6.2 Elastic and plastic behaviour

Elastic deformation disappears when the load is removed; plastic deformation remains. The elastic limit is the greatest load or stress before permanent deformation begins.

Separate the elastic limit from the limit of proportionality: a material may stop being linear before it becomes permanently deformed.

A metal wire unloaded within its elastic region returns to its original length; loaded beyond its elastic limit it remains longer.

Elastic does not mean perfectly linear, and plastic does not mean the object has already broken.

Work done by a changing force is the area under the force–extension graph, W=∫F dx; for a linear spring from zero, W=½Fx=½kx².

Use the loading path and the correct graph axes. The area represents energy transferred into elastic or other deformation stores.

A spring reaching 0.20 m under 40 N with a straight-line graph stores 4.0 J of elastic energy.

The area is not simply F×final extension unless force is constant; unloading can enclose a different area when energy is dissipated.

A material deformed within its elastic limit stores elastic potential energy, equal to the work done in deforming it.

The energy is recoverable when the load is removed. Use the loading force–extension relationship rather than assuming all deformation energy is retained.

A stretched spring can return to its original length while releasing its stored elastic energy to a moving mass.

Elastic potential energy is not the same as gravitational potential energy, and plastic deformation can dissipate some input energy.

Within the proportional region, E_P=½Fx=½kx² because the average force during loading is F/2.

Use final force and extension only for a straight-line force–extension graph from zero. For a non-linear graph, find the area under the curve.

A spring with k=200 N m⁻¹ stretched 0.10 m stores 1.0 J.

Do not use Fx for a spring whose force changes during loading; that would overestimate the work by a factor of two in the linear case.