13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- 3. Identification of the model parameters The nuclear graphite grade modelled was Gilsocarbon (GCMB grade, IG-110) graphite, a near isotropic material [23]. Typical material properties are reported as 11.9 GPa for the Young’s modulus and the tensile strength of 20 MPa [23]. The Poisson’s ratio was taken as 0.21 [23]. The numerical strategy for solving the non-local DP problem requires the knowledge of the constitutive material parameters of Gilsocarbon, which include the definition of the yield surface, the flow rule, the load response and the material degradation. 3.1. Yield Surface and Flow Rule The plane stress cross section for the failure surface in the principal stress space is shown in Figure 1a. The data shown was extracted from various literature sources on the biaxial behaviour of Gislocarbon (which have been listed in the captions for convenience). The typical uniaxial compressive yield stress to biaxial yield compressive stress ratio was found to be 0.81 [24]. The dilatancy and eccentricity values, ψ and the ϵcc respectivly, were extracted from Brocklehurst [2,25] as shown in Figure 1b. The dilation angle, measured in the p - q plane at high confining pressure, was calculated as 30ᵒ. Note, similar values were found for concrete, a quasi-brittle material, where ψ is between 30ᵒ to 40ᵒ [26]. Figure 1 shows that the Ducker-Prager criterion is an excellent fit to the failure data. Since a plane stress problem is assumed the triaxial parameter λ is of little significance [21]. 3.2. Stiffness Degradation The tension softening behaviour or post-yield behaviour is defined according to the fracture energy criterion Gf, which is approximately 250 J/m2 [15] for Gilsocarbon. To determine the stiffness degradation behaviour requires a complex testing apparatus, such as the tests done by Gopalaratnam and Shah [27] for concrete. At point in time when this work was undertaken these data were not available and thus a linear evolution of the damage variable with efffective plastic displacement is currently assumed. This ensures that when the effective plastic displacement reaches a critical value, the material stiffness will be fully degraded. The compressive load response was defined according to Oku [28]. The stiffness degradation behaviour was also defined as a linear evolution of the damage variable with effective plastic displacement. As static conditions are simulated a strain rate independent model is assumed. The parameters are summarised in Table 1. Table 1: Material parameters of the DP model for Gilsocarbon Elastic Properties: Young’s modulus E0 11.9 GPa Poisson’s ratio v 0.21 Yield Surface and Flow Rule: Dilation angle ψ 30ᵒ Eccentricity ϵcc 4.8 Biaxiality ratio 0.81 Tension softening: Fracture energy 250 J/m2 Compression hardening: 20 MPa 0 mm 65 MPa 0.015 mm 1 MPa 0.045 mm
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