Issue 49

O. Naimark, Frattura ed Integrità Strutturale, 49 (2019) 272-281; DOI: 10.3221/IGF-ESIS.49.27 274 the microstructure and deformation behavior of the material. The TCD provides two new material parameters: the distance L and the stress ratio 0 u   , where u  is the tensile stress, u  is, the so-called, characteristic strength of materials. These parameters are recognized as potential characteristics of a material’s brittleness, notch sensitivity and susceptibility to size effects. The TCD is recognized as the approach providing a bridge between continuum-mechanics and micromechanical models, stress-based methods and stress-intensity methods, fatigue failure and brittle fracture with application to different classes of materials. S OME RESULTS IN CRACK MECHANICS AND FAILURE he subject of variety of crack paths is one whose roots go back to the classical work of Griffith [15]. With a goal to study the crack path problem and the interaction of the main crack with the defect ensemble in the process zone we will consider briefly the classical results in the crack mechanics, where much analytical progress has been made in assuming that the medium behaves according to the equations of linear elasticity. According to the Griffith theory the additional characteristics of the crack resistance were introduced in the form of the energy of the development of the new surface at the crack tip. The energy U of elastic materials with a crack is represented in the form (Fig.1, curve 1) 2 2 2 2 4 a U a E             , (3) where  is the surface energy;  is the applied stress; a is the crack length; E is the elastic modulus. Figure 1: The Griffith (1) and Fraenkel (2) energy form of elastic solid with a crack . Irwin [16] developed the Griffith conception and proposed the force version of the crack stability (the stress intensity factor) related to the intermediate self-similar singular solution for the stress field at the crack tip area 1 2 ( ) ik I ij K r f     I K a    , (4) where I K is the stress intensity factor, , r  are the coordinates of point, ( ) ij f  is the  dependence in the first term of asymptotical solution. Two classical treatments are based on the Griffith criterion and stress-intensity factor criterion and reflect the physical contradiction related to incorrectly prediction of an infinite load at failure due to the global instability (singularity) of stress field at the crack tip. Barenblatt [17] proposed a variant of the force version of the crack stability that reflects another view on the role of stress in the crack tip area. It was assumed the existence of the cohesion forces ( ) B G s at the process (cohesive) area with the size d   0 s d   . The self-similarity of the crack tip evolution are the consequence of the small ratio of the applied stress  and the cohesion force B G : 1 B G   . This fact reflects the intermediate-asymptotic character of quasi-brittle failure theories and the material parameter was introduced, the so-called the cohesive modulus, as the independent strength property of materials: B B K G d  . Despite the similar form of the cohesive modulus B K and the stress intensity T