In solid mechanics, Young's modulus or modulus of elasticity (and also elastic modulus) is a measure of the stiffness of a given material. It is defined as the limit for small strains of the rate of change of stress with strain. This can be experimentally determined from the slope of a stress-strain curve created during tensile test s conducted on a sample of the material.
Units
The SI unit of modulus of elasticity is the Pascal.
Other units
The modulus of elasticity can also be measured in other units of pressure, for example pounds per square inch (psi).
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.
Linear vs Non-linear
For many materials, Young's modulus is a constant over a range of strains. Such materials are called linear, and are said to obey Hooke's law. Examples of linear materials include steel, carbon fiber and glass. Rubber is a non-linear material.
Calculation
The modulus of elasticity, λ, can be calculated by dividing the stress by the strain, i.e.
where
λ is the modulus of elasticity, measured in pascals
F is the force, measured in newtons
A is the cross-sectional area through which the force is applied, measured in square metres
x is the extension, measured in metres
l is the natural length, measured in metres
Tension
The modulus of elasticity of a material can be used to calculate the tension force it exerts under a specific extension.
where
T is the tension, measured in newtons
Elastic potential energy
The elastic potential energy stored is given by the integral of this expression with respect to x, i.e. energy stored E is given by:
where
E is the elastic potential energy, measured in joules
Approximate values
Approximate Young's Moduli of Various Solids
Material |
Young's modulus (E) in MPa
|
Young's modulus (E) in PSI
|
Young's modulus (E) in [GPa] (source cornell university) |
Soft cuticle of pregnant locust
|
0.21 |
30 |
Rubber (small strain)
|
6.9 |
1000 |
Shell membrane of egg
|
7.58 |
1100 |
Human cartilage
|
24.13 |
3500 |
Human tendon
|
551.6 |
80,000 |
Wallboard |
1,379 |
200,000 |
Unreinforced plastics, polyethene, nylon
|
1,379 |
200,000 |
Plywood
|
6,895 |
1,000,000 |
Wood (along grain)
|
6,895 |
1,000,000 |
Fresh bone
|
20,685 |
3,000,000 |
Magnesium metal
|
41,370 |
6,000,000 |
Ordinary glasses
|
68,950 |
10,000,000 |
Aluminium alloys
|
68,950 |
10,000,000 |
Brasses and bronzes
|
117,215 |
17,000,000 |
103 - 124 |
Titanium (Ti)
|
|
|
116 |
Iron and steel
|
206,850 |
30,000,000 |
Beryllium (Be)
|
|
|
200 - 289 |
Aluminium oxide (Al2O3) (Sapphire)
|
413,700 |
60,000,000 |
390 |
Tungsten carbide (WC)
|
|
|
450 -650 |
Silicon carbide (SiC)
|
|
|
450 |
Diamond (C)
|
1,172,150 |
170,000,000 |
1000 |
See also
Last updated: 02-06-2005 14:20:04
Last updated: 05-03-2005 17:50:55