The United Kingdom has fourteen gas-cooled, graphite-moderated Advanced Gas-Cooled nuclear reactors that have approached the end of their design lives but are capable of additional safe operation subject to an improved understanding and continuing evaluation of their graphite core behaviour. EdF Energy Generation Ltd has continued to make a large investment into increasing the knowledge of graphite irradiation behaviour, both on the microstructural scale and in terms of the performance of large graphite components. All graphite moderated reactors suffer ageing and degradation to the graphite during service. The degradation poses a threat to the functionality of the graphite core
, and potentially, to the safe operation of the reactor. As the graphite components of these reactor cores cannot be replaced, it is important to ensure that effective strategies are in place to secure safe and reliable operation ultimately beyond their planned design life. The importance of extending the safe operating life of a reactor is increasing due to the political and socio-economic demands to reduce greenhouses gases and to diversify energy supply, along with the widely-publicised delays in providing replacement generation capacity as older reactors have been shut down along with fossil-fuelled plant. Thus, the importance of modelling and measuring reactor core graphite properties and performance becomes ever more significant as life extension continues.
The objective of the present conference is again to display and to discuss the extensive research and analysis performed by a number of expert organisations in support of the Advanced Gas-Cooled Reactors, and especially to consider the performance of whole components and structures: thus, on this fifth occasion, we examine the ‘collaboration’ of science and engineering. A key feature of this conference is that time is again allocated within the programme for debate on four important issues: through these, the conference seeks both to obtain independent peer review of its technical developments and to identify where there remain deficiencies in understanding.
This conference is the most recent in a series, with the first four being held in Cardiff, Nottingham, Aston and again in Nottingham in 2005, 2008, 2011 and 2014 respectively. The proceedings of these earlier conferences can be found in the following books.
Neighbour, G. B. (Editor) (2007). Management of Ageing in Graphite Reactor Cores (308 pages). RSC Publishing (Royal Society of Chemistry, Cambridge) (ISBN: 978-0-85404-345-3).
Neighbour, G. B. (Editor) (2010). Securing the Safe Performance of Graphite Reactor Cores (270 pages). RSC Publishing (Royal Society of Chemistry, Cambridge) (ISBN - 978-1-84755-913-5).
Neighbour, G.B. (Editor) (2013). Modelling and Measuring Reactor Core Graphite Properties and Performance (211 pages). RSC Publishing (Royal Society of Chemistry, Cambridge) (ISBN 978-1-84973-390-8)
Flewitt P.E.J. and Wickham A.J. (Editors). Engineering Challenges Associated with the Life of Graphite Reactor Cores (477 pages). EMAS Publishing (Warrington) (ISBN: 978-0-9576730-5-2).
This present conference features graphite-component cracking as its main topic area, since this issue is now starting to have an impact upon operational safety cases for the AGRs. Other topics included in the programme include inspection and monitoring, the study of graphite microstructure, irradiation-induced creep in graphite and the prediction of weight loss as a result of radiation chemistry interactions between the graphite and the reactor coolant. During the conference, discussions led by a facilitator will address the major issues, and the minutes of these discussions will be recorded and published as part of the proceedings.
PROGRAMME AND ABSTRACTS
SCIENCE AND ENGINEERING IN COLLABORATION TO SUPPORT SAFE OPERATION OF THE GRAPHITE REACTOR CORES
A Conference at The Grand Harbour Hotel, Southampton.
9th – 12th May, 2016
under the auspices of The British Carbon Group
Registration will begin at 1400 hrs on Monday May 9th 2016 in the Mayflower Foyer at the hotel. Access to rooms cannot be guaranteed before this time
, but a secure baggage store is available.
Car parking is available at the hotel on a first-come first-served basis in a barriered facility – entry from West Quay Road (eastbound).
In general, delegates who arrive by train should travel to Southampton rail station. From here, a taxi may be obtained to the hotel which takes less than 10 minutes. From London, travel to Southampton from Waterloo station. There are also direct services from Bristol and South Wales.
From London Heathrow airport, travel to Waterloo via London Underground – Piccadilly line to Oxford Circus then Bakerloo line southbound. From Gatwick airport, take a Southern train to Clapham Junction where you can change directly to a Southampton service without needing to travel further into the city.
A secure baggage storage area will be available on the final day of the conference since rooms must be vacated at 10am on Thursday May 12th.
Free WiFi is available to registered delegates in all areas: obtain the code from main reception upon arrival. The hotel offers an indoor swimming pool and spa. All rooms have tea and coffee making facilities. Please note that any issues arising in connection with your hotel accommodation must be taken up directly with the hotel management: the conference organisers accept no responsibility in this regard.
All further enquiries regarding the conference arrangements should be directed to the conference office in the Speedwell Room (off the Mayflower Foyer). Conference Manager, Prof. A J Wickham, email@example.com, (07785 567 577).
PRESENTATIONS & AUDIO/VIDEO FACILITIES
Presentations will be 15 minutes plus 5 minutes for discussion, except for the Plenary Lecture and introductory items. All presentations will take place in the Mayflower Suite.
Presenters are encouraged to bring their presentations on a USB memory stick and not to use their own computers. Whilst the latest PowerPoint software and computer facilities will be available, presenters should check their presentation prior to their session. To facilitate smooth running of the programme, presenters are also encouraged to introduce themselves to the session chairpersons prior to their session.
A copy of all presentations must be left on the computer so that they may be collected and issued to delegates before the end of the conference.
VISIT TO BEAULIEU, home of the Motor Museum and Other Attractions
This visit, by luxury coach, is free to all delegates.
The trip will take place on Wednesday afternoon
May 11th, and participants must be ready to leave at 13h00 PROMPT. Departure from Beaulieu will be at 17h00 PROMPT, and anyone missing the return coach transport will be obliged to take a taxi at their own expense…
CATERING ARRANGEMENTS & CONFERENCE DINNER
Breakfast and lunch will be served in the Boardwalk Restaurant. Coffee breaks will be available in the Mayflower Foyer, where small exhibitions may be in place, and the conference sessions will take place in the Mayflower Suite. Adjacent rooms will be used for breakout sessions as indicated in the programme Delegates should retain their conference badges at all times and may be requested to show their badges to obtain service.
On Monday and Tuesday evenings, dinner will be served ‘at leisure’ in the Boardwalk Restaurant (but please note that there is a short programme on Monday evening including a welcome drink in the Mayflower Foyer at 7pm (accompanied by the Annual General Meeting of The British Carbon Group to which all are invited) and a scheduled introductory talk by Dr Jim Reed at 8.30pm in the Mayflower Suite. You are encouraged to take dinner ‘in between’ these two events. Any alcoholic beverage ordered ‘at table’ in the restaurant is at your own cost, and accounts for items charged to your room must be settled with the hotel upon checkout.
A Gala Conference Dinner will be held on the Wednesday evening in the Mayflower Suite, preceded by a complimentary drink in the Mayflower Foyer at 7.30pm. Dress code for this event is business casual.
Those with special dietary needs are asked to make themselves known to the waiting staff in the restaurant
, whereupon their requirements will be met.
Monday 9th May 2016
14.00: Registration Desk Opens (adjacent to main reception)
Subsequently, the Conference Office will be found in the Speedwell Room, manned throughout the conference
19.00: Welcome Drink and Overview of the Conference: Mayflower Foyer
Prof. Peter Flewitt, University of Bristol and Conference Chairman
The British Carbon Group AGM (all are invited)
20.30: “A Forward Perspective for Electricity Generation in the UK”
Dr James Reed, EdF Energy Generation Ltd
Tuesday 10th May 2016
07h30: Breakfast (Boardwalk Restaurant)
08h00: Conference Service Desk Opens, Speedwell Room
08h30: PLENARY SESSION:
Chairman: Prof Peter Flewitt (University of Bristol & Conference Chair)
“Microstructural Studies of Carbon and Graphite Materials”
Prof. Brian Rand, Prof Emeritus, The Universities of Leeds and Pretoria; Visiting Academic, The University of Manchester
09h30: “Forward Graphite Strategy to Support Safe Operation of AGRs”
Dr James Reed (EdF Energy)
10h00: Regulatory Approach to The Challenge of AGR Graphite Core Ageing
M. Bamber, ONR
The UK’s fleet of seven graphite moderated Advanced Gas-cooled Reactors (AGR) are the only power producing nuclear reactors in the world that have a graphite moderated core cooled by carbon dioxide gas operating at > 500°C.
The graphite core cannot be replaced and during its lifetime it is subject to the combined ageing effects of irradiation and oxidation. These ageing mechanisms change the mass, dimensions and material properties of the graphite bricks within the core. The mechanisms are complex, inter-related, and difficult to accurately predict and can potentially effect safe operation. As such they pose unique challenges to the reactor operator.
The challenge presented to the Office for Nuclear Regulation (ONR) as the UK nuclear industry regulator is how to adequately assess the safety claims made by the licensee of these unique reactors, particularly when the technical community is largely within or supports the licensee’s organisation. Furthermore, there are few comparators in terms of operational experience, experimental data or codes and standards relative to water cooled/moderated reactors.
The Energy Act 2013 entitles the ONR
, as part of its function, to carry out research in connection with the ONR’s purpose or arrange for such research to be carried out on its behalf. If appropriate, the nuclear industry is invited to commission research to address these topics and share the results with the ONR. In terms of research on nuclear graphite, the ONR has previously determined that it needs to have research undertaken independently of the work of the major reactor licensees in order to provide independent, robust challenge to the licensee’s safety claims and assess the degree of conservatism. The ONR’s research includes work on average graphite core weight loss, statistical determination of core condition, the rate of graphite dimensional change and the development of internal stresses within graphite reactor components. It is important to note that the ONR’s research does not seek to prescribe safety limits or directly promote less conservative methods.
This paper will review some of the engineering challenges posed by the graphite cores of AGR and summarise some of the work the ONR has commissioned as part of its regulatory activity. The paper seeks to demonstrate how the work commissioned by the ONR on nuclear graphite serves to develop an independent pool of expertise, separate from the licensee, which can provide diverse thinking on problems posed by the UK’s unique graphite moderated carbon dioxide cooled reactors. It is important that the ONR funds such work to maintain a pool of independent experts who can advise the ONR and help it reach informed regulatory decisions about the adequacy of the licensee’s safety cases.
10h20: Coffee break. Mayflower Foyer
MICROSTRUCTURE AND CREEP (1)
Chairman: Dr. James Reed
10h40: Micromechanistic Model of Graphite Irradiation Behaviour
A. Tzelepi, J.F.B. Payne, L. Delannay and M.P. Metcalfe
NNL has developed a micromechanistic model of polycrystalline graphite irradiation behaviour based on finite element modelling of the individual crystals. This computational method has been used extensively on other materials, such as alloys, to derive the macroscopic properties of the polycrystalline material from single crystal properties. The development of this modelling approach for graphite included comparisons against similar but less computationally intensive mechanistic models of materials (e.g. mean-field models) and it was demonstrated that this is the only approach that can predict the observed irradiation induced dimensional change. Furthermore, the model qualitatively predicts the changes in Coefficient of Thermal Expansion (CTE) for virgin and irradiated graphite under compressive load, the behaviour of Young’s and shear modulus with irradiation and the effect of oxidation on CTE.
This paper aims to provide insights relating to the first two conference themes, namely: Microstructure and Irradiation Creep. Specifically, the paper will demonstrate that the 2D model qualitatively predicts the observed behaviour for irradiation induced dimensional change of bulk graphite using only single crystal properties, known from historical MTR experiments. Furthermore, the paper investigates the effect of irradiation creep on dimensional change and demonstrates that basal plane shear contributes to the relaxation of internal stresses and hence, irradiation creep indirectly influences the polycrystalline volume change. Finally, this paper will present the most recent results of the 3D model.
11h00: Overview of the Micro-Mechanical Testing Applied to Carbonaceous Materials
Dong Liu, Oliver Lord, Peter Flewitt and Ken Mingard
This paper considers a range of micro-mechanical tests that have been applied to carbonaceous materials including vitreous carbon (pore-free), filter graphite (PG25 with 50 vol.% porosity), Gilsocarbon graphite (20 vol.% porosity) and PGA graphites (both unirradiated and neutron irradiated with a 33.2 × 1020 n·cm-2 DIDO equivalent dose and a weight loss of 15%). Micro-scale cantilever specimens, typically between 1x1x5 µm and 6x6x40 µm created by focussed Ga+ ion beam milling in the regions of interest were tested in situ within the work chamber of an FEI Helios 600i Dualbeam Workstation to obtain load-displacement curves and fracture characteristics. Specimens on this scale allowed the material between the macro-pores to be tested, but the specimens still contained sub-micrometre pores. Depending on the pore geometry and distribution, some of the specimens showed premature failure while other pore-free cantilevers displayed high elastic modulus and flexural strength. These higher values represent a lower bound of the ‘true’ material properties, and the scatter of the measured values describes the variation of local properties within these graphites. In addition, larger length-scale, cantilever specimens of the size of 20x20x100 µm to 40x40x200 µm were prepared by ultra violet laser ablation. These specimens were tested in situ using an in-SEM nano-indentation system fitted with a flat diamond tip. Focussed ion beam milling was adopted to section these large cantilevers at the site of fracture to obtain its cross-sectional area for the determination of mechanical properties. It was found that these cantilevers contain a large number of micro-pores such that the measured elastic properties represent an average of the data obtained from the smaller cantilever specimens. Values of the elastic modulus, fracture strength and failure strain were determined and compared with the smaller cantilever specimen data. The results will be discussed by comparison with macro-scale bend geometry test data and have implications for the dependence of mechanical properties on length-scale over the micrometre to centimetre range for these carbonaceous materials.
11h20: X-ray Tomography Analysis of the Microstructure and Porosity Distributions of Irradiated AGR Graphite
J.E.L. Taylor, M. A. Davies, A.N. Jones and P.M. Mummery
The EdF ACCENT programme has generated irradiated graphite to aid the current understanding of the microstructure and property relationships used to assist the EdF AGR safety case. Of particular importance is understanding how graphite components become damaged during the operation of the AGRs
, and how this damage affects the operational lifetimes of the components.
Graphite samples with various starting conditions were analysed pre and post irradiation using X-ray tomography to acquire microstructural data. Digital image analysis was performed to examine the evolution of the microstructure and changes to porosity, under irradiation and with and without an applied load.
Total porosity, pore volumes and pore orientations were studied across a range of samples to quantify the stress-induced and irradiation-induced changes to the microstructure of graphite during reactor operation. The consequences for the UK’s AGRs were discussed, and a proposal for the acquisition of further X-ray tomography data from the ACCENT programme was made.
11h40: Microstructure-based 3D Fracture Modelling of Radiolytically Oxidised Gilsocarbon Graphite
Ye. Vertyagina and T.J. Marrow
The results of 3D multi-scale simulations of the Young’s modulus and tensile strength for irradiated and radiolytically oxidised Hinkley Point B graphite are presented and compared with experimental data with weight loss in the range of 8.1% - 68.2% from the Blackstone experiment. Virgin Heysham II graphite is also simulated and compared with experimental data. 3D X-ray tomography data are used to inform a cellular automata model with microstructure complexity, and the distribution and types of porosity lead to an inhomogeneous variation of microstructural properties. Irradiation and oxidation effects are then considered.
The agreements between the simulations and data are good. A proposed geometrical model for the bulk Young's modulus estimation can predict the elastic modulus value at the given weight loss. Microstructures of the filler particles and matrix in virgin and irradiated oxidised Gilsocarbon graphite demonstrate different behaviour at uniaxial tensile load. Microstructural changes in matrix are more extensive than in the filler during radiolytic oxidation, and this strongly controls the strength degradation. The developed model is applied to examine the effects on elastic modulus and tensile strength of variations in the proportion of matrix to filler, and also the influence of larger scale porosity.
12h00: Experimentally-Informed Modelling the Deformation and Fracture of Irradiated PGA Graphite
B. Šavija, D. Liu, G.E. Smith, P.J. Heard, K.R. Hallam, E. Schlangen, and P.E.J. Flewitt
Gas-cooled nuclear reactors operated in the UK are cooled by circulating carbon dioxide gas and the cores contain graphite bricks to both moderate the fast neutrons and fulfil structural requirements. The bricks become more porous during service due to radiolytic oxidation. Furthermore, mechanical properties of the graphite also change due to the neutron irradiation introducing crystal defects that cause the strength of the material to be increased. These opposing processes cause changes in the mechanical properties of the material
, and have the potential to modify the fracture characteristics of these quasi-brittle materials. Hence both contributions need to be taken into account in order to correctly model deformation and fracture.
In this work, an experimentally-informed model of mechanical and fracture properties of Pile Grade A (PGA) graphite is presented. First, a microstructural model which captures the main graphite features is developed. In order to mimic the degradation of the graphite microstructure, an increase in porosity is simulated in a model. Then, numerical analyses are performed to determine the mechanical properties and fracture characteristics appropriate to PGA graphite. Micro-mechanical properties of virgin and irradiated PGA graphite are used as an input for the simulations. The only experimental inputs used are mechanical properties of the specific graphite material resulting from micro-cantilever beam tests. The results provide an increased understanding of how the PGA graphite properties and fracture characteristics change in service.
12h20: Annealing Studies of Irradiated AGR Graphite
Tzelepi, P. Ramsay, T.L. Shaw and B.C. Davies
The mechanism of irradiation creep and its effect on the internal stresses of AGR core graphite are not well understood. Historical studies on Materials Test Reactor (MTR) creep specimens have shown that thermal annealing can lead to recovery of creep strain. In order to enhance understanding of irradiation creep and support the results of the MTR programme ACCENT, a thermal annealing test programme using irradiated trepanned AGR samples has commenced.
This paper describes the objectives of the annealing programme and reports the results from the first set of annealing runs. These have been carried out on eight Dungeness B samples, trepanned in 2014. The measurements include (i) laser mensuration of sample lengths and diameters, (ii) coefficient of thermal expansion (CTE) across sample thickness (radial direction) using a Netzsch dilatometer, (iii) CTE using Electronic Speckle Pattern Interferometry (ESPI) across the sample diameter (axial and hoop directions) and (iv) dynamic Young’s modulus (DYM). Further annealing tests are planned and will be undertaken under the Innovate-UK project “Influence of Creep and Geometry on Strength of Irradiated Graphite Components”.
12h40: Lunch. Boardwalk Restaurant.
MICROSTRUCTURE AND CREEP (2)
Chairman: Prof. Paul Mummery
13h30: Atomistic Models of Nuclear Graphite
T. Trevethan and M. Heggie
The properties of isotropic polycrystalline graphite are governed by how the anisotropic properties of the lattice combine with how individual crystallites are connected at grain boundaries. How this influences the response of the material to applied strain, and how the anisotropic irradiation induced property changes to individual crystallites leads to the overall isotropic changes to dimension
, elastic moduli and thermal expansion are a crucial part of understanding the mechanisms of irradiation induced creep in nuclear graphite. Atomistic models of polycrystalline graphite can provide a direct insight into the relationship between the crystallite properties, the microstructure and the isotropic behaviour. By employing a reactive interatomic potential that accurately reproduces the mechanical and thermal properties of graphite crystals, we have developed a methodology for constructing large-scale (multi-million atom) atomistic models of polycrystalline graphite that can reproduce the properties and behaviour of bulk material. Using the molecular dynamics method, the elastic properties and thermal expansion of these models has been investigated and compared with typical experimental observations. By examining the changes to atomistic strain tensors under applied stress or thermal expansion we have analysed how global strains are transmitted through the deformation of individual crystallites. These models also provide a basis for investigating the evolution of the bulk material properties under displacing irradiation. To investigate the links between crystallite and bulk dimensional change, distributions of extended defects (corresponding to different degrees of thermally annealed irradiation displacement damage) are incorporated into the polycrystal models. The resultant changes to the bulk properties are simulated using the molecular dynamics method. In addition to an atom level insight into the structural changes that occur, the atomistic models enable the explicit simulation of the X-ray diffraction patterns of the material which have been compared to experimental measurements.
13h50: Atomistic Approaches to Radiation Damage and What They Mean for Mechanism
M.I. Heggie, C.D. Latham, A.J. McKenna, T. Trevethan, A. Vuong, P.J.L. Young
Molecular dynamic calculations describe the prompt displacements of carbon nuclei after a neutron collision. They rely on interatomic potentials, which approximate energy in terms of more-or-less simple functions of atomic positions. The description of electrons and quantum mechanical behaviour, which is at the heart of chemical bonding, is sacrificed for speed. Density functional theory (DFT) calculations on the other hand take very good account of the electrons and gives reliable formation and migration energies of the various defects produced in the cascade, enabling the longer time scales of the cascade to be deduced as a function of irradiation temperature. In addition, this evolution can be followed in detail by kinetic Monte Carlo methods using DFT energies.
Many highly sophisticated experiments have been reported from nuclear research entities in the UK, USA and Japan which give clear evidence of very rich underlying defect physics with evidence for (i) radiation annealing, (ii) reverse annealing via three different processes, and (iii) stored energy release at 200 °C via three different processes.
In this talk we examine the modelling outputs and compare their predictions with experimental measurements, in order to validate mechanistic understanding of radiation damage and its physical property changes.
14h10: Innovate UK Project: Influence of Creep and Geometry on Strength of Irradiated Graphite Components – WP1 Objectives and Progress
S. Wilkinson, A. Tzelepi, B. Davies and A. G. Steer
The Innovate UK project is a joint venture by EDF Energy, NNL and the University of Manchester. It aims to improve the understanding of graphite fracture and irradiation creep behaviour by studying large specimens extracted from AGR and Magnox reactors. Valid fracture and creep data from these specimens would be used to reduce the major uncertainties in life predictions hence removing unnecessary conservatism and premature reactor shutdown. This feeds into the overall objective of the Innovate UK project being to maintain the continued safe and reliable operation of the existing AGR nuclear power stations.
This report details the objectives and progress of work package one of the project which concentrates on understanding graphite fracture. This started with developing machining techniques for cutting large irradiated graphite samples to the correct geometry and feature e.g.
keyway root. Now complete, the project moves to performing work of fracture (WoF) testing; fracture tests on large samples and those with keyway root features (KWF), dynamic Young’s modulus measurements and microstructural characterisation. This work will investigate size effects and properties of the measurements techniques. The microstructural characterisation aims to improve our understanding of the stress-strain relationship and cracking behaviour of graphite.
Chairman: Prof. Malcolm Heggie
14h30: Dealing with the "Known Unknowns”: Improving the Forecasting of Keyway Root Cracking
Probabilistic forecasts of keyway root cracking are the end point of a complex calculation that represents a system containing both variability and uncertainty. Neither the central estimate behaviour nor the variability is known perfectly – they are “known unknowns”. Therefore, it should not be unsurprising that forecasts may be imperfect or that they should evolve as new information becomes available and knowledge of the system improves. Yet, changes in forecasts in response to new information can sometimes be taken as evidence for an increase in the very uncertainty that the revised estimates should be reducing. It is therefore important to be able to answer the question “do we really understand the basis for the confidence we have in our forecasts?”
This paper outlines the approach that EDF Energy is taking to identify the “unknowns”, define their significance and update the forecasts, with reference to Rumsfeld’s now famous (or infamous) statement and the principle of Bayesian updating. It sets the scene for later presentations by outlining work that is being carried out in response to the observation of the onset of keyway root cracking in Hunterston B, with the aim of arriving at a position of increased confidence in the future forecasts.
14h50: Statistical Modelling of AGR Graphite Thermomechanical Properties and Dimensional Change
P.R. Maul, P.C. Robinson, J.F. Burrow and B.H. Hill
Understanding the evolution of AGR graphite brick properties as reactor cores age is essential for demonstrating continued safe operation and for estimating the remaining reactor lifetimes.
This paper describes the development and application of statistical models for measurable thermomechanical properties and dimensional change. Key features of the approach taken are:
• Model complexity is determined by the quality and quantity of available data.
• The models represent system variability and uncertainty separately and explicitly.
• Models are updated as new information becomes available, through changes to the model parameters and/or to the underlying modelling assumptions.
Examples are given of how comparisons have been made between predictions produced before a reactor inspection is undertaken and the measurements subsequently made; this provides information on model performance and predictive power.
Data from the trepanning of AGR bricks at reactor inspections needs to be supplemented by information from materials test reactor (MTR) experiments in order to provide information on the long term evolution of graphite properties. Details are given of how data from the Blackstone MTR experiments have been used for this purpose.
15h10: Stress Analysis Modelling of AGR Graphite Bricks using Statistical Models for Graphite Properties
A.E. Bond, P.C. Robinson, J.F. Burrow and P.R. Maul
Quintessa has developed methods for modelling the evolution of brick shapes and stresses in graphite bricks in AGRs. The calculations are undertaken using COMSOL Multiphysics® software together with statistical models for graphite property evolution. The development and application of these methods to Hinkley Point B and Hunterston B is described. The approach enables sensitivity studies and ‘what if’ questions to be addressed more rapidly than with traditional methods.
Keyway root cracks have been seen at the Hunterston B reactors, and the stress analysis calculations have been used to describe the expected evolution of cracking at the four reactors.
Conclusions that have been drawn from recent studies include:
• Calculated correlations between metrics for bore shape evolution and keyway root cracking risks can be used to provide input to predictions and forecasts of keyway root cracking.
• The calculated progression of keyway root cracking depends critically on system variability. An important contribution to the variability in brick cracking times comes from the variability in graphite dimensional change rates.
• It appears that detailed differences in brick geometries (such as the orientation of end-face keyways relative to axial keyways) may be relevant in determining cracking risks.
15h30: Coffee break Mayflower Foyer
15h50: Computational Modelling of Static and Dynamic Crack Propagation
C.J. Pearce and L. Kaczmarczyk
The theoretical basis for simulating unstable crack propagation in 3D hyperelastic continua within the context of configurational mechanics, and the associated numerical implementation, will be presented. The approach taken is based on the principle of global maximum energy dissipation for elastic solids, with configurational forces determining the direction of crack propagation. The work builds on the developments made by the authors for static analysis , incorporating the influence of the kinetic energy. The nonlinear system of equations is solved in a monolithic manner using Newton-Raphson scheme. Initial numerical results are presented.
We develop the physical and mathematical description to determine (a) when a crack will propagate, (b) the direction of propagation and (c) how far/fast the crack will propagate. Furthermore, we require a numerical setting to accurately resolve the evolving displacement discontinuity within the context of the Finite Element Method.
In this study, we present a mathematical derivation and numerical implementation that can achieve these goals
, solving for conservation of momentum in both the spatial and material domains. We adopt the Arbitrary Lagrangian-Eulerian (ALE) method, which is a kinematic framework to describe movement of the nodes of the finite element mesh independently of the material. Thus, we are able to resolve the propagating crack without influence from the original finite element mesh, and maintain mesh quality. The deformation and crack direction are solved simultaneously and the propagating fracture is continuously resolved by adapting the FEA mesh in a smooth and completely novel way, avoiding the need for element splitting or enrichment. Mesh quality is maintained by an efficient mesh smoothing technique coupled with a face flipping, node merger and edge splitting algorithm. The efficient solution of 3D crack propagation, with a large numbers of degrees of freedom, requires the use of an iterative solver for solving the system of algebraic equations. In such cases, controlling element quality enables us to optimise matrix conditioning, thereby increasing the computational efficiency of the solver.
The application of this work is the predictive modelling of crack propagation in nuclear graphite bricks, which are used as the moderator in UK advanced gas-cooled nuclear reactors (AGRs).
 Kaczmarczyk, Ł., Mousavi, M. and Pearce, C.J. Three-dimensional brittle fracture: configurational-force-driven crack propagation. International Journal for Numerical Methods in Engineering
, 531–550 (2014)
16h10: Designing a Computer Experiment to Study the Rate of Crack Opening in High Shrinkage Bricks
K. McNally, M. Fahad, M. Treifi, G.N. Hall, N. Warren and P. Mummery
The opening of full-thickness cracks and the subsequent effects on brick distortion and brick key/interactions are considered to be important factors when evaluating the behaviour of AGR cores. The observation of such full-thickness cracks in a sub-population of high shrinkage bricks in the Hunterston B (HNB) R4 core in 2014 provides a unique opportunity to assess the adequacy of prediction capabilities using a group of bricks that are perceived to be forerunners of the main population. However, in order to use the cracked high shrinkage bricks as a forerunner it is necessary to develop representative dimensional and material properties models for the graphite, since the graphite differs from the material in the main population.
In this work we describe research to calibrate the dimensional change relationship in finite element models (FE) of HNB R4 moderator bricks using a longitudinal dataset from core-monitoring of high-shrinkage bricks. Computer experiments for moderator bricks in layers four to nine were run with calibration based upon the data generated in these experiments. The work makes use of surrogate models (emulators) which delivers a substantial reduction in the computational burden of calibration.
16h30: Statistical Modelling of Keyway Root Cracking in AGR Graphite Bricks
P.C. Robinson, B.J. Hill, J.F. Burrow and P.R. Maul
Statistical methods for modelling the evolution of bore-initiated cracks in graphite bricks have been developed and applied over many years. The numbers of bricks that will experience bore cracking can now be forecast with confidence.
Cracks that originate at the outside of the brick (keyway root cracks) have now been seen at Hunterston B. In this paper details are given of how statistical modelling methods are being extended to address key issues associated with this type of cracking.
The CoreStats code is used to provide predictions for cracking at reactor inspections and long-term forecasts for the numbers of cracked bricks. It is used to address the question: Given the cracking seen to date, what cracking can be expected in future? Allowance has to be made for ‘bias’ in channel selection as some bricks are chosen for inspection because previous observations have suggested that they are more likely to be cracked than average.
The CrackSim code provides simulations for the evolution of cracking. It is used to address the question: Given the current understanding of the evolution of the processes of interest, is the planned inspections regime adequate to demonstrate that the probability of core integrity criteria being exceeded in a given time period is sufficiently low?
16h50: Dynamic Crack Propagation within AGR Graphite Bricks
T. Crump, G. Ferté, A. Jivkov, P. Mummery, P. Martinuzzi and V.X Tran
It has been postulated for many decades and recently observed that axial cracks originating in keyway corners can occur in AGR graphite bricks late in life. One of the possible consequences is Prompt Secondary Cracking (PSC), in which it is postulated that the superposition of shear strain waves generated by the opening of the first axial crack could initiate a second axial crack in one of the keyway corners directly opposite.
To assess the likelihood of this occurring, a robust method of modelling dynamic fracture developed in Code_Aster is considered. The approach uses a quasi-explicit time scheme and is known as: eX
ethod with rate-dependent cohesive elements (XCZM).
XCZM is used to model the primary crack in a thin 3D brick slice under an external hoop stress loading. The effects of dynamic crack propagation on the primary crack and global stress state are discussed including: stress amplification remotely to the crack and any possible crack bifurcation or fragmentation from this.
17h10: Prediction of Keyway Root Cracking in the Graphite Core of Advanced Gas Cooled Nuclear Reactors
Emma Tan, M. Fahad, G.N. Hall and N. Warren
Over the life of the AGRs, irradiation gives rise to degradation of the graphite core leading to internal stresses within the graphite fuel bricks and substantial decline in strength. Late in life these twin effects are predicted to lead to the formation of cracks originating from the keyways that could challenge the safe operation of the reactors.
The Finite Element (FE) Analyses of graphite components in a reactor are normally carried out using empirical relationships that describe the irradiation and oxidation induced changes to material properties. However, confidence in the analyses is constrained due to uncertainties in material property parameters.
These uncertainties as well as the variability in start-of-life material properties may be accounted for using Monte Carlo simulation, however such an approach is computationally expensive using FE analysis. This work makes use of a Gaussian Process emulator, a surrogate for the FE model, delivering a substantial reduction in the computational burden of stress predictions. We explore the most influential parameters and by comparing emulator predictions of stress with predictions of strength, present predictions of the rate of keyway root cracking using a probabilistic methodology. We also describe calibration of predictions of cracking with observations.
17h30: Introduction to Breakout Sessions
Dr James Reed / Prof Peter Flewitt
Rooms to be confirmed
: Cracking of Components
: Are the consequences of cracking greater for single cracking compared with doubly-cracked bricks?
Leader: Dr. Neil McLachlan Mayflower Suite
: Microstructure: Is there a common position amongst the specialists on what really counts (to determine irradiation behaviour)?
Irradiation Creep: Is irradiation creep just an amendment upon dimensional-change behaviour?
Leaders: Dr David Knowles / Prof Brian Rand Mayflower Foyer
: Reactor Inspection: Can we inspect just part of a core to understand the state of the whole core with adequate confidence?
Leader: Dr Philip Maul (Room to be advised)
Dinner – ad hoc
– discussion groups may continue afterwards!!