Uniaxial Tension Test Report: Stress-Strain Analysis Insights

1 MAE 375 Section (8) Experiment (3): (Uniaxial Tension Test) Experiment Conducted: (9/22/2023) Report Submitted: (9/29/2023) Author: (John Holland) Group Team: (A3)

2 I. Objective and Expectations: In this experiment, the goal is to measure the attributes of a frame as it is loaded until failure, and use the data recorded to finish a Stress strain plot, find modulus of elasticity, and the 0.2% yield strength or the frame. Additionally, the steel type of the frame is give, to see how accurate the our results were. I expect that the stress strain curve for the frame will follow the general outline of the stress strain through both elastic and plastic regions until failure. Thus, first we will see linear increase for the elastic region, before it curves as it starts to plastically deform, then a bell curve up until the ultimate strength, before curving downwards to the breaking strength. II. Experimental Procedure: 1. Schematic of the Specimen: Figure 1. Typical uniaxial tension test specimen with rectangular cross section.

3 Figure 2. Failed uniaxial tension test specimen. Figure 3. Experimental set-up.

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4 2. Description of Equipment: • Universal testing machine • Extensometer • Test specimens • Calipers • Safety Glasses 3. Procedure: The first step is gathering the required items. This includes safety goggles, collecting the specimen for the text, and opening the Partner software on the computer and logging in. Next, set up the universal testing machine, create two marks 1 to 1 inches on either side of the center mark on the specimen and measure the dimensions of the specimen at three equally spaced center. Record this information into the test procedure app, secure the specimen into the machine, and line up the testing machine with Jog Up, Jog Down, and Fine Position knobs. After that, connect the extensometer and have the GTA calibrate the extensometer. Use the fine position knob again to create between 40 and 50 micro strain, and zero all measurements Finally, click run test and wait for the experiment to complete, making sure to record the data from the computer afterwards, remove the specimen from both the testing machine and the extensometer. and measure the new length between gauge length markings. 4. Introduction of Equation/s:

5 Put only result-giving equation/s here. Numbering the equations and defining the parameters are required, and equations should be typed out using an equation editor. Example, Stress experienced can be found using the following equation. 𝜎 = 𝑃 ? × ? (1) where: σ = Stress [𝑃?] P = applied load [𝑙??] (given in Lab Data) b = width [𝑖?] t = thickness [𝑖?] ? ?????? = 0.002 + ? (2) where: ? ?????? = 0.2% Strain Offset for Yield [𝑖?/𝑖?] ε = Strain [𝑖?/𝑖?] (given from Lab Data) 𝜎 ?????? = 𝐸 × ? ?????? (3) where: 𝜎 ?????? = 0.2% Stress Offset for Yield [??𝑖] E = Modulus of Elasticity [??𝑖] (given from Excel trend line of Stress vs Strain in elastic region) Parameters should be defined immediately after the equation in which they are first used, and they do not need to be redefined for each equation they appear in

6 %𝐸𝑙??? = 𝐿 ? − 𝐿 0 𝐿 0 (4) where: %𝐸𝑙??? = Percent of elongation at break in specimen [%] 𝐿 ? = Length after fracture [𝑖?] (recorded in Worksheet) 𝐿 0 = Length before fracture [𝑖?] (recorded in Worksheet) 5. Reference: “The experiment was performed following the steps listed in Chapter 4, Section 4 in the laboratory manual [1].” 6. Deviation: There were no deviations made to the instructions in the manual. III. Data Summary: Measured Data from Worksheet: Width b = 0.503 in Thickness t = 0.117 in Gauge Lenths: Before Fracture ( 𝐿 0 ) = 2 in

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7 After Fracture ( 𝐿 ? ) = 2.44 in Net Elongation ( ? ) = 0.44 in Specimen Material: T6-6061 Table 1. Sample data from Excel for ___ loading Time (min) Strain (in/in) Displacement (in) (Position) Load (lbf) 0.00183 4.00E-6 0.0006 1.6 0.00338 1.10E-5 0.0011 3.9 IV. Calculations: Sample Calculations for Excel data: Equation 1, from the load found from lab data and thickness and width recorded on the work sheet: 𝜎 1 = 1.6 0.503 × 0.117 = 27.187 𝜎 2 = 3.9 0.503 × 0.117 = 66.269 Equation 2, from the Strain that is given from Lab Data: ? ?????? 1 = 0.002 + ? 1 = 0.002004 ? ?????? 2 = 0.002 + ? 2 = 0.002011

8 Using Figure 6, Stress vs Strain plot for elastic deformation from Excel, found in the Graph section below, we know E is 9,358,026 psi. Equation 3, from E given below and ? ?????? just calculated: 𝜎 ?????? 1 = 𝐸 × ? ?????? 1 = 18,753 ??𝑖 𝜎 ?????? 2 = 𝐸 × ? ?????? 2 = 18,819 ??𝑖 Equation 4, from 𝐿 ? and 𝐿 0 from Worksheet: %𝐸𝑙??? = 2.44 − 2 2 = 22% Graph/s: Figure 4. Load vs Displacement plot from Excel and Lab Data 0 500 1000 1500 2000 2500 3000 0 0.1 0.2 0.3 0.4 0.5 0.6 Load (lbf) Displacement (in) Load vs Displacement

9 Figure 5. Stress vs Strain plot from Excel, Calculations, and Lab Data Figure 6. Stress vs Strain plot for elastic deformation from Excel, Calculations, and Lab Data 0 5000 10000 15000 20000 25000 30000 35000 40000 45000 0.00E+00 5.00E-02 1.00E-01 1.50E-01 2.00E-01 Stress (psi) Strain (in/in) Stress vs Strain y = 9,358,026.46x + 295.00 R² = 0.9982 0 5000 10000 15000 20000 25000 30000 35000 40000 0.00E+00 1.00E-03 2.00E-03 3.00E-03 4.00E-03 5.00E-03 Stress (psi) Strain (in/in) Elastic Deformation

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10 Figure 7. Stress vs Strain (2% Offset for Yield) plot from Excel, Calculations, and Lab Data 0 5000 10000 15000 20000 25000 30000 35000 40000 45000 0.00E+005.00E-031.00E-021.50E-022.00E-022.50E-023.00E-023.50E-024.00E-024.50E-02 Stress (psi) Strain (in/in) Stress vs Strain (0.2% Offset for Yield)

11 V. Discussion: 1. Comparison of Results: Results Table Published [2] Experiment % Difference ( ??𝑏?𝑖?ℎ??−𝐸?𝑝??𝑖???? ??𝑏?𝑖?ℎ?? × 100% ) Modulus of Elasticity (E psi) 10,000,000 ksi 9,358,026 ksi (From Figure 6) 6.42% 0.2% Yield Stress ( 𝜎 ? psi) 40,000 psi 38,500 psi (From Figure 7) 3.75% (Ultimate) Tensile Strength ( 𝜎 ? psi) 45,000 psi 42703 (Found in Lab Data) 5.10% % Elongation at Break 12% 22% 83.33% 2. Result/s Discussion: For the experimental values, it starts being off very accurate with the Modulus of Elasticity only having a % Difference of 6.42%, a 0.2% Yield Stress that is 3.75% off, and a Tensile Strength that is 5.10% off. However, the last value, % Elongation at Break, is extremely far off, with a massive

12 83.33% off. Regardless of the large % Differences for the % Elongation, however, the plotted data does follow the expected outline of a strain-stress graph from elastic deformation to failure. 3. Sources of Errors: The most likely source of error for the % Elongation at Break is the difference in cross sectional area, or at least the thickness, of the specimen versus the expected thickness that is given for the material on the website I used for the Published value. I could not find any formula for this published value online either, so I couldn ’ t check what the exact ‘ Published ’ , or theoretical, value for the % Elongation at break should have been. For the lesser impactful sources of error for this experiment, in my opinion, two of them occur in the same general step in the procedure, of setting up the specimen in the testing machine. Specifically, the most likely one, in my opinion, is in setting up the extensometer, as I was the one who set it up, and thinking back, I easily could have put it on wrong, or something similar. As the extensometer measures strain, and the strain is then used to find stress, where both yield strength and ultimate tensile strength would be affected most heavily, yet as both stress and strain are incorrect by the same ratio due to the extensometer being set up incorrectly, it would leave the Modulus of Elasticity relatively untouched. VI. Conclusion and Recommendations: In the experiment, the general stress-strain plot for a material from elastic deformation to failure was observed and recorded. Using that data, we then calculated other important information about the material, such as the Modulus of Elasticity, 0.2% Yield Strength, Ultimate Tensile Strength, and % Elongation at Break.

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13 Although the experimental calculations did not match up with the published value for elongation percent at break, all of the other values were within a reasonable range of error. This experiment also gave experience in using those given values to find those values for Modulus of Elasticity, 0.2% Yield Strength, and Ultimate Tensile Strength.

14 VII. References: (See Canvas home page of 375 labs to find manual version. Reference all the sources used in the following format) [1] MAE/CE 375 - Mechanics of Materials- Laboratory Manual, University of Alabama in Huntsville, Version 8.0, August 2022. [2] MatWeb, http://www.matweb.com, accessed: 9/29/2023.

15 VIII. Appendix:

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16

17 Figure 9. Worksheet for Lab 2

Exp 2 Lab Report

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