Tensile Testing, also known as tension testing, is a destructive engineering and materials science test whereby controlled tension is applied to a sample either as a load for proof testing or until it entirely fails. Tensile properties indicate how the material will react to forces applied in tension. A tensile test is a fundamental mechanical test where a carefully prepared specimen is loaded in a very controlled manner while measuring the applied load and the elongation of the sample over some distance. Tensile tests determine the modulus of elasticity, elastic limit, elongation, proportional limit, reduction in area, tensile strength, yield point, yield strength, and other tensile properties. 

The main product of a tensile test is a load versus elongation curve, which is then converted into a stress versus strain curve. Since the engineering stress and the engineering strain are obtained by dividing the load and elongation by constant values (specimen geometry information), the load-elongation curve will have the same shape as the engineering stress-strain curve. The stress-strain curve relates the applied stress to the resulting strain, and each material has its unique stress-strain curve. A typical engineering stress-strain curve is shown below. If the true stress, based on the actual cross-sectional area of the specimen, is used, it is found that the stress-strain curve increases continuously up to fracture.

Linear-Elastic Region and Elastic Constants

The figure shows that the stress and strain initially increase with a linear relationship. This is the curve’s linear-elastic portion, indicating that no plastic deformation has occurred.  When the stress is reduced in this curve region, the material will return to its original shape.  In this linear region, the line obeys the relationship defined as Hooke’s Law, where the ratio of stress to strain is constant.  

The slope of the line in this region where stress is proportional to strain is called the modulus of elasticity or Young’s modulus.  The modulus of elasticity (E) defines the properties of a material as it undergoes stress, deforms, and then returns to its original shape after the stress is removed.  It is a measure of the stiffness of a given material.  To compute the modulus of elasticity, simply divide the stress by the strain in the material. Since strain is unitless, the modulus will have the same units as the stress, such as KPI or MPa.  The modulus of elasticity applies specifically to a stretched component with a tensile force. This modulus is of interest when it is necessary to compute how much a rod or wire extends under a tensile load. 

Several moduli kinds depend on how the material is stretched, bent, or distorted.  When a component is subjected to pure shear, for instance, a cylindrical bar under torsion, the shear modulus describes the linear-elastic stress-strain relationship.

Axial strain is always accompanied by lateral strains of opposite signs in the two directions mutually perpendicular to the axial tension.  Strains that result from an increase in length are designated as positive (+), and those that result in a decrease in size are represented as negative (-).  Poisson’s ratio is the negative ratio of the lateral strain to the axial strain for a uniaxial stress state.


Poisson’s ratio is sometimes also defined as the ratio of the absolute values of lateral and axial strain.  This ratio, like strain, is unitless since both strains are unitless.  For stresses within the elastic range, this ratio is approximately constant.  For a perfectly isotropic elastic material, Poisson’s Ratio is 0.25, but for most materials, the value lies in 0.28 to 0.33.  Generally, for steel, Poisson’s ratio will have a value of approximately 0.3.  This means that if there is one inch per inch of deformation in the direction of stress, there will be 0.3 inches per inch of deformation perpendicular to the direction in which force is applied.  

Only two of the elastic constants are independent, so if two constants are known, the third can be calculated using the following formula:

E = 2 (1 + n) G.

Where:E=modulus of elasticity (Young’s modulus)
 n=Poisson’s ratio
 G=Modulus of rigidity (shear modulus). 

A couple of additional elastic constants encountered include the bulk modulus (K) and Lame’s constants (m and l). The bulk modulus describes the situation where a piece of material is subjected to a pressure increase on all sides.  The bulk modulus is the relationship between the change in pressure and the resulting strain produced. Lame’s constants are derived from the modulus of elasticity and Poisson’s ratio. 

Yield Point

In ductile materials, at some point, the stress-strain curve deviates from the straight-line relationship, and Law no longer applies as the strain increases faster than the stress. From this point in the tensile test, some permanent deformation occurs in the specimen, and the material is said to react plastically to any further increase in load or stress. When the load is removed, the material will not return to its original, unstressed condition. In brittle materials, little or no plastic deformation occurs, and the material fractures near the end of the linear-elastic portion of the curve. 

With most materials, there is a gradual transition from elastic to plastic behavior, and the exact point at which plastic deformation begins to occur is hard to determine. Therefore, various criteria for the initiation of yielding are used depending on the sensitivity of the strain measurements and the intended use of the data. (See Table) For most engineering design and specification applications, yield strength is used. The yield strength is defined as the stress required to produce a small amount of plastic deformation. The offset yield strength is the stress corresponding to the intersection of the stress-strain curve and a line parallel to the elastic part of the curve offset by a specified strain (in the US, the offset is typically 0.2% for metals and 2% for plastics). 

To determine the yield strength using this offset, the point is found on the strain axis (x-axis) of 0.002, and a line parallel to the stress-strain line is drawn. This line will intersect the stress-strain line slightly after it begins to curve, and that intersection is defined as the yield strength with a 0.2% offset.  A good way of looking at offset yield strength is that after a specimen has been loaded to its 0.2 percent offset yield strength and then unloaded, it will be 0.2 percent longer than before the test. Even though the yield strength represents the exact point at which the material becomes permanently deformed, 0.2% elongation is considered an acceptable sacrifice for the ease it creates in defining the yield strength.

Some materials, such as gray cast iron or soft copper, exhibit no linear-elastic behavior. The usual practice for these materials is to define the yield strength as the stress required to produce some total strain. 

  • Actual elastic limit is a meager value related to the motion of a few hundred dislocations. Therefore, microstrain measurements are required to detect strain on 2 x 10 -6 in/in. 
  • Proportional limit is the highest stress at which stress is directly proportional to strain. It is obtained by observing the deviation from the straight-line portion of the stress-strain curve. 
  • Elastic limit is the most significant stress the material can withstand without any measurable permanent strain remaining on the complete release of load. It is determined using a tedious incremental loading-unloading test procedure. With the sensitivity of strain measurements usually employed in engineering studies (10 -4in/in), the elastic limit is greater than the proportional limit. With the increasing sensitivity of strain measurement, the value of the elastic limit decreases until it eventually equals the actual elastic limit determined from microstrain measurements. 
  • Yield strength is the stress required to produce a small-specified amount of plastic deformation. The yield strength obtained by an offset method is commonly used for engineering purposes because it avoids the practical difficulties of measuring the elastic limit or proportional limit. 

Ultimate Tensile Strength
The ultimate tensile strength (UTS), or, more simply, the tensile strength, is the maximum engineering stress level reached in a tension test. The strength of a material is its ability to withstand external forces without breaking. The UTS will be at the end of the linear-elastic portion of the stress-strain curve or close to the elastic limit in brittle materials. The UTS will be well outside the flexible portion into the plastic part of the stress-strain curve in ductile materials. 

The UTS is the highest point on the stress-strain curve above, where the line is momentarily flat. Since the UTS is based on engineering stress, it is often not the same as the breaking strength. For example, strain hardening occurs in ductile materials, and the stress will continue to increase until a fracture occurs. Still, the engineering stress-strain curve may decline the stress level before a fracture occurs. This results from engineering stress being based on the original cross-section area and not accounting for the necking in the test specimen. Therefore, the UTS may not entirely represent the highest level of stress that a material can support, but the value is not typically used in the design of components. For example, the current design practice for ductile metals uses the yield strength for sizing static details. However, since the UTS is easy to determine and quite reproducible, it helps specify material and quality control purposes. On the other hand, for brittle materials, the design of a component may be based on the material’s tensile strength. 

Measures of Ductility (Elongation and Reduction of Area)
The ductility of material measures the extent to which a material will deform before fracture. The elasticity is essential when considering forming operations such as rolling and extrusion. It also indicates how visible overload damage to a component might become before it fractures. Ductility is also used as a quality control measure to assess the level of impurities and proper material processing. 

The conventional measures of ductility are the engineering strain at fracture (usually called the elongation ) and the reduction of area at fracture. These properties are obtained by fitting the specimen together after fracture and measuring the length and cross-sectional area changes. Elongation is the change in axial length divided by the original size of the sample or portion of the specimen. It is expressed as a percentage. Because an appreciable fraction of the plastic deformation will be concentrated in the necked region of the tensile specimen, the elongation value will depend on the gage length over which the measurement is taken. The smaller the gage length, the greater the large localized strain in the necked region will factor into the calculation. Therefore, when reporting elongation values, the gage length should be given. /var/folders/52/_t8ctg212p9c5wwxhd144ymc0000gn/T/com.microsoft.Word/WebArchiveCopyPasteTempFiles/Brittle-Ductile.gif

One way to avoid the complication of necking is to base the elongation measurement on the constant strain to the point at which necking begins. This sometimes works well, but some engineering stress-strain curves are often relatively flat near maximum loading. It is difficult to establish the strain when necking starts to occur precisely.

Reduction of the area is the change in a cross-sectional area divided by the original cross-sectional area. This change is measured in the necked-down region of the specimen. Like elongation, it is usually expressed as a percentage.