Predicting a Unified Fatigue Life Curve Through the Competition Between Plastic Deformation and Fatigue Damage

A unified description of the fatigue life curve, based on the competition between plastic deformation and damage accumulation, is proposed. Despite significant recent advances in fatigue modeling, most existing approaches still rely on regime-specific calibrations and empirical transition criteria. Fatigue experiments on steel 20 under constant-amplitude loading (375–490 MPa) demonstrate that plastic deformation governs the low-cycle fatigue regime, becomes negligible in the high-cycle regime, and interacts with damage evolution throughout the transition region. To describe this behavior, a novel coupled relaxation–kinetic model, combining a relaxation-based plasticity formulation with the simplest possible damage equation, is employed. The key novelty lies in the experimental comparative diagram that directly juxtaposes the evolution of stabilized plastic strain and the strain at fracture as functions of cycle number—a diagram that has not previously been reported for this class of materials. This diagram makes it possible to establish the transition from plastic strain accumulation to damage-controlled evolution not empirically, but physically, through the stabilization stage, in which the accumulated strain energy defines the initial damage level. The model reproduces the experimental fatigue life curve over a wide range of cycles to failure using only a few physically meaningful material parameters.