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# Tensile strength

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 Ftu within equations,[1][2][3] is the capacity of a material or structure to withstand loads tending to elongate, as opposed to compressive strength, which withstands loads tending to reduce size. In other words, tensile strength resists tension (being pulled apart), whereas compressive strength resists compression (being pushed together). Ultimate tensile strength is measured by the maximum stress that a material can withstand while being stretched or pulled before breaking. In the study of strength of materials, tensile strength, compressive strength, and shear strength can be analyzed independently.

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.

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 can be defined for liquids as well as solids under certain conditions. For example, when a tree[4] draws water from its roots to its upper leaves by transpiration, the column of water is pulled upwards from the top by the cohesion of the water in the xylem, and this force is transmitted down the column by its tensile strength. Air pressure, osmotic pressure, and capillary tension also plays a small part in a tree's ability to draw up water, but this alone would only be sufficient to push the column of water to a height of less than ten metres, and trees can grow much higher than that (over 100 m).

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), or kilo-pounds per square inch (ksi, or sometimes kpsi), which is equal to 1000 psi; kilo-pounds per square inch are commonly used in one country (US), when measuring tensile strengths.

## Concept

### Ductile materials

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.

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.

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.[5]

The UTS is a common engineering parameter to design members made of brittle material because such materials have no yield point.[5]

## Testing

Round bar specimen after tensile stress testing

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

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 6,370 MPa, the UTS of a derived composite is 3,040 MPa – less than half the strength of the fiber.[7]

## Typical tensile strengths

Typical tensile strengths of some materials
Material Yield strength
(MPa)
Ultimate tensile strength
(MPa)
Density
(g/cm³)
Steel, structural ASTM A36 steel[8] 250 400–550 7.8
Steel, 1090 mild 247 841 7.58
Chromium-vanadium steel AISI 6150 620 940 7.8
Human skin 15 20 2
Steel, 2800 Maraging steel[9] 2617 2693 8.00
Steel, AerMet 340[10] 2160 2430 7.86
Steel, Sandvik Sanicro 36Mo logging cable precision wire[11] 1758 2070 8.00
Steel, AISI 4130, water quenched 855 °C (1570 °F), 480 °C (900 °F) temper[12] 951 1110 7.85
Steel, API 5L X65[13] 448 531 7.8
Steel, high strength alloy ASTM A514 690 760 7.8
Acrylic, clear cast sheet (PMMA)[14] 72 87[15] 1.16
High-density polyethylene (HDPE) 26–33 37 0.85
Polypropylene 12–43 19.7–80 0.91
Steel, stainless AISI 302 – cold-rolled 520[citation needed] 860 8.19
Cast iron 4.5% C, ASTM A-48 130 200 7.3
"Liquidmetal" alloy[citation needed] 1723 550–1600 6.1
Beryllium[16] 99.9% Be 345 448 1.84
Aluminium alloy[17] 2014-T6 414 483 2.8
Polyester resin (unreinforced)[18] 55 55
Polyester and chopped strand mat laminate 30% E-glass[18] 100 100
S-Glass epoxy composite[7] 2358 2358
Aluminium alloy 6061-T6[19] 270 310 2.7
Copper 99.9% Cu[20] 69 220[citation needed] 8.92
Cupronickel 10% Ni, 1.6% Fe, 1% Mn, balance Cu 130 350 8.94
Brass 200 + 500 8.73
Tungsten 941 1510 19.25
Glass   33[21] 2.53
E-Glass N/A 1500 for laminates,
3450 for fibers alone
2.57
S-Glass N/A 4710 2.48
Basalt fiber[22] N/A 4840 2.7
Marble N/A 15 2.6
Concrete N/A 2–5 2.7
Carbon fiber N/A 1600 for laminates,
4137 for fibers alone
1.75
Carbon fiber (Toray T1000G)[23] (the strongest man-made fibres)   6370 fibre alone 1.80
Human hair 140–160 200–250[24]
Bamboo   350–500 0.4
Spider silk (see note below) 1000 1.3
Spider silk, Darwin's bark spider[25] 1652
Silkworm silk 500   1.3
Aramid (Kevlar or Twaron) 3620 3757 1.44
UHMWPE[26] 24 52 0.97
UHMWPE fibers[27][28] (Dyneema or Spectra) 2300–3500 0.97
Vectran   2850–3340
Polybenzoxazole (Zylon)[29] 2700 5800 1.56
Wood, pine (parallel to grain)   40
Bone (limb) 104–121 130 1.6
Nylon, molded, type 6/6 450 750 1.15
Nylon fiber, drawn[30] 900[31] 1.13
Rubber 16
Boron N/A 3100 2.46
Silicon, monocrystalline (m-Si) N/A 7000 2.33
Ultra-pure silica glass fiber-optic strands[33] 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 2.62[34]
Diamond 1600 2800 3.5
Graphene N/A 130000[35] 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[36] N/A
High-strength carbon nanotube film N/A 9600[37] N/A
Iron (pure mono-crystal) 3 7.874
Limpet Patella vulgata teeth (Goethite) 4900
3000–6500[38]
^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 labs producing them at a tensile strength of 63 GPa,[39] still well below their theoretical limit of 300 GPa.[citation needed] The first nanotube ropes (20 mm in length) whose tensile strength was published (in 2000) had a strength of 3.6 GPa.[40] The density depends on the manufacturing method, and the lowest value is 0.037 or 0.55 (solid).[41]
^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).[42] 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.[43]
^d Human hair strength varies by ethnicity and chemical treatments.
Typical properties for annealed elements[44]
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 alloy 85–105 200–400 200–400
nickel 170 140–350 140–195
silver 83 170
gold 79 100
aluminium 70 15–20 40–50

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