Issue 41

S.M.J. Razavi et alii, Frattura ed Integrità Strutturale, 41 (2017) 424-431; DOI: 10.3221/IGF-ESIS.41.53 429 By using the values of σ t = 30 MPa and E = 8000 MPa, the critical SED for the tested graphite is W 1c = 0.05625 MJ/m 3 . Under torsion loads, this critical value can be determined from the ultimate shear strength τ t according to Beltrami’s expression for the unnotched material: 2 3 2 t c W G   (5) By using the values of τ t = 37 MPa and G = 3300 MPa, the critical SED for the tested graphite is W 3c = 0.2074 MJ/m 3 . In parallel, the control volume definition via the control radius R c needs the knowledge of the mode I and mode III critical notch stress intensity factor K 1c and K 3c and the Poisson’s ratio ν , see Eqs (1) and (2). For the considered material K 1c and K 3c have been obtained from specimens weakened by sharp V-notches with an opening angle 2 α = 10° and a notch radius less than 0.1 mm. A pre-crack was also generated with a razor blade at the notch tip. The resulting values are K 1c = 1.06 MPa m 0.5 and K 3c = 1.26 MPa m 0.5 which provide the control radii R 1c = 0.405 mm and R 3c = 0.409 mm, under pure tension and pure torsion, respectively. For the sake of simplicity, a single value of the control radius was kept for the synthesis in terms of SED setting R c = R 1c = R 3c . As discussed in previous papers [20,21], the control radii under tension and torsion can be very different and this is particularly true when the material behaviour differs from a brittle one: the difference is higher for materials obeying a ductile behaviour. For this specific case, the values are so close to each other that a single value can be employed for the final synthesis. The SED criterion has been applied here for the first time to mixed mode I+III loading conditions. The proposed formulation is a reminiscent of the work by Gough and Pollard [28] who proposed a stress-based expression able to summarize together the results obtained from bending and torsion. The criterion was extended in terms of the local SED to V-notches under fatigue loading in the presence of combined tension and torsion loadings [29]. In agreement with Lazzarin et al. [29, 30] and by extending the method to the static case, the following elliptic expression: 3 1 1 3 1 c c WW W W   (6) is obtained. In Eq. (6) W 1c and W 3c are the critical values of SED under pure tension and pure torsion. For the considered graphite, W 1c = 0.05625 MJ/m 3 and W 3 c = 0. 2074 MJ/m 3 . The values of 1 W and 3 W have, instead, to be calculated as a function of the notch geometry and of the applied mode mixity ratio. Each specimen reaches its critical energy when the sum of the weighted contributions of mode I and mode III is equal to 1, which represents the complete damage of the specimen. Figure 3 : Synthesis of the results from combined tension and torsion tests based on the averaged SED.