Tear length

The tear length is a characteristic material property . This is the length at which a freely hanging cross section of a material (for example a wire ) breaks off due to its own weight at the fastening.

calculation

The tear length can be calculated from the strength and density measured in the tensile test . Accordingly, the material fails when the load from the weight is equal to the force that the material can absorb. From this balance of power ${\displaystyle R_{m}}$ ${\displaystyle \rho }$ ${\displaystyle L_{R}\,A\,\rho \,g}$ ${\displaystyle R_{m}A}$

${\displaystyle R_{\mathrm {m} }\,A\;=\;L_{\mathrm {R} }A\,\rho \,g}$

is obtained by dissolving for the tear length to ${\displaystyle L_{\mathrm {R} }}$

${\displaystyle L_{\mathrm {R} }={\frac {R_{\mathrm {m} }}{\rho \,g}}}$

It is defined as the ratio of tensile strength to the product of density and acceleration due to gravity . The tear length is usually given in kilometers. In the textile industry, the term ripping kilometer with the abbreviation Rkm is common. The tear length is independent of the size and shape of the cross-sectional area, since not only does the strength increase linearly with the cross-sectional area, but also the mass. A pipe and a cylinder of the same material, regardless of their cross-sectional area, have the same tear length. ${\displaystyle R_{\mathrm {m} }}$ ${\displaystyle \rho }$ ${\displaystyle g}$

The ratio of tensile strength to density is called specific strength : ${\displaystyle R_{\text{spez}}}$

${\displaystyle R_{\text{spez}}={\frac {R_{\mathrm {m} }}{\rho }}}$

meaning

The tearing length is a helpful indicator when the mass of a component is important. Because of the equivalence of inert and heavy mass , this is the case when a load is caused by its own weight or by inertial forces.

For example, the load on a picture hook due to its own weight is negligible due to its mass and, given the shape, the strength is sufficient as a parameter. In the case of a bridge , the load caused by its own weight can exceed the load caused by use. Then the material with a longer tear length is preferable.

However, the mass of a component induces a load not only through gravity , but possibly also through its inertia . This is why the tearing length becomes more important when components are exposed to great inertial forces due to strong acceleration. This is the case with turbine blades or connecting rods .

In practice, however, the tearing length often takes a backseat when selecting the material, as other criteria such as cost, processability or durability dominate. If there is no alternative to steel , for example , strength is decisive, as the density of steels hardly varies. That is why the tearing length serves the technical-physical understanding rather than the concrete work of a designer .

The space elevator is a much discussed application for new materials with extreme tear lengths .

Examples

Tear length of various materials

material	Tensile strength ( MPa )	Density ( g / cm³ )	Specific tear strength (kN m / kg)	Tear length ( km )	Swell)
concrete	5.2	2.400	4.35	0.44
rubber	15th, 0	0.920	16.30	1.66
Brass	580, 0	8.550	67.80	6.91
Polyamide (nylon)	78, 0	1.130	69.00	7.04
Oak wood (along the grain)	60, 0	0.690	86.95	8.86
Polypropylene	80, 0	0.900	88.88	9.06
magnesium	275, 0	1.740	158, 00	16.11
Aluminum alloy	600, 0	2.700	222, 00	22.65
steel	2,000, 0	7.860	254, 00	25.93
titanium	1,300, 0	4.510	288, 00	29.38
Piano wire , spring steel	2,300, 0	7.860	292, 00	29.82
Bainite	2,500, 0	7.870	321, 00	32.40
Balsa wood (along the grain)	73, 0	0.140	521, 00	53.20
Scifer steel wire (typically 0.015-0.1 mm dia.)	4,000 to 5,500, 0 , 0	7.870	706, 00	71.20
Carbon fiber reinforced plastic (fabric 0 ° / 90 °)	1,240, 0	1.580	785, 00	80, 00
Silicon carbide	3,440, 0	3.160	1,088, 00	110, 00
Glass fiber (without matrix)	3,400, 0	2.600	1,307, 00	133, 00
Basalt fiber	4,840, 0	2.700	1,790, 00	182.70
1 .mu.m iron - Whisker	14,000, 0	7.870	1,800, 00	183, 00
aromatic polyester (Vectran)	2,900, 0	1.400	2,071, 00	211, 00
Carbon fiber (without matrix)	4,300, 0	1.750	2,457, 00	250, 00
Aramid (kevlar)	3,620, 0	1.440	2,514, 00	256, 00
Polyethylene fiber ( Dyneema , Spectra; e.g. kite line)	3,510, 0	0.970	3,619, 00	369, 00
Cylon	5,800, 0	1.540	3,766, 00	384, 00
Carbon nanotubes	63,000, 0	0.037 to 1.340	46,268 to N / A	4,716 to N / A
Graph	135,000, 0	2.260	55,367, 00	5,655, 00
Colossal carbon tube	6,900, 0	0.116	59,483, 00	6,066, 00

Sample calculation:

Example wood with R _m = 100 N / mm² and a density of 500 kg / m³ (acceleration due to gravity g ≈ 10 m / s²):

${\displaystyle L_{\mathrm {R} }={\frac {100\,{\frac {\mathrm {N} }{\mathrm {mm} ^{2}}}}{500\,{\frac {\mathrm {kg} }{\mathrm {m} ^{3}}}\cdot g}}={\frac {100\cdot 10^{6}\,{\frac {\mathrm {N} }{\mathrm {m} ^{2}}}}{500\,{\frac {\mathrm {kg} }{\mathrm {m} ^{3}}}\cdot g}}\approx 20.000\,\mathrm {m} =20\,\mathrm {km} }$

Web links

• Meyers-1905

Individual evidence

1. ↑ RoyMech: Copper Alloys
2. ↑ Goodfellow: Polyamide - Nylon 6 ( Memento of the original from June 9, 2008 in the Internet Archive ) Info: The archive link has been inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. 
3. ↑ Delft University of technology: Oak wood ( Memento of October 9, 2007 in the Internet Archive )
4. ↑ Goodfellow: Polypropylene ( Memento of the original from June 2, 2008 in the Internet Archive ) Info: The archive link was automatically inserted and not yet checked. Please check the original and archive link according to the instructions and then remove this notice. 
5. ↑ eFunda: Magnesium Alloys
6. ↑ ^{a b c d e f} Vectran fiber: Tensile Properties ( Memento of the original dated December 30, 2013 in the Internet Archive ) Info: The archive link was automatically inserted and not yet checked. Please check the original and archive link according to the instructions and then remove this notice. 
7. ↑ Archived copy ( Memento of the original dated February 12, 2016 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. http://www.koch.ch , Bolzenschneider tensile strength piano wire 2300 N / mm2, accessed February 12, 2016. 
8. ↑ ^{a b c} 52nd Hatfield Memorial Lecture: "Large Chunks of Very Strong Steel" ( Memento of the original from December 23, 2012 in the web archive archive.today ) Info: The archive link was automatically inserted and not yet checked. Please check the original and archive link according to the instructions and then remove this notice. by HKDH Bhadeshia 2005 
9. ↑ MatWeb: Tropical Balsa Wood
10. ↑ http://www.sheffield.ac.uk/polopoly_fs/1.395277!/file/52nd_shortpaper.pdf HKDH Bhadeshia: Bulk nanocrystalline steel, Hatfield Memorial Lecture, In: Ironmaking and Steelmaking, vol. 32, no. 5, 2005, pp. 405-410. here: p. 406, accessed February 12, 2016.
11. ↑ McGRAW-HILL ENCYCLOPEDIA OF Science & Technology, 8th Edition, 1997, Volume 1, page 375
12. ^ Specialty Materials, Inc. SCS Silicon Carbide Fibers
13. ↑ albarrie.com: Basalt Continuous Fibers ( Memento of the original from December 29, 2009 on WebCite ) Info: The archive link was automatically inserted and not yet checked. Please check the original and archive link according to the instructions and then remove this notice. 
14. ^ Network Group for Composites in Construction: Introduction to Fiber Reinforced Polymer Composites .
15. ↑ Honeywell Advanced Fibers and Composites: Spectra Fiber .
16. ↑ Toyobo Co., Ltd .: ザ イ ロ ン ® (PBO 繊 維) 技術 資料 (2005) (free download PDF) Archived from the original on April 26, 2012. Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. Retrieved January 16, 2015. 
17. ↑ Min-Feng Yu, O Lourie, MJ Dyer, K Moloni, TF Kelly, RS Ruoff: Strength and Breaking Mechanism of Multiwalled Carbon Nanotubes Under Tensile Load . In: Science . 287, No. 5453, 2000, pp. 637-640. bibcode : 2000Sci ... 287..637Y . doi : 10.1126 / science.287.5453.637 . PMID 10649994 .
18. ↑ K.Hata: From Highly Efficient Impurity-Free CNT Synthesis to DWNT forests, CNTsolids and Super-Capacitors (PDF; 3.0 MB) Retrieved on May 21, 2011.
19. ^ Peng, H .; Chen, D .; et al., Huang JY et al .: Strong and Ductile Colossal Carbon Tubes with Walls of Rectangular Macropores . In: Phys. Rev. Lett. . 101, No. 14, 2008, p. 145501. bibcode : 2008PhRvL.101n5501P . doi : 10.1103 / PhysRevLett.101.145501 . PMID 18851539 .