Super-Arrhenius dynamics for sub-critical crack growth in two-dimensional disordered brittle mediaP.-P. Cortet, L. Vanel and S. Ciliberto
Laboratoire de Physique, CNRS UMR 5672, Ecole Normale Supérieure de Lyon 46 allée d'Italie, 69364 Lyon Cedex 07, France
received 7 November 2005; accepted in final form 21 March 2006
published online 7 April 2006
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 Gaussian 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 , where is related to the thermodynamical temperature and to the disorder variance.
05.70.Ln - Non-equilibrium and irreversible thermodynamics.
62.20.Mk - Fatigue, brittleness, fracture and cracks.
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