Uniaxial tension test is used to determine yield strength, Young’s modulus, Poisson’s ratio, true stress-strain. Finite element analysis, Kartik Srinivas

1. UNIAXIAL TENSION TEST: THE MOTHER OF ALL
MECHANICAL TESTS
Kartik Srinivas
Principal Engineer
Advanced Scientific and Engineering Services (AdvanSES)
212, Shukan Mall, Sabarmati-Gandhinagar Highway,
Motera, Sabarmati, Ahmedabad 380005 India.
E-mail: kartik.srinivas@advanses.com, Phone: +91-9624447567
http://www.advanses.com
INTRODUCTION:
In engineering design and analysis, stress-strain relationships are needed to establish and verify
the load-deflection properties of an engineering component under service loads and boundary
conditions. From the tensile testing carried out to evaluate materials, various mechanical
properties such as the yield strength, Young’s modulus, Poisson’s ratio etc. are obtained. Strain
hardening and true stress-strain etc. values can be calculated by means of conversion using
equations from the stress-strain curve. The uniaxial tensile test is the primary method to evaluate
the material and obtain the parameters. Uniaxial tension test is also the primary test method used
for quality control and certification of virtually all ferrous and non-ferrous type of materials.
Standards for tensile testing were amongst the first published and the development of
such standards continues today through the ASTM and ISO organizations. Reliable tensile data,
which is now generated largely by computer controlled testing machines, is also crucial in the
design of safety critical components automotive, aerospace and biomedical applications.
Tensile testing is also important for polymeric materials as they depend strongly on the
strain rate because of their viscoelastic nature. Polymers exhibit time dependent deformation like
relaxation and creep under service applications. Polymer properties also show a higher
temperature dependency than metals. Multiple temperatures and strain rates are generally used to
fully characterize polymer materials.

2. Figure 1: Uniaxial Tension Test on a Material Sample
Figure 2 shows sample uniaxial stress-strain results from testing a metal specimen. The X axis
depicts the strain and Y axis the stress. The stress (σ) is calculated from;
σ = Load / Area of the material sample ............................................(1)
The strain(ε) is calculated from;
ε = δl (change in length) / l1 (Initial length) ............................................(2)
The slope of the initial linear portion of the curve (E) is the Young's modulus and given by;
E = (σ2- σ1) / (ε2- ε1) ............................................(3)
Point A in the graph shows the proportional limit of the material beyond which the material starts
to yield. When this point is not clearly visible or decipherable in a test, the off yield strength at B
is taken by offsetting the strain (F-G) by 0.2 % of the gauge length. Similarly, extension by yield
under load (EUL) is calculated by offsetting the strain 0.5% of the gauge length. The region
between points A and B on the graph is also purely elastic, with full recovery on the unloading of
the metal, but it is not essentially linear.

3. Figure 2: Sample Uniaxial Stress-Strain Results from a Metal Specimen
TRUE STRESS-STRAIN CURVE:
Figure 2 shows the engineering stress-strain curve where the values of stress beyond the
proportional limit do not give the true picture of stress in the sample as the cross-sectional area
of the sample is assumed to be constant. The engineering stress-strain values can be converted to
true stress-strain values by the following relation;
σt = σe (1 + εe) = σeλ , ............................................(4)
εt = ln (1 +εe) = ln λ, where λ = initial length / final length .........................................(5)

4. Figure 3: Sample Uniaxial Stress-Strain Results for a Polymeric Rubber Material
Figure 3 shows typical uniaxial stress-strain results from a test on a 40 durometer rubber
material. Unlike the results for the metal specimen the elastomer test results do not have or
exhibit a yield limit. The material extends in the classical 'S' shape and results in a fracture at the
end of the tests. Polymeric rubber materials exhibit the following characteristics;
 The load-deflection behavior of an elastomer is markedly non-linear.
 The recoverable strains can be as high 700 %.
 The stress-strain characteristics are highly dependent on temperature and rate effects are
highly pronounced.
 Nearly incompressible behavior.
 Viscoelastic effects are significant.
Typical test results for rubber materials show the values of modulus at 100%, 200% and 300%.
Modulus represents stress in such results.
SPECIFIC MECHANICAL ISSUES IN TESTING:
1. Strain Rate
2. Extensometry
3. Alignment and Gripping
4. Testing Machine Frame Compliance
5. Young’s Modulus Measurement
6. Specimen Geometry
Strain rate range of different material characterization test methods
1) Quasi-static tension tests 10-5
to 10-1
S-1
2) Dynamic tension tests 10-1
to 102
S-1
3) Very High Strain Rate or Impact tests 102
to 104
S-1
A fundamental difference between a high strain rate tension test and a quasi-static tension
test is that inertia and wave propagation effects are present at high rates. An analysis of results
from a high strain rate test thus requires consideration of the effect of stress wave propagation
along the length of the test specimen in order to determine how fast a uniaxial test can be run to
obtain valid stress-strain data.
IMPORTANCE OF THE UNIAXIAL TENSION TEST:
At the basic level apart from giving us an understanding about the ultimate strain and stress
capabilities of the material, tensile tests provide us with information about the factor of safety
that needs to be built-in the products using these materials.
1) Fatigue life of engineering materials can be calculated from tensile tests carried out on
notched and unnotched specimens.
2) Aging and other environmental effects can be incorporated in the test procedure to
characterize the material, as well as predict service life using techniques like Arrhenius equation.

5. 3) Endurance limits in design calculations are calculated from the results obtained from uniaxial
tension tests.
4) In manufacturing of rubber materials and products, it is used to determine batch quality and
maintain consistency in material and product manufacturing.
5) Electromechanical servo based miniature tensile testing machines can be developed to study
material samples of smaller size.
REFERENCES:
1. Dowling, N. E., Mechanical Behavior of Materials, Engineering Methods for Deformation,
Fracture and Fatigue Prentice-Hall, NJ, 99
2. Roylance, D., Mechanical Properties of Materials, MIT, 2008.
3. Gedney, R., Tensile Testing Basics, Tips and Trends, Quality Magazine, 2005.
4. Loveday, M. S., Gray, T., Aegerter, J., Testing of Metallic Materials: A Review, NPL,
2004
5. Srinivas, K., and Pannikottu, A., Material Characterization and FEA of a Novel
Compression Stress Relaxation Method to Evaluate Materials for Sealing Applications at
the 28th Annual Dayton-Cincinnati Aerospace Science Symposium, March 2003.
6. Ong, J.H., An Improved Technique for the Prediction of Axial Fatigue Life from Tensile
Data, International Journal of Fatigue, 15, No. 3, 1993.
7 Manson, S.S. Fatigue: A Complex Subject--Some Simple Approximations, Experimental
Mechanics, SESA Annual Meeting, 1965.
8. Yang, S.M., et al. Failure Life Prediction by Simple Tension Test under Dynamic Load,
International Conference on Fracture, 1995.
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