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This thesis focuses on the study of the size effect in the elastic-viscoplastic response of pure face centered cubic polycrystalline materials. First, the effect of vacancy diffusion is studied via the use of a two-phase self-consistent scheme in which the inclusion phase represents grain interiors and the matrix phase represents grain boundaries. The behavior of the inclusion phase is driven by the activity of dislocations, described with typical strain hardening laws, and by the activity of Coble creep. The behavior of the matrix phase is modeled as elastic-perfect plastic. This model is then extended to account for the possible activity of Lifschitz sliding. The active role of grain boundaries to the viscoplastic deformation is studied with the introduction of a novel method allowing the scale transition from the atomistic scale to the macroscopic scale. A model describing the mechanism of grain boundary dislocation emission and penetration is informed with molecular simulations and finite element simulations. The macroscopic response of the material is then predicted with use of several self-consistent schemes, among which two novel three-phases schemes are introduced. The most refined micromechanical scheme proposed is based on a two-phase representation of the material and is valid in the elastic-viscoplastic regime and accounts for the effect of slightly weakened interfaces.

This research is concerned with the mechanisms of diffusion in the Earth and the implications of such an understanding. Specifically, this work is concerned with one particular aspect of diffusion: Grain Boundary Diffusion (GBD). An experimental investigation of GBD has been conducted by considering three specific scenarios; GBD of H in stoichiometric Mg-spinel, GBD of Ti in Quartz and GBD of Li in olivine. By considering the GBD of three very different elements it has been possible to synthesise an understanding of some of the mechanisms involved in the process. GBD is potentially a very important process within the Earth with wide ranging implications. Grain boundaries may provide fast pathways for transportation of a range of compatible and incompatible diffusing species in the Earth’s interior – potentially acting as storage locations and also as efficient pathways between different geological reservoirs. It is also potentially very important in the application of a number of techniques including dating and geothermometry and geobarometry. Here, an experimental study of the GBD of H has been carried out with the overall finding that GBD appears to occur at slightly greater yet broadly similar rates to lattice diffusion. This finding is considered in terms of the mantle properties which are affected by the presence and transport of H. A follow up series of experiments was conducted looking at Li diffusion. Li was chosen due to its volatile nature and larger atomic radius as compared to H. As such, it provided a useful test of the hypothesis that the radius of a diffusant might affect its chosen method of diffusion. A third set of experiments were carried out to investigate the GBD of Ti in quartz with particular reference to the TitaniQ geothermo(baro)meter. This set of experiments provided a very useful comparison to the data which had previously been obtained from lighter elements. This investigation has found that a combination of factors including charge, diffusant diameter and the specific mineralogical characteristics of the host phase will define the dominant diffusive mechanism and the size of the contribution made by that mechanism towards observed bulk diffusivities. A characterisation of the temperature dependency of diffusion within each setting has also been completed. As such, it also makes a useful contribution to the current dataset for GBD.

A simplified model with only 2 degrees of freedom is developed for cavity growth along a grain-boundary by surface and grain-boundary diffusion following a similar model for a row of grains used by Sun et al, (1996). A variational principle for the coupled diffusion problem is used to follow the cavity growth. The approximate solution can be reduced to the well-established equilibrium cavity growth model at the fast surface diffusion extreme. By comparing the 2 degree of freedom model with the full finite element solution by Pan et al, (1997), a 'Validity Map' is constructed in terms of the relative diffusivity and applied stress relative to the capillarity stress. It is found that the simplified model accurately describes the evolution process, in terms of overall cavity profile and propagation rate for engineering alloys subject to normal levels of applied stresses. The 2 degree of freedom model for a single cavity was then extended to allow the modelling of multiple cavities. These cavities can be either pre-existing or nucleated during the lifetime of the system. The relative rotation between the grains is also considered. The initial 2 degrees of freedom were increased to six, and a cavity element has been derived. The cavity elements are assembled together using the classical finite element approach. This allows the evolution of multiple cavities and their interactions to be modelled under different applied loads and material parameters. This simplified multiple cavity finite element model was compared with a model for cavity evolution based on a 'smeared-out' approach. It was shown that the 'smeared-out' model does not accurately predict the creep damage for realistic engineering materials and conditions and results in an under prediction of creep lifetime. Using the simplified finite element model the effect of surface diffusion on the evolution of the creep damage was investigated. The evolution of a large pre-existing 'crack-like' cavity was modelled and the effects of nucleation, surface diffusion and loading were also investigated. It was shown that in the majority of cases as the surface diffusion was increased the rupture time was also increased. The results from the large 'crack-like' cavity simulations showed that there was very little crack propagation through the material and the smaller cavities tended to grow independently of the large 'crack-like' cavity.

Molecular dynamics simulations of the diffusion process in ordered B2 compounds at high temperature were performed using an embedded atom interatomic potential developed to fit NiAl properties. Diffusion in the bulk occurs through a variety of cyclic mechanisms that accomplish the motion of the vacancy through nearest neighbor jumps restoring order to the alloy at the end of the cycle. The traditionally postulated six-jump cycle is only one of the various cycles observed and some of these are quite complex. Diffusion at the grain boundary mainly takes place through sequences of coordinated nearest neighbor jumps yielding to a rearrangement of the grain boundary structure. Two distinct mechanisms resulting in a structural unit migration of the vacancy are also identified. The results are analyzed in terms of the activation and configuration energies calculated using molecular statics simulations. / Master of Science

Sigma 3 grain boundaries play a large role in the microstructure of fcc materials in general, and particularly so in grain boundary engineered materials. A recent survey of grain boundary properties revealed that many of these grain boundaries possess very large mobilities, and that these mobilities increase at lower temperature, contrary to typical models of thermallyactivated grain boundary motion. Such boundaries would have a tremendous mobility advantage over other boundaries at low temperature, which may explain some observed instances of abnormal grain growth at low temperature. This work explains the boundary structure and motion mechanism that allows for such mobilities, and explores several of the unique factors that must be considered when simulating the motion of these boundaries. The mobilities of a number of boundaries, both thermally-activated and antithermal, were then calculated over a wide temperature range, and several trends were identified that relate boundary crystallography to thermal behavior and mobility. An explanation of the difference in thermal behavior observed in sigma 3 boundaries is proposed based on differences in their dislocation structure.

abstract: The initial microstructure of oxide fuel pellets can play a key role in their performance. At low burnups, the transport of fission products has a strong dependence on oxygen content, grain size distribution, porosity and grain boundary (GB) characteristics (crystallography, geometry and topology), all of which, in turn depend on processing conditions. These microstructural features can also affect the fuel densification, thermal conductivity and microstructure evolution inside the reactor. Understanding these effects can provide insight into microstructure evolution of fuels in-pile. In this work, mechanical and ion beam serial sectioning techniques were developed to obtain Electron Backscatter Diffraction (EBSD) data, both in 2-D and 3-D, for depleted UO2+X pellets manufactured under different conditions. The EBSD maps were used to relate processing conditions to microstructural features, with emphasis on special GBs according to the Coincident Site Lattice (CSL) model, as well as correlations between pore size and location in the microstructure. Furthermore, larger grains (at least 2.5 times the average grain size) were observed in all the samples and studied. Results indicate that larger grains, in samples manufactured under different conditions, dominate the overall crystallographic texture and have a fairly strong GB texture. Moreover, it seems that the preferential misorientation axis for these GBs, regardless of the O/M, is {001}. These results might be related to GB energy and structure and, suggest that the mechanism that controls grain growth seems to be independent of both processing conditions and stoichiometry. Additionally, a sample was heat treated to relate grain growth and crystallography. The results indicate that at least two mechanisms were involved. Lengthening of GBs was observed for larger grains. Another mechanism of grain growth was observed, in this case, grains rotate to match a neighboring grain forming a larger grain. In the new grain, the misorientation between the two neighboring grains decreases to less than 5 degrees, forming a new larger grain. The results presented in this work indicate that detailed studies of the initial microstructure of the fuel, with emphasis on the crystallography of grains and GBs could help to give insights on the in-pile microstructural evolution of the fuel. / Dissertation/Thesis / Ph.D. Materials Science and Engineering 2014

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Diffusion controlled phase transformations are studied bymeans of the phase-field method. Morphological evolution ofdendrites, grains and Widmanst\"atten plates is modeled andsimulated. Growth of dendrites into highly supersaturated liquids ismodeled for binary alloy solidification. Phase-field equationsthat involve both temperature and solute redistribution areformulated. It is demonstrated that while at low undercoolingheat diffusion does not affect the growth of dendrites, i.e.solidification is nearly isothermal, at high cooling rates thesupersaturation is replaced by the thermal undercooling as thedriving force for growth. In experiments many crystals with different orientationsnucleate. The growth of randomly oriented dendrites, theirsubsequent impingement ant formation of grain boundaries arestudied in two dimensions using the FEM on adaptive grids. The structure of dendrites is determined by growthconditions and physical parameters of the solidifying material.Effects of the undercooling and anisotropic surface energy onthe crystal morphology are investigated. Transition betweenseaweeds, doublons and dendrites solidifying out of puresubstance is studied and compared to experimental data. Two-and three-dimensional simulations are performed in parallel onadaptive and uniform meshes. A phase-field method based on the Gibbs energy functional isformulated for ferrite to austenite phase transformation inFe-C. In combination with the solute drag model, transitionbetween diffusion controlled and massive transformations as afunction of C concentration and temperature is established byperforming a large number of one dimensional calculations withreal physical parameters. In two dimensions, growth ofWidmanstaetten plates is governed by the highly anisotropicsurface energy. It is found that the plate tip can beapproximated as sharp, in agreement with experiments. Keywords:heat and solute diffusion, solidification,solid-solid phase transformation, microstructure, crystalgrowth, dendrite, grain boundary, Widmanstaetten plate,phase-field, adaptive mesh generation, FEM. / <p>NR 20140805</p>

Student Number : 0405740V - MSc (Eng) dissertation - School of Chemical and Metallurgical Engineering - Faculty of Engineering and the Built Environment / Silicon carbide ceramics have many attractive properties, one of which is their high degree of corrosion resistance. Even though corrosion is slow, it does occur. Standard procedures for corrosion testing such as the immersion method is limited due to the low corrosion rates of most of these materials: it does not elucidate the mechanism of corrosion, but only gives the rate and degree of dissolution. Electrochemical techniques offer the possibility to further elucidate corrosion mechanisms and establish the resistance stability of conducting or partially-conducting ceramic materials, thus enhancing the understanding of ceramic material behaviour. In conjuction with microstructural changes, the electrochemical corrosion behaviour of solid state sintered silicon carbide (SSiC) and liquid phase sintered silicon carbide (LPSSiC) have successfully been studied at room temperature in acidic and alkaline environments by using potentiodynamic polarisation measurements. Several hypotheses were proposed to assist in establishing the effect of silicon and carbon on the corrosion mechanisms of these materials. The effect of the secondary phase on the electrochemical corrosion of the LPSSiC was also investigated. Corrosion current densities of the LPSSiC materials were much lower than the SSiC materials in all test solutions. The SSiC materials showed pseudo-passive behaviour in HCl and HNO3, due to the formation of thin layer of SiO2 on the surface. The carbon in the SiC compound increased the corrosion current densities in all test solutions for SSiC materials. The electrochemical corrosion of LPSSiC is due to the dissolution of SSiC and not the oxides; the chemcial attack on the oxide phases is mainly by acid-base type of reactions, rather than electrochemical corrosion involving redox reactions.