In Silico Grain Boundary Engineering by Analysis on Discrete Complexes

Abstract

The objective of grain boundary engineering is to introduce a significant quantity of specialised grain boundaries into the grain boundary structures, with the purpose of enhancing material properties influenced by grain boundaries, such as creep resistance, ductility, and resistance to cracking. In addition to considering the proportion of specialised grain boundaries, investigating different types of grain boundary connectivity provides valuable insights into the mechanisms driving grain boundary structure evolution in polycrystalline materials. Exploring these aspects can significantly enhance our understanding and analysis of materials. The current challenge lies in the absence of appropriate analytical models, which hinders the effective analysis and utilisation of vast experimental data in materials science. In this thesis, the discovery of a topological structure transition in the grain boundary network is presented, described by discrete cell complexes (or polytopal cell complexes). The discrete cell complexes framework has emerged as a powerful approach for handling assemblies of varying dimensions within this context – the topological structure of the grain boundary network encompasses nodes (quadruple nodes, 0-cells), edges (triple junctions, 1-cells), faces (grain boundaries, 2-cells), and polyhedrons (grains, 3-cells). Moreover, it provides an extensive range of topological tools, such as Betti numbers and Euler characteristics, for analysis, which are crucial for comprehending fundamental questions in physics. However, the utilisation of this discrete framework in the analysis of materials science processes has been relatively limited thus far. Furthermore, up to date, there is a lack of appropriate methods to dynamically monitor the evolution of grain boundary networks. In this thesis, the discrete structure analysis is employed as a novel and effective tool for characterising grain boundary networks. By incorporating various transforming mechanisms aligned with distinct evolution principles, we dynamically and systematically simulate the entire evolution process. The primary goal of this study is to predict and analyse the topological structure that governs specific material behaviours. These objectives are discussed in individual chapters, providing comprehensive insights into the research findings.

Date of Award	31 Dec 2023
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Elijah Borodin (Supervisor) & Andrey Jivkov (Supervisor)