Weapons have explicitly listed hardnesses and hit points:
Many medieval weapons were known for breaking; most notably, in jousting, breaking a lance scored points:
Given that in D&D we often have impressive characters using unimpressive weapons (think weapons sized for Medium creatures used by Large creatures, or a 30 strength score), it seems to make sense to me that striking might logically break your weapon, but I'm not sure if that's in the rules.
From a strictly balance perspective, there might be uses for weapon breakage:
Then again, the rules explicitly reference sundering as a way of breaking a weapon:
And from a DMing perspective, it seems like it would be a lot of extra bookkeeping.
What's the right way?
I have seen fumble rolls break weapons, and leather armor go bad after a rainstorm if not maintained in games. That's different.
I'm referring more explicitly to attacks. If a weapon is used to attack, does it suffer damage, which if beyond the weapon's DR, could take away its hit points? Over time, this would result in a broken weapon, but not right away.