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Calculations of breaking length

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

where L {\displaystyle L} is the length, T s {\displaystyle T_{s}} is the tensile strength, ρ {\displaystyle \rho } is the density and g {\displaystyle \mathbf {g} } is the acceleration due to gravity ( ≈ 9.8 {\displaystyle \approx 9.8} m/s 2 {\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	49	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	1314
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
Reversibly Assembled Cellular Composite Materials	0.073	0.0072	10,139	1035	2324
Self-Reprogrammable Mechanical Metamaterials	0.01117	0.0103	1,084	111	25
Balsa	73	0.14	521	53.2	26
Carbon–epoxy composite	1240	1.58	785	80.0	27
Spider silk	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
Glass fiber	3400	2.60	1,307	133	30
Basalt fiber	4840	2.70	1,790	183	31
1 μm iron whiskers	14000	7.87	1,800	183	32
Vectran	2900	1.40	2,071	211	33
Carbon fiber (AS4)	4300	1.75	2,457	250	34
Kevlar	3620	1.44	2,514	256	35
Dyneema (UHMWPE)	3600	0.97	3,711	378	36
Zylon	5800	1.54	3,766	384	37
Carbon fiber (Toray T1100G)	7000	1.79	3,911	399	38
Carbon nanotube (see note below)	62000	0.037–1.34	46,268–N/A	4716–N/A	3940
Colossal carbon tube	6900	0.116	59,483	6066	41
Graphene	130500	2.090	62,453	6366	42
Fundamental limit			9×1013	9.2×1012	43

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,⁴⁴ 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.⁴⁵ The density is different depending on the manufacturing method, and the lowest value is 0.037 or 0.55 (solid).⁴⁶

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.⁴⁷⁴⁸ A functional Earth space elevator would require a tether of 30–80 megaYuri (corresponding to 3100–8200 km of breaking length).⁴⁹

Fundamental limit on specific strength

The null energy condition places a fundamental limit on the specific strength of any material.⁵⁰ The specific strength is bounded to be no greater than c2 ≈ 9×1013 kN⋅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. 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.⁵¹ A tenacity of 1 {\displaystyle 1} corresponds to: 1 g ⋅ 9.80665 m s − 2 1 g / 9000 m = 9.80665 m s − 2 1 / 9000 m = 9.80665 m s − 2 9000 m = 88259.85 m 2 s − 2 {\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.

See also

• Specific modulus
• Space elevator
• Space tether

External links

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

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