Aero Lab: Sheet Failure
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Transcript of Aero Lab: Sheet Failure
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Statement of Hypothesis:
Under the mode of tensile failure, we predict that the aluminum sheet will be able to withstand 1120
lbs., the aluminum rod will be able to withstand 2209.5 lbs., and the hot-rolled steel rod will be able to
withstand 2705.4 lbs. The hypothesized maximum loads are neatly provided in the following table:
Aluminum Sheet
(2024-T3)
Aluminum Rod (6061-
T6)
Hot-Rolled Steel
(SAE 1020)
Predicted Failure Load 1120 lbs. 2209.5 lbs. 2705.4 lbs.
Pre-Lab Evaluation, Criticism, and Comparison (Differences in Conceptual Approach, any
errors found, and the root cause of those errors):
Differences In Conceptual Approach - For any given laboratory experiment, a team or individual
must filter through a plethora of conceptual approaches before the most efficient and robust
method is found. This is what science would describe as the design phase, however, this
particular experiment required no such design phase because all testing specimens were
provided by the university beforehand. This meant that there was no process of determining
which materials should be tested, what lengths they should have, what shape they should be,
how they should be tested, etc. Since every team member was already on the same page,
the only remaining task was to simply begin the testing of all given materials and record their
respective failure loads, elongations, and stress/strain plots. In conclusion, there could be no
difference in conceptual approach between all three team members for this particular laboratory
experiment with the exception of deciding which site to trust for material data. In general
Matweb website was used considering since it was prompted by Dr. Holland for an earlier
prelab.
Differences in Calculations - Within this laboratory experiment, each team member was required
to calculate and hypothesize the maximum possible load each specimen could withstand before
undergoing tension failure. After evaluating the calculations of all three pre--labs, we could
not help but notice a few slight differences between the final answers. This was due to thefact that some team members utilized different online sources to find their Ultimate Tensile
Strength values. As a result, our predicted maximum loads had a specific range for each tested
specimen. All predicted values from all three pre--labs are tabulated below:
*For future reference, all calculations were done using the equations given in the Numerical Predictions
section.
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Predicted FailureLoads
Tory Johansen Matt Beyer Sam Houser
Aluminum Sheet 1120 lbs. 1040 lbs. 1120 lbs.
Aluminum Rod 2208.9 lbs. 2208 lbs. 2209.5 lbs
Hot-Rolled Steel 2704.7 lbs. 3190 lbs. 2705 lbs
As you can see from the table, even a small difference in a materials ultimate tensile strength
can slightly affect its calculated maximum load. However, it is also smart to keep in mind that
the equation used to calculate the values above depends on only three things: cross-sectional
area, maximum load, and the ultimate tensile strength. Remembering that the cross-sectional
area of each specimen was already pre-determined, we could exactly pinpoint the teams sole
source of error between our maximum load predictions.
Final Thoughts - After thorough comparison, it is clear that each team member performed all
of the necessary calculations correctly. The lack of a design phase eliminated the need to filter
through countless variables, thus forcing the team to choose a single pre-lab strictly based off
which ultimate tensile strength values seemed most reasonable. *The team quickly choose the
above hypothesized values because the ultimate tensile strength values used in their calculation
had the largest amount of repetition within the online materials community. Even though one
group member had differing predicted failure loads, the team as a whole still did not have
enough information to say with certainty that those particular values were impossible, and even
further, incorrect. In conclusion, each team member did their respective part and no blatant
errors were discovered between the three pre-labs.
*What was the basis for selecting the approach/calculations from one prelab overanother?
Numerical Predictions(of quantities to be measured: stiffness, strength, etc.)
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For a few select material properties, we were required to perform research on the internet and
find reasonable values for all three specimens to be tested. These material properties included:
yield strength, ultimate tensile strength, modulus of elasticity, and Poissons ratio.These values
were to be used as a reference in which to compare our experimental data obtained from the
Instron Machine. In the end, the team decided upon values from two different sites, Matweb and
SubTech (see References below for website citations) --- the values and cross--sectional areasare tabulated below:
Yield Strength UltimateStrength
Modulus ofElasticity
Poissons Ratio Cross-SectionalArea
Aluminum Sheet 50,000 psi 70,000 psi 10,600 ksi 0.33 0.016 in2
Aluminum Rod 40,000 psi 45,000 psi 10,000 ksi 0.33 0.0491 in2
Hot-Rolled Steel 29,700 psi 55,100 psi 29,000 ksi 0.28 0.0491 in2
*The cross-sectional areas were calculated using a rod diameter of 0.25 in. and a plate thickness and
width of 0.008 in. and 2 in. respectively - for equations see the end of this section.
As for our calculated failure loads, we used the following equation: Maximum Load = (Ultimate
Tensile Strength) * (Cross-Sectional Area). Since the ultimate tensile strength and cross-
sectional area were found online and provided beforehand (respectively) we were able
to quickly determine the hypothesized failure loads previously stated above. The actual
calculations for our predictions are as follows:
Aluminum Sheet: Maximum Load = (Ultimate Tensile Strength) * (Cross-Sectional Area)
Maximum Load = (70,000 psi) * (0.016 in^2) = 1120 lbs.
Aluminum Rod: Maximum Load = (Ultimate Tensile Strength) * (Cross-Sectional Area)
Maximum Load = (45,000 psi) * (0.0491 in^2) = 2209.5 lbs.
Hot-Rolled Steel: Maximum Load = (Ultimate Tensile Strength) * (Cross-Sectional Area)
Maximum Load = (55,100 psi) * (0.0491 in^2) =2705.4 lbs.
*Assume a transverse strain so that we can have a Poissons Ratio - Explain how our
assumption affected our calculations.
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Lab Actions:
First review and follow all laboratory safety rules prior to any handiwork
Measure and record the width, length, and thickness of each specimen (as needed)
Install the appropriate Instron grips for each specimen
Create/name a file (for each specimen) and save it to a USB Drive
Securely install the specimen into the Instrons lower grip
Adjust the height of the Instrons upper grip (as necessary) to match that of the
specimen
Complete the installation process by tightening the upper grip onto the specimen as well
Carefully attach the extensometer onto the middle of the rod (for rods only)
Click Auto Offset to zero all values on the Instron Machine
Click Run
Watch the real-time stress plot (wait for the specimen to being yielding)
Click Stop once the specimen has begun to yield
Remove the extensometer from the rod
Click Run to resume the test
Click Stop once failure has occurred
Click Finish to output data
Make sure the specimens data saved correctly
Remove each specimen from the Instron Machine
Repeat for all specimens For aluminum samples after failure, touch the failed surface. Do you observe the rise in
temperature? Also, observe the failed surface and report the condition in your report.
Lab Pics: Include a picture of the setup
Tory
Measurement Results from lab:
*For all measurement results, see Appendices A, B, and C
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See data files
How did we calculate our hypothesized elastic limit for each individual specimen?
How did we calculate our hypothesized Modulus of Resilience for each individual
specimen? UR = (Elastic Limit^2)/(2E)
Calculate the area under the linear portion of the stress-strain curve (from the
data file)
How did we calculate our hypothesized Modulus of Toughness for each individual
specimen?
UT = [(Elastic Limit+Ultimate Tensile Strength)*(Lf-L0)]/(2*L0)
Calculate the area under the entire stress-strain curve (from the data file)
Calculate poissons ratio:
(deltaVolume/Volume)=0=(1+(deltaL/L))^(1-2*nu)-12705.
Comparison of measurement results with the calculations above:
Compare our predicted failure load with the actual failure load
Compare the calculated material properties with the actual properties from our
source(s)
Evaluation of how well measurement results match prelab calculations and what are the
sources of error and variation: Be specific and detailed on your sources of error, no
more hand waving
Aluminum sheet:
This sample produced results that compare very poorly to those calculated before the lab. The
yield strength was found to be 6777 psi, which is significantly lower than the researched value
of 50,000 psi. The ultimate strength was found to be 16,705 psi, also significantly lower than
the researched value of 70,000 psi. The modulus of elasticity was 3,280,023 psi compared to
10,600,000 psi, poissons ratio ratio was .5 compared to .33, and finally the failure load
experimentally was 267.28 lbf compared to 1120 lbf. The results for each property being
compared to calculations have at best a 50% error. This large error cannot be simply due to
experimental error; the only logical cause is that either the dimensions of the sheet are vastly
incorrect or that the material is not, as we have been told to assume, aluminum 2024-T3.
Beyond this major problem, further sources of error exist that certainly contributed to
discrepancies when compared to calculated values. Chief among these errors is the human
component in selecting the yield point and the 20% offset. The number of data points if very
limited (around 20) in the linear region, causing the estimate for yield to be rough at best. When
determining where plot leaves the linear range, no two humans will pick exactly the same value
which is further compounded by the large slope (E) of the linear range. A slight difference in
opinion on the point where the linear region ends encompases a large range in stress. For
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example, a strain of .001 corresponds to a stress of 4390 psi, while a strain of .0011
corresponds to a stress of 5100 psi. The percent change in strain is much less than that for
stress. These errors in yielding determination compound throughout many of the rest of the
calculations. Elastic limit, elastic modulus, modulus of resilience, modulus of toughness,
poissons ratio, and yield strength all depend upon yielding values. For example, the modulus
of resilience depends both inversely upon the elastic modulus and directly to a second power ofthe modulus. The experimental poissons ratio calculation is flawed as well. This calculation
assumes constant volume and density, the second of which likely is not the case. If density is
not constant, then the volume can change making our calculation incorrect.
Aluminum Rod:
After thoroughly reviewing the data output for the aluminum rod, the final results showed
surprisingly large amounts of accuracy to theoretical results. For this particular experiment,
we were only required to compare the four material properties stated previously. For the
aluminum rod, the percent errors were typically on a reasonable range, considering the data
output we were allowed to work with. The yield strength had the largest percent error because
its calculation is based off of a 0.2% permanent deformation which for the data and graph we
possessed, was difficult to estimate since 0.2% is extremely small on a scale of 5% increments.
The ultimate strength, when compared to our reference value, only had a percent error of
around 5.5%. The experimental value was found directly from the Instron Machine and thus
there was no real calculation necessary. However, the presence of a small percent error could
be a result of the theoretical value found from the online source. All materials depend on certain
variables such as temperature which when taken into account this specific material, could
modify the ultimate tensile strength enough to create the calculated percent error. Obviously
not all materials consist of the exact same composition, thus allowing each individual specimen
(even within the same family) to have their own ultimate tensile strength values.
The modulus of elasticity, or the elastic modulus, was calculated by averaging the (stress/strain)values for the linear portion of the stress-strain plot. Part of the 7.4% error could have easily
been caused by the skewed beginning values on the plot. This plot shows a jump where the
Instron Machine did not evenly pull the rod (in an imperfect world, this is inevitable). When we
calculated the average, therefore, our values are going to be slightly lower than they should be.
The predicted failure load, when compared to our theoretical value, came out to only a 1.5%
error. Considering all of the potential variables, this is a very positive result. Just like the the
ultimate strength, the maximum load was pulled directly from the Instron Machines data output.
Sources of this slight error would most likely look very similar to the sources of error for the
ultimate strength. Our theoretical value, after translating it to a theoretical failure load, could vary
for every individual specimen due to things such as temperature and composition (impurities).
Experimental Theoretical % Error
Elastic Limit 15000 psi
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Yield Strength 55000 psi 48000 psi 14.58
Ultimate Strength 72000 psi 65000 psi 10.77
Modulus of Elasticity 31800000 psi 29500000 psi 7.8
Modulus of Resilience
3.54
Modulus of Toughness
18500
Poissons Ratio 0.5 0.28 78.57
Failure Load 3540.91 lbs 2705.4 lbs 30.88
Experimental Theoretical % Error
Elastic Limit 9120 psi
Yield Strength 36000 psi 40000 psi 11.11
Ultimate Strength 47559 psi 45000 psi 5.69
Modulus of Elasticity 9260697 psi 10000000 psi 7.39
Modulus of Resilience4.332
Modulus of Toughness
10286
Poissons Ratio 0.5 0.33 51.52
Failure Load 2242.11 lbs 2209.5 lbs 1.48
Experimental Theoretical % Error
Elastic Limit 5128.66 psi
Yield Strength 6776.58 psi 50000 psi 86.45
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Ultimate Strength 16704.96 psi 70000 psi 76.14
Modulus of Elasticity 3280023 psi 10600000 psi 69.06
Modulus of Resilience
4.01
Modulus of Toughness 1095.28
Poissons Ratio 0.5 0.33 -51.52
Failure Load 267.28 lbs 1120 lbs 76.14
Conclusion
similarities and differences between materials
see questions
Reference
"Online Materials Information Resource."Matweb material property data. Matweb, LLC., 2011.
Web. 25 Mar 2012. .
Holland, Steve. "AerE 321L: Aerospace Structures Laboratory." Thermography Research
Group. Iowa State Univeristy, n.d. Web. 25 Mar 2012. .
"AISI Steel Mechanical Characteristics."Engineers Edge: Solutions By Design. Engineers
Edge, 2012. Web. 26 Mar 2012. .
Aerospace Metal Distributor. ASM Aerospace Specification Metals Inc, 0. .
Kopeliovich, Dmitri. "Carbon Steel SAE 1020." SAE Technical Papers. SubsTech: Substances
and Technology, 2008. Web. 26 Mar 2012. .
"Carbon Steel AISI 1020 ." eFunda. eFunda , 2012. Web. 26 Mar 2012.
.
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Report
1) Determine and tabulate the following properties
Elastic limit, yield strength, ultimate strength, modulus of elasticity, modulus of resilience,
modulus to toughness, poissons ratio
2) Compare the following to reference values calculating the source of error: yield strength,ultimate strength, modulus of elasticity, poissons ratio
3) Discuss reasons for sources of error
4) Provide a stress-strain plot appropriately labeled for all specimens
5) Summarize in words the similarities and differences in material properties for the two
materials tested, Present relationships between various material properties for the materials
tested
6) Provide the E value to the TA. He/she will collect all values for the class and provide them to
you
7) include technical drawings of the specimens
8) Include all items from the formal test report checklist.
Questions:
1) The specimen probably failed somewhere other than directly in the middle. What
determines where a specimen fails?
Sample impurities and locations of stress concentrations. Also, each sample likely hadunknown internal loads.
2) Why is it often difficult to evaluate the elastic limit?
It is difficult to find transition from linear relationship between stress and strain for a
limited number of data points. Also, the large slope of the linear region means that a slight
difference in location of transition corresponds to a great difference in the elastic limit.
3) What is the effect of poor alignment of the specimen? Why is the estimate of tensile
strength of a specimen more accurate for an aligned specimen than an inaccurately
aligned specimen?
Need to account for transverse strain in addition to longitudinal, grain orientation
4) Why would a stress-strain diagram be preferable to a load elongation diagram for
presenting the results of a tension test?
The elongation is extremely small, appears linear even after yielding. After yielding
sample continues to elongate but also changes dimensions cross sectionally. This causes
behavior that can change quickly and is no longer proportional to poisson's ratio, so it is
unpredictable.
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5) Report the condition of failed surface. Report why there is a rise in temperature in
aluminum samples. Also, explain why the failed surface in aluminum sample is at an
angle?
Both rods had significant necking. Our Al rod didnt have any angle