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
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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
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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,[36] 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.[41] The density is different depending on the manufacturing method, and the lowest value is 0.037 or 0.55 (solid).[37]
The 'Yuri' and space tethers
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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.[42][43] A functional Earth space elevator would require a tether of 30–80 megaYuri (corresponding to 3100–8200 km of breaking length).[44]
Fundamental limit on specific strength
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The null energy condition places a fundamental limit on the specific strength of any material.[40] 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)
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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.[45] A tenacity of 1 {\displaystyle 1} corresponds to:[citation needed] 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
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References
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Titanium is an enormously useful metal. Its unique properties mean it sees widespread usage in an array of critical applications.
It is not without fault however and does suffer some disadvantages. It is enormously energy intensive to produce; titanium used for high-performance applications contributes to its high expense considering its relative abundance in the earth’s crust.
Titanium is highly resistant to chemical attack and has the highest strength to weight ratio of any metal. These unique properties make Titanium suitable for a wide range of applications. It’s stiffness to weight ratio as steel is similar to steel meaning it can be used as a substitute where weight is an important consideration.
This is well highlighted in aviation where its use in landing gear and compressor fans has drastically improved thrust to weight ratios. Titanium is highly recyclable which reduces costs involved in its production. Its inertness means that it can survive weathering and consequentially has a lower lifetime cost that other metals used in architecture and construction.
It is also biocompatible making it well suited to medical usage where it is nontoxic and able to osseointegrate.
The primary disadvantage of Titanium from a manufacturing and engineering perspective is its high reactivity, which means it has to be managed differently during all stages of its production. Impurities introduced during the Kroll process, VAR or machining were once near impossible to remove. The EBCHR process has reduced this risk, but it doesn’t come cheap.
It is not suited in high-temperature ranges, above 400 degrees Celsius, where it begins to lose its strength and nickel-based superalloys, are better equipped to handle the conditions.
It is incredibly important to use the right cutting tools and speeds and feeds during machining. Other metals can be relatively forgiving but titanium isn’t. If you get it right, you will have nothing to worry about.
Titanium does have negative externalities which require mitigation. The issues regarding the extraction processes of titanium ores are well publicised. Depending on location trees are often clear cut to access bedrock. This can contribute to soil degradation and cause the escape of heavy metals into the soil. Which can, if not adequately addressed pose a significant risk of drinking water contamination.
Whilst we are in no danger of running out of titanium, the expense and negative externalities of its extraction and manufacture means efficiency is an important consideration for the industry. At SGS our cutting tools are part of the solution. Designed to reduce waste and improve the efficiency of the Titanium machining process.