Does Applecare Cover Dents. This is beyond Apples control. The answer depends on whether you have AppleCare and how bad the damage is.

Every iPhone comes with one year of hardware repair coverage through its limited warranty and up to 90 days of complimentary technical supportBoth AppleCare and AppleCare with Theft and Loss extend that coverage 1 and give you additional features such as 247 priority tech support and accidental damage protection. As long as there is something to turn it or not if you have theftloss coverage you can get a replacement phone provided you a are willing to pay the deductible and b have an incident left. They should definitely replace it.
Buy an AppleCare plan on your device.
Apples basic device warranties cover manufacturer defects or failures like bending dents or dead pixels. This is beyond Apples control. However if the damage is more serious than depending on the severity it will be qualified either Tier1 or Tier2 Service Event. The length of the warranty and what exactly it covers and doesnt cover varies depending on the manufacturer but AppleCare lasts for one year and covers any defects and things that break that arent the fault of the user eg the power button randomly not working anymore etc.
