Tensile Testing and Four-Point Bending to
Determine Strength Characteristics
Experiment Number 1
Alex High
MatSE 462, Section 4
19 February 2015
Abstract
Tensile tests and four-point bending tests are crucial for determining a material’s
strength properties. This experiment involved performing tensile tests on metals and
polymers and performing four-point bending tests on ceramics. The metal used was 3003
aluminum (3003Al), while the polymers used were high-density polyethylene (HDPE)
and low-density polyethylene (LDPE). The ceramic used was silicon carbide (SiC). The
tests all provided data on the strength of the material, which is useful in subsequent
applications. The data was used to identify strength and stress values. The SiC data did
not seem to match the literature values. Conversely, the polymer (LDPE and HDPE)
values all fell within the literature value ranges, while the 3003Al values were within a
few standard deviations of the literature values. Therefore, the 3003Al, HDPE and LDPE
values are all useful, while the SiC values may not be of much help.
Introduction
This strength testing experiment was conducted in order to identify the strength of
a certain metal, certain polymers, and a certain ceramic. The metal and polymer samples
were tested using a tensile testing machine. The ceramic sample was tested using a fourpoint bending process. The data results were then studied, and finally the results were
graphed. Additionally, the data provided critical data values, such as tensile strength,
yield stress, and elongation percent. These values were then compared to established
literature values to identify the accuracy of the values. The tensile test was performed
using an Instron 5866. Bluehill software was used to control the tensile tests and to
monitor and record the data. The four-point bending tests were conducted using an
Instron 4202.
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Experimental Procedures
For the tensile tests, all samples had the necessary dog-bone shape. The following
procedure for the tensile tests was employed for the 3003Al samples. First, the lower
grip was loaded with the sample. Care was taken to ensure that the grip did not cover any
part of the gauge. Next, the upper grip was jogged down until it could be tightened
around the top of the sample. The upper grip was placed approximately the same distance
away from the center of the sample, as was the lower grip.
For the polymer samples, slightly different steps were taken to load the sample.
Both HDPE and LDPE samples were loaded using this method. Because the polymer is a
soft sample, the sample was loaded into the upper grip first. The upper grip was then
jogged down so that the sample would rest in the lower grip. The lower grip was then
tightened around the sample, with care taken to ensure that both grips were equidistant
from the center of the sample. For all samples, after a sample was loaded, the load was
zeroed using the fine position, and the gauge length was reset. Then the tensile test was
conducted. The 3003Al sample had a gauge length of 30 mm, and both polymer samples
had gauge lengths of 15 mm.
For the four-point bending test, the following procedure was employed. First, the
top and bottom fixtures were inspected to ensure that there was no leftover material from
a previous test and to ensure that the pins were all in the required positions. Next, the
sample was marked using a marker. The outer span has a distance of 40 mm, so to mark
the sample, the center of the sample was identified, and two lines were drawn. The lines
were drawn 20 mm away on each side of the center. This step was taken so that when the
sample fractured, it could be easily determined of the fracture had occurred within the
outer span pins. If the fracture was outside the span, then the test would be faulty.
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Next, the sample was loaded onto the lower fixture, with the marked lines being
placed over the outer span pins. The upper fixture was then placed over the sample. For
all samples, the gauge length was zeroed, the load cell was zeroed, the fixture weight was
tared, and the load units were calibrated. Then the ball was jogged down so it touched the
upped fixture, with a load less than -1 N. The test setting were as follows: the sampling
rate was 500 ms; the loading speed was 0.5; and the load failure detection was -0.5 N.
With these settings in place, the four-point bending test was then conducted.
Results and Discussion
Data samples from the tensile tests were graphed on a plot of load (N) vs
extension (mm). From this data, the offset yield strength was calculated. From the data
samples, the elongation at fracture was identified which was used to calculate percent
increase of the gauge length. The data samples also provided the tensile strength, which
was obtained by the maximum force divided by the original cross sectional area of the
sample.
Gauge length formula: ef = (Lf – L0)/L0, where ef = elongation
Lf = final length
L0 = initial length
Graphing the data gave the following graphs (Fig. 1, Fig. 2, and Fig. 3). For the
3003Al sample the graph looks as expected (Fig. 1). There is the obvious elastic
deformation region, where the slope of the line is linear, followed by an arcing line,
which is the plastic deformation region. The plastic deformation region is where necking
became visible in the sample. These regions are followed by a failure point, which is
around when the sample was extended ~1.75 mm.
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3003 Al
Load (N)
800
600
400
200
0
0
0.5
1
1.5
2
2.5
Extension (mm)
Fig. 1. – Stress-vs.-strain curve for 3003Al.
The polymer samples also offered excellent graphs from the data (Fig. 2, Fig. 3).
The elastic regions are very short, because the polymers are soft materials. The plastic
region follows the elastic region. In terms of viewing the sample, this region is the most
obvious. In the region, the sample is drawn out, and due to the nature of polymers, the
drawing out requires time. The polymer chains in HDPE and LDPE are both stretched out
from their previously amorphous positions. This allows for the polymers to be drawn out
until the fully-stretched out polymers break. The break point can be seen where the line
drops rapidly towards a 0 N load.
Though both polyethylene-based polymers, HDPE and LDPE both have different
properties. This can be observed in the difference between the graphs. The HDPE has a
higher strength, so the elastic region for HDPE (Fig. 2) is larger than the elastic region in
the LDPE graph (Fig. 3). LDPE is weaker and deforms much more quickly than HDPE,
so the LDPE sample handled less load over a lower extension. This can be seen by the
ultimate failure data in both graphs.
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Load (N)
HDPE
120
100
80
60
40
20
0
0
50
100
150
Extension (mm)
Fig. 2. - Stress-vs.-strain curve for HDPE
Load (N)
LDPE
60
50
40
30
20
10
0
0
20
40
60
80
100
Extension (mm)
Fig. 3. - Stress-vs.-strain curve for LDPE.
The four-point bending test provided data samples which allowed for the
calculation of strength in the sample and for a plot of load (N) vs extension (mm). The
strength in the sample was calculated by the following formula: S(strength) = 3PL/4bd2.
SiC
1000
Load (N)
800
600
400
200
0
-200 0
0.1
0.2
0.3
Extension (mm)
0.4
0.5
Fig. 4. - Stress-vs.-strain curve for SiC.
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SiC
Avg.
Tensile
Strength
(MPa)
891
3003 Al
Avg.
Tensile
Strength
(MPa)
150.55
LDPE
Avg.
Tensile
Strength
(MPa)
21.41
HDPE
Avg.
Tensile
Strength
(MPa)
26.21
STD
Tensile
Strength
(MPa)
34.69
STD
Tensile
Strength
(MPa)
1.91
Avg. Yield
Stress
(MPa)
108.69
STD Yield
Stress
(MPa)
9.9
STD
Tensile
Strength
(MPa)
4.74
Avg. Yield
Stress
(MPa)
25.37
STD Yield
Stress
(MPa)
5.17
STD
Tensile
Strength
(MPa)
2.49
Avg. Yield
Stress
(MPa)
23.59
STD Yield
Stress
(MPa)
2.07
Avg.
Elongation
(%)
4.78
STD
Elongation
(%)
0.32
Table 1. – Average tensile strengths for SiC, 3003Al, LDPE, and HDPE; average yield
stresses for 3003Al, LDPE, and HDPE; average elongation percentage for
3003Al; and standard deviation values for all average values.
The average SiC tensile strength was calculated to be 891 MPa, with a standard
deviation of 34.69 MPa (Table 1). The Weibull Analysis calculated the strength value to
be 947.34 MPa (Fig. 5, Table 2). The literature values give the tensile strength as ~4600
MPa1.
The average 3003Al tensile strength value was 150.55 MPa, with a standard
deviation of 1.91 MPa (Table 1). The Weibull Analysis (Fig. 6, Table 2) offered the
3003Al tensile strength value at 155.44. Literature values present the tensile strength
value of 3003Al to be 145 MPa under normal conditions2, which are under what these
tests were conducted. The average yield stress of 3003Al was calculated to be 108.69
MPa, with a standard deviation of 9.9 MPa (Table 1). This is compared to a literature
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value of 43.0 MPa2. The average elongation of the 3003Al was calculated to be 4.78%
with a standard deviation of 0.32% (Table 1). This compares to a literature value of
4.00%2.
The average HDPE tensile strength was calculated to be 26.21 MPa, with a
standard deviation of 2.49 MPa (Table 1). The Weibull Analysis offered the tensile
strength value of 28.23 MPa (Fig. 7, Table 2). These compare to a literature value of
10.0-43.0 MPa3. The average yield stress was calculated to be 23.59 MPa, with a
standard deviation of 2.07 MPa (Table 1). A literature value gives the yield stress of
HDPE to be 11.0-43.0 MPa3.
The average LDPE tensile strength was calculated to be 21.41 MPa, with a
standard deviation of 4.74 MPa (Table 1). The Weibull Analysis offered the tensile
strength value of 24.39 MPa (Fig. 8, Table 2). These compare to a literature value of 2.856.5 MPa4. The average yield stress was calculated to be 25.37 MPa, with a standard
deviation of 5.17 MPa (Table 1). A literature value gives the yield stress of HDPE to be
7.7-136 MPa4.
Weibull Plot for SiC
3.00
LN(LN(1/(1-F)))
2.00
y = 7.7898x - 53.387
1.00
0.00
-1.006.20
6.40
6.60
6.80
7.00
7.20
-2.00
-3.00
-4.00
-5.00
LN(strength)
Fig. 5. – Weibull Analysis Plot for SiC.
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Weibull Plot for 3003Al
LN(LN(1/(1-F)))
2.00
y = 16.44x - 82.959
1.00
0.00
-1.004.70
4.80
4.90
5.00
5.10
5.20
-2.00
-3.00
-4.00
-5.00
LN(strength)
Fig. 6. – Weibull Analysis plot for 3003Al.
Weibull Plot for HDPE
LN(LN(1/(1-F)))
2.00
y = 6.2629x - 20.91
1.00
0.00
-1.000.00
1.00
2.00
3.00
4.00
-2.00
-3.00
-4.00
LN(strength)
Fig. 7. - Weibull Analysis plot for HDPE.
Weibull Plot for LDPE
2.00
y = 2.059x - 6.5797
LN(LN(1/(1-F)))
1.00
0.00
0.00
-1.00
1.00
2.00
3.00
4.00
5.00
-2.00
-3.00
-4.00
-5.00
LN(strength)
Fig. 8. - Weibull Analysis plot for LDPE.
σ is the characteristic strength. The data values are taken from the Weibull Plots.
The Weibull modulus, m, is equal to the slope of the line. The zero condition is used, –
ln(strength) = 0 – and therefore the negative of the intercept of the line is equal to the
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modulus multiplied by the natural logarithm of the characteristic strength. This gives
[m*ln(σ)=-(intercept)].
From Fig. 5:
53.39 = 7.79ln(σ)
σ = 947.34 MPa
From Fig. 6:
82.96 = 16.44ln(σ)
σ = 155.44 MPa
From Fig. 7:
6.58 = 2.06ln(σ)
σ = 24.39 MPa
From Fig. 8:
20.91 = 6.26ln(σ)
σ = 28.23 MPa
Weibull Data
SiC
3003Al
LDPE
σ (MPa)
947.34
155.44
24.39
Table 2. – Weibull Analysis Data of characteristic strengths.
HDPE
28.23
The 3003Al samples had very close strength, yield stress, and elongation values to
that of the literature values. Most of the calculated values were within one or two
standard deviations of the literature values. The SiC samples, however, had much higher
strength values when compared to the literature values. The literature values fell well
outside even three deviations of the calculated strength values. This could be due to an
error in calculations, or due to the SiC samples used in the tests having different
structures, etc., than samples used to determine the literature values. The HDPE and
LDPE all had excellent tensile strength and yield stress values. All of these polymer
values fell within the literature value ranges.
Conclusions
The HDPE and LDPE results all were excellent, while the 3003Al results were
satisfactory. The SiC values, however, did not agree with literature values, which may be
caused by an unknown variable in the tested SiC samples. The tensile testing was overall
successful, while the four-point bending test did not provide accurate results.
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Citations
1. SiC Properties, MatWeb.
<http://www.matweb.com/search/DataSheet.aspx?MatGUID=dd2598e783ba4
457845586b58c8ea9fb>, 2/18/15
2. 3003Al Properties, MatWeb.
<http://www.matweb.com/search/datasheet.aspx?matguid=09c63ea8e10e4eea
8398256801bb8514&ckck=1>, 2/18/15
3. HDPE Properties, MatWeb.
<http://www.matweb.com/search/DataSheet.aspx?MatGUID=fce23f90005d4f
be8e12a1bce53ebdc8>, 2/19/15
4. LDPE Properties, MatWeb.
<http://www.matweb.com/search/DataSheet.aspx?MatGUID=557b96c10e084
3dbb1e830ceedeb35b0>, 2/19/15
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