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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.

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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.

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In this thesis, molecular dynamics simulations were performed to characterize the atomic motions governing grain boundary migration in a series of [001] twist boundaries. Particularly, migrations of a =36.87 5, a =22.63 13 and a =40.23 general high angle [001] twist boundaries driven by stored elastic energy in fcc Ni were investigated. Atomic motions during migration were identified as the combination of single atom jump and string-like cooperative atomic motions. The simulation results confirmed that the collective 4-atom shuffle motion was the rate controlling atomic motion during the migration of 5 twist boundary. As grain boundary local symmetry decreasing, string-like cooperative atomic motions became increasingly important. Eventually, both random single atom jump and string-like cooperative motions became dominant during the migration of general non- twist boundary. Furthermore, simulations showed that activation energy for grain boundary migration was well correlated with the average string length occurring within boundary. / Materials Engineering

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.

The heat affected zone (HAZ) of friction stir welded Al 7075 T7 shows diminished corrosion resistance properties when compared with the parent material. Corrosion attack in this region of the weld is primarily intergranular and is associated with the presence of precipitate free zones. Current TEM research conducted at Brigham Young University by Dr. Bin Cai finds a correlation between precipitate free zone (PFZ) width and grain boundary geometry. As both grain boundary geometry and the PFZ are associated with modes of failure in 7XXX aluminum, this paper makes a comparison of grain boundary character distributions (GBCD) in the HAZ and the parent metal via multi-section plane five-parameter stereology. The stereology is conducted in a convenient macroscopic coordinate frame, associated with the HAZ. This is the first investigation to determine the GBCD in the HAZ of friction-stirred weld material and requires multiple section plane sampling. It is discovered that aluminum here exhibits the property of non-sidedness, a long assumed but unproven characteristic. Further comparisons between the two microstructures are conducted relative to (2-dimensional) grain boundary network connectivity, recovered from EBSD data in each section plane. It is shown that the relative fraction of grain boundaries of misorientation character associated with smaller PFZ size is larger in the HAZ as compared to the parent material. A commensurate decrease in the connectivity (radius of gyration) of grain boundaries of character conducive to larger PFZ size is also found in the HAZ, relative to the parent material. Distribution of inclinations changes as a function of grain boundary geometry. Surface area per unit volume of CSL and low angle random (LAR) misorientations increases in the HAZ, while high angle random (HAR) boundaries decrease. In the case of LAR and some CSL boundaries, a reorientation occurs in which macroscopic normals of these interfaces rotate. It is anticipated that these significant changes in the GBCD within the HAZ could be important in terms of understanding the post-weld mechanical and physical properties in friction-stirred materials.