Scaling and fractality in subcritical fatigue crack growth: Crack-size effects on Paris' law and fatigue threshold

The present contribution investigates the crack-size effects on Paris' law inaccordance with dimensional analysis and intermediate asymptotics theory,which makes it possible to obtain a generalised equation able to provide aninterpretation to the various empirical power-laws available in the Literature.Subsequently, within the framework of fractal geometry, scaling laws aredetermined for the coordinates of the limit-points of Paris' curve so that a theo-retical explanation is provided to the so-called short cracks problem. Eventu-ally, the proposed models are compared with experimental data available inthe literature which seem to confirm the advantage of applying a fractal modelto the fatigue problem.