13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- preceded by a fracture process zone (FPZ) ahead of the crack tip. Therefore, fracture processes in graphite may depend primarily on the stability of the interfacial cracks (micro-cracks) which is a function of the material structure [6,15,16]. Becker et al. [15] has shown, using the Double Torsion geometry [17] and an algorithm to calculate the fracture parameters from digital image correlation obtained displacement fields [18], that: - The LEFM fracture parameters GIc or KIc are dependent on specimen geometry and size. - The non-linear contributions to the energy dissipated during fracture seem dependent on specimen geometry and size. - R-curve behaviour seems dependent on specimen geometry and size. However - The elastic contributions to the energy dissipated during fracture appear to be independent of specimen geometry and size. These mechanisms of fracture are not unique. Quasi-brittle materials, like concrete, rock and many other materials including various fiber composites and particulate composites, coarse-grained or toughened ceramics, ice, cemented sands, grouted soils, bone, paper, wood, wood-particle board, etc experience similar mechanism of fracture [19]. Such materials are generally considered as brittle, yet behave in a non-linear fashion due to the development of a sizable FPZ that can occupy a large portion of the structure and is believed to be geometry and size dependent [19]. One way to model quasi-brittle fracture is the use of a non-local damage plasticity model, such as proposed by Lubliner and coauthors [20] and Lee and Fenves [21]. Here, the behavior of micro cracking is modelled on a macroscopic level by stiffness degradation combined with plasticity to provide an appropriate evolution of a yield surface during the formation of damage. The model uses a fracture energy based scalar damage variable to represent the damage state. In addition to the damage variable, the model introduces elastic and plastic degradation variables to simulate the degradation of elastic stiffness. This paper presents the utilisation of this non-local damage-plasticity (DP) model for quasi-brittle materials to simulate graphite fracture. The framework of the non-local DP model is presented and the calibration of the model parameters with experimental data for Gilsocarbon. Finally, the model is implemented using two different test geometry examples, namely a three point bend (3PB) geometry and two compact tension (CT) geometries. 2. Framework for plastic-damage model for nuclear graphite The model simulates failure implicitly in the Finite Element (FE) environment and consists of a combination of non-associated multi-hardening plasticity and scalar (isotropic) damaged elasticity variables to describe the irreversible damage that occurs during the fracture. This requires the definition of a yield surface and a flow rule. The degradation mechanisms of tensile cracking and compressive crushing are defined respectively as Gf, the fracture energy, and as a stress-displacement hardening relationship in compression . The degradation of the elastic stiffness in tension and compression is defined as a scalar, which is a function of the cracking displacement or strain. As static conditions are simulated, a strain rate independent model is assumed. For details regarding the model derivation, the reader is referred to the papers by Lubliner [20] and Lee and Fenves [21].
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