Can I use my warranty for this?

I got an iPhone 5c in December 2013 and my warranty doesn't wear out until December 30 2014, my friend dropped my phone and it shattered. A few weeks later it's shutting off by itself and it takes a few tries to get it back on. Then it finally gives out and stops Turing on. Can I use my warranty to get a new one for something like this?

You can always try. Most warranties depend on the wording you use to describe the condition. My best advice is to focus on the functionality issues NOT why it started. Do not mention your friend dropping it, only that your experiencing hardship because it won't stay on.

Hope this helps