Lee Margetts

Graphite is a candidate material for Generation IV concepts and is used as a moderator in Advanced Gascooled Reactors (AGR) in the UK. Spatial material variability is present within billets causing different material property values between different components. Variations in material properties and irradiation effects can produce stress concentrations and diverse mechanical responses in a nuclear reactor graphite core. In order to characterise the material variability, geostatistical techniques called variography and random field theory were adapted for studying the density and Young's modulus of a billet of Gilsocarbon and NBG-18 graphite grades. Variography is a technique for estimating the distance over which material property values have significant spatial correlation, known as the scale of fluctuation or spatial correlation length. The paper uses random field theory to create models that mimic the original spatial and statistical distributions of the original data set. This study found different values of correlation length for density and Young's modulus around the edges of a Gilsocarbon billet, while in the case of NBG-18, similar correlation lengths where found across the billet. Examples of several random fields are given to reproduce the spatial patterns and values found in the original data.

The stochastic finite element method is an extension of the FEM that considers the uncertainty of a system that arises through variations in initial conditions, materials or geometry. Systems which display a measurable degree of disorder can be studied efficiently using a probabilistic approach. Different scenarios can be randomly generated with the SFEM to study the behaviour of systems that take into account prior knowledge of the differing variations in properties. This review paper introduces the most commonly used techniques: direct Monte Carlo simulation, the perturbation method and the spectral stochastic finite element method. It then looks at the currently available software for the SFEM and provides examples from the disciplines of materials science, biomechanics and engineering to illustrate different procedures by which the SFEM is practically used. The aim of the paper is to help scientists and engineers quickly assess how they might apply SFEM to their own research and guide them towards key publications.

The objective of this study is to investigate whether there is significant spatial variability in the mechanical properties of Gilsocarbon nuclear graphite at different sections of the billet; specifically the dynamic Poisson's ratio, dynamic shear modulus, dynamic Young's modulus and density. Similar studies have been done, usually in the context of manufacturing, to assess the quality of graphite components for nuclear reactors. In this new study, the measurements have been carried out at a much higher spatial resolution than previously. A Torness/Heysham B billet was machined into cubes so that measurements could be made across the circumference and height of the billet. ASTM standards were followed to assess the measurements of the samples. The spatial variability of material properties is described and analysed statistically. The study shows that material variability is present at different heights and circumferential locations of the billet. This discovery will have a significant impact on the structural integrity and through life performance predictions made in industry; both in current and future nuclear reactors. The computer modelling of graphite components may predict different outcomes to standard analyses (that use mean values) if this variability is incorporated into the analysis workflow; specifically through stochastic modelling

The objective of this study is to investigate whether there is significant spatial variability in the mechanical properties of Gilsocarbon nuclear graphite at different sections of the billet; specifically the dynamic Poisson's ratio, dynamic shear modulus, dynamic Young's modulus and density. Similar studies have been done, usually in the context of manufacturing, to assess the quality of graphite components for nuclear reactors. In this new study, the measurements have been carried out at a much higher spatial resolution than previously. A Torness/Heysham B billet was machined into cubes so that measurements could be made across the circumference and height of the billet. ASTM standards were followed to assess the measurements of the samples. The spatial variability of material properties is described and analysed statistically. The study shows that material variability is present at different heights and circumferential locations of the billet. This discovery will have a significant impact on the structural integrity and through life performance predictions made in industry; both in current and future nuclear reactors. The computer modelling of graphite components may predict different outcomes to standard analyses (that use mean values) if this variability is incorporated into the analysis workflow; specifically through stochastic modelling.

The extreme environments found within the nuclear sector impose large safety factors on modelling analyses to ensure components operate in their desired manner. Improving analysis accuracy has clear value of increasing the design space that could lead to greater efficiency and reliability. Novel materials for new reactor designs often exhibit non-linear behaviour; additionally material properties evolve due to in-service damage a combination that is difficult to model accurately. To better describe these complex behaviours a range of modelling techniques previously under-pursued due to computational expense are being developed. This work presents recent advancements in three techniques: Uncertainty quantification (UQ); Cellular automata finite element (CAFE); Image based finite element methods (IBFEM). Case studies are presented demonstrating their suitability for use in nuclear engineering made possible by advancements in parallel computing hardware that is projected to be available for industry within the next decade costing of the order of $100k.