Specific strength

Short description: Ratio of strength to mass for a material

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.

## Contents

* 1 Calculations of breaking length
* 2 Examples
* 3 The 'Yuri' and space tethers
* 4 Fundamental limit on specific strength
* 5 Tenacity (textile strength)
* 6 See also
* 7 References
* 8 External links

## Calculations of breaking length

L=Ts/ρ𝐠

where L is the length, Ts is the tensile strength, ρ is the density and 𝐠 is the acceleration due to gravity (≈9.8 m/s 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 | [citation needed]
Polyoxymethylene; POM | 69 | 1.42 | 49 | 4.95 | [1]
Rubber | 15 | 0.92 | 16.3 | 1.66 | [citation needed]
Copper | 220 | 8.92 | 24.7 | 2.51 | [citation needed]
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 | [citation needed]
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 N⋅m/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 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.[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 1 corresponds to:[citation needed] 1g⋅9.80665ms−21g/9000m=9.80665ms−21/9000m=9.80665ms−29000m=88259.85m2s−2 Mostly Tenacity expressed in report as cN/tex.

## See also

* Specific modulus
* Space elevator
* Space tether

## References

1. ↑ "Acetal Polyoxymethylene Homopolymer - POM". August 30, 2001. https://www.azom.com/article.aspx?ArticleID=762.
2. ↑ "Polypropylene - online catalogue source - supplier of research materials in small quantities - Goodfellow". http://www.goodfellow.com/E/Polypropylene.html.
3. ↑ "Polyacrylonitrile-butadiene-styrene - online catalogue source - supplier of research materials in small quantities - Goodfellow". http://www.goodfellow.com/E/Polyacrylonitrile-butadiene-styrene.html.
4. ↑ "Polyethylene terephthalate - online catalogue source - supplier of research materials in small quantities - Goodfellow". http://www.goodfellow.com/E/Polyethylene-terephthalate.html.
5. ↑ "ASTM A228 Steel (UNS K08500)". http://www.matweb.com/search/datasheet_print.aspx?matguid=4bcaab41d4eb43b3824d9de31c2c6849.
6. ↑ "Polylactic acid - Biopolymer - online catalogue source - supplier of research materials in small quantities - Goodfellow". http://www.goodfellow.com/E/Polylactic-acid-Biopolymer.html.
7. ↑ "AISI 1010 Steel, cold drawn". http://www.matweb.com/search/datasheetText.aspx?bassnum=M1010A.
8. ↑ "ASM Material Data Sheet". http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=MQ304A.
9. ↑ "SSA Corp Maraging Data Sheet". https://matmatch.com/learn/material/maraging-steel.
10. ↑ "Properties of Copper Alloys". roymech.co.uk. http://www.roymech.co.uk/Useful_Tables/Matter/Copper_Alloys.html.
11. ↑ "Polyamide - Nylon 6 - online catalogue source - supplier of research materials in small quantities - Goodfellow". http://www.goodfellow.com/E/Polyamide-Nylon-6.html.
12. ↑ "ASM Material Data Sheet". http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=MTU020.
13. ↑ "ASM Material Data Sheet". http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=m4130r.
14. ↑ "ASM Material Data Sheet". http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=M4130A.
15. ↑ "ASM Material Data Sheet". http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=MA6061T6.
16. ↑ "Environmental data: Oak wood". http://www.io.tudelft.nl/research/dfs/idemat/Onl_db/Id192p.htm.
17. ↑ "ASM Material Data Sheet". http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=NINC35.
18. ↑ "eFunda: Typical Properties of Magnesium Alloys". https://www.efunda.com/Materials/alloys/magnesium/properties.cfm.
19. ↑ "ASM Material Data Sheet". http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=MA7075T6.
20. ↑ "American Eastern White Pine Wood". http://www.matweb.com/search/datasheet_print.aspx?matguid=1bec7114d2524b63826044c3cc6c344c.
21. ↑ "AZo Materials Data Sheet". 11 February 2003. http://www.azom.com/article.aspx?ArticleID=1843.
22. ↑ 22.0 22.1 52nd Hatfield Memorial Lecture: "Large Chunks of Very Strong Steel" by H. K. D. H. Bhadeshia 2005. on archive.is
23. ↑ "MatWeb – The Online Materials Information Resource". matweb.com. http://www.matweb.com/search/DataSheet.aspx?MatGUID=368427cdadb34b10a66b55c264d49c23.
24. ↑ McGRAW-HILL ENCYCLOPEDIA OF Science & Technology, 8th Edition, (c)1997, vol. 1 p 375
25. ↑ "Specialty Materials, Inc SCS Silicon Carbide Fibers". http://www.specmaterials.com/silicarbsite.htm.
26. ↑ NanoComp Technologies Inc.. "Miralon Yarn". https://cdn2.hubspot.net/hubfs/339583/Offers/Miralon_Yarn.pdf.
27. ↑ 27.0 27.1 27.2 "Vectran". Vectran Fiber, Inc.. http://www.vectranfiber.com/properties/tensile-properties/.
28. ↑ "RWcarbon.com – The Source for BMW & Mercedes Carbon Fiber Aero Parts". rwcarbon.com. http://www.rwcarbon.com.
29. ↑ "Network Group for Composites in Construction: Introduction to Fibre Reinforced Polymer Composites". http://www.ngcc.org.uk/info/ch1.html.
30. ↑ "Dyneema Fact sheet". DSM. 1 January 2008. http://www.dsm.com/products/dyneema/en_GB/home.html.
31. ↑ Toyobo Co., Ltd.. "ザイロン®(PBO 繊維)技術資料 (2005)" (free download PDF). http://www.toyobo.co.jp/seihin/kc/pbo/technical.pdf.
32. ↑ Toray Composites Materials America, Co., Ltd.. "T1100S, INTERMEDIATE MODULUS CARBON FIBER" (free download PDF). https://www.torayca.com/en/download/pdf/torayca_t1100g.pdf.
33. ↑ 33.0 33.1 Yu, Min-Feng; Lourie, Oleg; Dyer, Mark J.; Moloni, Katerina; Kelly, Thomas F.; Ruoff, Rodney S. (28 January 2000). "Strength and Breaking Mechanism of Multiwalled Carbon Nanotubes Under Tensile Load". Science 287 (5453): 637–640. doi:10.1126/science.287.5453.637. PMID 10649994. Bibcode: 2000Sci...287..637Y. http://www.bimat.org/assets/pdf/00_287yu.pdf.
34. ↑ 34.0 34.1 K.Hata (2007). "From highly efficient impurity-free CNT synthesis to DWNT forests, CNT solids, and super-capacitors". in Razeghi, Manijeh; Brown, Gail J. From Highly Efficient Impurity-Free CNT Synthesis to DWNT forests, CNTsolids and Super-Capacitors. Quantum Sensing and Nanophotonic Devices IV. 6479. pp. 64791L. doi:10.1117/12.716279. http://www.nanocarbon.jp/english/research/image/review.pdf. Retrieved 2009-12-02.
35. ↑ Peng, H. et al. (2008). "Strong and Ductile Colossal Carbon Tubes with Walls of Rectangular Macropores". Phys. Rev. Lett. 101 (14): 145501. doi:10.1103/PhysRevLett.101.145501. PMID 18851539. Bibcode: 2008PhRvL.101n5501P.
36. ↑ "2010 Nobel Physics Laureates". nobelprize.org. http://www.nobelprize.org/nobel_prizes/physics/laureates/2010/advanced-physicsprize2010.pdf.
37. ↑ 37.0 37.1 Brown, Adam R. (2013). "Tensile Strength and the Mining of Black Holes". Physical Review Letters 111 (21): 211301. doi:10.1103/PhysRevLett.111.211301. PMID 24313473. Bibcode: 2013PhRvL.111u1301B.
38. ↑ Li, F.; Cheng, H. M.; Bai, S.; Su, G.; Dresselhaus, M. S. (2000). "Tensile strength of single-walled carbon nanotubes directly measured from their macroscopic ropes". Applied Physics Letters 77 (20): 3161–3163. doi:10.1063/1.1324984. Bibcode: 2000ApPhL..77.3161L.
39. ↑ "Strong Tether Challenge 2013". http://www.isec.org/images/StrongTetherChallenge/2013/Handbook-ts2013.rev0.pdf.
40. ↑ "Terminology". isec.org. http://www.isec.org/sec/index.php/about-the-space-elevator/terminology#MegaYuri.
41. ↑ "Specific Strength in Yuris". keithcu.com. http://keithcu.com/wiki/index.php/Specific_Strength_in_Yuris.
42. ↑ Rodriguez, Ferdinand (1989). Principles of Polymer Systems (3rd ed.). New York: Hemisphere Publishing. p. 282. ISBN 9780891161769. OCLC 19122722. https://archive.org/details/principlesofpoly0000rodr/page/282.

## External links

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

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