# Density, ρ

Density is the mass per unit volume of a material, a measure of how much mass each cubic metre of volume contains. Density if given by the equation:

Where ρ is density, m is mass in kilograms and V is volume in metres cubed.

Density is measured in kilograms per metre cubed, kg/m3 or kg m-3

# Elasticity

Materials extend in length when a stress is applied to them (masses hung from them). A material can be described as elastic if it returns to its original length when the stress is removed. They obey Hooke’s Law as extension is proportional to the force applied.

# Limit of Proportionality, P

Up to this point the material obeys Hooke’s Law; extension is proportional to the force applied.

# Elastic Limit, E

The elastic limit is the final point where the material will return to its original length if we remove the stress which is causing the extension (take the masses off). There is no change to the shape or size of the material.

We say that the material acts plastically beyond its elastic limit.

# Yield Point, Y

Beyond the elastic limit a point is reached where small increases in stress cause a massive increase in extension (strain). The material will not return to its original length and behaves like a plastic.

# Plasticity

Materials extend in length when a stress is applied to them (masses hung from them). A material can be described as plastic if it does not return to its original length when the stress is removed. There is a permanent change to its shape

# Breaking Stress – Ultimate Tensile Strength, UTS

This is the maximum amount of stress that can be applied to the material without making it break. It is sometimes referred to as the strength of the material.

# Breaking Point, B

This is (surprisingly?) the point where the material breaks.

# Stiffness

If different materials were made into wires of equal dimensions, the stiffer materials bend the least.

Stiff materials have low flexibility

# Ductility

A ductile material can be easily and permanently stretched. Copper is a good example, it can easily be drawn out into thin wires. This can be seen in graph d below.

# Brittleness

A brittle material will extend obeying Hooke’s Law when a stress is applied to it. It will suddenly fracture with no warning sign of plastic deformation. Glass, pottery and chocolate are examples of brittle materials.

# Stress-Strain Graphs

In the first graph we see a material that stretches, shows plastic behaviour and eventually breaks.

In the second graph we can see that material a is stiffer than material b because the same stress causes a greater strain in b.

In the third graph we see materials c and e are brittle because they break without showing plastic behaviour.

The fourth graph shows how a material can be permanently deformed, the wire does not return to its original length when the stress is removed (the masses have been removed).