samples
pulled at two different strain rates. Figure 5 shows a plot of pure paraffin wax with the
relevant areas of the stress vs. strain curve marked. The plots have a yield point from
which the maximum tensile strength was obtained. The elastic modulus was obtained by a
linear fit of the region of the curve exhibiting Hookean behavior. Since the beginning of
the curve shows a toe, the x axis intercept of the linear fit was used as the “corrected zero”
strain for obtain the percent elongation. The measured material properties are shown in
table 2 and 3. Table 2 shows the measured elastic modulus (in MPa) and percent
elongation for the paraffin wax samples. Table 3 shows the measured maximum tensile
strength (MPa).
Figure 6 shows the melting point(s) observed for paraffin wax and LDPE. The red
points show the softening region of the paraffin wax. The softening point was taken as the
region where the wax turns from a solid to a cloudy slush. The blue points show the final
melting point of the mixture. The melting point was indicated as where the wax turns
from a cloudy slush to a clear liquid. The final melting point decreased as the percentage
of LDPE in the paraffin wax decreased. The final melting point was previously related to
the melting of the LDPE in the paraffin wax matrix 16. The melting point previously
observed for LDPE and paraffin wax is shown by the green boxes.16 Figure 7 shows the
density measured for the paraffin wax and LDPE samples. There is a slight trend of
increasing density with increased concentration of LDPE in the paraffin wax. However
any such trend is overwhelmed by the variance between samples. The large variance in
the paraffin wax density demonstrates the paraffin waxes ability to form both amorphous
and crystalline areas that have significant variability in the density of the paraffin wax.
Discussion
Except for the 4 % data the current experimental results were in good agreement
with the previous results from experiments.7 Some of the 4 % samples had extensive
bubble formation, as shown in figure 8. These bubbles appear to be a result of small air
leaks in the mold itself. As the wax cools inside the mold, the wax begins to contract.
This contraction creates a small vacuum that will then bring in outside air. A second run of
the 4 % in a mold that was checked using a high vacuum line to be air leak free was also
conducted. As seen in figure 9, these samples were devoid of these tiny bubbles. The
tensile strength and elastic modulus were both greater for the non-bubbled dogbones than
the samples that had bubbles.
Previously it was observed that as the percentage of the polyethylene waxes was
increased, all physical properties increased to produce a harder, tougher wax.7 Figure 10
shows a plot of the paraffin wax tensile strength data as a function of the purity of the
wax. Included in the figure is the Eastman Kodak data for waxes of similar melting points
to the current experiments. In general the tensile strength was found to increase with
increased concentration of LDPE in the paraffin wax. Much of the 2 % data is slightly
higher than expected based on the trend. The average maximum tensile strength
previously measured for HTBP solid rocket fuel was 0.89 MPa.4-6 Essentially the pure
paraffin wax has similar maximum tensile strength to HTBP and the addition of small
percentage of polyethylene only increases the maximum tensile strength beyond what is
commonly found in HTPB based motors.
Figure 11 shows a plot of the paraffin wax elastic modulus data as a function of the
purity of the wax. The elastic modulus increases as the percent of LDPE was increased.
The data in figure 11 was fit to a linear equation where the elastic modulus of the LDPE
doped paraffin wax was determined as a function of paraffin wax purity.
-48.8
(purity percentage) + 5121 = elastic modulus (MPa)
(1)
The average elastic modulus previously measured for HTPB solid rocket fuel was 5.44
MPa.4-6 The paraffin wax with the LDPE would have a much greater elastic modulus than
the HTPB based solid rocket fuels.
Figure 12 shows a plot of the paraffin wax percent elongation data as a function of
the purity of the wax. The percent elongation may slightly increase as the percent of
LDPE was increased. The data in figure 12 was fit to a linear equation where the percent
elongation of the LDPE doped paraffin wax was determined as a function of paraffin wax
purity.
-0.037
(purity percentage) + 4.28 = percent elongation (%)
(2)
However the data trend is heavily dependent on one Kodak measurement at 3 %.
Removing that point strongly suggests no significant change in percent elongation with
increase LDPE. The average percent elongation previously measured for HTBP solid
rocket fuel was 36.5 %.4-6 Even a pure LDPE wax motor would not have this much
elongation. Thus doped paraffin wax motors do not have the same amount of elasticity
that the rubber based fuels have.
The advantages of modifying paraffin with polyethylene waxes are higher
softening points7, increased hardness, greater tensile strength, larger elastic modulus and
larger percent elongation than pure paraffin wax based motors. Another advantage of
addition of polyethylene to the paraffin wax was the production of a more uniform wax.
Previous work7 has found that unmodified paraffin wax when solidified contains large
pieces of crystalline material and large pieces of amorphous material. The addition of
small percentages of polyethylene wax caused the large crystalline and amorphous areas to
become smaller and more uniform. This uniformity explains why some the physical
properties such as hardness, tensile strength, and percent elongation were significantly
improve with such a small addition of polyethylene. However the density measurements
didn’t show a significant decrease in the variance with increased LDPE concentration.
The pure LDPE has a rather large spread in density from measurement to measurement.
This would indicate the LDPE probably has a large range of chain lengths in it.
The addition of the LDPE wax also likely increases the surface tension in the
liquid paraffin wax. The viscosity of the liquid paraffin wax was previously observed to
increase with increased concentration of LDPE wax (from 3.5 MPa s for pure paraffin wax
to 4.8 MPa s for 97 % paraffin wax at 394 K).7 Since they are both related to the strength
of intermolecular forces of the liquid, surface tension tends to increase with increased
viscosity. Surface tension encourages the evaporation of small droplets, and the collapse
of small bubbles. Thus the increase in surface tension could potentially help suppress the
formation of tiny bubble voids which thus aids in the aggregation of voids towards the
center of the paraffin wax motor during centrifugal casting. The presents of these voids
would certainly decrease the tensile strength of the tested material. As seen with the 4 %
data voids clearly affected the maximum tensile strength and the elastic modulus.
Bader previously observed the change in the melting point with the addition of
LDPE to paraffin wax16 by using a differential scanning calorimeter (DSC). He found
that the polymer had no big influence on the melting point and the melting range of the
paraffin wax, but the paraffin wax seems to have a big influence on the melting point of
the polymers tested. For 45 % LDPE doped in paraffin wax, the peak temperature was at
about 373 K, whereas the melting point of the pure LDPE was at about 387 K. He
theorized that the reason for this decrease of the melting point of the polymers seems to be
the paraffin wax. The paraffin wax melts at lower temperature than the polymer. This
paraffin fluid in the polymeric matrix seems to decrease the forces between the molecule
chains of the polymers and with this, also the melting point. The results of the current
melting point experiment agree with these previous observations. They also suggest for
the small concentrations of LDPE used in hybrid motors little change in the bulk paraffin
wax melting point should be expected.
The current experiments suggest only a modest amount of LDPE may be beneficial
to the paraffin wax motor. The addition of LDPE makes a stiffer wax motor, however the
stiffest motors tested tended to also fracture at slightly lower maximum stress. Thus the
stiffest motors may be too brittle for practical use as motors. Indeed the 4 % motor
actually cracked in the casting process. Most common wax motors us 2% or less LDPE
which has been shown to slightly increase tensile strength and the elastic modulus with no
adverse effects to elasticity. There is no positive benefit to the temperature tolerances of
the rocket motor at these low concentrations of LDPE. The major upside to using the
LDPE would appear to be the Kodak observations of the crystal domain
Conclusion
The tensile strength, elastic modulus and percent elongation of paraffin wax doped
with small concentrations of LDPE where successfully measured. The paraffin wax
samples were prepared by the centrifugal casting process that is commonly used to cast
paraffin wax hybrid motors. The maximum tensile strength and elastic modulus
increased with increasing concentration of LDPE. The results show that paraffin wax
motors can be created that have greater elastic modulus and similar tensile strengths to
current HTPB rubber hybrid motors. However the paraffin wax motors are found to be
less elastic than HTPB rubber with a much lower percent elongation. The addition of
LDPE potentially has the advantage of reducing the amount of small voids in the paraffin
wax.
Table 1. Previous measurements of material properties of paraffin wax and doped
paraffin wax. Listed are the melting point of the paraffin wax used, the additive, purity,
tensile strength (MPa) and percent elongation.
Paraffin Wax
Additive
Percent
purity
52 –54 C
52 –54 C
None
Epolene C-15
Wax
Epolene C-15
Wax
Epolene C-15
Wax
None
Epolene C-15
Wax
Epolene C-15
Wax
Epolene C-15
Wax
ethylene
vinyl acetate
16 %/
Petroleum
resin 5 %
Graphite
foam
100
99 .5
52 –54 C
52 –54 C
60 –63 C
60 –63 C
60 –63 C
60 –63 C
66 C
56 C
99
97
100
99 .5
99
97
Tensile
Strength
MPa
1.38
1.38
1.38
1.86
1.03
1.03
1.24
1.93
79
Percent
Elongation
Reference
0.8
0.8
7
7
0.8
7
1.6
7
0.6
0.6
7
7
0.6
7
1.1
7
8
3.10
1.30
9
Table 2. Elastic Modulus and percent elongation measured for paraffin wax samples in
MPa.
Sample
Pull rate cm min-1
Percent elongation
Elastic modulus in
MPa
Pure wax
50.8
0.35
239
Pure wax
0.51
0.51
192
Pure wax
0.51
0.55
207
Pure wax
50.8
0.39
260
2 % LDPE
0.51
0.71
412
2 % LDPE
0.51
0.74
379
2 % LDPE
0.51
0.59
314
2 % LDPE
0.51
0.92
362
2 % LDPE
0.51
1.02
389
2 % LDPE
50.8
0.71
365
4 % LDPE*
0.51
0.33
384
4 % LDPE*
0.51
0.56
316
4 % LDPE*
0.51
0.90
329
4 % LDPE*
0.51
0.35
356
4 % LDPE*
0.51
0.67
313
4 % LDPE
0.51
0.59
384
4 % LDPE
0.51
0.35
462
4 % LDPE
0.51
0.54
392
* Showed extensive bubble formation.
Table 3. Maximum tensile strength measured for paraffin wax samples in MPa
Sample
Pull rate cm min-1
Pure wax
50.8
Pure wax
0.51
Pure wax
0.51
Pure wax
50.8
2 % LDPE
0.51
2 % LDPE
0.51
2 % LDPE
0.51
2 % LDPE
0.51
2 % LDPE
0.51
2 % LDPE
50.8
4 % LDPE
0.51
4 % LDPE
0.51
4 % LDPE
0.51
4 % LDPE
0.51
4 % LDPE
0.51
4 % LDPE
0.51
4 % LDPE
0.51
4 % LDPE
0.51
* Showed extensive bubble formation.
Tensile strength
MPa
0.863
0.885
0.994
0.920
2.511
2.513
1.863
2.602
3.008
2.437
1.28*
1.23*
1.37*
1.25*
1.26*
2.08
1.46
1.88
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Austin, D.; Combs, C. “ First Steps in the Development and Testing of Nontoxic,
Bioderived Fuels for Hybrid Rocket Motors” 43rd AIAA Aerospace Sciences
Meeting and Exhibit, Reno Nevada, January 2005.
2. -, M. A.; Zilliac, G.; Cantwell, B.; De Zilwa, S. R. N.; Castellucci, P. “Scale-Up
Tests of High Regression Rate Paraffin-Based Hybrid Rocket Fuels” Journal of
Propulsion and Power, Vol. 20, No. 6, Nov.–Dec. 2004, pp. 1037–1045.
3. Altman, D., “Hybrid Rocket Development History,” AIAA Paper 91-2515, June
1991.
4. Maruizumi, H.; Kosaka, K.; Suzuki, S.; Fukuma, D. “Development of HTPB
Binder for Solid Propellants” 24th AIAA/ASME/SAE/ASEE Joint Propulsion
Conference & Exhibit 11-13, Boston Massachusettes, July 1988.
5. Kivity, M.; Hartman, G.; Achlama, A. M. “Aging of HTPB Propellant” 41st
AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit 10-13, Tucson
Arizona, July 2005.
6. Chung , H. L.;Kawata, K.; Itabashi, M. Journal of Applied Polymer Science 1993,
50, 57-66.
7. “Epolene Waxes as Candle Additive” Eastman Chemical Company Kingsport, TN
1998.
8. Jones, Richard L. “Process for producing a petroleum wax composition” United
States Patent 5010126 CONOCO INC (US) 04/23/1991.
9. Richard Wirtz, Alan Fuchs, Venkat Narla, Yuyi Shen, Tianwen Zhao and Yanyao
Jiang AIAA-2003-513 41st Aerospace Sciences Meeting and Exhibit, Reno,
Nevada, Jan. 6-9, 2003
10. Karabeyoglu, M. A.; Altman, D.; Cantwell, B. J “High Regression Rate Hybrid
Rocket Propellant” U.S. Patent 6684624, Feb. 4 2004.
11. Wang, J.; Severtson, S. J.; Stein, A. “Significant and Concurrent Enhancement of
Stiffness, Strength, and Toughness for Paraffin Wax Through Organoclay
addition” Adv. Mater. 2006, 18, 1585-1588.
12. “Typical Properties of polyethylene wax” Engineering Laboratories Inc. Oakland,
NJ 2008. http://www.plasticballs.com/lopoly.htm
13. “Low Density Polyethylene (LDPE)” Curbell Plastics Inc. Orchard Park, NY 2008.
www.curbell.com
14. “Standard Test Methods for Vulcanized Rubber and Thermoplastic ElastomersTension” ASTM D 412 – 06a ASTM International, West Conshohocken, Pa 2006.
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ASTM International, West Conshohocken, Pa 2003.
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Storage” Department of Chemical and Material Engineering, The University of
Auckland, New Zealand, February 2002.
Figure 1. Photograph of the paraffin wax rocket motor casting mold.
Figure 2. Photograph of the paraffin wax rocket motor after casting.
Figure 3. Photograph of a dogbone made of paraffin wax used for the tension tests.
Figure 4. Plot of the stress versus strain for four separate pure paraffin wax
samples. The four samples were pulled at two different pulling rates 50.8 cm min-1
(samples 1 and 4) and 0.51 cm min-1 (samples 2 and 3).
Figure 5. Plot of the stress versus strain for a sample of pure paraffin wax (sample
3 in figure 4). The linear fit to the Hookean region of the plot yields the elastic
modulus (slope = elastic modulus = 2.07 MPa). The yield point is marked out
where the maximum tensile strength was observed (0.994 MPa). The percent
elongation (0.55) is obtained as the difference in the elongation at the yield point to
the x-intercept of the linear fit to the Hookean region of the plot.
Figure 6. The melting point of paraffin wax/ LDPE mixtures. The red points are
the softening point of the paraffin wax. The blue points are the final melting point
of the mixture. The green boxes are the two melting peaks observed by Bader.15
Figure 7. The density (g/cm-3) of paraffin wax/ LDPE mixtures.
Figure 8. Photo of the broken dogbone for the 4 % LDPE in paraffin wax. There
are clearly observed voids (tiny bubbles) throughout these dogbones.
Figure 9. Photo of the dogbone for the 4 % LDPE in paraffin wax. The paraffin
wax was cast after checking the mold for air leaks. There are clearly less voids
(tiny bubbles) throughout these dogbones than those in figure 8.
Figure 10. The tensile strength (MPa) of the LDPE doped paraffin wax samples as
a function of paraffin wax purity.
Figure 11. The elastic modulus (MPa) of the LDPE doped paraffin wax samples as
a function of paraffin wax purity.
Figure 12. The percent elongation of the LDPE doped paraffin wax samples as a
function of paraffin wax purity.
Brass fittings used to pour wax into mold
Aluminum end cap
Phenolic tubing
Aluminum end cap
Fig 1.
Fig 2.
5.08 cm
1.27 cm
0.95 cm
Fig 3.
1.0
Stress (MPa)
0.8
0.6
0.4
-1
Sample 1 50.8 cm min
-1
Sample 2 0.51 cm min
-1
Sample 3 0.51 cm min
-1
Sample 4 50.8 cm min
0.2
0.0
0.0
Fig 4.
0.5
1.0
Strain %
1.5
2.0
1.0
Slope =
elastic modulus
0.6
Stress (MPa)
Corrected zero strain point
removing toe
Stress (MPa)
0.8
0.4
0.2
Maximum tensile strength
Yield point
Percent
elongation
0.0
0.0
Fig 5.
0.5
1.0
Strain %
1.5
2.0
370
Temperature K
360
350
340
330
0
Fig 6.
20
40
60
Percent LDPE in paraffin wax
80
100
1.10
-3
Density (g cm )
1.05
1.00
0.95
0.90
0.85
0
Fig 7.
20
40
60
Percent Polyethylene
80
100
Figure 8.
Figure 9.
3.0
Tensile Strength (MPa)
2.5
2.0
1.5
1.0
96
Fig 10.
97
98
Percent purity of paraffin wax
99
100
450
Elastic modulus (MPa)
400
350
300
250
200
96
Fig 11.
97
98
Percent purity of paraffin wax
99
100
Percent elongation
1.0
0.8
0.6
0.4
96
Fig 12.
97
98
Percent purity of paraffin wax
99
100