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A: Proportional limit| B: Elastic limit| C: Upper YP | D: Lower YP

Let us say, the gage length was 100mm (random, just for the sake of understanding). I know that if I unload the body anywhere between OB (O is the origin), the body will return back to its original shape and size. So if in the region OB it got to a length of say 102mm while loading, after unloading the body will again come back to 100mm.

I have two questions,

  1. If suppose, I stretch the body up to anywhere in the region BC to a length of 104mm (say), then while unloading the body, the body wont come back to 100mm but to somewhere say 103mm. (some elastic recovery will take place). I have seen this in one of the videos on Youtube but I want to make sure if this is right?

  2. If suppose I stretch the body up to anywhere in the region DE to say 110mm, then on unloading will the body remain at 110mm itself or will it show some recovery?

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Question 1: Elastic recovery will always take place until the material surpasses the Ultimate Tensile Strength (UTS) of it. This means that when ever you load a material and if it doesn't surpass its UTS, then it won't fracture but will be longer in length (in a Tensile loading) than its initial length when unloaded. Between B and C, the material is on the verge of moving past the yield strength and it is extremely small, like negligible. But yes, you are right that there will be some permanent plastic deformation but it is going to be so small in the frame of B and C as compare to the elastic recovery that we can consider it negligible. Most of the times, engineers don't even care of the region between B and C since it is not a point of interest unless you are doing your PhD onto the material behavior during this region frame. Usually the point B is completely taken out of context by the engineers and there only exist point A and C, where A is the propotionality limit and C is the Yield Strength or in other words, Elastic limit.

Question 2: The body always show elastic recovery unless it surpasses the Ultimate Tensile Strength of the material. The fact is that the permanent plastic deformation after going past Yield Strength point and then getting unloaded will be considerable and might also be observable/measurable as compare to the permanent plastic deformation that we get in the region between B and C.

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Generally what happens is that if when the load is removed (quasi statically) the material will return in a path which is parallel to the elastic region.

Eg. for load up to E and F the following behaviour is observed.

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Notice that the slope of the red arrows is identical to the slope of OA section (region up to proportionality point).

hysteresis

If the load is not removed quasi-statically (fancy word for very slowly), then the path that the material returns to the point will change. (see black lines).

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This is because the internal damping of the material has an additional stiffening effect.

Despite the change in the path, the final position that the material eventually returns to should remain the same (assuming you are not doing this in elevated temperatures etc).

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