_DefBods_Report2_DL

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University of Windsor *

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GENG 2180

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Mechanical Engineering

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Apr 3, 2024

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1 UNIVERSITY OF WINDSOR Faculty of Engineering Mechanics of Deformable Bodies (GENG 2180) Laboratory #2 – Torsion Test Submitted on March 8 th , 2021 Demetri, Lambrinos Student ID: 110007561 Section:

2 Table of Contents Laboratory #2 -Torsion Test--------------------------------------------------------------------------- Table of Contents----------------------------------------------------------------------------------------2 Objectives, Equipment, Specimens, Procedure---------------------------------------------3 Drawing Setup-----------------------------------------------------------------------------------3 Results, Sample Calculations------------------------------------------------------------------4 Figures 1,2,3--------------------------------------------------------------------------------------5 Figures 4,5,6--------------------------------------------------------------------------------------6 Figure 7: Fracture Surfaces---------------------------------------------------------------------7 Discussion, Conclusion--------------------------------------------------------------------------8

3 Objective: To study the behavior of ductile and brittle materials subject to torsion. Equipment: • Torsion testing machine Tinius Olsen • Micrometer • Scale Specimens: ▪ Steel ▪ Aluminum ▪ Cast iron Procedure: 1. Using the micrometer measure the diameter of specimen to the nearest 0.02 mm at several points along the length of the specimen and record the average diameter. 2. Load the specimen in the torsion testing machine. Set the load indicator dial to zero. 3. Apply the load slowly by manually operating the machine. Take readings of torque (T) and angle of twist (  ) simultaneously, at the specified increments, without stopping the machine, and carefully record these experimental data. 4. After the yield point (for ductile material) has been exceeded, apply the load until failure occurs. Readings in this range are based on deformation increments. 5. For cast iron, the specimen should be loaded manually until failure occurs. 6. Examine the fracture surface, and the type of failure that occurred in each specimen. Drawing of the Setup:

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4 Results: Material Steel Aluminum Cast Iron Type of Specimen Ferrous Non-Ferrous Ferrous Length (mm) 200 200 200 Average Diameter (mm) 18.93 19.01 20.30 Average Cross-Sectional Area (mm 2 ) 281.4434 283.8272668 323.6547292 Proportional Limit in Shear (MPa) 381.7252742 234.5319015 361.1282252 Yield Point or Yield Strength in Shear at 0.001 Radians Offset (MPa) 410.5667394 226.9933761 0 Modulus of Rigidity (Shear Modulus) (GPa) *avg 51.34999624 30.29463016 38.82922481 Ultimate Shearing Stress (MPa) 502.1808052 275.5749842 106.5593467 Shearing Stress at Rupture (MPa) 502.1808052 275.5749842 106.5593467 Modulus of Elasticity (Calculated using v = 0.30) (GPa) 133.5099902 78.7660384 100.9559845 Sample Calculations: Steel CSA = πr 2 = π*(9.465) 2 = 281.4434 mm 2 J = π/2 * R 4 = 12606.72706 Shearing Strain: γ =ρ * ϕ /L = (9.465) * (27.34930938) / 200 = 1.294306066 Mpa Shearing Stress at Criterion: (T*R)/J = (5920*9.465) / 12606.72706 = 502.1808052 MPa Modulus of Rigidity (avg from excel) G = shear stress / shear strain = 51.34999624 GPa Modulus of Elasticity E = 2G(1+v) = 2*(1.149223893) *(1+0.3) = 133.5099902 GPa

5 Figure 1: Stress vs Strain of Steel Figure 2: Stress vs Strain of Aluminum Figure 3: Stress vs Strain of Cast Iron

6 Figure 4: Offset Stress of Steel + Elastic Region Figure 5: Offset Stress of Aluminum + Elastic Region Figure 6: Elastic Region of Cast Iron 0 100 200 300 400 500 Stress Strain Stress vs Strain of Cast Iron

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7 Figure 7: Fracture Surfaces It was observed that little deformation occurred on the Steel and Aluminum Specimens on the fracture points and because of this we can describe these specimens to be ductile. A more noticeable deformation occurred on the Cast Iron and this can be explained due to the fact that Cast Iron is considered to be more brittle compared to the other materials. These deformations can be observed from the stress strain graphs previously displayed.

8 Discussion: When comparing the specimens, we can look at the max and rupture torque that all of the specimen has endured. Of the three specimens, cast iron withstood the most torque but as we know from previous tests with the tensile lab, the cast iron specimen is a brittle material, and we can see this property again due to the fact that it had a very low shear strain at the rupture and had few rotations compared to the other specimens. This observation can be further supported by the stress-strain graph of cast iron due to the fact that we cannot easily observe a yield point and a non-elastic region of the graph unlike the ductile specimens. On the other hand, Aluminum had many rotations and had good shear strain in when comparing to the other materials but had low shear stress compared to the others and this statistic showed by its inability to withstand a large amount of torque evidence by the rupture by the relatively low torque captured at rupture but its ductility properties showed due to how many rotations it survived. With this supporting evidence and with knowledge of the previous tensile test, we can still conclude that aluminum is a ductile material. Steel appeared to be the most balanced of the three materials and quite possibly the best choice for a material under these conditions. The steel displayed ductile properties as it was able to undergo multiple rotations of torsion and withstand a relatively high torque force of 5920lb-in. This translated well to the stress and strain properties as well as it displayed the highest shear stress, a very close second highest max strain value and displayed the highest values in all other areas of study meaning the ductility was the best of the three and quite possibly the better choice of material depending on the use. Errors in this lab could be attributed to multiple factors. Firstly, the values provided may not have accurately been recording due to be rattled off while the test was being conducted as well as trying to record multiple values at the same time. This can immediately rule out precision in the data but thankfully accuracy was all that was needed to get an understanding of the lab. Additionally, some values that were asked to be determined were in fact estimated in the final report when trying to determine proportional limit and yield point at 0.001 rad offset. The previous method used was not able to determine the value so a work around was resorted to. Conclusion: To conclude, after we had applied a torsion force to each of the specimens and reviewed the results, we were able to determine that ductile materials have a proportional limit that allows them to deform and withstand multiple revolutions of torsion with little deformation. Unlike the brittle cast iron which had a low proportional limit which restricted it from deforming and causing a premature fracture compared to the other specimens.