Ultimate tensile strength

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Two vises apply tension to a specimen by pulling at it, stretching the specimen until it fractures. The maximum stress it withstands before fracturing is its ultimate tensile strength. Tensile testing on a coir composite.jpg
Two vises apply tension to a specimen by pulling at it, stretching the specimen until it fractures. The maximum stress it withstands before fracturing is its ultimate tensile strength.

Ultimate tensile strength (UTS), often shortened to tensile strength (TS), ultimate strength, or within equations, [1] [2] [3] is the maximum stress that a material can withstand while being stretched or pulled before breaking. In brittle materials the ultimate tensile strength is close to the yield point, whereas in ductile materials the ultimate tensile strength can be higher.

Contents

The ultimate tensile strength is usually found by performing a tensile test and recording the engineering stress versus strain. The highest point of the stress–strain curve is the ultimate tensile strength and has units of stress. The equivalent point for the case of compression, instead of tension, is called the compressive strength.

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

Definition

The ultimate tensile strength of a material is an intensive property; therefore its value does not depend on the size of the test specimen. However, depending on the material, it may be 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.

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

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 International System of Units (SI), the unit is the pascal (Pa) (or a multiple thereof, often megapascals (MPa), using the SI prefix mega); or, equivalently to pascals, newtons per square metre (N/m2). A United States customary unit is pounds per square inch (lb/in2 or psi). Kilopounds per square inch (ksi, or sometimes kpsi) is equal to 1000 psi, and is commonly used in the United States, when measuring tensile strengths.

Ductile materials

Figure 1: "Engineering" stress-strain (s-e) curve typical of aluminum
Ultimate strength
Yield strength
Proportional limit stress
Fracture
Offset strain (typically 0.2%) Stress v strain Aluminum 2.png
Figure 1: "Engineering" stress–strain (σ–ε) curve typical of aluminum
  1. Ultimate strength
  2. Yield strength
  3. Proportional limit stress
  4. Fracture
  5. Offset strain (typically 0.2%)
figure 2: "Engineering" (red) and "true" (blue) stress-strain curve typical of structural steel.
1: Ultimate strength
2: Yield strength (yield point)
3: Rupture
4: Strain hardening region
5: Necking region
A: Apparent stress (F/A0)
B: Actual stress (F/A) Stress v strain A36 2.svg
figure 2: "Engineering" (red) and "true" (blue) stress–strain curve typical of structural steel.

Many materials can display linear elastic behavior, defined by a linear stress–strain relationship, as shown in figure 1 up to point 3. The elastic behavior of materials often extends into a non-linear region, represented in figure 1 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 does 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 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, figure 2); 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.

Ultimate tensile strength 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. [4]

The ultimate tensile strength is a common engineering parameter to design members made of brittle material because such materials have no yield point. [4]

Testing

Round bar specimen after tensile stress testing Al tensile test.jpg
Round bar specimen after tensile stress testing
Aluminium tensile test samples after breakage
Aluminiumzugprobe 01.jpg
The "cup" side of the "cup–cone" characteristic failure pattern
Aluminiumzugprobe 02.jpg
Some parts showing the "cup" shape and some showing the "cone" shape

Typically, the testing involves taking a small sample with a fixed cross-sectional area, and then pulling it with a tensometer at a constant strain (change in gauge length divided by initial gauge length) rate until the sample breaks.

When testing some 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. [5] This practical correlation helps quality assurance in metalworking industries to extend well beyond the laboratory and universal testing machines.

Typical tensile strengths

Typical tensile strengths of some materials
MaterialYield strength
(MPa)
Ultimate tensile strength
(MPa)
Density
(g/cm3)
Steel, structural ASTM A36 steel 250400–5507.8
Steel, 1090 mild2478417.58
Chromium-vanadium steel AISI 61506209407.8
Steel, 2800 Maraging steel [6] 261726938.00
Steel, AerMet 340 [7] 216024307.86
Steel, Sandvik Sanicro 36Mo logging cable precision wire [8] 175820708.00
Steel, AISI 4130,
water quenched 855 °C (1570 °F), 480 °C (900 °F) temper [9]
95111107.85
Steel, API 5L X65 [10] 4485317.8
Steel, high strength alloy ASTM A514 6907607.8
Acrylic, clear cast sheet (PMMA) [11] 7287 [12] 1.16
High-density polyethylene (HDPE)26–33370.85
Polypropylene 12–4319.7–800.91
Steel, stainless AISI 302 – cold-rolled520 [ citation needed ]8608.19
Cast iron 4.5% C, ASTM A-481302007.3
"Liquidmetal" alloy[ citation needed ]1723550–16006.1
Beryllium [13] 99.9% Be3454481.84
Aluminium alloy [14] 2014-T64144832.8
Polyester resin (unreinforced) [15] 5555 
Polyester and chopped strand mat laminate 30% E-glass [15] 100100 
S-Glass epoxy composite [16] 23582358 
Aluminium alloy 6061-T62413002.7
Copper 99.9% Cu70220[ citation needed ]8.92
Cupronickel 10% Ni, 1.6% Fe, 1% Mn, balance Cu1303508.94
Brass 200 +5008.73
Tungsten 941151019.25
Glass 33 [17] 2.53
E-Glass N/A1500 for laminates,
3450 for fibers alone
2.57
S-Glass N/A47102.48
Basalt fiber [18] N/A48402.7
Marble N/A152.6
ConcreteN/A2–52.7
Carbon fiber N/A1600 for laminates,
4137 for fibers alone
1.75
Carbon fiber (Toray T1100G) [19]
(the strongest human-made fibres)
 7000 fibre alone1.79
Human hair 140–160200–250 [20]  
Bamboo fiber  350–5000.4-0.8
Spider silk (see note below)10001.3
Spider silk, Darwin's bark spider [21] 1652
Silkworm silk500 1.3
Aramid (Kevlar or Twaron)362037571.44
UHMWPE [22] 24520.97
UHMWPE fibers [23] [24] (Dyneema or Spectra)2300–35000.97
Vectran  2850–33401.4
Polybenzoxazole (Zylon) [25] 270058001.56
Wood, pine (parallel to grain) 40 
Bone (limb)104–1211301.6
Nylon, molded, 6PLA/6M [26] 75-851.15
Nylon fiber, drawn [27] 900 [28] 1.13
Epoxy adhesive 12–30 [29]
Rubber16 
Boron N/A31002.46
Silicon, monocrystalline (m-Si)N/A70002.33
Ultra-pure silica glass fiber-optic strands [30] 4100
Sapphire (Al2O3)400 at 25 °C,
275 at 500 °C,
345 at 1000 °C
19003.9–4.1
Boron nitride nanotube N/A330002.62 [31]
Diamond16002800
~80–90 GPa at microscale [32]
3.5
Graphene N/Aintrinsic 130000; [33]
engineering 50000–60000 [34]
1.0
First carbon nanotube ropes ?36001.3
Carbon nanotube (see note below)N/A11000–630000.037–1.34
Carbon nanotube compositesN/A1200 [35] N/A
High-strength carbon nanotube filmN/A9600 [36] N/A
Iron (pure mono-crystal)37.874
Limpet Patella vulgata teeth (goethite whisker nanocomposite)4900
3000–6500 [37]
^a Many of the values depend on manufacturing process and purity or composition.
^b Multiwalled carbon nanotubes have the highest tensile strength of any material yet measured, with one measurement of 63 GPa, still well below one theoretical value of 300 GPa. [38] The first nanotube ropes (20 mm in length) whose tensile strength was published (in 2000) had a strength of 3.6 GPa. [39] The density depends on the manufacturing method, and the lowest value is 0.037 or 0.55 (solid). [40]
^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). [41] 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. [42]
^d Human hair strength varies by ethnicity and chemical treatments.
Typical properties for annealed elements [43]
ElementYoung's
modulus
(GPa)
Offset or
yield strength
(MPa)
Ultimate
strength
(MPa)
silicon 1075000–9000
tungsten 411550550–620
iron21180–100350
titanium 120100–225246–370
copper130117210
tantalum 186180200
tin 479–1415–200
zinc alloy85–105200–400200–400
nickel 170140–350140–195
silver83170
gold79100
aluminium7015–2040–50
lead1612

See also

Related Research Articles

Structural geology Science of the description and interpretation of deformation in the Earths crust

Structural geology is the study of the three-dimensional distribution of rock units with respect to their deformational histories. The primary goal of structural geology is to use measurements of present-day rock geometries to uncover information about the history of deformation (strain) in the rocks, and ultimately, to understand the stress field that resulted in the observed strain and geometries. This understanding of the dynamics of the stress field can be linked to important events in the geologic past; a common goal is to understand the structural evolution of a particular area with respect to regionally widespread patterns of rock deformation due to plate tectonics.

Ductility Degree to which a material under stress irreversibly deforms before failure

Ductility is a mechanical property commonly described as a material's amenability to drawing. In materials science, ductility is defined by the degree to which a material can sustain plastic deformation under tensile stress before failure. Ductility is an important consideration in engineering and manufacturing. It defines a material's suitability for certain manufacturing operations and its capacity to absorb mechanical overload. Some metals that are generally described as ductile include gold and copper. However, not all metals experience ductile failure as some can be characterized with brittle failure like cast iron. Polymers generally can be viewed as ductile materials as they typically allow for plastic deformation.

Composite material Material made from a combination of three or more unlike substances

A composite material is a material which is produced from two or more constituent materials. These constituent materials have notably dissimilar chemical or physical properties and are merged to create a material with properties unlike the individual elements. Within the finished structure, the individual elements remain separate and distinct, distinguishing composites from mixtures and solid solutions.

Youngs modulus Mechanical property that measures stiffness of a solid material

Young's modulus, the Young modulus, or the modulus of elasticity in tension or compression, is a mechanical property that measures the tensile or compressive stiffness of a solid material when the force is applied lengthwise. It quantifies the relationship between tensile/compressive stress and axial strain in the linear elastic region of a material and is determined using the formula:

In engineering, deformation refers to the change in size or shape of an object. Displacements are the absolute change in position of a point on the object. Deflection is the relative change in external displacements on an object. Strain is the relative internal change in shape of an infinitesimally small cube of material and can be expressed as a non-dimensional change in length or angle of distortion of the cube. Strains are related to the forces acting on the cube, which are known as stress, by a stress-strain curve. The relationship between stress and strain is generally linear and reversible up until the yield point and the deformation is elastic. The linear relationship for a material is known as Young's modulus. Above the yield point, some degree of permanent distortion remains after unloading and is termed plastic deformation. The determination of the stress and strain throughout a solid object is given by the field of strength of materials and for a structure by structural analysis.

Stress–strain curve Concept in engineering and materials science

In engineering and materials science, a stress–strain curve for a material gives the relationship between stress and strain. It is obtained by gradually applying load to a test coupon and measuring the deformation, from which the stress and strain can be determined. These curves reveal many of the properties of a material, such as the Young's modulus, the yield strength and the ultimate tensile strength.

Fracture Split of materials or structures under stress

Fracture is the separation of an object or material into two or more pieces under the action of stress. The fracture of a solid usually occurs due to the development of certain displacement discontinuity surfaces within the solid. If a displacement develops perpendicular to the surface, it is called a normal tensile crack or simply a crack; if a displacement develops tangentially, it is called a shear crack, slip band or dislocation.

The field of strength of materials, also called mechanics of materials, typically refers to various methods of calculating the stresses and strains in structural members, such as beams, columns, and shafts. The methods employed to predict the response of a structure under loading and its susceptibility to various failure modes takes into account the properties of the materials such as its yield strength, ultimate strength, Young's modulus, and Poisson's ratio. In addition, the mechanical element's macroscopic properties such as its length, width, thickness, boundary constraints and abrupt changes in geometry such as holes are considered.

Compressive strength Capacity of a material or structure to withstand loads tending to reduce size

In mechanics, compressive strength or compression strength is the capacity of a material or structure to withstand loads tending to reduce size. In other words, compressive strength resists compression, whereas tensile strength resists tension. In the study of strength of materials, tensile strength, compressive strength, and shear strength can be analyzed independently.

Fracture mechanics Field of mechanics which studies the propagation of cracks in materials

Fracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. It uses methods of analytical solid mechanics to calculate the driving force on a crack and those of experimental solid mechanics to characterize the material's resistance to fracture.

Work hardening Strengthening a material through plastic deformation

In materials science, work hardening, also known as strain hardening, is the strengthening of a metal or polymer by plastic deformation. Work hardening may be desirable, undesirable, or inconsequential, depending on the context.

Fracture toughness Stress intensity factor at which a cracks propagation increases drastically

In materials science, fracture toughness is the critical stress intensity factor of a sharp crack where propagation of the crack suddenly becomes rapid and unlimited. A component's thickness affects the constraint conditions at the tip of a crack with thin components having plane stress conditions and thick components having plane strain conditions. Plane strain conditions give the lowest fracture toughness value which is a material property. The critical value of stress intensity factor in mode I loading measured under plane strain conditions is known as the plane strain fracture toughness, denoted . When a test fails to meet the thickness and other test requirements that are in place to ensure plane strain conditions, the fracture toughness value produced is given the designation . Fracture toughness is a quantitative way of expressing a material's resistance to crack propagation and standard values for a given material are generally available.

Yield (engineering) Phenomenon of deformation due to structural stress

In materials science and engineering, the yield point is the point on a stress-strain curve that indicates the limit of elastic behavior and the beginning of plastic behavior. Below the yield point, a material will deform elastically and will return to its original shape when the applied stress is removed. Once the yield point is passed, some fraction of the deformation will be permanent and non-reversible and is known as plastic deformation.

Hardness is a measure of the resistance to localized plastic deformation induced by either mechanical indentation or abrasion. In general, different materials differ in their hardness; for example hard metals such as titanium and beryllium are harder than soft metals such as sodium and metallic tin, or wood and common plastics. Macroscopic hardness is generally characterized by strong intermolecular bonds, but the behavior of solid materials under force is complex; therefore, there are different measurements of hardness: scratch hardness, indentation hardness, and rebound hardness.

The specific strength is a material's strength 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.

A cryogenic treatment is the process of treating workpieces to cryogenic temperatures in order to remove residual stresses and improve wear resistance in steels and other metal alloys, such as aluminum. In addition to seeking enhanced stress relief and stabilization, or wear resistance, cryogenic treatment is also sought for its ability to improve corrosion resistance by precipitating micro-fine eta carbides, which can be measured before and after in a part using a quantimet.

Mechanical properties of carbon nanotubes

The mechanical properties of carbon nanotubes reveal them as one of the strongest materials in nature. Carbon nanotubes (CNTs) are long hollow cylinders of graphene. Although graphene sheets have 2D symmetry, carbon nanotubes by geometry have different properties in axial and radial directions. It has been shown that CNTs are very strong in the axial direction. Young's modulus on the order of 270 - 950 GPa and tensile strength of 11 - 63 GPa were obtained.

Material failure theory is an interdisciplinary field of materials science and solid mechanics which attempts to predict the conditions under which solid materials fail under the action of external loads. The failure of a material is usually classified into brittle failure (fracture) or ductile failure (yield). Depending on the conditions most materials can fail in a brittle or ductile manner or both. However, for most practical situations, a material may be classified as either brittle or ductile.


Concrete is widely used construction material all over the world. It is composed of aggregate, cement and water. Composition of concrete varies to suit for different applications desired. Even size of the aggregate can influence mechanical properties of concrete to a great extent.

References

  1. "Generic MMPDS Mechanical Properties Table". stressebook.com. 6 December 2014. Archived from the original on 1 December 2017. Retrieved 27 April 2018.
  2. Degarmo, Black & Kohser 2003 , p. 31
  3. Smith & Hashemi 2006 , p. 223
  4. 1 2 "Tensile Properties". Archived from the original on 16 February 2014. Retrieved 20 February 2015.
  5. 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)
  6. "MatWeb – The Online Materials Information Resource". Archived from the original on 15 December 2013. Retrieved 20 February 2015.
  7. "MatWeb – The Online Materials Information Resource". Archived from the original on 21 February 2015. Retrieved 20 February 2015.
  8. "MatWeb – The Online Materials Information Resource". Archived from the original on 21 February 2015. Retrieved 20 February 2015.
  9. "MatWeb – The Online Materials Information Resource". Archived from the original on 28 March 2017. Retrieved 20 February 2015.
  10. "USStubular.com". Archived from the original on 13 July 2009. Retrieved 27 June 2009.
  11. Archived 23 March 2014 at the Wayback Machine IAPD Typical Properties of Acrylics
  12. strictly speaking this figure is the flexural strength (or modulus of rupture), which is a more appropriate measure for brittle materials than "ultimate strength."
  13. "MatWeb – The Online Materials Information Resource". Archived from the original on 21 February 2015. Retrieved 20 February 2015.
  14. "MatWeb – The Online Materials Information Resource". Archived from the original on 21 February 2015. Retrieved 20 February 2015.
  15. 1 2 "Guide to Glass Reinforced Plastic (fibreglass) – East Coast Fibreglass Supplies". Archived from the original on 16 February 2015. Retrieved 20 February 2015.
  16. "Properties of Carbon Fiber Tubes". Archived from the original on 24 February 2015. Retrieved 20 February 2015.
  17. "Soda-Lime (Float) Glass Material Properties :: MakeItFrom.com". Archived from the original on 3 July 2011. Retrieved 20 February 2015.
  18. "Basalt Continuous Fibers". Archived from the original on 3 November 2009. Retrieved 29 December 2009.
  19. "Toray Properties Document" . Retrieved 17 September 2018.
  20. "Tensile Testing Hair". instron.us. Archived from the original on 28 September 2017.
  21. Agnarsson, I; Kuntner, M; Blackledge, TA (2010). "Bioprospecting Finds the Toughest Biological Material: Extraordinary Silk from a Giant Riverine Orb Spider". PLOS ONE. 5 (9): e11234. Bibcode:2010PLoSO...511234A. doi: 10.1371/journal.pone.0011234 . PMC   2939878 . PMID   20856804.
  22. Oral, E; Christensen, SD; Malhi, AS; Wannomae, KK; Muratoglu, OK (2006). "PubMed Central, Table 3". J Arthroplasty. 21 (4): 580–91. doi:10.1016/j.arth.2005.07.009. PMC   2716092 . PMID   16781413.
  23. "Tensile and creep properties of ultra high molecular weight PE fibres" (PDF). Archived from the original (PDF) on 28 June 2007. Retrieved 11 May 2007.
  24. "Mechanical Properties Data". www.mse.mtu.edu. Archived from the original on 3 May 2007.
  25. "MatWeb – The Online Materials Information Resource". Archived from the original on 21 February 2015. Retrieved 20 February 2015.
  26. https://advancednylons.co.za/Materialproperties.pdf [ bare URL PDF ]
  27. "Nylon Fibers". University of Tennessee. Archived from the original on 19 April 2015. Retrieved 25 April 2015.
  28. "Comparing aramids". Teijin Aramid. Archived from the original on 3 May 2015.
  29. "Uhu endfest 300 epoxy: Strength over setting temperature". Archived from the original on 19 July 2011.
  30. "Fols.org" (PDF). Archived from the original (PDF) on 25 July 2011. Retrieved 1 September 2010.
  31. "What is the density of Hydrogenated Boron Nitride Nanotubes (H-BNNT)?". space.stackexchange.com. Archived from the original on 13 April 2017.
  32. Dang, Chaoqun; et al. (1 January 2021). "Achieving large uniform tensile elasticity in microfabricated diamond". Science. 371 (6524): 76–78. Bibcode:2021Sci...371...76D. doi: 10.1126/science.abc4174 . PMID   33384375.
  33. 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. S2CID   206512830. Archived from the original on 19 February 2009.
  34. Cao, K. (2020). "Elastic straining of free-standing monolayer graphene". Nature Communications. 11 (284): 284. Bibcode:2020NatCo..11..284C. doi: 10.1038/s41467-019-14130-0 . PMC   6962388 . PMID   31941941.
  35. IOP.org Z. Wang, P. Ciselli and T. Peijs, Nanotechnology 18, 455709, 2007.
  36. Xu, Wei; Chen, Yun; Zhan, Hang; Nong Wang, Jian (2016). "High-Strength Carbon Nanotube Film from Improving Alignment and Densification". Nano Letters. 16 (2): 946–952. Bibcode:2016NanoL..16..946X. doi:10.1021/acs.nanolett.5b03863. PMID   26757031.
  37. Barber, A. H.; Lu, D.; Pugno, N. M. (2015). "Extreme strength observed in limpet teeth". Journal of the Royal Society Interface . 12 (105): 105. doi:10.1098/rsif.2014.1326. PMC   4387522 . PMID   25694539.
  38. 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.
  39. Li, F.; Cheng, H. M.; Bai, S.; Su, G.; Dresselhaus, M. S. (2000). "Tensile strength of single-walled carbon nanotubes directly measured from their macroscopic ropes". Applied Physics Letters. 77 (20): 3161. Bibcode:2000ApPhL..77.3161L. doi:10.1063/1.1324984. Archived from the original on 28 December 2012.
  40. K.Hata. "From Highly Efficient Impurity-Free CNT Synthesis to DWNT forests, CNTsolids and Super-Capacitors" (PDF). Archived (PDF) from the original on 12 June 2010.
  41. Elices; et al. "Finding Inspiration in Argiope Trifasciata Spider Silk Fibers". JOM. Archived from the original on 15 January 2009. Retrieved 23 January 2009.
  42. Blackledge; et al. (2005). "Quasistatic and continuous dynamic characterization of the mechanical properties of silk from the cobweb of the black widow spider Latrodectus hesperus". Journal of Experimental Biology. The Company of Biologists. 208 (10): 1937–1949. doi:10.1242/jeb.01597. PMID   15879074. S2CID   9678391. Archived from the original on 1 February 2009. Retrieved 23 January 2009.
  43. A.M. Howatson, P. G. Lund, and J. D. Todd, Engineering Tables and Data, p. 41

Further reading