Ultimate tensile strength

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Ultimate tensile strength (UTS), often shortened to tensile strength (TS) or ultimate strength,[1][2] is the maximum stress that a material can withstand while being stretched or pulled before failing or breaking. Tensile strength is not the same as compressive strength and the values can be quite different.

Some materials will break sharply, without plastic deformation, in what is called a brittle failure. Others, which are more ductile, including most metals, will experience some plastic deformation and possibly necking before fracture.

The UTS is usually found by performing a tensile test and recording the engineering stress versus strain. The highest point of the stress-strain curve (see point 1 on the engineering stress/strain diagrams below) is the UTS. It is an intensive property; therefore its value does not depend on the size of the test specimen. However, it is dependent on other factors, such as the preparation of the specimen, the presence or otherwise of surface defects, and the temperature of the test environment and material.

Tensile strengths are rarely used in the design of ductile members, but they are important in brittle members. They are tabulated for common materials such as alloys, composite materials, ceramics, plastics, and wood.

Tensile strength is defined as a stress, which is measured as force per unit area. For some non-homogeneous materials (or for assembled components) it can be reported just as a force or as a force per unit width. In the SI system, the unit is the pascal (Pa) (or a multiple thereof, often megapascals (MPa), using the mega- prefix); or, equivalently to pascals, newtons per square metre (N/m²). A customary unit is pounds-force per square inch (lbf/in² or psi), or kilo-pounds per square inch (ksi, or sometimes kpsi), which is equal to 1000 psi; kilo-pounds per square inch are commonly used for convenience when measuring tensile strengths.

Concept[edit]

Ductile materials[edit]

"Engineering" stress (σ) vs. strain (ε) curve typical of aluminum
1. Ultimate strength
2. Yield strength
3. Proportional limit stress
4. Fracture
5. Offset strain (typically 0.2%)
"Engineering" (red) and "true" (blue) stress vs. strain curve typical of structural steel
1. Ultimate strength
2. Yield strength
3. Fracture
4. Strain hardening region
5. Necking region
A: Engineering stress
B: True stress

Many materials display linear elastic behavior, defined by a linear stress-strain relationship, as shown in the left figure up to point 3. The elastic behavior of materials often extends into a non-linear region, represented in the figure by point 2 (the "yield point"), up to which deformations are completely recoverable upon removal of the load; that is, a specimen loaded elastically in tension will elongate, but will return to its original shape and size when unloaded. Beyond this elastic region, for ductile materials, such as steel, deformations are plastic. A plastically deformed specimen will not completely return to its original size and shape when unloaded. For many applications, plastic deformation is unacceptable, and is used as the design limitation.

After the yield point, ductile metals will undergo a period of strain hardening, in which the stress increases again with increasing strain, and they begin to neck, as the cross-sectional area of the specimen decreases due to plastic flow. In a sufficiently ductile material, when necking becomes substantial, it causes a reversal of the engineering stress-strain curve (curve A, right figure); this is because the engineering stress is calculated assuming the original cross-sectional area before necking. The reversal point is the maximum stress on the engineering stress-strain curve, and the engineering stress coordinate of this point is the ultimate tensile strength, given by point 1.

The UTS is not used in the design of ductile static members because design practices dictate the use of the yield stress. It is, however, used for quality control, because of the ease of testing. It is also used to roughly determine material types for unknown samples.[3]

The UTS is a common engineering parameter when designing brittle members, because there is no yield point.[3]

Testing[edit]

Round bar tensile specimen after testing

Typically, the testing involves taking a small sample with a fixed cross-section area, and then pulling it with a tensometer, gradually increasing force until the sample breaks.

When testing metals, indentation hardness correlates linearly with tensile strength. This important relation permits economically important nondestructive testing of bulk metal deliveries with lightweight, even portable equipment, such as hand-held Rockwell hardness testers.[4]

It should be noted that, while most metal forms, such as sheet, bar, tube, and wire, can exhibit the test UTS, fibers, such as carbon fibers, being only 2/10,000th of an inch in diameter, must be made into composites to create useful real-world forms. As the datasheet on T1000G below indicates, while the UTS of the fiber is very high at 6,370MPa, the UTS of a derived composite is 3,040MPa - less than half the strength of the fiber.[5]

Typical tensile strengths[edit]

Typical tensile strengths of some materials
Material Yield strength
(MPa)
Ultimate strength
(MPa)
Density
(g/cm³)
Steel, structural ASTM A36 steel 250 400-550 7.8
Steel, 1090 mild 247 841 7.58
Human skin 15 20 2.2
Steel, Micro-Melt 10 Tough Treated Tool (AISI A11)[6] 5171 5205 7.45
Steel, 2800 Maraging steel[7] 2617 2693 8.00
Steel, AerMet 340[8] 2160 2430 7.86
Steel, Sandvik Sanicro 36Mo logging cable precision wire[9] 1758 2070 8.00
Steel, AISI 4130, water quenched 855°C (1570°F), 480°C (900°F) temper[10] 951 1110 7.85
Titanium 11 (Ti-6Al-2Sn-1.5Zr-1Mo-0.35Bi-0.1Si), aged[11]
Steel, API 5L X65[12] 448 531 7.8
Steel, high strength alloy ASTM A514 690 760 7.8
Clear acrylic cast sheet (PMMA)[13] 72 114[14] 1.16
High-density polyethylene (HDPE) 26-33 37 0.95
Polypropylene 12-43 19.7-80 0.91
Steel, stainless AISI 302 - cold-rolled 520[citation needed] 0860 8.19
Cast iron 4.5% C, ASTM A-48 130 200  
"Liquidmetal" alloy[citation needed] 1723 550-1600 6.1
Beryllium[15] 99.9% Be 345 448 01.84
Aluminium alloy[16] 2014-T6 414 483 2.8
Polyester resin (unreinforced)[17] 55    
Polyester and chopped strand mat laminate 30% E-glass[17] 100    
S-Glass epoxy composite[18] 2358    
Aluminium alloy 6061-T6 241 300 2.7
Copper 99.9% Cu 70 220 8.92
Cupronickel 10% Ni, 1.6% Fe, 1% Mn, balance Cu 130 350 8.94
Brass 200 + 550  
Tungsten 941 1510 19.25
Glass   33[19] 2.53
E-Glass N/A 1500 for laminates,
3450 for fibers alone
2.57
S-Glass N/A 4710 2.48
Basalt fiber[20] N/A 4840 2.7
Marble N/A 15  
Concrete N/A 3 2.7
Carbon fiber N/A 1600 for laminates,
4137 for fibers alone
1.75
Carbon fiber (Toray T1000G)[21]   6370 fibre alone 1.80
Human hair   380  
Bamboo   350-500 0.4
Spider silk (see note below) 1000 1.3
Spider silk, Darwin's bark spider[22] 1652
Silkworm silk 500   1.3
Aramid (Kevlar or Twaron) 3620 3757 1.44
UHMWPE[23] 0.24 52 0.97
UHMWPE fibers[24][25] (Dyneema or Spectra) 2300-3500 0.97
Vectran   2850-3340  
Polybenzoxazole (Zylon)[26]   2700 1.56
Wood, pine (parallel to grain)   40  
Bone (limb) 104-121 0130 1.6
Nylon, type 6/6 45 75 1.15
Epoxy adhesive - 12 - 30[27] -
Rubber - 16  
Boron N/A 3100 2.46
Silicon, monocrystalline (m-Si) N/A 7000 2.33
Silicon carbide (SiC) N/A 3440  
Ultra-pure silica glass fiber-optic strands[28] 4100
Sapphire (Al2O3) 400 at 25°C, 275 at 500°C, 345 at 1000°C 1900 3.9-4.1
Boron nitride nanotube N/A 33000  ?
Diamond 1600 2800 3.5
Graphene N/A 130000[29] 1.0
First carbon nanotube ropes  ? 3600 1.3
Colossal carbon tube N/A 7000 0.116
Carbon nanotube (see note below) N/A 11000-63000 0.037-1.34
Carbon nanotube composites N/A 1200[30] N/A
Iron (pure mono-crystal) 3 7.874
^a Many of the values depend on manufacturing process and purity/composition.
^b Multiwalled carbon nanotubes have the highest tensile strength of any material yet measured, with labs producing them at a tensile strength of 63 GPa,[31] still well below their theoretical limit of 300 GPa.[citation needed] The first nanotube ropes (20mm in length) whose tensile strength was published (in 2000) had a strength of 3.6 GPa.[32] The density depends on the manufacturing method, and the lowest value is 0.037 or 0.55 (solid).[33]
^c The strength of spider silk is highly variable. It depends on many factors including kind of silk (Every spider can produce several for sundry purposes.), species, age of silk, temperature, humidity, swiftness at which stress is applied during testing, length stress is applied, and way the silk is gathered (forced silking or natural spinning).[34] The value shown in the table, 1000 MPa, is roughly representative of the results from a few studies involving several different species of spider however specific results varied greatly.[35]
^d Human hair strength varies by ethnicity and chemical treatments.
Typical properties for annealed elements[36]
Element Young's
modulus
(GPa)
Offset or
yield strength
(MPa)
Ultimate
strength
(MPa)
silicon 107 5000–9000
tungsten 411 550 550–620
iron 211 80–100 350
titanium 120 100–225 246–370
copper 130 117 210
tantalum 186 180 200
tin 47 9–14 15–200
zinc (wrought) 105 110–200
nickel 170 140–350 140–195
silver 83 170
gold 79 100
aluminium 70 15–20 40-50
lead 16 12

See also[edit]

References[edit]

  1. ^ Degarmo, Black & Kohser 2003, p. 31
  2. ^ Smith & Hashemi 2006, p. 223
  3. ^ a b NDT-ed.org
  4. ^ E.J. Pavlina and C.J. Van Tyne, "Correlation of Yield Strength and Tensile Strength with Hardness for Steels", Journal of Materials Engineering and Performance, 17:6 (December 2008)
  5. ^ http://www.carbonfibertubeshop.com/tube%20properties.html
  6. ^ http://www.matweb.com/search/datasheet.aspx?matguid=638937fc52ca4683bc0c3f18f54f5a24
  7. ^ http://www.matweb.com/search/DataSheet.aspx?MatGUID=de22e04486ff4598a26027abc48e6382
  8. ^ http://www.matweb.com/search/DataSheet.aspx?MatGUID=64583c8ce6724989a11e1ef598d3273d
  9. ^ http://www.matweb.com/search/DataSheet.aspx?MatGUID=c140b20b165941c7a948e782eeced4ea
  10. ^ http://www.matweb.com/search/datasheet.aspx?MatGUID=722e053100354c02a6d450d5d7646d82
  11. ^ http://www.matweb.com/search/DataSheet.aspx?
  12. ^ USStubular.com
  13. ^ IAPD Typical Properties of Acrylics
  14. ^ strictly speaking this figure is the flexural strength (or modulus of rupture), which is a more appropriate measure for brittle materials than "ultimate strength."
  15. ^ Beryllium I-220H Grade 2
  16. ^ Aluminum 2014-T6
  17. ^ a b East Coast Fibreglass Supplies: Guide to Glass Reinforced Plastics
  18. ^ Tube Properties
  19. ^ Material Properties Data: Soda-Lime Glass
  20. ^ "Basalt Continuous Fibers". Archived from the original on |archiveurl= requires |archivedate= (help). Retrieved 2009-12-29. 
  21. ^ Toray Properties Document
  22. ^ I Agnarsson, M Kuntner, T A Blackledge, Bioprospecting Finds the Toughest Biological Material: Extraordinary Silk from a Giant Riverine Orb Spider
  23. ^ http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2716092/table/T3/
  24. ^ Tensile and creep properties of ultra high molecular weight PE fibres
  25. ^ Mechanical Properties Data
  26. ^ Zylon Properties Document
  27. ^ Uhu endfest 300 epoxy: Strength over setting temperature
  28. ^ Fols.org
  29. ^ Lee, C. et al. (2008). "Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene". Science 321 (5887): 385–8. Bibcode:2008Sci...321..385L. doi:10.1126/science.1157996. PMID 18635798. Lay summary. 
  30. ^ IOP.org Z. Wang, P. Ciselli and T. Peijs, Nanotechnology 18, 455709, 2007.
  31. ^ Yu, Min-Feng; Lourie, O; Dyer, MJ; Moloni, K; Kelly, TF; Ruoff, RS (2000). "Strength and Breaking Mechanism of Multiwalled Carbon Nanotubes Under Tensile Load". Science 287 (5453): 637–640. Bibcode:2000Sci...287..637Y. doi:10.1126/science.287.5453.637. PMID 10649994. 
  32. ^ F. Li, H. M. Cheng, S. Bai, G. Su, and M. S. Dresselhaus, "Tensile strength of single-walled carbon nanotubes directly measured from their macroscopic ropes". doi:10.1063/1.1324984
  33. ^ K.Hata. "From Highly Efficient Impurity-Free CNT Synthesis to DWNT forests, CNTsolids and Super-Capacitors" (PDF). 
  34. ^ Elices, et al. "Finding Inspiration in Argiope Trifasciata Spider Silk Fibers". JOM. Retrieved 2009-01-23. 
  35. ^ Blackledge, et al. "Quasistatic and continuous dynamic characterization of the mechanical properties of silk from the cobweb of the black widow spider Latrodectus hesperus". The Company of Biologists. Retrieved 2009-01-23. 
  36. ^ A.M. Howatson, P.G. Lund, and J.D. Todd, Engineering Tables and Data, p. 41

Further reading[edit]

  • Giancoli, Douglas, Physics for Scientists & Engineers Third Edition (2000). Upper Saddle River: Prentice Hall.
  • Köhler, T., Vollrath, F. (1995). "Thread biomechanics in the two orb-weaving spiders Araneus diadematus (Araneae, Araneidae) and Uloboris walckenaerius (Araneae, Uloboridae)". Journal of Experimental Zoology 271: 1–17. doi:10.1002/jez.1402710102. 
  • T Follett, Life without metals
  • Min-Feng, Yu, Lourie, O, Dyer, MJ, Moloni, K, Kelly, TF, Ruoff, RS (2000). "Strength and Breaking Mechanism of Multiwalled Carbon Nanotubes Under Tensile Load". Science 287 (5453): 637–640. Bibcode:2000Sci...287..637Y. doi:10.1126/science.287.5453.637. PMID 10649994. 
  • George E. Dieter, Mechanical Metallurgy (1988). McGraw-Hill, UK