Crackling noise in sub-critical fracture of heterogeneous materials

We present a theoretical study of the sub-critical fracture of heterogeneous materials under a constant external load. A generic fiber bundle model is proposed, which provides a direct connection between the microscopic fracture mechanisms and the macroscopic time evolution of the sub-critical system. In the model, material elements either fail due to immediate breaking or undergo a damage accumulating ageing process. On the macrolevel the model reproduces the empirical Basquin law of rupture life, and it makes it possible to derive a generic scaling form for the deformation histories of different load values. On the microlevel we found that sub-critical 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. When the load is equally distributed over the fibers, 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 equal load sharing counterparts. In the presence of stress concentration the failure process accelerates resulting in a higher value of the waiting time exponent compared to the case of homogeneous stress distribution.