I present a model study of brittle fracture of polymers. I show that the re
lation nu=nu( F) between the crack-tip velocity nu and the driving force F
exhibit discontinuous transitions and hysteresis. For short polymers, at th
e onset of crack propagation the polymer chains separate by pulling out the
molecular chains, while a discontinuous transition to a new state of rapid
crack motion occurs at higher driving force, where the polymer chains brea
k. In contrast to earlier atomistic studies of crack motion involving britt
le materials such as silicon, for short polymers we find (at zero temperatu
re) that the onset of crack motion is continuous, i.e., the crack-tip veloc
ity nu increases continuously from zero when F is increased above the criti
cal value F (c) necessary for starting crack motion. The difference is attr
ibuted to inertia, which is less important during pull-out of the molecular
chains, than in models where the crack motion involves breaking strong sho
rt-ranged bonds. I also present a detailed study of the polymer chain pull-
out process. (C) 1999 American Institute of Physics. [S0021-9606(99)50119-0
].