יחס חוזק/משקל

יחס חוזק/משקלאו יחס חוזק למשקל, נקרא גם חוזק סגולי (באנגלית: specific strength, strength-to-weight ratio או strength/weight ratio או אפילו strength-to-mass ratio) הוא היחס בין החוזק של חומר (שמוגדר ככוח ליחידת שטח, או המאמץ ברגע הכשל) ובין הצפיפות שלו. בחומרים רכים כמו טקסטיל מדובר על כשל במשיכה. בחומרים קשים מדובר על כשל במשיכה או בדחיסה.

עוד דרך לתאר את החוזק הסגולי של חומר היא לבחון את האורך לכשל, או את אורך הנשיאה העצמי של החומר. נדמיין עמוד או מוט ארוך של החומר, שתלוי רק מלמעלה. ברור, שבאורך מספיק גדול, המקטע העליון לא יוכל לשאת את המשקל וייקרע. לצורך זה, הכוח שגורם לכשל הוא כוח הכבידה של כדור הארץ, שמחושב על פני כל האורך של עמודת החומר לקבלת המשקל בכשל. לדוגמה, חבל טיפוס ששוקל כ-60גרם למטר, יכול לשאת משקל של 2200קילוגרם, בערך. זה אומר שאורך הקריעה הנשיאה העצמי שלו הוא קצת יותר מ-36.5 ק״מ!

ברור, שחבל שלא יכול לשאת את משקלו העצמי לא יתפקד בכלל כחבל...

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 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.

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)	Breaking length (km)	Source
Concrete	2–5	2.30	5.22	0.44
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	<ref>http://www.goodfellow.com/E/Polypropylene.html</ref>
(Poly)acrylonitrile-butadiene-styrene / ABS	41–45	1.05	39–43		<ref>http://www.goodfellow.com/E/Polyacrylonitrile-butadiene-styrene.html</ref>
Polyethylene terephthalate / Polyester / PET	80	1.3–1.4	57–62		<ref>http://www.goodfellow.com/E/Polyethylene-terephthalate.html</ref>
Piano wire / ASTM 228 Steel	1590-3340	7.8	204-428		<ref>http://www.matweb.com/search/datasheet_print.aspx?matguid=4bcaab41d4eb43b3824d9de31c2c6849</ref>
Polylactic acid / Polylactide / PLA	53	1.24	43		<ref>http://www.goodfellow.com/E/Polylactic-acid-Biopolymer.html</ref>
Low Carbon Steel (AISI 1010)	365	7.87	46.4	4.73	<ref>תבנית:Cite web</ref>
Stainless steel (304)	505	8.00	63.1	6.4	<ref>תבנית:Cite web</ref>
Brass	580	8.55	67.8	6.91	<ref name="roymech">תבנית:Cite web</ref>
Nylon	78	1.13	69.0	7.04	<ref>http://www.goodfellow.com/E/Polyamide-Nylon-6.html</ref>
Titanium	344	4.51	76	7.75	<ref>תבנית:Cite web</ref>
CrMo Steel (4130)	560–670	7.85	71–85	7.27–8.70	<ref>תבנית:Cite web</ref><ref>תבנית:Cite web</ref>
Aluminium alloy (6061-T6)	310	2.70	115	11.70	<ref>תבנית:Cite web</ref>
Oak	90	0.78–0.69	115–130	12–13	<ref>תבנית:Cite web</ref>
Inconel (X-750)	1250	8.28	151	15.4	<ref>תבנית:Cite web</ref>
Magnesium alloy	275	1.74	158	16.1	<ref>תבנית:Cite web</ref>
Aluminium alloy (7075-T6)	572	2.81	204	20.8	<ref>תבנית:Cite web</ref>
Titanium alloy (Beta C)	1250	4.81	260	26.5	<ref>תבנית:Cite web</ref>
Bainite	2500	7.87	321	32.4	<ref name="Bhadeshia"> 52nd Hatfield Memorial Lecture: "Large Chunks of Very Strong Steel" by H. K. D. H. Bhadeshia 2005. on archive.is </ref>
Balsa	73	0.14	521	53.2	<ref>תבנית:Cite web</ref>
Carbon-epoxy composite	1240	1.58	785	80.0	<ref> McGRAW-HILL ENCYCLOPEDIA OF Science & Technology, 8th Edition, (c)1997, vol. 1 p 375</ref>
Spider silk	1400	1.31	1069	109
Silicon carbide fiber	3440	3.16	1088	110	<ref>Specialty Materials, Inc SCS Silicon Carbide Fibers</ref>
Glass fiber	3400	2.60	1307	133	<ref name="vectran">תבנית:Cite web</ref>
Basalt fiber	4840	2.70	1790	183	<ref>תבנית:Cite web</ref>
1 μm iron whiskers	14000	7.87	1800	183	<ref name="Bhadeshia" />
Vectran	2900	1.40	2071	211	<ref name="vectran" />
Carbon fiber (AS4)	4300	1.75	2457	250	<ref name="vectran" />
Kevlar	3620	1.44	2514	256	<ref name="ngcc">תבנית:Cite web</ref>
Dyneema (UHMWPE)	3600	0.97	3711	378	<ref>תבנית:Cite web</ref>
Zylon	5800	1.54	3766	384	<ref name="Toyobo Co., Ltd.">תבנית:Cite web</ref>
Carbon fiber (Toray T1100G)	7000	1.79	3911	399	<ref name="Toray Composites Materials America, Co., Ltd.">תבנית:Cite web</ref>
Carbon nanotube (see note below)	62000	0.037–1.34	46268–N/A	4716–N/A	<ref name="Strength and Breaking">תבנית:Cite journal</ref><ref name="K.Hata">תבנית:Cite web</ref>
Miralon carbon nanotube yarn C-series	1375	0.7–0.9	1100	112	<ref name="NanoComp">תבנית:Cite web</ref>
Colossal carbon tube	6900	.116	59483	6066	<ref name="CCT">תבנית:Cite journal</ref>
Graphene	130500	2.090	62453	6366	<ref name="nobelprize.org">תבנית:Cite web</ref>
Fundamental limit			תבנית:Val	תבנית:Val	<ref name="Brown 2012">תבנית:Cite journal</ref>

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,<ref name="Strength and Breaking"/> 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.<ref>

"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. תבנית:Doi </ref> The density is different depending on the manufacturing method, and the lowest value is 0.037 or 0.55 (solid).<ref name="K.Hata"/>

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.<ref>Strong Tether Challenge 2013</ref><ref>תבנית:Cite web</ref> A functional Earth space elevator would require a tether of 30-80 MegaYuri (corresponding to 3100–8200 km of breaking length).<ref>תבנית:Cite web</ref>

Fundamental limit on specific strength

The null energy condition places a fundamental limit on the specific strength of any material.<ref name="Brown 2012"/> The specific strength is bounded to be no greater than c² ~ תבנית:ValkN·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.תבנית:Cn

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.<ref>תבנית:Cite book</ref> A tenacity of עיבוד הנוסחה נכשל (קובץ ההפעלה <code>texvc</code> אינו זמין. נא לעיין ב־math/README כדי להגדירו.): 1 corresponds to:תבנית:Cn עיבוד הנוסחה נכשל (קובץ ההפעלה <code>texvc</code> אינו זמין. נא לעיין ב־math/README כדי להגדירו.): \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}}

See also

• Specific modulus
• Space elevator
• Space tether

External links

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