Continuum damage mechanics analysis of fatigue crack initiation

The crack initiation period in an originally defect-free component can be a significant portion of its total fatigue life. The initiation phase is generally believed to constitute the nucleation and growth of short cracks, but the threshold crack length at which initiation occurs lacks a uniform definition. Moreover, available methods for predicting fatigue damage growth usually require an existing flaw (e.g. Paris law) and may be difficult to apply to the initiation phase. This paper presents a continuum damage mechanics-based approach that estimates cumulative fatigue damage, and predicts crack initiation from fundamental principles of thermodynamics and mechanics. Assuming that fatigue damage prior to localization occurs close to a state of thermodynamic equilibrium, a differential equation of isotropic damage growth under uniaxial loading is derived that is amenable to closed-form solution. Damage, as a function of the number of cycles, is computed in a recursive manner using readily available material parameters. Even though most fatigue data are obtained under constant amplitude loading conditions, most engineering systems are subjected to variable amplitude loading, which can be accommodated easily by the recursive nature of the proposed method. The predictions are compared with available experimental results.