Discrete Lattice Model of Quasi-Brittle Fracture in Porous Graphite

Abstract

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.

A multi-scale three-dimensional Cellular Automata fracture model of radiolytically oxidised nuclear graphite

“…However, in this case the pore structure was simplified as spheres, and no effect of pore geometry could be considered. Recent developments using multi-scale experimental characterisation and modelling have demonstrated a dominant effect of large pores on graphite strength and elastic modulus [26], and the collective behaviour of micro-cracks in graphite was considered using a 3D site-bond model for tensile strength [27]. This approach was subsequently developed into a dual scale model [28] for virgin Gilsocarbon graphite.…”

3D Cellular Automata fracture model for porous graphite microstructures

“…Pore shape approximation by spheres or ellipsoids may not necessarily represent the graphite microstructure adequately. Various attempts have been performed in the recent years to develop 3D heterogeneous models of fracture in graphite using FE-based methods (Berre et al 2006;Saucedo-Mora and Marrow 2014;Smith et al 2013) or lattice models (Morrison et al 2014). The use of FE methods introduces some difficulties since it can require particular algorithms to be applied for creation of the FE-mesh around the pores of irregular shapes while enlargement of the mesh to simulate representative volumes of material leads to increasingly time consuming computations, especially in 3D.…”

On the application of the method of difference potentials to linear elastic fracture mechanics

“…Discrete lattice models are now also being used to account for micro‐structure effects near the crack tip at a relatively fine scale. The method has been shown to account for nonlinearity caused by the formation of microfractures near the crack tip in quasi‐brittle and porous materials and is particularly suited for deriving damage evolution laws that can be used at a macro scale in calculations. While bottom up approaches, recognising the inherent discreteness of fracture through lattice models has provided penetrating insight into the dynamics of the fracture process, as noted by Du and Lipton , they do not scale up to finite size samples with multiple freely propagating cracks for which peridynamics seems more appropriate .…”