  Fatigue fracture in ductile materials, e. g. metals, is caused by cyclic
plasticity. Especially regarding the high numbers of load cycles, plastic
material models resolving the full loading path are computationally very
demanding. Herein, a model with particularly small computational effort is
presented. It provides a macroscopic, phenomenological description of fatigue
fracture by combining the phase-field method for brittle fracture with a
classic durability concept. A local lifetime variable is obtained, which
degrades the fracture resistance progressively. By deriving the stress-strain
path from cyclic material characteristics, only one increment per load cycle is
needed at maximum. The model allows to describe fatigue crack initiation,
propagation and residual fracture and can reproduce Paris behaviour.
