Specific strength#Tenacity (textile strength)

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

: $L=\frac{T_s/\rho}{\mathbf {g} }$

where $L$ is the length, $T_s$ is the tensile strength, $\rho$ is the density and $\mathbf {g}$ is the acceleration due to gravity ( $\approx 9.8$ m/s $^2$ )

Examples

class="wikitable sortable" style="text-align:right; margin: 1em auto 1em auto" \|+ Specific tensile strength of various materials ! Material ! data-sort-type="number" \| 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
align="left"\| Concrete	2–5	2.30	5.22	0.44	{{CN\|date=June 2023}}
align="left"\| Polyoxymethylene; POM	69	1.42	49	4.95	{{Cite web\|url=https://www.azom.com/article.aspx?ArticleID=762\|title=Acetal Polyoxymethylene Homopolymer - POM\|date=August 30, 2001\|website=AZoM.com\|access-date=July 22, 2020\|archive-date=July 22, 2020\|archive-url=https://web.archive.org/web/20200722103423/https://www.azom.com/article.aspx?ArticleID=762\|url-status=live}}
align="left"\| Rubber	15	0.92	16.3	1.66	{{CN\|date=June 2023}}
align="left"\| Copper	220	8.92	24.7	2.51	{{CN\|date=June 2023}}
align="left"\| Polypropylene; PP	25–40	0.90	28–44	2.8–4.5	{{Cite web\|url=http://www.goodfellow.com/E/Polypropylene.html\|title=Polypropylene - online catalogue source - supplier of research materials in small quantities - Goodfellow\|website=www.goodfellow.com\|access-date=2017-04-24\|archive-date=2018-08-07\|archive-url=https://web.archive.org/web/20180807011205/http://www.goodfellow.com/E/Polypropylene.html\|url-status=live}}
align="left"\| (Poly)acrylonitrile-butadiene-styrene; ABS	41–45	1.05	39–43		{{Cite web\|url=http://www.goodfellow.com/E/Polyacrylonitrile-butadiene-styrene.html\|title=Polyacrylonitrile-butadiene-styrene - online catalogue source - supplier of research materials in small quantities - Goodfellow\|website=www.goodfellow.com\|access-date=2018-07-29\|archive-date=2018-12-20\|archive-url=https://web.archive.org/web/20181220212033/http://www.goodfellow.com/E/Polyacrylonitrile-butadiene-styrene.html\|url-status=live}}
align="left"\| Polyethylene terephthalate; polyester; PET	80	1.3–1.4	57–62		{{Cite web\|url=http://www.goodfellow.com/E/Polyethylene-terephthalate.html\|title=Polyethylene terephthalate - online catalogue source - supplier of research materials in small quantities - Goodfellow\|website=www.goodfellow.com\|access-date=2018-07-29\|archive-date=2019-04-17\|archive-url=https://web.archive.org/web/20190417193244/http://www.goodfellow.com/E/Polyethylene-terephthalate.html\|url-status=live}}
align="left"\| Piano wire; ASTM 228 Steel	1590–3340	7.8	204–428		{{Cite web\|url=http://www.matweb.com/search/datasheet_print.aspx?matguid=4bcaab41d4eb43b3824d9de31c2c6849\|title=ASTM A228 Steel (UNS K08500)\|website=www.matweb.com\|access-date=2019-01-17\|archive-date=2019-01-19\|archive-url=https://web.archive.org/web/20190119121710/http://www.matweb.com/search/datasheet_print.aspx?matguid=4bcaab41d4eb43b3824d9de31c2c6849\|url-status=live}}
align="left"\| Polylactic acid; polylactide; PLA	53	1.24	43		{{Cite web\|url=http://www.goodfellow.com/E/Polylactic-acid-Biopolymer.html\|title=Polylactic acid - Biopolymer - online catalogue source - supplier of research materials in small quantities - Goodfellow\|website=www.goodfellow.com\|access-date=2018-07-29\|archive-date=2018-07-29\|archive-url=https://web.archive.org/web/20180729230355/http://www.goodfellow.com/E/Polylactic-acid-Biopolymer.html\|url-status=live}}
align="left"\| Low carbon steel (AISI 1010)	365	7.87	46.4	4.73	{{Cite web \|title = AISI 1010 Steel, cold drawn \|url = http://www.matweb.com/search/datasheetText.aspx?bassnum=M1010A \|website = matweb.com \|access-date = 2015-10-20 \|archive-date = 2018-04-18 \|archive-url = https://web.archive.org/web/20180418115128/http://www.matweb.com/search/datasheetText.aspx?bassnum=M1010A \|url-status = live }}
align="left"\| Stainless steel (304)	505	8.00	63.1	6.4	{{Cite web\|title = ASM Material Data Sheet\|url = http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=MQ304A\|website = asm.matweb.com\|access-date = 2015-10-20\|archive-date = 2018-10-01\|archive-url = https://web.archive.org/web/20181001114838/http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=mq304a\|url-status = live}}
align="left"\| Maraging steel (18Ni(350))	2450	8.2	298.78	29.7	{{Cite web\|title = SSA Corp Maraging Data Sheet\|url =https://matmatch.com/learn/material/maraging-steel \|website=matmatch.com/learn/material/maraging-steel }}
align="left"\| Brass	580	8.55	67.8	6.91	{{cite web\|url=http://www.roymech.co.uk/Useful_Tables/Matter/Copper_Alloys.html\|title=Properties of Copper Alloys\|work=roymech.co.uk\|access-date=2006-04-17\|archive-date=2019-03-30\|archive-url=https://web.archive.org/web/20190330064952/http://www.roymech.co.uk/Useful_Tables/Matter/Copper_Alloys.html\|url-status=live}}
align="left"\| Nylon	78	1.13	69.0	7.04	{{Cite web\|url=http://www.goodfellow.com/E/Polyamide-Nylon-6.html\|title=Polyamide - Nylon 6 - online catalogue source - supplier of research materials in small quantities - Goodfellow\|website=www.goodfellow.com\|access-date=2017-04-24\|archive-date=2019-04-17\|archive-url=https://web.archive.org/web/20190417193533/http://www.goodfellow.com/E/Polyamide-Nylon-6.html\|url-status=live}}
align="left" \| Titanium	344	4.51	76	7.75	{{cite web\|title = ASM Material Data Sheet\|url = http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=MTU020\|website = asm.matweb.com\|access-date = 2016-11-14\|archive-date = 2019-03-22\|archive-url = https://web.archive.org/web/20190322124633/http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=MTU020\|url-status = live}}
align="left" \| CrMo Steel (4130)	560–670	7.85	71–85	7.27–8.70	{{Cite web\|title = ASM Material Data Sheet\|url = http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=m4130r\|website = asm.matweb.com\|access-date = 2016-08-18\|archive-date = 2019-04-06\|archive-url = https://web.archive.org/web/20190406133032/http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=m4130r\|url-status = live}}{{Cite web\|title = ASM Material Data Sheet\|url = http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=M4130A\|website = asm.matweb.com\|access-date = 2016-08-18\|archive-date = 2012-03-15\|archive-url = https://web.archive.org/web/20120315091534/http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=M4130A\|url-status = live}}
align="left" \| Aluminium alloy (6061-T6)	310	2.70	115	11.70	{{Cite web\|title = ASM Material Data Sheet\|url = http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=MA6061T6\|website = asm.matweb.com\|access-date = 2016-08-18\|archive-date = 2018-10-22\|archive-url = https://web.archive.org/web/20181022154932/http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=MA6061t6\|url-status = live}}
align="left"\| Oak	90	0.78–0.69	115–130	12–13	{{cite web \|url=http://www.io.tudelft.nl/research/dfs/idemat/Onl_db/Id192p.htm \|title=Environmental data: Oak wood \|access-date=2006-04-17 \|url-status=bot: unknown \|archive-url=https://web.archive.org/web/20071009144917/http://www.io.tudelft.nl/research/dfs/idemat/Onl_db/Id192p.htm \|archive-date=9 October 2007 }}
align="left"\| Inconel (X-750)	1250	8.28	151	15.4	{{Cite web\|title = ASM Material Data Sheet\|url = http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=NINC35\|website = asm.matweb.com\|access-date = 2015-10-20\|archive-date = 2018-10-04\|archive-url = https://web.archive.org/web/20181004090335/http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=NINC35\|url-status = live}}
align="left"\| Magnesium alloy	275	1.74	158	16.1	{{Cite web\|url=https://www.efunda.com/Materials/alloys/magnesium/properties.cfm\|title=eFunda: Typical Properties of Magnesium Alloys\|website=www.efunda.com\|access-date=2021-10-01\|archive-date=2020-01-30\|archive-url=https://web.archive.org/web/20200130045338/http://www.efunda.com/materials/alloys/magnesium/properties.cfm\|url-status=live}}
align="left" \| Aluminium alloy (7075-T6)	572	2.81	204	20.8	{{Cite web\|title = ASM Material Data Sheet\|url = http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=MA7075T6\|website = asm.matweb.com\|access-date = 2015-10-20\|archive-date = 2018-10-16\|archive-url = https://web.archive.org/web/20181016063536/http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=MA7075T6\|url-status = live}}
align="left" \|Pine wood (American eastern white)	78	0.35	223	22.7	{{Cite web\|url=http://www.matweb.com/search/datasheet_print.aspx?matguid=1bec7114d2524b63826044c3cc6c344c\|title=American Eastern White Pine Wood\|website=www.matweb.com\|access-date=2019-12-08\|archive-date=2019-12-08\|archive-url=https://web.archive.org/web/20191208162819/http://www.matweb.com/search/datasheet_print.aspx%3Fmatguid%3D1bec7114d2524b63826044c3cc6c344c\|url-status=live}}
align="left" \| Titanium alloy (Beta C)	1250	4.81	260	26.5	{{cite web\|title = AZo Materials Data Sheet\|url = http://www.azom.com/article.aspx?ArticleID=1843\|website = azom.com\|date = 11 February 2003\|access-date = 2016-11-14\|archive-date = 2017-06-23\|archive-url = https://web.archive.org/web/20170623175914/http://www.azom.com/article.aspx?ArticleID=1843\|url-status = live}}
align="left"\| Bainite	2500	7.87	321	32.4	[https://web.archive.org/web/20060828062831/http://www.msm.cam.ac.uk/phase-trans/2005/chunk.html 52nd Hatfield Memorial Lecture: "Large Chunks of Very Strong Steel"] by H. K. D. H. Bhadeshia 2005. [https://archive.today/20121223005514/http://www.msm.cam.ac.uk/phase-trans/2005/chunk.html on archive.is]
align="left" \| Reversibly Assembled Cellular Composite Materials \|0.073 \|0.0072 \|10,139 \|1035 \|{{Cite web \|date=2013-08-16 \|title=Toylike blocks make lightweight, strong structures \|url=https://www.sciencenews.org/article/toylike-blocks-make-lightweight-strong-structures \|access-date=2024-03-21 \|language=en-US}}{{Cite journal \|last1=Schaedler \|first1=Tobias A. \|last2=Jacobsen \|first2=Alan J. \|last3=Carter \|first3=Wiliam B. \|date=2013-09-13 \|title=Toward Lighter, Stiffer Materials \|url=https://www.science.org/doi/10.1126/science.1243996 \|journal=Science \|language=en \|volume=341 \|issue=6151 \|pages=1181–1182 \|doi=10.1126/science.1243996 \|pmid=24031005 \|bibcode=2013Sci...341.1181S \|issn=0036-8075\|url-access=subscription }}
align="left" \| Self-Reprogrammable Mechanical Metamaterials \|0.01117 \|0.0103 \|1,084 \|111 \|{{Cite web \|last=Krywko \|first=Jacek \|date=2024-02-08 \|title=Building robots for "Zero Mass" space exploration \|url=https://arstechnica.com/science/2024/02/building-robots-for-zero-mass-space-exploration/ \|access-date=2024-03-21 \|website=Ars Technica \|language=en-us}}
align="left"\| Balsa	73	0.14	521	53.2	{{cite web\|url=http://www.matweb.com/search/DataSheet.aspx?MatGUID=368427cdadb34b10a66b55c264d49c23\|title=MatWeb – The Online Materials Information Resource\|work=matweb.com\|access-date=2009-06-29\|archive-date=2015-04-02\|archive-url=https://web.archive.org/web/20150402150853/http://www.matweb.com/search/DataSheet.aspx?MatGUID=368427cdadb34b10a66b55c264d49c23\|url-status=live}}
align="left"\| Carbon–epoxy composite	1240	1.58	785	80.0	McGRAW-HILL ENCYCLOPEDIA OF Science & Technology, 8th Edition, (c)1997, vol. 1 p 375
align="left"\| Spider silk	1400	1.31	1,069	109	{{CN\|date=June 2023}}
align="left"\| Silicon carbide fiber	3440	3.16	1,088	110	{{Cite web\|url=http://www.specmaterials.com/silicarbsite.htm\|title=Specialty Materials, Inc SCS Silicon Carbide Fibers\|access-date=2006-04-17\|archive-date=2018-04-04\|archive-url=https://web.archive.org/web/20180404200749/http://www.specmaterials.com/silicarbsite.htm\|url-status=live}}
align="left"\| Miralon carbon nanotube yarn C-series	1375	0.7–0.9	1,100	112	{{Cite web \|author=NanoComp Technologies Inc. \|title=Miralon Yarn \|url=https://cdn2.hubspot.net/hubfs/339583/Offers/Miralon_Yarn.pdf \|access-date=2018-12-19 \|archive-date=2018-12-20 \|archive-url=https://web.archive.org/web/20181220230552/https://cdn2.hubspot.net/hubfs/339583/Offers/Miralon_Yarn.pdf \|url-status=live }}
align="left"\| Glass fiber	3400	2.60	1,307	133	{{cite web\|url = http://www.vectranfiber.com/properties/tensile-properties/\|title = Vectran\|publisher = Vectran Fiber, Inc.\|access-date = 2017-06-12\|archive-date = 2019-07-08\|archive-url = https://web.archive.org/web/20190708154158/https://www.vectranfiber.com/properties/tensile-properties/\|url-status = live}}
align="left"\| Basalt fiber	4840	2.70	1,790	183	{{cite web\|url=http://www.rwcarbon.com\|title=RWcarbon.com – The Source for BMW & Mercedes Carbon Fiber Aero Parts\|work=rwcarbon.com\|access-date=2021-10-01\|archive-date=2019-05-03\|archive-url=https://web.archive.org/web/20190503041337/https://www.rwcarbon.com/\|url-status=live}}
align="left"\| 1 μm iron whiskers	14000	7.87	1,800	183
align="left"\| Vectran	2900	1.40	2,071	211
align="left"\| Carbon fiber (AS4)	4300	1.75	2,457	250
align="left"\| Kevlar	3620	1.44	2,514	256	{{cite web \|url=http://www.ngcc.org.uk/info/ch1.html \|title=Network Group for Composites in Construction: Introduction to Fibre Reinforced Polymer Composites \|access-date=2006-04-17 \|url-status=bot: unknown \|archive-url=https://web.archive.org/web/20060118112908/http://www.ngcc.org.uk/info/ch1.html \|archive-date=January 18, 2006 }}
align="left"\| Dyneema (UHMWPE)	3600	0.97	3,711	378	{{cite web \|title= Dyneema Fact sheet \|publisher= DSM \|url= http://www.dsm.com/products/dyneema/en_GB/home.html \|date= 1 January 2008 \|access-date= 23 May 2016 \|archive-date= 8 August 2019 \|archive-url= https://web.archive.org/web/20190808151151/https://www.dsm.com/products/dyneema/en_GB/home.html \|url-status= live }}
align="left"\| Zylon	5800	1.54	3,766	384	{{Cite web\|author=Toyobo Co., Ltd.\|title=ザイロン®(PBO 繊維)技術資料 (2005)\|url=http://www.toyobo.co.jp/seihin/kc/pbo/technical.pdf\|format=free download PDF\|archive-url=https://web.archive.org/web/20120426001116/http://www.toyobo.co.jp/seihin/kc/pbo/technical.pdf\|archive-date=2012-04-26}}
align="left"\| Carbon fiber (Toray T1100G)	7000	1.79	3,911	399	{{Cite web\|author=Toray Composites Materials America, Co., Ltd.\|title=T1100S, INTERMEDIATE MODULUS CARBON FIBER\|url=https://www.torayca.com/en/download/pdf/torayca_t1100g.pdf\|format=free download PDF\|access-date=2021-06-29\|archive-date=2021-07-13\|archive-url=https://web.archive.org/web/20210713044348/https://www.torayca.com/en/download/pdf/torayca_t1100g.pdf\|url-status=live}}
align="left"\| Carbon nanotube (see note below)	62000	0.037–1.34	46,268–N/A	4716–N/A	{{Cite journal \|first1=Min-Feng \|last1=Yu \|date=28 January 2000 \|title=Strength and Breaking Mechanism of Multiwalled Carbon Nanotubes Under Tensile Load \|doi=10.1126/science.287.5453.637 \|journal=Science \|volume=287 \|issue=5453 \|pages=637–640 \|pmid=10649994 \|last2=Lourie \|first2=Oleg \|last3=Dyer \|first3=Mark J. \|last4=Moloni \|first4=Katerina \|last5=Kelly \|first5=Thomas F. \|last6=Ruoff \|first6=Rodney S. \|bibcode=2000Sci...287..637Y \|s2cid=10758240 \|url=http://www.bimat.org/assets/pdf/00_287yu.pdf \|archive-url=https://web.archive.org/web/20110304124625/http://www.bimat.org/assets/pdf/00_287yu.pdf \|archive-date=4 March 2011 }}{{Cite book \|author=K.Hata \|title=From Highly Efficient Impurity-Free CNT Synthesis to DWNT forests, CNTsolids and Super-Capacitors \|year=2007 \|editor1-last=Razeghi \|editor1-first=Manijeh \|series=Quantum Sensing and Nanophotonic Devices IV \|volume=6479 \|pages=64791L \|chapter=From highly efficient impurity-free CNT synthesis to DWNT forests, CNT solids, and super-capacitors \|doi=10.1117/12.716279 \|access-date=2009-12-02 \|editor2-last=Brown \|editor2-first=Gail J \|chapter-url=http://www.nanocarbon.jp/english/research/image/review.pdf \|archive-url=https://web.archive.org/web/20141214201915/http://www.nanocarbon.jp/english/research/image/review.pdf \|archive-date=2014-12-14 \|url-status=usurped \|s2cid=136421231}}
align="left"\| Colossal carbon tube	6900	0.116	59,483	6066	{{cite journal \|author1=Peng, H. \|author2=Chen, D. \|author3=et al., Huang J.Y. \| year = 2008 \| title = Strong and Ductile Colossal Carbon Tubes with Walls of Rectangular Macropores \| journal = Phys. Rev. Lett. \| volume = 101 \| issue = 14 \| pages = 145501 \| doi = 10.1103/PhysRevLett.101.145501 \| pmid = 18851539 \| bibcode=2008PhRvL.101n5501P\|display-authors=etal}}
align="left"\| Graphene	130500	2.090	62,453	6366	{{cite web \|url=http://www.nobelprize.org/nobel_prizes/physics/laureates/2010/advanced-physicsprize2010.pdf \|title=2010 Nobel Physics Laureates \|publisher=nobelprize.org \|access-date=2019-03-28 \|archive-date=2018-07-01 \|archive-url=https://web.archive.org/web/20180701222510/https://www.nobelprize.org/nobel_prizes/physics/laureates/2010/advanced-physicsprize2010.pdf \|url-status=live }}
align="left"\| Fundamental limit			{{val\|9\|e=13}}	{{val\|9.2\|e=12}}	{{cite journal \|last=Brown \|first=Adam R. \|arxiv=1207.3342 \|title=Tensile Strength and the Mining of Black Holes \|year=2013 \|doi=10.1103/PhysRevLett.111.211301 \|volume=111 \|issue=21 \|journal=Physical Review Letters \|page=211301 \|pmid=24313473 \|bibcode=2013PhRvL.111u1301B\|s2cid=16394667 }}

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, 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.{{cite journal|last1=Li|first1=F.|last2=Cheng|first2=H. M.|last3=Bai|first3=S.|last4=Su|first4=G.|last5=Dresselhaus|first5=M. S.|author-link5=Mildred Dresselhaus|title=Tensile strength of single-walled carbon nanotubes directly measured from their macroscopic ropes|journal=Applied Physics Letters|year=2000|volume=77|issue=20|pages=3161–3163|doi=10.1063/1.1324984|bibcode=2000ApPhL..77.3161L|doi-access=free}} The density is different depending on the manufacturing method, and the lowest value is 0.037 or 0.55 (solid).

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.{{Cite web|url=http://www.isec.org/images/StrongTetherChallenge/2013/Handbook-ts2013.rev0.pdf|title=Strong Tether Challenge 2013|archive-url=https://web.archive.org/web/20160114223616/http://www.isec.org/images/StrongTetherChallenge/2013/Handbook-ts2013.rev0.pdf|archive-date=2016-01-14}}{{cite web|url=http://www.isec.org/sec/index.php/about-the-space-elevator/terminology#MegaYuri|title=Terminology|work=isec.org|archive-url=https://web.archive.org/web/20120527065913/http://www.isec.org/sec/index.php/about-the-space-elevator/terminology#MegaYuri|archive-date=2012-05-27}} A functional Earth space elevator would require a tether of 30–80 megaYuri (corresponding to 3100–8200 km of breaking length).{{cite web|url=http://keithcu.com/wiki/index.php/Specific_Strength_in_Yuris|title=Specific Strength in Yuris|work=keithcu.com|access-date=2012-06-02|archive-date=2019-02-09|archive-url=https://web.archive.org/web/20190209124522/http://keithcu.com/wiki/index.php/Specific_Strength_in_Yuris|url-status=live}}

Fundamental limit on specific strength

The null energy condition places a fundamental limit on the specific strength of any material. The specific strength is bounded to be no greater than c² ≈ {{val|9|e=13|u=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|date=December 2018}}

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.{{cite book |title=Principles of Polymer Systems |first=Ferdinand |last=Rodriguez |page=[https://archive.org/details/principlesofpoly0000rodr/page/282 282] |publisher=Hemisphere Publishing |location=New York |year=1989 |edition=3rd |isbn=9780891161769 |oclc=19122722 |url-access=registration |url=https://archive.org/details/principlesofpoly0000rodr/page/282 }}

A tenacity of $1$ corresponds to:{{citation needed|date=December 2018}} $\frac{1 {\rm \, g} \cdot 9.80665 {\rm \, m s^{-2}}}{1 {\rm \, g}/9000 {\rm \, m}}=\frac{9.80665 {\rm \, m s^{-2}}}{1/9000 {\rm \, m}}=9.80665 {\rm \, m s^{-2}} \, 9000 {\rm \, m} = 88259.85 {\rm \, m^2 s^{-2}}$

Mostly Tenacity expressed in report as cN/tex.

References

External links

[http://www-materials.eng.cam.ac.uk/mpsite/interactive_charts/spec-spec/NS6Chart.html Specific stiffness - Specific strength] chart, University of Cambridge, Department of Engineering

Category:Engineering ratios

Category:Materials science

Category:Solid mechanics