org-cycle-open-archived-trees

org-cycle-open-archived-trees is a variable defined in `org.el'.
Its value is

nil

Documentation:
Non-nil means `org-cycle' will open archived trees.
An archived tree is a tree marked with the tag ARCHIVE.
When nil, archived trees will stay folded. You can still open them with
normal outline commands like `show-all', but not with the cycling commands.

You can customize this variable.