Universality behind Basquin's Law of Fatigue.

Basquin's law of fatigue states that the lifetime of the system has a power-law dependence on the external load amplitude, tf approximately sigma 0- alpha, where the exponent alpha has a strong material dependence. We show that in spite of the broad scatter of the exponent alpha, the fatigue fracture of heterogeneous materials exhibits universal features. We propose a generic scaling form for the macroscopic deformation and show that at the fatigue limit the system undergoes a continuous phase transition. On the microlevel, the fatigue fracture proceeds in bursts characterized by universal power-law distributions. We demonstrate that the system dependent details are contained in Basquin's exponent for time to failure, and once this is taken into account, remaining features of failure are universal.