Tensile Testing

Objectives

This experiment is intended to explore the stress-strain behavior of ductile metals subject to tensile loads and to introduce transducers that are used in mechanical testing. The tensile test is the most basic structural test of a material and is used to characterize its response to structural loads. The characterization data obtained from a tensile test is used directly for structural analysis and design. This experiment requires the use of several mechanical transducers that are used to measure the elongation of an aluminum specimen and the force applied by a load frame. As part of this lab, you will also be exposed to the physical principles that are used in these devices. Two tests will be performed: (1) a monotonic loading where the specimen will be gradually loaded until failure to observe the full stress-strain response, (2) a cyclic loading where a second specimen will be repeatedly loaded and unloaded until failure to observe elastic versus inelastic behavior.

Safety

Wear close-toed shoes in the lab to avoid injuries to your feet if you drop lab equipment, and the eye protection glasses supplied to you. This experiment also involves the use of chemical adhesives and solvents; so make sure to wash your hands after performing the lab.

Background

Stress and Strain

A tensile test is designed to experimentally characterize the relationship between stress and strain. Stress and strain are fundamental concepts in the study of mechanics of materials and we briefly summarize them here.

Stress is a measure of the intensity of a force exerted over an area. In this test, we will measure axial or normal stress. Consider a prismatic bar with a cross-sectional area $A_0$ , loaded at both its ends with opposing forces with magnitude P, the stress in the bar is given by:

\large \sigma = P/A_0

(1)

which is the normal stress. Stress has units of force per unit area, which in SI units are pascals [Pa] and in English units are pounds per square inch [psi]. Since the magnitude of stress can be large, it is common to use units of megapascals [MPa] and ksi (i.e., thousands of psi). Note that during the tensile test, the cross-sectional area of the specimen will change; however, we will continue to normalize the force by the initial area. This is usually referred to as engineering stress.

Strain is a measure of the elongation of the structure per unit length. Given a prismatic bar of initial length $L_0$ and the elongation of the bar, $\delta$ , under load, the normal strain is given by:

\large \varepsilon=\delta/L_0

(2)

Since both $\delta$ and $L_0$ have dimensions of length, strain is a dimensionless quantity. The length of the bar will change during the test, especially at high loads. However, we will always use the initial bar length as a reference.

Tensile Testing Specimens

In this experiment, you will measure the strain in a bar using a strain gauge, and the elongation of the bar under load using an extensometer. These measurement devices are described in a later section.

You will use aluminum that has been machined into a typical material specimen shape, specifically, a dog bone specimen, as shown in Figure 1. The shape of the specimen is designed to produce a uniform tensile stress and tensile strain in the gauge section. If the specimen were to fail outside this region, in either the grip or shoulder areas, then the results from the test could not be used because stress and strain in these regions are not uniform. The dog bone specimen is designed so that we can fasten the test machine to the grips at either end of the specimen to apply an axial load.

Stress-Strain Diagrams and Material Models

In this experiment, you will generate experimental stress-strain diagrams. A sketch of a stress-strain diagram for a generic ductile metal is shown in Figure 2. As engineers, we use mathematical approximations that are designed to model the measured stress-strain response. Thus, we can explore how closely these mathematical models match the measured stress-strain diagram.

Material models can be classified as either elastic or inelastic. An elastic response is one in which the loads on the structure are low enough so that no permanent deformation or damage to the specimen occurs. Once the loads are removed, the specimen returns to its original shape, and the experiment could be repeated to produce the same stress-strain response. An inelastic response is one in which permanent deformation occurs, so that when the specimen is unloaded it returns to a different shape than the original specimen.

The simplest mathematical model of an elastic stress-strain response is Hooke's Law. Hooke postulated a linear relationship between stress and strain, written as follows:

\large \sigma=E\varepsilon

(3)

Here, the proportionality constant, E, is called Young's modulus or the elastic modulus. Note that since the strain is dimensionless, Young's modulus has the same units as stress. Hooke's Law is often a good model for the stress-strain relationship when the stress is below a threshold called the proportional limit, $\sigma_p$ . Some ductile metals have a clearly defined proportional limit, others do not. Beyond the proportional limit, the material may still exhibit an elastic response but the relationship between stress and strain is nonlinear. Another important point on the stress-strain diagram is the yield stress, $\sigma_y$ . Above the yield stress, materials exhibit inelastic behavior where permanent inelastic deformation occurs, even when the load is removed. Again, this is a model of the response of a ductile metal, and some metals have a clearly defined yield point while others do not.

In ductile metals, as the specimen enters the yielding regime it undergoes a large elongation without a large increase in stress. The slope of the stress-strain diagram, called the stiffness, is much smaller than before yielding. As the yielding progresses, metals often exhibit strain hardening (also called work hardening) where the stress increases as the specimen elongates. At some stress, called the ultimate stress, $\sigma_u$ , a neck begins to form in the specimen. In this necking region, the local stress and strain increase beyond the engineering stress and strain normalized by the initial length and area of the specimen. In this region, the stiffness is negative, and the load must be reduced as the specimen elongates further. Finally, the specimen will rupture or fail.

True Stress and Strain

Thus far, we have examined engineering stress and engineering strain, which are force and elongation normalized by the INITIAL geometric properties. In addition, there are also true stress and true strain; they represent the force normalized by the instantaneous area, and the elongation normalized by the instantaneous length.

The true stress and true strain can be evaluated from the engineering quantities under a constant material volume assumption. Assuming a constant volume, such that $A_0L_0=AL$ , we can find the ratio

\large \frac{A_0}{A}=\frac{L}{L_0}=\frac{L_0+\delta}{L_0}=1+\epsilon

By combining the area ratio above with the expression for engineering stress, Eq. (1), the true stress is given by:

\large \sigma_T=\frac{P}{A}=\frac{P}{A_0}\frac{A_0}{A}=\sigma(1+\varepsilon)

(4)

Similarly the true strain can be related to the engineering strain,

\large \varepsilon_T=\int_{L_0}^L\frac{dL}{L}=\ln\left(\frac{L}{L_0}\right)=\ln(1+\varepsilon)

(5)

Note that when the engineering stress and strain are small, then $\sigma_T\approx\sigma$ and $\varepsilon_T\approx\varepsilon$ .

Within the strain hardening regime, ductile materials often satisfy the strain hardening law:

\large \sigma_T=K\varepsilon_{T}^n

(6)

where K is called the strength coefficient, and n is called the strain hardening exponent. On a logarithmic scale, this strain hardening law becomes linear:

\large \ln\sigma_T=\ln K+n\ln \varepsilon_T

(7)

Plotting the logarithm of the true stress and true strain for the entire loading history produces a piecewise linear curve, where the first curve is from the linear elastic regime, that is,

\large \ln\sigma_T=\ln E+\ln\varepsilon_T

(8)

and the second is from the strain hardening regime. An example of a log-log diagram for true stress and true strain is shown in Figure 3. The y-intercept is $\ln K$ and the slope in the strain hardening regime is n.

Tensile Testing Equipment

Load Frame

In this lab, we will use a load frame to apply a tensile load to a coupon of an aluminum alloy. The load frame in our lab is an Instron 5982 (see Figure 4) that is capable of delivering 100 kN of axial force to the specimen for testing purposes. It consists of two columns with a crosshead and a base. The crosshead moves up and down the columns driven by lead screws. The crosshead is attached to a load cell, which measures the force applied to the specimen. The test specimen is fastened between two test fixtures attached through pin joints to the base of the frame and the load cell/crosshead. The pin joints ensure that no moments are transmitted to the test specimen.

The load frame controller can operate in either displacement-control mode or a force control mode. In load control mode, the load frame applies a commanded load and measures the extension. Under displacement control, the controller measures the applied force through the load cell and finds the force required to produce the specified displacement. For this experiment, you will use displacement control to measure the full response of the specimen up to the point of rupture or failure.

Strain Gauge

A strain gauge is a device that is used to measure the strain at the surface of a structure. The gauge consists of a thin conductive metal foil grid pattern that is mounted on a flexible backing (see Figure 5).

The backing is then bonded with an adhesive to the test specimen. The strain gauge measurement is determined by the change in resistance of a current passing through the gauge. This change in resistance is proportional to the strain through the gauge factor, $S_g$ , which is provided by the manufacturer. The strain is then measured as:

\large S_g=\frac{1}{\varepsilon}\frac{\Delta R}{R}\Rightarrow\varepsilon=\frac{1}{S_g}\frac{\Delta R}{R}

(9)

where $\Delta R$ is the change in resistance. The gauge factor for many gauges is about 2, however, each gauge may have a slightly different gauge factor and it is therefore important to note this factor in your notes during the experiment. The ratio of the change in resistance to the initial resistance, $\Delta R/R$ , is measured using the Wheatstone bridge circuit. The details of the analysis of this circuit are straightforward but beyond the scope of this lab. In our lab, the resistance of the strain gauge is measured by the Strain Gauge Bridge Completion Box. You will input the gauge factor into the system which will output the strain directly for later data analysis.

Before beginning the structural test, you will first bond the pre-wired linear strain gauge to the specimen. The quality of the bond between the strain gauge and specimen has a direct impact on the quality of the strain measurements. Achieving a good bond between the strain gauge and the specimen requires careful surface preparation while avoiding contamination. Surfaces that have not been thoroughly cleaned must be treated as if they are contaminated. Touching the strain gauge contaminates it and can lead to poor bond quality. Therefore before bonding the strain gauge to the specimen, the surface of the specimen must be prepared.

Extensometer

The extensometer is a linear variable differential transformer (LVDT) that measures the relative displacement between two points on the specimen. As shown in Figure 6, the LVDT is attached to the specimen using arms that are attached to the body of the extensometer. In the lab, you must measure the initial distance between the attachment points on the specimen.

The LVDT is a transducer that measures the displacement using the principle of induction. The LVDT consists of a central primary coil and two secondary coils wired in sequence within an assembly with a movable internal core. An AC current is passed through the primary coil while the induced current is measured in the secondary coils. The secondary coils are wound in opposite directions on either side of the primary coil. The movable core within the assembly is attached to the object whose displacement is being measured. An AC current in the primary coil induces an AC current in the second coil that depends on the relative displacement of the core. The displacement of the core within the LVDT can be estimated by measuring the output AC signal relative to the input signal. An advantage of the LVDT is that it experiences little wear during use and is very robust. In addition, the LVDT can have a high resolution of the displacement.

Load Cell

A load cell is a transducer that is used to measure force. Most load cells are made from an arrangement of strain gauges on a load carrying material with known material properties. The strain gauges are arranged to reduce the sensitivity of the measurement. In subsequent labs, we will see a load cell used to measure forces on an airfoil in a wind tunnel. These instruments and transducers for measuring the stress-strain data are connected as shown in Figure 7.

Pre-Lab Preparation

Before coming to lab:

Read this lab manual thoroughly
~~Watch the following online Vishay Precision Group videos about surface preparation and strain gauge bonding.~~ (Not Needed Fall 2024-Present)
1. ~~Surface preparation:~~ ~~https://youtu.be/a5n4wHYThCc~~
2. ~~Strain gauge bonding:~~ ~~https://youtu.be/SjXpF61HRys~~
~~Read the MicroMeasurements strain gauge application technical bulletin below.~~ (Not Needed Fall 2024-Present)

259KB

MicroMeasurements Strain Gauge Application

pdf

Procedure

Specimen Preparation

Gather your materials
1. Obtain 2 dogbone test specimens from the TAs.
  1. One of these will be Aluminum 2024-T3
  2. The other will be a "mystery material" specimen
Determine the test specimen dimensions
1. Using the ruler and calipers provided, measure the length, width, and thickness of the reduced section of the test specimen.
  1. The reduced section is the section of the specimen that is narrower
    Do NOT include the transition region of the specimen (the region where the cross sectional area is getting smaller). See the figure below for reference.
    Have multiple members of your group perform this measurement so you can compare and converge on the correct dimensions.
2. A further dimension you need to know is the specimen gauge length $(L_0)$ , which in this case corresponds to the initial separation of the extensometer (knife edges). The gauge length for our extensometer is 2 inches. This corresponds to the "gauge section" in the above image.
3. Note: The dog bone specimens are manufactured in the AE Machine Shop using the CNC (computer numerical control) waterjet cutter and geometry defined by a CAD (computer aided design) file. The dimensions can be determined from the CAD file directly. However, machining imperfections can result in varying geometry so it's always best to verify accurate dimensions post-fabrication.

Monotonic Loading Test

!!! SAFETY WARNING !!! DO NOT OPERATE THE INSTRON UNLESS THE TAs GIVE YOU THE GO AHEAD AND EVERYONE IS CLEAR OF THE FRAME Extremely large forces are generated even with small displacements so it's very easy to cause damage or injury. Make sure everyone is wearing the appropriate PPE during execution of the lab.

In this test, continuous load and strain data will be acquired by the system while it automatically loads a test specimen in tension until it fails. Load will be applied to the specimen by traversing the crosshead upwards at a rate of 0.15 inches per minute. Strain data will be acquired from an extensometer that is clipped onto the test specimen.

Prepare the Instron - To operate the Instron it must be powered on and have a successful connection with the Bluehill software on the PC. To do this:
1. Turn on the main power switch on the right hand side of the base of the frame; it will take a minute or so to fully initialize.
2. Turn on the PC connected to the Instron load frame; small button on the back of the PC.
3. Open the Bluehill Universal software. Once it is open, the Instron Machine will connect to the PC (you will hear a click/pop) and you'll see the control panel on the Instron displaying position/load values.
Open the appropriate testing method - Go to Bluehill and configure the following items:
1. In Bluehill, Click Test and select Browse Methods under "New Sample"
2. Navigate to the current folder: C:\Users\Public\Documents\Instron\Bluehill Universal\Templates\AE_Labs\AE2610\<Semester Year> and open the "AE2610_Monotonic.im_tens" method
3. Once the sample is ready for testing, select OK. There is no need to set any travel limits as they have already been set for you.
  1. If you see any errors thrown during this part of the process, there is a method error or a connection error. If an error persists, call the Head TA or the Lab Manager.
  2. DO NOT edit the method or fix Instron connections on your own!
4. Your screen should appear as follows:
Input calibration parameters and calibrate transducers - Open the system details box by clicking the button in the top-right corner of the screen (right of the Extensometer reading and below the close software button)
1. On the top right of the system details screen, click the extensometer transducer icon under system settings.
2. On the extensometer, there are two knobs (one on each arm of the extensometer). One knob has a cone and the other has a dimple. Gently press the cone into the dimple such that the arms of the extensometer do not move. What this process does is ensure that you are now holding the knife edges exactly 2 inches apart, which is the gauge length of this particular extensometer. See the images below for reference.
  1. Cone:
  2. Dimple:
  3. Pressing Cone into Dimple:
  4. How you should now be holding the extensometer:
3. Input the parameters as follows:
  1. Gauge Length: 2 in
  2. Calibration type = Automatic
  3. Click Calibrate and OK
  4. Once calibration is complete, click Close
4. Close the System details window if the transducer calibrated properly
  1. If the calibration fails, check the wiring - usually it fails when there is an open circuit which can come from a faulty connection
  2. Note: If the transducer icon turns gray, it means that the transducer did not calibrate properly
Install the test specimen in the Instron - With the assistance of your TAs, carefully mount, align, and clamp your test specimen into the the grips of the Instron.
1. If the Tensile Grips are not already installed in the machine, aid your TA in mounting the Grip attachments to the Instron load frame.
2. Traverse the crosshead up/down to the needed crosshead height. It should be at a height at which you can grip both ends of the dogbone specimen.
  1. Note: Be careful when jogging the Instron up/down. Take care not to pinch your fingers or bend the specimen. The crosshead applies A LOT of load with very little displacement! Use the fine position dial if needed.
3. Mount your specimen. Ensure that your specimen is square to the jaws of the instron. If it is not, you will be loading the specimen at an angle.
4. Tighten both grips such that they are gripping the dogbone specimen securely.
Install the extensometer
1. Verify the extensometer is working correctly by observing the live display of extensometer strain while carefully moving the knife edges manually. If there are any issues, have the TAs call the Head TA or the Lab Manager to help debug.
2. On the extensometer, gently press the cone into the dimple such that the arms of the extensometer do not move (same process as above).
3. Mount the extensometer in the center of the test specimen's necked region ensuring that the knife edges are not moved from their 2 inch gauge length.
4. If either knife edge of the extensometer is loose and does not grip to the dogbone specimen, inform your TA. They will fix this.
Run the test
1. Ensure everyone and everything is clear of the Instron and everyone is wearing the appropriate PPE. Ensure that the blast door is closed.
2. On the bottom of the screen, click Balance All and Zero Displacement- this zeroes all values. Observe the 4 live readings at the top of the screen to ensure everything is essentially zero.
  1. If you start to see drift in your extensometer reading, ensure that the knife edges are not sliding down the neck of the dogbone specimen; You may need to slightly adjust where the extensometer is clamped. If the issue persists, call the Head TA or Lab Manager.
3. When you are ready, hit Start.
4. During the test, observe the force-strain plots for the extensometer (bottom plot) as the Instron's crosshead traverses upwards. Discuss anything of interest that you see occurring.
5. Note: If at any point during the test you or the TAs see something going wrong, click Stop in Bluehill. If this does not work, hit the E-Stop button on the right pillar of the Instron Machine.
At the end of the test
1. Once the specimen fails, Bluehill will automatically stop the crosshead.
2. Select the "Export options" button on the top right of the screen under the Extensometer live display. Select "Export to Monotonic.csv" from the drop down menu
3. Verify the data output file - In Windows Explorer, navigate to C:\Users\Public\Documents\Instron\Bluehill Universal\Templates\AE_Labs\AE2610\<Semester Year>
  1. Open the "Monotonic-1.csv" file containing your raw data in Notepad
  2. Ensure your data is present and accounted for; scroll through the data and look at the numbers to make sure all the data is present and accurate. Don't simply open and close the file!
  3. Close the csv file and rename it to "Monotonic_Axx" with "xx" being your section number
  4. Open the "Section Data" Folder and create a new folder with your section number (e.g. A14). Cut and paste the "Monotonic_Axx.csv" file into your sections folder
4. Remove the extensometer from the broken test specimen and remove the specimen from the Instron jaws.
5. Measure the fractured region area - Using the digital caliper provided, measure the cross-sectional dimensions of the specimen's fractured region--the specimen width and thickness exactly where it has fractured.
6. Measure the uniform deformation region area - Using the digital caliper provided, measure the width and thickness of the region adjacent to the final fracture that undergoes uniform deformation (about 1cm away from where it has fractured is a good location to measure this).
7. Measure the final length of the specimen - Place the two parts of the specimen roughly together. Using the ruler provided, measure the length of the reduced section of the specimen.
8. Repeat the experiment if needed - check and discuss your data with the TAs to ensure that the experiment proceeded as expected. If it did not, you may need to run the experiment again.
9. Click the Home button on the top left of the screen on Bluehill. When prompted to save changes to the sample, click No. If you are prompted to save changes to the method (you shouldn't get this prompt!), click No.
REPEAT THE ENTIRE SPECIMEN PREPARATION AND MONOTONIC TEST PROCEDURE WITH THE MYSTERY SPECIMEN

Data To Be Taken

Reduced section dimensions of both specimens:
1. Length, width, and thickness of the specimen before testing
2. Width and thickness of the fracture region after failure
3. Width and thickness of the uniformly deformed region after failure
4. Final length after failure
Initial gauge lengths, $L_0$ , for both specimens corresponding to the initial extensometer separation.
Two raw csv data files (one for each of the two) Monotonic Specimens containing:
1. Time
2. Load
3. ~~Strain Gauge Strain~~ (this data will be recorded, but will not be used as of Fall 2024-Present)
4. Extensometer Strain

Data Reduction (Do this for both specimens!)

Compute the engineering stress at each data obtained point based on the load data from the Instron and the initial cross-section area you measured
Using the linear elastic region:
1. Isolate and truncate a segment of the data from this region from each data set
2. Estimate the Young’s modulus
Using the load and strain data, estimate the following for both specimens:
1. Engineering ultimate tensile strength (UTS), in [ksi] and [MPa] from the initial specimen dimensions
2. True ultimate tensile strength, in [ksi] and [MPa] from the uniform deformation region dimensions
3. True fracture stress, (in [ksi] and [MPa]) from your fractured specimen dimensions
4. Engineering fracture stress, (in [ksi] and [MPa]) from the initial specimen dimensions
5. True ultimate tensile strain from extensometer readings
6. Engineering fracture strain from your initial and fractured specimen dimensions
7. True fracture strain from your initial and fractured specimen dimensions
8. True fracture strain from extensometer readings
From the data obtained in the plastic regime, use the procedure explained in the background section to determine the strain hardening index n and strength coefficient K

Results Needed For Data Report

Note: Closely follow the instructions on Canvas for preparation of the Data Report.

A table containing the following values for both specimens:
1. Reduced section length, width, and thickness before testing
2. Fracture region width and thickness after failure
3. Uniform deformation region width and thickness after failure
4. Final length of reduced section after failure
5. Gauge length of extensometer
A single graph of engineering stress vs. strain for the aluminum specimen
1. Plot the stress axis using MPa and the strain axis in microstrain (increments of $10^{-6}$ )
A single graph of engineering stress vs. strain for the mystery specimen
1. Plot the stress axis using MPa and the strain axis in microstrain (increments of $10^{-6}$ )
A table that lists three elastic (Young’s) modulus in both ksi and MPa units
1. Young's modulus estimate of the aluminum specimen
2. Young's modulus estimate of the mystery specimen
3. Published Young's modulus values for the aluminum alloy used in the experiment, which is 2024-T3. You will be responsible for finding a reputable source for this published value!
Two tables (one for each specimen) containing:
1. Engineering ultimate tensile stress in ksi and MPa
2. True ultimate tensile stress in ksi and MPa
3. Engineering fracture stress in ksi and MPa
4. True fracture stress in ksi and MPa
5. True ultimate tensile strain obtained from extensometer
6. True fracture strain from extensometer
7. True fracture strain calculated from dimensions
8. Engineering fracture strain calculated from dimensions
Two graphs (one for each specimen) of the stress vs. extensometer strain for the monotonic specimen with two curves:
1. One curve with the the engineering stress
2. A second curve with the true stress
  1. Plot the true fracture stress and true ultimate tensile stress points calculated above on the same plot. Label these points clearly!
  2. From the start of the plastic region, roughly try to connect the true stress-strain points to create a true stress-strain plot. Try to look up some literature to do this properly!
3. Clearly label the plots in such a way to distinguish between the engineering and true stress curves
4. Plot the stress axis using MPa and the strain axis in microstrain (increments of $10^{-6}$ )
A table of your measured strain hardening index n and strength coefficient K for both specimens
A table with your guess as to what the mystery material is and a justification for your selection. Your options include:
1. 145 Copper
2. 4130 Steel
3. 220 Nickel
4. 110 Copper
5. 510 Bronze
6. Stainless Steel 316
7. 260 Brass
8. Aluminum 7075
9. 353 Brass
10. 17-4 Stainless Steel
11. Inconel 625

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