Stress-strain curve

The stress-strain curve can be used to read off the structural loadability of materials. For many materials, including metals, their loading bearing capability (loadability) is one of the most important material properties. The loading capacity of metals is tested in a so-called tensile test. In this test a standardised metal bar is slowly pulled apart (stressed in tension) until the bar gives way under the load and breaks. From the start of the tensile test until the breaking point (rupture), the material to be tested behaves in different ways and this is illustrated in the stress-strain curve.

PhasesIn addition, the curve can also be used to read off the elastic deformation limit (yield point), the plastic deformation limit, the maximum tensile strength and the fracture or rupture point. These values are very important, especially for design engineers, as it enables them to find out how much force a material can withstand with regard to the cross-section used without deforming permanently.

The graph shows how much the material extends under the increasing stress. If the curve is examined more closely, in most cases the behaviour of the material can be divided into four phases or regions.

These are called:

  • elastic deformation
  • plastic deformation / flow region
  • plastic deformation / strain hardening
  • plastic deformation / necking

The tensile test then ends with the fracture (rupture) of the metal bar.

This means that it is only within the first phase, the elastic deformation, that the material returns to its initial condition without deformation or damage, if the tensile force is reduced. In the following phases the deformation is permanent and therefore irreversible.

The data provided by a stress-strain curve is reliable. However, the given values are dependent on several variables, which influence the measured results directly. These include the material production method, the material composition, microscopic imperfections and the temperature. For this reason, the diagram of each tensile test is slightly different and several tensile tests are always required in order to draw up a reliable stress-strain curve using the average values.

The interpretation

In order to understand this graph properly, it is important to understand several technical terms. As already described, the stress-strain curve illustrates the mechanical properties of materials, for example, steel, stainless steel or aluminium.

The diagram can be used to read off by how much the material can stretch in proportion to an increasing applied force.

stress strain curveThe horizontal axis of the curve gives the strain as a percentage. The stress is shown on the vertical axis. The graph is divided into four areas (A-D), of which the first section represents elastic deformation. In the remaining areas, plastic deformation only takes place. However, the material behaves differently in each individual phase of plastic deformation. Area B defines the flow region. This is the area in which the material is stressed beyond its elastic loadability and the first plastic deformations occur.

Within the flow zone, the stress (load per unit cross-section) changes very irregularly with increasing strain (elongation per unit length), so that a wavy line results in the curve. In section C the stress continues to increase sharply, and the plastic deformation also increases. If the maximum loadability the material’s cross-section begins to reduce in size taper. The necking and associated loss in material thickness results in further, fast and advancing weakening of the material, until the metal bar ultimately tears apart.

Elastic deformation (A)

In the first phase of the stress-strain damage we speak of elastic deformation. As soon as the stress acting on the material is removed, the material shortens back to its original length. This is called complete recovery or resilience. The area of elastic deformation can in turn be divided into two phases. In the first phase the material stretches proportionally to the stress acting on it. This extension is also called linear-elastic or proportional deformation.

This behaviour of materials within the range of proportional deformation was described in 1668 by the English polymath Robert Hooke, in Hooke’s law named after him. The point at which the maximum linear-elastic elongation (strain) is reached is called the proportional limit. Beyond this limit elastic deformation still takes place, however, greater elongation occurs in this section under increasing applied force. The elongation or strain is therefore greater than the increasing stress.

The flow region (B)

A further, small increase in stress can be enough to cause the proportional limit to be exceeded. Under this force the material begins to flow and the first plastic deformation occurs. The area in which the material flows lies between the upper and lower flow limit. The highest flow point is the point accompanied by an initial, sudden loss of quality. As a result, the stress required to continue to elongate (strain) the material reduces immediately and reaches the lowest flow point.

After these points are exceeded the material has definitively deformed irreparably, even if the force were to be removed immediately. If the force continues to increase, the crystal defects (dislocations) start to wander and increase, which leads to further quality losses at the first flow point and stress and strain behave irregularly in relation to each other. This produces the characteristic, wavy curve section.

Material hardening (C)

If the stress is increased further, an increasing number of upright dislocations form in the crystal lattice, which prevent movement of the previous still sliding dislocations. At the same time, the stress in the crystal lattice continues to increase, which causes hardening of the material. This means that an increasingly larger force is required for further plastic deformation. However, this process cannot be continued infinitely. Each material has its specific maximum force.

Necking (D)

If the maximum force is exceeded the material begins to neck. In the crystal lattice of the metal bar so many dislocations have occurred that they can no longer lead to hardening but instead contribute to the formation of voids or cavities. Apart from necking, the voids also cause the material cross-section to reduce. The stress now acts on an increasingly smaller cross-section, which enhances this process still further.
As the tensile test continues the necking increases until the tapered cross-section can no longer withstand the stress. This is when the metal bar tears at the weakest point.

Using the stress-strain curve

The diagram or curve shows how materials behave under increasing force. In practice, the flow limit is one value, because from this point materials deform plastically. At Rime this value is very interesting, as this point enables the sheet panels to be formed by bending or roll bending. Especially in load-bearing constructions, attention must be paid on ensuring that the load never reaches the flow limit, so that no unwanted deformation occurs.
Important characteristics

Several important and informative characteristics can be read off the curve:

specific values

Elastic limit

At the start of a tensile test, stress and strain are proportional. This can be seen in the diagram by the straight part of the curve.
The end point of the straight section of curve is the proportional limit, which for many metals is also the elastic limit. Recovery to the original state is only possible if this point has not been exceeded.

Tensile strength

This value provides information about how much a material can be loaded without forming necking.

Variables in the stress-strain curve

Several important steel properties can be derived from the shift of the curve and different steel grades can be compared.

the change of properties

stiff / elastic

In the elastic deformation area the graph is a straight line. The slope angle of this straight line can be used to deduce how stiff the material is. The steeper this line rises the stiffer the material. If the graph is shallower, the material is elastic.

hard / soft

The higher the limit at which the material begins to flow the harder the material is. Harder materials have the advantage that they can withstand far higher forces before they deform. This is especially important for load-bearing constructions. Soft materials on the other hand are easier to deform.

strong / weak

Strong materials can withstand far higher tensile forces. Weak materials form necking very quickly, even at low stress values, which means they also tend to tear more quickly.

brittle / tough

The last important property is the differentiation between brittle and tough materials. Brittle materials cannot withstand high tensile forces and break significantly faster. Tough materials also have the advantage that when overloaded they form marked deformations before they tear. This means that material fatigue is visible long before tearing, so that action can be taken in response.