Issue 49

O. Naimark, Frattura ed Integrità Strutturale, 49 (2019) 272-281; DOI: 10.3221/IGF-ESIS.49.27 273 The TCD had independent inventions in different forms for the prediction of quasi-brittle fracture [3, 4]. The theory of critical distances operates with the phenomenological estimation of the process zone L arising from the continuum mechanics models. Commonly used length scale L in the TCD is given by 2 0 1 c K L          , (1) where c K is the fracture toughness of the material, and 0  is material tensile strength. In fatigue problems the same equation has used, replacing these material constants with the relevant cyclic ones: the crack propagation threshold th K  and fatigue limit 0   . Estimated by (1) the values of L for fracture and fatigue of brittle and ductile materials (silicon carbide and alumina [5], steel [6, 7], fiber composite laminate [4]) separate the “damage induced” and “crack induced” fracture scenario: for small cracks the experimental data deviate from the Linear Fracture Mechanics (LFM) line towards tensile strength 0  . Scale of L occurs in the middle of transient region for “Fracture stress” versus “Defect size” curve [1].The value of L determines structure-induced damage and fracture processes and are related to a microstructural parameter, for example, the grain size for ceramic materials. For metal fatigue L is associated with the length of non- propagating cracks [8]. Critical Distance approach is generalization of the Griffith energy balance theory assuming a finite amount of crack extension, that is so-called as the Finite Fracture Mechanics (FFM) [9,10]. This FFM can be formulated in the form: 2 2 2 0 2 L c K da K L    . (2) Three-point bending analysis showed the deviation both LFM and FFM for “normalized strength” 0   versus “normalized beam height” 2 h L at the vicinity of L : the LM and FFM tend to opposite extremes as the beam height approaches L . However, a combined approach, in which both LFM and FFM criteria apply, show realistic results supporting numerous structural observations revealing the variety of length L . Using this approach it was the prediction of the size effect in notched and un-notched beams [ 10] and the fracture criterion was proposed with application to laminate cracking analysis [11,12]. Comparing experimental data on fracture strength as a function of crack length revealed the similarity in form for both monotonic fracture in brittle materials such as ceramics, and for fatigue limit behavior in metals. It is the cases, when Linear Fracture Mechanics breaks down at short-cracks scale, that are significant in predicting the material responses to small defects such as manufacturing flaws, and in estimating the number of cycles needed for small fatigue cracks to grow. The anomalous short-crack behavior highlights more general problem of size effects or scaling effects. The TCD is useful for the applications, when the size of the sample is approaching to L [1, 9, 10]. It is important observation that the effect of notch-root radius has also interpretation in TCD phenomenology to introduce a critical root radius for crack-like behavior. This characterization of notch effects is based on the TCD phenomenology and has important applications for more complex effects related to multiaxial loading and finite life predictions [2, 8]. The interpretation of variation in specimen strength when the size of the entire specimen is changed (saving the shape) is another complex problem addressing to TCD with applications to high cycle fatigue and the fracture of quasi-brittle materials necessitating a modified form of the approach in which L becomes a variable quantity [13,14]. The power of TCD approach in predicting a wide range of phenomena in different materials, and capability of engineering applications stimulate the question – why does this theory work and what is the ranges [1]? Theoretical basis of the TCD is the Finite Fracture Mechanics (FFM) formulation that is combined the criticality features related to two stress-based factors: strength and fracture toughness [9]. Understanding of the scientific basis of the TCD includes the study of the nature of cohesive (process) zone, applications of local and non-local approaches. There is the question concerning the range of validity of the TCD since FFM formulation shares common features of singularities with LFM. It means, that the underlying scaling phenomena are related to the smallscale yielding criterion. The smallscale yielding criterion, for instance, for the notch-root plastic zone assumes a small fraction of specimen dimensions providing crack instability. The structural and mechanical basis of FMM and the “critical distances” conception is the existence of characteristic length providing the discontinuous and branching scenario of crack growth on the distances determined by