What is Poisson's ratio?
This is a specific form of Hooke's law of elasticity. The units of Young's modulus in the English system are pounds per square inch (psi), stress-strain relation. The change in length per unit length (Δl/l) is called the For small change in the length of the wire, the ratio of the longitudinal stress to the Young's modulus of elasticity of the wire. Stress is the force on unit areas within a material that develops as a result of the For particular expressions of Hooke's law in this form, see bulk modulus;.
While discussing this graph, let's observe that, although the Hooke's law approximation for U r is symmetrical about its minimum, these curves and more realistic curves are not.
- Young's modulus, Hooke's law and material properties
- Elasticity: Young’s modulus & Hooke’s Law
- What is Hooke's Law?
This asymmetry about the minimum in U r is responsible for the thermal expansion of most condensed phases: At finite temperatures, the atoms are not found exactly at the minimum of U, because they have finite kinetic energy due to their thermal motion. Oversimplifying in the interests of brevity, we can argue that the average value of U at a value above the minimum lies to the right of the minimum, and increases as more thermal energy is added.
Deriving Young's modulus from atomic forces The curves shown above are simple polynomials. They are analytical approximations to realistic interatomic forces, but will illustrate how to relate atomic properties to macroscopic material properties.
Consider the potential where A, B, n and m are constants that we shall discuss below. Using 2 and rearranging: We can substitute this value into 1 to get the minimum value U r0.
In a diatomic molecule, this value would give an estimate of the binding energy but, as it's more complicated for a crystal, we'll leave that calculation aside. The sketch shows a simple model of a crystalline solid.
Elasticity: Young's modulus & Hooke's Law - SchoolWorkHelper
In the horizontal x axis, the interatomic separation is r. In both perpendicular directions, the separation is y, as shown in this sketch.
Young's modulus Y for a material is defined as the ratio of tensile stress to tensile strain. However, the repulsive term is simply a convenient, differentiable function that gives a very strong repulsion.
So, we have related Young's modulus to individual atomic forces and energies: To relate Hooke's law to Young's modulus in the experiment above, it would be necessary to consider bending of the wire.
In bending, one side of an object is stretched and the other compressed. Not to be confused with[ edit ] Material stiffness should not be confused with these properties: Usage[ edit ] Young's modulus enables the calculation of 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.
Hooke’s Law and Modulus of Elasticity
The Young's modulus directly applies to cases of uniaxial stress, that is tensile or compressive stress in one direction and no stress in the other directions. Young's modulus is also used in order to predict the deflection that will occur in a statically determinate beam when a load is applied at a point in between the beam's supports. Other elastic calculations usually require the use of one additional elastic property, such as the shear modulusbulk modulus or Poisson's ratio.
Any two of these parameters are sufficient to fully describe elasticity in an isotropic material. Linear versus non-linear[ edit ] Young's modulus represents the factor of proportionality in Hooke's lawwhich relates the stress and the strain.
However, Hooke's law is only valid under the assumption of an elastic and linear response. Any real material will eventually fail and break when stretched over a very large distance or with a very large force; however all solid materials exhibit nearly Hookean behavior for small enough strains or stresses. If the range over which Hooke's law is valid is large enough compared to the typical stress that one expects to apply to the material, the material is said to be linear.
Otherwise if the typical stress one would apply is outside the linear range the material is said to be non-linear.