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Ryan M. Sullenberger Engineering Research Center Colorado State University 1320 Campus Delivery Fort Collins, CO 80523-1320 Attn: Subject: Re: Date:

John McWilliams Tensile Tests for 3 Metals and Hardness Testing Test Results February 12, 2009

Dear John McWilliams, We have received your request to test three metal specimens including hot-rolled steel, cold-rolled steel and aluminum that you obtained from your local extruding company. We performed the hardness tests and the tensile tests using our Instron 4400R. Our results have been included in tabular and graphical form. Axial testing works by applying an increasing uniaxial tensile load to a material of known cross sectional area and length. Tensile stress is calculated by dividing the applied load by the area of the specimen. The strain of the material is calculated by dividing the elongation of the test piece by its original length. These two quantities are then graphed together as something that is referred to as a stress vs. strain curve. The stress vs. strain curve of a material can tell us many things: the modulus of elasticity is the slope of the initial linear portion of the curve, ultimate stress can be chosen as the maximum stress shown, and the yield stress is found by observing the highest stress region at the end of the initial linear portion. For our experimental results dealing with Modulus of Elasticity, we used strain data collected by a strain gage. This was used to more accurately measure the slope to obtain the Elastic Modulus. Hardness testing is done by making an indentation into a material. Rockwell Hardness Testing is done by comparing the depth of penetration of a large load to that of a preload. We performed Rockwell B testing on the materials you sent us, which uses a 1/16 inch diameter sphere as the indenter. The Rockwell Hardness B value obtained for the materials were used to find tensile strengths. The stress vs. strain curves we obtained for the three metals have been included for convenience on one graph together in this letter and can be found in Appendix B: Figures 1 and 2. Figures 3-5 show the stress vs. strain curves for each specimen on its own graph, and Figures 6-8 show each materials corresponding linear region of the stress vs. strain diagrams. Please refer to Table 2 in Appendix A for a list of our numerical results for the tensile tests. Table 1 contains all the expected values for the metals, and Table 3 shows the percent error between expected and experimental data. For all three metals our tensile tests yielded higher ultimate stresses and yield stresses compared to the expected values. You can also find the results for the hardness tests in Appendix A: Table 4, and the percent error for the hardness tests in Table 5. There is one major mishap that occurred during testing that I would like to point out. When we tested the cold-rolled steel the sample failed very close to the jaws of the machine. This may have happened out of chance, but mostly happens because the jaws apply a compressive force to the sample, so where the material meets the jaws the sample is not in pure tensile stress. We believe there is little to worry about in this case because the ultimate load was reached before the sample fractured. 1

The experimental results were not exactly in line with the expected values, but this is not unheard of. Variations in results can be caused by factors dealing with the manufacturing processes of the metals, where the expected values are given as a standard for that specific material. Due to this, it is not uncommon to come across samples of a material that have greater ultimate stress and yield stress than advertised. Some batches will come out stronger or weaker than others. We recommend if you are using these materials in high sensitive or high stress environments that you obtain another three samples to be tested, just for good measure. It has been a pleasure serving you and we hope you consider us in the future. Sincerely,

Ryan M. Sullenberger Project Engineer (Student)

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Appendix A Table 1: Expected Values Elastic Modulus (psi)

Yield Stress(ksi)

Ultimate Stress (ksi)

3.00E+07 3.00E+07 1.00E+07

36 65 21

58 80 30

Hot-Rolled Steel Cold-Rolled Steel Aluminum

Table 2: Experimental Values for Tensile Test Elastic Modulus (psi)

Yield Stress(ksi)

Ultimate Stress (ksi)

3.12E+07 2.87E+07 8.80E+06

47.4 100.5 33.1

64 115.6 38.6

Hot-Rolled Steel Cold-Rolled Steel Aluminum

Table 3: Percent Error for Tensile Test Elastic Modulus (psi)

Yield Stress(ksi)

Ultimate Stress (ksi)

4.05% -4.23% -12.05%

31.67% 54.62% 57.62%

10.34% 44.50% 28.67%

Hot-Rolled Steel Cold-Rolled Steel Aluminum

Table 4: Rockwell Hardness & Ultimate Tensile Strength

Hot-Rolled Steel Cold-Rolled Steel Aluminum

Rockwell B 50.1 111.8 84.3

Ultimate Strength (ksi) <56 >116 81

Table 5: Percent Error for Hardness Test

Hot-Rolled Steel Cold-Rolled Steel Aluminum

Ultimate Strength (ksi) -3.45% 45.00% 170.00%

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Appendix B 140000 120000

Stress (psi)

100000 80000 Aluminum 60000

CRS HRS

40000 20000 0 0

0.1

0.2

0.3

0.4

0.5

Strain (in/in) Figure 1: Stress vs Strain for Al, CRS, HRS

50000 y = 3.12E+07x - 5.99E+03 45000 40000 y = 2.87E+07x - 4.25E+03

Stress (psi)

35000 Aluminum

30000

CRS

25000 y = 8.80E+06x + 5.74E+02 20000

HRS Linear (Aluminum)

15000

Linear (CRS)

10000

Linear (HRS)

5000 0 0

0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004 Strain (in/in)

Figure 2: Stress vs Strain for Al, CRS, HRS, linear region

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Appendix B Continued 45000 40000 35000 Stress (psi)

30000 25000 20000 Aluminum

15000 10000 5000 0 0

0.05

0.1

0.15

0.2

Strain (in/in)

Figure 3: Stress vs Strain for Aluminum

140000 120000

Stress (psi)

100000 80000 60000

CRS

40000 20000 0 0

0.02

0.04

0.06

Strain (in/in)

Figure 4: Stress vs Strain for CRS

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0.08

0.1

Appendix B Continued 70000 60000

Stress (psi)

50000 40000 30000

HRS

20000 10000 0 0

0.1

0.2

0.3

0.4

0.5

Strain (in/in)

Figure 5: Stress vs Strain for HRS

35000 30000 y = 8,795,396.07x + 574.35 25000

Stress (psi)

20000 Aluminum

15000

Linear (Aluminum) 10000 5000 0

-0.001

0 -5000

0.001

0.002

0.003

0.004

Strain (in/in)

Figure 6: Stress vs Strain for Aluminum, linear region

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Appendix B Continued 50000 y = 28,729,585.43x - 4,251.81 40000

Stress (psi)

30000

CRS

20000

Linear (CRS) 10000

0 -0.0005

0 -10000

0.0005

0.001

0.0015

0.002

Strain (in/in)

Figure 7: Stress vs Strain for CRS, linear region

50000 y = 31,214,205.58569x - 5,992.37628 40000

Stress (psi)

30000 20000 HRS 10000

Linear (HRS)

0 -0.0005

0

0.0005

0.001

0.0015

-10000 -20000

Strain (in/in)

Figure 8: Stress vs Strain for HRS, linear region

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0.002

Appendix C Commonly used equations in Solid Mechanics: ߪൌ

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EQ 1 ( Stress = Force/Area ) EQ2 ( Strain = Elongation/Length)

Definitions: Modulus of Elasticity – The slope of the initial linear region of the stress vs. strain curve for a given material. Units of stress. Proportional Limit – The highest stress on a stress vs. strain curve where stress and strain still have a linear relationship. Elastic Limit – Highest stress a material can undergo and still return to its original shape when unloaded. Yield Point – Stress just usually above the proportional limit such an increase in stress does not increase or decrease the stress. Yield Stress – The maximum stress of a material without undergoing plastic deformation for materials that do not have a definite yield point. Ultimate Stress – The maximum stress as seen on a stress vs. strain curve for a uniaxial tension test. Elongation – The change in length of a material under a uniaxial tension test. Modulus of Resilience – The area under the linear region of the stress vs. strain curve for a given material. This is a measure of a materials ability to absorb energy. Units of in-lb/in^3. Modulus of Toughness – The area under the entire stress vs. strain curve.

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