# Specific strength

The specific strength is a material's (or muscle's) strength (force per unit area at failure) divided by its density. It is also known as the strength-to-weight ratio or strength/weight ratio or strength-to-mass ratio. In fiber or textile applications, tenacity is the usual measure of specific strength. The SI unit for specific strength is Pam3/kg, or N⋅m/kg, which is dimensionally equivalent to m2/s2, though the latter form is rarely used. Specific strength has the same units as specific energy, and is related to the maximum specific energy of rotation that an object can have without flying apart due to centrifugal force.

Another way to describe specific strength is breaking length, also known as self support length: the maximum length of a vertical column of the material (assuming a fixed cross-section) that could suspend its own weight when supported only at the top. For this measurement, the definition of weight is the force of gravity at the Earth's surface (standard gravity, 9.80665 m/s2) applying to the entire length of the material, not diminishing with height. This usage is more common with certain specialty fiber or textile applications.

The materials with the highest specific strengths are typically fibers such as carbon fiber, glass fiber and various polymers, and these are frequently used to make composite materials (e.g. carbon fiber-epoxy). These materials and others such as titanium, aluminium, magnesium and high strength steel alloys are widely used in aerospace and other applications where weight savings are worth the higher material cost.

Note that strength and stiffness are distinct. Both are important in design of efficient and safe structures.

## Calculations of breaking length

${\displaystyle L={\frac {T_{s}/\rho }{\mathbf {g} }}}$

where ${\displaystyle L}$ is the length, ${\displaystyle T_{s}}$ is the tensile strength, ${\displaystyle \rho }$ is the density and ${\displaystyle \mathbf {g} }$ is the acceleration due to gravity (${\displaystyle \approx 9.8}$ m/s${\displaystyle ^{2}}$)

## Examples

Specific tensile strength of various materials
Material Tensile strength
(MPa)
Density
(g/cm3)
Specific strength
(kN·m/kg)
Breaking length
(km)
Source
Concrete 2–5 2.30 5.22 0.44
Polyoxymethylene; POM 69 1.42 4.95 [1]
Rubber 15 0.92 16.3 1.66
Copper 220 8.92 24.7 2.51
Polypropylene; PP 25–40 0.90 28–44 2.8–4.5 [2]
(Poly)acrylonitrile-butadiene-styrene; ABS 41–45 1.05 39–43 [3]
Polyethylene terephthalate; polyester; PET 80 1.3–1.4 57–62 [4]
Piano wire; ASTM 228 Steel 1590–3340 7.8 204–428 [5]
Polylactic acid; polylactide; PLA 53 1.24 43 [6]
Low carbon steel (AISI 1010) 365 7.87 46.4 4.73 [7]
Stainless steel (304) 505 8.00 63.1 6.4 [8]
Maraging steel (18Ni(350)) 2450 8.2 298.78 29.7 [9]
Brass 580 8.55 67.8 6.91 [10]
Nylon 78 1.13 69.0 7.04 [11]
Titanium 344 4.51 76 7.75 [12]
CrMo Steel (4130) 560–670 7.85 71–85 7.27–8.70 [13][14]
Aluminium alloy (6061-T6) 310 2.70 115 11.70 [15]
Oak 90 0.78–0.69 115–130 12–13 [16]
Inconel (X-750) 1250 8.28 151 15.4 [17]
Magnesium alloy 275 1.74 158 16.1 [18]
Aluminium alloy (7075-T6) 572 2.81 204 20.8 [19]
Pine wood (American eastern white) 78 0.35 223 22.7 [20]
Titanium alloy (Beta C) 1250 4.81 260 26.5 [21]
Bainite 2500 7.87 321 32.4 [22]
Balsa 73 0.14 521 53.2 [23]
Carbon–epoxy composite 1240 1.58 785 80.0 [24]
Spider silk 1400 1.31 1069 109
Silicon carbide fiber 3440 3.16 1088 110 [25]
Miralon carbon nanotube yarn C-series 1375 0.7–0.9 1100 112 [26]
Glass fiber 3400 2.60 1307 133 [27]
Basalt fiber 4840 2.70 1790 183 [28]
1 μm iron whiskers 14000 7.87 1800 183 [22]
Vectran 2900 1.40 2071 211 [27]
Carbon fiber (AS4) 4300 1.75 2457 250 [27]
Kevlar 3620 1.44 2514 256 [29]
Dyneema (UHMWPE) 3600 0.97 3711 378 [30]
Zylon 5800 1.54 3766 384 [31]
Carbon fiber (Toray T1100G) 7000 1.79 3911 399 [32]
Carbon nanotube (see note below) 62000 0.037–1.34 46268–N/A 4716–N/A [33][34]
Colossal carbon tube 6900 0.116 59483 6066 [35]
Graphene 130500 2.090 62453 6366 [36]
Fundamental limit 9×1013 9.2×1012 [37]

The data of this table is from best cases, and has been established for giving a rough figure.

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,[33] still well below their theoretical limit of 300 GPa. The first nanotube ropes (20 mm long) whose tensile strength was published (in 2000) had a strength of 3.6 GPa, still well below their theoretical limit.[38] The density is different depending on the manufacturing method, and the lowest value is 0.037 or 0.55 (solid).[34]

## The 'Yuri' and space tethers

The International Space Elevator Consortium uses the "Yuri" as a name for the SI units describing specific strength. Specific strength is of fundamental importance in the description of space elevator cable materials. One Yuri is conceived to be the SI unit for yield stress (or breaking stress) per unit of density of a material under tension. One Yuri equals 1 Pa⋅m3/kg or 1 Nm/kg, which is the breaking/yielding force per linear density of the cable under tension.[39][40] A functional Earth space elevator would require a tether of 30–80 megaYuri (corresponding to 3100–8200 km of breaking length).[41]

## Fundamental limit on specific strength

The null energy condition places a fundamental limit on the specific strength of any material.[37] The specific strength is bounded to be no greater than c2 ~ 9×1013 kNm/kg, where c is the speed of light. This limit is achieved by electric and magnetic field lines, QCD flux tubes, and the fundamental strings hypothesized by string theory.[citation needed]

## Tenacity (textile strength)

Tenacity is the customary measure of strength of a fiber or yarn. It is usually defined as the ultimate (breaking) force of the fiber (in gram-force units) divided by the denier. Because denier is a measure of the linear density, the tenacity works out to be not a measure of force per unit area, but rather a quasi-dimensionless measure analogous to specific strength.[42] A tenacity of ${\displaystyle 1}$ corresponds to:[citation needed] ${\displaystyle {\frac {1{\rm {\,g}}\cdot 9.80665{\rm {\,ms^{-2}}}}{1{\rm {\,g}}/9000{\rm {\,m}}}}={\frac {9.80665{\rm {\,ms^{-2}}}}{1/9000{\rm {\,m}}}}=9.80665{\rm {\,ms^{-2}}}\,9000{\rm {\,m}}=88259.85{\rm {\,m^{2}s^{-2}}}}$ Mostly Tenacity expressed in report as cN/tex.

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