Would you say that steel is elastic or viscoelastic?

In elasticity, when in the elastic range, deformation did not depend on time at all. If you deform the material very fast, or if you deformed it very slow, you would always have the
same stress strain curve.

If a material has elastic properties and not viscoelastic properties then there is no damping in the elastic range.

If this is true, you could take a cantilever beam, pull it back and then release it (theoreticly that is).

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The beam would oscilate back and fowardth forever (neglecting wind resistance and other small factors)

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But in the real world, if you were to conduct this experiment, the beam would come to a stop as if there were some internal friction or damping. On page 1 of Goodier and Timeshenko's elasticity book, steel is said to be not quite homogenous but still can be considdered elastic.

I have searched on the net and can not find what steel is defined as, elastic or viscoelastic. Does anyone know which it is and if there is a place to find a listing of materials and this property?