Fatigue short-crack growth mechanism and multi-scale rate modeling under multi-condition loading

Short fatigue crack growth is strongly affected by microstructural heterogeneity, crack-size effects, and loading-path dependence, leading to nonlinear, intermittent, and locally sensitive propagation behavior. Conventional long-crack growth models based on linear elastic fracture mechanics are therefore insufficient for describing short-crack propagation under different loading conditions. To address this issue, this study proposes a multi-scale short fatigue crack growth rate model that couples crack-tip strain energy density, crack-size effect, microstructural barrier resistance, and crack closure correction. Compared with the existing short-crack models, the proposed model introduces a microstructural barrier penetration function and a crack-opening correction factor to describe crack arrest, re-initiation, growth-rate fluctuation, and the effective crack-driving force. The model is validated using literature-reported experimental datasets for LZ50 steel, EA4T steel, CuNi ₂ Si alloy, and 42CrMo steel under different load sequences, loading frequencies, loading paths, loading modes, and load levels. The results show that the proposed model can reasonably capture the nonlinear evolution of short-crack growth rates under multi-condition loading. Quantitative evaluation shows an average log-scale coefficient of determination of 0.894, with 96.1% of the evaluated data points falling within the factor-of-three error band. These results indicate that the proposed model provides a physically interpretable framework for short fatigue crack growth assessment. Further validation under random or spectrum loading is still required.