In solid mechanics, the slope of the stress-strain curve at any point is called the tangent modulus. The tangent modulus of the initial, linear portion of a stress-strain curve is called Young’s modulus, also known as the tensile modulus. It is defined as the ratio of the uniaxial stress over the uniaxial strain in the range of stress in which Hooke’s Law holds. is a measure of the stiffness of an elastic material and is a quantity used to characterize materials. It can be experimentally determined from the slope of a stress-strain curve created during tensile tests conducted on a sample of the material. In anisotropic materials, Young’s modulus may have different values depending on the direction of the applied force with respect to the material’s structure.
It is also commonly, but incorrectly, called the elastic modulus or modulus of elasticity, because Young’s modulus is the most common elastic modulus used, but there are other elastic moduli measured, too, such as the bulk modulus and the shear modulus.
Young’s modulus is named after Thomas Young, the 19th century British scientist. However, the concept was developed in 1727 by Leonhard Euler, and the first experiments that used the concept of Young’s modulus in its current form were performed by the Italian scientist Giordano Riccati in 1782, predating Young’s work by 25 years.
Young’s modulus is the ratio of stress, which has units of pressure, to strain, which is dimensionless; therefore, Young’s modulus has units of pressure.
The SI unit of modulus of elasticity (E, or less commonly Y) is the pascal (Pa or N/m² or m−1·kg·s−2). The practical units used are megapascals (MPa or N/mm²) or gigapascals (GPa or kN/mm²). In United States customary units, it is expressed as pounds (force) per square inch (psi).
The Young’s modulus calculates the change in the dimension of a bar made of an isotropic elastic material under tensile or compressive loads. For instance, it predicts how much a material sample extends under tension or shortens under compression. Some calculations also require the use of other material properties, such as the shear modulus, density, or Poisson’s ratio. It also helps in selection of materials for particular structural applications.
Linear versus non-linear
For many materials, Young’s modulus is essentially constant over a range of strains. Such materials are called linear, and are said to obey Hooke’s law. Examples of linear materials are steel, carbon fiber and glass. Non-linear materials include rubber and soils, except under very small strains.
Young’s modulus is not always the same in all orientations of a material. Most metals and ceramics, along with many other materials, are isotropic, and their mechanical properties are the same in all orientations. However, metals and ceramics can be treated with certain impurities, and metals can be mechanically worked to make their grain structures directional. These materials then become anisotropic, and Young’s modulus will change depending on the direction from which the force is applied. Anisotropy can be seen in many composites as well. For example, carbon fiber has much higher Young’s modulus (is much stiffer) when force is 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 structures.
Young’s modulus, E, can be calculated by dividing the tensile stress by the tensile strain in the elastic (initial, linear) portion of the stress-strain curve:
- E is the Young’s modulus (modulus of elasticity)
- 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.
via Young’s modulus