We have a number of 4-year PhD studentships available to start in October 2017, fully funded for EU and UK candidates. Successful candidates will have an aptitude for theory and simulation and already have, or expect to achieve, a first class (or equivalent) Bachelor’s or Master’s degree in the physical sciences or a branch of engineering. Applicants should apply via the usual route, making it clear in their personal statement which project they are interested in. For further information on these projects please contact the CDT Senior Administrator.

1. Accurate Modelling of Sintering and Residual Stresses in Polycrystalline Diamond

Supervisors: Dr Dini and Dr Balint (Mechanical Engineering, Imperial College London)
Collaborators: Serdar Ozbayraktar (Element Six)

Polycrystalline diamonds (PCD) are systems composed of diamond granules sintered in the presence of a catalyst (e.g. cobalt) under very high pressure and temperature.  They are hard abrasive materials used in oil and gas drilling. PCD cutting discs are embedded within the drill head, and experience a complicated multi-axial loading state in contact with irregular rock, and high temperature from frictional interaction [1, 2]. Cutting disc failures lead to the removal of the drill from the rock, resulting in lost drilling time and significant associated costs; discs typically fail by a combination of intra- and trans-granular fracture through the PCD, and or spallation of the PCD from the cutting disc substrate (typically tungsten carbide). Being able to predict the microstructure and residual stress state generated by the manufacturing process affect the mechanism of fracture is a very important problem for companies such as Element 6 (E6), who manufacture the cutting discs [3-5].  A better understanding could lead to a change in process parameters to produce better microstructures and residual stress states for performance and durability, or lead to new possibilities in the sintering process (e.g. the choice of catalyst).

Understanding how the pressure versus temperature cycle that the PCD experiences during compaction, sintering and bonding to the tungsten carbide substrate of the cutting disc, affects the microstructure, residual stress state and component performance, is the overall objective of this project. The effect of the pressure-temperature cycle is felt at the microscopic and macroscopic levels; generally in the former via its effect on the PCD microstructure and locally varying residual stress state, and in the latter via its effect on layer stresses and strains in the cutting disc and macroscopic residual stress. The layers in the cutting disc have different thicknesses, coefficients of thermal expansion, elastic properties, time-independent and time-dependent (creep) plastic properties, and the PCD materials (carbon, cobalt) have differing physical parameters relevant to the sintering process. Grain size and its distribution, relative grain orientations and the precise role of the catalyst are all expected to play a role.  This project is linked to a previous project undertaken by one of the TSM CDT students in Cohort 4 and a Diamond and Science Technoloy (DST) CDT project started in 2015.

References
[1] Irifune, A., Kurio, T., Sakamoto, S., Inoue, T., Sumiya, H., Materials: Ultrahard polycrystalline diamond from graphite, Nature, 621(6923):599-600, 2003.
[2] Katzman K., Libby, W.F., Sintered diamond compacts using metallic cobalt binders, Science, 172:1132-1133, 1971.
[3] Pagget, J.W., Drake, E.F., Krawitz, A.D., Winholtz, R.A., Griffin, N.D., Residual stress and stress gradients in polycrystalline diamond compacts, International Journal of Refractory Metals and Hard Materials, 20:187–194, 2002.
[4] Kanyanta, V., Ozbayraktar, S., Maweja, K., Effect of manufacturing parameters on polycrystalline diamond compact cutting tool stress-state, International Journal of Refractory Metals and Hard Materials, 45:147–152, 2014.
[5] Kanyanta, V., Dormer, A., Murphy, N., Invankovic, A., Impact fatigue fracture of polycrystalline diamond compact (PDC) cutters and the effect of microstructure, International Journal of Refractory Metals and Hard Materials, 46: 145–151, 2014.

2. Unravelling the role of mechanochemistry in lubrication mechanisms

Supervisors: Dr Dini (Mechanical Engineering, Imperial College London) and Dr. Mostofi (Materials/Physics, Imperial College London)
Collaborator: Joseph Remias (Afton Chemical Corp.) and Hugh Spikes (Mechanical Engineering, Imperial College)

Mechanochemistry is attracting much attention within the chemistry community since it may lead to the synthesis of new compounds as well as shedding light on how chemical reactions progress.  It also impinges on stem cell research and on how the mechanical environment controls cell growth and differentiation.  In studying lubrication and polymer melts, it has been applied to describe irreversible polymer breakdown in solution at high shear rates.

It might be expected that mechanochemistry would have particular relevance to Tribology (the science of friction, lubrication and wear) since lubricants are often subjected to large mechanical forces during their operation.  It is surprising therefore that it has received little attention in research on tribofilm formation. However, the Tribology Group at Imperial College (led by Professors Dini and Spikes) has recently shown conclusively that the applied shear stress and thus mechanochemistry controls the reaction of the most widely applied antiwear additive, zinc dialkylthiphosphate (ZDDP) [1]This research greatly simplifies our understanding of how some additives work, to the extent that we can begin to relate film formation quantitatively to both the applied conditions and the additive structure. In principle, we can design molecules that respond to particular levels of applied stress; and develop quantitative models of film formation a priori.

A general and important issue is the relationship between applied shear stress and the actual mechanical forces experienced by bonds within additive molecules.  This is not at all straightforward since, based on our current understanding, it will depend on the flexibility and shape of both the solvent and the additive molecules [1]. This will be studied in the proposed project using molecular dynamics (MD) simulations, extending the work recently carried out by Professor Dini and his team [2,3]In particular, solutions of ZDDP, MoDTC and other additive molecules of interest to the industrial sponsor and experimentally explored by Professor Spikes, will be modelled with emphasis on the estimation of intramolecular forces during shear.  Classical MD using reactive potentials which allow bond-breaking as well as quantum mechanical MD, will be used to improve the description of additive systems and to determine molecular reaction pathways towards the formation of tribofilms.

References
[1]      Zhang J, Spikes H. On the Mechanism of ZDDP Antiwear Film Formation. Tribol Lett 2016;63:24. doi:10.1007/s11249-016-0706-7.
[2]      Maćkowiak S, Heyes DM, Dini D, Brańka AC. Non-equilibrium phase behavior and friction of confined molecular films under shear: A non-equilibrium molecular dynamics study. J Chem Phys 2016;145:164704. doi:10.1063/1.4965829.
[3]      Ewen JP, Gattinoni C, Morgan N, Spikes H, Dini D. Nonequilibrium Molecular Dynamics Simulations of Organic Friction Modifiers Adsorbed on Iron Oxide Surfaces. Langmuir 2016;32:4450–63. doi:10.1021/acs.langmuir.6b00586.

3. Thermodynamic Modelling of Small-Molecule Interactions with Amorphous Solids

Supervisors: Amparo Galindo and Daryl Williams (Chemical Engineering, Imperial College London)
Collaborators: George Jackson (Chemical Engineering, Imperial College London) and Steve Page (P&G Cincinnati)

The process by which small gas phase molecules are taken up by solids is commonly described as gas sorption. Gas sorption, especially of water, flavor and fragrance molecules, into amorphous polymers, foods, pharmaceutical solids and biomaterials is an important problem in many academic and industrial fields. Recent work has highlighted the complexity of these sorption processes in amorphous solids, highlighting the importance of the small molecule solubility into the amorphous phases present.

The project will use molecular based models to predict small molecule solubility in amorphous solids in order to model the sorption isotherms of small molecules in amorphous solids, using of both equilibrium and non-equilibrium approaches. The challenge is to incorporate in the SAFT approach a way to account for crystalline or amorphous polymers (usually, we take them always to be amorphous). We will calculate phase diagrams related to the “VLE” (of fluid-vapour”) or solubility boundaries of the gas and the polymers at different conditions and for different polymers/gases. There will be no simulations at this level of modelling.  We will compare some of these results with more classic polymer equations based on equilibrium lattice fluid models (e.g., Sanchez–Lacombe), non-equilibrium lattice fluid theory (NEFL) and the molecular-based statistical associating fluid theory (SAFT)1.  The NELF model can describe the solubility of gases and liquids in amorphous polymers whilst the SAFT models have been applied the solubility of CO2 and gases in polymers.  The SAFT approach is firmly based on statistical mechanics, starting from the proposition of a molecular-scale model (an intermolecular pair potential), and delivering accurate bulk properties at the macroscale.

A further challenge of bridging across scales will be addressed in the project by the development and use of coarse-grain models, at the nanoscale, which will be developed using the SAFT methodology and which can be implemented at the nanoscale via molecular dynamics simulations to study longer time-scale processes. The united atom SAFT models with be mapped into coarse grain models then linked to finite element modelling of single amorphous particles. It is interesting, in parallel to develop, SAFT-based models at the coarse-grain level, where a bead accounts for a larger number of atoms, usually 3 carbons+corresponding hydrogens. With SAFT we have quick access to characterising the bead-bead intermolecular interactions at this level, and in previous works we have characterised the intramolecular (bending, torsions) aspects of the force field. We will use MD simulations at this level to study time-dependent phenomena, and to look into structural changes of the polymers as the gases are adsorbed.

Macroscopic models based on COMSOL or similar FE environments will be used to model single amorphous solid particle properties on the 1 to 100m dimensional scale using key input data sets from the coarse grain models such as time dependent chemical, transport and mechanical descriptors. Solids of interest include polyethylene, polypropylene, MCC, collagen and hair.

Experimental data to inform and validate this modelling project will come from studentship in the ACM-CDT which will in start October 2017. Both projects are supported by P&G USA, and it is anticipated that both students will regularly visit and collaborate with researchers in the USA.

References
T. Lafitte, A. Apostolakou, C. Avendaño, A. Galindo, C.S. Adjiman, E.A. Müller, and G. Jackson, J. Chem. Phys. 139, 154504 (2013).
Dilatometry of powder compacts: Characterizing amorphous-crystalline transformations,  G.D. Wang et al, Powder Technology 236, 12–16 (2013).

4. Cyclic loading and delayed hydride cracking in Zr-alloys

Supervisors: Prof Adrian Sutton (Physics, Imperial College London), Dr Daniel Balint (Mechanical Engineering, Imperial College London) and Dr Mark Wenman (Materials, Imperial College London)
Collaborator: Mr Mike Martin (Rolls-Royce)

Zr alloys are used in pressurized water nuclear reactors to clad the nuclear fuel and sep-arate it from the water coolant. A corrosion reaction with the water coolant takes place at the surface of the zirconium resulting in hydrogen entering the metal. The hydrogen is attracted elastically to the stress concentrations such as cracks and notches where it accumulates, eventually precipitating in the form of zirconium hydrides. The hydrides are brittle and cracks form and grow - this is delayed hydride cracking. Cyclic loading means the application of an oscillatory stress.

Building on an earlier very mathematical CDT project on delayed hydride cracking in Zr alloys, in collaboration with Rolls-Royce, this project will address the additional effects of cyclic loading. Cyclic loading with periods varying between hours and days occurs dur-ing normal operation of a nuclear reactor, e.g. during power fluctuations and during shut down and start up which create cyclic thermal stresses and pressure variations exerted by the fuel and coolant on the cladding. It can cause an extreme form of localization of plasticity in ‘persistent slip bands’ (PSBs) leading to very sharp fatigue cracks at the sur-face of the metal, especially at regions of stress concentration such as notches. This lo-calisation of plasticity may be significantly enhanced by hydrogen, and this provides one link to the other cluster project.

The formation of PSBs and delayed hydride cracking may influence each other. For ex-ample, the introduction of a sharp fatigue crack at a notch will raise the local stress concentration significantly, attracting more hydrogen and promoting the formation of brittle hydrides, and enabling the fatigue crack to advance rapidly. Pre-existing hydrides may accelerate the growth or deflect the path of PSBs by providing paths of easy frac-ture, in a manner with similarities to another very successful CDT project on the inter-action between cracks and inclusions developed in collaboration with Element Six. The PSBs may also be sites that trap hydrogen and this provides a second link to the other cluster project.

The intellectual challenge of this project will be to bring these ideas together 

to understand and quantify the mechanisms by which cyclic loading and delayed hydride cracking ultimately limit the structural integrity of irradiated Zr alloy components, pos-sibly acting in concert. Spending some time at Rolls-Royce will be essential to obtain a thorough understanding of the background to the problem. The research will be concep-tually and mathematically very demanding, working across several fields of mechanics of materials. 

5. Understanding the role of hydrogen-dislocation interactions in the corrosion and hydrogen uptake of irradiated zirconium fuel cladding alloys

Supervisors: Mark Wenman (Materials, Imperial College London), Andrew Horsfield (Materials, Imperial College London) and Adrian Sutton (Physics, Imperial College London)

Nuclear reactor fuel pins are commonly clad in zirconium alloys.  Whilst corrosion resistant they do corrode over time in service producing atomic hydrogen.  The hydrogen has high mobility but a low solubility limit in a-Zr and precipitates in the metal as brittle hydrides. The cladding toughness is therefore reduced posing risks for postulated accident conditions and for storage of spent fuel.  Recent changes in US nuclear regulations also mean that hydrogen content of fuel pins is now the life limiting factor.  In addition, the uptake rate of hydrogen is known to increase after neutron irradiation but the reasons for this are unclear.

We will study the interactions of H with defective Zr lattices including vacancies, Frenkel pairs and irradiation induced dislocations (a-loops and c-loops). We want to understand how the presence of hydrogen is attracted to and modifies the flow/core of dislocations. All involve the need to predict the interaction of H at dislocations accurately. Calculating the interaction between H and an extended defect is very expensive for density functional theory, while embedded atom models do not accurately capture the physics. In this project we will build a robust Gaussian Tight Binding [1] model for H in Zr, using DFT to provide reference data. We will use the model to investigate the interaction of H with individual dislocations in Zr.

Reproducing the particle distributions observed experimentally is beyond molecular dynamics (both time and length scales are too big), thus these will be simulated using kinetic Monte Carlo with long ranged interactions. Values obtained from the Tight Binding calculations will be used as input.

The project is sponsored by Rolls-Royce but forms part of a much wider collaboration led by Westinghouse internationally through the MUZIC-3 (Mechanistic understanding of Zirconium Corrosion).  Later in the project we will focus on irradiation effects and as part of this you will attend 6 month meetings in Europe and the US to report results and interact with 20 other PhD students studying the same topic using different methods.

This project is linked with a second project in a related area funded by Rolls Royce and lead by Prof Sutton on the formation of fatigue cracks and their interaction with hydride precipitates in Zr-alloys. The interaction of hydrogen with dislocations may be a key factor in the nucleation of fatigue cracks, and conversely persistent slip bands, which are the precursors of fatigue cracks, may attract hydrogen.

[1] Gaussian polarizable-ion tight binding, M. Boleininger, A. A. Guilbert, and A P Horsfield, J Chem Phys 145 (2016)

6. Multi-scale investigation of the influence of structure on oral processing of soft solid confectionery systems

Supervisors: Dr M. Charalambides, Dr P. Cann and Dr M. Masen (Mechanical Engineering, Imperial College London)
Collaborators: Dr H. Powell, Dr I Celigueta Torres (Nestlé, NPTC York)

Soft food systems are often used in confectionery products, such as emulsion or foam fillings, to provide consumers with an indulgent and unique experience. Traditionally, the mechanical and rheological properties of these systems are studied in combination with sensory evaluation to describe their in-mouth flow properties. However, oral processing of food is very complex and several mechanisms take place at the same time in the mouth. This is especially noticeable when dealing with more complex systems, e.g. when hard particles (inclusions) are included within a semi solid system, or products with different micro- and macroscopic structure, e.g. aerated systems. This makes it very difficult to make predictions of the in-mouth behaviour of the food. Knowledge of this behaviour is crucial as it is directly linked to sensory perception.

The aim of this project is to develop models for predicting the deformation and fracture of food materials during the oral process as well as the ensuing complex interaction of the food pieces with the mouth surfaces (tongue-palate contact) as food turns into a ‘bolus’ on mastication and mixing with saliva. The mechanical response of the food during ‘first bite’ loading depends on the mechanical properties of the material which are in turn greatly affected by its microstructure. For example, for composite or cellular/aerated foods, micromechanical based models in conjunction with fracture mechanics based progressive damage modelling techniques will be used to simulate structure breakdown. The study will highlight the influence of food formulation on friction behaviour and structure breakdown. Novel experimental methods and modelling techniques for assessing the influence of product structure on the different steps involved in oral perception will be developed. Furthermore, in oral mastication, fluid/solid interactions continually occur in the oral cavity. Multi-scale computational models will therefore be developed to describe the interaction between fluid and solid structures at the different scales. This research field is different from traditional engineering applications; however it is a novel application of mechanics to research and has the potential to deliver state of the art techniques that can truly transform food product design whilst at the same time providing the drive for advancing interdisciplinary research into multi-scale material models.

Nestlé Product Technology Center, York, UK, is the partner and co-funder of this project.Nestlé confectionery has a long-established wide range of composite confectionery products manufactured and sold world-wide. Within this portfolio of products there is a significant proportion of confectionery filled products which are becoming increasingly important as the industry strives to reduce the calorific density and saturated fat associated with fat-based masses. As a Nestlé PhD student, you will be part of a community of students based at top UK and overseas universities. To complement your university-based research training, Nestlé will offer soft skills and industrial training that will enhance your readiness for employment. As part of this training a short term placement at the Nestlé centre in York spread over the course of the PhD will be offered.