Issue 42

M. Peron et alii, Frattura ed Integrità Strutturale, 42 (2017) 214-222; DOI: 10.3221/IGF-ESIS.42.23 217 Figure 1 : Notched specimens on tensile, (a) lateral rounded V notch, (b) lateral U notches, (c) circular hole and (d) ASCB specimen; (e) typical load-displacement curves on tensile and bending specimens . T HEORETICAL BACKGROUND erto and Lazzarin [27], and later Radaj and Vormwald [34], presented comprehensive overview of the volume- based strain energy density criterion. Below, only a reminder of the main concepts of the SED regarding brittle fracture of notched components is reviewed. SED criterion assumes that failure occurs when the mean value W of deformation energy in a local finite volume around the notch tip (control volume) reaches a critical value W c ; the failure occurs when c W W  , independent of the notch opening angle and loading type. If the material exhibits an ideally brittle behaviour until fracture, the parameter W c is calculated from the ultimate tensile strength σ u : 2 / 2 c u W E   (2) Under the situations when plain specimens exhibit a non-linear behaviour, whereas the notched specimens behave linear, Seweryn [35] recommended that the stress σ u should be replaced by “the maximum normal stress existing at the edge at the moment preceding the cracking” determined on tensile specimens with blunt curvature radius, where semi-circular notches are recommended. In plane problems, the control volume becomes a circle or a circular sector with a radius R c in the case of cracks or pointed V-notches in mode I or mixed, I + II, mode loading (Fig. 2a and b). Under plane strain conditions, a useful expression for R c has been provided considering the crack case [36, 37]:    2 1 5 8 4 Ic c t v v K R            (3) If the critical value of the NSIF is determined by means of specimens with α ≠ 0, the critical radius can be estimated by means of the expression:     1 1 2 2 2 1 1 1 4 c c c I K R EW               (4) When 2 α = 0, K 1 C equals the fracture toughness K IC . For rounded V-notches, a crescent-shaped control volume bounded by two radii differently centered was introduced: a circular notch edge with radius q as the inner boundary and a circle arc with radius r 0 + R c as the outer boundary, (Fig. 2c). The length r 0 represents the distance between the origin of the polar coordinates (used to express the stress field) and the notch tip. The parameters r 0 depends from q then it’s function only from the geometry (the opening angle 2 α ); r 0 is defined as 0 / ( 1) r qR q   where (2 2 ) / q      . B