A phase-field model for low-cycle fatigue of brittle materials

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• A phase-field model for low-cycle fatigue of brittle materials is proposed. • The model introduces a fatigue degradation function, which modifies the fracture toughness . • The model can reproduce total-life and defect-tolerant approaches to fatigue. • It can handle complex geometries, loading conditions, and crack patterns without ad hoc additions to the theory. A phenomenological phase-field model for the formation and growth of fatigue macro-cracks in brittle materials is proposed. Additionally to the classical elastic stiffness degradation in the phase-field approach to overload fracture, a fracture toughness degradation is further introduced. The model can reproduce both total life approaches, such as the Basquin empirical relation, and the Paris law, which lies at the core of most of the defect-tolerant approaches, with exponents characteristic of brittle fatigue crack growth. The numerical implementation of the model in an efficient scheme is described and its ability to handle complex geometries and loading conditions demonstrated.