Ageing infrastructure and the move towards more advanced materials raises new, currently unsolved, inspection challenges. Fatigue and creep damage are two of the most common modes of failure in engineering structures, yet both are extremely difficult to detect in early stages of development. Similarly, there is a growing need to inspect bonded joints, be it adhesively bonded composites for major engineering components, or diffusion bonded metal components such as super-plastically deformed fan blades. This lack of inspection technique is artificially limiting the lifetimes and use of engineering components and was recently highlighted as a key requirement on the 5-10 year horizon by a group of industrial end-users of Non-Destructive Evaluation (NDE). They specifically highlighted the need for ``techniques identified for crack precursors, difficult and new engineering materials''. This fellowship will enable the applicant to develop practical and deployable nonlinear ultrasonic inspection techniques for monitoring of each of these damage scenarios, making use of recent developments in ultrasonic equipment, specifically highly flexible phased array systems and novel experimental techniques. The use of phased arrays, which are specifically tailored for NDE, is key. They allow multiple measurements without sensor repositioning, eliminating the high coupling and alignment variability that can readily mask the extremely small nonlinear signals. Even more importantly, the approach in this fellowship will enable localisation of nonlinearity within a specimen. This is currently not possible with any degree of reliability and represents a key barrier to wider adoption of this exciting inspection approach.

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.

The objective of this project is to obtain a step-change improvement in the detection and characterisation of defects in safety-critical components across a range of industries including nuclear power generation and the defence sector. This will be achieved through data-fusion of the multiple views of a component's interior that can be obtained through modern ultrasonic array imaging techniques. Previous work by the team has demonstrated a two-order-of-magnitude improvement in detection performance when data fusion was applied to ultrasonic data obtained from separate scans performed with single-element probes. This was in a case where the expected defects were small, point-like inclusions that scatter roughly uniformly in all directions. The proposed project will develop the data-fusion philosophy for improving defect detection performance from multi-view array data in the much more complex case where the defect morphology cannot be assumed in advance and the scattering pattern may be strongly directional. Therefore, the project will necessarily address the critical challenges of applying data fusion to defect classification and sizing from multi-view array data. Demonstrator software will be produced that will show an image of the test component with indications ranked by the probability of them being produced by a defect; it will then be possible to probe any of these indications to show detailed classification (e.g. crack, void, inclusion etc.) and sizing information. The project is supported by EDF, Hitachi, BAE Systems and AMEC Foster Wheeler.

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.