Carbon frame strengh Almost every question Bicycles.SE about damaged carbon frames seems to get the same answer: "the frame isn't safe anymore."

How strong of a hit is needed to break a carbon frame? There are little stones that get thrown up by the wheels and hit the bottom of the frame, from time to time the bike falls down, etc.
The real problem with carbon is that it only has two modes -- not broken and broken.  When stressed beyond its strength limits the carbon fibers break and the frame is seriously weakened.  Plus, once this has happened, the "threshold" for further damage drops lower and lower.  And, except for cracks that MAY OR MAY NOT be reasonably visible, there's no obvious warning sign of impending failure -- nothing is "bent".

Steel, on the other hand, will (unless it's super-hard stuff) "yield" ("plastic" deformation) before it breaks, and "yielding" (within limits) only slightly reduces the strength of the metal.  Thus the frame will visibly bend before it breaks (unless, of course, it's run over by a truck or some such), and catastrophic failure is very rare.

(Aluminum is somewhat in-between the other two.  It unfortunately has a tendency to "work harden", and thus can, over a long term (years of rough roads), develop cracks that lead to catastrophic failure without obvious bending before-hand.  But it reacts more like steel in the face of short-term impact-type forces.)