12-15 rounds per minute is what the AR can take as a sustained rate of fire for an indefinite length of time without overheating.
So....yes....you can overheat and damage the barrel (on any rifle). 140 rounds or so continuous can raise the chamber temp to the "cookoff" point- which isn't a good thing, either...
This isn't an issue for most shooters since any reasonable rate of fire will be well below that.