will jailbreak cause any damage to the device
During the process of jail-breaking an iDevice, there can be complications.  It can sometimes render the device unusable or it can brick the device. 

The device being unusable is usually fixable by simply putting the phone in DFU mode and restoring the software back onto the device.  This would cause your device to lose its information such as contacts, emails, photos, apps, app information.  This is usually recoverable because we usually have a back up.

When a device is bricked, it will not function. Your iDevice will not turn on, as if the device has no battery at all or will just sit at the Apple Logo and keep restarting.  This is the worst case scenario.  Sometimes, a brick device can be restored.  This is very very rare occurrence though and never usually happens. 

If my iDevice is not working, you take it to the Genius Bar.  Make an appointment and see a Genius.  Now, if you take a jailbroken iDevice to a Genius, they can not service them in their current condition.  

Example: I have a battery issue where the battery only lasts half an hour, I take it to the Genius Bar and tell them that this is happening, I am under warranty.  They will look over your device and inspect it to see if something else could be causing the issue before replacement.  They see it is jailbroken.  Usually they will tell you that reason this could be happening is because it is jailbroken.  You did something to the iDevice that you "weren't" supposed to, so it is technically your fault.  Every time this happens though, they will tell you to just go home and restore it back to normal.  Removing the Jailbreak might fix the issue, if it doesn't, bring it back un-jailbroken and they will replace it.

This is just a small example of one of the things that would cause you to go to the Genius Bar to have service done.  But it shows that if your device can be looked through and they can tell it is jailbroken because they can see the software that is on it is obviously jailbroken, they can not act on their warranty until the jailbreak is removed.  

This being said, if your device is bricked or you device is at a point where your device can't be powered on or they can not turn it on to see it is jailbroken, then they will assume positive intent and replace it under warranty if it possible about 80% of the time. (Physically Damaged Items are Replaced for a Fee).  This is never a sure fire thing but just optimistic and don't say that you have ever jailbroken your device if they ask.

So, if you are going to try and jailbreak your iDevice, the best thing you can do is learn as much as possible about it before hand.  Know the risks that come with it.  Always have a back up of your information.  Don't update to the newest version of iOS if you are on an older version because it will remove the jailbreak.  And if you are having issues with your iDevice and it might need to be replaced, simply remove the jailbreak before hand, see if that fixes the issue, if not, then take it in.  As long as it is under warranty and it isn't jailbroken, you should be fine, or as long as they can't tell it is jailbroken (IE it won't boot and you obviously didn't smash it or disassemble it and it is totally obvious that you did)

I hope that this helps clear some things up about jail-breaking and helps you out.