Abstract
The 3-point bend test is a standard test used to study the flexural properties of materials when subjected to loads. For this experiment, three specimens of different
materials (a carbon fiber nylon composite, a glass carbon fiber composite, and basswood) were subjected to a 3-point bend test to gather data on the stress and strain
experienced by the materials. This data was then used to calculate the maximum
shear stress, flexural strain at failure, modulus of rupture, flexural modulus, standard
deviation of the stress, and the standard deviation of the strain. It was hypothesized
that the rank of the materials from highest flexural modulus to lowest flexural modulus would be the carbon fiber nylon composite, the basswood, and then the glass
fiber nylon composite. Our data, however, disproved this hypothesis, with the carbon
fiber nylon composite being the highest, followed by the glass fiber nylon composite,
and then the basswood with the lowest. Possible reasons for this incorrect hypothesis
could be the quality of the lab equipment, human error, or the fact that the equations
used come from the ASTM D790 document, which contains the standard for flexural
properties of unreinforced and reinforced plastics and electrical insulating materials,
while one of the materials is wood.
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Table of Contents
Introduction
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Testing Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
2
3
Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Discussion and Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
5
8
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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iii
Introduction
Understanding how, why, and when materials fail is imperative for designing any engineering structure. One important aspect of this understanding comes from flexural
testing. Uniaxial tension and compression tests may not provide all of the information
needed about a material’s behavior. As a material bends or flexes, the combination
of forces and loads it is subjected to becomes complex and can experience tension,
compression, and shear all at once [1]. The 3-point bend test is one method of flexural
testing and allows for all of these forces to be taken into consideration. Because of
this, bend testing is often used to see how materials will react to realistic loading
situation, especially if a material will be used in a support structure [1].
In a 3-point bend test, a rectangular cross-section of a material rests on two supports
and is loaded midway between the supports with a loading nose [2]. The specimen
is then deflected until either rupture occurs or a maximum strain of 5% is reached,
whichever occurs first [2]. From this test, material properties such as flexural stress,
strength, strain, and modulus and modulus of rupture can be calculated [2]. This
data can be useful for quality control and specification purposes [2], and, in wooden
samples, instigating the effect of parameters that might influence the properties of
the material, such as moisture content, temperature, knot size and location, or slope
of the grain [3].
The objective of this experiment is to conduct a flexural test, using the 3-point
bend test method, on wooden beam and composite specimens and determine the
flexural strength, maximum shear stress at failure, flexural strain at failure, modulus
of rupture, and flexural modulus. The materials of the three specimen used in this
experiment will be basswood, a glass fiber nylon composite, and a carbon fiber nylon
composite.
Before the 3-point bend test was performed, a hypothesis was formed regarding the
flexural modulus of the materials. The flexural modulus, also call the modulus of
elasticity in bending, is the ratio, within the elastic limit, of stress to corresponding
strain. Based on available data on the materials, the material with the highest flexural
modulus will be the carbon fiber nylon composite [4], followed by the basswood [5],
followed by the glass fiber nylon composite with the lowest flexural modulus [6] .
1
Experimental Methods
Materials
The materials utilized in this flexural test were a glass fiber nylon composite, a carbon
fiber nylon composite, and one wooden beam composed of basswood. These specimens
are pictured below in Figure 1.
Figure 1: Labeled specimen used in the experiment.
The initial dimensions of length and width were measured using a Vernier caliper.
The measurements for width and thickness were taken at 3 different points near the
midpoint on each specimen. Next, the specimen dimensions measured were averaged
for approximate dimensions that were the input into the software. All the measurements were taken using mm and are shown in Figure 2 and Table 1 below.
2
Figure 2: Dimensions of the specimen.
Table 1: Average Specimen Dimensions
Dimension (mm)
Carbon Fiber
Glass Fiber
Basswood
Width
Thickness
12.59
3.19
12.56
3.21
9.43
9.43
Testing Methodology
The mechanical test frame utilized for the tensile testing is the Instron 1321 Servohydraulic Test System with a 100kN load cell that was fitted with a 3-point bend test
fixture. A specimen was then centered horizontally on the supports of the 3-point
bend test fixture as exemplified in the Figure 3. The span of the support was 65 mm.
3
Figure 3: Specimen centered on the supports.
Once the specimen was accurately placed, the average dimensions that were previously
measured were then entered into the computer software. The machine was then
turned on to begin the load application of 3mm/min. While the load was applied,
the computer recorded the load and displacement data. The experiment concluded
once the specimen bent and failed. This procedure was repeated for the other two
test specimens.
4
Results and Discussion
Calculation
The data collected from the experiment was formatted into a spreadsheet for each
material specimen recording the load and the amount of elongation experienced by
the specimen at each time step of 0.1 seconds. To compare each material specimen,
the results were used to calculate the bending stress strain curve for each material.
Using the equation below to calculate bending, or flexural, stress:
σf =
3P L
2bd2
(1)
Where σf is the flexural stress, P is the load applied to the specimen measured in
Newtons, L is the support span in mm, b is the width of the beam in mm, and d is
the thickness of the beam in mm. For the Basswood beam specimen, the width and
the thickness were both measured to be 9.43 mm. The value for L, the support span,
was 65 mm. Therefore, using Equation (1) from above for a 50 N applied load, the
flexural stress can be calculated to be 5.81 MPa as seen below.
σf =
3(50)(65)
= 5.81M P a
2(9.43)(9.43)2
(2)
To calculate flexural strain the following equation was used
f =
6Dd
L2
(3)
Where f is flexural strain, D is the deflection or extension measured in mm, L is the
support span in mm, and d is the thickness of the beam in mm. Equation (1) for
bending stress and Equation (3) for bending strain were obtained from source [2] and
were used to produce the stress-strain curve which can be seen in Figure 4.
5
350
300
Carbon Fiber
Fiberglass
Stress (MPa)
250
Basswood
200
150
100
50
0
0
0.02
0.04
0.06
0.08
0.1
0.12
Strain
Figure 4: The bending stress vs strain graph.
From the stress and strain curve, the flexural stress and strain at failure can be
collected. To obtain the maximum shear stress the following equation was used
3P
(4)
4bd
Where P is the applied load in Newtons, b is the width of the beam in mm, and d
is the thickness of the beam in mm. To find the modulus of rupture Equation (5)
was used to first find Mmax , which is required to solve Equation (6) for modulus of
rupture.
Pmax L
Mmax =
(5)
4
Where Mmax is the maximum moment, Pmax is the maximum applied load before
failure in Newtons, and L is the support span in mm. Taking the calculated value for
Mmax , modulus of rupture was found using Equation (6)
τmax =
σ=
Mmax c
I
(6)
Where Mmax is the maximum moment, c is the distance from the neutral axis, and I
is the moment of inertia of the cross-sectional area of the beam. This value of σ, or
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modulus of rupture, was compared to the maximum bending stress for each specimen
seen in Figure 4 and confirmed to be the same value.
The last value calculated for this experiment was the flexural modulus using the
following equation
EB =
L3 m
4bd3
(7)
where EB is the modulus of elasticity in bending or the flexural modulus, L is the
support span in mm, m is the slope of the linear section of the stress strain curve, b
is the width of the beam in mm, and d is the thickness in mm. The calculated values
can be found in Table 2.
Table 2: Calculated Result Values
Values and Units
Glass Fiber
Carbon Fiber
Basswood
Maximum Shear Stress (MPa)
Flexual Strain at Failure (mm/mm)
Modulus of Rupture (MPa)
Flexural Modulus (MPa)
Standard Deviation of Stress (MPa)
Standard Deviation of Strain (MPa)
5.51
0.0254
223.19
1532929
72.68
0.0080
7.80
0.0207
318.06
2745621
99.59
0.0069
3.06
0.0680
42.13
5197.99
11.86
0.033
The standard deviations for stress and strain were calculated using Equation (8) from
source [2]
s
s=
(ΣX 2 − nX̂ 2 )
(n − 1)
(8)
where s is the estimated standard deviation, X is the value at a single point, n is the
number of data points being considered, and X̂ is the mean of values in the set of
points. This equation can be used to find the standard deviation for any calculated
values within a larger data set.
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Discussion and Errors
The material with the highest flexural modulus was the carbon fiber composite followed by the glass fiber composite. The basswood had the lowest flexural modulus.
This differs from the hypothesis developed at the beginning of the experiment in
that the hypothesis conjectured that the glass fiber would have the lowest flexural
modulus instead of the basswood. One possible source of error were the calculations
conducted using the raw data. The equations that were used came from the ASTM
D790 (Source [2]) which is the standard test methods for flexural properties of unreinforced and reinforced plastics and electrical insulating materials. This could have
contributed to the significantly lower flexural modulus for the basswood because it is
a wood which is neither a plastic nor an electrical insulating material.
The physical flexural response of all three materials was similar. The carbon fiber
composite, the glass fiber composite, and the basswood all warped under the stress
of the load until they reached their yielding point, where they then experienced a
fracture at the point the load was being applied as exemplified in Figure 5. One
difference between the materials is that the basswood specimen compressed slightly
at the point of the load before beginning to bend.
Figure 5: Fractured materials.
It should also be noted that the calculated values for the modulus of rupture was
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similar in value to the automated result values from the computer generated data.
Meanwhile, the flexural modulus calculated values had a much larger difference in
comparison to the automated result values from the computer generated data. This
error can be attributed to calculation errors resulting from human error or due to the
precision, or lack thereof, of the computer software/testing machine. The automated
result values that were computer generated from the software are listed in Table 3
below.
Table 3: Automated Result Values
Values and Units
Modulus of Rupture (MPa)
Flexural Modulus (MPa)
Glass Fiber Carbon Fiber
226.4
20477
9
318.3
29290
Basswood
43.25
2460
Conclusion
This experiment was conducted to test the flexural strengths of three different material specimens. The three-point bend test was used to calculate the flexural stress and
the flexural strain of each specimen, maximum shear stress at failure, the modulus
of rupture, and the flexural modulus. From these calculations, it was concluded that
the carbon fiber nylon composite had the highest maximum shear stress, modulus
of rupture, and flexural modulus, and the lowest flexural strain at failure while the
basswood had the lowest maximum shear stress, modulus of rupture, and flexural
modulus, and the highest flexural strain at failure.
The hypothesis stated that the material with the highest flexural modulus would be
be the carbon fiber nylon composite, followed by the basswood, followed by the glass
fiber nylon composite. Based on results previously discussed, however, the order was
actually the carbon fiber nylon composite, followed by the glass fiber nylon composite,
followed by the basswood. The reason for this difference is likely due to calculation
errors, quality of lab equipment, or, as previously discussed, the equation used to
solve for the flexural modulus.
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References
[1] “What is Bend Testing?” Instron.
[2] “Standard Test Methods for Flexural Properties of Unreinforced and Reinforced
Plastics and Electrical Insulating Materials,” ASTM International , 2010.
[3] “Standard Test Methods for Mechanical Properties of Lumber and Wood-Base
Structural Material,” ASTM International , 2010.
[4] Plasticomp, “Product Data Sheet for Complet LCF30-PA6,” 2014.
[5] “American Basswood Wood,” MatWeb Material Property Data.
[6] PlastiComp, “Product Data Sheet for Complet LGF30-PA6,” 2014.
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