Issue 48

R. Brighenti et alii, Frattura ed Integrità Strutturale, 48 (2019) 1-9; DOI: 10.3221/IGF-ESIS.48.01 5 The knowledge of the kinematic relationship between deformed and reference configuration, 1 2 cos ,  sin / 2 y cr y a r     [20], allows to express the true stress components in terms of the polar coordinates ( ,   ) in the deformed (current) configuration (Fig. 1b, Fig. 2). Along the deformed upper parabolic crack profile, the true stress components are: 2 2 1 4 2 11 12 21 22 π π ,   , ,  , ,   0 2 4 2 8 C A C A                                     (7) where only the singular terms have been reported and the relationship / 2    has been considered due to the fact that the deformed crack profile at the crack tip becomes parallel to the vertical axis (the tangent to the parabolic profile is vertical) [20]. (a) (b) Figure 2 : (a) Undeformed cracked plate and deformed configuration with the related reference systems. (b) Crack tip detail of the stress field. In large deformation, the singularity of the true stress 22  is sharper along the 2 y axis than along the 1 y axis. Expected crack path in large deformation From Eqs (6),(7) it can be remarked that the stress component 22  along the deformed parabolic crack profile ( π / 2   ) has a singularity -2 (i.e. 2   ), while the same stress component has a singularity -1 (i.e. 1 r  ) ahead of the crack tip ( 0   ). This different singularity can trigger the appearance of a secondary crack, departing from the blunted deformed one (crack tip splitting), leading to a tortuous crack path or to a rough crack profile. In other words, the singularity of the true stress 22  is sharper along the 2 y axis than along the 1 y one (see Fig. 2); thus the material tends easily to break apart close to the crack tip along 2 y , leading to the appearance of secondary cracks, responsible for curved crack paths.