Mechanics of Materials - Poisson's Ratio
Mechanics of Materials - Poisson's Ratio
Mechanics of Materials - Poisson's Ratio
Lab #5
Poisson's Ratio
David Clark
Group C
9/15/2006
Abstract
The purpose of the following experiment is to determine Poisson's ratio for 2024-
T6 aluminum, as well as serve as an outline for the procedure to test various other
materials. Poisson's ratio refers to a characteristic dimensionless number which
accurately predicts the amount of strain experienced in non-parallel directions to an
applied load. To find this value, a cantilever setup was combined with dual strain gages to
record changes in lateral and longitudinal strain. Poisson's ratio for the aluminum
specimen was found to be 0.307, which is less than 1% from the scientifically accepted
0.310.
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Table of Contents
1. Introduction & Background............................................................4
4. Results..........................................................................................9
5. Conclusions...................................................................................9
6. References....................................................................................9
7. Raw Notes...................................................................................10
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1. Introduction & Background
When a material experiences deformation, it not only changes on the axis of the
applied load, but also in the perpendicular direction as well. This is known as Poisson's
effect and can be predicted by Poisson's ratio. For a specimen experiencing a simple
uniaxial load, this ratio is expressed as:
ε lateral
υ=−
ε longitudinal
Equation 1
More complex loading configurations utilize the same principles; however these
setups were not used in the determination of Poisson's ratio in this exercise. These more
advanced conditions are beyond the scope of this lab.
Table 1
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The following experiment determines Poisson's ratio for 2024-T6 aluminum. This
process uses the change in strain from an unloaded to a loaded configuration. The change
in strain for both lateral and longitudinal directions is easily found, however due to the
nature of the instrumentation used, correction must be used. The following form is the
final equation used in this experiment.
ε longitudinal
υ=− ⋅C
ε lateral
Equation 2
where C is the correction factor. For more information and an example of determining
this correction factor, see section 3.
2. Metal beam: In this experiment, 2024-T6 aluminum was tested. The beam
should be fairly rectangular, thin, and long. Specific dimensions are
dependant to the size of the cantilever flexure frame and available weights.
The specimen should be secured in the flexure frame such that an applied force
can be placed opposite of the securing end of the fixture. The strain gage on the top of the
test material should run longitudinally (or parallel to the length) at the same length as a
second strain gage running perpendicularly on the adjacent side.
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Figure 1
Whenever taking a reading from a strain gage, consult the strain gage
measurement device for optimal setup. When this experiment was performed, the
following setup was utilized:
The strain indicator should be initially set to read zero strain for the longitudinal
gage. The indicator should then be set to read the initial strain for the lateral gage. A load
should be placed such that an increase in strain is created. (Note: The load applied should
be verified to be below the yield stress to minimize damage to the specimen and ensure
the integrity of the results.)
Next, the strain indicator should be reconfigured to read the longitudinal gage.
The net change in stress for both gages should be recorded for later calculations.
The following table lists the initial and final strain gage measurements, along with
the net strain.
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Longitudinal (με) Lateral (με)
Undeflected 0 80
Deflected 1645 580
Net Strain 1645 -500
Table 2
The net longitudinal and lateral strain were found by the following equations:
Equation 3
Equation 4
The initial calculation of Poisson's ratio can be found using these two strains.
ε longitudinal − 500
υ=− =− = 0.304µε
ε lateral 1645
Equation 5
The correction factor that appears in equation 2 is found from visual inspection of
the transverse sensitivity correction chart. Kt is supplied by the manufacturer of the strain
gage. This value should be traced up to the 0.304 line on the chart. Since this line is not
graphed, visual estimation must be used.
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Figure 2
The estimated correction factor in this case is 1.01. Inserting this value into
equation 2, the new determination for Poisson's ratio is found in equation 6.
υ=−
( − 500) C =−
( − 500)(1.01) = 0.307
εˆlongitudinal 1645
Equation 6
The scientifically accepted value for Poisson's ratio of 2024-T6 aluminum is:
υ std = 0.31
Equation 7
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The percent error in the calculated ratio can be found using equation 8.
Equation 8
4. Results
Poisson's ratio for the 2024-T6 beam was 0.307. This value has an error of
0.967% from the accepted 0.31.
The main source of error may be in the correction factor for transverse sensitivity.
Since this factor was found by visual inspection of a chart, the actual value is difficult to
determine. Other sources of error include, but are not limited to, imperfections in the
adhesive on the strain gage and resolution of the strain indicator.
5. Conclusions
For most materials that are available in bar form, the following experiment
provides acceptable results. This was reflected in the percent error using aluminum 2024-
T6, which was less than 1% from the accepted value.
6. References
Gilbert, J. A and C. L. Carmen. "Chapter 7 – Poisson's Ratio Flexure Test." MAE/CE 370
– Mechanics of Materials Laboratory Manual. June 2000.
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7. Raw Notes
Figure 3
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Figure 4
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