LABORATORY “8”
Tensile Testing of GFR Nylon 6,6, Nylon
6,6, GFR PP, PP, PS, and LDPE
Mohammed Alzayer
Chris Clay
Xinhang Shen
Mat E 453
Lab Section 2
November 4th, 2014
1
ABSTRACT
Eight polymer samples were analyzed under tensile testing. Glass Fiber Reinforced
Nylon 6, 6 (GFR(N6,6)), Glass Fiber Reinforced Polypropylene (GFR(PP)), and
Polystyrene(PS) were brittle. The polypropylene (PP), low-density polyethylene (LDPE)
and Nylon 6,6 without glass reinforcement were more ductile. PP and LDPE were tested
under different strain rates, with no strain rate sensitivity being observed. Young’s
Modulus for each sample was calculated and analyzed by plotting both the engineering
and the true stress-strain curves.
1. INTRODUCTION
1.1 Tensile Testing
Tensile testing is a
technique in which the
mechanical properties of
materials can be
determined. A tensile
tester subjects a sample to
an axial load and
Figure 1 Schematic of the ASTM D 638 [1] (right), an actual
unit (left).
measures the amount of
deformation in mm and load in N that the sample is experiencing during the test (Figure
1). This information can be used to plot a stress versus strain plot for the tested sample.
This plot can be useful in determining properties such as yield strength, ultimate tensile
strength, 0.2 offset yield strength, Young’s modulus, and strain at fracture. Tensile testing
2
has the setback of destroying the sample. In other words, tensile testing is a destructive
method.
1.2 Stress vs Strain Curves
The stress is related to the load measured by the instrument by the following equation:
𝐹
𝜎=𝐴,
(1)
where
σ: stress in Pa,
F: load in N,
A: cross sectional area of sample in m2.
From Equation 1, the stress is
measured by the unit 𝑁/𝑚2 which is
often referred to as Pascal (Pa). The
strain is given by the equation below:
𝜀=
𝐿−𝐿0
𝐿0
Figure 2. Dog-bone shaped samples used for tensile testing.
,
(2)
where
ε: strain in m/m,
L: instantaneous length of the sample in m,
L0 : initial length of the sample, aka gauge length, in m.
The polymeric specimens used in tensile testing are often given in a dog bone shape
(Figure 2). The specimens are aligned parallel to the instrument and are pulled to
elongate until they break. In order to determine the stress these samples experience, the
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cross sectional area must be calculated first. For a dog-bone shaped sample, this area is
given by the product of its width and thickness in any part of the straight portion of the
specimen before it curves. The length of the straight part in the middle of the specimen is
known as the gauge length (Figure 2), which is 𝐿0 in Equation 2. The quantity 𝐿 − 𝐿0 is
the displacement of the sample relative to its original length and is measured by the
instrument. Hence, 𝐿0 must be measured before the test in order to calculate the strain.
When using Equations 1 and 2, the resulted
stress versus strain curve is labeled as an
“engineering” curve. The engineering stressstrain curve does not account for a
phenomenon known as ‘necking.’ Necking
happens when the material reaches its
ultimate tensile strength, which is the peak of
the stress versus strain curve. After this point,
the cross-sectional area of the sample
decreases dramatically, causing the sample to
Figure 3 Necking of samples
neck. Equations 1 and 2 yield an engineering
stress-strain curve because they assume a constant cross-sectional area throughout the
entire test including the part when the sample necks.
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Two other equations were derived in order to account for necking. These equations are as
follows:
𝐿
𝜎𝑇 = 𝜎 𝐿 ,
(3)
0
where
𝜎𝑇 : true stress in Pa,
𝜎: instantaneous stress in Pa,
L: instantaneous length of the sample in m,
L0 : initial length of the sample, aka gauge length, in m.
And the true strain can be calculated as follows:
𝐿
𝜀𝑇 = 𝑙𝑛 (𝐿 ) ,
(4)
0
where
𝜀𝑇 : true strain in m/m,
L: instantaneous length of the sample in m,
L0 : initial length of the sample, aka gauge length, in m.
A typical stress-strain curve consists of four regions: elastic region, yielding region, strain
hardening region, and necking region (Figure 4). The initial linear portion of the curve
represents the elastic regime. The slope of this line gives an important quantity that is
called Young’s modulus. According to Callister, Young’s modulus, also known as the
modulus of elasticity, is “the ratio of stress to strain when deformation is totally elastic;
also a measure of the stiffness of a material.” Accordingly, the Young’s modulus differs
from material to another. By this definition, Young’s modulus is given by the following
equation:
5
𝜎
𝐸 = 𝜀,
(5)
where
𝐸: Young’s modulus in Pa,
σ: stress in Pa,
ε: strain in m/m.
In the yielding region, the material exhibits a plastic behavior which is a permanent
deformation. Strain hardening commonly occurs in metals. In this region there is an
increase in the stress experienced by the sample meaning the material becomes harder.
The material finally starts to neck before it fractures.
Figure 4 Vairous regions and points on the stress-strain curve [2]
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1.3 Modes of Fracture
Polymers will exhibit different types of fracture depending on how free the polymer
chains are to move past each other when a stress is applied.
A polymer is said to be hard if it shows a high slope in the region of elastic deformation,
indicating that it requires a higher stress to cause the polymer chains to stretch elastically.
Similarly, if a polymer shows a low slope in the region of elastic deformation. It should
be noted that “hard” and “soft” are relative terms, as almost all polymers would be
considered soft when compared to metals or ceramics.
If the polymer chains are completely fixed in place, the polymer will break immediately
after the elastic stretching has completed. This is called brittle fracture, as no plastic
deformation is observed. Brittle fracture typically results in shiny surfaces where the
fracture occurs as the lack of plastic deformation results in relatively smooth surfaces that
light can specularly reflect off of. Chains are typically more immobile in cross-linked
polymers and when bulkier side groups are present to prevent slippage.
If the polymer chains are less fixed in place, the chains can start to slip past each other
after elastic deformation has concluded. This results in ductile fracture, which is evident
because of rough, uneven surfaces which light reflects diffusely off of, meaning that the
fracture will not appear shiny.
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If a polymer deforms plastically, its toughness will increase as more energy will be
required to cause chain slippage before it fractures. In a stress-strain curve, the area under
the curve is equal to the toughness.
Another common fracture mode is known as crazing. Crazing causes fracture in regions
of high hydrostatic tension or in regions of localized yielding in thermoplastic polymers.
Crazing occurs in polymers due to the combination of weak forces such as Van der Waals
and the stronger covalent bonds. If a local stress is sufficient, it can overcome the Van der
Waals force, allowing a narrow gap to form. The covalent bonds which hold the chains
together prevent further widening of the gap. Oftentimes, a craze cannot be felt on the
surface of a material. A craze is different from a crack in that it can continue to support a
load.
Typical stress strain curves for the different fracture modes are shown in Figure 5.
Figure 5 Plots of stress-strain curves of typical polymeric materials [2]
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2. EXPERIMENTAL PROCEDURES
2.1 Materials
Table 1 shows the repeating units of each material tested in this lab:
Table 1: Repeating units of samples tested in lab.
In total, 8 specimens were tested:
1. Glass Fiber Reinforced Nylon 6,6 at 5 mm/min.
2. Nylon 6,6 at 5 mm/min.
3. Glass Fiber Reinforced Polypropylene at 5 mm/min.
4. Polypropylene at 5 mm/min
5. Polypropylene at 50 mm/min.
6. Polystyrene at 5 mm/min.
7. Low-density polyethylene at 5 mm/min.
8. Low-density polyethylene at 50 mm/min.
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2.2 Specimen Measurement
The polymer specimens were cut into dog-bone shapes.
1) The thickness and width of polymer samples were measured using a micrometer.
2) Sample defects were made note of.
2.3 Software Setup
1) The tensile test instrument and the video extensometer were turned on.
2) On the main page, “Test” was selected to start a new sample.
3) The load cell was calibrated. All loads were removed from the load cell and calibrated.
4) The load was zeroed once the clamps were installed.
5) The up and down arrows were pressed on the controller until the clamps were just
touching.
6) The up and down arrows were used until the clamps were about 100 mm apart.
7) The polymer sample was placed vertically between the grips of both the tensile test
instrument.
8) The extension and the load were zeroed.
9) Geometrical dimensions of the sample were entered.
10) The “Start” button was clicked. Observed the experiment at a safe distance at an
angle and note of the failure mode was taken when the specimen failed.
2.4 End of Task
1) The two handles were turned in the open directions to remove the sample.
2) The data file was saved.
3) Broken fragments were cleaned up.
4) The instrument was turned off and the program was closed.
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3. RESULTS
3.1 Engineering Stress vs Strain
The engineering stress-strain curves obtained from the raw data are shown in Figure 6.
The Instron tensile tester actually measures the load it is applying as well as the sample's
elongation. However, as the sample's cross sectional width and thickness were measured
by micrometer (Appendix Table A1) and entered into the instrument software, the
software can calculate the stress using Equation 1. Similarly, as the instrument
automatically measured the initial gauge length, the software calculated the change in
strain as elongation occurred using Equation 2. Using the outputted data files, the stress
vs strain curves could be plotted using Excel (Figure 6).
Stress (MPa)
100
80
60
40
20
0
0
0.5
1
1.5
Strain (mm/mm)
Nylon 6,6 GFR
Nylon 6,6
PP GFR
PP (50 mm/min)
PP (5 mm/min)
PS
LDPE (50 mm/min)
LDPE (5 mm/min)
Figure 6. Plot of engineering stress-strain behavior of eight samples
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The Young's Modulus of the materials could be estimated by taking the slope of the
linear region of elastic deformation (Figure 7). The results of the Young's Modulus
calculation, as well as the final elongation distances and loads, are summarized in Table
2.
y = 1512.4x + 10.349
Strss (MPa)
100
80
60
y = 2640.3x - 25.734
y = 1469.3x - 8.2448
y = 719.79x - 3.087
40
20
y = 705.01x - 3.7455
y = 65.871x + 0.5062
y = 75.06x + 0.9093
0
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
Strain (mm/mm)
Nylon 6,6 GFR
Nylon 6,6
PP GFR
PP (50 mm/min)
PP (5 mm/min)
PS
LDPE (50 mm/min)
LDPE (5 mm/min)
Figure 6. Elastic region of engineering stress-strain behavior of eight samples
3.2 True Stress vs Strain
Equations 1 and 2 used to calculate the engineering stresses and strains are not entirely
accurate, as they assume the cross-sectional area of the specimen does not change during
tensile loading. During the region of elastic deformation, this is a reasonable assumption
to make. However, once plastic deformation, and in particular necking, begin to occur,
the cross-sectional area of the specimen can change dramatically (Figure 3). This change
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in cross-sectional area is accounted for in the equations for true stress and
strain, Equations 3 and 4. Using these equations, the true stress vs true strain graphs
could be generated (Figure 8).
140
120
Stress (MPa)
100
80
60
40
20
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Strain (mm/mm)
Nylon 6,6 GFR
Nylon 6,6
PP GFR
PP (50 mm/min)
PP (5 mm/min)
PS
LDPE (50 mm/min)
LDPE (5 mm/min)
Figure 7 Plot of true stress-strain behavior of eight samples
The Young's Modulus could be estimated in the same manner using the true stress-strain
curves as was done for the engineering stress-strain curves (Figure 9, Table 2)
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120
y = 1971.5x + 0.4721
100
80
60
y = 3232.1x - 26.029
40
y = 1841.6x - 8.8873
y = 902.05x - 3.3832
20
y = 807.07x - 3.0887
y = 87.806x + 0.3796
y = 94.294x + 0.9857
0
0
0.01
0.02
0.03
0.04
0.05
0.06
Nylon 6,6 GFR
Nylon 6,6
PP GFR
PP (50 mm/min)
PP (5 mm/min)
PS
LDPE (50 mm/min)
LDPE (5 mm/min)
0.07
0.08
Figure 8 Elastic region of true stress-strain behavior of eight samples
Table 2. Loads, extensions, and engineering, true and literature Young’s Moduli
Material
Load
Extension
Engineering
True E
Literature
(N)
(mm)
E (GPa)
(GPa)
E (GPa)
GFR Nylon 6,6
27.9
8.66
1.51
1.97
2.70-8.56 [4]
Nylon 6,6
17.3
98.2
0.720
0.900
1.60 [5]
GFR PP
58.6
3.65
2.64
3.23
7.40 [6]
PP (50 mm/min)
35.6
111
0.710
0.810
0.90-1.10 [5]
PP (5 mm/min)
785
103
0.710
0.880
PS
27.0
1.96
1.47
1.84
1.90-2.90 [5]
LDPE (50
11.5
91.6
0.0751
0.0943
0.30 [5]
409
56.5
0.0659
0.0878
mm/min)
LDPE (5
mm/min)
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4. DISCUSSION
4.1 Mechanical Properties
The glass-fiber reinforced polymers showed the highest Young's Modulus because glass
itself has a higher Young's modulus than any polymer. The benefit of reinforcing
polymers with glass fibers instead of just using glass fibers is that the polymer coating
protects the glass fibers from sudden impacts that could cause the glass to fracture. Also,
if one glass fiber has a significant defect such as a crack in it and fails before the rest, the
polymer coating separates it from the rest of the fibers preventing catastrophic failure.
Thee glass reinforced polymers also showed little plastic deformation as expected,
because glass is a brittle material.
The polymer with the next highest Young's modulus was polystyrene, which also showed
little plastic deformation. This agrees with expectations, as the bulky phenyl group on the
polymer chain (Table 1) acts to prevent chain slippage.
Nylon 6,6 showed the next highest Young's modulus and also showed significant amount
of plastic deformation. This indicates that chains are able to slide past each other and
uncoil beyond the region of elastic deformation.
The polymers with the two lowest Young's moduli were polypropylene and low-density
polyethylene, with PP being slightly higher. These polymer both showed huge amounts
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of plastic deformation, as polyethylene has no side groups, and polypropylene has only a
small methyl side group.
The Young's moduli calculated with the true stress and strain equations were higher than
those calculated with the engineering stress and strain equations. The reason for this is
the true equations took into account the decrease in cross-sectional area, making the true
stress values higher than the engineering stresses.
The experimental values for Young's moduli were all lower than the literature values.
One possible reason for this include inaccuracies in the measured specimen thicknesses
and widths, as these were only measured once with a digital micrometer. More
measurements could lead to more accurate thicknesses and widths. A more probable
reason for the deviation from literature values is that the Instron measures the gauge
length to be longer than it actually is, due to the angling of the specimen between the
actual gauge and where the specimen is being held.
Both polypropylene and LDPE showed little sensitivity to strain rate, as the stress-strain
curves are almost identical. However, as the 5 mm/min samples were stopped before they
got to the strain that the 50 mm/min samples failed at, this testing is inconclusive. The
stoppage occurred due to time constraints. If the 5 mm/min samples had been allowed to
continue, they would have been expected to reach higher strain values than did their 50
mm/min counterparts.
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4.2 Fracture Comparisons
Polymers with glass fiber reinforcement and bulky side groups (e.g. polystyrene) showed
brittle fracture characteristics such as a smooth shiny surface, as the chains are unable to
slip past each other effectively. Polypropylene and LDPE showed almost complete
ductile fracture (rough, uneven surfaces, while reinforced Nylon 6,6 showed intermediate
properties (Figure 10). Polypropylene showed high amounts of crazing, easily seen by
the fiber pullouts. The trend of more immobile chains having tendencies for brittle
fracture agrees with expectations.
Figure 9 Cross-sections of fours samples after fracture (left), all the eight samples after
tensile testing (right)
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5. CONCLUSIONS
1. Glass fiber reinforced polymers showed the highest Young's moduli and brittle
fracture.
2. Polymers with less mobile chains, such as Nylon 6,6 and PS, showed higher Young's
moduli and a tendency for brittle fracture.
3. Polymers with more mobile chains, such as LDPE and PP, showed lower Young's
moduli and a tendency for ductile fracture.
4. No strain-rate sensitivity was observed due to time constrains of the lab.
5. Using true stress-strain equations instead of engineering stress-strain equations resulted
in higher calculated stresses and therefore higher Young's moduli.
6. The experimental values for the Young's moduli were consistently lower than literature
values.
6. ACKNOWLEDGMENTS
The group would like to thank Dr De Leon for providing the polymer dogbone samples.
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7. REFERENCES
[1] Callister, W., David R. Materials Science and Engineering: An Introduction. Wiley
Inc., 2010.
[2] De Leon, Jose. “Lab 8: Tensile Testing.” Iowa State University. Web.
[3] “Understanding Crazing.” Orton Firing Institute. Web.
[4] “Overview of materials for Nylon 66/6, 20% Glass Fiber Reinforced” MatWeb. Web.
[5] MakeItFrom.com. Web
[6] “Borealis Nepol™ GB303HP Long Glass Fiber Reinforced Polypropylene” MatWeb.
Web.
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Appendix
Table A1. Geometrical dimensions of eight samples before tensile testing. A standard
gauge length of 78 mm was used in all calculations.
Material
Width (mm)
Thickness (mm)
GFR Nylon 6,6
10.34
4.06
Nylon 6,6
10.30
3.95
GFR PP
9.85
3.99
PP (50 mm/min)
10.71
3.97
PP (5 mm/min)
10.57
4.04
PS
10.61
3.98
LDPE (50 mm/min)
10.34
4.04
LDPE (5 mm/min)
10.08
4.04
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