Modulus of Elasticity and Poisson's Ratio

It will be assumed herein that students have been trained in the use and safety precautions required to operate a universal testing machine.

1. Obtain a rectangular aluminum bar (12 in. x 1 in. x ¼ in.); an aluminum 6061 T6xxx or stronger is recommended. A hole should be drilled about 1 in. from one beam end to serve as a loading point.
2. Mark a location on the beam about 8.0 in. from the center of the hole on the top surface of the beam. Draw alignment marks for the rosette strain gages and make sure that the axes of the rosette are inclined at a small angle (about 10° to 15°) to the longitudinal axis of the beam.
3. Mark a similar location on the bottom surface of the beam. A single strain gage will be installed here and should be aligned with the longitudinal axes of the beam.
4. Measure width (b) and thickness (t) of the bar carefully using calipers. Perform three replicates at three different locations to obtain a good average of the dimensions. From these measurements, calculate the moment of inertia (I) and the distance from the neutral axis to the extreme fiber of the bar (c=t/2).
5. Obtain a rosette strain gage with a sensing grid of approximately ¼ in. long by 1/8 mm wide on each gage and a similar single strain gage. Note the calibration factors (or gage factor) for all the gages.
6. To install the rosette strain gage, first degrease and clean the surface carefully; sand the surface using progressively finer sandpaper until a very smooth surface is obtained; clean the surface with a neutralizer; and glue the strain gage according to the manufacturer's specifications. Allow the glue to cure properly before proceeding.
7. Test the resistance of the gages (typically 120 ohms) and their current leakage to the bar (resistivity, ideally greater than 5 Mohms) before proceeding.
8. Repeat steps 1.5 to 1.7 for the single gage to be installed on the lower surface.
9. Insert the specimen in the cantilever apparatus and secure appropriately.
10. Connect the strain gages to a recording device, such as a Vishay P3 strain indicator. Make sure that the wiring is correct as per the strain indicator instructions and that you know which channel corresponds to each strain gage.
11. Enter the appropriate gage factors for each gage in the indicator.
12. Check the device calibration by inputting a known voltage that will result in a reading of 5000με at a gage factor of 2.00.
13. Record initial load and strains.
14. Slowly apply 9 increments of 1.1 lbs (0.5kg) or similar at the beam end. Pause at every step and allow measurements to stabilize before recording readings.
15. Slowly apply 9 decrements of 1.1 lbs (0.5kg) or similar. Pause at every step and allow measurements to stabilize before recording readings.
16. Disconnect strain gage from strain indicator and turn the indicator off.
17. Plot the strain in the longitudinal gage vs. the strain in the transverse gage. The slope of this line corresponds to Poisson's ratio, v.
18. Determine the slope of the best fit line from the plot of stress vs. longitudinal strain, which is equal to Young's modulus, E.
19. Compare your values of E and v with previously established or published values (in general, there will be a range of values given rather than a single discrete value).