A damage mechanics approach to multiaxial fatigue

The fatigue assessment of structural components under a complex multiaxial stress history is one of the most difficult engineering challenge. As is well-known, several materials present a conventional fatigue strength at a given number of cycles under constant amplitude fatigue loading, while a conventional fatigue strength at a given number of cycles cannot be defined in the case of arbitrary varying and/or multiaxial stress histories. Several approaches have been developed to study this problem: empirical models, critical plane approaches, average stress criterion and stress invariant approaches. The damage phenomena can also be assessed by using an endurance function. In the present paper, a model for fatigue damage evaluation in the case of an arbitrary multiaxial loading history is proposed by using a damage function which allows us to evaluate the final failure of the material. By introducing an evolution equation for the material damage , the final collapse of the material is assumed to occur when the damage is complete, that is to say, when reaches the unity. The parameters of the model are determined through a Genetic Algorithm (GA) once a complex stress history and its effects on the material fatigue life are known. The proposed model presents the advantage to avoid any evaluation of a critical plane and any cycle counting algorithm to quantify the fatigue life, because it simply considers the loading process step by step and its effect in terms of damage.