Super - Arrhenius dynamics for sub - critical crack growth in disordered brittle media

– Taking into account stress fluctuations due to thermal noise, we study thermally activated irreversible crack growth in disordered media. The influence of material disorder on sub-critical growth of a single crack in two-dimensional brittle elastic material is described through the introduction of a rupture threshold distribution. We derive analytical predictions for crack growth velocity and material lifetime in agreement with direct numerical calculations. It is claimed that crack growth process is inhibited by disorder: velocity decreases and lifetime increases with disorder. More precisely, lifetime is shown to follow a super-Arrhenius law, with an effective temperature θ − θ d , where θ is related to the thermodynamical temperature and θ d to the disorder variance. Introduction. – Sub-critical rupture occurs when a material is submitted to a stress lower than a critical threshold. It is known since the early work of Zhurkov or Brenner [1, 2] that sub-critical rupture can be thermally activated. However, prediction of the lifetime, i.e. the time it takes for a sample to break under a given load, has proved difficult when the material is heterogeneous. In addition, although there have been several theoretical attempts to predict the lifetime for homogeneous [3–5] and sometimes disordered [6, 7] elastic materials, there have been very few theoretical studies of the actual rupture dynamics in heterogeneous media when thermal activation is the driving mechanism [8–10]. Recently, this dynamics has been modelled for a single macroscopic crack in two-dimensional homogeneous elastic media taking into account stress fluctuations [11]. This model has been successfully faced with experiments of crack growth in fax paper sheets even though this material is actually heterogeneous [12]. In the present letter, we will take into account heterogeneity by introducing, in the thermal activation rupture model, disorder in the rupture thresholds. We will show that disorder slows down macroscopic crack growth contrary to previous results [8,9] that show the rupture dynamics to be accelerated by disorder in the case of diffuse damage.