Intrinsic material length, Theory of Critical Distances and Gradient Mechanics: analogies and differences in processing linear-elastic crack tip stress fields

The Theory of Critical Distances (TCD) is a bi-parametrical approach suitable for predicting, under both static and high-cycle fatigue loading, the non-propagation of cracks by directly post-processing the linear-elastic stress fields, calculated according to continuum mechanics, acting on the material in the vicinity of the geometrical features being assessed. In other words, the TCD estimates static and high-cycle fatigue strength of cracked bodies by making use of a critical distance and a reference strength which are assumed to be material constants whose values change as the material microstructural features vary. Similarly, Gradient Mechanics postulates that the relevant stress fields in the vicinity of crack tips have to be determined by directly incorporating into the material constitutive law an intrinsic scale length, the main advantage of such a modus operandi being that linear-elastic stress fields become non-singular also in the present of cracks and sharp notches. The above idea can be formalised in different ways allowing, under both static and high-cycle fatigue loading without assuming a priori the failure point. the propagation (or non-propagation) of cracks to be predicted through a suitable reference strength. In this scenario, the present paper aims to investigate the existing analogies and differences between the TCD and Gradient Mechanics, the latter formalised according to the so-called Implicit Gradient Method (IGM), when such theories are used to process linear-elastic crack tip stress fields.