How amorphous carbon breaks: atomistic models and machine learning

Amorphous carbon (a-C) has many industrial applications, from electrochemical sensors to wear-resistant coatings. Fracture plays a crucial role in the degradation of its performance, with coatings often failing by shear or flexural cracks. This means that as well as being able to predict fracture toughness, it is crucial to understand the response to mixed tensile and shear loads and predict the trajectory of cracks. In this project, we will build on data-driven approaches that use machine learning techniques to produce quantum mechanically accurate models at a fraction of the cost, and use them to produce a complete description of crack growth in a-C.

Only atomistic simulations have the capability of being truly predictive, since larger scale models such as X-FEM, phase-field and others invariably include empirical crack growth algorithms. The project will involve collaboration with Prof. Lars Pastewka at the University of Freiburg, with whom the project supervisor has recently shown that atomistic modelling can be used to produce quantitative predictions of the fracture toughness of a-C in good agreement with experiment [1]. This work used standard continuum linear elastic boundary conditions, and thus required large atomistic domains, preventing extension to crack path selection or mixed-mode loading.

The project will also employ a novel numerical continuation enhanced flexible boundary condition scheme, NCFlex, that has recently been developed by the supervisor with Dr Maciej Buze (University of Birmingham) [2] who will also be involved in the team. The approach fuses materials modelling techniques with numerical analysis to produce bifurcation diagrams for cracks.

Fracture of a-C represents a "sweet spot" where the process zone is nanoscale and hence accessible to direct atomistic simulation, but still of immediate technological importance. It is currently the only isotropic material whose fracture properties can be studied with predictive atomistic methods. For truly predictive models, improved accuracy is also needed in the interatomic potential. In this project, we will build on data-driven approaches such as [3] that use machine learning techniques to produce QM-accurate force fields at a fraction of the cost, and go beyond tensile loading simulations to produce a complete description of crack growth in a-C.

Impact on Students. The primary impact will be on the 50+ PhD students trained by the Centre. They will be high-quality computational scientists who can develop and implement new methods for modelling complex systems in collaboration with scientists and end-users, who are comfortable working in interdisciplinary environments, have excellent communication skills and be well prepared for a wide range of future careers. The students will tackle and disseminate results from exciting PhD projects with strong potential for direct impact. Exemplar research themes we have identified together with our industrial and international partners: (i) design of electronic devices, (ii) catalysis across scales, (iii) high-performance alloys, (iv) direct drive laser fusion, (v) future medicine exploration, (vi) smart nanofluidic interfaces, (vii) composite materials with enhanced functionality, (viii) heterogeneity of underground systems.

Impact on Industry. Students trained by HetSys will make a significant impact on UK industry as they will be ideally prepared for R&D careers to help to address the skills shortage in science and engineering. They will be in high demand for their ability to (i) work across disciplines, (ii) perform calculations that come along with error estimates, and (iii) develop well-designed software that other researchers can readily use and modify which implements novel solutions to scientific problems. More generally, incorporating error bars into models to take account of incomplete data and insufficient models could lead to significantly enhanced adoption of materials modelling in industry, reducing trial and error, and costly/time-consuming R&D procedures. The global market for simulation software is expected to more than double from now to 2022 indicating a very strong absorptive capacity for graduates. Moreover, a recent European Materials Modelling Consortium report identified a typical eight-fold return on investment for materials modelling research, leading to cost savings of 12M Euros per industrial project.

Impact on Society. Scarcity of resources and high energy requirements of traditional materials processing techniques raise ever-increasing sustainability concerns. Limitations on jet engine fuel efficiency and the difficulties of designing materials for fusion power stations reflect the social and economic cost of our incomplete knowledge of how complex heterogeneous systems behave. High costs of laboratory investigations mean that theory must aid experiment to produce new knowledge and guidance. By training students who can develop the new methodology needed to model such issues, HetSys will support society's long term need for improved materials and processes.

There will also be a direct impact locally and regionally through engagement by HetSys in outreach projects. For example we will encourage CDT students to be involved with annual 'Inspire' residential courses at Warwick for Year 11 girls, which will show what STEM subjects are like at degree level. CDT students will present highlights from projects to secondary-school pupils during these courses and also visit local schools, particularly in areas currently under-represented in the student body, in coordination with relevant professional bodies.

Impact on collaboration. Our international partners have identified the same urgent challenges for computational modelling. We will build flourishing links with research institutes abroad with long term benefit on UK research via our links to computational science networks. Shared research projects will strengthen links between academic staff and industry R&D personnel and across disciplines. The work will also lead to accessible, robust and reusable software. The Centre will achieve cross-disciplinary academic impact on the physical and materials sciences, engineering, manufacturing and mathematics communities at Warwick and beyond, and on the generation of new ideas, insights and techniques.