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The movement of a purely elastic interface driven on a disordered energy potential is characterized by a depinning transition: when the pulling force σ is larger than some critical value the system is in a flowing regime and moves at a finite velocity. On the other hand, if the interface remains pinned and its velocity is zero. We show that in the case of a one-dimensional interface, the inclusion of viscoelastic relaxation produces the appearance of an intervening regime between the pinned and the flowing phases in a well-defined stress interval , in which the interface evolves through a sequence of avalanches that give rise to a creep process. As the creep velocity vanishes as a power law. As the creep velocity increases as a power law due to the increase of the typical size of the avalanches. The present observations may serve to improve the understanding of fatigue failure mechanisms.
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