Craig N. Morrison

Meso-scale site-bond model for elasticity: theory and calibration

Abstract A meso-scale site-bond model is proposed to simulate the macroscopic elastic properties of isotropic materials. The microstructure of solids is represented by an assembly of truncated octahedral cells with sites at the cell centres and bonds linking the nearest neighbouring sites. Based on the equivalence of strain energy stored in a unit cell to strain energy stored in a continuum of identical volume, the normal and shear stiffness coefficients of bonds are derived from the given macroscopic elastic constants: Young’s modulus and Poisson’s ratio. To validate the obtained spring constants, benchmark tests including uniaxial tension and plane strain are performed. The simulated macroscopic elastic constants are in excellent agreement with the theoretical values. As a result, the proposed site-bond model can be used to simulate the macroscopic elastic behaviour of solids with Poisson’s ratios in the range from −1 up to 1/2.

Discrete Lattice Model of Quasi-Brittle Fracture in Porous Graphite

Lattice models allow the incorporation of length scale dependent micro-structural features and damage mechanisms into analyses of the mechanical behaviour of materials. We describe our 3D lattice implementation and its use in fracture simulations. The method is particularly suitable for modelling fracture of nuclear graphite. This is a quasi-brittle material in which there is considerable non-linearity prior to final fracture due to the inherent porosity which triggers a field of local distributed failures upon mechanical and thermal loading. Microstructure representative models are generated with experimentally measured particle and pore size distributions and volume densities in two graphite grades. The results illustrate the effect of distributed porosity on the emerging stress-strain response and damage evolution. It is shown how the failure mode shifts from graceful, plastic-like, behaviour associated with substantial energy dissipation via distributed damage at lower porosities, to glass-like behaviour with negligible energy dissipation at higher porosities. Thus the work proposes a microstructure-informed methodology for integrity assessment of aging structures, where porosity increase is driven by environmental factors, such as radiation of nuclear graphite components.

Lattice-spring modeling of graphite accounting for pore size distribution

Lattice models allow length scale dependent micro-structural features and damage mechanisms to be incorporated into analyses of mechanical behaviour. They are particularly suitable for modelling the fracture of nuclear graphite, where porosity generates local failures upon mechanical and thermal loading. Our recent 3D site-bond model is extended here by representing bonds with spring groups. Experimentally measured distributions of pore sizes in graphite are used to generate models with pores assigned to the bonds. Microscopic damage is represented by failure of normal and shear springs with different criteria based on force and pore size. Macroscopic damage is analysed for several loading cases. It is shown that, apart from uniaxial loading, the development of micro-failures yields damage-induced anisotropy in the material. This needs to be accounted for in constitutive laws for graphite behaviour in FEA of cracked reactor structures.