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Learning Objectives. To understand that once the elastic limit has been exceeded, the force-extension graphs for loading and unloading are unequal To know that such curves are called hysterisis curves. To be able to describe such graphs for different materials
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Learning Objectives To understand that once the elastic limit has been exceeded, the force-extension graphs for loading and unloading are unequal To know that such curves are called hysterisis curves. To be able to describe such graphs for different materials To describe the energy changes during loading/unloading Materials : Loading & Unloading Book Reference : Pages 170-171
Ductile materials have a very large plastic region. Just before it fails the material necks Materials : Further Definitions Cross sectional reduces, and as stress = F/A the neck sees an increase in tensile stress. Brittle materials show little plastic deformation. Failure is sudden and ‘catastrophic’. Better under compression
We have seen that providing the elastic limit of the material is not exceeded then Hooke’s law is obeyed and the graph obtained during loading and unloading will be identical Materials : Loading & Unloading However, once the limit of elasticity has been exceeded this is no longer true
Such curves are called Hysteresis curves Materials : Metal For a material such as a metal wire, the curve obtained during unloading, (red) follows parallel to the original loading curve (blue) There has been a permanent extension
Very low limit of proportionality Materials : Rubber In contrast a very elastic material such as rubber, loads and unloads in a very different way • Curled when unstretched • Uncurled when stretched • Curling / uncurling is different
Plastic deformation. Permanent extension Materials : Polythene Tangled when unstretched, weak intermolecular cross links exist between the molecules. These break during stretching but new bonds reform when the tension is removed.
Earlier we saw that the area under a force-extension graph shows the work done to stretch the material. This is more correctly called the strain energy When the graph is linear the work done during stretching is recovered when it is unloaded Materials : Strain Energy 1
Rubber... Materials : Strain Energy 2
In a material such as polythene, much of the work done during loading is used to deform the material permanently Materials : Strain Energy 3
