aero lab: sheet failure

7/29/2019 Aero Lab: Sheet Failure

1/10

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.


2/10

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.)


3/10

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.


4/10

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


5/10

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


6/10

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


7/10

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


Elastic Limit 9120 psi

Yield Strength 36000 psi 40000 psi 11.11

Ultimate Strength 47559 psi 45000 psi 5.69


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


Elastic Limit 5128.66 psi

Yield Strength 6776.58 psi 50000 psi 86.45


8/10

Ultimate Strength 16704.96 psi 70000 psi 76.14


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.

.


9/10

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.


10/10

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

aero lab: sheet failure

Documents