Objective: To investigate the deformation of wire subjected to static torsion.
The Experiment: This Lab experiment is required to use the torsion tester provided, as shown in Figure 2.1 to determine the shear properties of materials under static torsional conditions. The conduct of this experiment is given under Methodology.
Equipment: brass rod, aluminum rod, steel rod, long ruler, vernier calipers, string, spring Balance
Groove
Disc Wire Drill Chuck
Pulley
Support
Figure 2.1: Experimental Set-up.
Methodology: 1. The apparatus used to conduct the torsion experiment were set up as Figure 2.1. The first material of specimen tested was aluminum rod. 2. The diameter of the aluminum rod was measured and recorded by using vernier caliper. 3. Aluminum rod was attached tight on to one rigid point and another end was fixed on a movable disc. A string is fixed to the movable disc and run on a pulley. 4. Forces were applied against rod by pulling the spring balance attached on the end of the string. The forces applied to the aluminum rod were 2.0N, 3.0N and 4.0N. 5. The angle before and after twist were recorded and converted from degree to radian form. 6. All the data and measurement were collected and tabulated in table. 7. The whole experiment (step 1-6) was repeated by using steel rod and brass rod.
Result: Polar moment of inertia, Modulus of rigidity,
Steel Aluminium Brass
Length, m 0.477 0.472 0.476
Radius, m
Torsion, N 2 3 4
Steel Angle, rad 0.175 0.314 0.489
Aluminium Angle, rad 0.524 0.559 0.611
Brass Angle, rad 0.524 0.908 1.222
Graph of tension, N against angle, rad (steel)
0.6 0.5 0.4 y = 0.157x - 0.145 0.3 0.2 0.1 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Graph of tension, N against angle, rad (aluminium)
0.62 0.61 0.6 0.59 0.58 0.57 0.56 0.55 0.54 0.53 0.52 0.51 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 y = 0.0435x + 0.4342
Graph of tension, N against angle, rad (brass)
1.4 1.2 1 0.8 y = 0.349x - 0.1623 0.6 0.4 0.2 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Gradient of graph =
Calculation:
Steel: Modulus of rigidity, = =
Aluminum: Modulus of rigidity, = =
Brass: Modulus of rigidity, = =
Analysis: The theoretical modulus of rigidity, G of aluminum is 27 GPA. The theoretical modulus of rigidity, G of brass is 40 GPa and theoretical modulus of rigidity, G of steel is 78 GPa. In our experiment, it is observed that aluminum has the lowest modulus of rigidity compared to brass and steel and the diameter of aluminum rod used is also the biggest among the three. Among the three rods used, it is seen that steel rod meets plastic deformation first, followed by brass rod and finally aluminum rod. Theoretically, a material which has a higher value of polar moment of inertia will achieve plastic deformation at a later stage compared to material which has lower value of polar moment of inertia.
Problems encountered during experiment: 1. The string attached to disc and spring balance was too short causing difficulty in measurement. 2. The straightness of the rod could not be determined accurately at starting of the experiment by viewing with our naked eye. We just assumed the rod is straight and tighten correctly. 3. The measuring tool used like the dynamometer (readings on disc) was not at zero. We have to record the initial and final measurements and take the reading again to ensure accuracy. Precautions: 1. Make sure the rod tested is fixed straight from one end to another end. 2. Make sure the experiment is stopped when the angle of twist deviates from the linear relationship it is supposed to have with applied torque or when the disc does not return to its rest position without slip. 3. Make sure that the rod is tightening properly at the drill chuck to ensure no slip occurs. 4. Make sure that the eyes aligned to scale at disc when measuring the angle to avoid parallax errors.
Discussions: The experimental values are seen to be different from the theoretical values. There are many reasons causes this happened. Firstly, it may have an error in taking diameter of the typical torsion of test specimen (rod). Besides that, specimen malformation may occur also. Secondly, we did this experiment in room temperature. This temperature may yield different result compared with the theoretical value. The air resistance in the lab also will affect our result. Although these two are small factors, it will give error and result become not accurate. From the data obtained by conducting the experiment, it proves that a material with higher polar moment of inertia will have a higher resistance to plastic deformation under torsion. We can see that aluminum has highest polar moment of inertia compared to brass and steel. It deformed at later stage compared to brass and steel.
Conclusion: This experiment shows that each material has different torsional behavior and plastic deformation due to modulus of rigidity. However, it proves that material with higher polar moment of inertia will has a greater resistance to plastic deformation under torsion condition.
