The various definitions of tensile strength are shown in the following stress-strain graph for low-carbon steel:

Steel has a very linear stress-strain relationship up to its yield point, as shown in the figure. The yield point is not a sharply defined point, though; the figure is wrong. For stresses below this yield strength all deformation is recoverable, and the material will relax into its initial shape when the load is removed. For stresses above the yield point, a portion of the deformation is not recoverable, and the material will not relax into its initial shape. This unrecoverable deformation is known as plastic deformation. For many applications plastic deformation is unacceptable, and the yield strength is used as the design limitation.

After the yield point, steel and many other ductile metals will undergo a period of strain hardening, in which the stress increases again with increasing strain up to the ultimate strength. If the material is unloaded at this point, the stress-strain curve will be parallel to that portion of the curve between the origin and the yield point. If it is re-loaded it will follow the unloading curve up again to the ultimate strength, which has become the new yield strength.

After steel has been loaded to its yield strength it begins to "neck" as the cross-sectional area of the specimen decreases due to plastic flow. When necking becomes substantial, it may cause a reversal of the engineering stress-strain curve, where decreasing stress correlates to increasing strain because of geometric effects. This is because the engineering stress and engineering strain are calculated assuming the original cross-sectional area before necking. If the graph is plotted in terms of true stress and true strain the curve will always slope upwards and never reverse, as true stress is corrected for the decrease in cross-sectional area. Necking is not observed for materials loaded in compression. The peak stress on the engineering stress-strain curve is known the ultimate tensile strength. After a period of necking, the material will rupture and the stored elastic energy is released as noise and heat. The stress on the material at the time of rupture is known as the breaking stress.

Ductile metals do not have a well defined yield point. The yield strength is typically defined by the "0.2% offset strain". The yield strength at 0.2% offset is determined by finding the intersection of the stress-strain curve with a line parallel to the initial slope of the curve and which intercepts the abscissa at 0.002. A stress-strain curve typical of aluminum along with the 0.2% offset line is shown in the figure below.

Brittle materials such as concrete and carbon fiber do not have a yield point, and do not strain-harden which means that the ultimate strength and breaking strength are the same. A stress-strain curve for a typical brittle material is shown in the figure below.

Tensile strength is measured in units of force per unit area. In the SI system, the units are newtons per square metre (N/m²) or pascals (Pa), with prefixes as appropriate. The non-metric units are pounds-force per square inch (lbf/in² or PSI). Engineers in North America usually use units of ksi which is a thousand psi.

The breaking strength of a rope is specified in units of force, such as newtons, without specifying the cross-sectional area of the rope. This is often loosely called tensile strength, but this not a strictly correct use of the term.

In brittle materials such as rock, concrete, cast iron, or soil, tensile strength is negligible compared to the compressive strength and it is assumed zero for many engineering applications. Glass fibers have a tensile strength stronger than steel[1], but bulk glass usually does not. This is due to the Stress Intensity Factor associated with defects in the material. As the size of the sample gets larger, the size of defects also grows. In general, the tensile strength of a rope is always less than the tensile strength of its individual fibers.

Tensile strength can be defined for liquids as well as solids. For example, when a tree draws water from its roots to its upper leaves by transpiration, the column of water is pulled upwards from the top by capillary action, and this force is transmitted down the column by its tensile strength. Air pressure from below also plays a small part in a tree's ability to draw up water, but this alone would only be sufficient to push the column of water to a height of about ten metres, and trees can grow much higher than that. (See also cavitation, which can be thought of as the consequence of water being "pulled too hard".)

 

Yield strength

 

Yield strength, or the yield point, is defined in engineering and materials science as the stress at which a material begins to plastically deform. Prior to the yield point the material will deform elastically and will return to its original shape when the applied stress is removed. Once the yield point is passed some fraction of the deformation will be permanent and non-reversible. Knowledge of the yield point is vital when designing a component since it generally represents an upper limit to the load that can be applied. It is also important for the control of many materials production techniques such as forging, rolling, or pressing

In structural engineering, yield is the permanent plastic deformation of a structural member under stress. This is a soft failure mode which does not normally cause catastrophic failure unless it accelerates buckling.

In three dimensional space of principal stresses (?₁,?₂,?₃), an infinite number of yield points form together a yield surface