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# Ultimate tensile strength  ( Materials Science )

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Ultimate tensile strength ( UTS), often shortened to tensile strength ( TS), ultimate strength, or $F_\text\left\{tu\right\}$ within equations, is the maximum stress that a material can withstand while being stretched or pulled before breaking. In materials the ultimate tensile strength is close to the , whereas in materials the ultimate tensile strength can be higher.

The ultimate tensile strength is usually found by performing a 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.

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

Ductile materials
[[File:Stress v strain Aluminum 2.png|thumb|left|figure 1: "Engineering" stress–strain (σ–ε) curve typical of aluminum
1. Ultimate strength
2.
3. Proportional limit stress
4. Fracture
5. Offset strain (typically 0.2%) ]]

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 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 members because design practices dictate the use of the . 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.

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

Testing
Typically, the testing involves taking a small sample with a fixed cross-sectional area, and then pulling it with a 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.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) 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 7.8 7.58 7.8 8.00 7.86 8.00 7.85 7.8 7.8 1.16 0.85 0.91 8.19 7.3 6.1 1.84 2.8 2.7 8.92 8.94 8.73 19.25 2.53 2.57 2.48 2.7 2.6 2.7 1.75 1.79 0.4 1.3 1.3 1.44 0.97 0.97 1.56 1.6 1.15 1.13 – 2.46 2.33 3.9–4.1 2.62 3.5 1.0 1.3 0.037–1.34 N/A N/A 7.874 Limpet Patella vulgata teeth (Goethite) 49003000–6500
Many of the values depend on manufacturing process and purity or composition.
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. The first nanotube ropes (20 mm in length) whose tensile strength was published (in 2000) had a strength of 3.6 GPa. The density depends on the manufacturing method, and the lowest value is 0.037 or 0.55 (solid).
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). 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.
Human hair strength varies by ethnicity and chemical treatments.

 +Typical properties for annealed elementsA.M. Howatson, P. G. Lund, and J. D. Todd, Engineering Tables and Data, p. 41 5000–9000 550–620 350 246–370 210 200 15–200 200–400 140–195 170 100 40–50 12

• Flexural strength
• Strength of materials
• Tensile structure
• Tension (physics)
• Young's modulus

• Giancoli, Douglas, Physics for Scientists & Engineers Third Edition (2000). Upper Saddle River: Prentice Hall.
• T Follett, Life without metals
• George E. Dieter, Mechanical Metallurgy (1988). McGraw-Hill, UK

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