Asymmetric bending and crack breathing: a mechanics-consistent model for fatigue cracks in rotating shafts

Abstract Fatigue cracks in rotating shafts introduce nonlinearity in stiffness due to crack breathing, directly affecting vibration response and structural integrity. Precise prediction of this behaviour needs a mechanics-consistent representation of the cracked cross-section, particularly when asymmetric bending occurs. Most existing analytical models rely on simplified assumptions, such as a neutral axis that remains parallel to the geometric centroid axes, which can lead to significant errors in estimating the closed crack area and the associated area moments of inertia. This paper presents an advanced analytical framework for modelling fatigue crack breathing in a rotating shaft by explicitly accounting for asymmetric bending and the inclination of the neutral axis in the cracked cross-section. Closed-form expressions are derived for the cracked and uncracked areas, centroid coordinates, and area moments of inertia for fully open, partially closed, and fully closed crack states. An iterative refinement procedure is used to achieve convergence of centroid location, neutral axis inclination, and sectional properties. The proposed model is implemented in MATLAB and validated against three-dimensional finite element simulations and a widely cited reference model. The results demonstrate that the neutral axis is normally inclined for partially open or fully open cracks and becomes horizontal only when the crack is fully closed. Overlooking this inclination leads to a systematic overestimation of the closed crack area and noticeable errors in area moment of inertia predictions. The proposed formulation provides improved mechanical fidelity and is well-suited for integration into rotodynamic models aimed at vibration analysis and predictive maintenance of rotating machinery.