Modelling the notch-induced anomalous growth of short fatigue cracks and the growth of long fatigue cracks with unified phase-field formulas

The notch-induced anomalous growth of short fatigue cracks is investigated by the variational approach to fracture. The phase-field framework is extended to model the notch-induced anomalous growth of short cracks in metal components. The phase-field model is based on (1) the variational principle of fractures in elastic–plastic solids, (2) an elastic-perfectly plastic constitutive model and (3) a fatigue degradation function, with damage driven by plastic work. The notch-induced anomalous growth observed in experiments is reproduced by the present model. Our study suggests that the notch-induced anomalous growth of short fatigue cracks can be correlated with the growth of long fatigue cracks with the unified phase-field model. Furthermore, the plastic work done in the plastic zone ahead of a crack tip can be considered as the unified driving force dominating both the notch-induced anomalous growth of short fatigue cracks and the growth of long fatigue cracks.