The Collaborative International Dictionary of English v.0.48:

Frangibility \Fran`gi*bil"i*ty\, n. [Cf. F. frangibilit['e].]
   The state or quality of being frangible. --Fox.
   [1913 Webster]

WordNet (r) 3.0 (2006):

frangibility
    n 1: quality of being easily damaged or destroyed [syn:
         fragility, breakability, frangibleness,
         frangibility]