# (3)Young's Modulus and Stress

- Created by: Olatunde
- Created on: 24-03-14 13:32

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Young's Modulus

Stiffness of material. Young Modulus = Stress/Strain. In GPa or

Nm^2.

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

force.

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

double.

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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