Nanocrystalline materials with grain size less than 100 nm have been receiving much attention because of their unparallel properties compared with their microcrystalline counterparts. Because of its high hardness, nanocrystalline nickel has been used for MEMS. Long term thermomechnical properties and deformation mechanism at both ambient and elevated temperatures need to be evaluated which is vital for reliability of its applications as structural material. In this thesis, nanoindentation creep of nanocrystalline nickel with an as-deposited grain size of 14 nm was characterized at elevated temperatures. The nanoindentation creep rate was observed to scale with temperature and applied load (or stress), and could be expressed by an empirical power-law equation for describing conventional crystalline solids. Creep activation energy was found to be close to that for grain boundary self-diffusion in nickel. The activation volume was also evaluated using a stress relaxation technique. The creep results were compared with those for fine-grained nickel in the literature. Possible mechanisms were discussed in light of the creep rate and temperature ranges. To provide a direct comparison, uniaxial creep tests were conducted on nanocrystalline nickel with an as-deposited grain size of 14 nm at 398 K. It was found that stress exponents under the two test conditions are almost the same, indicating a similar creep mechanism. However, the strain rate measured by nanoindentation creep was about 100 times faster than that by uniaxial creep. The rate difference was discussed in terms of stress states and the appropriate selection of Tabor factor. To further explore the time-dependent plastic behavior, multiple unload-reload tests were conducted on electrodeposited nanocrystalline nickel in both compression and tension. A hysteresis was observed during each unload-reload cycle, indicating irreversible energy dissipation. The dissipated energy was evaluated and the energy dissipation rate was found to increase with the flow stress to the third power and sensitive to the stress state (tension or compression). A mechanistic model based on grain boundary sliding was proposed to describe the unload-reload behavior. Experimental results were found to be in good agreement with the model predictions, suggesting the observed hysteresis was indeed caused by grain boundary sliding.

At the microscopic level, many materials are made of smaller and randomly oriented grains. These grains are separated by grain boundaries which tend to decrease the electrical and thermal conductivity of the material. The motion of grain boundaries is an important phenomenon controlling the grain growth in materials processing and synthesis. Mathematical modeling and simulation is a powerful tool for studying the motion of grain boundaries. The research reported in this thesis is focused on the numerical simulation and analysis of a coupled surface and grain boundary motion which models the evolution of grain boundary and the diffusion of the free surface during the process of grain growth. The “quarter loop” geometry provides a convenient model for the study of this coupled motion. Two types of normal curve velocities are involved in this model: motion by mean curvature and motion by surface diffusion. They are coupled together at a triple junction. A front tracking method is used to simulate the migration. To describe the problem, different formulations are presented and discussed. A new formulation that comprises partial differential equations and algebraic equations is proposed. It preserves arc length parametrization up to scaling and exhibits good numerical performance. This formulation is shown to be well-posed in a reduced, linear setting. Numerical simulations are implemented and compared for all formulations. The new formulation is also applied to some other related problems. We investigate numerically the linear stability of the travelling wave solutions for the quarter loop problem and a simple grain boundary motion problem for both curves in two dimensions and surfaces in three dimensions. The numerical results give evidence that they are convectively stable. A class of high order three-phase boundary motion problems are also studied. We consider a region where three phase boundaries meet at a triple junction and evolve with specified normal velocities. A system of partial differential algebraic equations (PDAE) is proposed to describe this class of problems by extending the discussion for the coupled surface and grain boundary motion. The linear well-posedness of the system is analyzed and numerical simulations are performed.

It is well documented that the mechanical response of polycrystalline metals depends on the metal's microstructure, for example the dependence of yield strength on grain size (Hall-Petch effect). Local continuum approaches do not address the sensitivity of deformation to microstructural features, and are therefore unable to capture much of the experimentally observed behavior of polycrystal deformation. In this work, a crystal plasticity model is developed that predicts a dependence of yield strength on grain size without grain size explicitly entering into the constitutive equations. The grain size dependence in the model is the result of non-local effects of geometrically necessary dislocations (GNDs), i.e. GNDs harden both the material at a point and the surrounding material. The conventional FeFp kinematics for single crystals have been augmented based on a geometric argument that accounts for the grain orientations in a polycrystal. The augmented kinematics allows an initial GND state at grain boundaries and an evolving GND state due to sub-grain formation within the grain to be determined in a consistent manner. Numerically, these non-local affects are captured using a non-local integral approach rather than a conventional gradient approach. The non-local crystal plasticity model is used to simulate the tensile behavior in copper polycrystals with grain sizes ranging from 14 to 244 micron. The simulation results show a grain size dependence on the polycrystal's yield strength, which are qualitatively in good agreement with the experimental data. However, the Hall-Petch exponent predicted by the simulations is more like d-1 rather than d-0.5. The effects of different simulation parameters including grain shape and misorientation distribution did not greatly affect the Hall-Petch exponent. The simulation results indicate that the Hall-Petch exponent is sensitive to the grain boundary strength: the Hall-Petch exponent decreases as grain boundary strength decreases. The intragrain misorientations predicted by the non-local model were compared with experiments on polycrystalline nickel. Experimentally, the intragrain misorientations were tracked by electron back scatter diffraction (EBSD) at various strain levels from the same location. On average, the simulation results predicted enough misorientation throughout the sample. However, the model did not correctly predict the spatial details of the intragrain misorientation.

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<p>Diffusion controlled phase transformations are studied bymeans of the phase-field method. Morphological evolution ofdendrites, grains and Widmanst\"atten plates is modeled andsimulated.</p><p>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.</p><p>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.</p><p>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.</p><p>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.</p><p><b>Keywords:</b>heat and solute diffusion, solidification,solid-solid phase transformation, microstructure, crystalgrowth, dendrite, grain boundary, Widmanstaetten plate,phase-field, adaptive mesh generation, FEM.</p>

At the microscopic level, many materials are made of smaller and randomly oriented grains. These grains are separated by grain boundaries which tend to decrease the electrical and thermal conductivity of the material. The motion of grain boundaries is an important phenomenon controlling the grain growth in materials processing and synthesis. Mathematical modeling and simulation is a powerful tool for studying the motion of grain boundaries. The research reported in this thesis is focused on the numerical simulation and analysis of a coupled surface and grain boundary motion which models the evolution of grain boundary and the diffusion of the free surface during the process of grain growth. The “quarter loop” geometry provides a convenient model for the study of this coupled motion. Two types of normal curve velocities are involved in this model: motion by mean curvature and motion by surface diffusion. They are coupled together at a triple junction. A front tracking method is used to simulate the migration. To describe the problem, different formulations are presented and discussed. A new formulation that comprises partial differential equations and algebraic equations is proposed. It preserves arc length parametrization up to scaling and exhibits good numerical performance. This formulation is shown to be well-posed in a reduced, linear setting. Numerical simulations are implemented and compared for all formulations. The new formulation is also applied to some other related problems. We investigate numerically the linear stability of the travelling wave solutions for the quarter loop problem and a simple grain boundary motion problem for both curves in two dimensions and surfaces in three dimensions. The numerical results give evidence that they are convectively stable. A class of high order three-phase boundary motion problems are also studied. We consider a region where three phase boundaries meet at a triple junction and evolve with specified normal velocities. A system of partial differential algebraic equations (PDAE) is proposed to describe this class of problems by extending the discussion for the coupled surface and grain boundary motion. The linear well-posedness of the system is analyzed and numerical simulations are performed.

No description available.

We have investigated several topics in the area of manganites including oxygen disorder, grain boundaries, low field magnetoresistance, magnetoresistive anisotropy and magnetic properties. Studied materials were in the form of polycrystalline samples and epitaxial thin films. The studied compounds were Sm(1-x)Sr(x)MnO3 (SSMO) and La(1-x)Ca(x)MnO3 (LCMO). 1-We have studied the effects of oxygen disorder and grain boundary disorder in the SSMO system close to half hole doping level. The temperature dependencies of resistivity and magnetoresistance were measured as a function of the vacuum annealing time. We observed a logarithmic increase of the resistivity as a function of vacuum annealing time. We have shown that an increasing grain boundary disorder softens the magnetic phase transition from a first order phase transition into a second order transition. Furthermore, the peaks in the resistivity and specific heat are broadened and there is an increase in the charge-carrier scattering rates in the metallic state. On the other hand, the polaronic hopping activation energies in the insulating state changed slightly as a function of grain boundary disorder. The origin of these phenomena is discussed. Magnetoresistive anisotropy has been studied as a function of the grain size. Results showed a strong grain size dependence of anisotropic electrical transport in granular samples of manganites. 2-We investigated the anisotropic magnetoresistance (AMR) in ultrathin LCMO films grown on various substrates. It was found that depending on the strain state, the AMR in some of these systems exceeds 100% and can even change sign. These changes are dramatic when compared to the few percent change in AMR in conventional ferromagnets. The mechanism behind these changes in the AMR is discussed. We have also studied the effects of strain on resistive peak broadening with a simple percolation model. We have shown that strain associated with a lattice mismatched substrate in thin films can cause new electronic behavior, not found in bulk materials or thicker films of the same chemical composition. Resistivity of the ultra thin films exhibit strong relaxation effects when measured as a function of time in a constant magnetic field.

This project explores the fundamental mechanisms of grain boundary sliding (GBS) with an emphasis on its role in superplasticity, using both micro- and macro-mechanical testing methods. GBS plays an important role in the deformation of polycrystalline materials, especially at high homologous temperatures (above half of the melting point). Classical models for GBS (Rachinger sliding and Lifshitz sliding) assume that all grains and grain boundaries undergo the same process, but recent research has shown this is not true. Individual grain boundaries differ in their ability to participate in sliding and diffusion. Therefore, it is important to investigate the response of individual grain boundaries to stress. This project uses microcantilevers, loaded using a nanoindenter, to investigate the response to stress of individual grain boundaries in Sn-1%Bi, which is expected to exhibit GBS at room temperature. The response of individual grain boundaries are correlated with grain boundary characters determined using electron backscattered diffraction (EBSD). On the macroscopic scale, both in-situ and ex-situ shear tests are conducted to investigate the superplastic behaviour of this material. The strain rate sensitivity index of the material with a grain size of 8.5 μm is found to be around 0.45. Surface marker lines have quantitatively revealed grain boundary sliding. The investigation from surface studies is expanded to the interior of bulk material in 3D by conducting an in-situ tensile test coupled with diffraction contrast tomography (DCT) at a synchrotron facility. The microcantilever tests enable grain boundary sliding and diffusion creep to be investigated separately by varying the normal and shear stresses on the grain boundary plane. GBS is dependent on grain boundary structure (misorientation angle, rotation axis and grain boundary plane orientation). The microcantilever size is similar to the grain size used in the macro-mechanical tests. It is demonstrated that the shear stress for steady-state GBS is comparable in micro- and macro-tests. Grain neighbour switching events have been identified in the interior of bulk material in 3D for the first time.

At the microscopic level, many materials are made of smaller and randomly oriented grains. These grains are separated by grain boundaries which tend to decrease the electrical and thermal conductivity of the material. The motion of grain boundaries is an important phenomenon controlling the grain growth in materials processing and synthesis. Mathematical modeling and simulation is a powerful tool for studying the motion of grain boundaries. The research reported in this thesis is focused on the numerical simulation and analysis of a coupled surface and grain boundary motion which models the evolution of grain boundary and the diffusion of the free surface during the process of grain growth. The “quarter loop” geometry provides a convenient model for the study of this coupled motion. Two types of normal curve velocities are involved in this model: motion by mean curvature and motion by surface diffusion. They are coupled together at a triple junction. A front tracking method is used to simulate the migration. To describe the problem, different formulations are presented and discussed. A new formulation that comprises partial differential equations and algebraic equations is proposed. It preserves arc length parametrization up to scaling and exhibits good numerical performance. This formulation is shown to be well-posed in a reduced, linear setting. Numerical simulations are implemented and compared for all formulations. The new formulation is also applied to some other related problems. We investigate numerically the linear stability of the travelling wave solutions for the quarter loop problem and a simple grain boundary motion problem for both curves in two dimensions and surfaces in three dimensions. The numerical results give evidence that they are convectively stable. A class of high order three-phase boundary motion problems are also studied. We consider a region where three phase boundaries meet at a triple junction and evolve with specified normal velocities. A system of partial differential algebraic equations (PDAE) is proposed to describe this class of problems by extending the discussion for the coupled surface and grain boundary motion. The linear well-posedness of the system is analyzed and numerical simulations are performed. / Science, Faculty of / Mathematics, Department of / Graduate