Laboratory 3: Tensile testing
L a b o ra t o ry 3
Tensile Testing
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Objectives
• Students are required to understand the principle of a uniaxial tensile testing and
gain their practices on operating the tensile testing machine to achieve the required
tensile properties.
• Students are able to explain load-extension and stress-strain relationships and
represent them in graphical forms.
• To evaluate the values of ultimate tensile strength, yield strength, % elongation,
fracture strain and Young's Modulus of the selected metals when subjected to
uniaxial tensile loading.
• Students can explain deformation and fracture characteristics of different materials
such as aluminium, steels or brass when subjected to uniaxial tensile loading.
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1. Literature Review
1.1 Uniaxial tensile testing
Uniaxial tensile test is known as a basic and universal engineering test to achieve material
parameters such as ultimate strength, yield strength, % elongation, % area of reduction and Young's
modulus. These important parameters obtained from the standard tensile testing are useful for the
selection of engineering materials for any applications required.
The tensile testing is carried out by applying longitudinal or axial load at a specific extension
rate to a standard tensile specimen with known dimensions (gauge length and cross sectional area
perpendicular to the load direction) till failure. The applied tensile load and extension are recorded
during the test for the calculation of stress and strain. A range of universal standards provided by
Professional societies such as American Society of Testing and Materials (ASTM), British standard,
JIS standard and DIN standard provides testing are selected based on preferential uses. Each standard
may contain a variety of test standards suitable for different materials, dimensions and fabrication
history. For instance, ASTM E8: is a standard test method for tension testing of metallic materials
and ASTM B557 is standard test methods of tension testing wronght and cast aluminium and
magnesium alloy products
A standard specimen is prepared in a round or a square section along the gauge length as
shown in figures 1 a) and b) respectively, depending on the standard used. Both ends of the
specimens should have sufficient length and a surface condition such that they are firmly gripped
during testing. The initial gauge length Lo is standardized (in several countries) and varies with the
diameter (Do) or the cross-sectional area (Ao) of the specimen as listed in table 1. This is because if
the gauge length is too long, the % elongation might be underestimated in this case. Any heat
treatments should be applied on to the specimen prior to machining to produce the final specimen
readily for testing. This has been done to prevent surface oxide scales that might act as stress
concentration which might subsequently affect the final tensile properties due to premature failure.
There might be some exceptions, for examples, surface hardening or surface coating on the materials.
These processes should be employed after specimen machining in order to obtain the tensile
properties results which include the actual specimen surface conditions.
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Figure 1: Standard tensile specimens
Type specimen
Sheet ( Lo /
Rod ( Lo /
United State (ASTM)
Great Britain
Germany
4.5
5.65
11.3
4.0
5.0
10.0
Ao )
Do )
Table 1: Dimensional relationships of tensile specimens used in different countries.
The equipment used for tensile testing ranges from simple devices to complicated controlled
systems. The so-called universal testing machines are commonly used, which are driven by
mechanical screw or hydraulic systems. Figure 2 a) illustrates a relatively simple screw-driven
machine using large two screws to apply the load whereas figure 2 b) shows a hydraulic testing
machine using the pressure of oil in a piston for load supply. These types of machines can be used not
only for tension, but also for compression, bending and torsion tests. A more modernized closed-loop
servo-hydraulic machine provides variations of load, strain, or testing machine motion (stroke) using a
combination of actuator rod and piston. Most of the machines used nowadays are linked to a
computer-controlled system in which the load and extension data can be graphically displayed
together with the calculations of stress and strain.
General techniques utilized for measuring loads and displacements employs sensors
providing electrical signals. Load cells are used for measuring the load applied while strain gauges are
used for strain measurement. A Change in a linear dimension is proportional to the change in
electrical voltage of the strain gauge attached on to the specimen.
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Figure 2: Schematics showing a) a screw driven machine and b) a hydraulic testing machine[3].
1.2 Stress and strain relationship
When a specimen is subjected to an external tensile loading, the metal will undergo elastic
and plastic deformation. Initially, the metal will elastically deform giving a linear relationship of load
and extension. These two parameters are then used for the calculation of the engineering stress and
engineering strain to give a relationship as illustrated in figure 3 using equations 1 and 2 as follows
σ=
ε=
P
Ao
L f − Lo
Lo
@(1)
=
∆L
Lo
@(2)
is the engineering stress
ε
is the engineering strain
P
is the external axial tensile load
is the original cross-sectional area of the specimen
Ao
Lo
is the original length of the specimen
Lf
is the final length of the specimen
The unit of the engineering stress is Pascal (Pa) or N/m2 according to the SI Metric Unit
whereas the unit of psi (pound per square inch) can also be used.
where
σ
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1.2.1 Young's modulus, E
During elastic deformation, the engineering stress-strain relationship follows the Hook's Law
and the slope of the curve indicates the Young's modulus (E)
E=
σ
ε
@(3)
Young's modulus is of importance where deflection of materials is critical for the required
engineering applications. This is for examples: deflection in structural beams is considered to be
crucial for the design in engineering components or structures such as bridges, building, ships, etc.
The applications of tennis racket and golf club also require specific values of spring constants or
Young's modulus values.
Figure 3: Stress-strain relationship under uniaxial tensile loading
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1.2.2 Yield strength, σy
By considering the stress-strain curve beyond the elastic portion, if the tensile loading
continues, yielding occurs at the beginning of plastic deformation. The yield stress, σy, can be
obtained by dividing the load at yielding (Py) by the original cross-sectional area of the specimen (Ao)
as shown in equation 4.
σy =
Py
@(4)
Ao
The yield point can be observed directly from the load-extension curve of the BCC metals
such as iron and steel or in polycrystalline titanium and molybdenum, and especially low carbon
steels, see figure 3 a). The yield point elongation phenomenon shows the upper yield point followed
by a sudden reduction in the stress or load till reaching the lower yield point. At the yield point
elongation, the specimen continues to extend without a significant change in the stress level. Load
increment is then followed with increasing strain. This yield point phenomenon is associated with a
small amount of interstitial or substitutional atoms. This is for example in the case of low-carbon
steels, which have small atoms of carbon and nitrogen present as impurities. When the dislocations
are pinned by these solute atoms, the stress is raised in order to overcome the breakaway stress
required for the pulling of dislocation line from the solute atoms. This dislocation pinning is related
to the upper yield point as indicated in figure 4 a). If the dislocation line is free from the solute
atoms, the stress required to move the dislocations then suddenly drops, which is associated with the
lower yield point. Furthermore, it was found that the degree of the yield point effect is affected by the
amounts of the solute atoms and is also influenced by the interaction energy between the solute atoms
and the dislocations.
Aluminium on the other hand having a FCC crystal structure does not show the definite yield
point in comparison to those of the BCC structure materials, but shows a smooth engineering stressstrain curve. The yield strength therefore has to be calculated from the load at 0.2% strain divided by
the original cross-sectional area as follows
σ 0.2% y =
P0.2%
Ao
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...(5)
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Laboratory 3: Tensile testing
Note: the yield strength values can also be obtained at 0.5 and 1.0% strain.
The determination of the yield strength at 0.2% offset or 0.2% strain can be carried out by
drawing a straight line parallel to the slope of the stress-strain curve in the linear section, having an
intersection on the x-axis at a strain equal to 0.002 as illustrated in figure 3 b). An interception
between the 0.2% offset line and the stress-strain curve represents the yield strength at 0.2% offset or
0.2% strain. However offset at different values can also be made depending on specific uses: for
instance; at 0.1 or 0.5% offset. The yield strength of soft materials exhibiting no linear portion to
their stress-strain curve such as soft copper or gray cast iron can be defined as the stress at the
corresponding total strain, for example, ε = 0005.
The yield strength, which indicates the onset of plastic deformation, is considered to be vital
for engineering structural or component designs where safety factors are normally used as shown in
equation 6. For instance, if the allowable working strength σw = 500 MPa to be employed with a
safety factor of 1.8, the material with a yield strength of 900 MPa should be selected. It should be
noted that the yield strength value can also be replaced by the ultimate tensile strength, σTS , for
engineering designs.
Safety factors are based on several considerations; the accuracy of the applied loads used in
the structural or components, estimation of deterioration, and the consequences of failed structures
(loss of life, financial, economical loss, etc.) Generally, buildings require a safety factor of 2, which
is rather low since the load calculation has been well understood. Automobiles has safety factor of 2
while pressure vessels utilize safety factors of 3-4.
σw =
σy
Safety Factor
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,
σ TS
Safety Factor
@(6)
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Laboratory 3: Tensile testing
Figure 4: a) Comparative stress-strain relationships of low carbon steel and aluminium alloy and b)
the determination of the yield strength at 0.2% offset.
1.2.3 Ultimate Tensile Strength, σTS
Beyond yielding, continuous loading leads to an increase in the stress required to
permanently deform the specimen as shown in the engineering stress-strain curve. At this stage, the
specimen is strain hardened or work hardened. The degree of strain hardening depends on the nature
of the deformed materials, crystal structure and chemical composition, which affects the dislocation
motion. FCC structure materials having a high number of operating slip systems can easily slip and
create a high density of dislocations. Tangling of these dislocations requires higher stress to
uniformly and plastically deform the specimen, therefore resulting in strain hardening.
If the load is continuously applied, the stress-strain curve will reach the maximum point,
which is the ultimate tensile strength (UTS, σTS). At this point, the specimen can withstand the
highest stress before necking takes place. This can be observed by a local reduction in the crosssectional area of the specimen generally observed in the centre of the gauge length as illustrated in
figure 5.
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σ TS =
Pmax
Ao
@(6)
1.2.4 Fracture Strength, σf
After necking, plastic deformation is not uniform and the stress decreases accordingly until
fracture. The fracture strength (σfracture) can be calculated from the load at fracture divided by the
original cross-sectional area, Ao, as expressed in equation 7.
σ fracture =
Pfracture
Ao
@(7)
1.2.5 Fracture Strain, εf
Figure 5: Necking of a tensile specimen occurring prior to fracture
1.2.6 Tensile ductility
Tensile ductility of the specimen can be represented as % elongation or % reduction in area
as expressed in the equations given below
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% Elongation =
% RA =
where Af
Ao − A f
Ao
∆L
× 100
Lo
× 100 =
∆A
× 100
A0
@(8)
@(9)
is the cross-sectional area of specimen at fracture.
The fracture strain of the specimen can be obtained by drawing a straight line starting at the
fracture point of the stress-strain curve parallel to the slope in the linear relation. The interception of
the parallel line at the x axis indicates the fracture strain of the specimen being tested.
1.2.7 Work hardening exponent, n
Furthermore, material behavior beyond the elastic region where stress-strain relationship is
no loner linear (uniform plastic deformation) can be shown as a power law expression as follows
σ = Kε n
Where
σ
is the true stress
ε
is the true strain
n
is the strain-hardening exponent
K
is the strength coefficient
@(10)
The strain-hardening exponent values, n, of most metals range between 0.1-0.5, which can be
estimated from a slope of a log true stress-log true strain plot up to the maximum load as shown in
figure 5. Equation 10 can then be written as follows
log σ = n log ε + log K
@(11)
Y = mX + C
@(12)
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While n is the slope (m) and the K value indicates the value of the true stress at the true strain
equal to unity as illustrated in figure 6. High value of the strain-hardening exponent indicates an
ability of a metal to be readily plastically deformed under applied stresses. This is also corresponding
with a large area under the stress-strain curve up to the maximum load. This power law expression
has been modified variably according to materials of interest especially for steels and stainless steels.
K
Figure 6: Slope of log true stress- log true strain curve up to the ultimate tensile strength indicating
the work hardening exponent (n value) [3]
1.2.8 Modulus of Resilence, UR
Apart from tensile parameters mentioned previously, analysis of the area under the stressstrain curve can give informative material behavior and properties. By considering the area under the
stress-strain curve in the elastic region (triangular area) as illustrated in figure 7, this area represents
the stored elastic energy or resilence. The latter is the ability of the materials to store elastic energy
which is measured as a modulus of resilence, UR, as follows
σ2
1
U R = σ oε o = o
2
2E
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@(13)
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The significance of this parameter is considered by looking at the application of mechanical
springs which requires high yield stress and low Young's modulus. For example, high carbon spring
steel has the modulus of resilence of 2250 kPa while that of medium carbon steel is only 232 kPa.
1.2.9 Tensile toughness, UT
Tensile toughness, UT, can be considered as the area under the entire stress-strain curve which
indicates the ability of the material to absorb energy in the plastic region. In other words, tensile
toughness is the ability of the material to withstand the external applied forces without experiencing
failure. Engineering applications that requires high tensile toughness is for example gear, chains and
crane hooks, etc. The tensile toughness can be estimated from an expression as follows
U T ≈ σ u ε f or
σo +σu
2
εf
@(14)
Fig 7: Area under the stress-strain curve of high carbon spring steel and structural steel [2].
1.3 Fracture characteristics of the tested specimens
Metals with good ductility normally exhibit a so-called cup and cone fracture characteristic
observed on either halves of a broken specimen as illustrated in figure 8. Necking starts when the
stress-strain curve has passed the maximum point where plastic deformation is no longer uniform.
Across the necking area within the specimen gauge length (normally located in the middle),
microvoids are formed, enlarged and then merged to each other as the load is increased. This creates
a crack having a plane perpendicular to the applied tensile stress. Just before the specimen breaks, the
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shear plane of approximately 45o to the tensile axis is formed along the peripheral of the specimen.
This shear plane then joins with the former crack to generate the cup and cone fracture as
demonstrated in figure 8. The rough or fibrous fracture surfaces appear in grey by naked eyes. Under
SEM, copious amounts of microvoids are observed as depicted in figure 9. This type of fracture
surface signifies high energy absorption during the fracture process due to large amount of plastic
deformation taking place, also indicating good tensile ductility. Metals such as aluminium and copper
normally exhibit ductile fracture behavior due to a high number of slip systems available for plastic
deformation.
For brittle metals or metals that failed at relatively low temperatures, the fracture surfaces
usually appear bright and consist of flat areas of brittle facets when examined under SEM as
illustrated in figure 10. In some cases, clusters of these brittle facets are visible when the grain size of
the metal is sufficiently large. The energy absorption is quite small in this case which indicates
relatively low tensile ductility due to limited amount of plastic deformation prior to failure.
Figure 8: Cup and cone fracture [4]
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Figure 9: Ductile fracture surface (Ductile metals) Figure 10: Brittle fracture surface (Brittle metals)
In summary, tensile properties should be considered as important design parameters for the
selection of engineering materials for their desired application. Engineers have played a significant
role in that they should be able to analyze and understand material behavior and properties through
these mechanical testing parameters. Table 2 lists tensile properties of various engineering materials.
Table 2
Tensile properties of metals [2]
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2. Materials and equipment
2.1 Tensile specimens
2.2 Micrometer or vernia calipers
2.3 Universal testing machine
2.4 Stereoscope
3. Experimental procedure
3.1 The specimens provided are made of aluminium, steel and brass. Measure and record
specimen dimensions (diameter and gauge length) in a table provided for the calculation of
the engineering stress and engineering strain. Marking the location of the gauge length along
the parallel length of each specimen for subsequent observation of necking and strain
measurement.
3.2 Fit the specimen on to the universal Testing Machine (UTM) and carry on testing. Record
load and extension for the construction of stress-strain curve of each tested specimen.
3.3 Calculate Young's modulus, yield strength, ultimate tensile strength, fracture strain, %
elongation and % area of reduction of each specimen and record on the provided table.
3.4 Analyze the fracture surfaces of broken specimens using stereoscope, sketch and describe the
results.
3.5 Discuss the experimental results and give conclusions.
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4. Results
Details
Aluminium
Steel
Brass
Diameter (mm)
Width (mm)
Thickness (mm)
Cross-sectional area (mm2)
Gauge length (mm)
Young's modulus (GPa)
Load at yield point (N)
Yield strength (MPa)
Maximum load (N)
Ultimate tensile strength (MPa)
% Elongation
% Area of reduction
Fracture strain
Work hardening exponent (n)
Fracture mode
Fracture surfaces
(Sketch)
Table 3: Experimental data for tensile testing.
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Engineering stress-strain curve of aluminium
Describe the engineering stress-strain curve
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Engineering stress-strain curve of steel
Describe the engineering stress-strain curve
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Engineering stress-strain curve of brass
Describe the engineering stress-strain curve
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5. Discussion
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6. Conclusions
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7. Questions
7.1 What is work hardening exponent (n)? How is this value related to the ability of metal to be
mechanically formed?
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7.2 If the tensile specimen is not cylindrical rod shaped but a flat rectangular plate, how do you
expect necking to occur in this type of specimen?
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7.3 Both yield strength and ultimate tensile strength exhibit the ability of a material to withstand
a certain level of load. Which parameter do you prefer to use as a design parameter for a
proper selection of materials for structural applications? Explain
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8. References
8.1 Hashemi, S. Foundations of materials science and engineering, 2006, 4th edition, McGrawHill, ISBN 007-125690-3.
8.2 Dieter, G.E., Mechanical metallurgy, 1988, SI metric edition, McGraw-Hill, ISBN 0-07100406-8.
8.3 Norman E. Dowling, Mechanical Behavior of Materials, Prentice-Hall International, 1993.
8.4 W.D. Callister, Fundamental of materials science and engineering/an interactive e. text,
2001, John Willey & Sons, Inc., New York, ISBN 0-471-39551-x
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