Final answer:
When a slinky does not return to its original shape after being stretched, it has been deformed in the plastic region of the stress-strain curve, indicating permanent deformation.
Step-by-step explanation:
When you stretch a slinky and it does not return to its original shape, you have stretched it into the plastic region of the stress-strain curve. In this region, the material has undergone plastic deformation and does not come back to its initial shape and size when the stress becomes zero. Initially, as stress is increased, there is a linear region where the material obeys Hooke's Law. This linear behavior ends at the linearity limit (point H).
Beyond this point, the stress-strain relationship becomes nonlinear but still elastic until the elasticity limit (point E). Past the elasticity limit E, we enter the plastic region, where permanent deformation occurs. Upon release of the load, for instance at point P, the material will relax to a new permanent shape and size following the green line on the stress-strain curve.