A unified interpretation of the power laws in fatigue and the analytical correlations between cyclic properties of engineering materials

A phenomenological description of the fatigue life of engineering components can be given either by plotting the applied stress range as a function of the total number of cycles to failure, i.e., according to the Wöhler’s curve, or, after the advent of fracture mechanics, by plotting the crack growth rate in terms of the stress-intensity factor range, i.e., using the Paris’ curve. In this work, an analytical approach is proposed for the study of the relationships existing between the Wöhler’s and the Paris’ representations of fatigue. According to dimensional analysis and the concepts of complete and incomplete self-similarity, generalized Wöhler and Paris equations are determined, which provide a rational interpretation to a majority of empirical power-law criteria used in fatigue. Then, by integration of the generalized Paris’ law, the relationship between the aforementioned generalized representations of fatigue is established, providing the link between the cumulative fatigue damage and the fatigue crack propagation approaches. Moreover, paying attention to the limit points defining the range of validity of the classical Wöhler and Paris power-law relationships, whose co-ordinates are referred to as cyclic or fatigue properties, alternative expressions for the classical laws of fatigue are proposed. Finally, the correlations between such fatigue properties are determined according to theoretical arguments, giving an interpretation of the empirical trends observed in the material property charts.