  Slow crack growth in a model of homogenous brittle elastic material is
described as a thermal activation process where stress fluctuations allow to
overcome a breaking threshold through a series of irreversible steps. We study
the case of a single crack in a flat sheet for which analytical predictions can
be made, and compare them with results from the equivalent problem of a 2D
spring network. Good statistical agreement is obtained for the crack growth
profile and final rupture time. The specific scaling of the energy barrier with
stress intensity factor appears as a consequence of irreversibility. In
addition, the model brings out a characteristic growth length whose physical
meaning could be tested experimentally.
