Table of Contents Abstract3 1. 0 Introduction3 2. 0 Experiment Design4 2. 1 Apparatus5 2. 2 Methods5 2. 3 Procedure6 3. 0 Results and Discussion7 4. 0 Error Analysis13 5. 0 Conclusion and Recommendation13 6. 0 References14 Abstract In this torsion testing experiment, the torsion test was evaluated as a system for calculating the torsional rigidity (GJ), modulus of rigidity (G) and the shear yield stress (? ) for aluminium, mild steel and brass. The both ends of the cylindrical specimen are tightened to hexagonal sockets, which one is fixed to a torque shaft and another is fixed to an input shaft.
By turning the input handwheel, the twisting moment has applied to produce the torque until the specimen fails. In the end of the experiment, it shows that the comparison of the behaviour of ductile and brittle materials under torsion. 1. 0 Introduction The responses of metals were deal by mechanical testing to applied forces. This testing includes torsion, tension, hardness, fatigue, creep and stress rupture, and impact tests. Torsion occurs when any shaft is subjected to a torque. The torque causes the shaft to twist. This makes one of the ends to rotate relative to the other; shear stress is induced on any cross section.
Besides that, torsion testing is made on materials to determine modulus of elasticity in shear, torsion yield strength and the modulus of ruptures. The shearing stress at any point on a transverse cross section varies directly proportional as the distance from the centre of the shaft, when a simple circular solid shaft is twisted. Therefore, during twisting, the cross section is initially planar remains a plane and rotates only about the axis of the shaft. 2. 0 Experiment Design Figure 7: 360 degree protractor scale Figure 6: Three specimen mild steel (top), brass (middle), and aluminium (bottom) after experiment.
Figure 5: Three specimen mild steel (top), brass (middle), and aluminium (bottom) before experiment. Figure 2: Torque meter Figure 3: Deflection arm, dial gauge, levelling handwheel and linear potential meter Figure 4: Input handwheel with 6 degree protractor scale Figure 1: Torsion testing machine 2. 1 Apparatus There were only few apparatus and materials involved in this experiment, such as: 1) 3 pieces of specimens (Aluminium, brass and mild steel) 2) Vernier Caliper 3) Torsion Testing Equipment 2. 2 Methods Firstly the apparatus was set up as shown in Figure 1.
The torque meter was switched on to allow the reading appear on the screen which connected to the torsion testing machine. Three specimens was carried out, mild steel, brass and aluminium. Each specimen was placed at the hexagonal sockets and it was tightened with the deflection arm. The handwheel was turn 90 degree each time to take the reading for angle of twist from the 360 protractor scale and torque from the torque meter of each specimen. Therefore, 12 readings were taken and evenly distributed. After taking the 12 readings, the handwheel was continuously turned until the specimen was fracture.
By the time the specimen was fractured, this shows that the maximum torque and the maximum angle of twist of the specimen. All the readings were recorded in a table form and calculations were done using the equations shown at section Results and Discussion. 2. 3 Procedure 1. The specimen as shown in figure 2 below was used for testing. The mild steel specimen was mounted on the torsion testing machine at position no. 4. 2. It was made sure that on the specimen there was no preload. Before starting the experiment, the hand wheel at the input of the worm gear was turned when necessary until the read out of the amplifier is zero.
There was still zero error on the amplifier. 3. Both the indicators at the input and output shaft of the worm gear was set to zero. 4. The dial gauge of the compensation unit was set to zero. 5. The revolution counter was reset. 6. The hand wheel was turned through 90° and the Scale Reading at Worm gear input was recorded in revolution(degrees) and the torque value was recorded in digital torque meter(6). 3. 0 Results and Discussion T/J = ? /R = G? /L Torsion equation TJ= G? L G=TLJ? ?=? d^432 Where T = Torque applied, Nm G = shear modulus, N/mm2 J = Polar moment of inertia, mm2 ? = Angle of twist, radian
L = Gauge Length, mm ? = shear stress, N/mm2 r = radius of the cylindrical bar, mm J=? d432=? (5)432=61. 36mm2 1) For mild steel, for example using point (7. 25, 17) G=TLJ? =7. 25(115)61. 36 0. 2974=45. 80N/mm2 ?=TRJ=7. 25(2. 5)61. 36=0. 295N/mm2 For brass, for example using point (5. 85, 17) G=TLJ? =5. 85(115)61. 36(0. 297)=36. 95N/mm2 ?=TRJ=5. 85(2. 5)61. 36=0. 238N/mm2 2) Torsional rigidity is ratio of torque applied about the centroidal axis of a bar at one end of the bar to the resulting torsional angle, when other end is held fixed means torsional rigidity =torqueangle For mild steel, Torsional rigidity = 7. 2517=0. 26 For brass, Torsional rigidity = 5. 8517=0. 344 Therefore, torsional rigidity of mild steel is higher than brass. 3) Specimen: Mild Steel Scale Reading at Worm gear input in Revolution (degrees)| Angle of Twist of Specimen (col. 1/62)| Torque (N. m)| 90| 0| 0. 05| 180| 0| 0. 05| 270| 2| 0. 05| 360| 4| 0. 05| 450| 5| 0. 10| 540| 8| 0. 10| 630| 9| 0. 10| 720| 10| 0. 35| 810| 11| 1. 25| 900| 12| 2. 85| 990| 14| 5. 00| 1080| 17| 7. 25| Until fracture| 4092| 21. 05| Specimen: Brass Scale Reading at Worm gear input in Revolution (degrees)| Angle of Twist of Specimen (col. 1/62)| Torque (N. m)| 90| 1| 0. 05| 180| 4| 0. 5| 270| 5| 0. 15| 360| 6| 0. 55| 450| 7| 1. 00| 540| 8| 1. 80| 630| 9| 2. 80| 720| 11| 3. 95| 810| 14| 4. 95| 900| 15| 5. 55| 990| 16| 5. 80| 1080| 17| 5. 85| Until fracture| 1047| 14. 50| Specimen: Aluminium Scale Reading at Worm gear input in Revolution (degrees)| Angle of Twist of Specimen (col. 1/62)| Torque (N. m)| 90| 1| 0. 05| 180| 2| 0. 15| 270| 4| 0. 20| 360| 6| 0. 30| 450| 8| 0. 45| 540| 9| 0. 85| 630| 10| 1. 40| 720| 11| 2. 30| 810| 13| 3. 20| 900| 15| 4. 20| 990| 17| 5. 25| 1080| 18| 6. 35| Until fracture| 311| 13. 50| Graph of torque against angle of twist of specimen (mild steel, brass and aluminium) ) Ductility is ability to deform under tensile stress when subject to stress; brittle materials absorb relatively little energy power to fracture. For ductile material, it will produce fracture surface along the plane of the maximum shear stress. For brittle material, the fracture plane is normal to the directions of tensile stress. Mild steel is the most ductile compared to brass and aluminium. Therefore, torque is the highest in mild steel. Aluminium is the most brittle compared to mild steel and brass. Therefore, torque is the lowest in aluminium. 5) Cast iron fractures more easily than mild steel.
Mild steel need more revolution at the worm gear input to fracture the specimen. This is because cast iron is more brittle than mild steel, it is loss ductile. Cast iron has high carbon content causing it to be very brittle and is weak in tension. 4. 0 Error Analysis From the results we obtained, there was a certain error happened. Firstly, the input handwheel with 6 degree protractor scale and the 360 degree protractor scale was not pointing at the zero reading. Thus, this causes zero error in the reading. Secondly, the deflection arm and levelling handwheel was tightened up with the specimen in between the shaft.
However, the specimen was not really tight, which the specimen was not really sustained in the place, whereas it still turned while the handwheel was turning and the torque of the specimen was not accurate. Therefore, the readings obtained might deviate from the correct one. 5. 0 Conclusion and Recommendation To conclude, ductile materials have higher torsional rigidity, modulus of rigidity and shear yield stress and it fractures at higher value of angle of twist, whereas brittle materials have lower torsional rigidity, modulus of rigidity and shear yield stress and it fractures at lower value of angle of twist.
In this experiment, it shows that mild steel is the most ductile material while aluminium is the most brittle material compared to mild steel and brass. To improve the results, it is important to keep the diameter constant and vary the length of the material to find the mean value so it is more accurate and the zero error is eliminated to find the actual value. The torsion testing machine should be changed, as it is old and less accurate. 6. 0 References 1) “Laboratory Handbook”, Taylor’s University, 2012/2013. ) J. L. Meriam and L. G. Kraige, 2006, Engineering Mechanics Statics. 6th Ed. 3) http://www. scribd. com/doc/136565/Mechanics-of-Materials-Torsion-Test 4) http://www. ce. siue. edu/330L/Lab%20Help%20Desk/Metal%20Torsion%20Test/Metal%20Torsion. pdf 5) http://www. scribd. com/doc/50848950/4/TORSION-TEST-ON-MILD-STEEL-ROD 6) http://eng. sut. ac. th/metal/images/stories/pdf/Lab_4Torsion_Eng. pdf 7) http://encyclopedia2. thefreedictionary. com/torsional+rigidity