Would a carbon disk be brittle or easily damaged by impact on the edge?

Qualification: I have held a Concorde carbon/carbon brake disk in my hands while visiting the facility in LA that made them many years ago.  And I worked a bit with carbon/carbon nose tips on intercontinental ballistic missiles where they get warm on re-entry  (like 15,000 degrees K), but I am no expert and long out of date. 

My suspicion: carbon brake disk plus runway and rocks = time to order a new carbon brake disk.  I suspect they will get nicked, dinged, chipped, or possibly worse.   However, I learned today that carbon brake disks are the hot set up on motorcycles now.  Hmmmm……

Fred