You may have been sarcastic here, but I can't be sure from the context, and I've met plenty of people who actually didn't understand this, so I'm going to reply as if it were an honest question.
Yes, a larger piece of a given material, of a given thickness will be more prone to breakage. If you want to see an example of this in action, here's how:
1) Buy a cheap wooden yard stick.
2) Place it across 2 chairs, such that only a few inches on either end are touching the chairs.
3) Press down on the yardstick in the middle until it breaks.
4) Repeat with the progressively smaller pieces until you can no longer press hard enough to break the yardstick.
You'll notice as you repeat the process, it will take more and more force to bend the smaller pieces of the yardstick to their respective breaking points.