Investigating Materials
 Hooke’s Law
A material obeys Hooke’s Law if the extension is proportional to the tension applied, i.e.
F = kx
 Spring Constant (k)
A measure of the stiffness of a spring, measured in newtons per metre (N m-1)
 Elastic Limit
Below the elastic limit, a material will return to it’s original length when a tension is applied
and then removed.
 Limit of Proportionality/ Hooke’s Law Limit
The point above which tension and extension are no longer proportional. The springs
behaviour is no longer elastic but plastic.
 Energy Stored in a Spring
The area under a tension – extension graph. ΔW = ½ Fx = ½ kx2
 Plastic Flow
When a wire is deformed permanently, some of the atoms slide past each other – this
occurs at the yield point.
 Toughness
A tough material absorbs lots of energy by plastic deformation, so lots of energy is needed
to break it.
 Brittle
A brittle material cannot absorb lots of energy by plastic deformation, so needs little energy
to break it.
 Ductile
A ductile material can be pulled out into wires.
 Malleable
A malleable material can be beaten into shape.
 Tensile Stress
The tension divided by the cross sectional area is called the tensile stress, i.e. tensile
stress = tension / cross sectional area or σ = F / A.
Stress has the same units as pressure – the pascal (Pa) where 1 Pa = 1 N m-2.
 Strain
The strain of a material is the extension divided by the original length, i.e. strain =
extension / original length or ε = x / l.
Since extension and length have the same units, strain has no units.
 The Young Modulus
The gradient of a stress – strain graph is the Young Modulus, i.e. Young Modulus = stress /
strain or E = σ / ε.
Young Modulus is a measure of the stiffness of a material (a stiff material has a high
Young Modulus). The units of Young Modulus are Pa.
 Energy Density
The energy density of a wire is the area under a stress – strain curve, i.e. the work done
per unit volume of the wire.
During elastic deformation, energy density = ½ x stress x strain.
It also has the units N m-2 or Pa.
 Yielding
The yield stress is the stress at which permanent deformation occurs – i.e. where
dislocations begin to move.
 Fatigue
A material can fail even though it is below it’s below the yield stress. Loading and
unloading can produce tiny cracks that expand with time – this is called fatigue.
 Elastomers
An elastomer is a material which returns to its original shape when a distorting force is
removed, e.g. rubber.
 Hysteresis
Ever time an elastomer is stretched and released it becomes hot because energy is
absorbed. It then heats the surroundings. This is called a hysteresis loss.