1. Trimble 1
1. Abstract
The purpose of this lab is to examine the deformation of a rubber band from an applied
load that causes a displacement of about 20 inches. The relationship between stress and strain of
elastic materials is also examined. Important quantities determined are strain, loading/unloading
stress, and the loss of energy due to deformation (the elastic hysteresis). The procedure involves
stretching the rubber band at one inch increments from about 4 to 20 inches. Through the
experiment, it was determined that the rubber band undergoes considerable deformation due to
the breaking of weak, intermolecular secondary bonds between the polymer chains inside of the
rubber band. The stiff covalent bonds within the polymer chains are also stretched at larger
displacements once they are untangled, but this effort proves futile since these bonds recover
once the band is unloaded. However, the secondary bonds do not reform to a large extent since
the rubber band does not return quite to its original length. It also found in this experiment that
rubber bands initially have a small amount of stress for considerable deformation (strain), but
this switches once the band is pulled with a great displacement. Through this experiment, it is
proven that rubber is not a perfectly elastic material contrary to popular belief and undergoes
some deformation.
2. Introduction
The objective of this experiment is to determine strain and loading/unloading stress of a
rubber band being stretched and released while also determining the elastic hysteresis (the
energy dissipated per unit volume during the deformation process) of the band. The purpose of
this experiment is to show how most real-world materials are not perfectly elastic and how strain
and stress are related in elastic materials. A rubber band is made up of rubber which is a

2. Trimble 2
polymer. In a rubber band at rest, there are many long polymer chains tangled up. The force from
the initial stretching of the band goes into uncoiling these chains. Further stretching of the band
exerts force on the stronger covalent bonds inside of the polymer chains (Askeland, D.R., The
Science and Design of Engineering Materials). This indicates a higher elastic modulus (a
measure of stiffness or the slope of the strain vs. stress diagram). Due to molecules being
untangled initially during the stretching of the band, the force the band exerts will be much less
when it returns back to its original position. This means that only the strain will be reproduced
on the return trip while the stress (from force) will be less. The difference between the loading
and unloading curves on the displacement-position graph should represent the work that was
done to untangle the polymers in the band during initial stretching. The equation for engineering
strain is:
𝜺 =
𝒍−𝒍 𝒐
𝒍 𝒐
=
𝜟𝒍
𝒍 𝒐
(1)
where ε is the engineering strain at each stretch point, l is the length of the elastic band at each
stretch point, lo is the original (reference) length, and 𝛥l is the displacement in length. On the
other hand, the equation for engineering stress is:
𝝈 =
𝑭
𝑨 𝒐
(2)
where 𝝈 is the engineering stress, F is the applied axial force (divided between the two strands of
the band in this lab), and Ao is the original cross-sectional area of the loaded member.
In this lab, a rubber band is stretched to about 20 inches and released while recording the
force in one inch increments. This process must be done at a constant rate in order to not have
jumping results. The displacement of the band is recorded, and from this engineering strain and
stress are calculated. The experiment is performed as a group, but the analysis is individual.

3. Trimble 3
3. Procedures
The materials for this lab are a 3.5 inch long rubber band of size # 64 and dimensions
0.194 inch in width and 0.008 inch thick (both strands), a ruler, a 3 inch C-clamp, a 2 x 1 x 30
inches mounting board with a bolt one inch from the end, a sturdy bench to clamp onto, safety
goggles, work gloves (not used), a load scale for up to 50 pounds, and a caliper for
measurements under a quarter of an inch. For the procedure (performed as a group), the first
action taken was to clamp the mounting board on a work bench using a C-clamp near the bolt
end. Second, a yard stick was used to verify that the tick marks on the mounting board are at one
inch increments starting at the bolt center at zero. Third, the thickness and width of the band
were measured using the caliper. With this, the cross-sectional area was computed. Fourth, the
initial (reference) length of the elastic band was recorded and the remaining data of the
experiment was recorded into a data table with columns for current length, change in length,
engineering strain, loading force, unloading force, loading stress, and unloading stress. Fifth, the
elastic band was put over the bolt and through the hook of the load scale. Next, the band started
to be stretched from the four inch mark in one inch increments at a constant rate. The loading
forces were recorded and stretching continued until a deflection of 20 inches without unloading.
Then, the first unloading force was recorded as the last unloading force. Last, unloading force
data was recorded in one inch increments until the original length was restored. The main safety
precaution for this lab was for the group members to wear safety glasses in order to protect the
eyes in case an elastic band broke when overstretched or accidentally unloaded.

4. Trimble 4
4. Results
From this experiment, it was expected that the unloading curve would exert less force
than the loading curve which turned out to be true. The elastic modulus (measure of stiffness)
was also expected to be higher for additional stretching. This can be shown when taking the
slope of the strain vs. stress diagram at different points. For example, the elastic modulus for
some earlier points measured to be 1.12x103 psi while that for some latter points measured to be
7.59x103 psi. This shows a great change in slope and hence stiffness in the band. When
beginning the experiment, the initial computations/measurements were 0.194 inches for the
elastic band width, 0.008 in. for the thickness of both strands, 1.55x10-3 in.2 for the original
cross-sectional area of the band, and 3.50 in. for the original length. Using the trapezoidal
method for integration, it was found out that the area under the loading curve for the
displacement (m) vs. load (N) graph was 16.23 J while the area under the unloading curve was
8.43 J. The difference between these areas represents the work done to unwind the polymer
chains in the rubber band which came out to be 7.80 J. In the table on the next page, the data
collected for stretching the rubber band every inch for loading and unloading is shown including
the current length, the displacement from the original rubber band length, the engineering strain,
the loading force, the unloading force, the loading stress, and the unloading stress. The unloading
forces and stresses were considerably lower than the loading ones.

5. Trimble 5
l
(in.)
𝛥l
(in.)
ε
(in./in.)
"Loading"
Force (lb.)
"Unloading"
Force (lb.)
"Loading"
Stress (psi)
"Unloading"
Stress (psi)
3.50 0.0 0.0 0.0 0.0 0.0 0.0
4.00 0.50 0.14 1.50 0.0 966 0.0
5.00 1.50 0.43 2.00 1.25 1.29x103 805
6.00 2.50 0.71 2.50 1.50 1.61x103 966
7.00 3.50 1.00 2.75 2.00 1.77x103 1.29x103
8.00 4.50 1.29 3.00 2.25 1.93x103 1.45x103
9.00 5.50 1.57 3.25 2.40 2.09x103 1.55x103
10.00 6.50 1.86 3.50 2.50 2.26x103 1.61x103
11.00 7.50 2.14 3.75 2.50 2.42x103 1.61x103
12.00 8.50 2.43 4.25 2.50 2.74x103 1.61x103
13.00 9.50 2.71 4.75 2.50 3.06x103 1.61x103
14.00 10.50 3.00 5.25 2.60 3.38x103 1.68x103
15.00 11.50 3.29 5.75 2.75 3.70x103 1.77x103
16.00 12.50 3.57 6.50 2.90 4.19x103 1.87x103
17.00 13.50 3.86 7.00 3.00 4.51x103 1.93x103
18.00 14.50 4.14 8.50 3.25 5.48x103 2.09x103
19.00 15.50 4.43 10.00 3.50 6.44x103 2.26x103
20.00 16.50 4.71 12.00 4.00 7.73x103 2.58x103
21.00 17.50 5.00 12.50 4.50 8.05x103 2.90x103
22.00 18.50 5.29 16.50 6.50 1.06x104 4.19x103
23.00 19.50 5.57 17.50 11.50 1.13x104 7.41x103
24.00 20.50 5.86 21.00 21.00 1.35x104 1.35x104
Table 1. Data collected from the elastic band experiment include (left to right by column) the
current length, the displacement from the original position, the engineering strain, the loading
force, the unloading force, the loading stress, and the unloading stress.

6. Trimble 6
In the figure below, displacement vs. the load of the rubber band for every one inch
increment is plotted. The load on the unloading curve (red) was substantially than that for
loading (blue), indicating that some of the elasticity of the band was lost in the work done to
uncoil the polymers.
Figure 1. Plot of the displacement of the rubber band vs. its load. Notice the significant
reduction in force for unloading.
In the figure below, strain vs. stress in the rubber band is plotted. As before, less force
and hence stress is experienced in the unloading curve. In general, the slope increases for
additional stretching of the band, representing the stiffness or elastic modulus.
-5
0
5
10
15
20
25
0 5 10 15 20 25
Load(lb.)
Displacement (in.)
Loading For Change in Displacement
(standard)
Loading
Unloading

7. Trimble 7
Figure 2. Plot of strain vs. stress experienced by the rubber band. Notice the significant
reduction in stress for the unloading curve.
5. Discussion
When beginning the stretching of the rubber band, the rubber polymer chains are initially
uncoiling, causing great strain for relatively little stress. Most of the force applied goes solely
into this. However, additional stretching of the rubber band leads to the opposite condition, or a
lot of stress for very little strain because eventually the polymer chains become untangled and
only the covalent bonds within the polymer chains are stretched. The covalent bonds are very
strongly held together in comparison, causing a lot of stress for very little deformation.
According to the strain vs. stress graph (Figure 2), the uncoiling part of the loading curve has a
low (1.12x103 psi) modulus of elasticity (a measure of stiffness which is the slope of the curve)
while the stretching of the polymer carbon chain has a higher (7.59x103 psi) one. This changing
slope represents the increased difficulty to stretch the band after the molecules have been
untangled (Askeland, D.R., The Science and Design of Engineering Materials). It can also be
-2000
0
2000
4000
6000
8000
10000
12000
14000
16000
0 2 4 6 8
Stress(psi)
Strain (in./in.)
Elastic Band Strain vs. Stress
Loading
Unloading

8. Trimble 8
shown that elastic bands are not perfectly elastic since the unloading curve of the strain vs. stress
graph has stress values decrease dramatically fast in comparison to the strain. This is because the
polymers are untangled and will not resist as much for lower strain values. In other words, the
band will not exert much of a force until higher strain values, so it has deformed. The band has
been stretched, so its original position cannot be recovered.
Although covalent bonds hold the atoms in the rubber polymer strands together, weak
intermolecular secondary bonds are what keeps the polymer molecules tangled up before the
experiment. When the band has been stretched, the secondary bonds do not largely form again
when it is unloaded because these forces were already weak and the band has undergone
deformation. This is similar to pulling a tangled rope. The rope will straighten out and the
covalent bonds will then be stretched (Schoolphysics.co.uk, Web). Once the person lets go, the
covalent bonds will recover, but the rope will not become tangled again. As shown in Table 1,
there is a strain value that has 0 stress for unloading but nonzero stress for loading. This means
the band has deformed and will not return quite to its initial position.
When looking at the displacement vs. load graph (Figure 1), the area under the two
curves represent energy which is significantly less for the unloading curve. This means that work
was done and energy was lost. The areas under the curves were found out (using a different
metric figure) to be 16.23 J for loading and 8.43 J for unloading. The difference (the elastic
hysteresis), which represents work done and energy lost, came out to be 7.80 J. This work was
done on the secondary bonds that kept the rubber band polymer chains tangled up initially. Once
these chains were untangled, they could not be restored. On the other hand, the covalent bonds
were restored because these were stronger.

9. Trimble 9
Few errors probably occurred in this experiment. One possible error was measuring the
thickness of the rubber band because this measurement is very tiny. An error in this would make
the cross-sectional area and stress calculations slightly off, but that is relatively unimportant here
because only trends are being examined.
From this experiment, the findings suggest that rubber is not a perfectly elastic material
contrary to popular belief.
6. Conclusion
In this lab, a rubber band was stretched and released in one inch increments while
measuring the force and displacement. These values were later used to determine the engineering
stress and strain for the points as well as the change in energy and the elastic modulus. It was
concluded that the rubber band has undergone considerable deformation from the initial load
applied onto the rubber band that untangled the rubber polymer chains. The energy lost with this
deformation is the elastic hysteresis which was found out to be 7.80 J. The experiment also
showed that the band was at rest for a larger deformation value. In general, there is more stress
and less deformation when stretching a rubber band.

10. Trimble 10
7. Appendices
Figure 3. Plot of the displacement of the rubber band vs. its load in metric units. Notice the
significant reduction in force for unloading.
-20
0
20
40
60
80
100
0 0.1 0.2 0.3 0.4 0.5 0.6
Load(N)
Displacement (m)
Loading for Change in Displacement
(Metric)
Loading
Unloading