Mechanical Engineering Composite Laboratory
EXPERIMENT P8: UNIAXIAL TENSILE TEST
Department of Mechanical Engineering
McMaster University - Hamilton, Ontario
Editor: John Colenbrander
August 2021
Version Number: 00
Version Date: August 2021
Introduction
This lab manual describes the Uniaxial Tensile Test laboratory experiment, which can can be found in the lab locations document on
Avenue2Learn. The author of the original lab manual is unknown. It
has been updated to this format by the editor in 2021. Several edits have been made for clarity or to better correspond to the current
course oering. Typesetting is in LATEX using the refman template.
Contents
1 Objective
2 Theory/Background
3 Experimental Apparatus, Procedure and Data Collection
4 Results & Discussion
5 Conclusion
Appendices
A Property Calculations (Sample Calculations)
B Material Data Tables
2
2
8
10
11
12
12
15
1 Objective
To familiarize the students with the measurement of mechanical properties
(yield strength, ultimate tensile strength, %elongation, ductility) of engineering materials via the uniaxial tensile test.
2 Theory/Background
The uniaxial tension test is widely used to provide information on the
strength and plastic properties of materials. In this test, a sample of material is elongated by a uniaxial load. The axial load, F, and the change of the
sample's length,
∆l,
are recorded. The test is performed on a tensile test
frame equipped with load and displacement sensors and recording devices.
Fig. 1 illustrates a typical, F(∆l ), tensile curve for a ductile material.
Figure 1: Tension load - extension curve
The actual range of the load and displacement depends on the material and
dimensions of the sample. In order to compare dierent materials, the effect of sample dimensions is eliminated by translating load into force per
unit cross-sectional areatensile stresses,
elongation-tensile strain,
σ (ϵ),
ϵ.
σ,
and displacement into relative
Fig. 2 illustrates a typical stress-strain curve,
for an elastic plastic material. The basic mechanical properties per-
taining to the strength and ductility of the material are referred to in terms
of stresses and strains.
Particularly, so called
eective stress
and
strain
utilized in strength analysis, translate any general three-dimensional stressstrain state to values
equivalent
to the uniaxial tensile test data,
σ,
and
ϵ.
The stress strain curve shown in g. 2 contains several characteristic points
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Experiment P8:
Uniaxial Tensile Test
usually listed in standard material data sheets. The slope of the initial linear portion of the
σ−ϵ
curve is referred to as Young's modulus,
E,
which
is the elastic stiness of the material under normal stress. Upon unloading
from a stress-strain state within this range of deformation, the sample fully
recovers its initial dimensions, i.e., the deformation is purely elastic,
ϵel .
Some materials may exhibit a non-linear elasticity, i.e., the value of Young's
modulus,
E,
may not be constant, yet there is full elastic shape recovery
upon unloading.
Figure 2: Stress-strain curve, elastic-plastic material model
If, during loading, the strain exceeds a specic limit, upon unloading the
initial shape of the sample is not fully recovered and some portion of the total
loading strain,
ϵ,
as plastic strain,
becomes permanent. This permanent strain is referred to
ϵpl .
ϵpl , cannot be induced without
ϵel , the stress level at which the
referred to as the yield stress, Yo , of the
The plastic strain,
being preceded by elastic deformation,
plastic deformation is initiated is
material. Any structural application of a given material should ensure that
the maximum value of the eective stress remains below the yield stress,
otherwise under expected loading the shape of the structure would become
permanently distorted due to plastic deformation. Most materials do not
exhibit the presence of a distinct point,
without a distinct yield point,
Yo ,
Yo , on the σ − ϵ curve.
For materials
the yield stress is usually dened as the
stress level at which the permanent plastic strain is 0.2%. In the material
data sheets this kind of yield stress is referred to as
R0.2 .
Dierent national
standards also list other denitions of the yield stress such as
R0.1 , R0.02 ,
etc., which refer to 0.1% and 0.02% plastic elongation at the yield point.
Beyond the yield point the deformation is elastic-plastic.
This range of
deformation is of primary importance for forming technology applications
in which dierent mechanical components are shaped by plastic strains. In
the forming technology applications, the plastic strain may become of two
or more orders of magnitude greater than the elastic strain. Often, in the
analysis of these applications, the elastic properties are neglected, and the
material behavior is simplied by the so called rigid-plastic material model,
Experiment P8:
Uniaxial Tensile Test
3
for which the curve,
σ(ϵpl ),
begins at the initial yield stress,
Yo (ϵ = 0)
and
ignores the elastic strain, (g. 3).
Figure 3: Stress-strain curve, rigid plastic material model
In the elastic-plastic range of deformation the level of stress may increase
with the magnitude of the strains.
hardening.
This increase is referred to as
strain
Strain hardening indicates that the material is gaining strength
due to the induced plastic deformation.
If a strain hardened material is
unloaded from the elastic-plastic range of deformation and reloaded again,
the plastic deformation will not resume at the stress level indicated by the
initial yield point,
σ(ϵpl ),
In
Yo
or
R0.2 ,
but at the stress level near or at the level,
reached just before the unloading.
[r1 , r2 , r3 ]
uniaxial tension test, only one of the principal stress com-
ponents is non-zero - the axial stress,
σ = σ1 ,
while the remaining two
components associated with the planes orthogonal to the tensile direction
are zero,
σ = σ2 = σ3 . The elongation of the sample is measured by the
ϵ = ϵ1 . However, as the volume of the sample is conserved, its
axial strain,
cross-sectional area decreases, and therefore, none of the principal strains
ϵ1 > 0, ϵ2 < 0andϵ < 0. In the elastic-plastic range a sinσ1 , results in six principal strain components, three
strains, [ϵ1 , ϵ2 , ϵ3 ]el , and three plastic strains, [ϵ1 , ϵ2 , ϵ3 ]pl . The axial
is zero, i.e.,
gle stress component,
elastic
stress and strain are used as the reference but in general the deformation in
tensile test has all the same stress and strain characteristics as any other deformation process. The uniaxial tension stress-strain state exists as long as
the sample is being deformed uniformly. The initial increase of the tension
load, F(Deltal ),shown in g. 1 is due to the strain hardening (monotonic
increase of the stress level of the,
σ = σ1 ,
σ(ϵ),
curve). However, the axial stresses,
are carried by the decreasing cross-section area, A, of the sample.
At some point the eect of stress increase on the tension force becomes
equal to the eect of the cross-section area decrease. At this point the force
reaches a maximum value,
Fm ax..
Any further elongation of the sample
results in the drop of force and elastic unloading of the previously stressed
material with the exception of one zone, which due to micro-structural or
dimensional defects has the lowest load carrying capacity. At this stage, the
overall extension of the sample length results in localization of the plastic
deformation only in the weakest zone referred to as the neck. The stress
state in the neck changes to a tri-axial tension, which is caused by the non-
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Experiment P8:
Uniaxial Tensile Test
co-linearity of the neck prole with the sample axis. Essentially the stress
state in the neck is undened and only the portion of the
σ − ϵ curve within
the uniform elongation range is considered valid.
2.1 Stress and strain measures
There are two basic stress and strain measures used in material data sheets:
the engineering and the true measure.
The engineering stress and strain
measures are obsolete; nevertheless, many national standards still utilize
these traditional measures. The engineering stress,
ratio of the instantaneous tensile force,
of the sample,
Fi ,
σeng ,
is dened as the
to the initial cross-section area
Ao ,
σeng =
Fi
A0
(1)
and the engineering percent strain, e%, as the % ratio of the length increase,
∆l,
to the initial length, lo , of the sample:
e% =
∆l
100%
lo
(2)
Figure 4: Engineering Stress-strain Curve
However, during a tensile test the cross-section area of the sample,
A,
de-
creases due to elongation while each subsequent increase of sample length,
dl,
takes place over an already elongated sample length, l. It is evident that
by neglecting the change in the cross-section area,
l,
A,
and sample length,
the engineering measures are not representative of the actual strain and
stress state of the material.
The stress-stain curve expressed in the engi-
neering measures is shown in g. 4. Apparently, based on the engineering
stress denition (1) the value of engineering stress decreases past the point
marked with the symbol U.T.S. This is misleading; in reality the true stresses
continuously increase.
Experiment P8:
Uniaxial Tensile Test
5
The so-called true stress and true strain measures dene the stress and strain
state correctly. The true stress,
applied force,
Fi ,
σ , is dened as the ratio of the instantaneous
Ai :
to the instantaneous cross-section area,
σ=
and true strain,
ϵ,
Z
li
l0
lo ,
(3)
is dened as the product of integration, given by:
ε=
where,
Fi
Ai
li ,
is the initial and,
dl
= ln
l
li
lo
(4)
is the instantaneous length of the sample.
The true strain is also often referred to as the logarithmic strain.
2.2 Strain-strain curve for plastic deformation
The relationship, between true stress and strain measures is referred to as
the
stress-strain curve
. For many materials, the experimental,
σ − ϵpl ,
data can be modeled by an exponential function of the form:
n
σ = K (εo + εpl )
where
K , ϵo
and
n
(5)
are material constants. These constants are determined
by tting a curve expressed by equation (5) between experimental points
obtained from a tensile test.
Usually the curve-tting algorithm neglects
the small elastic deformation. The constant,
K , is referred to as ow stress
= 1.0 and its value indicates
constant. It represents the stress level for ϵo +ϵpl
the overall stress level at which the material is deformed plastically.
constant,
ϵo ,
The
is referred to as initial strain oset. This constant shifts the
exponential curve (5) to a position at which for,
ϵpl = 0,
(the beginning
of plastic deformation) the stress level is equal to the initial yield stress,
σ = Yo .
The constant,
n,
is referred to as the strain hardening exponent.
It indicates the rate of material strain hardening. On a logarithmic scale
graph, g.
5, the stress-strain curve,
becomes a straight line with slope
σ(ϵpl ),
represented by equation (5)
n,
log(σ) = n log (εo + εpl ) + log(K)
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Experiment P8:
(6)
Uniaxial Tensile Test
Figure 5: Stress-strain curve in logarithmic scale
2.3 Coecient of Anisotropy, r
An isotropic material exhibits identical properties in all directions in its
volume. In general, an anisotropic material is characterized by dierent values of characteristic properties such as Young's modulus, yield stress, strain
hardening etc. depending on the orientation of the loading direction in the
material space. Particularly in sheet forming technology applications (for
example, forming automotive body panels) a desirable deformation behavior
is such that the material resists deformation in its thickness direction but
is easily deformable in its plane. This behaviour promotes shaping of the
surface over localized thinning and ultimately, splitting, of the sheet during
forming. The uniaxial tension test is used to evaluate this property of sheet
r, dened as the ratio of
ϵ2 = ϵw , measured in the direction of sample's width over
ϵ3 = ϵt , measured in the thickness direction:
products by means of the coecient of anisotropy,
the true strain,
the strain,
r = εw /εt
The coecient of anisotropy,
◦
◦
r,
(7)
is determined for three dierent directions
◦
0 , 45 , 90 in the sheet plane with respect to the rolling direction of the
sheet,
r0 , r45 , r90 .
2.4 Tensile test data sheet
Standard tensile test data sheets provide the following data:
ˆ
Sample dimensions - National standards list several standard dimensions for tensile test samples. They are dierent for at, bar and wire
products. The 4:1 gage length/width type sample used in the laboratory comply with the ISO/ASTM recommendations for at (sheet)
products with recommended gage length of 60mm (2.25 in) and width
12.5mm (0.5 in),
Experiment P8:
ˆ
Young's modulus,
ˆ
Yield stress,
Uniaxial Tensile Test
Yo
or
E,
R0.2 ,
- expressed as engineering stresses
7
ˆ
Ultimate tensile strength
U.T.S
- expressed as engineering stresses
U.T.S = F max /Ao
ˆ
Total Elongation,
et %
- obtained by putting a fracture sample back
together and measuring the % of total length change,
∆lmax /lo .
ˆ
ef % =
$ 100%
Reduction of area,
fractured section
q, A.R.
or
%At
- % of the area reduction of the
2.5 Additional data
ˆ
Plastic stress-strain curve parameters
ˆ
Uniform elongation,
ϵu
or
K, ϵo , n,
(true measures),
%ϵu , - maximum elongation of the material
outside the neck expressed in true or engineering strain measures,
ˆ
Coecient of anisotropy,
r0 , r45 , r90
(used for at products only).
3 Experimental Apparatus, Procedure and Data Collection
3.1 Apparatus
The Instron 4460 test apparatus and it's components are are shown in Figure
6. A test sample is shown with the extensometer installed, mounted in the
jaw grippers, in Figure 7. Your TA will provide details of operation of the
apparatus.
Figure 6: Components of the Instron 4460 Uniaxle Test Apparatus
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Experiment P8:
Uniaxial Tensile Test
Figure 7: A test sample installed in the jaws of the Instron.
3.2 Safety
The participants of the experiment must wear safety glasses.
All participants of this lab experiment must be familiar and follow the Standard Operating Procedure, (SOP), entitled P5 Plastic properties of sheet
metal (Instron 1140). The full text of the SOP is available in JHE 207.
3.3 Experimental Procedure
The objective of the experiment is to generate a complete material data
sheet for a at product. The experiment will be performed on a standard
tensile testing machine equipped with load cells, displacement, and strain
gages. Prior to the experiment, the students should plan the steps of the
experimental procedure. As part of the experimental procedure the students
should perform full calibration of all the gages. A set of weights and a device
equipped with micrometer screw will be provided to perform the calibration
of the load and displacement sensors.
Experiment P8:
Uniaxial Tensile Test
9
4 Results & Discussion
This section in your
Full Lab Report will contain the answers to the questions
posed to the student in the various lab elements (lab video, Procedure or
Results sections, and
Live Lab Session ).
Of note, the expectation is that the student will not only answer the questions outlined in the Results section of the lab manual, but integrate them
into a well-formatted and logical discussion
1 by interpreting the results. The
student will link the results to theory presented in the
Lab Manual
or the
literature, and demonstrate an understanding of the physics and engineering
implications arising from the lab. The data tables, plots etc. prepared in the
Results section and the appropriate information in the Background/Theory
should be referred to throughout this section in order to support (or validate, or explain) the interpretation. Students are reminded to properly cite
any references they use in their Discussion.
The
Full Lab Report Rubric and Example Full Lab Report on Avenue provide
more details on how to address the Discussion section.
After performing the lab, students should prepare the following graphs and
address the following questions in the Full Lab Report. Please see the Lab
Assignment for data that all students should prepare.
1. Create a graph of true stress/strain and engineering stress/strain for
each sample. Plot both graphs on the same gure.
2. Plot the elastic zone for each sample and indicate the properties which
can be extracted from the curve.
3. Fit a curve to the plastic region of the true stress/strain graph using
the method described and equation (6). Show the logarithmic plots
with the sample calculations and plot the empirical curve on the same
gure as the engineering stress/strain and true stress/strain curves.
What is the purpose of tting a curve to the stress/strain graph?
4. What dierences could be expected by making an extension vs. time
graph and a displacement vs. time graph? What signicance would
this portray?
(Extension data is not provided, do not create the
graphs)
5. Complete the property calculations sheets
6. Discuss the following results of the lab.
ˆ
Were the yield strengths of the materials what were expected or
this material? Justify your results with information from the literature, or handbooks, remembering to correctly cite all sources.
ˆ
Do these values make sense according to the rolling direction of
the samples?
ˆ
Discuss the signicance of the coecient of anisotropy.
Which
rolling direction would be best suited for high amounts of metalworking?
1 This
means that the discussion section should NOT look like an assignment; it should
be composed of paragraphs with full sentences and linking of ideas, so that a logical
progression through the results/questions is presented.
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Experiment P8:
Uniaxial Tensile Test
7. Describe and discuss at least four sources of error in this lab which
could aect the quality of results obtained.
5 Conclusion
The student will be asked to draw conclusions concerning the results of their
experiments with particular emphasis on the discussion question(s) given.
Summarize the major conclusions regarding the experiment. By comparing
the
σ−ϵ
curves of the dierent samples,what inuence does the rolling
direction have on tensile properties?
Experiment P8:
Uniaxial Tensile Test
11
Appendix
A Property Calculations (Sample Calculations)
Sampled Rolled in 0◦ Directions:
Property
Formula
Calculation
Young's
Modulus
Note: Please indicate on
graph also
Ultimate
Tensile
Strength
Total Elongation
U.T.S =
Fmax /Ao
et % =
(∆lo /lo ) X100%
Reduction
of Area
Flow Stress
Constant
Strain
Hardening
Exponent
Initial
Strain Oset
Uniform
Elongation
Coecient
of
Anisotropy
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Experiment P8:
Uniaxial Tensile Test
Sampled Rolled in 45◦ Directions:
Property
Formula
Calculation
Young's
Modulus
Note: Please indicate on
graph also
Ultimate
Tensile
Strength
Total Elongation
U.T.S =
Fmax /Ao
et % =
(∆lo /lo ) X100%
Reduction
of Area
Flow Stress
Constant
Strain
Hardening
Exponent
Initial
Strain Oset
Uniform
Elongation
Coecient
of
Anisotropy
Experiment P8:
Uniaxial Tensile Test
13
Sampled Rolled in 90◦ Directions:
Property
Formula
Calculation
Young's
Modulus
Note: Please indicate on
graph also
Ultimate
Tensile
Strength
Total Elongation
U.T.S =
Fmax /Ao
et % =
(∆lo /lo ) X100%
Reduction
of Area
Flow Stress
Constant
Strain
Hardening
Exponent
Initial
Strain Oset
Uniform
Elongation
Coecient
of
Anisotropy
14
Experiment P8:
Uniaxial Tensile Test
B Material Data Tables
Sampled Rolled in 0◦ Directions:
Parameter
Standard
Material
Data
Sheet
Value
Gage length
Initial
Sample
25.4mm
Gage width
Gage thickness
Dimensions
Final
Gage width
Gage thickness
Sampled Rolled in 45◦ Directions:
Parameter
Standard
Material
Data
Sheet
Value
Gage length
Initial
Sample
25.4mm
Gage width
Gage thickness
Dimensions
Final
Gage width
Gage thickness
Sampled Rolled in 90◦ Directions:
Parameter
Standard
Material
Data
Sheet
Value
Gage length
Initial
Sample
25.4mm
Gage width
Gage thickness
Dimensions
Final
Gage width
Gage thickness
Experiment P8:
Uniaxial Tensile Test
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