Issue 49

O. Naimark, Frattura ed Integrità Strutturale, 49 (2019) 272-281; DOI: 10.3221/IGF-ESIS.49.27 277 singularities (attractor types) and allow the discussion of the area, when the TCD can be effectively used. The area of competition between two attractors belongs to the intermediate temporal scales of the loading rate, that is close to 6 5 10 10 t s     [23]. a b Figure 3: Typical fractographic images of fracture surface for steady-state (a) and branching (b) regime of crack dynamics [24]. The TCD is based on the “force” version of failure criteria and, as a consequence, the large class of load conditions (with characteristic times approaching to the time of blow-up damage kinetics) could not be considered in the framework of the TCD phenomenology. Characteristic example for such situation is the transition from the steady-state to the branching crack dynamics in PMMA with qualitative changes of the fracture surface morphology: continuously mirror fracture surface for the steady-state crack dynamics and pronounced roughness with numerous mirror zones having different characteristic sizes (Fig.3). Steady-state crack dynamics and mirror morphology corresponds to the LFM asymptotical solution (4). The branching crack scenario corresponds to the set of collective modes of damage localization (the set of mirror zones), that represents the “degrees of freedom” responsible for the creation of the “process zone length” providing the crack advance. The formation of the “process zone length” is the consequence of the free energy metastability and “decomposition” of the metastable states due to the generation of collective blow-up defects modes corresponding to the self-similar solution (8) [26]. The existence of self-similar profile of damage distribution   f  , localized on the set of scales ( , 1, 2,... H c L kL k K   ), explains the nature of the Critical Distances, that provides both scenario of damage-failure transition corresponding to stress-based and stress-intensity phenomenology. The selection of wide spectrum of scales in the range , 1, 2,... H c L kL k K   is realized under dynamic and shock wave loading according to the presence of wide spectrum of finite amplitude stress modes and, as the consequence, corresponding spectrum of blow-up damage localization modes. Phenomenological basis of the DCT approach corresponds to the quasi- static loading conditions, when the “complex” blow-up mode can be initiated with the length H c L KL  . Namely this scale can be associated with the effective length in the Theory of Critical Distance in the framework of elasto-plastic models. F ATIGUE LENGTH SCALES . INTERPRETATION OF B ATHIAS -P ARIS ’ S DIAGRAM OF FATIGUE CRACK GROWTH pplication of the TCD to fatigue problems assumes that fatigue damage depends on the stress field distribution in the vicinity of the stress concentrator and the appropriate stress field parameter responsible for the damage in fatigue process zone could be introduced. It was proposed the calculation of the effective stress field parameter in the process zone according to the following relationship [27]:     1 0 0 1 0, 1 eff L eff eff r r dr L                , (9) where  is the stress gradient of the elasto-plastic stress field:     1 1 0, 1 0, d r r dr          . (10) A 1 mm