  We present a model for the thermally activated propagation of cracks in
elastic matrices. The propagation is considered as a subcritical phenomenon,
the kinetics of which being described by an Arrhenius law. In this law, we take
the thermal evolution of the crack front into account, assuming that a portion
of the released mechanical energy is transformed into heat in a plastic process
zone. We show that such a model leads to a two-phase crack propagation: a first
phase at low velocity in which the temperature elevation is of little effect
and the propagation is mainly governed by the mechanical load and by the
toughness of the medium, and a second phase in which the crack is thermally
weakened and propagates at greater velocity. Such a dual behavior can
potentially explain the usual stick-slip in brittle fracturing, and we
illustrate how with numerical simulations of mode I cracks propagating in thin
disordered media. In addition, we predict the existence of a limiting ambient
temperature above which the weakened phase ceases to exist and we propose this
critical phenomenon as a novel explanation for the brittle-ductile transition
of solids.
