1. Molecular Explanation of Hooke’s Law
When the stress is zero the mean separation of the moleculesis ro
A tensile stress acts in opposition to the attractive forces between the ions and is therefore capable of increasing their separation

2. Intermolecular force
For values of r close to ro the graph can be considered to be linear, and provided that the stress is not so large as to take the intermolecular separation out of this region equal increases in tensile stress will produce equal increases in extension
r=ro
Intermolecular separation
The energy used in stretching the wire is stored in the potential energy of the stretched individual bonds.
Note that this graph also implies that Hooke’s Law applies to compresion

3. Stress Strain Curves

4. Stress Strain Curve For A Ductile Material
Ductility is a term used to describe a material which can be deformed plastically. Hence a ductile material is one which can be drawn into wires.
e.g. Copper and mild steel are ductile whereas
concrete and cast Iron are brittle

5. Stress Strain Graph For a Ductile Material
point of maximum stress
elastic limit
(yield point)
stress
N/m2
breaking stress
fracture
limit of proportionality
strain

6. Stress Strain Graph For Cast Iron
It can be seen that the concrete curve is almost a straight line.
There is an abrupt end to the curve.
This, and the fact that it is a very steep line, indicate that it is a brittle material.
The curve for cast iron has a slight curve to it. It is also a brittle material.
Both of these materials will fail with little warning once their limits are surpassed.
Cast Iron
breaking stress
fracture
stress
N/m2
breaking stress
concrete
strain

7. Note the position of stress and strain on the graph axes.
Note that strain is a pure number
Up to the elastic limit,
the graph takes the form y=mx
stress
Nm-2
The gradient of this graph is called the modulus of elasticiy or:
Young’s Modulus
Young’s Modulus (E) = tensile stress
tensile strain
strain

8. The Units of Young’s modulus
Young’s Modulus (E) = tensile stress
tensile strain
tensile strain has no units So the dimensions of Young’s modulus are identical to the dimensions of stress (Nm-2)
However as force units can be written as kgms-2
F = m a
(N) = kg ms-2
and stress =Force/Area
i.e. kgms-2m-2
So Young’s modulus is often written in the units
kg m -1s-2