Young's modulus
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 tests conducted on a sample of the material.
The Young's modulus allows engineers and other scientists to calculate the behavior of a material under load. 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.
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.
Approximate Young's Moduli of Various Solids
| Material
| Young's modulus (E) in MPa
| Young's modulus (E) in PSI
|
| 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
|
| Iron and steel
| 206,850
| 30,000,000
|
| Aluminium oxide (sapphire)
| 413,700
| 60,000,000
|
| Diamond
| 1,172,150
| 170,000,000
|
The modulus of elasticity of a material can be used to calculate the force it exerts under a specific extension. For an object with modulus of elasticity λ and natural length l under an extension of x, the tension T is given by:
- <math>T = \frac{\lambda x}{l}<math>
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:
- <math>E = \frac{\lambda x^2}{2 l}<math>
See also: Deformation, Stress, Strain
