1.1. To understand that once the elastic limit has To understand that once the elastic limit has been exceeded, the force-extension graphs been exceeded, the force-extension graphs for loading and unloading are unequalfor loading and unloading are unequal

2.2. To know that such curves are called hysterisis To know that such curves are called hysterisis curves.curves.

3.3. To be able to describe such graphs for To be able to describe such graphs for different materialsdifferent materials

4.4. To describe the energy changes during To describe the energy changes during loading/unloadingloading/unloading

Book Reference : Pages 170-171Book Reference : Pages 170-171

DuctileDuctile materials have a very materials have a very large plastic region. Just before large plastic region. Just before it fails the material necksit fails the material necks

Cross sectional reduces, and as stress = F/A the neck sees Cross sectional reduces, and as stress = F/A the neck sees an increase in tensile stress. an increase in tensile stress.

BrittleBrittle materials show little plastic deformation. Failure is materials show little plastic deformation. Failure is sudden and ‘catastrophic’. Better under compressionsudden and ‘catastrophic’. Better under compression

We have seen that providing the elastic limit of We have seen that providing the elastic limit of the material is not exceeded then Hooke’s law is the material is not exceeded then Hooke’s law is obeyed and the graph obtained during loading obeyed and the graph obtained during loading and unloading will be identical and unloading will be identical

However, once the limit However, once the limit of elasticity has been of elasticity has been exceeded this is no longer exceeded this is no longer truetrue

For a material such as a metal wire, the curve For a material such as a metal wire, the curve obtained during unloading, (red) follows parallel obtained during unloading, (red) follows parallel to the original loading curve (blue)to the original loading curve (blue)

There has been a permanent extensionThere has been a permanent extension

Such curves are Such curves are called Hysteresis called Hysteresis curvescurves

In contrast a very In contrast a very elastic material such elastic material such as rubber, loads and as rubber, loads and unloads in a very unloads in a very different waydifferent way

Very low limit of Very low limit of proportionalityproportionality

•Curled when unstretchedCurled when unstretched

•Uncurled when stretchedUncurled when stretched

•Curling / uncurling is differentCurling / uncurling is different

Plastic deformation.Plastic deformation.

Permanent extensionPermanent extension

Tangled when unstretched, weak intermolecular cross Tangled when unstretched, weak intermolecular cross links exist between the molecules. These break during links exist between the molecules. These break during stretching but new bonds reform when the tension is stretching but new bonds reform when the tension is removed.removed.

Earlier we saw that the area under a force-Earlier we saw that the area under a force-extension graph shows the work done to extension graph shows the work done to stretch the material. This is more correctly stretch the material. This is more correctly called the called the strain energystrain energy

When the graph is linear the work done When the graph is linear the work done during stretching is recovered when it is during stretching is recovered when it is unloadedunloaded

Rubber...Rubber...

In a material such as polythene, much of the In a material such as polythene, much of the work done during loading is used to deform work done during loading is used to deform the material permanentlythe material permanently