Damage mechanics and Paris regime in fatigue life assessment of metals

The fatigue assessment of structural components under uniaxial or multiaxial stress histories can be performed by employing damage mechanics concepts and a physics-based approach. A model for fatigue damage evaluation for an arbitrary loading (uniaxial or multiaxial, cyclic or random) has recently been proposed by the authors using an endurance function which quantifies the damage accumulation in the material up to the final failure. On the other hand, the approach based on the Paris law interprets fatigue failure as the result of the crack propagation inside the material up to the final collapse. In the context of damage mechanics, the structure collapse is assumed to occur when a scalar damage parameter (evaluated by using a proper damage accumulation law depending on the material parameters) is equal to the unity, whereas the final failure according to the Paris law is assumed to occur when the growing crack reaches the ‘critical size’ which depends on the mechanical properties of the material. In the present paper, these two fatigue assessment methods (damage model and Paris approach) are compared in order to determine both a damage value according to the Paris law and the crack length corresponding to a given damage. Such two methods are shown to be different formulations of the same physics-based approach to fatigue.

► Both damage mechanics and the Paris law can be used to analyse fatigue problems.
► The proposed damage model examines the fatigue effects through damage increments.
► The damage approach is compared with the Paris approach.
► The two methods are shown to be different formulations of the fatigue problem.
► Applications to uniaxial cyclic and variable amplitude loading are presented.