lab 2 report

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The City College of New York, CUNY *

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461

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Mechanical Engineering

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Jan 9, 2024

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Objective The experiment's main purpose was to determine the maximum load the material withstands before breaking. Also, we determined the force-elongation of the materials after necking. This experiment helped us determine several mechanical properties such as Youn g’s Modulus, Poisson’s ratio, yield strength, ultimate tensile strength, failure tensile strain, etc. All these mechanical properties can be obtained by the graphs plotted in excel with the results from the ‘BlueHill’ software used during the Tensile testing. The stress-strain curves were obtained for different types of Steel, Aluminum, and Iron. These materials were tested under different loads to experience real-life necking and deformation and eventually breaking. Different materials react differently to similar loads which signify the different properties of each material consists of. Equipment • An instron testing machine connected to a desktop with ‘Bluehill’ software • Extensometer • Caliper, micrometer, and a ruler Experimental Procedures Three materials were used in the experiment; Al 2024, HR steel, and Cast Iron, while Al 2024 and HR steel had two specimens each as they were tested at two different speeds of 5mm/min and 50mm/min. The specimens were measured before and after the tensile loading to determine the deformation. The length was measured by a ruler and the diameter was measured by a caliper. Then, the specifications of each specimen such as the material type, displacement rate, length, and

1 diameter were input into the ‘Bluehill software on the desktop. The extensometer was mounted in the middle of the specimen to determine the extension of the material and to measure the strain. Then, the fractured specimen was removed, and the length and diameter were measured after the tensile loading. The extensometer was only used for the displacement of 5mm/min as 50mm/min is very fast. ‘Table 1’ below represents the materials used, along with the displacement rates and the extensometer specifications. Table 1: Testing matrix Results Specimen Displacement rate (mm/min) Initial gage length (mm) Final gage length (mm) Initial diameter (mm) Final diameter (fracture) (mm) Final diameter (unbroken) (mm) HR Steel 5 103 124 8.52 7.05 7.91 Aluminum 6061 5 102 115 8.45 7.25 8.25 Cast Iron - 101 101 8.53 8.53 - Table 2: Measurements of specimen parameters at a displacement rate of 5 mm/min

2 Specimen Displacement rate (mm/min) Initial gage length (mm) Final gage length (mm) Initial diameter (mm) Final diameter (fracture) (mm) Final diameter (unbroken) (mm) HR Steel 50 102 123 8.54 7.17 7.98 Aluminum 6061 50 103 114 8.52 7.85 8.19 Cast Iron - - - - - - Table 3: Measurements of specimen parameters at a displacement rate of 50 mm/min The parameters of the graphs were calculated using the following formulas. Engineering Stress: Engineering Strain: True Stress: True Strain: Here, F: Load Applied A 0: Cross-sectional area of specimen before deformation has taken place A: Cross-sectional area of specimen at which the load is applied 𝛿: Total elongation L 0: Original value of the gage length L: Successive values of the length as it changes

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3 Figure 1: Engineering stress vs. Engineering strain graphs for the three specimens at low displacement rate Figure 2: True stress vs. True strain graphs for the three specimens at low displacement rate

4 Figure 3: Engineering stress vs. Engineering strain graphs for the Aluminum and HR Steel specimens at high displacement rate Figure 4: True stress vs. True strain graphs for aluminum and HR steel at low displacement rate

5 Figure 5: Load-extension graph to calculate total energy for aluminum Figure 6: Load-extension graph to calculate total energy for HR steel

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6 Figure 7: Load-extension graph to calculate total energy for cast iron Note: The areas under the load-extension curves are a measure of the Reiman sum of the individual areas of rectangles formed by consecutive load and extension values. The rule used was the Trapezoid rule. Specimen Ultimate Tensile Stress (Mpa) Young’s Modulus, E Failure Tensile Stress (MPa) Aluminum 346.4041 19068 273.48 HR Steel 600.9009 18934 422.42 Cast Iron 280.8143 22089 280.02 Table 4: Comparison of specimen properties at low displacement rate

7 Specimen Ultimate Tensile Stress (MPa) Young’s Modulus, E Failure Tensile Stress (MPa) Aluminum 309.08 19639 245.23 HR Steel 452.54 19333 368.47 Table 5: Comparison of specimen properties at high displacement rate Discussions The elongation of steel is the highest, while the lowest is cast iron which means that steel is the most ductile among all the specimens. Elongation helps us choose the material type according to the project. The gradient of the elastic region provides Young’s Modulus which affects the deflection of material under different loads. Necking is more in steel than aluminum, while cast iron has no necking. Hence, steel has higher yield strength than aluminum. True strains are of higher values than engineering strains as true strains take place in transverse directions of the gage length. It can be noticed that steel requires the most stress and strain before fracture which proves that steel withstands the highest load before breaking and is the strongest of the specimens. This means that more energy is required to break steel than aluminum and cast iron. The engineering stress- strain curve shows the deformation specifications of the specimen, while the true stress-strain curve shows the true values of the changing deformation. HR steel has a lower and upper yield point as its local transitions from elastic to plastic behavior while aluminum has a gradual transition. The specimen’s fractures other than cast iron were at an angle of approximately 45 degrees like a cup cone as the specimens experienced rupture while breaking. Furthermore, to reduce error, I think it would be more accurate to obtain the stress-strain data by the machine directly. Conclusion

8 This tensile testing helped us know about different material properties using the tensile testing machine. The ductile fracture can be proved when our results show that the area of the specimen is reduced at the breaking point. Elastic and plastic deformation can be seen when the material is stretched in the machine. This experiment helped me with a better understanding of how materials react under different conditions such as speed and load. Review Questions 1. What divides the engineering stress-strain curve into two regions, namely, the elastic and plastic regions? - The Yield strength or yield point 2. What is the difference between the behavior of the material in the elastic and plastic regions of the engineering stress-strain curve? - Under elastic region, the material regains its original form after the load is removed. In plastic region, deformation becomes permanent. 3. What measurement should you have taken in order to be able to plot the true stress-true strain curve? - Load and the corresponding deformation parameters. 4. Why does low carbon steel have clear upper and lower yield points? Why doesn't the aluminum have the same? Explain the differences using your knowledge of the alloying and dislocation theories. - The reason is the presence of interstitial atoms. The dislocations are due to plastic deformation in carbon. The same is not true for aluminum since steel has a higher modulus of rigidity than aluminum.

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9 5. Did you observe parallel lines inclined about 45 o with the horizontal on the surface of the steel specimen, and in the area where necking later took place? What are those lines called? What do they reveal about the mechanism of deformation? Apply Schmid ’ s Law, see S LIP IN S INGLE C RYSTALS (Sec 7.5) of Ch 7: Dislocation and Strengthening Mechanisms . - The lines are called dislocation lines. The angle of 45 degrees implies maximum shear stress has reached. 6. Could you observe any similar lines on the aluminum specimen? What is the mechanism of deformation in this latter case? - Yes, the lines were visible in aluminum as well and the mechanism of deformation is the same. 7. Obtain the area under the load-extension curve (i.e., energy) for each specimen and divide it by the volume between the gage length in order to obtain the modulus of toughness. Compare the value of plain carbon steel and that of aluminum. Can you draw any conclusion? - Refer to the results section. It can be concluded that the amount of energy associated with each specimen revolves around the same value. 8. Looking at the curve indicating the distribution of elongation along the gage length, where did the maximum localized elongation take place? - In the middle of the specimen where necking occurred. 9. How do you interpret the shape of the above-mentioned curve? - High strain rate breaks the specimen faster. 10. What effect does the high strain rate have on the mechanical properties mentioned in Problem 8?

10 - High strain rate breaks the specimen faster. 10. Did the high strain rate have any effect on the mode of failure of any of the specimens? Why? - High strain rate caused faster elongation and, hence, failure. 12 . What effect does the high strain rate have on the mechanical properties mentioned below? - High strain rate, increases the Young’s modulus and failure strength of the specimens. 13. Design for Experiments : Rather than using the extensometer/change in gage length and change in diameter, the axial and lateral strains of the test can also be measured directly using a “T” strain rosette shown at right. If the strain-rosette mounted tensile test needs to be conducted under water, what additional step(s), if any, should be taken to ensure the success of the test. Hint : Refer to the Vishay Precision Group, Micro-Measurements website: http://www.vishaypg.com/micro-measurements/ . - For under-water testing, ultra-thins films and van-der walls adhesion will be needed.

11 References Li, J. Lab Manuals . CUNY Blackboard Website “Engineering Stress/Strain VS True Stress/Strain.” Yasin APAR , https://yasincapar.com/engineering-stress-strain-vs-true-stress- strain/#:~:text=Engineering%20strain%20is%20the%20amount,length%20over%20the%2 0original%20length Erhart, Angela. “Engineering Stress -Strain vs. True Stress- Strain.” AHSS Guidelines , 24 Mar. 2021, https://ahssinsights.org/forming/formability/engineering-stress-strain-true-stress- strain/

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