## Young’s Modulus Basics

In just the same way as resistance applies to a particular object or device, resistivity refers to the material from which the object is made. So, everybody knows Hooke’s Law – the law of springs refers to a particular spring, like a bed spring. We know that a force/extension graph is linear until we exceed the elastic limit (sometimes but not always coinciding with the limit of proportionality), thereafter the elastic behaviour is replaced by some degree of plasticity, until it yields then it fractures. A quick graphical reminder should help.

How could it be refined to take account of the material we happen to be trying to stretch?

First, it’s not just springs that stretch. Everything is stretchy to some extent because everything is held together with chemical bonds which are subject to deforming forces, so behave a little bit like spiral springs.

A few important words at this point, because different materials behave in different ways dependent on their constitution.

We need to know the meanings of the following words:

Elastic behaviour is shown by a material which returns to its original size and shape after deforming forces are removed.

Plastic behaviour is shown by materials which permanently deform after the stress is removed. Many materials undergo Hookian elastic behaviour followed by a plastic region (called the yield curve) where the layers of atoms tend to slide over each other. Copper is a good example of a material having an initial elastic region, then a plastic region where larger stresses are applied. Here’s a picture…

Stiffness= k – the measure of the resistance offered by the body to deforming forces – the slope or gradient of the force/extension graph. Stiff materials don’t deform much under large tensile forces. You should be able to see that in the graph above is

k = 10/20 = 0.50 N mm-1

Strong materials are those which can withstand large stresses without failure

Tough materials have the ability to absorb energy and deform plastically without fracturing.

Hard materials are those which are resistant to deformation, opposite, obviously to soft.

Brittle materials break without absorbing much energy and without significant deformation. Glass ‘snaps’ and the two halves fit together – an indication of brittleness.

Malleable materials are those which deform under compressive stress – in other words are easily hammered into shapes. Gold and copper are malleable so are used to make jewellery

Ductile materials are those like copper which deform under tensile (pulling) stress – so can easily be drawn out into wires and show the characteristic ‘necking’ as in the diagram

Also, in an exam, you might be asked to suggest a material which is stiff AND strong, for example.

We need to know the definitions of :

Stress(symbol sigma) = force/area (newtons per square metre)

Tensile strength or fracture stress is the stress applied to a material before it fractures.

Yield stress or yield strength is  the stress applied to a material before it deforms.

Strain (symbol epsilon) = original length/change in length (has no units)

Some values for Young’s Moduli: