Deformation of Materials
Objectives
The objectives of this laboratory are to:
1. Observe elastic deformation of materials.
2. Introduce the concepts of stress, strain, Young’s modulus Poisson’s ratio.
3. Practice properly citing graphs and tables in written documents.
Load and Deformation
All engineering materials deform under load, but we can look at the problem in two distinct
ways, giving us two experiments for ME 221. In the Deflection of Engineering Structures Lab you
are introduced to deformation in terms of deflection of large scale structures, that is, “real parts”
like beams, floors, and engine parts. That lab introduces you to the topics of linear beam
deflection theory and superposition.
In the Deformation of Materials Lab, you are introduced to deformation of the material
itself on a local scale as the whole part is being loaded. For example, in this lab you will see the
effects of loading on the shape of a grid marked on a “specimen” of rubber sheeting. You will be
introduced the effect of geometry (e.g. the presence of a hole) and the concepts of strain and
stress. These concepts are necessary in understanding why things fail—why they break. This is
why it is almost always a first topic of lecture in an Engineering mechanics class.
Stress, Strain, and Young’s Modulus
Suppose I pull1 on an elastic cord, like a rubber band, with some load and observe how
much the cord stretches. If I pull harder the cord stretches more 2. In addition to how hard I pull on
the cord, this stretching is a function of the length of the cord: given two cords of the same
material, cross sectional area, and applied load, the longer cord will stretch more than the shorter
one. The elongation of each will be proportional to the lengths of the two cords. However, I can
use the initial length of each cord to normalize the deflection and obtain a useful engineering
concept, the normal strain,  , given by Equation 1. Now although the two cords in this example
stretch differently because of their differing lengths, they will show the same strain for the same
load. Note that this quantity is dimensionless—it has no units3.

L
L
(1)
where,
L =the unloaded length, and
L =the deflection, the change in length from the original length, L.
We can also do something similar for the load. Dividing the load, F, by the cross
sectional area, A, we obtain what is called the normal stress,  , as given in Equation 2. It is not
dimensionless, having units of force per unit area (e.g. N/m2, or Pascals, Pa, and pounds per
square foot, or psi). But it likewise gives us a basis for comparing loads in a manner that is similar
to pressure—higher “pressure” puts a material closer to failure. Parts with large cross sectional
area can handle loads with less stress than parts with smaller areas.
In the Deflection of Engineering Structures Lab, the loading was so the part would bend. Here we’re
stretching the material because we’re after a fundamental concept in material properties.
2 That’s Hooke’s Law in action.
1

F
A
(2)
So now what? As already mentioned, stress is like pressure (same units too). Materials
fail when the stress becomes to high. But there is a more to failure than simply breaking. To
discuss it, we’ll begin with a version of Hooke’s Law for stress and strain. For small strains (i.e.
deflections), most materials behave elastically, returning to their original shape when the load is
removed. In cases when this elastic deformation is linear4, the strain and the stress are related by
the relationship given by Equation 3. In this equation, “E” is a unique material property called
Young’s modulus which describes the relative stiffness of the material5. It has the same units as
stress.
(3)
  E
What happens beyond the elastic “region” of the material response depends on the
material. Brittle materials like glass and cast iron simply snap in two. Ductile materials like
aluminum and steel begin to yield, that is, to take permanent deformations. When the load is
removed, the material relaxes some, but remains deformed—the stress exceeded the elastic
limit6. This yield stress, as it is called, is also a material property that can be looked up in a
materials handbook.
In a way, the yield stress is a measure to the strength of the material. However, there is
another important stress value, the ultimate stress, at which the ductile material finally breaks.
Usually this stress is not much higher than the yield stress, say 20% higher. However, while
yielding may begin at strains as low as 0.2%, some materials will continue to deform to very high
strains, making them useful for things such as battleship armor which must absorb a blast without
flying to pieces.
Some materials like plastic and rubber exhibit behavior that is neither brittle nor ductile.
For example, some materials creep; apply a load and wait and the material will be observed to be
slowly continuing to deform as the molecules rearrange themselves.
Poisson’s Ratio
We’ve just talked about strain in the direction of the loading, but there is also a strain
which happens in a direction perpendicular to the load—across the width of the sample, in our
case. You have seen this effect: as you stretch a large rubber band, it becomes longer and more
narrow. Like deflection under load, this happens in all engineering materials.
A French scientist S. D. Poisson observed this effect and noted there was a relationship
that was identifiable as a material property, just as was Young’s modulus. This property is called
Poisson’s Ratio,  (Greek letter “nu”), the ratio of the lateral strain (across the part) to the
longitudinal strain (along the line of action of the load), as given in Equation 4. The negative sign
is a convenience—Poisson’s ratio is almost always a positive number around 0.3. The ratio of the
You sometimes see it multiplied by 100 and called the percent strain, but it’s still dimensionless.
It is linear for just about every metal and substances like ceramic and glass. Some plastics and polymers
will exhibit linearity, but the some others while exhibit nonlinear elasticity.
5 Take the definitions given for stress and strain and put them into Equation 3. Collect terms to make it look
like Hooke’s Law, F  kL , and you’ll have a proof of sorts of the already asserted connection between
length and area with the “stiffness”, k, of an elastic rods.
6 This is why wires remain bent if you flex them too far.
3
4
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two strains is in fact negative because the two strains act with opposite trends: elongation of the
part results in contraction of the width7. The same is true of loads applied in compression.

 lat
 long
(4)
Procedure
A set of specimens with different geometries has been prepared for loading in a device
that attempts to stretch the samples. These specimens are made out a relative firm sheet rubber
so that deformations can be visually observed and measured with simple instruments such as
calipers and a ruler. Lines have been drawn on the samples to facilitate analysis of deformation
throughout the entire piece.
One end of the specimen is attached to a spring scale. The other end is indirectly
attached to a hydraulic jack which you will operate. The procedure for stretching the specimens is
outlined below.
Safety
BECAUSE OF THE LIKELIHOOD OF THINGS BREAKING, EVERYONE IS REQUIRED
TO WEAR SAFETY GOGGLES IN THE LAB WHILE ANYONE IS TESTING A SAMPLE ON
ANY OF THE MACHINES.
Bullet-Hole Specimens
Apply just enough load to take the slack out of the specimen. If the specimen appears to
be clamped crooked, take a moment to adjust it. Measure the following:


The height and width of the hole
The width of the material next to the hole
Now increase the load by 30, 60 and then 90 lbs above the baseline load required to take
the slack out, measuring and recording the above dimensions. Pay attention to shape of the
specimen as the load is increased. Finally increase the load until the specimen begins to fail. Note
the where the failure occurs and what you see.
Dog Bone Specimens
After removing the slack and adjusting the specimen, you will increase the load by 20, 40,
60 and 80 pounds above baseline. Your measurements are as follows:


At baseline and 80 pounds above baseline, measure the height of one inch high
squares along the length of the specimen. The specimens are marked with a halfinch grid, so take a moment to mark out the one-inch grid you’ll follow for your
measurements. Also, before applying the additional loads, measure and record the
width of the specimen at the middle of each square (don’t do this for the other loads).
For baseline and all loads, measure the length of a group of squares in the middle of
the specimen, e.g. about 3” long and the width of the specimen at this section.
Assignment
You are not writing a report, or even part of a report for this assignment. Just write a few
sentences or paragraphs that answer the questions posted further below. You are to create the
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A few materials such as composites and some plastics do exhibit a negative Poisson ratio, but they are
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following plots and tables and use them in your discussion which answers those questions. There
may be other plots you make in class as part of understanding the material, but that will not be
turned in.
Plots
1. For the dog bone specimen, plot in one figure the strain observed at each 1” square
along the length of the specimen for both applied loads.
2. For the dog bone specimen, we expect the normal stress and longitudinal strain at the
squares in the “middle section” should follow Equation 3. Plot the stress versus strain
for the group of squares in the middle section at baseline and the four loads. Add a
trend line through the group of points you get, but note you might have to “ignore” the
baseline data point. The slope of this line is Young’s modulus for the material.
3. For the bullet hole specimen, create a table of the width and height of the hole.
For your information, other plots you may make in class include the following:
1. A plot of longitudinal strain (change in length) versus lateral strain (change in width)
for the middle section of the dog bone specimen.
2. A plot of average stress across the specimen at each square for the 80 pound load.
Questions
Write a few paragraphs that address the following questions and cite the table and plots
you have made. Of course, the order in which you answer the questions may vary—don’t just
follow the list above without a thought to what reads well. The results are to be well formatted,
following the guidelines set by assignments to date.
1. For the dog bone specimen, what did you observe happening to the blocks along the
length of the specimen? (Remember, use the plot when answering this question, but
also describe what you see in terms of the average stress at each block.
2. What were the Young’s modulus and Poisson’s ratio for this material? In about one
sentence or two tell us how these were determined. The key word here is “slope”.
(This would probably fit in the same paragraph as the answer to question 1.
Experiment some to see what seems to work well.)
3. How did the accuracy of your measurements affect any of your results? Note that you
plotted stress and strain for each block, but calculated Young’s modulus and
Poisson’s ratio over larger areas—why do you think we had you do that?
4. For the bullet-hole specimen, did the material above and below the hole remain flat
during testing? What happened to the material here and at the edges of the hole as
the load was increased? Discuss what happened in terms of stress and strain. You
might have to consult the dog bone results to properly understand what you saw.
What does this mean for other holes in real parts?
the exceptions.
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