Torsion Test Experiment 2 PDF

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EXPERIMENT 2 TORSION TEST

1.0 Objective i. To determine the modulus of rigidity, maximum shearing stress, maximum shearing strain and Poisson`s ratio for the tested specimen. ii. To study the linearly elastic behaviour of the tested specimen under torsion and to obtain the relationship between torsional load and angle of twist for a full range of strains until failure. 2.0 Introduction The purpose of torsion testing usually parallels that of uniaxial tension tests. In this experiment, solid cylindrical specimen of steel or brass will be subjected to a torsional load. The test will be conducted until failure (i.e. it will end in the fracture). During the test, the angle of twist and the applied torque are measured as the test proceeds. From the applied torque, the student will calculate the shear stress and shear strain of the tested material. The modulus of rigidity will be obtained from the plotted graph and compared to reference value. 3.0 Background Torsional loads are created by propellers on aircraft, transmissions in cars or by highway signs that are twisted by wind. Torsion loading results in twisting of one section of a body with respect to a contiguous section. Torque is a moment that tends to twist a member about its longitudinal axis. Shearing strains are induced in members under torsion. Shafts are widely used in engineering applications to transmit power from one point to another. A torque, T is applied to the shaft as shown in Figure 1 where the shaft is fixed at one end and free at the other. As a result, complementary shear stresses are developed on the longitudinal planes which cause a distortion of filaments.

Figure 1

In a torque against angle of twist relationship, the modulus of rigidity or shear modulus of the tested specimen can be determined by using the following relationship: G = TL / Jφ

and G = τ / γ where; T = applied torque L = length of the shaft G = modulus of rigidity φ = angle of twist within the tested length. The largest shear stress occurs at the outside surface of the material and can be calculated using the following relationship: τ = Tr / J where; τ = shear stress r = radius of the shaft J = polar moment of inertia of the shaft The shearing strain occurs along the tested length of the shaft can be determined using the following relationship: γ = rφ / L where; γ = shear strain The relationship between the modulus of rigidity and modulus of elasticity within the linear elastic range of the material is described by Hooke`s law, which relates the Poisson`s ratio of the tested material is given by; E = 2G (1+v) where; v = Poisson`s ratio E = modulus of elasticity The torque can also be obtained by using the following relationship; T = G (Jθ) where; θ = φ / L = angle of twist per unit length

TORSION TEST MACHINE

STRAIN GAUGE

DEGREE DISK (dego)

REVOLUTION COUNTER

WORM GEAR

SPECIMEN PICTURE

DIAL GAUGE FOR COMPENSATION

MEASURING CALIPER

SPECIMEN (AFTER TEST)

SPECIMEN (BEFORE TEST)

5.0 Procedure

1. The diameter and length of each specimen is measured. 2. A straight line is drawn using pencil lead in order to observe the effect of twisting. The both end of the specimen is fixed to the specimen holder. 3. The specimen is mounted between the loading device and the torque measuring unit. The shifting specimen holder of the load is in the mid position is made sure. 4. The specimen is not initially loaded. The hand wheel clockwise is turned to provide the applied load. The measuring amplifier is turned on and set to zero. The read out values is the applied torque. 5. For the first rotation, an increment of a quarter rotation (900) is chosen, for the second and third rotation of a half rotation (1800) and for the fourth to 8th rotation of one rotation (3600). For the 9th 6. The angle of twist at the specimen is calculated, the rotations at the input are divided by the reduction ratio of 62. Usually, the fracture will occur between 100 to 200 rotations and 200 to 300 rotations for the mild steel and brass material respectively and continued to specimen fracture, the reading of the applied load and angle of twist for each 5 or 10 rotations is taken.

6.0 Result 1. The experimental data should be filled in the table as provided in the worksheet and complete the tables by using the appropriate equations (i.e. calculate the shear strain from experimental angle of twist and shear stress from applied torque). 2. Plot the graph: i. Torque (y-axis) vs angle of twist (x-axis) ii. Shear stress (y axis) vs shear strain (x-axis) 3. Determine the experimental modulus of rigidity from the graph (i) (i.e. the slope of the line). Then, in conjunction with the modulus of elasticity from a reference value, calculate the Poisson`s ratio. Also, determine the yield shear stress, ultimate shear stress and fracture shear stress. 4. Sketch the fracture surface of the tested specimen.

7.0 Discussion 1. Compare the results of this test between the experiment and reference (standard) value of modulus of rigidity, Poisson` ratio, shear stress and shear strain. Comment on any differences and possible sources of error. 2. Describe the behaviour of this material as it responds to increasing applied torque. 3. Is the Hooke's law for shearing stress and strain valid? Explain. 4. Describe the appearance of the fracture surface of the tested specimen and discuss the mode of failure (ductile failure or brittle failure under torsion). 5. Which should be able resist more torque – a solid bar or hollow bar of the same material and crosssectional area? Explain....