Asymptotic and numerical modelling of faults and thermal striping in materials with a micro-structure (linked proposal with I.S. Jones, LJMU)

The project incorporates two types of mathematical models for dynamic macro-cracks in structured media. Surface breaking cracks of finite size and subjected to a dynamic loading generated by a time-harmonic oscillation of temperature will be considered. This is related to the phenomenon of thermal striping which occurs, for example, within the cooling contours of nuclear reactors or in the mixing zones within piping systems due to the appearance of surface breaking cracks. The depth of such cracks is greatly dependent on the frequency of the external thermal oscillations. The first type of structures will involve truss-like lattices where flexural deformation can be neglected. The second type refers to macro-cracks in frame-like elastic structures incorporating bending of elastic links around the macro-crack. Particular attention will be paid to the effect of interaction between the macro-crack and micro defects modelled as imperfect spring-like junctions within the lattice.

The proposal will be beneficial not only to applied mathematicians but also to a wider engineering community, especially in the areas involving thermal structural integrity. In particular, the industries who will use the result of our work are nuclear and aerospace since the highly technical structural integrity calculations are typically required for applications in these areas. Our work provides a generic approach to a wide class of problems involving thermal fatigue and fracture, and the analytical results which follow from our project will be used, as they have in the past, in the development of the engineering design codes. One of our industrial collaborators from SERCO Assurance and his colleagues (see the letter of support attached) are keen to apply our models to the safety checks of welded joints, which have a micro-structure of a certain type and is also subjected to transient thermal load. We plan to publicize the results of our work by presenting lectures at the research seminars and industrial workshops. Some of such workshops are regularly run by the Research Centre in Mathematics and Modelling of the University of Liverpool, and we always have an excellent list of participants, both from academia and industry. The results of our work will be submitted for publication in the international refereed journal of high academic calibre and the work will be presented at international research conferences including the meetings of IUTAM, ICTAM, SIAM, IMA, ASME as well as BAMC and European Study Group with Industry. We will focus on industrial developments and will enhance our existing research contacts with SERCO and other industrial companies in the UK, and we will be happy to provide a full access to our theoretical and numerical results and our full cooperation on the stage of industrial implementation.