Reducing risk through uncertainty quantification for past, present and future generations of nuclear power plants

Lead Research Organisation: University of Manchester
Department Name: Materials

Abstract

To ensure national resilience and productivity in an uncertain world, the UK needs a safe, reliable energy supply. Electricity generated by domestic nuclear fission plant creates an important contribution to this, currently generating around one sixth of the UK's requirements. Future fusion-powered plant provide a vision of lower waste, higher safety energy generation from essentially limitless fuel.

However, poor public perception of nuclear safety is limiting uptake, whilst poor understanding of the behaviour of critical nuclear materials exposed to thermal, mechanical and radiation loading increases engineering uncertainty, hence escalating design risk and operational cost.

This programme of research uses a multi-scale, multi-technique approach, combining high performance computer models with imaging analysis, to build a deeper understanding of the mechanical behaviour of several vital engineering materials subject to such stresses:
* silicon ceramics used for the containment of historic nuclear waste,
* graphite used for moderating reactions in the current generation of nuclear plant,
* beryllium and tungsten used to line containment vessels for future fusion generation.

Developing better, experimentally-validated models of the structural integrity of such vital components will enable increased accuracy in design, hence reducing the cost of build and operation of power generation and waste storage facilities and giving greater public confidence in the industry.

The research combines the strengths of two computational approaches:
* Fully physically-based materials models, which are well-developed, but are not yet applicable to large and complex engineering systems;
* Empirical engineering models, which are useful in the domain for which they have been calibrated, but currently have limited transferability;
along with rigorous error analysis, to create an approach that is transferable across length scales, enabling the tracking of fundamental physical mechanisms through to engineering application.

The experimental elements of the programme, using X-ray tomography to create 3D images of strain and damage inside samples and Digital Image Correlation to track real-time crack propagation, will provide new insight into the behaviour of these critical materials under stress and observational parameters to inform the modelling.

The project will draw from the strengths of the interdisciplinary team to develop experts of the future. It will involve and inform industrial partners and other key stakeholders, from regulators to plant workers, to ensure results are relevant to and taken up by UK energy generation and other strategically important industries.

Planned Impact

In addition to the knowledge and people impacts generated, described in the academic beneficiaries section above, the research programme also generates economic and societal impact for a wide range of stakeholders and end users who will benefit from its outcomes.

For national resilience and productivity, the UK requires reliable baseline power generation. This has been put at risk through the phase out of conventional fossil fuel plant in line with international carbon reduction obligations, with increasing dependence on variable renewable resource. Threats of "brown outs" and load management through reduction of factory operating hours are leading to UK concerns about quality of domestic energy supply and reliability of industrial processes. In addition, the need to reduce reliance on overseas power supplies becomes ever more important given the uncertain global political situation. Hence research programmes such as this, which improve the reliability and safety of domestically-generated energy and accelerate the fission to fusion transition, are of vital national importance.

The owners and operators of existing power plant and waste storage facilities, from government agencies such as the Nuclear Decommissioning Agency to private companies such as EDF, will directly benefit from this research programme through a better understanding of expected behaviour of critical engineering materials, leading to safer and more effective processes and hence greater public confidence in and acceptability of nuclear power generation.

More widely, connections between the research team and their existing collaborators in national, European and wider international institutions such as Culham Centre for Fusion Energy, the National Nuclear Laboratory, the French Alternative Energies and Atomic Energy Commission (CEA), and Lawrence Livermore and Los Alamos National Laboratories, will ensure strong uptake of results, hence increasing safety nationally and globally.

Whilst the primary focus of this project is the nuclear industry, the generality of the fracture problem is such that the methodology and results can also be extended to other industries where fracture is a concern, and which BEIS recognises as strategically important, thereby further strengthening UK industrial strategy. This includes aerospace, shipbuilding, defence, renewable power and other fields where high strain rate is a concern. Thus stakeholders such as AWE, BAE and Rolls Royce will also benefit from research outcomes.

Collaboration with the Health & Safety Executive, through project interactions with staff from HSE's Health & Safety Laboratory, will enable results of the fracture tests to be incorporated into regulation around handling and use of demanding materials, such as beryllium and irradiated graphite, in the industrial environment - hence improving industrial safety standards.

All these stakeholders will be engaged through the Advisory Panel, the communications programme and other activities described in the Pathways to Impact section that follows.

Publications

10 25 50
 
Description The Work Package (WP) handled by the University of Manchester at Harwell (UoMaH) consisted in the experimental determination of key parameters to assess quantitatively the initiation and development of fracture in the key materials identified in the project. To this end, we performed 6 experimental campaigns at the I13-2 beamline of the Diamond Light Source facility, covering more than 600 hours of use of synchrotron radiation. To derive the most meaningful results, we focused on in-situ experiments where quantitative imaging of the materials always takes place under load during the fracture development. However, the very different materials targeted in the project imposed several distinct experimental constraints, and therefore different approaches for the data acquisition and analysis. For this reason, we will address the progresses made during this project by the UoMaH for each material separately.
1 - Graphite
Graphite is structural material with good neutron moderation properties. As such, it is currently the structural material of the core of most of today's UK nuclear power plant. This graphite property is also at the heart of one of the design envisaged for the 4th generation of power plant, namely the (very/) high temperature reactor (HTR or VHTR). However, the neutron irradiation leads to the deformation of the graphite bricks, and the fracture that eventually develop represent a safety hazard leading to the end of life of the reactor. The next generation of power plants will use graphite grades with much finer microstructure, and higher operating temperatures, which calls for a reassessment of the fracture properties of graphite as a function of size and temperature.
To this end, we have monitored the fracture initiation and development in a representative grade of fine grain graphite as a function of the specimen size and temperature. Specimens were machined into the double cleavage drilled compression (DCDC) geometry to allow for the generation of stable cracks under mode I opening, as shown in the figure 1. The nearly cylindrical symmetry of the rectangular samples is also an advantage for the imaging method we used, as it reduces the artefacts on the reconstructed tomographs. Three different sample sizes (24x12x12 mm3, 18x6x6 mm3 and 12x4x4 mm3) were compressed at four different temperatures (25°C, 200°C, 400°C and 600°C), with live tomography being used to capture changes in the internal structure of the sample.

Figure 1 - A sample in the DCDC geometry is visible in grey. The compressive load from the anvils in black transforms into a tensile load around the central cavity. The volume of interest for the computation of the displacement field is highlighted in purple. A typical high-density mesh used for the DVC analysis is shown together with the sample geometry. The colour coding on the mesh represents the magnitude of displacement component transverse to the crack plane.
The structure of graphite, formed of precursor particles embedded in a porous matrix, offers a high spatial density of resolvable features in tomography, allowing for the computation of the full field internal displacement fields from Digital Volume Correlation (DVC). DVC tracks the displacement of single elements from a mesh by finding on a deformed volume the position that maximizes the correlation with respect to the reference volume. Even with high-end computers, the hardware capability limits the overall mesh size, or the size of its elements. This leads respectively to a displacement field derived over a small volume of interest, or with a coarse spatial resolution. During this project, we have developed a workflow that enables global DVC on virtually any volume size by stitching together individual DVC processes performed on sub-regions of the global mesh. A typical mesh handled by this workflow is shown in the figure 1. Using this workflow, we obtained the internal displacement fields with the highest spatial resolution on each sample at each stage of the deformation. Moreover, the DVC technique helps with the segmentation of the crack, which is nearly impossible to visualise from the reconstructed volumes because the absorption contrast inside the crack is identical to that of the internal porosity. Using DVC the reference volume deformed with the obtained displacement field, a comparison with the deformed volume naturally highlights the crack and allows for an accurate segmentation of the new free volume.
Overall, the experiment allows the determination of the loading curve, the displacement field and the crack morphology. The displacement field can be used directly for an assessment of modelling codes, typically Finite Elements simulations. The quantitative outputs from the imaging include:
- The full field internal displacement field.
- The corresponding strain field.
- The position of the crack front.
- The crack width profile.
- The magnitude of the displacement corresponding to the opening modes I, II and III.
From the low magnitude of mode II and III displacements across the crack front, we are confident of the validity of our experiments. The loading curves indicate different energy dissipation mechanisms as a function of the size at room temperature, where larger samples continue to store elastic energy together with crack growth, while all further loading in smaller samples only expand the crack. This provides an estimate of the characteristic sample size where the process fracture zone (PFZ, the region ahead of the crack where inelastic energy dissipation occurs) interact with the sample boundaries. The analysis of the strain field is consistent with these different energy dissipation mechanisms: a well-defined PFZ can be identified in large samples, while inelastic strains are visible from the crack front to the sample boundaries in smaller samples.
Our current work is dedicated to the expansion of these results to include the effect of temperature, as these size effects at operating temperatures constitute an important parameter for a full-scale modelling. Also, in addition to adding to the results obtained during the grant period, we are now using the knowledge gained to expand the technique for all facility users who wish to adopt this technique by creating automated routines to collect and process the data. This will add value to investments at the facilities and build upon UKRI investment to ensure a better capability for UK going forward.

2 - Beryllium
Beryllium tiles were chosen as they are the plasma facing material to be used in the ITER Tokamak reactor. As such, the beryllium tiles will face extreme neutron irradiation and heat load, the latter being the main cause for the initiation and development of fracture due to the non-uniform thermal expansion across the material. While the magnitude of the in-operando conditions of a Tokamak reactor are very difficult to reproduce in the lab, there is currently a focus on assessing the behaviour of beryllium under such constraints. In this context, we worked on fracture development in beryllium to provide a fully experimental and quantitative description of crack development in a controlled mode I loading. The basic layout of the experiment is the same as for the graphite, with samples in the DCDC geometry compressed to generate stable crack in controlled mode I opening. To handle the significant hazards that beryllium presents, we developed and commissioned a double containment cell for compressive loading mechanical tests. This has now also been passed to the facilities for their use for all UK users who wish to do such experiments. This again represents value added for UKRI programme investment.
A typical Computed Tomography experiment provides the 3D map of the absorption of a sample. However, the very low atomic number of beryllium prevents this, as the negligible absorption leads to a poor contrast. Here, we used phase contrast imaging, where the boundaries of the sample are reconstructed from the phase changes induced in a partially coherent x-ray beam. Thanks to the coherence properties of the x-ray beam at the Diamond Light Source Synchrotron I13-2 beamline, we managed to reconstruct high quality volumetric data of beryllium samples at different stages of the fracture development. The segmentation of a crack from a homogeneous surrounding is a relatively easy task, and we could get the crack morphology from all tomographs, including the width and crack front position. However, the homogeneity of the beryllium prevents the derivation of the internal displacement field using DVC, as there is nearly no feature to track inside the reconstructed volume. As the DVC process does not work for beryllium, we are actively working on a new solution to track the displacement of the few individual features, which correspond to small voids or high-density inclusions.
To connect the crack front position to the local strain, and the new free surfaces of the crack to the energy dissipation measured from the loading curves, we added tungsten powder (< 14 ?m in size) on one sample edge and performed the 2D analogue of DVC, known as Digital Image Correlation (DIC). In addition to the 3D volumes derived from tomography, the 2D images of the absorption through the sample were recorded as function of the applied deformation, using the contrast from the tungsten powder to extract the displacement field on the sample surface.

Figure 2 - Displacement field on beryllium from Digital Image Correlation. The image of the sample at rest highlights the region of interest considered for the DIC. Two images illustrate the subsequent stages of the fracture development and the corresponding intensity of the transverse component of the displacement field. The scaling of the displacement magnitude is normalized in the image. It ranges from -182 ?m to 208 ?m (blue to yellow) in b) and from -338 ?m to 429 ?m (blue to yellow) in c).
As shown in the figure 2, the DIC process produced accurate displacement fields allowing the derivation of the local strain around the crack tip. Current work is focused on the derivation of the energy dissipated per crack surface area, the so-called J-integrals, directly from the displacement field. This quantity is more accurate that the total mechanical work transmitted to the sample, as part of this work is dissipated by the development of plastic hinges in the material, visible from the bulging of the sample in figure 2b and 2c.
We have used x-ray computed tomography and Digital Volume Correlation to enable quantitative monitoring of plasticity development in-situ in volume during the critical failure in nuclear materials. Using a specific sample test geometry particularly suited for x-ray tomography, the visualization of the plastic strains gives the extension of the fracture process zone during crack propagation, and energy dissipation is measurable. Moreover, dynamic experiments are now feasible using a recently suggested combination of X-ray computed tomography and Digital Volume Correlation.
3 - Eurofer
The high neutron irradiation within the fusion power plants threatens also the structural materials, such as steels, who are prone to swelling and embrittlement because of the implementation of hydrogen and helium as transmutation products of the incoming neutrons. So far, reduced activation ferritic-martensitic (RAFM) and oxide dispersion strengthened (ODS) steels are the main candidate materials to tackle this challenge. Among these, the Eurofer97 grade is currently the reference structural material for first wall and blanket of DEMO, the industrial prototype for a nuclear fusion reactor.
In this project, we have attempted to perform DIC across the scales, from the nanometre to millimetre, covering 6 orders of magnitude of length. During the tensile loading of a dog bone specimen, we have used the Transmission X-Ray Microscope of the Diamond Light Source Synchrotron I13-2 beamline to obtain 87 ?m wide images of the transmission through the 70 ?m thick sample, with a pixel size of 60 nm. We adopted a raster scan strategy to cover a surface of 4 x 1.2 mm2 (width x height), corresponding to the width of the sample in the region of interest. A pre-made notch helped to localize the strain and monitor the initiation of fracture. The stitching of the 390 frames, visible in the figure 3, is satisfactory and compensates the inevitable drifts during the 2-hour long data acquisition. The polishing marks provide the absorption contrast for the DIC, which was shown to work away from the crack. However, the acquisition time chosen to acquire images with sufficient quality when transmission is minimal (through the sample) led to an over-exposition at the notch tip, where the nanometre resolution is valuable. Therefore, even if we demonstrated the feasibility of the DIC combining high spatial resolution and wide field of view, we have no results regarding the steel itself. We did not have the time to reproduce the experiment with a more careful acquisition strategy. This may be possible with future funding bids that are in preparation.
Exploitation Route The investment in grant EP/R012423/1 has allowed innovation in a series of different programme areas. Firstly, we have developed, successfully used and in last few years cascaded to the facilities, a new methodology for the capture, analysis, and measurement of material failure under a controlled load. This is now incorporated for use on the Diamond Light Source Synchrotron and the ISIS Neutron and Muon Source IMAT station and users who require assistance are referred to the UoMaH for help with fielding and construction of cells if they need to. Secondly, the results are part of the ongoing efforts in UKAEA to field fusion powerplants for the UK and our work has been put into their planning routines for characterising materials for future development of the next generation plants into the future. Finally, our international partners at Los Alamos National Laboratory (US) have undertaken a series of similar tests, using the beryllium material, using a similar geometry, but adopting a different analysis technique to that we developed. I am delighted to report that they have obtained very similar values for the fracture toughness of the material to that which we derived in our work. The grant has proved principle as well as developing new techniques, and with the new data obtained has levered new possibilities for the testing and adoption of materials for future power plants in the most extreme environments.
Sectors Aerospace, Defence and Marine,Education,Energy

 
Description The investment in grant EP/R012423/1 has allowed innovation in a series of different programme areas. Firstly, we have developed, successfully used and in last few years cascaded to the facilities, a new methodology for the capture, analysis, and measurement of material failure under a controlled load. This is now incorporated for use on the DLS and the ISIS IMAT station and users who require assistance are forwarded to the UoMaH for help with fielding and construction of cells if they need to. Secondly, the results are part of the ongoing efforts in UKAEA to field fusion powerplants for the UK and our work has been put into their planning routines for characterising materials for future development of the next generation plants into the future. Finally, our international partners at Los Alamos National Laboratory (US) have undertaken a series of similar tests, using the beryllium material, using a similar geometry, but adopting a different analysis technique to that we developed. I am delighted to report that they have obtained very similar values for the fracture toughness of the material to that which we derived in our work. The grant has proved principle as well as developing new techniques, and with the new data obtained has levered new possibilities for the testing and adoption of materials for future power plants in the most extreme environments.
First Year Of Impact 2022
Sector Aerospace, Defence and Marine,Energy
 
Title Graphite and Beryllium Sample Analysis 
Description Beryllium (toxic) and graphite samples have been investigated using a combination of synchrotron X-ray computed tomography and mechanical loading (compression). Due to the design of the sample (containing a notch), the compressive load is transformed into a tensile one that drives the propagation of a crack. The main advance in data analysis methodology obtained in this project has been the development of a new method to be able to perform global digital volume correlation (DVC) on X-ray Computed Tomography (XCT) volumes larger than the capabilities of a given computer hardware. The method relies on dividing the large meshed volume into smaller overlapping volumes, and corresponding meshes, that can be handled successively by the computer hardware to perform global DVC. Then, the nodes in the overlapping regions are assessed and the resulting sub-volumes global DVC results are merged into a single output result file covering the entire XCT volume. The methodology was presented at the industrial Computed Tomography 2022 conference (Online, Wels, Austria, PDF: https://www.ndt.net/search/docs.php3?id=26629 ) "Global digital volume correlation of large volumes: a sub-volume adaptive meshing approach" Nondestructive Testing (NDT) Open Access Archive, Database, Conference Proceedings, Journal Articles, News, Products, Services. Professional Networking, Exhibition, Forums, Jobs www.ndt.net - Data handling and control systems that have applications outside of the original research area or technology (e.g. data matching, monitoring, modelling, grid infrastructure). Overall, the sub-volume adaptive meshing approach introduced above is a solution to overcomes hardware limitations in any case where global DVC is required over large volumes and meshing density can be user-defined to fit the expected damage location within the sample, regardless of the sample type, and can thus be used for any application or field of research using DVC. 
Type Of Material Data analysis technique 
Year Produced 2022 
Provided To Others? No  
Impact The main advance in data analysis methodology obtained in this project has been the development of a new method to be able to perform global digital volume correlation (DVC) on X-ray Computed Tomography (XCT) volumes larger than the capabilities of a given computer hardware. The method relies on dividing the large meshed volume into smaller overlapping volumes, and corresponding meshes, that can be handled successively by the computer hardware to perform global DVC. Then, the nodes in the overlapping regions are assessed and the resulting sub-volumes global DVC results are merged into a single output result file covering the entire XCT volume. 
 
Description UoMaH and Los Alamos National laboratory collaboration 
Organisation Los Alamos National Laboratory
Country United States 
Sector Public 
PI Contribution We have shared our research results with LANL
Collaborator Contribution Los Alamos National Laboratory (US) have undertaken a series of similar tests, using the beryllium material, using a similar geometry, but adopting a different analysis technique to that we developed. I am delighted to report that they have obtained very similar values for the fracture toughness of the material to that which we derived in our work. The grant has proved principle as well as developing new techniques, and with the new data obtained has levered new possibilities for the testing and adoption of materials for future power plants in the most extreme environments.
Impact n/a
Start Year 2022
 
Description UoMaH and UKAEA collaboration 
Organisation Culham Centre for Fusion Energy
Country United Kingdom 
Sector Academic/University 
PI Contribution The results of this research grant are part of the ongoing efforts in UKAEA to field fusion powerplants for the UK and our work has been put into their planning routines for characterising materials for future development of the next generation plants into the future.
Collaborator Contribution n/a
Impact n/a
Start Year 2022
 
Description UoMaH and UKAEA collaboration 
Organisation UK Atomic Energy Authority
Country United Kingdom 
Sector Public 
PI Contribution The results of this research grant are part of the ongoing efforts in UKAEA to field fusion powerplants for the UK and our work has been put into their planning routines for characterising materials for future development of the next generation plants into the future.
Collaborator Contribution n/a
Impact n/a
Start Year 2022
 
Description Attended and presented UKAEA/CCFE meeting with other nuclear profesiionals 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Professional Practitioners
Results and Impact Prof Neil Bourne and Dr Antoine Cornet attended and presented UKAEA/CCFE meeting with other nuclear professionals from Oxford and other Universities. Dr Cornet briefed experiments done as part of the Reducing Risk project.
Year(s) Of Engagement Activity 2020
 
Description Diamond Light Source/I13 beamline Scientist meeting presentation 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Professional Practitioners
Results and Impact A presentation entitled "High spatial resolution - large field of view in-situ imaging of Eurofer 97 steel with Transmission X-ray Microscope at I13-2 - Update" was given by PDRA Antoine Cornet as part of the I13 scientist weekly meetings, on 2/07/2020. The purpose of the meeting if for I13 professional practitioners to learn from other users of the I13 beamline at Diamond. As part of the presentation Antoine received suggestions/advice for future experiments setup.
Year(s) Of Engagement Activity 2020
 
Description Presentation at the "Postdocs in Nuclear Energy meeting (Pine)" 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact PDRA, Dr. Antoine Cornet presented at "Postdocs in Nuclear Energy meeting (Pine)", on the 30th September 2020 The title of presentation was "Size effect and fracture behaviour in nuclear graphite for the next generation of prismatic nuclear power plant".
Year(s) Of Engagement Activity 2020
 
Description Presentation to AWE Nov 2021 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Industry/Business
Results and Impact Presentations were made showing results of experiment on Graphite. Sparked interest from AWE and wish to start research collaborations between the project group and AWE
Year(s) Of Engagement Activity 2021
 
Description Presentation to AWE Nov 2021 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Industry/Business
Results and Impact Presentations were made showing results of experiment on Graphite. Sparked interest from AWE and wish to start research collaborations between the project group and AWE
Year(s) Of Engagement Activity 2021
 
Description Project Presentation at the HSE September 2021 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Policymakers/politicians
Results and Impact Presentation by the Project team at one of the HSE Chief Advisor Lunchtime seminars to 40-50 attendees. Project results were of interest to HSE as they are regulators especially for Nuclear plants.
Year(s) Of Engagement Activity 2021
URL https://events.manchester.ac.uk/event/event:mvf-kxaag6nc-ff2sms
 
Description Project Presentation made to UKAEA/MRF leadership visits To Rutherford Appleton Laboratories 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Industry/Business
Results and Impact Project Presentation was made explaining different performance results of experiments done on irradiated and non radiated graphite. Graphite performance is of interest to UkAEA as its the material used in their reactors. Presentation led to discussion of research collaborations that could occur in 2022
Year(s) Of Engagement Activity 2021