A stress-state dependent cyclic cohesive model, which accounts for accumulation of plasticity, during both tensile as well as compressive deformations, and incorporates accumulation of irreversible damage due to macroscopic plasticity as well as microstructural mechanisms, is formulated. The model is implemented in mode-I plane strain fatigue crack growth simulations. The model is validated by reproducing the effect of retardation in crack growth rates after different combinations of tensile and compressive overloads. We show accurate description of the elastic–plastic behaviour of the process zone is vital, in particular for negative stress ratios subsequent to a tensile over-load, as considerable plasticity occurs in compression at the crack-tip, significantly reducing retardation effects. © 2020, Springer Nature B.V.