What does the area between a curve and an unloading curve represent

13

So imagine a stress strain graph for a metal wire where the elastic limit has been exceeded the the wire undergoes plastic deformation. If you unload all the weights the unloading curve will be parallel to the loading curve but shifted to the right (as it will intersect the x axis not at 0 due to its permanent extension even at a fornce of 0N). What would the area between these two curves represent?

I understand the area under the loading curve would be the elastic energy stored in the wire (and also the work done to extend it) so would the area between represent some sort of lost elastic energy?

Thanks

Reply 1

hecandothatfromran

2

Original post by Davelittle

So imagine a stress strain graph for a metal wire where the elastic limit has been exceeded the the wire undergoes plastic deformation. If you unload all the weights the unloading curve will be parallel to the loading curve but shifted to the right (as it will intersect the x axis not at 0 due to its permanent extension even at a fornce of 0N). What would the area between these two curves represent?

I understand the area under the loading curve would be the elastic energy stored in the wire (and also the work done to extend it) so would the area between represent some sort of lost elastic energy?

Thanks

The area under the unloading curve represents the energy released from EPE (usually as heat/ke). Therefore, the area enclosed by the loading and unloading curve represents the work done in order to impose the permanent extension in the spring.

Reply 2

dr-jimmy

Original post by Davelittle

So imagine a stress strain graph for a metal wire where the elastic limit has been exceeded the the wire undergoes plastic deformation. If you unload all the weights the unloading curve will be parallel to the loading curve but shifted to the right (as it will intersect the x axis not at 0 due to its permanent extension even at a fornce of 0N). What would the area between these two curves represent?

I understand the area under the loading curve would be the elastic energy stored in the wire (and also the work done to extend it) so would the area between represent some sort of lost elastic energy?

Thanks

The area between the curves is lost energy- the elastic energy is converted into different forms, hence why elastic bands can get hotter when they stretch and recoil. :smile:

Reply 3

Stonebridge

13

It's the difference in the work done by you loading the wire and the work done by the wire when being unloaded.
The difference is the work done (useful energy) not recovered in the process. This was the work done (energy) that was required to permanently deform the material.

With elastic deformation all the energy from the work you do extending the wire is stored as elastic p.e.
All of this energy is recovered when the wire returns to its original length.

Reply 4

Davelittle

OP

13

ok so it's the work that has been done to permanently deform the material (so lost elastic potential energy) that you won't recover when the material is fully unloaded. :smile:

Thanks!

What does the area between a curve and an unloading curve represent

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