# 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 (N/m2)/(kg/m3) or more commonly N·m/kg.

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 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 Strength
(MPa)
Density
(g/cm³)
Specific Strength
(kN·m/kg)
Breaking length
(km)
source
Concrete 10 2.30 4.35 0.44
Rubber 15 0.92 16.3 1.66
Copper 220 8.92 24.7 2.51
Brass 580 8.55 67.8 6.91 1
Nylon 78 1.13 69.0 7.04 2
Oak 60 0.69 87.0 8.86 3
Polypropylene 80 0.90 88.9 9.06 4
Magnesium 275 1.74 158 16.1 5
Aluminium 600 2.80 214 21.8 6
Stainless Steel 2000 7.86 254 25.9 6
Titanium 1300 4.51 288 29.4 6
Bainite 2500 7.87 321 32.4 7
Balsa (axial load) 73 0.14 521 53.2 8
Scifer steel wire 5500 7.87 706 71.2 7
carbon-epoxy composite 1240 1.58 785 80.0 9
spider silk 1400 1.31 1069 109
Silicon carbide 3440 3.16 1088 110 10
Glass Fiber 3400 2.60 1307 133 6
Basalt fiber 4840 2.70 1790 183 11
1 μm iron whiskers 14000 7.87 1800 183 7
Vectran 2900 1.40 2071 211 6
Carbon fiber (AS4) 4300 1.75 2457 250 6
Kevlar 3620 1.44 2514 256 12
Dyneema (UHMWPE) 3600 0.97 3711 378 13
Zylon 5800 1.54 3766 384 14
Carbon nanotube (see note below) 62000 .037-1.34 46268-N/A 4716-N/A 1516
Colossal carbon tube 6900 .116 59483 6066 17

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,15 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.18 The density is different depending on the manufacturing method, and the lowest value is 0.037 or 0.55(solid).16
1. ^ RoyMech: Copper Alloys
2. ^ Goodfellow: Polyamide - Nylon 6
3. ^ Delft University of technology: Oak wood
4. ^ Goodfellow: Polypropylene
5. ^ eFunda: Magnesium Alloys
6. ^ a b c 52nd Hatfield Memorial Lecture: "Large Chunks of Very Strong Steel" by H. K. D. H. Bhadeshia 2005
8. ^ McGRAW-HILL ENCYCLOPEDIA OF Science & Technology, 8th Edition, (c)1997, vol. 1 p 375
9. ^ Specialty Materials, Inc SCS Silicon Carbide Fibers
10. ^ http://www.albarrie.com/techfabrics/continuousfiber.aspx
11. ^ Network Group for Composites in Construction: Introduction to Fibre Reinforced Polymer Composites
12. ^ "Dyneema Fact sheet". DSM (Company). 1 January 2008.
14. ^ a b Yu, Min-Feng; Lourie, O; Dyer, MJ; Moloni, K; Kelly, TF; Ruoff, RS (2000). "Strength and Breaking Mechanism of Multiwalled Carbon Nanotubes Under Tensile Load". Science 287 (5453): 637–640. Bibcode:2000Sci...287..637Y. doi:10.1126/science.287.5453.637. PMID 10649994.
15. ^ a b K.Hata. "From Highly Efficient Impurity-Free CNT Synthesis to DWNT forests, CNTsolids and Super-Capacitors" (free download PDF).
16. ^ Peng, H.; Chen, D.; et al., Huang J.Y. et al. (2008). "Strong and Ductile Colossal Carbon Tubes with Walls of Rectangular Macropores". Phys. Rev. Lett. 101 (14): 145501. Bibcode:2008PhRvL.101n5501P. doi:10.1103/PhysRevLett.101.145501. PMID 18851539.
17. ^ "Tensile strength of single-walled carbon nanotubes directly measured from their macroscopic ropes" by F. Li, H. M. Cheng, S. Bai, G. Su, and M. S. Dresselhaus. doi:10.1063/1.1324984

## Relation to velocity

Since N·m/kg (the unit of specific strength) expands to (kg·m/s2)·m/kg or (m/s)2, a specific strength can also be understood as the square of a speed, hence represented by it square root, a speed. Further, the structural analysis for whether a particular material is strong enough for some purpose can sometimes be expressed in terms of comparing this speed to the speed of a relevant part of the structure. For example, a spinning cylindrical shell (as in an idealized flywheel or an idealized cylinder space ship) is only feasible if built of a material whose square root of specific strength is at least the speed at which the spinning shell moves.

$\sqrt{\tfrac{E}{\rho}}\ge v$

## The Yuri and Space Tethers

The International Space Elevator Consortium has proposed the Yuri (unit) as a unit of specific strength useful for describing space tether designs. 1 Yuri = 1 (m/s)2 = N/(kg/m)1 and 1 MYuri (capital M denoting mega- and capital "Y" being typical for this non-SI unit) is equal to 1 N/Tex = 1 GPa-cc/g.2 A functional space elevator would require a tether of 30-80 MYuri.3