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Encyclopedia > Young's modulus

The SI unit of modulus of elasticity (E, or less commonly Y) is the pascal. Given the large values typical of many common materials, figures are usually quoted in megapascals or gigapascals. Some use an alternative unit form, kN/mm², which gives the same numeric value as gigapascals. Look up si, Si, SI in Wiktionary, the free dictionary. ... For other uses, see Pascal. ...

The modulus of elasticity can also be measured in other units of pressure, for example pounds per square inch. A pressure gauge reading in PSI (red scale) and kPa (black scale) The pound-force per square inch (symbol: lbf/inÂ²) is a non-SI unit of pressure based on avoirdupois units. ...

## Usage

The Young's modulus allows the behavior of a material under load to be calculated. For instance, it can be used to predict the amount a wire will extend under tension, or to predict the load at which a thin column will buckle under compression. Some calculations also require the use of other material properties, such as the shear modulus, density, or Poisson's ratio. This article is about engineering. ... In materials science, shear modulus, G, or sometimes S or Î¼, sometimes referred to as the modulus of rigidity, is defined as the ratio of shear stress to the shear strain:[1] where = shear stress; force acts on area ; = shear strain; length changes by amount . ... For other uses, see Density (disambiguation). ... Figure 1: Rectangular specimen subject to compression, with Poissons ratio circa 0. ...

### Directional materials

Most metals and ceramics, along with many other materials, are isotropic: their mechanical properties are the same in all directions, but metals and ceramics can be treated to create different grain sizes and orientations. This treatment makes them anisotropic, meaning that Young's modulus will change depending on which direction the force is applied from. However, some materials, particularly those which are composites of two or more ingredients have a "grain" or similar mechanical structure. As a result, these anisotropic materials have different mechanical properties when load is applied in different directions. For example, carbon fiber is much stiffer (higher Young's modulus) when loaded parallel to the fibers (along the grain). Other such materials include wood and reinforced concrete. Engineers can use this directional phenomenon to their advantage in creating various structures in our environment. Copper is an excellent conductor of electricity and is used to transmit electricity over long distance cables, however copper has a relatively low value for Young's modulus at 130 GPa and it tends to stretch in tension. When the copper cable is bound completely in steel wire around its outside this stretching can be prevented as the steel (with a higher value of Young's modulus in tension) takes up the tension that the copper would otherwise experience. Isotropy (the opposite of anisotropy) is the property of being independent of direction. ... Look up anisotropy in Wiktionary, the free dictionary. ... Carbon fiber composite is a strong, light and very expensive material. ... For other uses, see Wood (disambiguation). ... Reinforced concrete at Sainte Jeanne dArc Church (Nice, France): architect Jacques Dror, 1926â€“1933 Reinforced concrete, also called ferroconcrete in some countries, is concrete in which reinforcement bars (rebars) or fibers have been incorporated to strengthen a material that would otherwise be brittle. ...

## Calculation

Young's modulus, E, can be calculated by dividing the tensile stress by the tensile strain: Stress is a measure of force per unit area within a body. ... In any branch of science dealing with materials and their behaviour, strain is the geometrical expression of deformation caused by the action of stress on a physical body. ...

$E equiv frac{mbox {tensile stress}}{mbox {tensile strain}} = frac{sigma}{varepsilon}= frac{F/A_0}{Delta L/L_0} = frac{F L_0} {A_0 Delta L}$

where

E is the Young's modulus (modulus of elasticity) measured in pascals;
F is the force applied to the object;
A0 is the original cross-sectional area through which the force is applied;
ΔL is the amount by which the length of the object changes;
L0 is the original length of the object.

For other uses, see Pascal. ...

### Force exerted by stretched or compressed material

The Young's modulus of a material can be used to calculate the force it exerts under a specific strain.

$F = frac{E A_0 Delta L} {L_0}$

where F is the force exerted by the material when compressed or stretched by ΔL.

From this formula can be derived Hooke's law, which describes the stiffness of an ideal spring: Hookes law accurately models the physical properties of common mechanical springs for small changes in length. ...

$F = left( frac{E A_0} {L_0} right) Delta L = k x ,$

where

$k = begin{matrix} frac {E A_0} {L_0} end{matrix} ,$
$x = Delta L ,$

### Elastic potential energy

The elastic potential energy stored is given by the integral of this expression with respect to L: The elastic potential energy stored in an elastic string or spring of natural length l and modulus of elasticity Î» under an extension of x is given by: This equation is often used in calculations of positions of mechanical equilibrium. ...

$U_e = int {frac{E A_0 Delta L} {L_0}}, dL = frac {E A_0 {Delta L}^2} {2 L_0}$

where Ue is the elastic potential energy.

The elastic potential energy per unit volume is given by:

$frac{U_e} {A_0 L_0} = frac {E {Delta L}^2} {2 L_0^2} = frac {1} {2} E {varepsilon}^2$, where $varepsilon = frac {Delta L} {L_0}$ is the strain in the material.

This formula can also be expressed as the integral of Hooke's law:

$U_e = int {k x}, dx = frac {1} {2} k x^2$

## Approximate values

Young's modulus can vary somewhat due to differences in sample composition and test method. The values here are approximate.

Approximate Young's moduli of various solids
Material Young's modulus (E) in GPa Young's modulus (E) in lbf/in² (psi)
Rubber (small strain) 0.01-0.1 1,500-15,000
PTFE (Teflon) 0.5 75000
Low density polyethylene 0.2 30,000
Polypropylene 1.5-2 217,000-290,000
Bacteriophage capsids 1-3 150,000-435,000
Polyethylene terephthalate 2-2.5 290,000-360,000
Polystyrene 3-3.5 435,000-505,000
Nylon 3-7 290,000-580,000
Oak wood (along grain) 11 1,600,000
High-strength concrete (under compression) 30 4,350,000
Magnesium metal (Mg) 45 6,500,000
Aluminium alloy 69 10,000,000
Glass (see also diagram below table) 65-90 9,400,000-13,000,000
Brass and bronze 103-124 17,000,000
Titanium (Ti) 105-120 15,000,000-17,500,000
Copper (Cu) 110-130 16,000,000-19,000,000
Carbon fiber reinforced plastic (50/50 fibre/matrix, unidirectional, along grain) 125-150 18,000,000 - 22,000,000
Wrought iron and steel 91-109 30,000,000
Beryllium (Be) 287 41,500,000
Tungsten (W) 400-410 58,000,000-59,500,000
Silicon carbide (SiC) 450 65,000,000
Tungsten carbide (WC) 450-650 65,000,000-94,000,000
Single carbon nanotube [1] 1,000+ 145,000,000
Diamond (C) 1,050-1,200 150,000,000-175,000,000
Influences of selected glass component additions on Young's modulus of a specific base glass ([3]).

This article or section does not cite any references or sources. ... In engineering mechanics, deformation is a change in shape due to an applied force. ... Look up hardness in Wiktionary, the free dictionary. ... Hookes law accurately models the physical properties of common mechanical springs for small changes in length. ... In materials science, shear modulus, G, or sometimes S or Î¼, sometimes referred to as the modulus of rigidity, is defined as the ratio of shear stress to the shear strain:[1] where = shear stress; force acts on area ; = shear strain; length changes by amount . ... // The impulse excitation technique is a nondestructive test method that uses natural frequency, dimensions and mass of a test-piece to determine Youngs modulus, Shear modulus, Poissons ratio and damping coefficient. ... This article is about the deformation of materials. ... Stress is a measure of force per unit area within a body. ... In materials science and metallurgy, toughness is the resistance to fracture of a material when stressed. ... Yield strength, or the yield point, is defined in engineering and materials science as the stress at which a material begins to plastically deform. ... This is a list of materials properties. ...

## References

1. ^ International Union of Pure and Applied Chemistry. "modulus of elasticity (Young's modulus), E". Compendium of Chemical Terminology Internet edition.
2. ^ The Rational Mechanics of Flexible or Elastic Bodies, 1638-1788: Introduction to Leonhardi Euleri Opera Omnia, vol. X and XI, Seriei Secundae. Orell Fussli.
3. ^ Glassproperties.com

IUPAC logo The International Union of Pure and Applied Chemistry (IUPAC) (Pronounced as eye-you-pack) is an international non-governmental organization established in 1919 devoted to the advancement of chemistry. ... Compendium of Chemical Terminology (ISBN 0-86542-684-8) is a book published by IUPAC containing internationally accepted definitions for terms in chemistry. ...

Results from FactBites:

 Elastic modulus - Wikipedia, the free encyclopedia (369 words) An elastic modulus, or modulus of elasticity, is the mathematical description of an object or substance's tendency to be deformed when a force is applied to it. Young's modulus is a mathematical consequence of the Pauli exclusion principle. The shear modulus or modulus of rigidity (
 Rubbers and Elastomers - An Introduction (1552 words) Their modulus is affected by both the cross-link density and the ambient temperature. The modulus shows an almost linear increase as the cross-link density increases but is mainly manipulated for engineering purposes by use of relatively large quantities of solid particulate materials called fillers. The early part of the Tensile curve is linear and the gradient of this is taken as a measure of the Youngs Modulus of the material (E).
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