Solids

Hooke's Law

States that F α Δx provided the limit of proportionality has not been exceeded.

F=k\Delta x

where k, spring constant is the force needed to extend the material by 1m.

Notes

Tensile force causes stretching.

Compressive force causes squashing.

k will be the same whether you stretch or squash the spring

Force - extension graph

Gradient: spring constant

Area: elastic strain energy

Energy stored in a spring

E=\frac12Fe=\frac12ke^2

Elastic Deformation

Goes back to original shape once load is removed.

Extension is temporary as atoms move relative to their equilibrium position without changing their overall position.

Plastic Deformation

Material becomes permanently deformed when the load is removed.

Resulting extension will be permanent as atoms do not return to their original position.

Stress

The force a material can take per unit area.

Strain

The ratio of extension to the original length.

\gamma=\frac{F\times x}{A\times\Delta x}

Stress - strain graph

Yield Point

A large amount of plastic deformation will take place with a small or reduced load.

Stress - Strain Terminology

Strong: Copes with a lot of stress before it breaks

Weak: Break if subject to too much stress

Stiff: Doesn't stretch much when loaded

Ductile: Stretches a lot under plastic deformation before breaking

Brittle: Undergoes no plastic deformation