Issue 49

O. Naimark, Frattura ed Integrità Strutturale, 49 (2019) 272-281; DOI: 10.3221/IGF-ESIS.49.27 278 Eq. (9) defines the effective stress using a weighted average of the elasto-plastic stress field damaging the fatigue process zone over a line having length equal to eff L . It is evident that the length eff L , as the integration path, is assumed to be dependent on the notch geometry. The non-locality effect is the key structural factor responsible for the characteristic length eff L providing the correct predictions for the application of the TCD [28 ]. There is data concerning the TCD application in predicting the high-cycle fatigue strength of real mechanical components. The eff L value in fatigue damage is associated somehow with the grain size, but, in general, its value is of an order of magnitude higher than the average grain size. This experimental observation in the fatigue process zone leads to the definition of structural volume concept for the interpretation of link between the linear-elastic stress distribution within such a volume and the initial crack path. The structural volume idea takes as starting point for the assumption that all physical processes resulting in the formation of fatigue cracks are confined within a finite volume. The size of this volume is assumed to be constant (but different for different materials) and it depends on the stress field damaging the fatigue process zone. Mentioned features of fatigue damage and fatigue crack advance in the interpretation of the TCD can be explained in terms of singularity dualities. The illustration of both these approaches (the TCD and duality of singularities) can be given by the interpretation of the Bathias-Paris diagram of fatigue crack growth, when both, stress and stress- intensity based scenario of damage-failure transition, are presented. The solutions (4) and (8) represent two types of singularities (two attractors corresponding to intermediate asymptotic solutions for stress distribution and damage kinetics), which provide the interpretation of the Bathias-Paris diagram of fatigue crack initiation and growth, Fig.4. The blow-up damage kinetics is the consequence of specific nonlinearity (metastability) of free energy release in the presence of non-locality effects of defects interaction that allows the explanation of transition from damage localization to the fatigue crack nucleation stage. Figure 4. Crack advance diagram in HCF [29]: is the Burgers vector, 0 K  and eff K  are stress intensity factors corresponding to the crack lengths 0 a and i a . The K  - independent area of fatigue crack initiation corresponds to the transition to the blow-up damage kinetics with explosive jump from structure dependent scales of defects int a to macroscopically recognized 0 a . The power law   2 int n da dN b a a  reflects the self-similar (blow-up) stage of damage kinetics over c L scale that allows to estimate 0 a ~ c L . This length is related to the stress based scenario of fatigue crack nucleation. Starting from this scales 0 a the singularity related to the stress intensity factor 0 K  is combined with the blow-up singularity (6), that provides fatigue crack kinetics up to the scale l a . The drop of the crack velocity is the consequence of subjection of crack kinetics to the stress intensity factor th K  according to the Paris law. The process zone scale in this