13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Modelling Damage in Nuclear Graphite Thorsten Becker 1,*, James Marrow2 1 Department of Mechanical and Mechatronic Engineering, Stellenbosch University, Stellenbosch 7600, South Africa 2 Department of Materials, University of Oxford, Oxford OX1 3PH, United Kingdom * Corresponding author: tbecker@sun.ac.za Abstract In this paper a non-local coupled plasticity and damage model for nuclear graphite is presented. The model is the adaption of an existing model for quasi-brittle materials that allows for the degradation (as a function of load) of the material properties. The model arises from the continuum-based approach and uses concepts of isotropic damaged elasticity in combination with isotropic tensile and compressive plasticity to represent inelastic behaviour. In this work fracture of Gilsocarbon polygranular graphite is simulated in the FE environment for compact tension and three point bend specimens. The model consists of a combination of non-associated multi-hardening plasticity and scalar (isotropic) damage elasticity that describe the irreversible damage that occurs during the fracturing process in graphite. The simulations exhibit the observed softening and degradation of the material and found to be size and geometry independent. Keywords Nuclear graphite, fracture mechanics, micro-cracking, non-local damage plasticity model. 1. Introduction Nuclear graphite, a high purity grade polygranular graphite, is used for structural components as well as neutron moderators in high temperature nuclear reactors. Functionally, graphite components are arranged in the form of keyed bricks to accommodate the thermal and radiation induced deformations throughout the life of a reactor. Potentially, these dimensional changes may lead to stresses that are sufficient for crack initiation in the brittle graphite, particularly at keyway roots and other discontinuities. The structural integrity of such components is of importance, and has been assessed historically with either probability of failure methodologies (such as the Weibull approach) [1–4] or the fracture mechanics methodology [5–12]. Weibull’s weakest link theory anticipates that the larger the volume of material the greater the chance that a defect exists within the volume [13]. Simple application of this theory is inconsistent with experimental results; failure predictions of graphite components from small specimens do not agree with those of larger specimens [14]. An adaptation to the Weibull approach has been proposed by Hindley et al. [1] which incorperates a fixed volume size to ensure size independence; however, the results have shown to be conservative [1]. Recent studies have shown graphite behaviour to be non-linear [15] for non-irradiated medium grained graphites (Gilsocarbon and NBG10). Crack propagation is associated with a fracture process zone (FPZ) in which extensive micro-cracking results in irreversable energy dissipation. One of the biggest challenges in predicting component failure in graphite when using conventional fracture mechanics is that the fracture process is influenced by the graphite’s micro-, meso- and macrostructures, which are characterised by the number and distribution of internal pores and cracks [15]. For example, crack propagation in Gilsocarbon is primarily linked with damage initiation and propagation from these internal features. In a notched specimen under an increasing load, isolated and randomly distributed micro-cracks develop predominantly ahead of the notch tip and propagate orthogonally to the tensile strain in the loading direction. It is during this phase that damage accumulates; ultimately the micro-cracks coalesce into a macro-crack. The propagation of the macro-crack is accompanied by bridging or branching through the maze of micro flaws and is
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