You can find examples of this in testing of micro- or nanoscale whiskers. Those thin wires can grow without any defect, thus you can load them to their theoretical strength, upon which the lattice finally collapses locally (this would be at the surface) and nucleation of a dislocation takes place.

Another example would be during nanoindentation of well annealed materials, where the small probed volume is again defect free, causing an nucleation-controlled elastic-plastic transition as evidenced by a pop-in.

An just for completeness, these perfect crystals you think of won't be really perfect, as they still contain vacancies.Which is evidenced by their electrical resistivity as well as the fact that the presence of single or multiple vacancies can have quite an effect on the pop-in behavior during nanoindentation.

You are on the right track. Perfect crystals would be amazingly elastic (and brittle). But a large stress would induce creation of imperfections. They dislocation would  be born and then would slip as usual.

You can find examples of this in testing of micro- or nanoscale whiskers. Those thin wires can grow without any defect, thus you can load them to their theoretical strength, upon which the lattice finally collapses locally (this would be at the surface) and nucleation of a dislocation takes place.

Another example would be during nanoindentation of well annealed materials, where the small probed volume is again defect free, causing an nucleation-controlled elastic-plastic transition as evidenced by a pop-in.

An just for completeness, these perfect crystals you think of won't be really perfect, as they still contain vacancies.Which is evidenced by their electrical resistivity as well as the fact that the presence of single or multiple vacancies can have quite an effect on the pop-in behavior during nanoindentation.

Only from a crystallographic point of view a short remark: Actually, plastically deformed means that the crystal does not change the volume, what dos not mean that it cannot change the shape :-). Sound surprising but it means that you can (theoretically) deform a crystal perfectly until the all dislocation left the crystal. Then you observe a change of shape, the volume is the same, the crystal is plastically deformed, but it is still perfect.

Immediately if you introduced dislocations (e.g by nano-indentation or anything else) the crystal is already no more perfect and plastically deformed. In so far, any measurement of elastic constants is a more or less close to the exact values. As Daniel pointed out: the term perfect needs to be put in the right perspective.  

Dear Gert Nolze, your mean that perfect crystal (lattice-defect-free crystal) still can make permanent deformation which only deforms the shape of a crystalline not the volume? As far as I consider, I think the elastic parameters only rely on interatomic forces , and the plastic parameters depend not only on interatomic forces but also its array of atoms disorder (e.g. dislocations). So I agree with Igor's point that perfect crystal is some kind of extremely brittle material and cannot allow any permanent deformation. Thanks for answering！：-）

It is perhaps best explained by the attached image copied from the given link. Plastic deformation per se means delta V=0. What you call plastic deformation is a technical term which includes both, a plastic deformation (where all dislocations already left the crystal) and a perhaps big amount of pinned dislocations which are responsible for the accumulated elastic deformation (delta V0).

http://images.google.de/imgres?imgurl=http%3A%2F%2Fpracticalmaintenance.net%2Fwp-content%2Fuploads%2FStages-of-Plastic-Deformation.jpg&imgrefurl=http%3A%2F%2Fpracticalmaintenance.net%2F%3Fp%3D1135&h=199&w=527&tbnid=d95KnvKVBKzKeM%3A&docid=uQsK_LEWyPTLFM&ei=3HVnV4bXNcWTa460rJgK&tbm=isch&iact=rc&uact=3&dur=353&page=1&start=0&ndsp=56&ved=0ahUKEwiGtcbx5rXNAhXFyRoKHQ4aC6MQMwglKAIwAg&bih=1032&biw=1920