Report Mini Project

INTRODUCTION

Stress is a measure of forces acting on a deformable body. Complex shape of a body

has certain stress distribution and stress concentration. A stress concentration is a location in

an object where stress is concentrated. Geometric irregularities on loaded members can

dramatically change stresses in the structure. Geometric discontinuities cause an object to

experience a local increase in the intensity of a stress field. The examples of shapes that cause

these concentrations are cracks, sharp corners, holes and, changes in the cross-sectional area

of the object. High local stresses can cause the object to fail more quickly than if it wasn't

there. Engineers must design the geometry to minimize stress concentrations in some

applications. One of the applications of stress concentration is used in orthopaedics which a

focus point of stress on an implanted orthosis.A simple irregularity, a plate with a drilled hole,

is studied within this experiment such that the effects of this feature can be analyzed and

explored. For a hole, the maximum stress is always found at the closest position to the

discontinuity as shown in the figure below. The nominal stress refers to the ideal stress based

on the net area of the section.In this project, strain gauges are used to determine the strain and

stress distribution across the plate with a hole. Then, the experiment values are compared with

theoretical values.

LITERATURE REVIEW

THEORY

A stress concentration (often called stress raisers or stress risers) is a location in an

object where stress is concentrated. An object is strongest when force is evenly distributed

over its area, so a reduction in area, e.g. caused by a crack, results in a localized increase in

stress. A material can fail, via a propagating, when a concentrated stress exceeds the material's

theoretical cohesive strength. The real fracture strength of a material is always lower than the

theoretical value because most materials contain small cracks or contaminants (especially

foreign particles) that concentrate stress. Fatigue cracks always start at stress raisers, so

removing such defects increases the fatigue strength.

Figure. Internal force lines are denser near

the hole

Figure: stress distribution on flat plate with circular hole at the center under tensile.

Circular hole in an infinite plate under remote tensile

The stress distributions around a central hole can be estimated for the simple case ofan

infinitely wide plate subjected to tensile loading. The overall stress distributionsin the plate are

given by (Figure 1)

For θ=π /2,the hoop stress in eq. (3b) attains its maximum value ofσ θ=σ max=3σ . This

corresponds to the peak of the stress distribution circumferential stress distribution shown in

Figure 2a. Hence we may say that the stress concentration factor (the ratio of the maximum

local stress [component] to the far field stress [component] for this geometry is equal to 3.

However, it is important to note that stress near the hole greatly exceeds the far field stress.

Consequently, failure process may initiated locally at the edge of the hole under of far field

stress which are themselves sufficiently small to preclude such failure from occurring

remotely .

Figure 2b, which shows the radial variation ofσ θθalong the ray θ=π /2, emphasizes that the

magnitude of the stress concentration associated with the hole decays rapidly with increasing

distance from the notch. This is a clear example of St. Venant’s principle, which states that the

perturbations in a linear elastic stress field due to the presence of an isolated geometrical

discontinuity of size ‘d’ are localized within a region of characteristic linear dimension 3d

from the discontinuity. The stress levels outside this region are therefore close to the nominal

applied stress levels (un perturbed)

Figure 2: Distribution of hoop stress component σ θθ(a) around the circumference of circular

hole in a large body, and (b) radial distribution along the ligament where θ=π /2.

APPARATUS

Tensile test machine, data logger ,aluminium plate, cutting machine, drilling machine, sand

paper,sellotape,super glue ,strain gage,wire,solder,solvent and screw driver.

Tensile test machine data logger aluminium plate

Sand paper tape super glue

Strain gage wire solder

Acetone

PROCEDURE

Aluminium plate procedure:

1. Cut the aluminium plate dimension (70mm x150mm x 4mm) using cutter machine

2. Drill a circular hole at the center of the aluminium plate with diameter 10mm.

3. Remove the burr around the hole using file

Strain gauge installation procedure:

1. Clean the aluminium plate surface from dirt, oil or grease using solvent acetone.

2. Use the sand paper 400 grit to polish the uneven surface and smooth the gaging area

on the aluminium plate.

3. Use a clean rule and a fine pencil (2H or harder) or ball-point pen to draw the layout

lines, usually a dash-cross, a cross skip the targeting strain gage area, for alignment.

4. Re-clean the gaging area using solvent acetone.

5. Carefully open the folder containing the gage. Use a tweezers, not bare hands, to grasp

the gage. Avoid touching the grid. Place on the clean working area with the bonding

side down.

6. Use sellotape to pick up the strain gage and transfer it to the gaging area of the

specimen. Align the gage with the layout lines. Press one end of the tape to the

specimen, and then smoothly and gently apply the whole tape and gage into position.

7. Lift one end of the tape such that the gage does not contact the gaging area and the

bonding site is exposed. Apply super glue evenly and gently on the gage.

8. Apply enough adhesive to provide sufficient coverage under the gage for proper

adhesion.Place the tape and the gage back to the specimen smoothly and gently.

Immediately place thumb over the gage and apply firm and steady pressure on the

gage for at least one minute

9. Repeat the step 6,7 and 8 for two another strain gage

10. Tape the aluminium plate under the strain gauge wire to avoid the strain gage wire

contact with aluminium plate surface.

11. Cutsix lead wires to the desired lengthatleast 1 meter.Twist each bundle of conductors

together. Do not damage the lead wires by over twisting or nicking them.

12. Connect all six strain gage wires with lead wire using solder.

13. Taped the wire solder area to fix the position.Make sure that no non-insulated

conductors contact with the specimen. Secured the leadwires to the specimen (when

possible) by a durable tape.

Figure: Specimen with strain gage

Tensile machine test procedure:

1. Clamp the aluminium plate (specimen) on the tensile test machine at both sides. Make sure clamps the specimen tightly to avoid it slip during the process.

2. Taped all the leadwire on the machine body to avoid it moving during operation that will affect the operation result

3. Connect all the leadwire to strain gage’s data logger. Make sure all the connection is correct.

4. Set all the parameter required such as type of material, specimen dimension, force, speed and so on.

5. Start the operation

6. Stop the operation when forces reach 10 KN.

7. finish

RESULT &CALCULATION

Experimental

Strain gauges position

Points Radius, r (mm)1 52 103 15

Wherea = 5mm

1 2 3

a

Result tensile test using strain gauges:

1 2 3 1 2 3 1 2 3 1 2 3 1 2 3

1 0.215712 10 9 7 31 6.362906 250 189 168 61 12.64388 362 268 238 91 21.35253 512 371 337 121 29.99858 700 510 4712 0.2561574 13 11 8 32 6.66566 254 193 172 62 12.88477 366 271 240 92 21.65844 524 377 343 122 30.26378 707 519 4793 0.2954959 15 12 10 33 6.934075 263 198 175 63 13.14935 368 272 241 93 21.95861 524 382 346 123 30.5631 716 524 4844 0.346366 22 17 15 34 7.222808 266 202 178 64 13.43529 372 276 246 94 22.28726 530 386 352 124 30.86351 734 531 4915 0.3695315 24 21 18 35 7.468294 271 205 182 65 13.68871 374 279 249 95 22.55598 536 391 356 125 31.17073 733 535 4956 0.3929126 33 26 23 36 7.710573 273 207 183 66 13.97849 382 282 251 96 22.88976 544 395 361 126 31.49663 742 542 5017 0.4111652 39 31 28 37 7.991981 277 209 186 67 14.24545 386 285 253 97 23.1631 546 398 362 127 31.79917 747 546 5078 0.4291487 50 39 35 38 8.235724 282 212 188 68 14.51517 389 286 254 98 23.45994 554 403 367 128 32.11996 759 553 5129 0.4530886 57 46 40 39 8.503033 286 214 191 69 14.81359 395 290 258 99 23.75997 559 406 370 129 32.4326 764 558 517

10 0.478077 73 57 52 40 8.737648 286 217 192 70 15.06249 399 293 261 100 24.02986 564 411 375 130 32.75153 769 567 52611 0.5263396 81 65 57 41 8.951037 297 220 196 71 15.35348 399 295 262 101 24.34661 576 416 380 131 33.07105 783 572 53012 0.6236681 96 76 68 42 9.155992 297 222 198 72 15.62105 412 297 265 102 24.61602 580 422 384 132 33.3668 792 579 53813 0.7615084 104 83 74 43 9.328287 299 226 201 73 15.8885 415 301 268 103 24.90301 584 424 388 133 33.6974 798 584 54314 0.9486645 117 93 83 44 9.534362 303 228 203 74 16.18704 422 305 271 104 25.18001 591 431 394 134 34.00188 807 591 54915 1.166882 127 99 87 45 9.70513 307 231 207 75 16.45054 422 308 274 105 25.445 594 435 397 135 34.29832 812 596 55416 1.403025 133 103 92 46 9.889058 308 232 207 76 16.73683 427 312 278 106 25.76175 599 437 401 136 34.62344 819 596 55317 1.67194 143 110 97 47 10.0579 313 235 210 77 17.01876 431 316 283 107 26.02177 606 441 404 137 34.90001 813 591 54918 1.926713 149 117 102 48 10.22203 316 235 210 78 17.30543 435 317 284 108 26.31002 613 445 409 138 35.22314 805 586 54619 2.181179 161 123 108 49 10.40351 320 239 214 79 17.60441 442 322 288 109 26.59593 617 450 413 139 35.52276 802 584 54320 2.451603 167 128 112 50 10.5536 320 242 216 80 17.87638 446 325 292 110 26.85886 628 456 419 140 35.8151 802 582 54021 2.78487 178 136 119 51 10.72563 325 234 219 81 18.17005 449 328 294 111 27.16847 636 461 42322 3.151077 186 140 123 52 10.89232 328 245 219 82 18.46784 463 336 302 112 27.43136 640 465 42823 3.520988 195 146 128 53 11.04514 332 249 223 83 18.77509 465 339 305 113 27.72333 643 471 43224 3.906265 199 151 132 54 11.22976 337 252 225 84 19.12022 472 343 309 114 27.99432 651 474 43625 4.281545 210 158 139 55 11.38712 341 254 226 85 19.40931 476 347 314 115 28.27424 654 478 43926 4.646209 217 162 142 56 11.57061 341 257 229 86 19.76138 484 352 319 116 28.57889 663 484 44527 5.014659 222 169 148 57 11.73821 347 261 230 87 20.08263 489 354 321 117 28.84151 668 487 44828 5.356027 230 174 154 58 11.92511 357 262 233 88 20.38947 493 359 326 118 29.14074 677 492 45329 5.715757 239 181 159 59 12.16191 350 264 234 89 20.73077 500 364 330 119 29.41277 683 497 46030 6.041447 245 184 163 60 12.38317 361 266 237 90 21.01798 508 367 333 120 29.68536 694 506 467

TENSILE STRESS

σₒ (Mpa)

STRAIN (µm)TIME

TENSILE STRESS

σₒ (Mpa)

STRAIN (µm)STRAIN (µm)TIME

TENSILE STRESS

σₒ (Mpa)

STRAIN (µm)TIME

STRAIN (µm)TIME

TENSILE STRESS

σₒ (Mpa)TIME

TENSILE STRESS

σₒ (Mpa)

Stress of interest:

TIME (s)

TENSILE STRESS σ(MPa)

STRAIN (µ)At position 1 At position 2 At position 3

33 5.014659 222 169 14853 10.0579 313 235 21093 20.08263 489 354 321130 30.86351 734 531 491

Sample of Calculation:

Stress-strain relationship

εE=σ

Where

ɛ=Strain

σ=Stress

E= Modulus of Elasticity

Aluminum Infinite Plate with Modulus of Elasticity, E= 70GPa

At σ= 5.015659 MPa

When strain, ɛ = 222 x 10-6

σ θ=(222×10−6 ) ( 70×109 )=15.54×106 Pa

Result of stress at points :

Tensile Stress,σ = 5.014659(Mpa)Strain Gauge Position Stressσ θ(Mpa)

1 15.542 11.833 10.36

Tensile Stress, σ= 10.0579(Mpa)Strain Gauge Position Stressσ θ(Mpa)

1 21.912 16.453 14.7

Tensile Stress, σ = 20.08263(Mpa)Strain Gauge Position Stressσ θ (Mpa)

1 34.232 24.783 22.47

Tensile Stress, σ= 30.86351(Mpa)Strain Gauge Position Stress σ θ(Mpa)

1 51.382 37.173 34.37

5 10 150

10

20

30

40

50

60

15.5411.83 10.36

21.91

16.4514.7

34.23

24.7822.47

51.38

37.1734.37

Stress versus Strain Gauge Position

tensile stress = 5.014659MPa

tensile stress = 10.0579MPa

tensile stress = 20.08263MPa

tensile stress = 30.86351MPa

Strain Gauge Position from center of hole (mm)

Stre

ss, M

Pa

Theoretical

By formula,

σ θ=σ tensile

2 [2+ a2

r2 + 3a4

r4 ]Sample calculation:

At σ tensile=5MPa and radius r=5mm,

σ θ=5×106

2 [2+ 0.0052

0.0052+

3 (0.005 )4

0.0054 ]=15MPa

At σ tensile=5MPa and radius r=15mm,

σ θ=5×106

2 [2+ 0.0052

0.0152+

3 (0.005 )4

0.0154 ]=5.37MPa

At σ tensile=5MPa and radius r=25mm,

σ θ=5×106

2 [2+ 0.0052

0.0252+

3 (0.005 )4

0.0254 ]=5.112MPa

Result value of σ θ:

σpoints

5 10 20 30

1 (r=5mm) 15.00 30.00 60.00 90.00

2(r=15mm) 5.37 10.74 21.48 32.22

3 (r=25mm) 5.11 10.22 20.45 30.67

Comparison between experimental and theoretical

σ (MPa) σ θ(MPa)1 2 3

theoretical experimental theoretical experimental theoretical experimental5 15 15.54 5.37 11.83 5.11 10.3610 30 21.91 10.74 16.45 10.22 14.720 60 34.23 21.48 24.78 20.45 22.4730 90 51.38 32.22 37.17 30.67 34.37

Point 1:

Point 2:

Point 3:

DISCUSSION

From the comparison table between theoretical and experimental result, both are

showing different value of stress σ θ. According to the theory, the maximum stress will occur

at point 1 ( r = a), where σ θ = 3σ . However the stresses value for experimental does not follow

the theory. At point 1, only σ θ with σ = 5MPa having the same value of tangential stress while

the other give lower value than the theoretical. This shows that, at point 1 with σ = 5MPa, the

induced tangential stress, σ θ is three times the applied tensile stress, σ . For point 2 and 3, the

experimental values of σ θ show a higher value than theoretical. This phenomenon may occur

due to several causes.

One of the causes that may affect the result is clamping condition of aluminium plate.

In this experiment, the clamp used was for the fabric material. Therefore, is not suitable to use

for clamping aluminium because it can cause sliding between the plate and clamp due to

insufficient grip force.

Besides that, the sensitivity of strain gauges are also can affect the result of

experimental value for tangential stress, σ θ. The wires used for wiring the strain gauges are

not soft enough and may give influence to the value of strain gauges.

The size of strain gauges used in not suitable for the aluminium plate. It is suppose to

use 2mm strain gauges to get an accurate value of strain at the points of interest. In this

experiment, 5mm strain gauge was too large for the half width of plate and give result of same

value of strain at point 2 and 3.

CONCLUSION

For this mini project student have gain more understanding on stress concentration on

infinite plate with hole. The application of strain gauge alsowere done and the stress

correspondence with this strain were calculated using stress strain relationship to find the

stress concentration on infinite plate for experimental value and were compare with

theoretical value. From the experimental result the highest stress were at the radius near to the

hole and the stress decreases when the radius point farthest from the hole and this trend also

occur for theoretical value. Although the value for theoretical and experimental were differ

this are because due to the error but the characteristic or trend of stress concentration still

follow the theoretical were the higher stress at the point near to the hole and we can conclude

that this experiment are successful.

RECOMMENDATION

1. To minimize errors;

a) Sensitive machine – The machine is very sensitive, the strain gauge value are

very sensitive and when we run the strain gauge and tensile machine it need to

start at the same time so that the value for each device will not effect the result

value such as when the tensile machine were run at curtain point but the strain

gauge value not count because the opperator not start the strain device

setup.This maen the result for strain gauge and tensile test were not parallel

with each other.

b) The position of strain gauge position on the speciment shoud be alligment

properly with the hole axis.

c) The operator need to carefully operated the machine to avoid error.

2. The lab apparatus for strain gauge experiment in strength lab should be improved such

as the tensile machine clamp should have larger clamp area on the specimen so that

student can investigate the stress concentration at specimen with large surface area.

3. Other approach on determine the stress concentration on infinite plate can also be done

by simulation using FEA software such as ANSYS software or other finite element

software and compare with experimental result.

REFERENCES