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TORSION TEST REPORT / EMD4M1A

1.0 Title

MEC 424-APPLIED MECHANICS LAB

MATERIAL STRENGTH LAB

TORSION TEST

LECTURE: EN. ABDUL HAKIM B. ABDULLAH

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2.0Abstract

Ductile fracture is characterized by tearing of metal and significant plastic deformation. The

ductile fracture may have a gray, fibrous appearance. Ductile fractures are associated with

overload of the structure or large discontinuities. On both macroscopic and microscopic

levels, ductile fracture surfaces have distinct features. Macroscopically, ductile fracture

surfaces have larger necking regions and an overall rougher appearance than a brittle fracture

surface.

This experiment is about to determine the ductile of a sample from mild steel using torsion

test machine. Using a sample of 5.8mm and have length of 80mm, we have test it by using

the torsion machine and took the data stages by stages in order to get the most perfect data we

can get. On the 42nd data, the sample fracture. From the data that we have obtain, we have

found shear stress, τ, and shear strain, γ, by using the formula of ;

τ=TR/J

γ=RƟ/L

From this data of angle of twist, Ɵ, torque, T, shear stress, τ, and shear strain, γ, several

graphs have been plotted such as graph Torque vs. Angle of Twist and graph Shear Stress

vs. Shear Strain in order to get the value of Modulus of Rigidity, G.

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Table of Contents1.0 Title...........................................................................................................................................1

2.0 Abstract.....................................................................................................................................2

3.0 Introduction and Applications....................................................................................................5

4.0 Objectives..................................................................................................................................6

5.0 Theory.......................................................................................................................................7

6.0 Experimental Procedure.............................................................................................................9

5.1 Apparatus/Experimental Setup..............................................................................................9

5.2 Procedure.............................................................................................................................10

7.0 Data........................................................................................................................................11

8.0 References...............................................................................................................................15

9.0 Appendices..............................................................................................................................16

List of table:

Table 1: Data recorded during lab session...........................................................................................12Table 2: Data calculated for shear stress and shear strain..................................................................13

List of Figures:

Figure 1: Torsion in cylindrical bar.........................................................................................................5Figure 2: Shear stess vs. shear strain graph...........................................................................................8Figure 3: Torque test machine...............................................................................................................9Figure 4: Schematic diagram for apparatus set up................................................................................9Figure 5: Vernier calliper.......................................................................................................................9Figure 6: Torque meter..........................................................................................................................9Figure 7: Graph of torque vs. angle of twist........................................................................................12Figure 8: Graph of shear stress vs. shear strain...................................................................................14Figure 9: Graph of shear stress vs. shear strain (elastic regions).........................................................14Figure 10: Illustration of for angle of twist in torsion test...................................................................21Figure 11: Sample of fracture surface..................................................................................................21Figure 12: Preliminary stress-life data from torsion fatigue experiments...........................................21Figure 13: Observed fracture surfaces from static strength and fatigue tests....................................21Figure 14: Detailed images of a high cycle torsion fatigue specimen..................................................21

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List of Symbols

A Area over which force (F) acts (m2)

E Elastic modulus (GPa)

F Force (N)

( I ° )i Initial dimension in direction i (mm)

T Specimen thickness (m)

V chart Rate of chart displacement (mm/min)

V displacement Rate of sample displacement (mm/min)

w Specimen width (m)

δ chart Displacement of chart (mm)

δ sample Displacement of sample (mm)

ε Strain

ε ° =0 Predicted strain at zero stress

ε i Normal strain in direction i

∆E Error in the predicted elastic modulus (GPa)

∆F Error in the force (N)

∆ I i Change in dimension in direction i (mm)

∆t Error in the specimen thickness (m)

∆w Error in the width (m)

∆ ε° =0 Error in the predicted strain at zero stress

∆∅ Error in the predicted intercept of stress-stain data (MPa)

∆ σ Error in the stress (MPa)

∅ Predicted intercept of stress-strain data (MPa)

σ Engineering stress (MPa)

σ y Yield point (MPa)

σ ult Ultimate strength (MPa)

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3.0 Introduction and Applications

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 forge ability of the materials by means of torsion testing at elevated

temperatures.

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. 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 and then applying the twisting moment till failure. The torque and degree of rotation

are measured and plotted. 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

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Figure 1: Torsion in cylindrical bar


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 to produce torque until the

specimen fails.

4.0 Objectives

The purpose of this experiment is to :

1. To observe the material’s behaviors when subjected to pure torque

2. Identify Types of fracture surface under pure loading.

3. Validate the data between experimental and theoretical values.

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5.0 TheoryWe consider torsional moment T acting on a solid shaft of homogeneous material and

uniform cross-section with radius r and segment length L. A circular shaft subjected to

twisting moment along its pole axis. In order to accurately determine values for the modulus

of rigidity, shear stresses and shear strains equations must be derived which describe these

values in terms of values which can be measured. Shear stresses will be set up that are

proportional to the applied torque given by the following relation:

τ=Gγ (1)

γ= rθL (2)

From 1 and 2:

Where,

T = Applied Torque ……………………………………… Nm

J = Polar second moment of area…………………………mm4

G = Modulus of rigidity ………………………………….

Nmm2

θ = Angle if twist (over length L)……………………….. radians

τ = Shear stress at radius ‘r’……………………………

Nmm2

r = radius…………………………………………………. mm

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TJ=G×θ

L= τ

r


Hence, knowing shear stress,τ and shear strain,γ by calculating the slope of the graph, G can be determine.

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Figure 2: Shear stess vs. shear strain graph


6.0 Experimental Procedure

5.1 Apparatus/Experimental Setup

1) Loading Device2) Mild steel Specimen3) Torque measurement unit4) Wheel

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123

4

Figure 3: Torque test machine

Figure 4: Vernier calliper

Figure 6: Schematic diagram for apparatus set up

Figure 5: Torque meter


5.2 Procedure

1. The specimen size and the overall length is measured.

2. A straight line is drawn using pencil lead on the specimen length in order to observe

the effect of twisting on the specimen.

3. The specimen’s ends are fixed on the machine chuck and all readings on the gauge are

set up to zero.

4. The specimen is ensured to not initially load.

5. The hand wheel is turned on clockwise to provide the applied load.

6. Torque is measured by a reference torsion rod and strain gauge that is taken from the

torque meter.

7. For the first rotation, we chose an increment of a quarter rotations (90°). For the

second and third of a half rotation (180°) and for the fourth and to 10 th rotation of one

rotation (360°).

8. The angle of twist at the specimens defined by divides the rotation at the input by the

reduction of 62. Usually fracture will occur between 100 and 200 rotations.

Note:

o Quarter rotation 4 readings, half rotation 4 readings, 1 rotations until specimen

break.

o For each rotation of the hand wheel, the deformation of the specimen is

compensated by turning the hand wheel of the compensation unit, until the

dial gauge returns to its initial value (zero) and the torque taken from display.

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7.0 Data

Materials type = Mild steel, Length, L = 82 mm, Diameter, d = 5.90 mm

Scale readingsat the worm gear

input in rev.

Twisting angleat the specimen

in degrees

Load Torquein Nm

Dial Gaugein mm

0 0 0 0(1/4) 1.45 0.95 0.31(1/2) 2.9 2.7 0.5(3/4) 4.35 4.6 0.65

1 5.8 6.75 0.81.5 8.71 11.05 1.112 11.61 14.5 1.36

2.5 14.52 16.55 1.53 17.42 17.6 1.594 23.23 18.7 1.655 29.03 19.25 1.696 34.83 19.35 1.77 40.64 19.4 1.78 46.45 19.5 1.729 52.26 19.6 1.72

10 58.06 19.65 1.7211 63.87 19.7 1.7312 69.68 19.7 1.7313 75.48 19.4 1.714 81.29 19.4 1.715 87.1 19.35 1.716 92.9 19.3 1.717 98.71 19.3 1.6918 104.52 19.3 1.6919 110.32 19.3 1.6920 116.13 19.25 1.6921 121.94 19.25 1.6922 127.74 19.25 1.6923 133.55 19.15 1.6924 139.35 18.95 1.6725 145.16 18.3 1.6326 150.97 17.05 1.54

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L

d


27 156.77 15.05 1.428 162.58 11.1 1.129 168.39 4.75 0.6630 174.19 2.1 0.4631 180 0.6 0.3432 180.5 0 0

Table 1: Data recorded during lab session

Sample calculations to obtain the modulus of rigidity, G a table shear stress, τ and shearing strain, γ :

τ = G γ, where τ is proportional with γ

τ = TR , γ = Rθ , where R = 2.95 ×10-3m

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J L J = (1/32)πd4 = 1.19 ×10-10 m4

L = 82×10-3 m

τ = TR = (0.95Nm)( 2.95×10 -3 m) = 23.55 MPa1.19 ×10-10 m4

J

γ = Rθ = ( 2.95 ×10 -3 m)(0.025310566) = 0.0009106L 82×10-3 m

0 20 40 60 80 100 120 140 160 180 2000

5

10

15

20

25

Torque vs Angle of Twist

Angle of Twist, Ɵ (°)

Torq

ue, T

(Nm

)

Figure 7: Graph of torque vs. angle of twist


Scale readings

at the worm gear

input in rev.

Load Torquein Nm

Twisting angleat the specimen

in radians

Shear stress, τ (Pa)

Shear strain, γ (dimensionless)

0 0 0.000000 0.00 0.000000(1/4) 0.95 0.025311 23550420.17 0.000911(1/2) 2.7 0.050621 66932773.11 0.001821(3/4) 4.6 0.075932 114033613.45 0.002732

1 6.75 0.101242 167331932.77 0.0036421.5 11.05 0.152038 273928571.43 0.0054702 14.5 0.202659 359453781.51 0.007291

2.5 16.55 0.253455 410273109.24 0.0091183 17.6 0.304076 436302521.01 0.0109394 18.7 0.405493 463571428.57 0.0145885 19.25 0.506735 477205882.35 0.0182306 19.35 0.607977 479684873.95 0.0218727 19.4 0.709394 480924369.75 0.0255218 19.5 0.810811 483403361.34 0.0291699 19.6 0.912227 485882352.94 0.032818

10 19.65 1.013470 487121848.74 0.03646011 19.7 1.114886 488361344.54 0.04010912 19.7 1.216303 488361344.54 0.04375713 19.4 1.317545 480924369.75 0.04739914 19.4 1.418962 480924369.75 0.05104815 19.35 1.520379 479684873.95 0.05469716 19.3 1.621621 478445378.15 0.05833917 19.3 1.723038 478445378.15 0.06198718 19.3 1.824455 478445378.15 0.06563619 19.3 1.925697 478445378.15 0.06927820 19.25 2.027114 477205882.35 0.07292721 19.25 2.128530 477205882.35 0.07657522 19.25 2.229773 477205882.35 0.08021723 19.15 2.331189 474726890.76 0.08386624 18.95 2.432432 469768907.56 0.08750825 18.3 2.533848 453655462.18 0.09115726 17.05 2.635265 422668067.23 0.09480527 15.05 2.736507 373088235.29 0.09844828 11.1 2.837924 275168067.23 0.10209629 4.75 2.939341 117752100.84 0.10574530 2.1 3.040583 52058823.53 0.10938731 0.6 3.142000 14873949.58 0.11303532 0 3.150728 0.00 0.113349

From table 2 above, graph shear stress against shearing strain is plotted.

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Table 2: Data calculated for shear stress and shear strain


For calculating the modulus of rigidity, G, we have to plot a graph taking the values

between the elastic regions. The graph is shown below.

τ = G γ, where τ is proportional with γ, therefore, we have to calculate the gradient of

the graph which present the modulus of rigidity, G.

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0.000000 0.020000 0.040000 0.060000 0.080000 0.100000 0.1200000.00

100000000.00

200000000.00

300000000.00

400000000.00

500000000.00

600000000.00

Shear Stress vs Shear Strain

Shear Strain, γ (dimensionless)

Shea

r Str

ess,

τ (P

a)

Figure 8: Graph of shear stress vs. shear strain

0.000000 0.002000 0.004000 0.006000 0.008000 0.010000 0.0120000.00

50000000.00100000000.00150000000.00200000000.00250000000.00300000000.00350000000.00400000000.00450000000.00500000000.00

Shear Stress vs Shear Strain (elastic regions)

Shear Strain, γ (dimensionless)

Shea

r Str

ess,

τ (Pa

)

Figure 9: Graph of shear stress vs. shear strain (elastic regions)

G = ∆τ / ∆γ


8.0 References

1. http://www.ami.ac.uk/courses/topics/0124_seom/index.html. [Accessed 13/04/14].

2. Van Vlack, L.H., Introduction to Materials Science and Engineering - 6th Edition,

Addison Wesley, 1989, p 12.

3. Smith,W.F., Principles of Materials Science and Engineering - 2nd Edition,

McGraw Hill, 1990, p 268.

4. Dewey, B. R., Introduction to Engineering Computing - 2nd Edition, McGraw-

Hill, 1995, p 80.

5. Mechanics of materials, 3rd Edition, McGraw Hill by Ferdinand P. Beer, E.

Russell Johnston Jr. and John T. DeWolf. Page 223.

6. http//:www.wikipediatorsion.htm [Accessed 13/04/14].

7. Materials science and engineering an introduction, Wiley, By William D. Callister

Jr. Page 189.

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9.0 Appendices

Reference from manual book:

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