  We study the fatigue fracture of disordered materials by means of computer
simulations of a discrete element model. We extend a two-dimensional fracture
model to capture the microscopic mechanisms relevant for fatigue, and we
simulate the diametric compression of a disc shape specimen under a constant
external force. The model allows to follow the development of the fracture
process on the macro- and micro-level varying the relative influence of the
mechanisms of damage accumulation over the load history and healing of
microcracks. As a specific example we consider recent experimental results on
the fatigue fracture of asphalt. Our numerical simulations show that for
intermediate applied loads the lifetime of the specimen presents a power law
behavior. Under the effect of healing, more prominent for small loads compared
to the tensile strength of the material, the lifetime of the sample increases
and a fatigue limit emerges below which no macroscopic failure occurs. The
numerical results are in a good qualitative agreement with the experimental
findings.
