# Tensile strength

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

 Contents

## Concept

Once past the elastic limit, the material will not relax to its initial shape after the force is removed. See Hooke's law and modulus of elasticity. The tensile strength where the material becomes plastic is called yield tensile strength. This is the point where the deformation (strain) of the material is unrecovered, and the work produced by external forces is not stored as elastic energy but will lead to contraction (see Poisson), cracks and ultimately failure of the construction. Clearly, this is a remarkable point for the engineering properties of the material since here the construction may lose its loading capacity or undergo large deformations. On the stress-strain curve below this point is in between the elastic and the plastic region.

The ultimate tensile strength (UTS) of a material is the limit stress at which the material actually breaks, with sudden release of the stored elastic energy (released as noise and/or heat and/or more cracks e.g. for brittle materials). This point is the fracture marked X on the curve below.

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Stress-strain1.png
image:stress-strain1.png

For steel, the elastic limit is at about 0,2% and the breaking point is at 25% of the total (relative) extension (ε = ΔL/L - the figure is not to scale.) In steel constructions, the maximum allowable tensile stress at any point in the construction is 2/3 of the yield strength (or 0,2% deformation stress in metals or alloys without clearly defined yield stress). This comes down to a factor of safety of 1.5.

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). The non-metric units are pound-force per square inch (lbf/in² or 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 very high tensile strength, but bulk glass usually does not.

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".)

## Typical tensile strengths

Some typical tensile strengths of some materials:

Material Yield strength
(MPa)
Ultimate strength
(MPa)
Density
(g/cm3)
Structural steel ASTM-A36 250 400
Steel, high strength alloy ASTM A-514 690 760
Stainless steel AISI 302 - Cold-rolled 520 860
Cast iron 4.5% C, ASTM A-48 - 170
Titanium Alloy (6% Al, 4% V) 830 900 4.51
Aluminum Alloy 2014-T6 400 455 2.7
Copper 99.9% Cu 70 220 8.92
Brass   250
Glass (St Gobin "R") 4400 (3600 in composite)   2.53
Marble - 15
Concrete 2 ... 15 (?) 2
Spider silk 1150 (yield ? ultimate ?)
Silkworm silk
Kevlar 3620   1.44
Pine Wood (parallel to grain)   40
Bone (limb)   130
Nylon, type 6/6 45 75
Rubber - 15
Boron 3100   2.46
Silicon carbide (SiC) 3440
Sapphire (Al2O3) 1900   3.9-4.1

Single-walled carbon nanotubes have the highest tensile strength of any material yet measured, with the highest single measurement of a nanotube being 63 GPa (63000 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.

## Sources

• Giancoli, Douglas. Physics for Scientists & Engineers Third Edition. Upper Saddle River: Prentice Hall, 2000.

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