Issue 41

S.M.J. Razavi et alii, Frattura ed Integrità Strutturale, 41 (2017) 424-431; DOI: 10.3221/IGF-ESIS.41.53 428 where K Ic is the mode I fracture toughness, ν the Poisson’s ratio and σ t the ultimate tensile stress of a plain specimen. For a sharp V-notch, the critical volume becomes a circular sector of radius R c centred at the notch tip (Fig. 2b). When only failure data from open V-notches are available, R c can be determined on the basis of some relationships where K Ic is substituted by the critical value of the notch stress intensity factors (NSIFs) as determined at failure from sharp V- notches. Dealing here with sharp notches under torsion loading, the control radius R 3c can be estimated by means of the following equation: 1 1 3 3 3 3 1 c c t e K R             (2) where K 3c is the mode III critical notch stress intensity factor and τ t is the ultimate torsion strength of the unnotched material. Moreover, e 3 is the parameter that quantifies the influence of all stresses and strains over the control volume and (1- λ 3 ) is the degree of singularity of the linear elastic stress fields [27], which depends on the notch opening angle. Values of e 3 and λ 3 are 0.4138 and 0.5 for the crack case (2 α = 0°). For a blunt V-notch under mode I or mode III loading, the volume is assumed to be of a crescent shape (as shown in Fig. 2c), where R c is the depth measured along the notch bisector line. The outer radius of the crescent shape is equal to R c + r 0 , being r 0 the distance between the notch tip and the origin of the local coordinate system (Fig. 2c). Such a distance depends on the V-notch opening angle 2 α , according to the expression: 0 ( 2 ) (2 2 ) r         (3) For the sake of simplicity, complex theoretical derivations have deliberately been avoided in the present work and the SED values have been determined directly from the FE models. R c R c 2   R 2 =R c +r 0   R c r 0 (a) (b) (c) 2   2  =0    Figure 2 : Control volume for (a) crack, (b) sharp V-notch and (c) blunt V-notch, under mixed mode I+III loading. SED APPROACH IN FRACTURE ANALYSIS OF THE TESTED GRAPHITE SPECIMENS he fracture criterion described in the previous section is employed here to estimate the fracture loads obtained from the experiments conducted on the graphite specimens. In order to determine the SED values, first a finite element model of each graphite specimen was generated. As originally thought for pure modes of loading the averaged strain energy density criterion (SED) states that failure occurs when the mean value of the strain energy density over a control volume, W , reaches a critical value W c , which depends on the material but not on the notch geometry. Under tension loads, this critical value can be determined from the ultimate tensile strength σ t according to Beltrami’s expression for the unnotched material: 2 2 t Ic W E   (4) T