Strength of Materials Laboratory
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Strength of Materials Laboratory
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Tensile Test
Object:
To determine the mechanical properties of metals under tensile load.
Theory:
The tensile test is very useful and important for design and
forming of metals. A mono-axial stress is generated in material
sample. This stress is induced via external loading of the sample
in a longitudinal direction via a tensile force. The loading of the
sample is slowly and continuously increased until fails.
From the load and elongation results obtained the
engineering stress and engineering strain are :

F
A
F : Load (N).
Fig.(1)
The sample used
Ao: original cross-section area ( Ao  Do2 4 ).
While the engineering strain e is :

Lc  Lo
L
Lc: current length.
Lo: original length.
Important material data can be read from the stress-strain diagram, Fig.(2). A
linear stress-strain relation is found between points O-A, point A is called the limit of
proportionality, and the material conforms to Hook's lawwith the modulus of elasticity
E;
  E.
When stress is exceeded point A the deformation is no longer proportional to
the load but the material is still elastic till point B, which is called yield point or
elastic limit. From point B onwards, the material becomes continuously plastically
deformed, deformation remains when the load is relieved. The increasing in strain rate
is greater than that in the stress rate till point C, which is called ultimate stress or
maximum stress, from point C to D the strain rate will be increased with decreasing
in stress rate, the cracks and necking take place in the sample until its fail at D.
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Fig.(2)
Stress - strain diagram

The true stress and true strain can be calculated as:
True stress σt=F/Ac
Ac : current area
True strain ε= ln (Lc/Lo)
Lc : current length
To calculate Lc , Ac from volume constancy Vc=Vo where Vc , Vo are the
current and original volumes respectively
Ao Lo = Ac Lc
Lc=Lo+ ΔL
Ac = Ao Lo /Lc
The stress-strain diagram , Fig(3), shows the different behavior of the
individual materials. Each material has a characteristic pattern of stress and strain.
1.
2.
3.
4.
Hardness steel.
Tempered steel.
soft steel.
aluminum alloy.
Fig.(3)
Stress – strain diagram for various materials
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Apparatus used:
Fig.(4) shoes the components
of the tensile testing machine
1. Machine base.
2. Cross-head support.
3. Upper load frame.
4. Lower load frame.
5. Cylinder of hydraulic system.
6. Hand wheel.
7. Force display.
8. Elongation display.
9. Gripping hands.
10. Sample.
11. Hand grips.
Fig.(3)
tensile testing machine
Test procedure:
1.
2.
3.
4.
5.
Fixing the sample between the gripping heads.
Reset the force and elongation display.
The sample is than slowly and constantly loaded by rotating the hand wheel.
The application of force should be spread over a time interval of 5-10 min.
Record the elongation and its effective load.
Calculations and Results:
Tabulate the load and elongation as follows.
Load F(N)
Elongation ΔL(mm)
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From this table calculate:
1. The true and engineering stresses ;
Yielding stress σy , Ultimate stress σm , Fracture stress
2. The true and engineering strain.
3. Ductility which is determine by two parameters
a. Percentage elongation
Pe =(Lf-Lo)/Lo *100%
b. Percentage reduction in area
Pr =(Ao-Af)/Ao *100%
Where Lf and Af are final length and area respectively.
Discussion:
1. Compare between the engineering stress strain and true stress strain.
2. Discuss any source of error in the experiment.
σf .
Strength of Materials Laboratory
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Strength of Materials Laboratory
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Compression test
Object:
Determine the mechanical properties of metals under compression load.
Theory:
Compression tests are reverse of tensile tests, since the specimen is being
stretched under tensile load in the tensile test while in compression test the specimen
is being compression under compression load. Some materials are tested mainly in
compression. Among these are brick, wood, cast Iron, and tile.
Compression Testing of Ductile Materials:
Ductile metals such as steel, aluminum, and copper have proportional limits in
compression very close to those in tension; hence the initial regions of their
compression stress-strain diagrams are very similar to the tension diagrams.
However; when yielding begins, the behavior is quite different. In a tension
test, the specimen is being stretched.
Necking may occur, and ultimately fracture takes place. When a small
specimen of ductile material is compressed, it begins to bulge outward on the sides
and become barrel shaped. With increasing load, the specimen is fluttered out, thus
offering increased resistance to further shortening (which means the stress-strain
curve goes upward). These characteristics are illustrated in fig. (1), which shows a
compression stress-strain diagram for copper.
STRESS
(MPa)
STRAIN
Fig. (1)
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Compression Testing of Brittle Materials:
Brittle materials in compression typically have an initial linear region followed
by a region in which the shortening increase at a higher rate than dose the load. Thus,
the compression stress-strain diagram has a shape that is similar to the shape of the
tensile diagram. However the materials usually reach much higher ultimate stresses in
compression stress tension and actually fracture or break at the maximum load. Fig.
(2) shows the tension and compression for cast Iron.
Compression
STRESS
(MPa)
Tension
STRAIN
Fig. (2)
Apparatus used:
The testing machine used in this test is the same machine used in the tensile test
and its specification is explained elsewhere as shown in Fig. (3).
Fig. (3)
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Tensile test machine
Experimental procedure:
1. Prepare the testing machine unit for use in compression test.
2. Measure the dimensions of the specimen used. (its diameter, length and the
ratio of its length to its diameter).
3. Clean the surface of the specimen from any dirt and lubricant the faces of the
specimen to decrease the effect of friction.
4. Put the specimen on the lower compression ram.
5. Check and set the upper compression ram and select the most suitable speeds
for the chast recorder.
6. Check adjustments of loading range.
7. Note the loading range and chart speed.
8. Start the loading of specimen and record the load displacement diagram.
9. Measure the change in the values of the length of the specimen.
Calculation:
a. Compression stress (σc)
c 
P
A
Where
P: compression load (KN).
A  : Original area of the specimen. (mm2).
 c : Compression stress (KN/ mm2).
b. Compression strain (εc)
c 
L  Lf
L
L  : Original length of the specimen (mm).
L f : Final length of the specimen (mm).
 c : Compression strain.
[
c. Young’s Modulus (E)
E
c
c
Strength of Materials Laboratory
 c : Compression stress.
 c : Compression strain.
E : Young Modulus.
Requirements and results:
1. Redraw it suitable scale, the recorded load displacement diagram.
2. Determine the yield stress and modulus of elasticity.
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Strength of Materials Laboratory
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TORSION TEST
Object :
To measure the angle of rotation for a bar subjected to torsion load and
than calculation the modulus of rigidity of the same bar and compare it with
the theory modulus of rigidity .
Theory :
A cylindrical bar with length
Fig. 1 , if a force
F
L is securely clamped at one end ,
is applied , which acts on the lever arm in a plane
perpendicular to the bar axis , the bar is subjected to torsion by the moment
M
M=F×a
Where
F : the applied force ( N )
a : the lever arm ( mm )
To calculate the angle of rotation
of bar we assume that ;
Fig. 1
1. The twisting is uniform along the bar , that is , all normal cross – sections have
the distance apart suffer equal relative rotation .
2. Cross – sections remain plane during twisting .
3. Radii remain straight during twisting .
The angle of rotation in radian measure ;
θ
ML
G  Ip
where
G : the modulus of rigidity .
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I p : polar moment of inertia , for circular cross – section area I p 
π  d4
32
The angle of rotation in degrees ;
θo 
180  M  L
  G  Ip
than , the modulus of rigidity of the bar ;
G
180  M  L
π  θo  Ip
where θ is measured from experiment .
o
Apparatus Used :
Fig. 2 , shows the components of the torsion unit .
2
1. Test bar .
2. Dial gauge .
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3. Load body .
Fig. 2
4
1
3
5
Torsion unit
4. Rotating bearing clamping chuck with lever for application of load body.
5. Lever for generation of torsion moment using load body .
6. Rigidly connected clamping chuck .
Test Procedure :
1. Reset the dial gauge .
2. Fixing the bar between the rigid and the rotating chuck .
3. Applying load ( 1 kg ) 9.81 N in load body .
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4. Recording the angle of rotation from dial gauge .
Calculations and Results :
The dial gauge
is a distance of
s = 57.3 mm ,
Fig. 3, from the
axis of rotation
why ?
Fig. 3
load lever
From , Fig. 4 , the radian measure
θ=
b
s
Fig. 4
for a small angle
θ
direct display
on the dial gauge , Fig. 5 , than
θ=
y
the sector
b
can be very accurately replaced by
y
y
=
s
57.3
Fig. 5
To simplify the conversion between degrees and radian measure , a distance of
57.3 mm
has
been
selected , therefore
corresponds to an angle of rotation of
1o .
( 1 mm )
on the dial
gauge
Strength of Materials Laboratory
We
use
three
test bars made of
Free clamping length
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AL , Cu , St with L = 340 mm ,
L = 300 , a = 100 mm , d = 10 mm , m = 1 kg , F =
9.81 N
Theory modulus Experiment modulus display on dial
of rigidity N/mm
of rigidity N/mm
in degree θ
angle of rotation
gauge y in mm
26950
AL
4800
Cu
80850
St
To calculate the modulus of rigidity ;
G
180  M  L
π  θo  Ip
Note :
In this test there is ability to use different ( lengths , diameters , loads ) of bar .
Discussions :
1. Compare between the theoretical and experimental modulus of rigidity and
give a reasons for the difference ( source of error ) .
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Strength of Materials Laboratory
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Impact test
Object:
To test some metals as steel, aluminum and brass under impact stresses.
Theory:
Experience has shown that some materials, which offer considerable resistance
static stress often, shatter easily from a suddenly applied load, such as hammer blow.
This applies to such materials as cast iron, very high carbon steel, glass, and
some plastics. Impact testing or testing to find the energy absorbed by a specimen
when brought fracture by a hammer blow, offers an important measure of the quality
of a material particularly its ductility. Impact test before putting the material in service
would have detected its brittleness and prevented its service failure.
Impact tests are sensitive to variations in heat treatment, to alloy content to
sulfur or phosphorus content. Some materials such as glass are sensitive to pendulum
impact speed.
Apparatus used:
The pendulum impact-testing machine is shown in Fig.(1) .the essential parts of
an impact-testing machine are:
1. A moving mass known as hammer, of known kinetic energy, which should be
great, enough to cause fracture of test specimen placed in its path.
2. An anvile on which the test specimen is to receive the blow of the moving
mass.
3. A dial gauge for measuring the remaining kinetic energy in the moving mass
after the specimen has been fractured.
Hamer
anvile
Gage
Fig. (1)
impact-testing machine
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Testing procedure:
The following tests can be carried out on the machine:
a. Charpy test:
The pendulum strike’s upon a notched specimen Fig.(2) resting as a simple
beam on supports. The pendulum strike’s the specimen at the opposite side from the
notch. The test is implemented as follows:
1. Lift pendulum by hand until it latches in automatically in its stop position.
2. Insert specimen so that the notch is opposite to the impact contact with the
pendulum center it carefully.
3. Adjust reading pointer to 25 [N.m] by aright turn.
4. Press down the brake lower (11) and then the latch (7).
5. Wait until pendulum is reversing its direction of motion and begins to sewing
low.
6. There after bring pendulum carefully to a stand still by release the brake lever
to its right position.
7. Read the position of pointer on the scale and record it.
8. After each test all particle of specimen are to be removed from the tester.
t
Hammer
w
Fig. (2)
Charpy Test
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b. Izod test:
The pendulum strikes upon a notched specimen, which is fastened at one, end
in gripping device as a cantilever beam. Types of specimens and the shape of
pendulum striking nose is drawn in Fig. (3).
The procedure is similar to the charpy test. Except that the pointer of the dial
gauge should adjusted on value 0.
w
Hammer
Fig. (3)
Izod Test
Calculations and Results :
The notch impact strength of specimen is calculated from the relation:
Si 
Us
A
where:
Si : notch impact strength in (Nm / cm2).
Us : impact energy absorbed for the specimen rupture (Nm).
Us = E-Er
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A : cross-section area of the specimen below notch before test (cm2).
E : initial pendulum energy (Nm).
Er : remaining pendulum energy (Nm).
The results should be recorded in a sequence (highest to lowest) of the impact
strength, and compared the impact strength with the tensile strength for each
specimen, as shown in the table is low: -
Specimen
Tensile strength
Impact Value
Izod
Charpy
Discussion:
1. Discuss the significant of the results obtained
2. Explain why the specimens are notched, and how the test result can be used
to determine the properties of the material
3. What are the factor’s that affect the impact strength
4. Discuss the differences between the results of (Izod) and (Charpy) test