Energy-based multi-axial fatigue prediction for tubular structures under non-proportional loading

The tubular structure suffers from structural complexity, and it is also subjected to multi-axial loading, which makes the prediction of its fatigue life difficult. This study proposes a multi-axial fatigue life prediction model for tubular structures based on the energy method for non-proportional loading (MFLPM-ENPL). An energy-based method, considering the impact of residual stresses in welded joints, is first proposed. This model accurately captures the complexities of fatigue behavior by calculating the elastic strain energy of the tubular structure and the plastic strain energy at the welded part. To solve the problem of equivalent loading in the context of non-proportional load paths, a novel equivalent non-proportional factor is then designed. Tailored to the stress characteristics of tubular structures, it facilitates accurate load-equivalence conversion. Finally, by combining the designed non-proportional factor with the energy-based multi-axial fatigue life prediction method for tubular structures, a multi-axial fatigue life prediction model for tubular structures based on the energy method for non-proportional loading is developed. Through validation with diverse multi-axial test datasets—including various node types, material grades (e.g., C45 steel, Al6082-T6), and loading conditions—the proposed model achieves 93.6% accuracy within a 1.5× scatter band, surpassing existing methods in both predictive precision and robustness. Furthermore, its extensible design accommodates the incorporation of variable-amplitude loading scenarios and advanced damage-accumulation models, underscoring its potential to improve structural reliability across a broad spectrum of engineering domains.