Specific strength

The specific strength is a material'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. 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.

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.

Examples

Specific tensile strength of various materials

Material	Tensile strength (MPa)	Density (g/cm³)	Specific strength (kN·m/kg or KYuri)	Breaking length (km)	Source
Concrete	12	2.30	5.22	0.44
Rubber	15	0.92	16.3	1.66
Copper	220	8.92	24.7	2.51
Polypropylene	25-40	0.90	28-44	2.8-4.5	[1]
Stainless steel (304)	505	8.00	63.1	6.4	[2]
Brass	580	8.55	67.8	6.91	[3]
Nylon	78	1.13	69.0	7.04	[4]
Oak	90	0.78-0.69	115-130	12-13	[5]
Inconel (X-750)	1250	8.28	151	15.4	[6]
Magnesium alloy	275	1.74	158	16.1	[7]
Aluminium alloy (7075-T6)	572	2.81	204	20.8	[8]
Titanium	1300	4.51	288	29.4	[9]
Bainite	2500	7.87	321	32.4	[10]
Balsa	73	0.14	521	53.2	[11]
Carbon-epoxy composite	1240	1.58	785	80.0	[12]
Spider silk	1400	1.31	1069	109
Silicon carbide fiber	3440	3.16	1088	110	[13]
Glass fiber	3400	2.60	1307	133	[9]
Basalt fiber	4840	2.70	1790	183	[14]
1 μm iron whiskers	14000	7.87	1800	183	[10]
Vectran	2900	1.40	2071	211	[9]
Carbon fiber (AS4)	4300	1.75	2457	250	[9]
Kevlar	3620	1.44	2514	256	[15]
Dyneema (UHMWPE)	3600	0.97	3711	378	[16]
Zylon	5800	1.54	3766	384	[17]
Carbon nanotube (see note below)	62000	.037-1.34	46268-N/A	4716-N/A	[18][19]
Colossal carbon tube	6900	.116	59483	6066	[20]
Fundamental limit			9×10^13	9.2×10^12	[21]

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,^[18] 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.^[22] The density is different depending on the manufacturing method, and the lowest value is 0.037 or 0.55 (solid).^[19]

The 'Yuri' and space tethers

The International Space Elevator Consortium has proposed 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. So, the units for one Yuri are Pa m³ / kg. This unit is equivalent to one N m / kg, which is the breaking/yielding force per linear density of the cable under tension.^[23][24] A functional space elevator would require a tether of 30-80 MegaYuri.^[25]

Fundamental limit on specific strength

The null energy condition places a fundamental limit on the specific strength of any material.^[21] The specific strength is bounded to be no greater than c² ~ 9×10¹³kN·m/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.

Tenacity (textile strength)

Tenacity is the customary measure of strength of a fiber or yarn. In the U.S. 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.^[26] A tenacity of $1$ corresponds to: $\frac{1g \cdot 9.80665 m s^{-1}}{1g/9000m}=\frac{9.80665 m s^{-1}}{1/9000m}=9.80665 m s^{-1}9000m = 88259.85 m^2 s^{-2}=88259.85 Yuri=88.25985 kYuri$

See also

• Specific modulus
• Space elevator
• Space tether

References

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21. Brown, Adam R. (2012). "Tensile Strength and the Mining of Black Holes". arXiv:1207.3342v1.
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23. Strong Tether Challenge 2013
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26. Rodriguez, Ferdinand (1989). Principles of Polymer Systems (3rd ed.). New York: Hemisphere Publishing. p. 282. ISBN 9780891161769. OCLC 19122722.

External links

• Specific stiffness - Specific strength chart, University of Cambridge, Department of Engineering