Materials
Hooke's Law
The ratio of the force exerted on an elastic material to the extension of the material, up to the limit of proportionality.
Newtons per Metre - Nm−1
\(F=ke\)
Limit of Proportionality
The maximum extension for which extension in directly proportional to the load on the material
Elastic Limit
The maximum extension for which the material will return to it's original shape
Elastic Deformation
Will return to it's original shape once load is remove: Not permanent
Plastic Deformation
Will not return to it's original shape once load is remove: Permanent
Young's Modulus
Ratio of stress and strain of a material, up to limit of proportionality
Pascals - \(Pa\)
Stress
Ratio of force exerted to the area across which it is applied
Pascals - \(1\,Pa=1\,Nm^{2}\)
Strain
Ratio of extension to original length
Unitless
\(E=\frac{Stress}{Strain}=\frac{Fl}{eA}\)
\(Strain=\frac{e}{l}\)
\(Stress=\frac{F}{A}\)
Brittle Materials
Show no plastic deformation before fracture
Density
Mass per unit volume
\(kg\,m^{-3}\)
\(\rho=\frac{m}{V}\)
Breaking Stress
The stress at which a material will fracture
Ultimate Tensile Stress
The maximum stress that a material can be subject to
Elastic Strain Energy
The energy stored in an elastic material, that is released when the material returns to it's original shape
\(E=\frac{1}{2}Fe=\frac{1}{2}ke^{2}\)
Force Extension Graphs
Gradient
Spring constant
Area
Elastic strain energy stored up to that extension
- Springs in series add spring constant
- Springs in parallel add inverses of spring constants and take inverse
Stress-Strain curve
Gradient
Youngs modulus (Up to LOP)
Area
Energy stored per unit volume of material up to that point
When cracks form in the structure of the material, as the material is stretched beyond the elastic limit, there is no movement of particles into these cracks to prevent the small cracks from becoming much larger - causing material to fracture.
Rigid Structure