Tensile Test (Uniaxial Tension Test): Procedure, Stress-Strain Curve & Calculations

A tensile test, also called a uniaxial tension test, pulls a specimen along one axis at a controlled rate until it breaks. The recorded force and elongation are converted into a stress–strain curve, which gives Young’s modulus, yield strength, ultimate tensile strength (UTS), elongation at break, reduction in area and, with a second strain measurement, Poisson’s ratio. It is the most widely used mechanical test in materials science and engineering.

This guide explains how a uniaxial tension test works, which standards apply, how to read the stress–strain curve, how to run the test step by step and how to calculate the results. It ends with a worked lab example on 1018 steel, 6061 aluminum and cast iron, and an FAQ.

Why perform a tensile test?

Engineered products must be strong enough for their intended use, and strength depends on the material. The tensile test is a destructive test that measures the force needed to break a specimen and how far the specimen stretches before it fails. It is the basic source of design data for metals, plastics, composites, rubber and adhesives, and it is also used for quality control and for material selection.

Results include the stress–strain diagram, from which the tensile modulus, yield strength, tensile strength at break, tensile strain and percent elongation are read. Material properties from tensile tests are also entered into CAE software so that OEMs can build virtual models.

Alignment is critical when testing composites because they are anisotropic, meaning their properties change with the direction of the force. Tests must be aligned with the fiber orientation to give accurate results, which matters most in aerospace, where composites carry high tensile stress. Grips and fixtures are available for ambient, sub-ambient and high-temperature testing.

Tensile test standards for metals, plastics and composites

Use the standard that matches the material, because specimen shape, size and test speed differ between them:

Material	Common tensile test standards
Metals	ASTM E8/E8M and ISO 6892-1
Plastics	ASTM D638 and ISO 527-1/-2
Fiber-reinforced composites	ASTM D3039 and ISO 527-4/-5
Rubber and elastomers	ASTM D412 and ISO 37

Tensile test specimen geometry

The shape of the specimen strongly affects the quality of the result. Raw material is usually machined or cut into a “dogbone” shape: wide ends for gripping and a narrower center, called the gage region, where the stress concentrates and the specimen is meant to fail.

Dogbone specimens may be round or flat, and flat specimens are more common for sheet. Dimensions depend on the material, the standard and the intended use. For example, the standard ASTM E8 round specimen is 12.5 mm (0.500 in) in diameter with a 50 mm (2.0 in) gage length, and the flat sheet-type specimen is 12.5 mm wide with the same 50 mm gage length. ISO 6892-1 commonly uses proportional specimens with L₀ = 5.65√S₀.

What is tensile strength?

Tensile strength is the maximum engineering stress a material can withstand while being pulled before it fractures. To measure it, the material is machined to a specified shape and tolerance, gripped at both ends and pulled slowly until it breaks. The goal is to see how engineering materials respond to tensile loading.

Industry runs this test because it is a low-cost way to confirm that a selected material will withstand the forces and stresses it sees in service. When a new material is developed, its mechanical properties are not yet known, so testing finds the yield, ultimate and breaking stress.

What is uniaxial stress?

Uniaxial stress occurs when a material is loaded in one direction only. When a tensile specimen is loaded this way, the force produces tensile stress and strain in the material. The load is the same along the specimen, but the stress is highest in the narrow gage section, which is why that is where the specimen fails.

Manufacturers use these results to select the material best suited to an application and to make sure it will not fail from over-stress or over-strain. Elongation is measured from the change in specimen length after the test, and strain rate is the change in strain per unit time. An engineering stress–strain diagram is shown below.

Stress–strain curve: key points and properties

On the curve, σ_y marks the yield point, the end of elastic behavior, where the slope is Young’s modulus (E), a material-dependent property. Beyond yield the material deforms plastically with strain hardening, until increased loading ends in fracture.

The stress–strain curve gives design engineers the key parameters for their applications. These properties come from the curve:

• Modulus of elasticity (E): a measure of stiffness, equal to the slope of the elastic region. Typical values are about 30×10⁶ psi (207 GPa) for steel and about 10×10⁶ psi (69 GPa) for aluminum.
• Proportional limit: the point in the elastic region where the stress–strain relationship starts to deviate from linear.
• Elastic limit: the maximum stress beyond which the material starts to deform plastically.
• Yield point (Y): where plastic deformation begins. Some materials show a distinct yield region and others do not. When there is no abrupt change in slope, yield is defined by the proof strength, the stress at which a 0.2% strain offset from the straight line has occurred.
• Modulus of resilience: the area under the curve up to the yield point, u_r = σ_yε_y/2 = σ_y²/(2E), in lb·in/in³ or J/m³.
• Poisson’s ratio (ν): the absolute ratio of lateral strain to longitudinal strain.
• Plastic region: after yield, a ductile specimen lengthens while keeping an approximately uniform cross-section until necking begins. The load at the start of necking is the maximum load (F_max), and the engineering stress there is the ultimate tensile strength: TS = F_max/A₀.
• Necking: once maximum load is reached, deformation localizes in one region, the load falls and the specimen narrows until it fractures. The stress just before fracture is the fracture stress.
• Elongation: the total strain the material can endure before failure, EL% = [(L_f − L₀)/L₀] × 100, where L_f is the gage length after fracture.
• Reduction in area: another measure of ductility, AR% = [(A₀ − A_f)/A₀] × 100.

Yield strength vs ultimate tensile strength

Property	Symbol	What it marks	Why it matters
Yield strength	σy (or Sy)	Stress where permanent plastic deformation begins (0.2% offset if there is no distinct yield point)	Design limit for parts that must not deform permanently
Ultimate tensile strength	σu (or Su, TS)	Maximum engineering stress, reached at the start of necking	Upper limit of load capacity and a basis for comparing materials
Fracture stress	σf	Engineering stress at the moment of rupture	Lower than UTS for ductile metals because the area has shrunk

Example of the 0.2% offset method. For a steel with E = 200 GPa, draw a line parallel to the elastic slope that starts at a strain of 0.002. The line is σ = E(ε − 0.002), so it passes through 400 MPa at ε = 0.004. The stress where this offset line crosses the measured curve is the 0.2% offset yield strength.

Engineering vs true stress and strain

The engineering stress–strain curve uses the original area and length, so it falls after necking even though the metal itself keeps hardening. True stress and true strain use the instantaneous area and length. Up to the onset of necking, where deformation is uniform, they convert from the engineering values by:

• True stress: σ_t = σ(1 + ε)
• True strain: ε_t = ln(1 + ε)

For example, an engineering stress of 400 MPa at an engineering strain of 0.10 corresponds to a true stress of 400(1.10) = 440 MPa and a true strain of ln(1.10) = 0.0953. These conversions are not valid after necking begins. The plastic part of the true curve is often fitted with the power law σ_t = Kε_tⁿ, where K is the strength coefficient and n is the strain-hardening exponent.

Types of stress–strain curves

• Perfectly elastic: behavior measured by E alone, with little or no plastic deformation. Brittle materials such as glass and ceramics behave this way, and gray cast iron does approximately.
• Rigid, perfectly plastic: E is treated as infinite, and once stress reaches Y the material keeps deforming at constant stress.
• Elastic, perfectly plastic: the material has stiffness E, and once stress reaches Y it deforms plastically at constant stress (K = Y and n = 0).
• Rigid, linearly strain-hardening: the flow stress increases with increasing strain.
• Elastic and strain hardening: the material obeys Hooke’s law, σ = Eε, in the elastic region and follows σ = Kεⁿ in the plastic region.

Typical tensile properties of common materials

Material	Young’s modulus E	Yield strength	Ultimate tensile strength	Elongation at break
AISI 1018 steel (cold drawn)	205 GPa (29.7 × 106 psi)	370 MPa	440 MPa	15%
6061-T6 aluminum	69 GPa (10 × 106 psi)	276 MPa	310 MPa	12–17%
Ti-6Al-4V titanium (annealed)	114 GPa	880 MPa	950 MPa	14%
Copper (annealed)	117 GPa	70 MPa	220 MPa	45%
Gray cast iron (Class 30)	about 100 GPa (varies widely)	not defined (brittle)	about 210 MPa	under 1%
HDPE plastic	about 1 GPa	about 26 MPa	about 30 MPa	over 100%

What is the purpose of a uniaxial tension test?

Engineers and materials scientists use the test to check the tensile properties of the materials that go into products. Variations include the standard specimen pull test, adhesion and bond-strength tests, and tear-resistance tests. The automotive, metals and construction, and aerospace industries all depend on it.

Automakers use tensile data to evaluate the strength and structural rigidity (frame stiffness) of the body-in-white (BIW); good material selection can turn a good BIW into an excellent one, provided it already has a good structural load path.

Tensile data is also used extensively in sheet metal stamping. When stamping a part, automakers want to exceed the yield stress so the part holds its shape, but must stay below the fracture limit to avoid tearing the sheet. See sheet metal stamping and forming for more.

Tensile test equipment

Tensile tests are performed in materials testing laboratories on a pull tester, usually a universal testing machine (UTM). Electromechanical UTMs offer versatile test speeds and long displacements, while hydraulic machines are cost-effective for high-force applications. Protocols such as ASTM D638 apply to plastics.

Important machine capabilities are force capacity, speed range, precision and accuracy; the machine must generate enough force, reproduce service conditions and measure gage length and force accurately. Specimens must be aligned to avoid bending forces, which are especially damaging to brittle materials. Strain is measured with extensometers or strain gauges, and modern digital systems meet and exceed the accuracy requirements for metal tensile testing.

Tensile test procedure (step by step)

Materials required

• Test specimens (tensile specimens)
• Tinius Olsen universal testing machine
• 2″ gage punch
• Extensometer with a 2″ gage length
• Vernier calipers
• Steel scale
• Safety glasses

Steps

1. Zero the vernier calipers, then measure the specimen diameter just below the fillet but close to one end. Rotate the calipers 90° at the same place, take a second reading and record both.
2. Repeat at the center of the specimen and at the opposite end. With six readings per specimen, average them and use the average diameter to calculate the cross-sectional area.
3. Make a 2″ gage mark on each specimen with the gage punch.
4. Thread the specimen into the bottom collet, jog the crosshead up and secure the top end.
5. Install the extensometer on the specimen.
6. Leave a little slack so that the specimen is not stressed before the test begins.
7. Start the tensile test program on the computer and set the loading rate (position rate).
8. Start loading the first specimen, making sure nothing applies outside force to the machine during the test.
9. Remove the extensometer when the software prompts, after the material has yielded but before necking begins, to protect the instrument.
10. After the specimen fails, carefully remove it from the machine.
11. Fit the broken halves together and measure the diameter at the neck to calculate the reduction in area.
12. Record the new gage length.
13. Print the results, including the stress–strain diagram.
14. Repeat all steps with the second specimen.

How to calculate tensile test results

These are the formulas used in the worked example below. A₀ and L₀ are the original area and gage length, A_f and L_f are the values after fracture, and P is the applied load.

Quantity	Formula
Cross-sectional area (round specimen), A	A = πd2/4
Normal (engineering) stress, σ	σ = P/A0
Engineering strain, ε	ε = (L − L0)/L0 = ΔL/L0
Young’s modulus, E	E = σ/ε (slope of the elastic region)
Reduction in area, %RA	%RA = [(A0 − Af)/A0] × 100
Elongation, %EL	%EL = [(Lf − L0)/L0] × 100
Percent error	% error = |experimental − true| / true × 100

Published reference data

Worked example: tensile test of 1018 steel, 6061 aluminum and cast iron

Example calculations (6061 aluminum)

Stress–strain graphs for each material

Experimental data sets

Sample findings

Of the three materials, cast iron showed the largest deviation from its published values. Its stress–strain curve had no clear linear region and no distinct yield point, so it was much more uniform than the others, and that probably explains the large difference between the two cast-iron trials. Because there was no linear portion, the points chosen to calculate the slope changed the modulus (see Figures 1 and 2 above).

For example, the calculated average ultimate stress of the cast iron was 44,666 psi, while the published value of 200 MPa equals 29,007 psi, so the experimental result was about 54% high. For 6061 aluminum, the published ultimate strength of 300 MPa (43,511 psi) compares with an experimental average of 48,117 psi, an error of about 10.6%. For 1018 steel, the experimental Young’s modulus agreed with the handbook value of 29,700 ksi to within about 1% (1.05% error).

Sources of percent error

Several factors can increase the error. If the strain gauge is not bonded correctly to the specimen, the strain readings are off, and the accuracy and quality of the gauge matter as well. Only two trials were run for each material, and three or more would give much better statistics. The test measured Young’s modulus and the yield, ultimate and breaking stress. Density, ductility, compressive strength and the coefficient of thermal expansion came from published tables instead.

Tensile test failure modes and common mistakes

• Ductile fracture (cup and cone): the specimen necks visibly, then fails with a cup-shaped surface on one half and a cone on the other. Typical of annealed low-carbon steel and aluminum.
• Brittle fracture: little or no necking, with a flat fracture surface roughly perpendicular to the load. Typical of cast iron, glass and ceramics.
• Misalignment: off-axis loading adds bending, lowers the measured strength and ruins brittle specimens.
• Grip slippage or fracture at the grips: invalidates the result under most standards; the specimen should break inside the gage length.
• Wrong strain measurement: using crosshead displacement instead of an extensometer overstates strain, because the machine and grips also deflect.
• Uncontrolled test speed: yield and UTS depend on strain rate, so the rate set by the standard must be used.

Uniaxial tension vs uniaxial compression

Uniaxial compression loads the specimen along one axis in the opposite direction. Ductile metals behave similarly in tension and compression up to yield, but brittle materials such as cast iron, concrete and ceramics are much stronger in compression than in tension. Compression tests also have to guard against buckling in slender specimens; see column buckling.

Conclusion: what a tensile test tells you

As new materials such as ultra-high-strength and advanced high-strength steels are developed for the automotive industry, OEMs need to confirm that the properties meet the design specification. Lighter metals are tested to make sure they are still strong enough to hold together.

Steel is the better choice where a stronger and stiffer material is needed, because of its higher ultimate stress and Young’s modulus. If weight is a concern, aluminum is much less dense than steel. Comparable strength is possible with aluminum, but the section must be larger, which increases the moment of inertia and makes the part bulkier than a steel part of the same strength.

Tensile test FAQ

What is a uniaxial tension test?

A uniaxial tension test, or tensile test, pulls a specimen along a single axis at a controlled rate until it breaks. The force and elongation are recorded and converted into a stress–strain curve.

What does a tensile test measure?

It measures Young’s modulus, yield strength, ultimate tensile strength, elongation at break and reduction in area. With a lateral strain measurement it also gives Poisson’s ratio.

What is the difference between yield strength and tensile strength?

Yield strength is the stress at which permanent plastic deformation begins. Ultimate tensile strength is the maximum engineering stress reached before necking. UTS is always equal to or higher than yield strength.

Which standard is used for tensile testing of metals?

ASTM E8/E8M and ISO 6892-1 cover tension testing of metallic materials. ASTM D638 and ISO 527 are used for plastics, and ASTM D3039 for polymer matrix composites.

What is the 0.2% offset yield strength?

When a material has no distinct yield point, yield strength is taken as the stress where a line parallel to the elastic slope, offset by 0.2% strain, intersects the stress–strain curve.

What is the difference between engineering stress and true stress?

Engineering stress uses the original cross-sectional area, and true stress uses the instantaneous area. Before necking, σ_t = σ(1 + ε) and ε_t = ln(1 + ε).

Why is a dogbone specimen used?

The wide ends give the grips a secure hold, and the narrow gage section concentrates the stress so the specimen fails where it is being measured.

Related reading on materials and mechanics

• How to test mechanical properties: methods and techniques
• Impact testing: how temperature affects energy absorption and hardness
• Fatigue analysis, fatigue stress and S-N curves
• Combined loading: axial load, bending and normal stress formulas
• Internal loadings practice problems with solutions
• Understanding moment of inertia
• Column and panel buckling: formulas, examples and prevention
• Sheet metal stamping and forming design guide

References

• Engineers Edge, LLC, Yield Strength – Strength (Mechanics) of Materials.
• AZoM, AISI 1018 Mild/Low Carbon Steel.
• Morrow, H., and Kokernak, R., Pearson’s Statics and Strength of Materials, 7th edition, 2010, p. 480.
• Farhat, H., Chapter 3 – Materials and coating technologies, in Operation, Maintenance, and Repair of Land-Based Gas Turbines, Elsevier, 2021, pp. 63–87, ISBN 9780128218341, doi.org/10.1016/B978-0-12-821834-1.00007-1.
• ASTM E8/E8M, Standard Test Methods for Tension Testing of Metallic Materials; ISO 6892-1, Metallic materials – Tensile testing – Method of test at room temperature.