Classical fatigue theory informed phase-field model for high-cycle fatigue life and fatigue crack growth

Phase-field model (PFM) for fatigue has recently attracted intensive efforts, but its extension to high-cycle fatigue (HCF) with efficient computation still remains a challenge. Here we propose a PFM for predicting HCF life and fatigue crack growth (FCG) by leveraging the power of classical fatigue theory that integrates local stress–strain approach and cumulative fatigue damage theory. Six PFMs including three classical fatigue-life formulae (strain-, stress-, and energy-based approaches) and two equivalent-stress criteria (Neuber's and Glinka's rules) are presented. Therein the phase-field damage variable governing the fracture energy degradation is cumulatively calculated from a local lifetime as loading cycles increase. To bypass the direct-cyclic calculation that is computationally expensive, envelope loading and cycle jump techniques are utilized to efficiently calculate HCF life. In an example material 42CrMo4, our PFMs are demonstrated capable of predicting both the total life (e.g., S/E–N curves) and Paris’ law over the HCF and very-HCF regimes, along with a good agreement between simulation and experimental results. Our PFM realizes the prediction of FCG behavior by using S/E–N data as input and is promising for HCF and FCG issues in engineering problems.