Tensile strength

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Tensile strength measures the force required to pull something such as rope, wire, or a structural beam to the point where it breaks.

[edit] Explanation

The tensile strength of a material is the maximum amount of tensile stress that it can be subjected to before failure. The definition of failure can vary according to material type and design methodology. This is an important concept in engineering, especially in the fields of material science, mechanical engineering and structural engineering.

There are three typical definitions of tensile strength:

• Yield strength - The stress a material can withstand without permanent deformation. This is not a sharply defined point. Yield strength is the stress which will cause a permanent deformation of 0.2% of the original dimension.

• Ultimate strength - The maximum stress a material can withstand.

• Breaking strength - The stress coordinate on the stress-strain curve at the point of rupture.

[edit] Concept

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

Stress vs. Strain curve typical of structural steel
1. Ultimate Strength
2. Yield Strength
3. Rupture
4. Strain hardening region
5. Necking region.

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 revers, as true stress is corrected for the decrease in cross-sectional area. Necking 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.

Stress vs. Strain curve typical of aluminum
1. Ultimate Strength
2. Yield strength
3. Proportional Limit Stress
4. Rupture
5. Offset Strain (typically 0.002).

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.

Stress vs. Strain curve typical of a brittle material
1. Ultimate Strength
2. Rupture.

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 most 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 measured 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".)

[edit] Typical tensile strengths

Some typical tensile strengths of some materials:

• Note that many of the values depend on the manufacturing processes the materials were subjected to and on its purity/composition.

(Source: A.M. Howatson, P.G. Lund and J.D. Todd, "Engineering Tables and Data" p41)

Single-walled carbon nanotubes made in academic labs have the highest tensile strength of any material yet measured, with labs producing carbon nanotubes with a tensile strength of 63 GPa (63,000 MPa) well below its theoretical tensile strength of 300 GPa (300,000 MPa). As of 2004, however, no macroscopic object constructed using a nanotube-based material has had a tensile strength remotely approaching this figure, or substantially exceeding that of high-strength materials like Kevlar.

[edit] Sources

• A.M. Howatson, P.G. Lund and J.D. Todd, "Engineering Tables and Data"
• Giancoli, Douglas. Physics for Scientists & Engineers Third Edition. Upper Saddle River: Prentice Hall, 2000.
• Köhler, T. and F. Vollrath. 1995. Thread biomechanics in the two orb-weaving spiders Araneus diadematus (Araneae, Araneidae) and Uloboris walckenaerius (Araneae, Uloboridae). Journal of Experimental Zoology 271:1-17.
• Edwards, Bradly C. "The Space Elevator: A Brief Overview" http://www.liftport.com/files/521Edwards.pdf
• T Follett "Life without metals"

[edit] See also

• Tension (mechanics)
• Vertical strength
• Toughness
• Deformation
• Tensile structure

[edit] External links

• Tensile Strength Test
• January 2003 sci.physics thread on water tensile strength and trees
• Theory re the discrepancy in static vs dynamic measurements of water's tensile strength
• Engineering Stress-strain Curve
• Tensile Strength Testing