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