Can I send my journal article (under review) for a invited Elsevier book (not-to-be-refereed) chapter?
If you had published your paper on a journal and you had transferred the copyright to that journal, it's a violation of copyright. And typically you transfer the copyright at the time of submission. 

If you want to republish your paper somewhere else, you should first ask permission to the copyright owner.

Beware, moreover, that most of the invitations to "publish your research" in a book come from predatory publishers. In case, you don't want to send them any of your works.