Specific strength explained

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 Pa⋅m3/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

L=Ts/\rho
g

where

L

is the length,

Ts

is the tensile strength,

\rho

is the density and

g

is the acceleration due to gravity (

≈ 9.8

m/s

2

)

Examples

Tensile strength
(MPa)! data-sort-type="number"
Density
(g/cm3)		data-sort-type="number" Specific strength
(kN·m/kg)		data-sort-type="number" Breaking length
(km) !		Source
2–5 2.30 5.22 0.44
Polyoxymethylene
POM
69 1.42 49 4.95 [1]
15 0.92 16.3 1.66
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)) 24508.2 298.78 29.7 [9]
580 8.55 67.8 6.91 [10]
78 1.13 69.0 7.04 [11]
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]
90 0.78–0.69 115–130 12–13 [16]
Inconel (X-750) 1250 8.28 151 15.4 [17]
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]
2500 7.87 321 32.4 [22]
Reversibly Assembled Cellular Composite Materials0.0730.007210,1391035[23] [24]
Self-Reprogrammable Mechanical Metamaterials0.011170.01031,084111[25]
73 0.14 521 53.2 [26]
1240 1.58 785 80.0 [27]
1400 1.31 1,069 109
Silicon carbide fiber 3440 3.16 1,088 110 [28]
Miralon carbon nanotube yarn C-series 1375 0.7–0.9 1,100 112 [29]
3400 2.60 1,307 133 [30]
4840 2.70 1,790 183 [31]
14000 7.87 1,800 183
2900 1.40 2,071 211
Carbon fiber (AS4) 4300 1.75 2,457 250
3620 1.44 2,514 256 [32]
Dyneema (UHMWPE) 3600 0.97 3,711 378 [33]
5800 1.54 3,766 384 [34]
Carbon fiber (Toray T1100G) 7000 1.79 3,911 399 [35]
Carbon nanotube (see note below) 62000 0.037–1.34 46,268–N/A 4716–N/A [36] [37]
6900 0.116 59,483 6066 [38]
130500 2.090 62,453 6366 [39]
Fundamental limit [40]
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,[36] 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.[41] The density is different depending on the manufacturing method, and the lowest value is 0.037 or 0.55 (solid).[37]

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 N⋅m/kg, which is the breaking/yielding force per linear density of the cable under tension.[42] [43] A functional Earth space elevator would require a tether of 30–80 megaYuri (corresponding to 3100–8200 km of breaking length).[44]

Fundamental limit on specific strength

The null energy condition places a fundamental limit on the specific strength of any material.[40] The specific strength is bounded to be no greater than c2 ≈, 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.

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.[45] A tenacity of

1

corresponds to:
1{\rmg
⋅

9.80665{\rmms-2

}}=\frac=9.80665 \, 9000 = 88259.85 Mostly Tenacity expressed in report as cN/tex.

See also

External links

Notes and References

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