A review on phase field models for fracture and fatigue

Phase field fracture models have demonstrated great capacities in simulating crack nucleation, propagation, branching, and joining in brittle and ductile materials subjected to external stimulations. Because of their great flexibility, phase field fracture models can incorporate various material properties including anisotropy, elastoplasticity, viscoelasticity, hyperelasticity, piezoelectricity, etc. Recently, the models have been extended to fatigue, one of the most common material failure mechanisms in structural engineering. The purpose of this paper is to provide a comprehensive review of recent work on phase field models for fatigue damage and failures. Following a brief introduction to the development of phase field fracture models as well as the theories and models of fatigue, the fundamentals of the models for elastic and elasto-plastic cases are presented, including basic theories, formulas, tension–compression splits, and numerical implementations. Then, the emphasis is placed on different aspects of the phase field models for fatigue fracture involving the approaches of introducing fatigue damage, the descriptions of crack nucleation and propagation, the coupling of cyclic plasticity and phase field models, and the acceleration algorithms. Finally, the future research directions of phase field models for fatigue fracture and the major challenges to be conquered in their engineering applications are discussed.