3D Cellular Automata fracture model for porous graphite microstructures

Nuclear graphite has a complex porous microstructure, which depends on raw materials and manufacturing process; porosity can change with radiolytic oxidation and also in the absence of oxidation with very high neutron fluences. Porosity directly affects the fracture process and the graphite tensile strength. To understand the effects of porosity on component strength and its relation to small specimen data, microstructure sensitive models are needed that can simulate the statistics of strength of porous microstructures, also addressing size and strain gradients effects such as notches. This requires multi-scale models that capture the key microstructural features with sufficient fidelity, and also with sufficient computational economy to simulate component behaviour. To achieve this, an innovative technique to calculate the elastic stress distribution in a 3D porous solid under uniaxial or biaxial tension has been developed that uses Cellular Automata. Synthetic microstructures with arbitrary distributions of pore sizes and shapes are created that simulate realistic microstructures; a fracture algorithm simulates failure initiation and crack growth. The model calculates the tensile strength of a microstructure volume for any arbitrary failure criteria; the critical strain energy release rate is used as an example to demonstrate how porosity affects the fracture process. The presented Cellular Automata (CA) model is at least an order of magnitude more efficient than finite element methods of equivalent discretisation; CA are also scale independent and well suited for parallel computing. This would allow large volumes of representative microstructures to be simulated, with a Monte-Carlo based approach to investigate strength variability.