Rna Waheb Rameen HassanzadehRyan Oh Pavan Kumar NanneDhaval Prajapati Siddhesh SawantLab Time: Wednesday 8 pmLab Group #2MSE 527 Lab # 2 – Tensile Test Lab

AbstractTwo samples of 1018 steel and 2024 aluminum were tested under tension to generate stress-

strain curves, which were used to obtain their Ultimate Tensile Strength (UTS), Yield Strength (YS), Ductility, Young's Modulus (YM), and Strain Hardening Exponent (n). Two different methods for measuring the strain were used—one by the tool's internal measurement of displacement (cross head) and the other direct laser measurement between points on the samples. While the two methods gave similar results for UTS and YS, YM and n were found to be highly dependent on the gage length, with the laser-measured method proving to be more accurate.

ProcedureThe purpose of the Tensile Test was to obtain material properties and characteristics by pulling a

specimen of known geometry at a fixed rate of straining until it either breaks or stretches beyond the machines parameters.  A floor-mounted United Tensile Testing with a 20,000 lb capacity was used to perform the tests. The raw sample data was collected through a program connected to the tensile tester.

The experiment was performed on 2 samples of 2024 Aluminum and 2 samples of 1018 Carbon steel.  One coupon from each of the alloys were laser-marked for a precise gage length of 2 inches. A laser was used to measure the gage length. The remaining non-laser marked coupons had their gage length measured after was they were securely clamped. The width and thickness of the samples were all measured before being subjected to the tensile test.

After a sample had been clamped, the program DATUM was used with the previously measured dimensions to start the actual test. Afterwards, the raw data file was exported to Microsoft Excel. The raw data can be manipulated to generate curves that provide important information such as Young's Modulus, yield strength, ultimate tensile strength, fracture strength, and strain hardening exponent.

Results and DiscussionFigures 1-4 shows the engineering stress (psi) and true stress (psi) vs. the engineering strain (%

elongation). To correctly determine the true stress, the following formula was used:

Here, σT is the true stress, σE is the engineering stress, and εE is the engineering strain. Figures 5-8 shows the log of true stress vs. log of true strain of the plastic portion of the engineering stress-strain curve. The slope of the curve is the strain hardening exponent.

Figure 1. Engineering and True Stress-Strain curves for Aluminum Laser

Figure 2. Engineering and True Stress-Strain curves for Steel Laser

Figure 3. Engineering and True Stress-Strain curves for Aluminum Crosshead

Figure 4. Engineering and True Stress-Strain curves for Steel Crosshead

Figure 5. Log of True Stress vs. True Strain for Aluminum Laser

Figure 6. Log of True Stress vs. True Strain for Steel Laser

Figure 7. Log of True Stress vs. True Strain for Aluminum-Crosshead

Figure 8. Log of True Stress vs. True Strain for Steel-Crosshead

These plots clearly reveal a significant difference in the strain resulting from the difference in gage lengths.

From these stress-strain curves, it is possible to extract multiple properties of the alloys. Table 1 shows the Ultimate Tensile Strength, Yield Strength, Ductility, Young's Modulus, and Strain Hardening Exponent. The analysis methods used for these extractions, as well as a discussion for error, can be found in appendix sections 1-6.

Table 1: Properties of alloys, extracted from experimental stress-strain data

Sample

Ultimate Tensile

Strength (psi)

Yield Strength (psi)

Ductility (%)

Young Modulus

(ksi)

Strain Hardening Exponent

Aluminum-Laser 75963 44725.7 20.2 25112.5 0.18

Aluminum-Crosshead 69184.4 50343.3 16.1 1432.71 0.29

Steel-Laser 61075.9 38830.1 29.6 47305 0.21

Steel-Crosshead 60646.8 38366.3 23.4 1699.0 0.29

From Table 1, it is clear to see that, while the strength values agree reasonably for each alloy, the values that depend on the strain (Ductility, Young Modulus, and the Strain Hardening Exponent) are very different from each other. Table 2 shows the laser measured samples are more accurate than the non-laser measured samples when compared with published results.

Table 2: Published properties of 1018 steel and 2024 Aluminum

Alloy

Ultimate Tensile

Strength (psi)

Yield Strength (psi) Ductility (%) Young

Modulus (ksi)

Strain Hardening Exponent

2024 aluminum1 68000 47000 19 10600 0.173

1018 steel2 63800 53700 15 29700 0.213

This clearly shows that, as expected, direct measurement of the elongation of the samples shows a significant improvement over the tool's judgment of displacement.

Appendix

1. General ErrorThe nature of a tension measurement depends very heavily on the orientation of the sample under load. The tool used lacked any alignment system to ensure that the samples were loaded aligned parallel to the load, and a judgment was instead made by eye.

2. Finding Ultimate Tensile StrengthUltimate Tensile Strength was taken as the maximum stress measured on the stress/strain curve. In all cases, this is the peak of the plastic region of the stress/strain curve.

3. Finding Yield StrengthAn estimation of what region of the stress/strain curve represented the sample still in elastic deformation was taken by eye. The last stress point of this region gives the Yield Strength.

4. Finding DuctilityThe maximum strain experienced by the material before breaking (last data point) gives the total ductility.The difference found in the steel samples compared to published results is not well understood. This could depend heavily on the alignment of the measurement system, and more trials could give an increased understanding.

5. Finding Young's ModulusThe most linear portion of the sample while the material was still in the elastic regime was identified, and a linear fit was made to the data. The slope of that fit gives the young's modulus. An example is shown below.

It should be noted that, for laser-measured values, significant noise existed while in low strain. Because the measurement for the young's modulus depends heavily on this, the measuring and analysis could be significantly impacted.

6. Finding the Strain Hardening Exponent

The formula below was used in order to resolve n, the strain hardening exponent. Here, εT =ln(1+εE ) was used to get the true strain.

Using the principle of the the final formula, the most linear region Log(True Stress) vs Log(True Strain) in the plastic regime before necking occurred was identified, and a linear model was fit to it. The slope of that model gives n. An example is shown below

References1. http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=MA2024T 2. http://www.azom.com/article.aspx?ArticleID=6115 3. Callister, Jr., William D (2005), Fundamentals of Materials Science and Engineering (2nd

ed.), United States of America: John Wiley & Sons, p. 199, ISBN 978-0-471-47014-4, taken from https://en.wikipedia.org/wiki/Strain_hardening_exponent#cite_note-1