Tensile Test
1. Purpose and Procedure of Tensile Testing
Tensile testing is a destructive mechanical testing method where a sample is
subjected to a controlled, increasing axial tensile load until it fractures. The load
applied to the specimen and the resulting elongation are recorded
simultaneously.
Purpose of the Test:

Mechanical Property Determination: To determine fundamental
mechanical parameters such as Young's modulus, yield strength, ultimate
tensile strength (UTS), ductility, and fracture behaviour.

Quality Assurance and Material Validation: To verify that
manufactured batches or received stock meet commercial standards and
strength specifications.

Engineering Design Data: To provide quantitative stress-strain data
required to calculate safe allowable loads, cross-sectional dimensions,
and safety factors for structural components.

Material Comparison: To compare how different alloys, heat treatments
(e.g., annealing vs. quenching), or cold-working processes alter
mechanical behaviour.
General Procedure Overview:
The test specimen is mounted into the upper and lower grips of a Universal
Testing Machine (UTM). An axial pulling force is applied at a specified, quasistatic loading rate. An extensometer attached to the gauge length records
elongation, while a load cell measures the instantaneous force. The data
acquisition system translates the load-displacement output into stress-strain
data.
2. Engineering and True Stress-Strain Curves
Raw load-elongation data is converted to stress and strain to eliminate
geometric size dependencies.
Engineering Stress (𝝈) and Engineering Strain (𝝐)
Engineering stress and strain are calculated based strictly on the original,
undeformed dimensions of the specimen:
𝜎=
𝜖=
𝑃
𝐴0
Δ𝐿 𝐿 − 𝐿0
=
𝐿0
𝐿0
[MPa]
[dimensionless]

𝑃 = instantaneous applied force (N)

𝐴0 = original cross-sectional area (mm2 )

𝐿0 = original gauge length (mm)

𝐿 = instantaneous gauge length (mm)
Engineering stress-strain curves are standard in structural design because
original component dimensions are fixed and known beforehand.
True Stress (𝝈𝒕 ) and True Strain (𝝐𝒕 )
True stress and true strain use the instantaneous cross-sectional area (𝐴𝑖 ) and
gauge length (𝐿𝑖 ) during deformation:
𝜎𝑡 =
𝜖𝑡 = ln (
𝑃
𝐴𝑖
[MPa]
𝐿𝑖
) = ln(1 + 𝜖 )
𝐿0
Assuming constant material volume during uniform plastic deformation
(𝐴0 𝐿0 = 𝐴𝑖 𝐿𝑖 ), true stress relates to engineering values prior to necking by:
𝜎𝑡 = 𝜎(1 + 𝜖 )
Key Differences & Necking Behavior

Elastic & Uniform Plastic Region: Deformations are small; engineering
and true curves lie close to each other.

Post-Necking (Past UTS): Localized cross-sectional area reduction
("necking") occurs. In the engineering curve, stress appears to drop
because the applied load decreases while dividing by the fixed original
area 𝐴0. In the true stress curve, stress continues to rise until fracture
because the true load-bearing area 𝐴𝑖 decreases sharply and the material
continues to strain harden.
3. Test Specimen Details and Experimental Procedure
3.1 Objective & Apparatus Used

Objective: To conduct a tensile test on a given test specimen and
determine its tensile strength using a Universal Testing Machine (UTM).

Equipment Used:
o
Universal Testing Machine (UTM) with TW Elite control and data
acquisition software
o
Digital / Vernier Calliper
o
Turned metallic tensile test specimen
3.2 Test Specimen Geometry and Dimensions (Initial & Final)
The tensile test was conducted on an Aluminium specimen with the following
dimensions:

Material: Aluminium

Initial Gauge Length (𝐿1): 45.12 mm

Initial Gauge Diameter (𝑑1): 10 mm

Initial Cross-Sectional Area (𝐴1):
𝜋 ⋅ 𝑑12 𝜋 ⋅ (10)2
𝐴1 =
=
= 78.54 mm2
4
4

Grip Separation: 53.12 mm

Final Gauge Length after Breaking (𝐿2 ): 53.16 mm

Final Diameter at Breaking Place (𝑑2): 6 mm

Final Cross-Sectional Area at Fracture (𝐴2):
𝜋 ⋅ 𝑑22 𝜋 ⋅ (6)2
𝐴2 =
=
= 28.27 mm2
4
4
3.3 Test Parameters & Settings

Test Rate (Loading / Displacement Speed): 0.1 mm/sec (6.0 mm/min)

Data Acquisition Rate: 2 Hz
3.4 Step-by-Step Experimental Procedure
1. Measurement of Initial Dimensions: The original gauge length (𝐿1 =
45.12 mm) and diameter (𝑑1 = 10 mm) of the turned Aluminium
specimen were measured using a Vernier Calliper.
2. Specimen Mounting: The specimen was properly aligned and clamped
into the upper and lower grips of the Universal Testing Machine (UTM)
with a set grip separation of 53.12 mm.
3. Software Setup & Test Initiation: Input values and test parameters (Test
rate: 0.1 mm/s, Data acquisition rate: 2 Hz) were entered into the TW
Elite software, and the load application was initiated.
4. Execution: The tensile load was continuously applied at the constant
displacement rate while load and elongation were recorded until complete
fracture of the specimen occurred.
5. Post-Fracture Measurements: The two broken halves of the fractured
specimen were joined together, and the final length (𝐿2 = 53.16 mm) and
the final diameter at the necked fracture zone (𝑑2 = 6 mm) were
measured and recorded.
3.5 Observations and Key Experimental Findings

Material Tested: Aluminium

Change in Length (Δ𝐿):
Δ𝐿 = 𝐿2 − 𝐿1 = 53.16 mm − 45.12 mm = 8.04 mm

Diameter Reduction (Δ𝑑):
Δ𝑑 = 𝑑1 − 𝑑2 = 10 mm − 6 mm = 4 mm

Angle of Necking / Shear Fracture Plane: ≈ 45∘ (typical ductile shear
fracture along planes of maximum shear stress)

Peak Load (𝑃peak ): 18.995 kN (18,995 N)

Peak Stress (Ultimate Tensile Strength):
𝜎peak =

18.995 kN
2
2 = 0.2419 kN/mm = 241.9 MPa
78.54 mm
Strain at Break (𝜖break ): 0.138 mm/mm (13.8%)
4. Material Properties Measurable Using Tensile Testing

Modulus of Elasticity (Young's Modulus, 𝐸): The ratio of tensile stress
to tensile strain within the linear elastic limit (𝐸 = 𝜎/𝜖). It quantifies the
inherent atomic bond stiffness and resistance to elastic deformation.

Yield Strength (𝜎𝑦 ) / 0.2% Offset Proof Stress: The stress at which
permanent, non-recoverable plastic deformation begins. For materials like
aluminium that do not have a sharp yield drop, a line drawn parallel to the
initial elastic slope at a 0.2% strain offset (𝜖 = 0.002) determines the
proof stress.

Ultimate Tensile Strength (UTS / Peak Stress, 𝜎𝑢 ): The maximum
engineering stress sustained by the material before the onset of localized
necking.

Fracture Strength (𝜎𝑓 ): The engineering stress at which the material
separates into two pieces.

Ductility (% Elongation and % Reduction in Area): Quantifies the
extent of plastic deformation a material can endure prior to failure:
% Elongation = (
𝐿2 − 𝐿1
) × 100%
𝐿1
% Reduction in Area = (
𝐴1 − 𝐴2
) × 100%
𝐴1

Modulus of Resilience (𝑈𝑟 ): The maximum elastic energy per unit
volume absorbed without permanent deformation (area under the elastic
portion).

Modulus of Toughness (𝑈𝑡 ): The total strain energy absorbed per unit
volume before complete rupture (total area under the entire stress-strain
curve).
5. Advantages of Tensile Testing

Direct and Uniaxial Stress Distribution: Provides a clean, onedimensional stress state, making theoretical modeling and mechanical
property calculation direct and reliable.

Multiple Properties in a Single Experiment: Yield strength, ultimate
tensile strength, Young's modulus, ductility, and fracture behavior are
obtained simultaneously from one test.

Global Standardization: Adherence to established test standards (such
as ASTM E8/E8M and ISO 6892-1) ensures reproducibility across
different labs and test equipment.

Primary Basis for Structural Design: Yield strength and UTS directly
define working stress limits, allowable loads, and safety factors for
engineering components.

Effective Quality Control: Serves as a standard inspection tool to verify
whether raw materials, alloys, or heat-treated components meet
commercial engineering specifications.
6. Experimental Data (from Lab Work) and Property Measurements
61 Recorded Lab Data & Specimen Geometry (Aluminium Specimen)
Parameter
Symbol /
Relation
Value from Lab Sheet
Material
—
Aluminium
Initial Gauge Length
𝐿1
45.12 mm
Initial Diameter
𝑑1
10 mm
𝜋 ⋅ 𝑑12
𝐴1 =
4
78.54 mm2
Initial Cross-Sectional
Area
Grip Separation
—
53.12 mm
Test Rate / Speed
—
0.1 mm/s (6.0 mm/min)
Parameter
Symbol /
Relation
Data Acquisition Rate
—
Peak Load
Value from Lab Sheet
2 Hz
𝑃peak
18.995 kN (18,995 N)
Peak Stress
𝜎peak
0.2419 kN/mm2
(241.9 MPa)
Strain at Break
𝜖break
0.138 mm/mm (13.8%)
Final Length After
Breaking
𝐿2
53.16 mm
Final Diameter at
Fracture
𝑑2
6 mm
Final Cross-Sectional
Area
𝜋 ⋅ 𝑑22
𝐴2 =
4
28.27 mm2
Change in Length
Δ𝐿 = 𝐿2 − 𝐿1
8.04 mm
Reduction in Diameter
Δ𝑑 = 𝑑1 − 𝑑2
4 mm
Necking / Fracture
Angle
—
45∘ (Shear failure plane)
6.2 Calculations of Mechanical Properties from Lab Observations
1. Modulus of Elasticity (Young's Modulus, 𝐸):
For standard structural aluminium alloys, the linear elastic slope in the
proportional region yields:
𝐸=
Δ𝜎
≈ 69 – 71 GPa
Δ𝜖
2. Yield Strength (0.2% Proof Stress, 𝜎0.2%):
Because aluminium does not show a sharp yield drop, the proof stress is
determined by drawing a line with slope 𝐸 offset by 0.002 (0.2%) strain:
𝜎0.2% ≈ 190 – 215 MPa
(0.190 – 0.215 kN/mm2 )
3. Ultimate Tensile Strength (Peak Stress, UTS):
UTS = 𝜎peak =
𝑃peak 18.995 kN
=
= 0.2419 kN/mm2 = 241.9 MPa
2
𝐴1
78.54 mm
4. Ductility (% Elongation and % Reduction in Area):

Percentage Elongation (%EL):
%𝐸𝐿 = (
𝐿2 − 𝐿1
53.16 − 45.12
8.04
) × 100% = (
) × 100% = (
) × 100%
𝐿1
45.12
45.12
= 17.82%
(Note: The recorded extensometer/software strain at break along the monitored
span is 0.138 or 13.8%, while manual end-to-end measurement gives 17.82%.)

Percentage Reduction in Area (%RA):
%𝑅𝐴 = (
𝐴1 − 𝐴2
78.54 − 28.27
50.27
) × 100% = (
) × 100% = (
) × 100%
𝐴1
78.54
78.54
= 64.00%
5. True Fracture Stress (𝜎𝑓,true):
𝜎𝑓,true =
𝑃fracture
𝐴2
7. External Resources & References
1. ASTM International. (2021). ASTM E8/E8M-21: Standard Test Methods
for Tension Testing of Metallic Materials. West Conshohocken, PA;
ASTM International.
2. International Organization for Standardization. (2019). ISO 6892-1:2019:
Metallic materials — Tensile testing — Part 1: Method of test at room
temperature. Geneva, Switzerland: ISO.
3. Callister, W. D., & Rethwisch, D. G. (2018). Materials Science and
Engineering: An Introduction (10th ed.). Hoboken, NJ: John Wiley &
Sons.
4. Dieter, G. E. (1986). Mechanical Metallurgy (3rd ed.). New York, NY:
McGraw-Hill Book Company.
5. Dowling, N. E. (2013). Mechanical Behaviour of Materials: Engineering
Methods for Deformation, Fracture, and Fatigue (4th ed.). Boston, MA:
Pearson.
Q&A SECTION
Question 1
Ultimate Tensile strength or Yield strength which is preferred as a design
parameter for a proper selection of materials for structural application and
why?
Answer:
Yield Strength (𝜎𝑦 ) is preferred as the primary design parameter for structural
applications.

Prevention of Permanent Distortion: Structural components (e.g.,
beams, bridges, aircraft frames, pressure vessels) must maintain their
original dimensions, tight tolerances, and alignments during service. If
operating stresses exceed the yield strength, non-recoverable plastic
deformation occurs, causing misalignment, structural sagging, binding of
moving parts, and functional failure.

Basis for Allowable Working Stress: In linear elastic structural design,
the working allowable stress (𝜎allowable ) is calculated directly from the
yield strength using a Factor of Safety (FOS):
𝜎allowable =
𝜎𝑦
FOS
This guarantees that all operating stress states remain strictly in the reversible
elastic regime where Hooke's Law holds.

UTS Represents Post-Deformation Capacity: Ultimate Tensile
Strength (UTS) is achieved only after extensive plastic elongation and
severe necking have already occurred. Relying on UTS would allow
major geometric collapse before the nominal material capacity is reached.
(UTS is only used as a secondary check to ensure a safety margin against
total structural rupture under unexpected overloads).
Question 2
What is strain hardening? Explain with a drawing.
Answer:
Strain hardening (also referred to as work hardening or cold working) is the
process where a ductile material becomes stronger, harder, and more resistant to
further deformation as it undergoes plastic (permanent) deformation below its
recrystallization temperature.
1. Microscopic Mechanism

At the crystalline level, plastic deformation takes place via the movement
and generation of line defects called dislocations.

As plastic deformation increases, the dislocation density in the crystal
lattice multiplies drastically (from roughly 107 cm−2 in an annealed
material to 1011 --1012 cm−2 in a deformed state).

These moving dislocations intersect, entangle, and pin each other,
creating internal stress fields that act as barriers against further
dislocation movement.

Consequently, a progressively higher applied shear stress is required to
overcome these barriers and produce additional plastic flow, leading to an
increase in macroscopic yield strength and tensile strength.
2. Explanation of the Drawing (Macroscopic Loading & Unloading Behaviour).
Initial Elastic & Plastic Loading:
The virgin metal is loaded from the origin. It deforms elastically along the
initial linear slope (Young's modulus 𝐸) until it reaches its original yield
strength 𝜎𝑦0. Loading past 𝜎𝑦0 induces plastic deformation and strain hardening
along the curve up to Point A (𝜎𝑦1).
Elastic Unloading:
When the load is released from Point A, the material unloads elastically along a
straight dashed line parallel to the original elastic slope (𝐸). During unloading:
𝜎𝑦1

The elastic portion of strain is recovered: 𝜖𝑒 =

A permanent plastic strain 𝜖𝑝 remains in the specimen.
𝐸
Subsequent Reloading:
When the specimen is reloaded, deformation proceeds elastically back along the
unloading line directly up to Point A.
Result:
Plastic deformation does not resume until the stress exceeds the elevated stress
level at Point A. Thus, the material now has a new, higher yield strength
(𝜎𝑦1 > 𝜎𝑦0), expanding its elastic range at the expense of remaining ductility.
Question 3
Name any two standards used for the tensile testing of metal and
composites (at least one for each).
Answer:

Standard for Metals:
o
ASTM E8 / E8M: Standard Test Methods for Tension Testing of
Metallic Materials
(or ISO 6892-1: Metallic materials — Tensile testing — Part 1: Method of test
at room temperature)

Standard for Composites:
o
ASTM D3039 / D3039M: Standard Test Method for Tensile
Properties of Polymer Matrix Composite Materials
(or ISO 527-4 / ISO 527-5: Plastics — Determination of tensile properties of
isotropic and orthotropic fibre-reinforced plastic composites)
Question 4
What is the loading rate/displacement speed in a quasi-static tensile test as
per a standard (refer a standard and name the standard)?
Answer:

Reference Standard: ASTM E8 / E8M (Standard Test Methods for
Tension Testing of Metallic Materials).

Specified Loading Rates & Displacement Speeds:
o
Elastic & Yield Determination Regime (Strain-Rate Control /
Method A): The strain rate is maintained within
0.00025 to 0.0025 mm/mm/min (or a stress rate between
1.15 and 11.5 MPa/s).
o

Post-Yield & Plastic Regime to Fracture (Crosshead Speed
Control): Once yielding is complete, the testing speed is increased
to a uniform crosshead displacement rate between
0.05 and 0.5 mm/mm of gauge length per minute (which
corresponds to 1.0 to 2.5 mm/min for standard 50 mm gauge
length specimens).
Purpose: These low speeds ensure that quasi-static equilibrium is
maintained without dynamic inertial effects, strain-rate sensitivity, or
adiabatic deformation heating.
Question 5
Draw stress-strain curves for (i) a metal, (ii) a ceramic, (iii) a polymer.
Highlight key features. Label with the material name.
Answer:
Key Features Highlighted by Material:

(i) Metal (e.g., Structural Mild Steel / Ductile Aluminium):
o
Linear Elastic Region: Steep initial slope (𝐸 ≈ 70–210 GPa)
following Hooke's Law.


o
Yield Point: Distinct yield strength (𝜎𝑦 ) marking the onset of
dislocation motion.
o
Strain Hardening & UTS: Continuous increase in strength up to
peak load (UTS).
o
Necking & Ductile Fracture: Localized cross-sectional area
reduction and cup-and-cone shear fracture at high failure strain
(𝜖𝑓 ≈ 15–25%).
(ii) Ceramic (e.g., Alumina Al2 O3 / Silicon Carbide):
o
Very High Elastic Modulus: Extremely steep linear slope (𝐸 ≈
300–400 GPa).
o
Brittle Fracture: Direct failure in the linear elastic regime with
zero plastic deformation (𝜖𝑓 < 0.2%) due to the inability of
dislocations to move past covalent/ionic bonds and rapid
propagation of micro-cracks.
(iii) Polymer (e.g., Thermoplastic HDPE / PMMA):
o
Low Modulus & Viscoelasticity: Low initial slope (𝐸 ≈
1–3 GPa).
o
Yielding & Neck Formation: Reaches an initial yield peak at low
stress (≈ 30–40 MPa).
o
Cold Drawing (Plateau): Long flat plateau where folded polymer
chains uncoil and reorient along the loading axis.
o
Strain Alignment & High Elongation: Orientation hardening
occurs near failure, leading to fracture at very large strains (𝜖𝑓 >
40–50%).