The elastic limit means that if you extend the material beyond that point and then unload the material it will suffer a permanent deformation.
So you extend your material beyond the elastic limit and then remove the force.
Which graph gives a reasonable unloading curve such that at zero force there is a positive extension?
Your first graph.
You have to be a little careful about the energy stored in the material.
You should use the area of the unshaded triangle rather than the area of the shaded triangle.
Now as long as the graph is a straight line through the origin it does not matter but as when this is not so it does.
The area of the unshaded triangle represents the work done by the load in extending the material by $50.0$ cm.
The assumption is then made that all of that work done by the load is stores as elastic potential energy in the material.
Now continue beyond the elastic limit "under" the graph which still represents the work done by the load in extending the material but this is no longer the elastic potential energy stored in the spring.
The elastic potential energy stored in the material is the area "under" the blue graph and the area between those two graphs represents the work done by the load in permanently extending the material - that is, permanently breaking bonds.