Elastic limit
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The elastic limit is the point at which a material no longer undergoes a change in strain linearly proportional to the change in stress. At stress levels below the elastic limit the material is said to be elastic.
Once the material exceeds this limit, it is said to have undergone plastic deformation (also known as permanent deformation). This implies that the material will no longer return to its original length and it's elatic properties have been lost - it will no longer obey Hooke's Law.
This is only correct when referring to metals. For elastomers, such as rubber, the elastic limit is extremely large. It doesn't obey Hooke's Law and doesn't undergo and plastic/permanent deformation. Initially it can be easily stetched but becomes stiffer as the stress increases. Once it is released, it will return to its original length.