Andrade, Omori, and time-to-failure laws from thermal noise in material rupture

Using a simple mean-field rupture model with quenched disorder in the presence of thermal fluctuations introduced by S. Ciliberto et al., we provide an analytical theory of three ubiquitous empirical observations obtained in creep (constant applied stress) experiments: the initial Andrade-like and Omori-like 1/t decay of the rate of deformation and of fiber ruptures and the 1/(t(c)-t) critical time-to-failure behavior of acoustic emissions just prior to the macroscopic rupture. The lifetime of the material is controlled by a thermally activated Arrhenius nucleation process, describing the crossover between these two regimes, as shown by S. Ciliberto et al. Thus tiny thermal fluctuations may actually play an essential role in macroscopic deformation and rupture processes at room temperature. We also discover a reentrant dependence of the lifetime as a function of the amount of quenched disorder.