U-Pu-Zr nuclear fuels experience a redistribution of constituents and a number of phase transformations when subjected to the thermal gradient present in nuclear reactors. This redistribution and phase separation leads to several undesirable fuel performance issues. In an effort to better understand how different alloys compositions are affected by this thermal gradient, we utilize the recently introduced Hybrid Potts-phase Field Method to study the U-Pu-Zr system. The recently introduced Hybrid method couples microstructural and compositional evolutions of a system so that the two phenomena can be studied together rather than separately, as is frequently done. However, simulation of the U-Pu-Zr system required several adaptations to the modeling framework. First the model was adapted to incorporate a thermodynamic database for free energy calculations, as well as thermal diffusion (the Soret effect). These abilities were tested in the Al-Si system. Second, the modeling framework was expanded to simulate three component systems such that ternary U-Pu-Zr alloys could be studied.Simulations capture constituent redistribution and the appropriate phase transformations as compared to experimentally irradiated a U-16Pu-23Zr (at%) nuclear fuel. Additional simulations analyze constituent redistribution over the entire spectrum of U-Pu-Zr compositions. Analysis of these simulation results indicate alloys that are likely to experience minimal constituent redistribution and fewer phase boundaries, such that their fuel performance should be improved. The outcomes of the work include a coupled microstructural-compositional modeling framework for ternary alloys and suggestions of U-Pu-Zr alloys that could lead to improved fuel performance.

<p> This thesis details work done in the development of the phase field model which allows simulation of elasticity with diffuse interfaces and the extension of a thin interface analysis developed by previous authors to study non-dilute ideal alloys. These models are coupled with a new finite difference adaptive mesh algorithm to efficiently simulate a variety of physical systems. The finite difference adaptive mesh algorithm is shown to be at worse 4-5 times faster than an equivalent finite element method on a per node basis. In addition to this increase in speed for explicit solvers in the code, an iterative solver used to compute elastic fields is found to converge in O(N) time for a dynamically growing precipitate, where N is the number of nodes on the adaptive mesh. A previous phase field formulation is extended such as to make possible the study of non-ideal binary alloys with complex phase diagrams. A phase field model is also derived for a free energy that incorporates an elastic free energy and is used to investigate the competitive development of solid state structures in which the kinetic transfer rate of atoms from the parent phase to the precipitate phase is large. This results in the growth of solid state dendrites. The morphological effects of competing surface anisotropy and anisotropy in the elastic modulus tensor is analyzed. It is shown that the transition from surfaceenergy driven dendrites to elastically driven dendrites depends on the magnitudes of the surface energy anisotropy coefficient (E4 ) and the anisotropy of the elastic tensor (β) as well as on the super saturation of the particle and therefore to a specific Mullins-Sekerka onset radius. The transition point of this competitive process is predicted from these three controlling parameters. </p> / Thesis / Doctor of Philosophy (PhD)

Thermoelectric generators convert heat energy to electricity and can be used for waste heat recovery, enabling sustainable development. Selective Laser Melting (SLM) based additive manufacturing process is a scalable and flexible method that has shown promising results in manufacturing high ZT Bi2T e3 material and is possible to be extended to other material classes such as M g2Si. The physical phenomena of melting and solidification were investi- gated for SLM-based manufacturing of thermoelectric (M g2Si) powders through comprehen- sive numerical models developed in MATLAB. In this study, Computational Fluid Dynamics (CFD)-based techniques were employed to solve conservation equations, enabling a detailed understanding of thermofluid dynamics, including the temperature evolution and the con- vection currents of the liquid melt within the molten pool. This approach was critical for optimizing processing parameters in our investigation, which were also used for printing the M g2Si powders using SLM. Additionally, a phase field-based model was developed to sim- ulate the directional solidification of the M g2Si in MATLAB. Microstructural parameters like the Secondary and Primary Dendritic Arm Spacing were studied to correlate the effects of processing parameters to the microstructure of M g2Si. / Master of Science / Thermoelectric generators are devices that transform heat energy into electricity, offering a way to capture and utilize waste heat for sustainable purposes. A cutting-edge manufacturing method called Selective Laser Melting (SLM) has shown great potential in creating high-performance materials like Bi2T e3 for thermoelectric applications. Researchers are now exploring the extension of this technique to other materials, such as Mg2Si. This study delves into the intricate process of melting and solidifying Mg2Si powders using SLM. Advanced computer models were created in MATLAB, to simulate these processes in detail. By employing Computational Fluid Dynamics (CFD) techniques, heat and fluid flow within the molten material was also closely examined. These simulations were vital for fine-tuning the printing settings used to fabricate Mg2Si powders via SLM. Moreover, a specialized model based on phase field theory was developed to mimic the solidification of Mg2Si. The effects of changing manufacturing parameters on the microstructure of the final product were examined. Understanding these microstructural aspects is crucial for optimizing the manufacturing process and ultimately enhancing the performance of Mg2Si for thermoelectric applications.

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The mechanical performance evaluation of asphalt binder has always been a challenging issue for pavement engineers. Recently, the Phase Field Method (PFM) has emerged as a powerful computational tool to simulate the microstructure evolution of asphalt binder. PFM analyzes the structure from the free energy aspect and can provide a view of the whole microstructure evolution process. In this dissertation, asphalt binder performance is analyzed by PFM in three aspects: first, the relationship between asphalt chemistry and performance is investigated. The components of asphalt are simplified to three: asphaltene, resin and oil. Simulation results show that phase separation will occur under certain thermal conditions and result in an uneven distribution of residual thermal stress. Second, asphalt cracking is analyzed by PFM. The traditional approach to analyze crack propagation is Classic Fracture Mechanics first proposed by Griffith, which needs to clearly depict the crack front conditions and may cause complex cracking topologies. PFM describes the microstructure using a phase-field variable which assumes positive one in the intact solid and negative one in the crack void. The fracture toughness is modeled as the surface energy stored in the diffuse interface between the intact solid and crack void. To account for the growth of cracks, a non-conserved Allen-Cahn equation is adopted to evolve the phase-field variable. The energy based formulation of the phase-field method handles the competition between the growth of surface energy and release of elastic energy in a natural way: the crack propagation is a result of the energy minimization in the direction of the steepest descent. Both the linear elasticity and phase-field equation are solved in a unified finite element frame work, which is implemented in the commercial software COMSOL. Different crack mode simulations are performed for validation. It was discovered that the onset of crack propagation agrees very well with the Griffith criterion and experimental results. Third, asphalt self-healing phenomenon is studied based on the Atomic Force Microscopy (AFM) technology. The self-healing mechanism is simulated in two ways: thermodynamic approach and mechanical approach. Cahn-Hilliard dynamics and Allen-Cahn dynamics are adopted, respectively. / Ph. D.

A preconditioner to improve the convergence properties of Krylov subspace solvers is derived and analyzed in this work. This method is adapted to linear systems arising from a finite-element discretization of a phase-field crystal equation.

Submitted by Geandra Rodrigues (geandrar@gmail.com) on 2018-01-11T14:38:55Z No. of bitstreams: 1 danielmoutinhodesouza.pdf: 14087574 bytes, checksum: 14fbe9db31be8496c781a98af92ca3fd (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-01-23T13:42:47Z (GMT) No. of bitstreams: 1 danielmoutinhodesouza.pdf: 14087574 bytes, checksum: 14fbe9db31be8496c781a98af92ca3fd (MD5) / Made available in DSpace on 2018-01-23T13:42:47Z (GMT). No. of bitstreams: 1 danielmoutinhodesouza.pdf: 14087574 bytes, checksum: 14fbe9db31be8496c781a98af92ca3fd (MD5) Previous issue date: 2017-08-28 / A fibrilação ventricular é uma arritmia cardíaca listada como uma das principais causas de morte no mundo industrializado, por isso, a importância do estudo do comportamento elétrico cardíaco. O equipamento mais indicado para tentar reverter este quadro de arritmia é o desfibrilador, que submete o tórax do paciente a um campo elétrico de alta energia. Entretanto essa técnica pode causar efeitos graves como queimaduras e dor intensa. Técnicas menos agressivas vêm sendo estudadas e consideram, por exemplo, protocolos com múltiplos estímulos de baixa energia. Observou-se que, nessas estratégias alternativas, a rede vascular cardíaca pode ter papel importante com relação ao padrões espaço-temporais gerados pelos estímulos. Nesta mesma direção, este trabalho apresenta um estudo computacional sobre a influência da rede vascular durante estímulos por campo elétrico em tecidos cardíacos. O fenômeno é capturado por um sistema não-linear de equações diferenciais parciais. Para resolver este modelo numericamente os Métodos de Volumes Finitos (MVF) e de Phase-Field (MPF) foram combinados buscando assim a caracterização geométrica de vasos arteriais durante simulações de desfibrilação de tecido cardíaco. Os resultados obtidos sugerem que os métodos usados (MVF+MPF) são adequados para o estudo de protocolo para desfibrilação cardíaca. / The ventricular fibrillation is a cardiac arrhythmia listed as one of the leading causes of death within the industrialized world, hence the study of cardiac electrical behavior is an important research area. The most used equipment for the reversal of this condition is the defibrillator, which subjects the patient's chest to a high-energy electric field. However, it can have serious effects such as burns and severe pain. Less aggressive techniques have been studied and considered, for example, protocols with multiple low energy stimuli. It was observed that, in this alternative technique, the cardiac vascular network may play an important role in relation to the spatial-temporal patterns generated by the stimuli. This work presents a computational study about the influence of the vascular network during electrical field stimuli in cardiac tissues. The phenomenon is described by a nonlinear system of partial differential equations. To solve this model numerically the Finite Volume Method (FVM) and the Phase-Field Method (PFM) were combined, thus seeking a better geometric characterization of arterial vessels during simulations of cardiac tissue defibrillation. The results obtained in this work suggest that these methods (FVM + PFM) are suitable for the protocol study for cardiac defibrillation.

In this thesis, we present an experimental and numerical study of globularization during reheating of thixocast billet having non-dendritic microstructure. The process of reheating is an important step in the semisolid processing and is essential to control its microstructure and hence its mechanical properties. Material chosen for this study is Aluminum alloy, A356. The primary focus of this study is the heat treatment below eutectic temperature i.e. transformation in solid phase. It is found that during short duration heat treatment, globularization of primary α grains and spheroidization of eutectic Si flakes take place which improves the mechanical properties of semisolid cast products significantly. A prolonged heat treatment is found to degrade the properties of castings since it enhances the porosity and coarsening of Si. The study suggests that a precise heat treatment practice can be designed to improve the semisolid microstructure. A computational model based on Phase field approach has been proposed to study this phenomena. Predictions based on this model are qualitatively compared with corresponding experimental observations. Since eutectics form an important step in multiphase solidification, an attempt has been made to develop an enthalpy based explicit micro-scale model for eutectic solidification. In this preliminary study, growth of adjacent α and β phases in a two dimensional Eulerian framework has been simulated. The model is qualitatively validated with Jackson Hunt theory. Results show expected eutectic growth. This methodology promises significant saving in computational time compared to existing numerical models.

Phase field models have played an important role in shaping our understanding of a variety of micro structural phenomena in materials. Their attractive features include (a) their ability to capture instabilities in microstructures, and (b) their ability to handle topological transitions { such as splitting or coalescence { gracefully. Therefore, we have chosen to use a phase field model in our study of instabilities in cylindrical pores in nanoporous membranes which eventually lead to their failure. Our study is motivated by recent studies on thermal stability of nanoporous membranes of alumina, titania and zirconia. The key feature in our model is its ability to incorporate surface discussion as the mechanism for mass transport. We first benchmark the model through a critical comparison of our results on early stages of surface evolution during Rayleigh instability and grain boundary grooving with those from linear theories of these phenomena. We have then used longer simulations (which go beyond early stages, and therefore, can incorporate non-lineare effects) to study instabilities in a hollow cylinder in three different systems: single crystal or amorphous solid (which fails through Rayleigh instability), a model sys-tem with parallel grain boundaries (which fails through grain boundary grooving), and a polycrystal (whose failure depends on a combination of grain growth and grooving). In all the cases, the surface energy is assumed to be isotropic, and the operative mechanism for mass transport is assumed to be surface discussion.