The inspection of safety-critical components in the nuclear power industry depends on procedures that can detect defects to a given threshold of severity; the acceptance process for this is known as inspection qualification. Inspection qualification in the UK is a highly developed formal activity, and is representative of the best practice in the world. However it can be very conservative if there is uncertainty in the expected measured response. A vital example is the scattering of ultrasound from the tips of rough cracks, such as thermal fatigue cracks or stress corrosion cracks. Ultrasound scattering from crack tips is widely exploited to measure crack sizes, but while the nature of the scattering is well understood for smooth cracks, scattering from the tips of rough cracks can differ significantly, and is not readily predictable. Consequently the qualification of ultrasound inspections for rough cracks has to be subject to severely conservative assumptions, and even so there remains a risk of misinterpreting findings. This project aims to bring understanding to the nature of the scattering, and to develop predictive modelling tools, such that these conservative assumptions can be safely eroded and the reliability of inspections improved. This will enable industry to reduce the costs of manufacturing and repairing, and down-time from outages, as well as improving confidence in the safe operation of safety-critical plant. The project will build on a strong UK heritage of the knowledge of ultrasound scattering, including recent work by the proposers on the stochastic nature of wave reflections from rough surfaces. The key aim is to deliver a new analytical approach that will predict the statistically expected scattering from the tips of cracks of given characteristics of roughness. The work will also include experimental investigation of real cracks and numerical modelling studies. The new ideas will be applied to the primary ultrasound inspection techniques of Time-of-Flight-Diffraction, Pulse-Echo, and array imaging. The work will be undertaken as a collaboration between researchers in Mechanical Engineering and in Mathematics at Imperial College. The proposal is being submitted within the UK Research Centre in NDE (RCNDE) to its targeted research programme. The proposal has been reviewed internally by the RCNDE, approved by the RCNDE board, and supported financially by five RCNDE industrial members.

Ductile materials, like metals and alloys, are widely used in engineering structures either by themselves or as reinforcement. They usually can sustain a lot of plastic damage before failing. Engineers understand quite well the ways that metals fail and how tolerant they are to damage, so efficient and less massive structures may be designed with well-defined margins of safety or reserve strength to cope with extreme events. By comparison, elastic brittle materials such as glasses and ceramics can fail without prior warning, so much larger safety margins are needed. Quasi-brittle materials are an important class of structural materials. They are brittle materials with some tolerance to damage and include concrete, polygranular graphite, ceramic-matrix composites, geological structures like rocks and bio-medical materials such as bone and bone replacements. Although their damage tolerance is much less than many metals and alloys, it can be quite significant compared to brittle materials such as ceramics and glasses. But this is not accounted for very well when engineers design with, or assess, quasi-brittle materials, as there is not an adequate understanding of the role on their damage tolerance of factors such as the microstructure of the material or the state of stress. Quasi-brittle materials are usually treated as fully brittle, taking little or no account of their damage tolerance, so assessments incorporate very significant safety margins, leading to designs that may be inefficient and unnecessarily bulky. Even when some assessment of damage tolerance is included, the microstructure can change as the material ages over time, and we need ways to measure the effects of this and to predict what it will do to the safety of the structure. This project aims to develop a method to predict the performance and evaluate the integrity of structures and components made from quasi-brittle materials. This will extend opportunities for their use in engineering applications, enabling more efficient design with greater confidence in safety. Quasi-brittleness is a property that emerges from the material's microstructure. A quasi-brittle material can be made from a connected network of very brittle parts (for instance, a porous ceramic). It exhibits a characteristic "graceful" failure as parts break locally when loaded sufficiently, which gives it damage tolerance. The "gracefulness" of the failure is affected by the random variations of strength and stiffness of the network and the form of the connections. Such networks represent a key part of the microstructure of the material, and to understand quasi-brittle fracture we need to construct models that properly describe the microstructure. There is a need to understand and define the mechanisms that control the fracture at the small and the large scale within these quasi-brittle materials. This will allow us to capture sensitivity to microstructure differences and degradation, and to produce general models that are suitable for the wide range of quasi-brittle materials and applications. Three-dimensional models that are faithful to the microstructure can be created using modern 3D microscopy methods, such as X-ray computed tomography. But these models are far too complex to simply scale up to structures very large relative to the microstructure. There is no computer than can do this, yet. We will develop modelling methods that sufficiently represent the complexity of quasi-brittle microstructures over a wide range of length scales, such as cellular automata finite elements. We will use advanced tomography and strain mapping techniques to observe how damage develops and to test and refine our models. We will then use this and the understanding that we gain to design new material tests and characterisation methods so that our methods may be used in a wide range of materials, from concretes to advanced nuclear composites, bone replacement biomaterials and geological materials.

The technical basis of this proposal pertains to the Neutron Transport Equation (NTE), which is used to describe neutron density in a physical environment where nuclear fission is taking place, such as a reactor core. This equation is of prime importance in the nuclear industry as it is used to construct models of reactor cores, nuclear medical equipment (e.g. for proton therapy) and other industrial scenarios where irradiation occurs. Primarily these models are used to assess safety and inform regulatory procedure when handling radioactive materials. Although the NTE can be derived through physical considerations of mass transport, it can also be derived using entirely probabilistic means. To be more precise, the NTE can be derived from the stochastic analysis of a spatial branching process. The latter models the evolution of neutron particles as they behave in reality, incorporating the features of random scattering and random fission, with increasing numbers of particles as time evolves. The derivation using spatial branching processes has been known since the 1960/70s, however, since then, very little innovation in the literature has emerged through probabilistic analysis. This mirrors a general lull in fundamental mathematical research contributing to modelling of nuclear fission after the 1980s. In recent years, however, the nuclear power and nuclear regulatory industries have a greater need for a deep understanding the spectral properties of the NTE. Such analytical quantities help e.g. engineers model the criticality and density of nuclear fission activity within a reactor core. In turn this informs optimal reactor design from several different view points (safety, energy production, efficiency etc.) as well as address regulatory constraints. With the decommissioning of old and the construction of new, more efficient and environmentally friendly nuclear power stations the demand for mathematical modelling using the NTE was never greater. The inhomogeneous nature of the NTE as it is used in practice has seen industry turn to Monte-Carlo techniques based on the underlying probabilistic treatment from 40-50 years ago. Many of the associated algorithms can only be run on supercomputers as they boil down to costly Monte-Carlo cycles of the entire fission processes, in essence replicating a virtual physical reality in a computer. This has the huge drawback that computational parallelization is not possible. In the decades that new probabilistic developments have been absent from the treatment of the NTE, there has been a significant evolution in the mathematical theory of spatial branching processes and related stochastic processes. The research in this proposal aims to re-align the understanding of the NTE with the modern theory of spatial branching processes. This is principally motivated by the implication that a whole suite of completely new Monte-Carlo techniques can be developed, as desired by industry, which are, fundamentally, of a lower order of complexity than existing algorithms. The overall aim of this project is to develop a `proof of concept' for this completely new approach, providing the theoretical basis and a stochastic numerical analysis that quantifies relative efficiency. In particular, the most important feature of the new algorithms that will emerge is the ability to parallelize computations. The project will be carried out in close scientific collaboration with industrial partner Amec-Foster-Wheeler, a major UK-based energy consultancies and one of the global leaders in servicing the nuclear energy and nuclear medical industries with simulation software for safety and regulatory purposes. All research output will be made open source on a webpage dedicated to the project.

This project aims to provide a predictive model for creep deformation of in-core nuclear components in the presence of irradiation damage. Creep deformation is time-dependent permanent deformation of materials under load nominally at temperatures higher than half the material melting point. Creep deformation plays a crucial role in the structural integrity of engineering components that work at high temperature such as those in aerospace propulsion and energy generation. It is one of the main life limiting factors of nuclear power plants that work at high temperature. This includes fusion reactors, Gen IV fission nuclear reactors, and UK's unique Advanced Gas-cooled Reactors. The context of this project is nuclear. UK's energy mix currently is and planned to continue to benefit from substantive contributions from nuclear. In addition, UK is the only country in the world that has in-depth and knowledge of designing, building, and operating high temperature nuclear power plants with many of its structural components working in the creep regime. The immediate new build reactors at Hinckley Point, Wylfa, and Moorside do not work at temperatures that induce creep. However, fusion reactors and Gen IV fission nuclear reactors are envisaged to be working at much higher temperatures to increase their thermal efficiency and as such they are susceptible to creep deformation and damage. Therefore, there is a high risk that UK loses its current unrivalled authority on high temperature structural integrity by the time the next generation of nuclear power plants are built, currently planned for 2050. One of the objectives of this proposal is to maintain UK lead in high temperature structural integrity of nuclear industry by developing new knowledge and new skilled scientists in the field. The current creep engineering structural integrity codes are based on empirical equations extracted from tests in certain standard conditions. They ignore the material microstructure, which evolves during a 60 years' service of a power plants. An important limiting factor that is currently ignored in the engineering codes and will be highly influential in the mechanical response of components for next generation power plants is irradiation damage. One of our objectives is therefore to include the effects of irradiation damage on the macro-scale mechanical response of materials by including the changes it makes on the material microstructure in their constitutive laws. To this end our main objective is to develop a predictive, multi-scale, microstructurally informed creep deformation model. The model spans from the fundamental physical equations that govern the dislocation mobility at high temperature (dislocations are imperfection in material crystal structure and their movements under load account for most the material permanent deformation) to the behaviour of engineering components with complex geometries and varied loading history and conditions made from homogenised material. The model will help engineers to predict the behaviour of critical components in a nuclear reactor and make informed decision on their fitness for service which is a crucial safety decision. Once our creep model is validated and verified by experiments across three mico, meso, and macro length scales, it will provide the foundation for a new generation of engineering structural integrity codes that are based on a mechanistic understanding the material and its microstructure and therefore is predictive, more accurate and not confined to the test conditions it is based on. This will be an invaluable asset for the UK to play a major role in designing, building, and operating future nuclear power plants.

In UK Energy strategy, nuclear fission is growing rapidly in significance. Government's recent Nuclear Industrial Strategy states clearly that the UK should retain the option to deploy a range of nuclear fission technologies in the decades ahead, and that it should underpin the skill base to do so. The primary aim of Next Generation Nuclear is to provide high quality research training in the science and engineering underpinning nuclear fission technology, focused particularly on developing a multi-scale (from molecular to macroscopic), multi-disciplined understanding of key processes and systems. Nuclear fission research underpins strategic UK priorities, including the safe management of the historic nuclear legacy, securing future low carbon energy resources, and supporting UK defence and security policies. It has become clear that skills are very likely to limit the UK's nuclear capacity, with over half of the civil nuclear workforce and 70% of Subject Matter Experts due to retire by 2025. High level R&D skills are therefore on the critical path for all the UK's nuclear ambitions and, because of the 10-15 year lead time needed to address this shortage, urgent action is needed now. Next Generation Nuclear is a collaborative CDT involving the Universities of Lancaster, Leeds, Liverpool, Manchester and Sheffield, which aims to develop the next generation of nuclear research leaders and deliver underpinning (Technology Readiness Level (TRL) 1-3), long term science and engineering to meet the national priorities identified in Government's Nuclear Industrial Vision. Its scope complements the Nuclear IDC (TRL 4-6), with both Centres aiming to work together and exploit potential synergies. In collaboration with key nuclear industry partners, Next Generation Nuclear will build on the very successful Nuclear First programme to deliver a high quality training programme tailored to student needs; high profile, high impact outreach; and adventurous doctoral research which underpins real industry challenges.