Stress, Strain and Elastic Energy

A material subjected to a pair of opposite forces might deform.
Forces stretching material = tensile.
Forces squashing material = compressive.
Stress = tension (force applied) / CSA.
Units of stress = Nm^-2 or pascals (Pa).
Strain = extension (change in length) / original length.
Units of strain = none, given as a number or percentage.
Doesn’t matter whether forces producing stress and strain are tensile or compressive - same equations apply.
Think of tensile forces as positive and compressive forces as negative.

Greater and greater tensile force applied to material - stress on it increases.
Effect of stress is to start to pull atoms apart from one another.
Stress becomes so great that atoms separate completely, material fractures.
Shown on stress-strain graph where it curves towards the bottom. Fracture stress - the stress at which this occurs.
UTS = ultimate tensile strength - maximum stress material can withstand before breaking.
Engineers have to consider UTS and fracture stress of materials when designing a structure.

Material is stretched or compressed - work is done in deforming material.
Graph of force against extension - work done is given by area under graph.
Before elastic limit - all work done in stretching or compressing material is stored as energy in material.
This stored energy is called elastic strain energy.

Provided a material obeys Hooke’s Law, strain energy stored inside it can be calculated.
Work done on an elastic material in stretching = energy stored in material as elastic strain energy.
Work done = force X displacement.
Force on material isn’t constant. It rises from zero up to force (F). To calculate work done, use average force between zero and F:
Work done = 1/2FX.
Elastic strain energy (E) = E = 1/2FX
As Hooke’s Law is being obeyed, F = Kx, F can be replaced in the equation to give:
E = 1/2kx^2.
Material stretches beyond elastic limit - some work is done separating atoms. This energy will not be stored as elastic strain energy, and so isn’t released when force is removed.