Theory of Critical Distances versus Gradient Mechanics in modelling the transition from the short to long crack regime at the fatigue limit

Examination of the state of the art shows that over the last three decades, much work has been carried out to formalise specific methods suitable for accurately modelling the transition from the short to long crack regime, the Theory of Critical Distances (TCD) offering a suitable alternative to those methods based on the linear elastic fracture mechanics concepts. The TCD takes as a starting point the assumption that the propagation of fatigue cracks occurs when an effective stress range, depending on a material characteristic length, exceeds the material plain fatigue limit. Adopting a similar philosophy, gradient mechanics (GM) postulates that the relevant linear elastic stress fields can be determined by directly incorporating the material length scale into the stress analysis itself. The most remarkable feature of GM is that singular stress fields are smoothened. Thus, a finite value of the crack tip stress is obtained even if the constitutive law is linear elastic. In the present investigation then, after establishing an explicit theoretical link between the material intrinsic lengths calculated according to the TCD and GM, respectively, it is shown, through numerous experimental results taken from the literature, that the smoothened linear elastic crack tip stresses are successful in modelling the transition from the short to long crack region.