I haven't checked the 4* to 40, but I see no reason why the pattern described below would not hold.
I checked leveling 1*s to 10, 2* to 20, and 3* to 30. 
Not silver, time, dungeon divers points, or anything else.
I am exploring this purely from the point of view of energy savings. I kept hearing contradictory advice regarding whether or not farming Nightmare campaign is worth it, so I wanted to check for myself. If you are using raid pass, NM campaign is just better across the board. If you are running without raid pass, I would recommend to farm brutal for 2*s (and below), but nightmare for 3*s (and above). I would like to apologize for the confusion I may have caused. It is actually 5, which cuts the savings a fair bit. 
EDIT: An earlier version of this post said that it takes 4 runs to upgrade a 2* to 20.
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