(3)Young's Modulus and Stress

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  • Created on: 24-03-14 13:32
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Young's Modulus
Stiffness of material. Young Modulus = Stress/Strain. In GPa or
Stress = Force applied/Cross sectional Area. In Nm^2 or GPa
Strain = Extension/Original Length. No units.
Density = Mass/Volume
Elastic or Plastic
No material is absolutely rigid. Even a concrete floor changes shape as you walk across it. The behaviour
of a material subjected to a tensile (pulling) or compressive (pushing) force can be described as either
elastic or plastic.
a material is elastic if it returns to its original shape and size when the force is removed
a material is plastic if it does not return to its original shape and size when the force is removed
Most materials are elastic for a certain range of forces, up to the elastic limit, beyond which they are
plastic. Plasticine and play dough are plastic for all forces.
Hooke attempted to write a simple rule that describes the behaviour of all materials subjected to a tensile
Hooke's law states that:
the extension of a sample of material is proportional to the stretching force e F
this can be written as F = ke
where k represents the stiffness of the sample and has units of N m ­1
If the extension is proportional to the stretching force, then doubling the force causes the extension to
Metals and springs `obey' Hooke's law up to a certain limit, called the limit of proportionality. For small
extensions, the extension is proportional to the stretching force. Rubber and other polymeric solids do not
show this pattern of behaviour.
A polymeric solid is one made up of long chain molecules.
The graphs below contrast the behaviour of different materials subjected to an increasing stretching force.
Copper is a ductile material, which means that it can be drawn into wires. It is also malleable,
which means that it can be reshaped by hammering and bending without breaking. When stretched
beyond the point E on the graph it retains its new shape.
Rubber does not follow Hooke's law and it remains elastic until it breaks.
Glass is brittle it follows Hooke's law until it snaps.

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Kevlar is tough it can withstand shock and impact.
Mild steel is durable it can withstand repeated loading and unloading.
Diamond is hard it cannot be easily scratched.
Storing Energy
Some elastic materials are intended to absorb energy. The more a material is extended, the greater the
force required.
The energy stored as a material is deformed is represented by the area between the curve and the
extension axis.…read more

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