# Torsion Testing. Objectives

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1 Laboratory 4 Torsion Testing Objectives Students are required to understand the principles of torsion testing, practice their testing skills and interpreting the experimental results of the provided materials when failed under torsion. To determine the maximum shearing stress, shear stress at proportional limit, shear modulus or modulus of rigidity and relationships between torque and degree of rotation of the tested materials. Students are able to differentiate the ability of materials such as cast iron and brass to withstand torque prior to torsion failure. Analysis and interpretation of the test parameters obtained should be carried out in relation to the failure nature of each material. Students are capable of selecting materials for engineering applications associated with torsion. Mechanical metallurgy laboratory

2 1. Literature review In many areas of engineering applications, materials are sometimes subjected to torsion in services, for example, drive shafts, axles and twisted drills. Moreover, structural applications such as bridges, springs, car bodies, airplane fuselages and boat hulls are randomly subjected to torsion. The materials used in this case should require not only adequate strength but also be able to withstand torque in operation. Even though torsion test is not as universal as tension test and do not have any standardized testing procedure, the significance lies on particular engineering applications and for the study of plastic flow in materials. Torsion test is applicable for testing brittle materials such as tool steels and the test has also been used to determine the forgeability of the materials by means of torsion testing at elevated temperatures. 1.1 Torsion test Figure 1: Torsion in cylindrical bar [1]. Generally, torsion occurs when the twisting moment or torque is applied to a member according to figure 1. The torque is the product of tangential force multiplied by the radial distance from the twisting axis and the tangent, measured in a unit of N.m. In torsion testing, the relationship between torque and degree of rotation is graphically presented and parameters such as ultimate torsional shearing strength (modulus of rupture), shear strength at proportional limit and shear modulus (modulus of rigidity) are generally investigated. Moreover, fracture surfaces of specimens tested under torsion can be used to determine the characteristics of the materials whether it would fail in a brittle or a ductile manner. Mechanical metallurgy laboratory

3 Figure 2: Torsion testing machine [2]. In order to study the response of materials under a torsional force, the torsion test is performed by mounting the specimen onto a torsion testing machine as shown in figures 2-4, and then applying the twisting moment till failure. The torque and degree of rotation are measured and plotted as shown in figure 5. It can be seen that higher torsional force is required at the higher degrees of rotation. Normally, the test specimens used are of a cylindrical rod type since the stress distribution across the section of the rod is the simplest geometry, which is easy for the calculation of the stresses. Both ends of the cylindrical specimen are tightened to hexagonal sockets in which one is fitted to a torque shaft and another is fitted to an input shaft. The twisting moment is applied by turning the input handwheel as illustrated in figure 3 to produce torque until the specimen fails. Mechanical metallurgy laboratory

4 Figure 3: Schematic diagram showing details of torsion testing machine [2] Figure 4: Torsion specimen [2] When the twisting moment is applied, the torque is reacted by a torque shaft, which moves in relation to the deflection arm. The movement of the deflection arm is measured by a linear potentiometer, which is connected to a calibrated TQ digital torque meter to give a readout of the torque in a unit of Nm or lb.in. The more we turn the input handwheel clockwise to increase the degree of rotation, the more torque is produced. At the initial stage, the graphical relationship of the torque and degree of rotation measured is linear as demonstrated in figure 5. The specimen is Mechanical metallurgy laboratory

5 elastically deformed and the recovery of the specimen to its original shape is possible if the specimen is unloaded. However, if a high degree of rotation is applied passing a proportional limit, the specimen starts to deform plastically and will not return to its original shape when the input handwheel is turned anti-clockwise. The degree of rotation can be read out from two protractors, elastic and plastic range protractors. First, an elastic range protractor scale is fitted on the input handwheel connected to the input shaft of the gear box. This protractor scale provides an accurate reading of 0.1 o and thus one revolution represents 6 o. A resettable revolution counter is fitted to the gearbox to record the overall input revolutions. When the twisting moment is large, the second protractor scale is required for the readouts in the plastic range of deformation. The second protractor is fitted onto the output shaft and provides a reading of 1 o with one revolution representing 360 o. Figure 5: Relationship between torque and angle of twist [2]. Considering a cylindrical bar with one end being twisted as shown in figure 6, the twisting moment M T is resisted by the shear stress τ existing across the specimen section. This shear stress is zero at the center of the bar, increases linearly with its radius and finally reaches its maximum value at the peripheral of the bar. If the cylindrical bar with a length of L, the twisting moment can be related to the shear stress as follow Mechanical metallurgy laboratory

6 M T J Gθ τ = L r = (1) The shear strain, γ, can be calculated from equation 2 rθ γ =tan θ = (2) L where J is the polar moment of inertia, mm 2 or in 2 G is the shear modulus, N/mm 2 or lbf/in 2 θ r L is degree of rotation, radian is the radius of the cylindrical bar, mm or in is the length of the cylindrical bar, mm or in τ is the shear stress, N/mm 2 or lbf/in 2 Figure 6: Torsion of a solid bar [3]. According to the graphical relationship of torque and degree of rotation, we can notice that the torsion specimen deformed elastically and then plastically similar to the case of the tension tested specimen. The initial stage of elastic behavior shows a linear relationship of torque and degree of rotation with its slope representing the shear modulus of the modulus of rigidity, G. The stress at the proportional limit is frequently determined at 0.04 rad.m -1 of the gauge length. Beyond the proportional limit, specimen deformed in a plastic manner and the relationship between the torque and the degree of rotation is no longer linear. However the determination of the proportional limit carried out using a torsional specimen of a thin-wall tube type will provides a more accurate value in comparison to that obtained from a cylindrical rod type specimen. Since the stresses vary across the section of the specimen from the center toward the peripheral of the specimen as mentioned Mechanical metallurgy laboratory

7 previously, the reduced effect of stress distribution in the thin-walled specimen is therefore beneficial for the calculation of the stress. Within the elastic range of deformation, the shear stress can be calculated according to equation 1 M T r = J τ (3) For a solid cylindrical specimen, the polar moment J = πd 4 /32, we can therefore determine the shear stress as shown in equation 4 MTD/ 2 16M τ = 4 πd / 32 πd = (4) T 3 For a tube specimen, the maximum shear stress at the peripheral of the tube can be calculated from equation 5 16M 1 = T π 4 ( D D D τ (5) ) where D 1 D 2 is the outer diameter of the tube is the inner diameter of the tube Therefore, if the torque and the degree of rotation are known according to the experimental result, the shear stress and the shear strain can be determined from equations 2 and 4. The obtained information is then used for the construction of the graphical relationship between the modular shear stress (16M T /ad 3 ) and the shear strain (θr/l) as illustrated in figure 7. The curve is somewhat similar to those typical stress-strain curves tested under tension, giving elastic and plastic ranges with respect to the torsional stress applied. Nevertheless, the calculated shear stress according to equation 4 is only suitable for the evaluation of the stresses in the elastic range. The plastic stress obtained from the shear stress-shear strain curve is therefore larger than the real stress. Furthermore, in the case that there is a large amount of plastic deformation involved, the length of the specimen is considerably changed, which can result in the superposition of the longitudinal stresses on the torsional shear stresses. Even Mechanical metallurgy laboratory

8 though, the former is considered to be small and can be neglected, they might also affect the torsional failure strain of the specimen. Nadai [3] has proposed the method for the calculation of the stress in the plastic range from a known torque-degree of rotation curve as expressed in equation 6 3M τ = (6) u max 3 2πa where M max a is the maximum twisting moment is the distance from the center to the peripheral of the specimen according to figure 4. Figure 7: Relationship between modular shear stress and shear strain [2]. 1.2 Types of torsion failures Torsion failures are different from tension failures and normally provide little deformation or elongation. The characteristic of the fracture surface is related to the state of stress at the point on the bar surface, which can be described as shown in figure 8. It can be seen that the maximum shear stresses exist along two planes, which are perpendicular to each other. One is perpendicular to the longitudinal axis (yy) and another is aligned parallel to the longitudinal axis (xx). The principle Mechanical metallurgy laboratory

9 stresses σ 1 and σ 3 are inclined at 45 o to the longitudinal axis and have their magnitudes equal to those of the shear stresses. The principle stress σ 1 is tensile while the principle stress σ 3 is compressive. The intermediate stress σ 2 is zero under torsion. As mentioned previously, the characteristics of torsion fractures are influenced by torsional and tensile forces. These result in two types of torsion failures; 1) ductile failure due to the shear stresses and 2) brittle failure due to the tensile stresses. The former produces the fracture surface along the plane of the maximum shear stress and more frequently normal to the longitudinal axis as shown in figures a) and b). The latter exhibits the fracture planes normal to the directions of the tensile stresses, which are 45 o to the longitudinal axis. Figure 9 shows brittle and ductile fracture surfaces observed from a driveshaft and a brass rod respectively failed under torsion. This means the driveshaft failed under a brittle manner influenced by the tensile stresses while the ductile failure of the brass rod was affected by the shear stresses. However, if the specimen fails into little pieces where the fracture plane cannot be determined, the fracture in this case is considered to start along the maximum shear stress parallel to the longitudinal axis of the specimen. In addition, it has also been shown in a study, which has indicated that the fracture characteristic is associated with the hardness of the tool steels. If the tool steel possesses the hardness values of higher than 720 VHN, failure is expected to be influenced by tensile stress. Conversely, if the hardness of the tool steel is lower than 720 VHN, the shear stress is responsible for such a failure. Figure 8: Types of failure in torsion [3]. Mechanical metallurgy laboratory

11 Figure 10: Calibration of the torsion testing machine [2]. Mechanical metallurgy laboratory

12 2. Materials and equipment 2.1 Test specimens 2.2 Micrometer or vernia caliper 2.3 Permanent pen 2.4 Torsion testing machine 3. Experimental Procedure 3.1 Measure initial diameter, initial length and initial gauge length of the specimen. Record these parameters on the table provided. 3.2 Draw a line using a permanent pen along the length of the test specimen. This line will help to notice the degree of rotation during applying the twisting moment. 3.3 Calibrate the testing equipment following section Grip the test specimen on to the torsion testing machine using hexagonal sockets and make sure the specimens are firmly mounted. Fit both ends of the specimen to input and torque shafts and set reading on the torque meter to zero. 3.5 Start twisting the specimen at strain increment of 0.5 o until failure occurs. Record the received data rotation in the table provided for the construction of torque and degree relationship 3.6 Construct the relationship between shear stress and shear strain. Determine maximum shear stress, shear stress at proportional limit and modulus of rigidity. 3.7 Sketch fracture surfaces of failed specimens and described their natures in the table provided. 3.8 Discuss and conclude the obtained experimental results. Mechanical metallurgy laboratory

13 4. Results Details Cast iron Brass Initial diameter (mm) Final diameter (mm) Initial gauge length (mm) Final gauge length (mm) Initial overall length of specimen (mm) Final overall length of specimen (mm) Strain increment (degree) Maximum torque (Nm) Maximum shear stress (MPa) Shear stress at proportional limit (MPa) Modulus of rigidity (GPa) Fracture surface details Table 1 Experimental results for torsion test of cast iron and brass. Mechanical metallurgy laboratory

14 5. Discussion Mechanical metallurgy laboratory

15 6. Conclusions Mechanical metallurgy laboratory

16 7. Questions 7.1 Did cast iron and brass fail in different fracture manners? Explain. 7.2 What are the differences between torsion and tension tests? Mechanical metallurgy laboratory

17 7.3 Which engineering applications do you think that torsion test is vital? Give three examples. 8. References SM1/2 Torsion testing machine, TecQuipment Ltd Dieter, G.E., Mechanical metallurgy, 1988, SI metric edition, McGraw-Hill, ISBN Mechanical metallurgy laboratory

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