Tension tests provide information on the strength and ductility of metals under uniaxial tensile stresses. Taking ASTM E8 Standard Test Methods for Tension Testing of Metallic Materials as a reference, this blog post goes over metals tensile testing concepts and theory with an emphasis on equations to measure each property.

An electro-mechanical or hydraulic universal testing machine equipped with the appropriate specimen grips, an extensometer and software capable of strain rate control and recording stress – strain data is required to conduct metals tensile testing.

Metals Tensile Testing Concepts

Strength refers to the ability of a structure to resist loads without failure due to excessive stress or deformation. 

Ductility is a measure of a metal’s ability to deform under tensile stresses. Ductility is important in metal forming processes, as metals that crack or break under stress cannot be manipulated by hammering, rolling or drawing. Two measures of ductility governed by ASTM E8/E8M are Total Elongation and Reduction of Area.

Total Elongation is the amount of uniaxial strain at fracture and is depicted as strain at point Z, below.  It includes both elastic and plastic deformation and is commonly reported as Percent Elongation at Break (The gauge length used for measurement is reported with the result.).

Reduction of Area is calculated by measuring the cross-sectional area at the fracture point and is expressed as a percent value.

Figure 1 Stress vs. Strain Curve

Ultimate Tensile Strength (UTS), which refers to the peak stress in a tensile test

Offset yield Strength (OYS), which represents a point just beyond the onset of permanent deformation

The Rupture (R) or Fracture Point where the specimen separates into pieces

The Strain Hardening Exponent, n, is a measure of how rapidly a metal becomes stronger and harder due to plastic deformation.  The deformation remaining after an applied load is removed is called plastic deformation.  ASTM E646, a tensile test that measures the stress-strain response in the plastic region, governs the determination of the Strain Hardening Exponent.  In the graph below, the plastic region is shown between point B, Yield Strength, and point D, Ultimate Strength. The n value is calculated by selecting five data pairs between the two points.

The Plastic Strain Ratio, r, indicates the ability of the sheet metal to resist thinning or thickening when being deep drawn into a cup for example. The r value is calculated from width and longitudinal strain and is a measure of sheet metal drawability.  ASTM E517 Standard Test Method for Plastic Strain Ratio r for Sheet Metal governs its determination. Unlike many other materials with r values that remain constant over the range of plastic strains, the r value of sheet varies with the applied axial strain and as such should be reported at the tested strain level.

Metals Tensile Testing Equations & Theory

A graphical description of the amount of deflection under load for a given material is the stress-strain curve in Figure 1, above.  Engineering stress (S) is obtained by dividing the load (P) at any given time by the original cross sectional area (A) of the specimen.

S = P/A                                                                            Equation. 1

Engineering strain (e) is obtained by dividing the elongation of the gage length of the specimen (∆l) by the original gage length (lo).

e = ∆l/ lo = (l – lo)/ lo                                                    Equation. 2

Figure 1 depicts a typical stress-strain curve. The shape and magnitude of the curve is dependent on the type of metal being tested. Point A represents the proportional limit of a material. A material loaded in tension beyond point A when unloaded will exhibit permanent deformation. The proportional limit is often difficult to calculate, therefore, two practical measurements, offset yield strength (OYS) and yield by extension under load (EUL), were developed to approximate the proportional limit. The initial portion of the curve below point A represents the elastic region and is approximated by a straight line. The slope (E) of the curve in the elastic region is defined as Young’s Modulus of Elasticity and is a measure of material stiffness.

E = ∆S /∆e = (S2-S1)/(e2-e1)                                        Equation. 3

Point B represents the offset yield strength and is found by constructing a line X-B parallel to the curve in the elastic region. Line X-B is offset a strain amount O-X that is typically 0.2% of the gage length. Point C represents the yield strength by extension under load (EUL) and is found by constructing a vertical line Y-C. Line Y-C is offset a strain amount O-Y that is typically 0.5% of gage length. The ultimate tensile strength, or peak stress, is represented by point D.  Ultimate tensile strength (UTS), offset yield strength (OYS) and Young’s Modulus of Elasticity are properties that define a metals strength.

Total elongation, which includes both elastic and plastic deformation, is the amount of uniaxial strain at fracture and is depicted as strain at point Z. Percent elongation at break is determined by removing the fractured specimen from the grips; fitting the broken ends together and measuring the distance between gage marks. Percent elongation at break reports the amount of plastic or permanent deformation only. The gage length used for measurement is reported with the result.

Elongation at break(%) = ez = 100*(lz-lo)/lo           Equation. 4

Reduction of area, like elongation at break, is a measure of ductility and is expressed in percent. Reduction of area is calculated by measuring the cross sectional area at the fracture point (Az).

Reduction of area(%) = (Ao-Az)/Ao                               Equation. 5

Featured Equipment

Universal Testing Machine

eXpert 2600 series universal testing machines are electromechanical testing systems available in tabletop or floor standing configurations from 2kN to 600kN. The configuration shown below is the eXpert 2614 100kN (22,500lbf) capacity UTM equipped with GW527 moving-body wedge grips, an axial extensometer, and the MTESTQuattro controller and software.

Universal Testing machine performing a tensile test on a metal sample

eXpert 2600 Metals Tensile Testing

ADMET also offer servo-hydraulic universal testing frames for high capacity metals testing. Unlike some other designs on the market, ADMET servo-hydraulic eXpert 1000 systems come with an integral power supply and electronics, thereby saving valuable lab space. eXpert 1600 systems are static servohydraulic machines, whereas the eXpert 1900 systems are configured for dynamic testing.

Controller & Software

Universal testing machines for metals testing come equipped with the MTESTQuattro controller and software pre-programmed with ASTM Standards such as ASTM E8A370, and E111. These systems configured for the metals industry allow automatic calculation of key parameters such as Peak Load, Ultimate Tensile Strength, Offset Yield, R-Value, N-Value. 



The most common grip setup for metals tensile testing includes wedge grips. Wedge grips can be used at high forces and supplied with serrated jaws for flat specimens and v-jaws for round specimens. Depending on the model chosen, wedge grips may come with handle extrusions (GW-10T), a retaining knob, or a door (GW-XT) that must be closed after the tensile specimen is secured in the jaw faces. ADMET also offers moving body wedge grips (GW-527), shown below, that avoid applying compressive loads on the samples as well as wedge grips that are designed to be installed in environmental chambers for high temperature testing (GW-T-T).