Definitions

# Tensile strength

Tensile strength $sigma_\left\{UTS\right\}$, or $S_U$ is the stress at which a material breaks or permanently deforms. Tensile strength is an intensive property and, consequently, does not depend on the size of the test specimen. However, it is dependent on the preparation of the specimen and the temperature of the test environment and material.

Tensile strength, along with elastic modulus and corrosion resistance, is an important parameter of engineering materials that are used in structures and mechanical devices. It is specified for materials such as alloys, composite materials, ceramics, plastics and wood.

## Explanation

There are three definitions of tensile strength:Yield strength: The stress at which material strain changes from elastic deformation to plastic deformation, causing it to deform permanently.Ultimate strength: The maximum stress a material can withstand when subjected to tension, compression or shearing. It is the maximum stress on the stress-strain curve.Breaking strength: The stress coordinate on the stress-strain curve at the point of rupture.

## Concept

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

Metals including steel have a linear stress-strain relationship up to the yield point, as shown in the figure. In some steels the stress falls after the yield point. This is due to the interaction of carbon atoms and dislocations in the stressed steel. Cold worked and alloy steels do not show this effect. For most metals yield point is not sharply defined. Below the yield strength all deformation is recoverable, and the material will return to its initial shape when the load is removed. For stresses above the yield point the deformation is not recoverable, and the material will not return to 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 a metal 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 as the ultimate 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 tensile strength.

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 0.2%. 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 most unusual stress-strain curve is shown in the figure below. Typical brittle materials do not show any plastic deformation but fail while the deformation is elastic. One of the characteristics of a brittle failure is that the two broken parts can be reassembled to produce the same shape as the original component. A typical stress strain curve for a brittle material will be linear. Testing of several identical specimens will result in different failure stresses. The curve shown below would be typical of a brittle polymer tested at very slow strain rates at a temperature above its glass transition temperature. Some engineering ceramics show a small amount of ductile behaviour at stresses just below that causing failure but the initial part of the curve is a linear.

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. One MegaPascal is 145.037738 pounds-force per square inch.

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 is 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 , 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".)

## Typical tensile strengths

Some typical tensile strengths of some materials:
Material Yield strength
(MPa)
Ultimate strength
(MPa)
Density
(g/cm³)
Structural steel ASTM A36 steel 250 400 7.8
Steel, API 5L X65 (Fikret Mert Veral) 448 531 7.8
Steel, high strength alloy ASTM A514 690 760 7.8
Steel, prestressing strands 1650 1860 7.8
Steel Wire     7.8
Steel (AISI 1060 0.6% carbon) Piano wire 2200-2482 MPa   7.8
High density polyethylene (HDPE) 26-33 37 0.95
Polypropylene 12-43 19.7-80 0.91
Stainless steel AISI 302 - Cold-rolled 520 860
Cast iron 4.5% C, ASTM A-48 130 200
Titanium alloy (6% Al, 4% V) 830 900 4.51
Aluminium alloy 2014-T6 400 455 2.7
Copper 99.9% Cu 70 220 8.92
Cupronickel 10% Ni, 1.6% Fe, 1% Mn, balance Cu 130 350 8.94
Brass approx. 200+ 550 5.3
Tungsten   1510 19.25
Glass   50 (in compression) 2.53
E-Glass N/A 3450 2.57
S-Glass N/A 4710 2.48
Basalt fiber N/A 4840 2.7
Marble N/A 15
Concrete N/A 3
Carbon Fiber N/A 5650 1.75
Spider silk 1150 (??) 1200
Silkworm silk 500
Aramid (Kevlar or Twaron) 3620   1.44
UHMWPE 23 46 0.97
UHMWPE fibers (Dyneema or Spectra) 2300-3500 0.97
Vectran   2850-3340
Polybenzoxazole (Zylon)   5800
Pine Wood (parallel to grain)   40
Bone (limb) 104-121 130 1.6
Nylon, type 6/6 45 75 1.15
Rubber - 15
Boron N/A 3100 2.46
Silicon, monocrystalline (m-Si) N/A 7000 2.33
Silicon carbide (SiC) N/A 3440
Sapphire (Al2O3) N/A 1900 3.9-4.1
Carbon nanotube (see note below) N/A 62000 1.34
Carbon nanotube composites N/A 1200 N/A

• Note: Multiwalled carbon nanotubes have the highest tensile strength of any material yet measured, with labs producing them at a tensile strength of 63 GPa, still well below their theoretical limit of 300 GPa. However as of 2004, no macroscopic object constructed of carbon nanotubes has had a tensile strength remotely approaching this figure, or substantially exceeding that of high-strength materials like Kevlar.
• Note: many of the values depend on manufacturing process and purity/composition.

Elements in the annealed state Young's Modulus
(GPa)
Proof or yield stress
(MPa)
Ultimate strength
(MPa)
Aluminium 70 15-20 40-50
Copper 130 33 210
Gold 79   100
Iron 211 80-100 350
Nickel 170 14-35 140-195
Silicon 107 5000-9000
Silver 83   170
Tantalum 186 180 200
Tin 47 9-14 15-200
Titanium 120 100-225 240-370
Tungsten 411 550 550-620
Zinc (wrought) 105   110-200
(Source: A.M. Howatson, P.G. Lund and J.D. Todd, "Engineering Tables and Data" p41)

## 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"
• Min-Feng Yu et. al (2000), Strength and Breaking Mechanism of Multiwalled Carbon Nanotubes Under Tensile Load, Science 287, 637-640

## References

• http://www.albarrie.com/Filtration/fil-basalt.html