The uniaxial tensile test is one of the most common material tests performed. It is employed most often to measure one or more of the following properties of a material: modulus, yield strength, ultimate tensile strength, Poisson’s ratio, elongation to failure and reduction of area. Several ASTM standards are available to provide guidance on performing tensile tests. Three of the most common standards are ASTM E8 for metallic materials, ASTM D3039 for polymer matrix composite materials and ASTM D638 for unreinforced and reinforced plastics.
Although there can be many variations on the standard tensile test, a tensile test most often involves loading a test specimen in a universal testing machine and applying an increasing uniaxial load to the specimen until failure occurs. The sample can be supported in the test frame any number of ways: hydraulic grips, mechanically fastened clevis grips or threaded grips. The method of gripping most often depends on the material being tested, its geometry and the capabilities of the test frame.
The test frame is designed to elongate the sample at a constant rate while accurately measuring the applied load. The load is measured using a load cell attached both to the test frame and the test specimen through a mechanical assembly. The recorded load data can be used to calculate the engineering stress using the formula:
s = F
Ao
Where:
F = the load applied to the specimen at any given time during the test, typically in units of pounds force (lbf) or newtons (N).
Ao= the original cross sectional area of the test specimen-within the gage length of the sample-before any load is applied, typically in units of in2 or m2.
s = calculated engineering stress, typically express in psi or Pa (Pascals).
For accurate measurement of the modulus, yield strength and elongation to failure, an external device called an extensometer must be used to precisely measure the deformation resulting from the applied load on the test sample. The extensometer accurately measures displacements in the gage section of the sample, which can be used to calculate the strain in the material using the formula:
e = Dl = li - lo
lo lo
Where:
Dl = change in length in the specimen’s gage length at any given time during the test, in units of inches or meters.
li = the instantaneous length of the specimen’s gage section at any given time during the test, in units of inches or meters.
lo = the original gage length of the test specimen before any load is applied, in units of inches or meters. The gage length is typically prescribed by the testing standard.
e = calculated engineering strain (in units of in/in or m/m).
Data from the universal test machine and extensometer often is recorded digitally using a PC. It also can be recorded using a chart recorder, although this option is less common with modern day systems. After the data has been recorded, standard material properties can be determined.
Metals are some of the most commonly tested materials, and the example that follows is based on data obtained from a steel alloy tensile test. Composite and plastic materials can be analyzed using similar techniques, but because they typically respond differently to uniaxial loading, refer to the appropriate standards for guidance on analyzing test results.
A standard flat, dog bone shaped sample prescribed by ASTM E8 was tested in tension. The sample had a 2-inch gage length and measured 0.5 inch wide by 0.045 inch thick. An axial extensometer was used to measure the strain in the sample in regions critical for modulus and yield strength determination. The extensometer used was a low strain version, so the test was paused and the extensometer was removed after sufficient data was recorded for these properties to be determined-although some extensometers may be left on through failure. The sample was then pulled to failure so that the ultimate tensile strength could be measured.
At very low levels of applied load, the values of stress and strain of most metallic material are proportionally related to one another through the relationship:
s = Ee
Where:
s = engineering stress
E = modulus of elasticity
e = engineering strain.
In the region where this relationship holds true, deformation of the material is called elastic deformation. If the applied load is removed from the material within this region, the specimen will return to its original shape. After yield has occurred, the material enters into the region of plastic deformation. If the applied load is removed from the material within this region, some amount of deformation will permanently remain in the sample.
The modulus of elasticity is calculated by determining the slope of the line generated from the stress vs. strain data plotted within the elastic region. The commonly prescribed method for determining the yield strength of a material is to offset the modulus curve by 0.2% along the X-axis, and record the value where the resulting offset curve crosses the stress vs. strain curve. The ultimate tensile strength is determined by recording the maximum stress reached during the test. Had an extensometer capable of measuring strain to failure been used, the elongation to failure could have been calculated from this.
Knowledge of some of these material properties is crucial to design engineers. Knowing a material’s modulus (E) allows for the calculation of deformations in the elastic region when stressed. Knowing the yield stress (sys) of a material allows for correctly designed components to avoid overstressing, which would result in permanently deformed or fractured parts. Measurement of these properties requires use load cells for accurately measuring use of load to calculate stress and extensometers to measure elongation to calculate strain.
Ken Blount is an Applications engineer at Epsilon Technology Corp. (Jackson, WY). For more information, call (307) 733-8360, e-mail [email protected] or visit www.epsilontech.com.
