Introduction to Torsion in Engineering Applications

EXPERIMENT 4 4 TORSION TEST 4.1 Introduction 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 occurs when the twisting moment or torque is applied to a member according to Error! Reference source not found.. 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. Figure 3: Torsion in Cylindrical Bar 4.2 Objective To determine the behavior of materials when subjected to torsion, and to obtain some of their mechanical properties. 4.3 Apparatus SM 21 Advanced torsion testing machine. Figure 4: Torsion Apparatus This free-standing apparatus enables forward and reverse torsion tests on a range of sizes and lengths of specimen requiring test torques of up to 200Nm or 200lbf in. Load is applied by a variable speed geared electric motor driving through a two stage 1200:1 reduction gearbox. The Torque reaction is provided by a pendulum whose angular movement is sensed by a rotary potentiometer. This potentiometer provides an output to a digital meter calibrated to read torque in either N-m or lbf-in. The input rotation is measured by protractor scales on the gearbox input and output shafts and by a digital counter on the input shaft. A separate scale measures the pendulum angle, and the angle of twist of the specimen is determined as the difference between the input and pendulum angles. The test specimen are held at each end by sockets mounted on the input and pendulum shafts, various sizes being supplied to enable use of variety of specimens. Figure 5: Torsion Specimen 4.4 Theory In torsion test, a solid or hollow cylindrical specimen is twisted, and the resultant deformation measured as angle through which the bar twisted. Figure 6: Torsion for a Solid Bar Considering a cylindrical bar with one end being twisted as shown in Error! Reference source not found., the twisting moment MT 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 relate d to the shear stress as follow: M T G    J L r The shear strain  , can calculated from equation 2: (9.1) 𝛾 = 𝑡𝑎𝑛 𝜃 = 𝑟𝜃 (9.2) 𝐿 Where, J is the polar moment of inertia, mm 2 G is the shear modulus, N/mm 2  is degree of rotation, radian r is the radius of the cylindrical bar,mm L is the length of the cylindrical bar,mm  is the shear stress,N/mm 2 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 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 𝜏= 𝑀𝑇 𝑟 (9.3) 𝐽 For a solid cylindrical specimen, the polar moment ( J   D 4 32 ), we can therefore determine the shear stress as shown in equation 4  M T D 2 16M T   D 4 32  D3 (9.4) For a tube specimen, the maximum shear stress at the peripheral of the tube can be calculated from equation 5