The warranty on your iPhone covers only manufacturing defects. It does not cover user-caused damage.
The glass cracked like it did because you dropped it. Nothing in Apple's information claims that the glass is invulnerable to damage due to being dropped, only that it's more resistant to scratches. What Otterbox claims for their cases I don't know.
Anyway, it's been reported that in some cases, an Apple Store has taken pity on a user in a similar situation and replaced the iPhone without charge. It won't hurt to take the iPhone to an Apple Store, explain what happened, and hope they take pity on you. They're not obligated, though, and if they can't do anything for you without charge, Apple will replace the iPhone for a flat fee; see the Repair Pricing section here:
There are independent iPhone repair services that may be able to replace the screen for less. Do a web search for "iphone repair".