Crackling noise in fatigue fracture of heterogeneous materials

We present a theoretical study of the fatigue fracture of heterogeneous materials. A generic fiber bundle model is proposed, which provides a direct connection between the microscopic fracture mechanisms and the macroscopic time evolution of fatigue. In the model, material elements fail either due to immediate breaking or undergo a damage accumulating ageing process. On the macro-level the model reproduces the empirical Basquin law of fatigue life, and it makes possible to derive a generic scaling form for the deformation histories of different load values. On the micro-level we found that fatigue fracture is accompanied by crackling noise, i.e. the competition of the two failure modes of fibers gives rise to a complex bursting activity, where slow damage sequences trigger bursts of breaking events. In the mean field limit, the size of damage sequences and of bursts, as well as the waiting times in between, are characterized by universal power law distributions, where only the cutoffs have material dependence. When stress concentrations arise in the vicinity of failed regions, the power law distributions of noise characteristics prevail but the exponents are different from their mean field counterparts.