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The following is what I read:

If, however, the elastic limit is exceeded, only the elastic strain will be recovered, and the plastic strain will remain as permanent set. The stress in the material will unload along a path parallel to the elastic modulus.

What is the difference between Permanent set and Elastic limit?

It is given that the stress in the material will unload parallel to the elastic modulus. Why is this the case? Also, is yield point and elastic limit two different points or the same? From the graph below it seems like they both are the same point. Stress - Strain Graph

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    $\begingroup$ The 'permanent set' is all the plastic deformation you have introduced. The unloading is indeed parallel to the elastic loading line since the material still has that elastic response in addition to the plastic response. The permanent set achieved depends on how far up the plastic deformation line you go - somewhere between c and d will yield more permanent set. Not that deformation to the 'elastic limit' actually induces some permanent set. $\endgroup$
    – Jon Custer
    Oct 23, 2019 at 13:56

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What is the difference between Permanent set and Elastic limit?

Permanent set is the deformation that stays in the material after the applied stress is removed. The elastic limit is the maximum stress that is still within the materials elastic range. If you apply a greater stress then the elastic limit, you get permanent set in the object - it gets deformed in a way that it doesn't fully recover when the load is removed.

It is given that the stress in the material will unload parallel to the elastic modulus. Why is this the case?

For a well behaved material, the plastic deformation shouldn't change the Young's modulus. This means that the loading behaviour in the new elastic range will still have the same slope, but because it is permanently set, it now has a strain even when all the applied stress is removed (this strain is the permanent/plastic deformation).

Also, is yield point and elastic limit two different points or the same?

They are synonyms in most contexts. Especially in simple engineering curves like this, yield is the point when plastic deformation begins to occur, and elastic limit is the limit where elastic deformation stops, so that makes them functionally identical.

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  • $\begingroup$ In most engineering definitions, the 'elastic limit' is actually after a little plastic deformation (0.1 to 1%). This has caused issues in some tight designs at work - the designers trusted the handbook numbers and pushed right up to the 'limit' that wasn't the right limit for their purposes. $\endgroup$
    – Jon Custer
    Oct 23, 2019 at 15:18
  • $\begingroup$ @JonCuster What definitions are they using? If we take elastic limit as "the maximum extent to which a solid may be stretched without permanent alteration of size or shape." doesn't that make it by definition the point where plastic deformation begins? $\endgroup$
    – JMac
    Oct 23, 2019 at 15:22
  • $\begingroup$ You would think so, but for materials properties in engineering handbooks they have often adopted a slightly different definition. Some small plastic deformation is allowed before the 'elastic limit'. Then, adding in a safety factor normally leaves the final design well within the elastic range. Well, until some designer has the bright idea to take something up to the elastic limit and expects nothing to happen. $\endgroup$
    – Jon Custer
    Oct 23, 2019 at 18:34
  • $\begingroup$ @JonCuster Would that be the "true elastic limit" they talk about here? en.wikipedia.org/wiki/Yield_(engineering)#Definition To me, it still seems like "elastic limit" and "yield point" are still trying to refer to the same thing. I don't see anything in the definitions that really makes a clear distinction. $\endgroup$
    – JMac
    Oct 23, 2019 at 19:05
  • $\begingroup$ It is more like the 'proof stress' a bit further down. $\endgroup$
    – Jon Custer
    Oct 23, 2019 at 20:23

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