Fracture energy of graphite from microstructure-informed lattice model

Graphite remains a key structural material in the nuclear industry, the integrity assessment of which in demanding reactor environments is critical for safe operation of plant. Fracture of graphite is preceded by growth and coalescence of distributed micro-cracks within a process zone, classifying it as a quasi-brittle material alongside cement-based and ceramic materials. The evolution of micro-crack population to failure is well represented by discrete lattice models, e.g. (Wang and Mora 2008). Here, a recently developed 3D lattice (Jivkov and Yates 2012), with elastic spring elements and brittle-damage behaviour is used to generate microstructure representative models of two graphite grades at a representative meso length scale. Micro-cracks are represented by spring failures and the macroscopic damage results from their collective behaviour. Presented results capture a transition from graceful, plastic-like failure at lower porosities, with energy dissipation via micro-cracking, to glass-like behaviour with negligible energy dissipation at higher porosities. The results are in good agreement with experimental data. Thus, the proposed methodology can calculate fracture energy from the stress-strain curve, or formulate cohesive and damage evolution laws for continuum models, based exclusively on microstructural features.