13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- In parallel, the control volume definition via the control radius Rc needs the knowledge of the fracture toughness KIc and the Poisson’s ratio ν, see Eq. (1). The critical load that is sustainable by a notched component can be estimated by imposing W equal to the critical value Wc which is considered here constant under mode I, mode II and in plane mixed-mode conditions. This assumption has been extensively verified for a number of different brittle and quasi-brittle materials [20-22]. As mentioned earlier, the properties of the graphite material used in the present investigation are: σt= 46 MPa, KIc = 1.0 MPa.m0.5, Poisson’s ratio ν=0.2. As a result, the critical SED for the tested graphite is Wc=0.13 MJ/m3 whereas the radius of the control volume is Rc ≅ 0.17 mm considering realistic plane strain conditions. Dealing with blunt notches under mixed mode loading, the problem becomes more complex than under mode I loading, mainly because the maximum elastic stress is out of the notch bisector line and its position varies as a function of mode I and mode II stress distributions. The maximum stress occurring along the edge of circular holes has been calculated numerically by using the FE code ANSYS 12.0®. For each geometry, two models were created. The first model was mainly oriented to the determination of the point where the maximum principal stress and the maximum SED were located; the second model was more refined, with an accurate definition of the control volume where the strain energy density should be averaged. All the analyses have been carried out by using eight-node elements under the hypothesis of plane strain conditions. Table 2 summarizes the outlines of the experimental, numerical and theoretical findings for the tested graphite specimens with four different inclination angles (β=0°, 30°, 45°, 60°), investigated in the present research. In particular, the table summarizes the theoretical (Fth) and the mean experimental load to failure (<F>) for every loading angle β and notch radius ρ. The Table also gives the maximum value of the principal stress ( σmax) and the SED value as obtained from the FE models of the graphite specimens by applying to the model the mean value of the critical loads. It is interesting to observe that the maximum principal stress along the notch edge is much greater (about two times) than the ultimate tensile stress of the material justifying the approach based on the average value of the SED over a control volume. As can be noted, the agreement between the experimental results obtained for the notched graphite specimens and the theoretical predictions based on a constant value of the local strain energy is satisfactory with a maximum relative deviation equal to 12%. 4. Crack initiation angles Dealing with crack initiation angles, they have been measured experimentally by using an optical microscope and a dedicate software called Las Leica Application Suite. The averaged value of the measured angles are compared in Table 3 with those obtained by numerical analyses identifying the point along edge where the SED and then the maximum stress reaches its critical value.
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