Modelling fatigue in quasi-brittle materials with incomplete self-similarity concepts

In this study, a generalized Barenblatt and Botvina dimensional analysis approach to fatigue crack growth is proposed in order to highlight and explain the deviations from the classical power-law equations used to characterize the fatigue behaviour of quasi-brittle materials. According to this theoretical approach, the microstructural-size (related to the volumetric content of fibers in fiber-reinforced concrete), the crack-size, and the size-scale effects on the Paris' law and on the Wöhler equation are presented within a unified mathematical framework. Relevant experimental results taken from the literature are used to confirm the theoretical trends and to determine the values of the incomplete self-similarity exponents. All this information is expected to be useful for the design of experiments, since the role of the different dimensionless numbers governing the phenomenon of fatigue is herein elucidated. Finally, a numerical model based on damage mechanics and nonlinear fracture mechanics is proposed for the prediction of uniaxial S-N curves, showing how to efficiently use the information gained from dimensional analysis and how the shape of the S-N curves is influenced by the parameters of the damage model.