ME 226 Laboratory 1
Mechanical Testing of Materials – The Tensile Test
In this experiment you will be determining Young’s modulus, the yield strength, tensile
strength, fracture stress, elongation, and other properties of several tensile bars using a screw
driven MTS load frame. After testing you will need to make graphs from your data. You will need
various measurements of sample geometry to calculate engineering stress versus engineering
strain to obtain the material properties. Your samples will include an annealed steel sample and a
cold worked steel specimen that have the same composition. Ideally, they were cut from the same
bar stock. However, because of heat treatment, the tensile samples should have quite different
Before coming to lab, read through this handout so that you will know what will be
expected of you in the lab. Each student should answer all the questions on the preliminary
question sheet to be turned in at the beginning of the lab. Each group will write one report by answering the questions at the back of this lab manual. You will receive the lab data as an Excel
file. Please return your floppy disk to Chris or you can use the ME office and turn in your group’s
Lab report at the same time. Reports are due in 1 week.
Timing: This lab takes about one hour. All write-ups are to be quite short (none are to exceed 4
pages excluding the graphs) but accompanied by several graphs on the same plot.
The background for this lab can be found in your ME 226 textbook, Mechanics of
Materials, by Bedford and Liechti and most introductory materials science texts such as
Materials Science and Engineering, by Callister.
Engineering stress is the force per unit (original) area.
Engineering strain is the elongation per unit (original) length. They are represented by the
F?l Engineering Stress, ?* = and Engineering Strain, e = lAoOA Where = original cross sectional area of specimen o
l = original length of the gauge section O
F = applied force
= change in length ?l
Hooke’s law relates these parameters,
?* = E e
where E is Young's modulus. It is implicit here that only axial stresses and strains are of interest.
Note, it is assumed ?* = 0 when e = 0 so that ?* = E e represents the first part of the load displacement curve, a straight line that represents the elastic region with E as the slope.
True stress and true strain differ from engineering stress and strain by referring to the
instantaneous areas and gauge lengths respectively. The symbols for these values are the Greek
letters (in bold here) and :
d l, id ? = True stress = F/A and true strain, i li
l where = instantaneous length of gauge section iA = instantaneous area. i
The strain has the natural logarithm or ln dependence because it is determined from the
instantaneous gauge length. For the instantaneous true strain increment d, we have
dld? = l
and by integration
dld? = lOlO
li? = In l O
234x1x1x1xIn a + x = In a + - + - + - aaaa 234 so that when
lo + ?l? =In = In 1 + e ? el O2-4?For strains of about 1%, the "error" is of order of or 10. Consequently, there is no significant difference in the engineering and true strains when all measurements are of small strains. The true
?stress and strain are also related by the modulus E, = E ε since the modulus is established at a
small strain level where A is approximately equal to A and l is approximately equal to l. i0io
For large strains when there is mainly plastic deformation, the volume of specimens are
approximately conserved. Because of this, the instantaneous area A can be calculated from the itrue strain.
Al = Al Volume = ooii
Or, taking the log derivative, rearranging and separating the differentials
Aloi? = In = In Al io
AThus, = A exp (-?). Note that a tensile true strain followed by an equal compressive true iostrain reproduces the initial length of the specimen. This is not true for engineering strain.
During a tension test, it is desirable to apply forces to the specimen large enough to break it. The grip region must have a large enough area to transmit the force without significant deformation or slipping. Consequently, most specimens have a reduced gauge length and enlarged grip regions. While most material properties are supposed to be specimen geometry and grip independent, there are some weak dependencies. Consequently, there are standard specimen geometries specified by the American Society for Testing Materials (ASTM). ASTM also prescribes test methods so that data reported for design purposes is obtained in a very standardized way. The specimen geometry is usually reported as part of the test results.
Returning to our discussion of the properties, the data you will record is the load vs elongation curve. Since many materials are rate-sensitive, the rate of elongation is controlled during the tensile test by moving one of the grips at a fixed displacement rate relative to the other. Usual
-3testing rates correspond to engineering strain rates of about 10/s where the strain rate represents
how quickly the strain in the gauge length is changing with respect to time. For example, if the
-3specimen had a one inch gauge length, the displacement of the machine is 10inches per second
and the load is recorded on a chart traveling at constant speed, say 1/10 inch per second, then it is
-33-clear that the 10/s strain rate will produce 10 inch displacement in 1/10 inch of chart or 1%
strain in one inch of chart. Chart length and strain are then parametric variables, both dependent on time. This is the simplest way of measuring the load-elongation curve and is the most common. However, the elongation determined in this way also includes the elongation of the grips, the ends of specimen, the load measuring transducer (load cell) and the deflection of everything in the test frame. Typically, the elastic compliance for most test frames, i.e. the elongation outside the gauge length is about 5 to 10 times larger than the elongation inside the gauge length!
Consequently, we cannot measure the elastic modulus from the slope of the load vs elongation curve determined in this way. To make direct measurements of engineering strain, an
extensometer is installed on the specimen that measures displacement within the gauge length. This transducer is designed to produce a linear voltage output with respect to displacement. Since the initial gauge length is fixed, the output is then proportional to the engineering strain. If the load signal (voltage which is proportional to the applied force) and the extensometer signals are plotted using an X-Y plot, the initial slope is then the elastic modulus.
For material stability, the load must increase all the time. The tensile deformation is inhomogeneous and strain is no longer uniform when the load reaches a maximum. Deformation stability is achieved when the specimen hardens during deformation. The result is uniform
elongation. If the hardening rate is too low, an unstable situation called necking develops. To
avoid neck formation, the hardening rate must be faster than the decrease in cross sectional area:
d?dA ? - ?A
V =Al or dV = 0 = Adl + ldANow if the volume remains constant
dldAd? = = - lASubstituting, we have
d? ? ? d?
In this case dF<0 and the sample is unstable. This can be shown as follows:
F? = or F = ?A A
dF = Ad? + ?dA
When the load is maximum, dF = 0
d?Ad? + ?dA = 0 or = ? d?
So the work hardening rate has reached the critical value. As a result the specimen may neck
down and begin local deformation. This occurs at the peak load. To determine the true stress
strain behavior beyond the peak load requires knowledge of the non-uniform geometry of the
neck in both the calculation of strain and the stress distribution. In this region the stress is non-
uniform because the A changes along the tensile bars length. In ductile materials, the true stress at
fracture can be several times the engineering fracture stress.
Most data you will be exposed to are engineering stress and strain unless otherwise specified. If
there is a yield point, namely, a sharp transition between elastic and plastic deformation, yield
stress is defined as the stress at the yield point. If there is a yield drop, there is an upper yield
point and a lower yield point. If the load vs displacement curve is smooth, the material is yielding
at a stress defined at a specific amount of plastic strain. Usually 0.2% permanent strain is used to
define the yield stress. Then the yield stress is so identified as 0.2% yield
the stress where the flow curve first deviates from linearity. This is intrinsically difficult to
measure because it is related to the sensitivity of your instruments. Try to estimate the
proportional limit when you analyze your data. The ultimate tensile strength is the largest
engineering stress achieved during the test to failure. This value has little or no meaning as it
represents the test not a material property. The true strain at this point has some meaning.
The elongation to failure is the permanent engineering strain at fracture determined at zero load.
It does not include elastic strain but does include both uniform strain and the localized, necking,
strain. The elongation to failure is usually stated as percent strain over a given gauge length. The
reduction in area is also a measure of ductility. The true strain at fracture is determined by
measuring the areas of the fractured specimen at the fracture site. Recall using the constant volume approximation that
AO? = In A i
The area under the engineering stress-strain curve is a measure of the energy needed to fracture the specimen. It has units of work/unit volume of the gauge length and it is sometimes referred to as a measure of a material's "toughness." However, the term fracture toughness more commonly refers to the energy required to fracture pre-notched and cracked samples. Although, these two quantities may be related in some extreme instances, this relationship is still unknown to the technical and scientific community.
In this experiment we will use an MTS machine designed to do tensile tests of specimens. The machine has a 11,200 lb. capacity (50.2 kN). It consists of a large heavy-duty test frame with a fixed beam at the bottom, a moving beam (referred to as a crosshead) and a gearbox and very large motor located in its base. The specimen is mounted between two grips, one attached to the fixed beam and the other attached to the moving crosshead. The crosshead beam contains a load cell (which works on the principle of strain gauges). It measures the applied force on the tensile specimen. The movement of the crosshead relative to the fixed beam generates the strain within the specimen and consequently the corresponding load. The gearbox below selects high and low speed ranges for movement of the crosshead.
Next to the test frame is the associated electronics console and computer that uses LabVIEW, a computer software package for controlling experiments and recording data. MTS calls the program Test Works. The program contains the main start/stop controls for testing and the adjustments for the sensitivity of the strain gauge load cell (a strain gauge bridge) as well as a "chart recorder" to read the output of the load cell bridge.
Young's Modulus is measured by adding an extensometer directly to the sample to measure the actual elongation between two given points on the sample and Test Works records a file of the load and engineering strain curve versus time for the region when the extensometer is in place.
3. Experimental procedure:
Review this general description to understand the procedures you will use in this experiment.
You will have Chris Pratt calibrate the instrument and the extensometer for you so that the data collected for this experiment is of high quality. She will help you obtain and understand the details of these adjustments. Be sure you record the gauge length of the extensometer along with the calibrated units for data file that records the extensometer displacement. Also record the selected load and displacement rate settings for the crosshead on the MTS for each individual sample. These settings may vary between samples and will be used to interpret your laboratory data later. Also make sure to avoid hysteresis effects when calibrating the extensometer, Chris will help you understand how to implement these procedures.
Once the instrument is calibrated you are ready to mount the sample and perform the actual test. Measure and record the diameter and lengths of all the samples. Install the first specimen in the grips. Be careful to follow the recommended installation procedures as given by Chris so that no damage occurs to yourself or the test equipment. Be careful to avoid placing any part of your body at a pinch point. The final coupling should be performed by trail and error by slipping the pin in by hand with the machine stopped. Move the crosshead up and down at a very slow speed until
you can do this manually. Zero and calibrate the load cell once the specimen is in place. Do this in Test Works, which can adjust the load cell bridge to match the zero line on the chart. The preliminary calculation that you have done in the preparatory questions should confirm that for the steel samples we should use about 5000 lb. full-scale range for measurement. Install the calibrated extensometer on the specimen. Be sure that it is centered and straight and that it is fully closed. Re-zero the extensometer so the data on the load and displacement versus time data file doesn't require you to remove the local zero offset that was used in calibration.
-3Strain rates on the order of 10/s are reasonable. Strengths are strain rate dependent but it is not
a very strong dependence. Heat treatment and chemical variations may differ for materials so some properties will not reflect the reported textbook values. The shape of the curves, however, remains fundamentally the same. We sometimes test faster than ideal in the interest of finishing the experiment within the time available. Set parameters to the values suggested by Chris.
Observe the specimen. Do not get too close because fracture of the specimen liberates all the stored elastic energy in the specimen. Do you see bands propagating along the steel specimen? These are Luders bands indicating the multiplication and motion of dislocations. They will not be visible unless the specimen is highly polished.
Be sure to record both load and strain vs time so you can obtain load vs strain for the test. After
a few percent strain just before fracture remove the extensometer and then continue the test
recording the load vs. time curve until fracture. Observe the neck formation. Note that it always occurs at the maximum load for ductile tensile tests.
Do this for all of your specimens. Record the conditions for each of your samples.
Report the following qualitative data for each of the samples if it exists:
0.2% yield strength
Upper and lower yield stresses
Strain at ultimate
True strain at fracture
Area strain at fracture
Reduction in area
True fracture stress
In your discussion please address the following:
1. The cold worked steel specimen does not show an upper yield point, the annealed
steel does. How does this effect uniform deformation? After plastically deforming the
sample, would either of these samples show a yield point upon reloading? Why?
2. Calculate the data for your Young's modulus from the load vs strain for both samples.
Test Works also find the in-line spring using load vs crosshead displacement. Which
is how strain is measured after extensometer is removed. Explain how Test Works
reconciles the numbers measured with an in-series spring.
3. When an automobile crashes we want the energy of impact to be expended in
deforming the car rather than the occupants. What material property corresponds to
energy absorption? Clearly, a very strong, brittle material would be a poor choice for
the car body. What about a material with high ductility but low strength? Of the
materials you tested in this experiment, which one would have the best performance as
an absorber? Why? Base your answers on the load vs displacement curves you
measured for these materials. How much better?
4. Can you obtain the true stress vs strain curve for the steel specimen using the load vs
extensometer strain data? Plot this data for the region where this calculation is valid.
Use your Excel data file. Show your equation for relating this data.
5. Plot engineering strain versus engineering stress only up to the ultimate. On the same
graph, plot true stress versus true strain from your data as recorded by Chris. The first
part up to the load maximum should be nearly the same. Are yours? After the
maximum load the meaningless engineering graph should diverge from the true stress
graph comment on why.
6. Mark in red on the strain axis on your graphs where the specimen’s cross sectional
area is not the same along the entire gauge length of the bar. Is the stress the same at
every cross section along the length of the bar in these strain regions? Comment.
EXPERIMENT 1 MECHANICAL TESTING-- TENSILE TEST
1. Does a steel stress strain curve differ from an aluminum curve? How?
2. You will be specifying aluminum wires to be used in construction. What load could the
wire support if its area was 0.035 inches squared? Explain why. Where is your data from? Hint
look in your ME 226 textbook Mechanics of Materials, by Bedford and Liechti in Appendix B-2
3. For a steel sample of the same composition and heat treatment as the unannealed specimen
used in the lab, with a length of 2.25" and a diameter of 0.235" calculate the maximum load you
would expect to have to apply to: fracture the sample. Also estimate the maximum elastic
elongation the sample would experience. Explain. (This has to be done after the lab.)
4. Why do we put an extensometer on the sample rather than just use the extension of the
frame of the MTS as recorded in Test Works? Is the use of the extensometer important in
measuring the elastic modulus?
5. How large should the load cell be if the aluminum wire in #2 was the specimen?