Lab Manual
Lab Manual
Lab Manual
2 To find out the impact strength of material using CHARPY & IZOD
load test.
1
EXPERIMENT NO. 1
Theory:
The denotation "Micro hardness" derives from the field of hardness determination by means of an indenter
entering the material to be tested with a specific load and dwell time. After removing the indenter, the
produced imprint is measured and the "hardness number" calculated.
The changes produced by the indenter entering the material are mainly determined by the elastic-plastic
characteristics of the material. Other determining factors are internal stress, tensile and compression
properties, cohesion, brittleness etc. Also the production process plays an important part. With
heterogeneous systems, e.g. Thin layers on a base material, the hardness number depends also on the way
the thin layer is applied to the base material.
The different methods of micro hardness testing are determined by the various shapes of indenters, as
e.g.:
The Knoop and Vickers methods have been generally accepted and are the most widely used. The Vickers
indenter is a four sided pyramid with square base and an apex angle between opposite sides of 𝛼 = 136° (±
15') The knoop indenter is also a four sided pyramid with rhombic base and longitudinal edge angles of 𝛼=
172° 30' (± 5') and 𝛽 = 130° The depth of the knoop imprint is therefore by the factor4. 4 shallower than
that of the Vickers imprint with equal diagonal length. The hardness number (HV or HK, resp.) is calculated
by dividing the load (indentation force) by the surface of the imprint. In case of Vickers, the surface is the
4 pyramid surfaces, whereas in case of knoop the basis is the projected pyramid surfaces into the specimen’s
surface.
α.... Face angle (Vickers) or edge angle (Knoop) of the pyramidal diamond indenter (°)
2
β... Edge angle (Knoop) of the pyramid diamond indenter (°)
𝛼 𝛼 𝛽
𝐹 sin 2 𝐹 𝐹 𝑡𝑎𝑛 2 cot 2 𝐹
HV = = 2F = 1.8544 HK = = 2F = 14.229
𝐴 𝑑2 𝑑2 𝐴 𝑑2 𝑑2
Indentation Depth
When investigating layers or coatings on a substrate material, the thickness of the layer has to be considered,
it should have a minimum thickness of the layer has to be considered. It should have a minimum thickness
in respect to the diagonal length, which is proportional to the indentation depth. To avoid an influence of
the substrate material, the minimum layer thickness should be approximately 10 times larger than the
indentation depth. Based on the geometric shape of Vickers and Knoop diamond following table gives the
correlation between diagonal length, indentation depth and minimum layer thickness:
The smaller the test forces and the smaller the indentations, the more the hardness measurement applies to
surface layers only. The hardness of the surface layers is usually different from the interior of the material
for various reasons. Therefore, hardness value measured with small test forces cannot be the same as
hardness values of larger test forces that penetrate more deeply into the material. On the other hand,
hardness values measured with small test forces can often give a better picture for material wear in practical
application.
Therefore the indentation depth of the indenter should be chosen according to whether surface hardness or
inner hardness is more important.
Distance between
Imprints
3
To avoid also a mutual influence of imprints, following table gives the relative distances between the
centres of individual imprints of an indentation series:
Vickers ≈ 4× d
Knoop ≈2×d
≈ 4 × d2
Vickers ≈ 2. 5 × d
Experiment No. 2
4
Aim: To find out the impact strength of material using CHARPY & IZOD load test.
Theory :
Impact strength is a complex characteristic which takes into account both toughness and strength of
material. The capacity of a material to resist or absorb shock energy before it fractures is called its impact
energy/strength. Impact strength is sensitive to rate of loading temperature as well as to stress raisers (e.g.
Notches) Ductile material posses higher impact strength than brittle material. Impact testing becomes
essential in order to study the behaviour of material under dynamics loading; an impact test determines the
behaviour of materials when subjected to high rates of loading usually in bending, tension or torsion. In
impacts test a specimen machined or surface ground and usually notched is struck and broken by a single
blow in a specially designed testing machine. The quantity measured is the energy absorbed on breaking
the specimen by a single blow. The ideal impact test would be one in which all the energy of blow is
transmitted to the test specimen. Two type of specimen are used on an impact testing machine i.e. IZOD
and CHARPY
1. As standard izod specimen is 75mm long and having cross-section area of 10×10mm. A notch is
constructed at a distance of 28mm from one end.
A standard charpy specimen is 55mm long and having a cross section area of 10×10mm. A notch is
constructed at centre.
2. The charpy specimen is placed in vice, so that it is just a simply supported beam whereas an izod
specimen is placed in the vice such that it is cantilever.
3. The charpy specimen is hit behind the V notch while the izod specimen is placed with the v notch
facing the pendulum and will hit above the notch.
4. In case of charpy specimen, the hammer is raised to an angle of140° while izod, it is raised to 90°.
Procedure: 1. The swinging pendulum is raised to standard height depending upon the type of
specimen to be tested.
2. With reference to the vice holding the specimen the higher the pendulum, the
more potential energy it has got.
3. As the pendulum is released its potential energy is converted into kinetic energy
and its strike the specimen.
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4. A portion of the energy possessed by the pendulum is used to rupture the specimen and
pendulum rises on other side of the machine to a height on the opposite side of the impact
testing machine.
5. The energy is kg-m is the notched impact strength and can be read from the dial
of the machine.
Discussion:
Experiment No. 3
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Objective: The fundamental objectives of this study are:
1. To perform the creep test on a polypropylene/Lead specimen and to observe the creep
phenomenon.
2. To experimentally obtain the creep curve.
3. To derive the creep constants from experimental data.
Apparatus required:
WP600 creep measurement apparatus, Polypropylene specimens, Vernier, Weights, Weight hanger,
Thermometer.
Theory:
What is Creep?
When a material like steel is plastically deformed at ambient temperatures its strength is increased
due to work hardening. This work hardening effectively prevents any further deformation from
taking place if the stress remains approximately constant. Annealing the deformed steel at an
elevated temperature removes the work hardening and restores the steel to its original condition.
However, if the steel is plastically deformed at an elevated temperature, then both work hardening
and annealing take place simultaneously. A consequence of this is that steel under a constant stress
at an elevated temperature will continuously deform with time, that is, it is said to "creep".
Creep in steel is important only at elevated temperatures. In general, creep becomes significant at
temperatures above about 0.4Tm where Tm is the absolute melting temperature. However,
materials having low melting temperatures will exhibit creep at ambient temperatures. Good
examples are lead and various types of plastic. For example, lead has a melting temperature of
326°C (599K) and at 20°C (293K, or about 0.5Tm) it exhibits similar creep characteristics to those
of iron at 650°C.
The WP600 Creep Measurement Apparatus is a simple unit designed for demonstrating and
investigating the creep characteristics of lead and polypropylene specimens at room temperature.
A temperature module is provided to enable investigation of the effects of temperature on creep
rate.
2. Creep in metals:
A creep test is carried out by applying a constant load to a specimen and observing the increase in
strain (or extension) with time. A typical extension - time curve is shown in Fig. 1.
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Three regions can be readily identified on the curve:
1 to 2 Primary Creep -creep proceeds at a diminishing rate due to work hardening of the
metal.
3 to 4 Tertiary Creep - the creep rate increases due to necking of the specimen and the
associated increase in local stress. Failure occurs at point 4.
In terms of dislocation theory, dislocations are being generated continuously in the primary stage
of creep. With increasing time, more and more dislocations are present and they produce increasing
interference with each other’s movement, thus causing the creep rate to decrease. In the secondary
stage, a situation arises where the number of dislocations being generated is exactly equal to the
number of dislocations being annealed out. This dynamic equilibrium causes the metal to creep at
a constant rate. Eventually, however, the creep rate increases and the specimen fails due to localized
necking of the specimen (or component), void and micro crack formation at the grain boundaries,
and various metallurgical effects such as coarsening of precipitates.
When in service, an engineering component should never enter the tertiary stage of creep. It is
therefore the secondary creep rate, which is of prime importance as a design criterion. Components,
which are subject to creep, spend most of their lives in the secondary stage, so it follows that the
metals or alloys chosen for such components should have as small a secondary creep rate as
possible. In general it is the secondary creep rate, which determines the life of a given component.
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Secondary creep rate for a particular metal or alloy depends on several variables, the most important
of which are stress and temperature. The most commonly used expression for relating secondary
creep rate ε to stress σ and absolute temperature T has the form
−E
= A n e RT …. (1)
where A and n are constants, E is the activation energy for creep in the metal and R is the
universal gas constant (8.31 J/mol K).
The equation shows that the creep rate is increased by raising either the stress or the
temperature. Taking natural logarithms gives:
E
ln ε = ln A + n ln σ - .…2
RT
Thus, for tests at constant temperature and varying stress, the stress exponent n can be found
by plotting ln ε against ln σ. alternatively, if the stress is kept constant and the temperature
varied, E can be determined by plotting In c against l/T. For the special case of lead, the stress
exponent n has a value of about 10 for the relatively high levels of stress used in the SM106
apparatus, and the activation energy E is approximately 120 kJ/mol.
The fact that the exponent n varies with stress demonstrates the inadequacy of simple laws for
correlation of data over a wide range of stress levels. In practice, more complicated equations
are used to correlate experimental data. For our purposes, however, it is sufficient to use the
equation 1 since the resulting plots are very nearly linear for the stress levels normally obtained
with the WP600 Apparatus. In this manual, the power law of equation 1 is used in the analysis of
results.
3. Creep in plastics:
Plastics also creep at ambient temperatures but, compared to lead, they are able to sustain much
greater extensions before failure, the creep curves are similar in shape to those for metals, but the
mechanism of deformation is quite different because of the difference in structure of the material.
A polymer consists of long chain-like molecules in a tangled and coiled arrangement; creep occurs
by chains untangling and slipping relative to one another. The creep rate is still dependent on stress
and temperature but equation 1 can no longer be applied.
The complex processes taking place during creep make it difficult to quote an equation that
describes the creep behaviour of all polymers. Many empirical equations have been proposed and
one, which applies to some of the common engineering plastics, has the form
ε = εο + Β σ m tk ….3
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where ε is the tensile creep strain after a time t, σ is the applied creep stress, εο is the instantaneous
or initial strain produced on loading, and Β, m, k are constants for a given polymer. The elastic
component of the initial strain can be calculated by dividing the creep stress by the tensile modulus
of the polymer, which for polypropylene is 1250 N/mm2. In many polymers this initial strain is
very small and can be ignored, so that in these cases
ε = Β σ m tk …4
A plot of log against log t will therefore be linear and the slope will give the value of the
exponent k. Values of k quoted in the literature range from 0.025 to 0.33. For polypropylene,
k is in the range 0.1 to 0.2 and tends to increase with stress level.
In cases where the stress exponent m is close to unity we have the situation where σ/ε is a constant
as k ➔ 0, in other words the material is behaving in an elastic manner. Alternatively with high
values of k, say k ➔ 1, then σ/εt is a constant and the material is behaving as a viscous fluid. The
value of k obtained from creep data is therefore a measure of the relative contribution of elastic and
viscous deformation to the creep process.
Finally, it should be noted that with polymer materials the primary creep stage, where the creep
rate is decreasing, is largely recovered when the creep load is removed. This behaviour is unlike
that observed in most metallic systems, and the effect can be easily demonstrated using the SM106
apparatus by removing the load after the polymer has been creeping for 20 to 30 minutes and
continuing to take strain readings. It will be found that the elastic strain is removed instantaneously,
but that further recovery of strain takes place over a period of several minutes. This time dependent
effect is due to recovery of the viscoelastic component of the creep strain. For the stress levels used
in the WP600 apparatus (typically 19 N/mm2), approximately 40% of the creep strain is recovered
after 5 minutes.
The WP600 Creep Apparatus uses a simple lever to apply a steady tensile load to a specimen. The
specimen is held at each end by a plain stainless steel pin inserted through each loading stirrup. The
pins are a close fit in the holes in the ends of the specimens and deformation of these holes during a test
is negligible compared to the elongation of the specimen (i.e. less than 2% of the total elongation).
Loads are applied by hanging weights on the end of the lever arm. A rest pin is provided to support the
weight of the lever arm when loading the specimen prior to a test. A dial gauge measures the elongation
of the specimen.
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If the mass added to the weight hanger is m kg then:
F= gN ...5
EXPERIMENTAL PROCEDURE:
Before starting the experiment a suitable load should be determined which will produce a complete
creep curve in the time available? A suitable load can be determined from, which shows time to failure
in terms of load and temperature. Normally, the load should be chosen to give a time of at least 15
minutes, but this can be reduced for simple demonstrations. For serious experiments it is recommended
that the specimens should be labelled.
Attched Graph
1. Measure the cross-section and gauge length using a calliper. This is to enable subsequent
calculation of stress and strain.
2. Raise the lever arm and support it by inserting the rest pin.
3. Slide the specimen into the stirrups and insert the load pins. (Be sure not to distort the specimen).
4. Remove the rest pin and gently lower the lever arm to take up any free movement, then zero the
dial gauge.
5. Raise the lever arm and replace the rest pin. Hang the weight hanger on the end of the arm and add
the required load.
6. Record the ambient temperature and set a stopwatch or stop-clock to zero, ready to start the test.
7. Remove the rest pin and gently lower the lever arm until the specimen takes up the full load. At the
same time start the stopwatch or clock.
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8. Record the extension of the specimen at suitable intervals of time (normally every 15 second, but
every minute is adequate for longer tests). The total loading period is 15 min.
9. The load is removed towards the end of the loading phase and further readings are taken to show
the recovery of creep strain. The recovery period is 5 min.
10. At the end of the test take another reading of temperature and record the load. Check that you have
recorded the dimensions of the specimen.
12. The time exponent k is obtained from the slope of the curve plotted between ln ε and ln t.
RESULTS:
Graph
Graph
DISCUSSIONS:
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Experiment No.4
Aim: To find out torsion property of material by performing test on Torsional testing machine
Apparatus: Torsional testing machine, test specimen, Vernier calliper, scale and revolution counter.
1. Modulus of rigidity, it is the ratio of the shear stress to shear strain while the material is in elastic
limit.
2. Limit of proportionality, it is determined by plotting a torque twist curve; similar to stress strain
curve in tensile testing and noting where the curve departs from straight line.
3. Maximum torque, it is the greatest force used to twist the object, before the proportional limit is
reached, it occurs well before the fracture.
4. Modulus of rupture, it is the point at which nominal surface stress occurs. It is calculated from
the normal elastic throughout the test.
5. Total limit of fracture, it is found out as the total number of twist or parts of a twist recorded
on a scale.
Torsion test is carried out on a torsion testing machine; the twisting action is applied to one end of test piece
while other end of the test piece is held stationary. As turning or twisting movement at the fixed end of the
test piece is registered by a system produced along with machine.
Procedure:
2. The specimen is held between the chucks of the torsion testing machine.
3. One end of specimen is holding stationary while the other is rotated at speed of 40rpm.
4. When the material fails, the machine is switched off by the automatic stopping switch and result will
display on screen.
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fs = Shear stress onb element (N/mm2)
3.'d' of specimen = mm
4.Material of specimen =
5.Length of specimen = mm
6.T = Kgm
7.No. of Revolution =
𝑇 𝑓𝑠
=
𝐽 𝑅
The property found out by using above formula is Torsional shear stress, max. torque and no. of
revolutions.
Result: Torsional test was performed on a specimen of mild steel and it was found that
no. of revolution =
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Experiment No. 5
Objectives: Make Brinell, Vickers and Rockwell hardness measurements on different materials specimens
and Compare the measurements in hardness with each other.
This experiment will include Brinell, Vickers and Rockwell tests which measure resistance to penetration.
The amount of deformation that occurs when a small, hard steel ball or diamond point is pressed into a
material surface at some designated load is the measure of the hardness of the material.
Brinell hardness test: The Brinell test for this experiment uses steel ball with different diameters which is
pressed into a specimen by a different load that is maintained for to seconds. The
Where:
P is the test load kg
D is the diameter of the ball mm
d is the average impression diameter of indentation(mm)
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Since the Brinell number is based on the area of indentation, the diameter of the indentation must be
measured. This is done with a microscope. The scale seen through the microscope is in millimetres. The
larger diameter indentation corresponds to a softer material and lower Brinell number.
The advantages of the Vickers hardness test are that extremely accurate readings can be taken, and just one
type of indenter is used for all types of metals and surface treatments.
16
resistance to permanent deformation. It can be determined either statistically or dynamically. Static
hardness test can be further classified as follows:-
1. Those expression the hardness number in terms of the load per unit area of indentations. e.g. Brinell and
Vickers test
2. The Rockwell hardness test in which the Rockwell number depends upon the depth of penetration of the
indenting tool. Significant information can be obtained from the hardness number of a specimen.
Uniform hardness numbers are nearly always a sufficient guarantee of the uniform quality of the
finished products.
In this test the depth of the penetration of the given indenture under a specified load is measured. The
type of indenter and load used depend upon the material to be tested. Scale B is used for the materials
having hardness number up to that of MS and CI. The indenture is then a hardened steel ball of 1/ 16”
dia. An initial load of 10 kg is applied on the ball. An additional load of 90 kg in then applied (major load). Scale
C is used for alloy steels. The indenture is a diamond cone of 120deg. included angle. Here 150 kg is
used as the major load.
3 Procedures:
The following procedure has been followed:
1 Keep the specimen on the machine table.
2 Turn the table upward so that distance between the indenture and specimen will be less than 8mm.
3 Select the scale with the help of touch screen display buttons.
4 For Vickers and Brinell Select the tours with the help of touch screen and Select load and scale display
buttons
Press the start button, it will automatically go down in the specimen to make the impression and will display
the HRC value.
HRB is used for Copper alloys, soft steels, aluminium alloys, malleable irons, etc.
HRC is used for Steel, hard cast irons, case hardened steel and other materials harderthan 100 HRB
Brinnel Hardness Number (BHN) also can find from this after changing the scale and indenter.
OBSERVATIONS
17
Experiment No. 6A
Aim: To find out mechanical properties of materials by performing tensile test with steel and aluminium
specimens.
Theory: The Ultra Wide materials testing machines have frame capacities of 50kN and are combined with
a variety of grips and fixtures, extensometers and application specific software to provide turnkey testing
systems that can perform tension and compression.
The various tensile properties calculations with the help of universal testing machine are as follows.
Load at yield point
(1)YIELD STRENGTH = Original area
Ultimate load
(2) ULTIMATE TENSILE STRENGHT = Original area
𝑙𝑝−𝑙𝑜
(3) % ELONGATION = × 100
𝑙𝑜
lp = Final length
lo = Original length
𝐴𝑜 −𝐴𝑓
(4) % REDUCTION IN AREA = × 100
𝐴𝑜
Ao =Original area
Af = final area
Stress at any point
(5) Young’s Modules= E= Strain at that point (within elastic limit)
Procedure:
2) Put the USB Dongle of Horizon Software in the USB Port of CPU
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5) Go to Configuration – Machine Setup-Check the status (if Not Connected then Press Connect)
8) Now go to Test & Recall Screen, select Testing Tab In Test & Recall Screen, Check the H50KT
Testing Tab opens & Machine Status: Stopped, Idle, Hold
9) Now, Click on Open the Testing Tab Options, then the following screen will display
10) Select the Test Method: ___________ & Testing Mode: Batch Mode, Unknown Number & Press
OK
11) If the Batch Testing Pop up Message comes then Select the Action : End Batch to End the Bat
Enter the Measured Width / Thickness / Verified the required Details Select All Results Shown then
following screen will be shown
B) Adjust the Crosshead to Attached / Fix the required Grip (for Tensile Test) / Fixture (for
Compression / Puncture Test)
C) Adjust the Hardware Lower Limit Switch accordingly to Grip / Fixture Attachment.
14) A) Zero the Force & Position (Note: Do not Place the Sample)
15) Place the Sample in the Grip / Fixture properly and Press F2 / Play button as shown below:
16) After completing the Test sample as shown following, Place the New Sample for testing and complete
all the Test Specimens:
17) Click on HORIZON icon (in the left hand upper corner)- Print Preview – Summary Report –
Completed Specimens
18) Print Out Directly to Printer / Save as XPS / BMP / HTML accordingly as follows : for e.g. Today’s
DATE_ Customer_ STANDARD_Product Code_Batch Code
Test is carried by griping the two ends on a tensile testing machine and applying an increasing pull on to
specimen till it fracture.
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After fracture, the two broken pieces are taken together and extension in length and decrease in area is
noted.
Lo= Lf =
Do = Df =
Ao = Af =
Ultimate load = kN
∆𝐿
% elongation = 𝐿𝑜
= %
∆𝐴
% Reduction in area = 𝐴 x 100
𝑜
= %
% elongation = %
% Reduction in area = %
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Experiment No-6B
Apparatus: Universal testing Machine, compressive Plate, Vernier callipers, test specimen.
Theory : Several Machine and structure component such as columns and struts are subject to compressive
load in application. There component are made up material of high strength in compression. Several
Materials which are good & many materials are poor in compression. On the other side many materials are
poor in tension but very strong in compression .e.g. cast iron. That's why determining ultimate compressive
strength is essential before using a material. This strength is determined by conducting compression test. In
compression test, the piece of material is subjected to end loading which provides crushing action. In a
tension test the piece elongates in a direction parallel to the applied load while in compression test shortens.
Brittle material is generally weak in tension but strong in compression, hence this test is normally
performed on cast iron, cement, concrete etc. The compression test is not as reliable as tensile test and
reduction of area test as an indicator of activity.
Specimen: Compression specimen or test piece are united to such as length that bending due to column
action does not take place, In a cylindrical specimen it is essential to keep h/d<10 to bending , this ratio
should not be exceeded for uniform stressing of compression specimens a circular section is to be performed
over those shapes.
1) For Specimen
Lo= cm bo = cm
Lf = cm bf = cm
Compression load = KN
𝑢𝑙𝑡𝑖𝑚𝑎𝑡𝑒 𝑐𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑖𝑣𝑒 𝑙𝑜𝑎𝑑
Ultimate compressive strength = = NM2
𝐴𝑜
After the material fails ,the machine is put off the control
Result:
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Precautions
1.The specimen should be aligned properly in testing machine and wear safety glass .
22
Experiment 7
Objectives: Assess the performance of strain gauges system FL100 for Bending beam, Torsion bar
Tension bars.
Apparatus:
FL100Strain Gauge Training System, Small set of weights 1 - 6 N, graduations 0.55 N for
* bending experiments - Large set of weights 5 - 50 N, graduations 5 N for torsion and tensile
experiments set
Theory:
Strain gauges permit simple and reliable determination of stress and strain distribution at real components
under load. The strain-gauge technique is thus an indispensable part of experimental stress analysis.
Widespread use is also made of strain gauges in sensor
Construction (scales, dynamometers and pressure gauges, torque meters). All test objects are provided with
a full-bridge circuit and are ready wired. A Perspex cover protects the element whilst giving a clear view
The test objects are inserted in a frame and loaded with weights. The measuring amplifier has a large
bright digital LED display.
The mechanical stress is a measure of the load and a factor governing failure. This stress cannot generally
be measured directly. As however the material strain is directly related to the material stress, the component
load can be determined by way of strain measurement. An important branch of experimental stress analysis
is based on the
Principle of strain measurement. The use of the strain-gauge technique enables strain
to be measured at the surface of the component. As the maximum stress is generally found at the surface,
this does not represent a restriction. With metallic strain gauges, the type most frequently employed, use is
made of the change in the electrical resistance of the mechanically strained thin metal strip or metal wire.
The change in resistance is the combination of tapering of the cross-sectional area and a change
in the resistivity. Strain produces an increase in To achieve the greatest possible wire resistance with small
dimensions, it is configured as a grid. The ratio of change in resistance to strain is designated k
Strain gauges with a large k-factor are more sensitive than those with a small one. The constantan strain
gauges used have a k-factor of 2.05.
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In order to be able to assess the extremely small change in resistance, one or more strain gauges are
combined to form a Wheatstone bridge, which is supplied with a regulated DC voltage (-+V).The bridge
may be fully (full bridge) or only partially
(half and quarter bridge) configured with active strain gauges. The resistors R required to complete the
bridge are called complementary resistors. The output voltage of the bridge reacts very sensitively to
changes in resistance in the bridge branches. The voltage differences occurring are then amplified in
differential amplifiers and displayed.
The design of a strain gauge is shown in the adjacent illustration. The wave-form metal strips are mounted
on a backing material, e.g. a thin elastic polyimide film and covered with a protective film. Today’s metal
strips are usually produced by etching from a thin
metal foil (foil-type strain gauges). Thin connecting wires are often welded directly to the strain gauge. The
strain gauge is bonded to the component with a special adhesive, which must provide loss-free transmission
of the component strain to the strain gauge
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III. Experimental work
Tensile experiment
According to Hooke’s law stress and strain are linked to one another by way of the
modulus of elasticity
For experimental determination of the tensile stress, two strain gauges each are fitted to the front and back
of the specimen; one strain gauge is attached in longitudinal, the other in transverse direction. The strain
gauges on each side form a branch of the bridge. Such a configuration is characterized by the following:
Utilization of linear and
superimposed bending stresses have no influence on the measurement result. The output signal UA of the
measuring bridge is referenced to the feed voltage UE. The sensitivity k of the strain gauge enables the
strain to be calculated for the full bridge as follows
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Where is Poisson’s ratio for the respective material
Fit the tension bar in the frame as shown using the holder with hook
- Load bar with large set of weights. Increase load in stages and note down reading. Readings are only very
small on account of the weak tensile stresses. Zero balancing is therefore to be performed with extreme
care.
The strains and stresses can be calculated from the measured bridge voltage UA/UE
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Stresses and strains for a load of 50N, Cross-sectional area 20 mm2
Bending experiment
The stress at the surface of the bending beam can be calculated from the bending moment Mb and the
section modulus Wy
ε= Mb/ Wy
Where F is the load and L the distance between the point at which the load is introduced and the
measurement point. The section modulus for the rectangular cross section of width b and height h is
Wy = b.h^2/6
For experimental determination of the bending stresses, the bending beam is provided with two strain
gauges each on the compression and tension sides. The strain gauges of each side are arranged diagonally
in the bridge circuit. This leads to summation of all changes in resistance and a high level of sensitivity.
The output signal UA of the measuring bridge is referenced to the feed voltage UE. The sensitivity k of
the strain gauge enables the strain ε to be calculated for the full bridge as follows
According to Hooke’s law the stress being sought is obtained with the modulus of elasticity E
Ʃ =ε.E
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- Fit bending beam in frame as shown using holder with two pins.
- Connect up and switch on measuring instrument.
- Set slider to distance of 250 mm.
- Use offset adjuster to balance display.
- Load beam with small set of weights. Increase
load in steps of 1.1 N (two weights) and note down reading
Attached Graph
Torsion experiment One area of application of strain-gauge technology is the measurement of Torsional
moments in shafts, where the torque in the shaft is calculated from the shear stress measured. For
experimental determination of the Torsional stress, the torsion bar is provided with four strain gauges at
an angle of 45°. The strain gauges are thus located in the direction of the principal normal
Stresses and hence the maximum strain. The strain gauges are arranged diagonally in the bridge circuit.
This leads to summation of all changes in resistance and a high level of sensitivity.
With pure shear stress the relationship between strain and shear is as follows
According to Hooke’s law the shear stress being sought is obtained with the shear modulus G
The relationship between shear stress τ at the surface of the torsion bar and Torsional moment Mt is as
follows
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where Wp is the section modulus of torsion for the circular cross section
Fit torsion bar in frame as shown. In doing so, place clamping end on upper pin of holder with two pins.
Support loose end of bar with other holder. Make sure bar is horizontally aligned.
- Connect up and switch on measuring instrument.
- Use offset adjuster to balance display.
- Suspend set of weights from lever arm and generate Torsional moment. Increase load in stages of 5 N
and note down reading.
Load in n 0 5 10 15 20
Torsional
moment in NM
Reading mv/v
Discussions:
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EXPERIMENT 8
Theory:
Photoelasticity is an experimental method to determine stress distribution in a material. The method is
mostly used in cases where mathematical methods become quite cumbersome. Unlike the analytical
methods of stress determination, photo elasticity gives a fairly accurate picture of stress distribution even
around abrupt discontinuities in a material. The method serves as an important tool for determining the
critical stress points in a material and is often used for determining stress concentration factors in irregular
geometries.
Operational Principle:
The method is based on the property of birefringence, which is exhibited by certain transparent materials.
Birefringence is a property by virtue of which a ray of light passing through a birefringent material
experiences two refractive indices. The property of birefringence or double refraction is exhibited by many
optical crystals. But photoelastic materials exhibit the property of birefringence only on the application of
stress and the magnitude of the refractive indices at each point in the material is directly related to the state
of stress at that point. Thus, the first task is to develop a model made out of such materials. The model has
a similar geometry to that of the structure on which stress analysis is to be performed. This ensures that the
state of the stress in the model is similar to the state of the stress in the structure.
Polariscope:
A polariscope is the device used to measure the photoelastic effects. When a ray of plane polarised light is
passed through a photoelastic material, it gets resolved along the two principal stress directions and each of
these components experiences different refractive indices. The difference in the refractive indices leads to
a relative phase retardation between the two component waves. The magnitude of the relative retardation
is given by the stress optic law:
where R is the induced retardation, C is the stress optic coefficient, t is the specimen thickness, σ11 is the
first principal stress, and σ22 is the second principal stress.
The two waves are then brought together in a polariscope. The phenomenon of optical interference takes
place and we get a fringe pattern, which depends on relative retardation. Thus studying the fringe pattern
one can determine the state of stress at various points in the material.
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Isoclinics and Isochromatics:
Isoclinics are the locus of the points in the specimen along which the principal stresses are in the same
direction.
Isochromatics are the locus of the points along which the difference in the first and second principal stress
remains the same. Thus they are the lines which join the points with equal maximum shear stress magnitude.
Types of Polariscope:
There are two main types of polariscope in use today, Plane Polariscope and the Circular Polariscope.
Plane Polariscope:
The setup consists of two linear polarizers and a light source. The light source can either emit
monochromatic light or white light depending upon the experiment. First the light is passed through the
first polarizer which converts the light into plane polarized light. The apparatus is set up in such a way that
this plane polarized light then passes through the stressed specimen. This light then follows, at each point
of the specimen, the direction of principal stress at that point. The light is then made to pass through the
analyzer and we finally get the fringe pattern.
The fringe pattern in a plane polariscope setup consists of both the isochromatics and the isoclinics. The
isoclinics change with the orientation of the polariscope while there is no change in the isochromatics.
Circular Polariscope:
In a circular polariscope setup two quarter-wave plates are added to the experimental setup of the plane
polariscope. The first quarter-wave plate is placed in between the polariser and the specimen and the second
quarter-wave plate is placed between the specimen and the analyser. The effect of adding the quarter-wave
plates is that we get circularly polarised light.
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There are four different kinds of arrangements for the circular polariscope. Each arrangement produces
either a dark field arrangement or a light field arrangement. In dark field arrangement, the fringes are shown
by bright lines and the background is dark. The opposite holds true for the light field arrangement.
The basic advantage of a circular polariscope over a plane polariscope is that in a circular polariscope setup
we only get the isochromatics and not the isoclinics. This eliminates the problem of differentiating between
the isoclinics and the isochromatics.
Apparatus:
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Procedure:
• Obtain the test specimen and measure and record its diameter and thickness using vernier calipers.
• Place the specimen within the apparatus and determine, using meter rod, the distance between the
hinge and the point of contact with the specimen and the distance between the hinge and the applied
load.
• Set the apparatus in the Light field arrangement and start applying loads and observe the dark
fringes formations. When the fringes are parallel to the vertical axis of the screen, take the reading.
• Now set the apparatus in the Dark field arrangement and repeat the above procedure, taking at least
five readings in total.
• Calculate the material fringe value.
Relevant Theory:
Theoretical aspects of the experiment ca be covered by the study of the following topics in adequate
detail.
Comments:
Comments relating to the observations made during the course of the experiment and possible practical
applications are
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