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Fall 2015 ME 2356 Mechanics of Materials Laboratory

Northeastern University Department of Mechanical and Industrial Engineering

Lab #1: Tension Test Due on Blackboard before normal lab time in week of 10/12

General There are two parts to this lab. You will be divided up into 3-4 small groups (about 5 students per group) for each part. In one part (~20 minutes) you will do a tension test of two different materials on the large Instron testing machine. Data will be collected which you will later analyze and include in your report.

In the second part (~60 minutes) you will use the table-top tension testers to do two tests. Each sub-group (~2 students) will perform their own tension test as the other members of the group observe and help if necessary. The Teaching Assistant will be present but you will perform the test. You will collect this data (from your own test and from other test in your group) and analyze it later as part of your report. Use the “report template” posted on Blackboard to prepare your report.

Tension Test on Instron Machine Procedure:

1. Measure the initial length Lo and initial diameter Do of the specimen. 2. Install the specimen into the “jaws” of the Instron machine. Make sure it is lined up with

the grooves in the jaws. Hand tighten. Tighten the upper jaw first, then the lower jaw to minimize sample deformation.

3. Connect the extensometer, fastening the extensometer on the sample with the clips provided.

4. Set up a tensile test in BlueHill software – the TA will walk you through this. The most important parameter is the strain rate. Consider what should be reasonable for your material (i.e. how much do you expect it to deform before breaking? what strain is that? how long do you want the test to last?) Important steps (you can skip many of the inputs except for the following): • Create Method – Tension Method • Set units – metric • Test control – Make sure to set under ‘Test’ the strain rate, and to tell it when to stop

under ‘End of Test’. Also select the option to ‘remove extensometer during test’ under the ‘strain’ menu. Removing the extensometer mid-test will protect the extensometer from damage when the samples breaks. (The extensometer is rated to go up to 20% strain, but it also can’t be on when the sample breaks. You will need to remove the extensometer after the sample reaches its yield point, which should happen before you reach about 4% or 5% strain.)

 

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• Export – File Setting (make sure you know where you are saving your data); Export raw data (which will save only load, displacement, and extensometer strain (which is strain 1))

5. Make sure your end points are set. This defines when the test will stop. It is a good idea to have an endpoint for fracture and one under the load cell capacity (written on the load cell).

6. Ensure the load cell is balanced and the elongation is zeroed. 7. Set the location and file name to be saved. 8. Run the test until it passes the yield point, which will occur by about 4-5%. Carefully

emove the extensometer. Then continue running the test until the specimen breaks. 9. Remove the sections from the Instron and measure the final length Lf and the final

diameter df. 10. Save the data to a memory stick or email it to yourself.

Notes:

The experimental data will be provided in “ascii-text” form. For the sample you will get:

• The relative displacement of the crossheads, δ = L - Lo • The applied force • The extensometer data. The extensometer will be used to measure the strain directly.

Note that the extensometer can measure strain more precisely, but can only do so when the strain is smaller than 20%, which is enough for our test. Since you will remove the extensometer mid-test, your extensometer data will be valid over the entire range over which they were recorded.

Calculations:

1. Reporting the experimental data: i) The raw data are collected in terms of force, displacement, and strain. Plot the raw force

and deformation data for the sample on the graph. - Label the “x” axis of the graph as “Deformation,” δ.

- Label the “y” axis of the graph as “Force,” F. Indicate the appropriate units and the sample name. Include this plot in your report. Do NOT give the tabulated data in the report. ii) Report the values of Lo, Lf, Do, Df, Ao, Af in a Table, where A0 and Af are the initial and final cross-sections of the specimen, respectively. 2. Plotting the stress-strain, σ-ε, curve: Express the experimental data in terms of engineering stress σ and engineering strain ε. These

quantities (σ and ε ) are what we learned about in class. You will determine engineering strain in two ways. First, use the extensometer data directly. These data will only be valid for low strains, but at low strains, they will give you more accurate results. Second, calculate engineering strain from the displacements of the crossheads, δ, and the original length of the sample. In your plot, include measured curves for both stress vs. extensometer strain and stress vs. engineering strain calculated from the displacements.

 

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In the plot clearly label: a) “x” and “y” axes as strain and stress, respectively, b) the curve for extensometer strain and the curve for strain calculated from the

displacements, and c) the “sample name.”

3. Calculate the following mechanical properties for the sample. Report the results in a table such as Table 1.

i) The Young’s modulus E, by determining the slope of the linear part of the σ-ε curve. (Use the extensometer data to determine the Young’s modulus.)

ii) The Yield Strength σY and the ultimate strength σu for the specimen. Because Aluminum does not have a pronounced yield point, you will need to use the 0.2% offset. Mark and label these points on the graph mentioned above.

iii) The “True Stress” (i.e. force divided by deformed area) in the necked region of the sample just prior to failure. iv) The “Reduction of Area” (R.A.), which is expressed as a percentage of the initial cross

sectional area, i.e. ( )

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v) Calculate the work done on the specimen up to the yield point. (Work done up to the yield point is the integral under the stress-strain curve up to the yield point.) How is this quantity related to the Modulus of Resilience? Recall that the yield point and proportional limit tend to be very close to each other.

5. In the discussion section of the report, indicate the major sources of error and give a brief

description of each.

Table 1. Material properties for the sample tested in this lab

Material Name of Sample Young’s Modulus, E (units) Yield Strength, σY (units) …

 

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Table-Top Tension Tester (PASCO)

The objective of this lab is to find the relationship between tensile normal stress and normal strain for various materials. The table-top stress-strain apparatus stretches (and in some cases breaks) a test coupon while it measures the amount of stretch and force experienced by the test coupon. Software generates a complete plot of stress versus strain, which allows the Young's Modulus, the yield point, the ultimate strength, and the fracture strength to be determined.

Set-Up

You will turn the crank of the Rotary Motion Sensor (Figure 1) slowly in order to stretch the test coupon. For every 360o turn of the crank, the screw advances 1 mm, so the stretch, x, in mm is equal to the angle of rotation (in degrees) divided by 360. Note that the angle through which the crank turns is measured by the Rotary Motion Sensor and is automatically converted into the distance x by the software. (Note that you will need to include one additional calibration factor to make sure that your answers are accurate – see step 3 below.)

 

Figure 1. Stress/Strain Apparatus Assembly

The force is measured by the Force Sensor. However there is a 5-to-1 lever arm mechanical advantage which makes the force applied to the coupon five times the reading of the force sensor. This correction is automatically accounted for by the software.

The tester elements are not perfectly rigid. A calibration has already been done in order to account for the finite stiffness of the tester.

 

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Procedure 1. While monitoring the position in a digits

display in the PASCO Capstone software, turn the crank slowly clockwise. A positive position should be displayed.

2. Make sure that the springs, clamps, washers, and nuts are as shown in Figure 2. Then we need to identify the calibration factor with which we will interpret the results. The real calibration is that for every 360o turn of the crank, the screw advances 1 mm; partial turns result in a partial millimeter of advancement. Due to an anomaly in the current calibration, the systems are currently reporting each 1 mm of advancement as 150 mm of advancement. You will therefore need to divide the measurements of advancement by 150 in order to obtain the correct values.

3. When installing a coupon, loosen the nuts but do not remove them. The coupon should be slid completely under the clamp top on each end (Figure 3). Turn the crank to make room for the coupon so the coupon does not buckle and is straight. Then tighten the nuts with the wrench as much as possible, making that sure the coupon does not twist.

 

Figure 3. Clamping a Coupon

4. Pre-loading a Coupon: This is the procedure you will follow each time a member of your group tests a coupon. You must pre-load the coupon so the initial slack is taken up and the force sensor is zeroed at position zero.

a. In the PASCO Capstone software, set up a Digits display of the Actual Force. b. Turn the crank so the lever bar does not touch the force sensor. Then zero the

force sensor. c. Start recording and turn the crank while watching the digits display of the force.

When the force reaches about 5N, stop recording and press the zero button on the force sensor.

Figure 2. Washer Arrangement

 

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d. Now the apparatus is ready to record the curve for the coupon. You should immediately start recording again and proceed to stretch the coupon over the entire range.

5. Set up a graph of “Material X Stress” vs. “Material X Strain” where X is the material that is being tested, i.e. the material of the test coupon. You will need to know the cross-sectional area and the length of the narrow part of the metal coupons (see section below). Calculate the “Material X Stress” by dividing the force by the cross-sectional area and the “Material X Strain” by dividing the stretch (x) by the length of the uniform portion of the coupon.

6. While recording, slowly turn the crank until the coupon breaks or the maximum stretch is reached. Then stop recording.

7. Name the data run to identify yourself and the type of material that was tested. Save the file on the laptop. It will be sent to you after the lab.

8. Now a different student in your group will install a coupon and repeat steps 4-7 above.

9. Continue the measurements until the group has had a chance to test two coupons of the following specimens: thick brass, thin brass, aluminum, plastic, or polycarbonate. Each student will include both specimens in his or her lab report.

Coupon Dimensions: All of the metal coupons have a length of 80 mm. The cross-sectional area for the thick brass (0.005 in) is 0.506 mm2 whereas all other metal coupons have a cross-sectional area 0.303 mm2. The dimensions for the polycarbonate are 80 mm long and a cross-section area of 1.513 mm2. For the plastic coupons the dimensions are 80 mm long with a cross-section area of 0.977 mm2. Test at least two samples.

Analysis for Each Coupon 1. Select the initial part of the straight slope at the beginning of the stress vs. strain plot. Fit a

straight line to it and find Young's Modulus from the slope.

2. What is the value of the stress at the yield point? 3. What is the maximum tensile strength for this material?

4. What is the maximum percent elongation? 5. Did it break? At what elongation?

6. Use annotations on the graph to identify different regions. Discuss the relationship between stress and strain in these regions.

7. Describe any features that you see that are different for different materials. For instance, what does the transition from the elastic region to the plastic region for look like for each material?

8. Does the coupon that can withstand the greatest force also experience the greatest stress? Explain.

9. Does the coupon that can withstand the greatest force also experience the greatest strain? Explain.