This study uses the Phase-field method to simulate the transient thermal current of the metal surface heated and molten by a massing energy. The flow field uses a two-dimension module, considered with the mass conservation equation, momentum equation, energy equation and level-set equation, to solve for the distribution in whole domain, including the interface, of temperature, velocity, pressure and level-set number. We ignore the effect of concentration diffusion, but consider about the effect of heat translation on the flow field. Finally the results will display the flows of air around molten area forced by buoyancy which is caused by high temperature, and the flows in molten area forced by thermocapillary which is caused by temperature gradient.

The microstructure resulting from the solidification of alloys can greatly affect their properties, making the prediction of solidification phenomena under arbitrary conditions a very important tool in the field of computer-aided design of materials. Although considerable attention has been allocated to the understanding of this phenomenon in cases in which the solidification front advances freely into the liquid, the actual microstructure of solidification is strongly dependent of interfacial interactions. Over the past decade, the phase-field approach has been proved to be a quite effective tool for the simulation of solidification processes. In phase-field models, one or more phase fields ø (conserved and/or non-conserved) are introduced to describe the microstructure of a complex system. The behavior of a given microstructure over time is then simulated by solving evolution equations written in terms of the minimization of the free energy of the entire system, which is written as a functional of the field variables as well as their gradients and materials’ constitutive equations. With the given free energy functional, the governing equations (phase-field equation, diffusion equation, heat equation and so on) are solved throughout the entire space domain without having to track each of the interfaces formed or abrupt changes in the topology of the microstructure. In this work I will present phase-field models for solidification processes, solid/liquid interactions as well as their applications.

<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>

The relatively recent discovery of the giant electrocaloric effect in ferroelectric ceramics may lead to new solid state cooling technologies that are energy efficient, reliable, portable, and environmentally friendly. This phenomenon, along with many other novel field-coupled properties of ferroelectrics, such as piezoelectricity, pyroelectricity, the electro-optic effect, phase changes, and polarization switching, make these materials useful for a wide range of technological applications including sensors, ultrasound, infrared cameras, sonar, diesel engine fuel injectors, ferroelectric random access memory, electro-optic modulators, vibration control, and electrocaloric cooling devices. Most of world’s current cooling and refrigeration technology is based upon the vapor-compression cycle of a refrigerant. Refrigeration systems that are based on this technology are bulky, require moving parts in the compressor and some of them have a less than optimal environmental impact. Thin film devices that utilize the electrocaloric effect could have a significant impact on refrigeration, heat pumps, air conditioning, energy scavenging, and computer cooling systems. Especially for the latter ones, the fan-based solutions are not likely to be able to keep up with the increases in computing power and the resulting current densities in integrated circuits. The ability to make quantitative predictions of the behavior of ferroelectric structures is of significant importance given the experimental efforts on the synthesis of barium titanate nanodots, nanorods, nanowires, and nanotubes, and lead zirconate titanate (PZT) thin films, and nanoparticles, and the potential for technological applications of these structures. The research contained herein implements a full thermo-electro-mechanical continuum framework and numerical methods based on phase-field modeling to study the domain and phase structure evolution associated with the electrocaloric effect in barium titanate ferroelectric nanodots. / text

京都大学 / 新制・課程博士 / 博士(工学) / 甲第23502号 / 工博第4914号 / 新制||工||1768(附属図書館) / 京都大学大学院工学研究科機械理工学専攻 / (主査)教授 平方 寛之, 教授 北條 正樹, 教授 嶋田 隆広, 教授 井上 康博 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

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Indiana University-Purdue University Indianapolis (IUPUI) / Sintering is a primary particulate manufacturing technology to provide densification and strength for ceramics and many metals. A persistent problem in this manufacturing technology has been to maintain the quality of the manufactured parts. This can be attributed to the various sources of uncertainty present during the manufacturing process. In this work, a two-particle phase-field model has been analyzed which simulates microstructure evolution during the solid-state sintering process. The sources of uncertainty have been considered as the two input parameters surface diffusivity and inter-particle distance. The response quantity of interest (QOI) has been selected as the size of the neck region that develops between the two particles. Two different cases with equal and unequal sized particles were studied. It was observed that the neck size increased with increasing surface diffusivity and decreased with increasing inter-particle distance irrespective of particle size. Sensitivity analysis found that the inter-particle distance has more influence on variation in neck size than that of surface diffusivity. The machine-learning algorithm Gaussian Process Regression was used to create the surrogate model of the QOI. Bayesian Optimization method was used to find optimal values of the input parameters. For equal-sized particles, optimization using Probability of Improvement provided optimal values of surface diffusivity and inter-particle distance as 23.8268 and 40.0001, respectively. The Expected Improvement as an acquisition function gave optimal values 23.9874 and 40.7428, respectively. For unequal sized particles, optimal design values from Probability of Improvement were 23.9700 and 33.3005 for surface diffusivity and inter-particle distance, respectively, while those from Expected Improvement were 23.9893 and 33.9627. The optimization results from the two different acquisition functions seemed to be in good agreement with each other. The results also validated the fact that surface diffusivity should be higher and inter-particle distance should be lower for achieving larger neck size and better mechanical properties of the material.

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Zirconia based ceramics are strong, hard, inert, and smooth, with low thermal conductivity and good biocompatibility. Such properties made zirconia ceramics an ideal material for different applications form thermal barrier coatings (TBCs) to biomedicine applications like femoral implants and dental bridges. However, this unusual versatility of excellent properties would be mediated by the metastable tetragonal (or cubic) transformation to the stable monoclinic phase after a certain exposure at service temperatures. This transformation from tetragonal to monoclinic, known as LTD (low temperature degradation) in biomedical application, proceeds by propagation of martensite, which corresponds to transformation twinning. As such, tetragonal to monoclinic transformation is highly sensitive to mechanical and chemomechanical stresses. It is known in fact that this transformation is the source of the fracture toughening in stabilized zirconia as it occurs at the stress concentration regions ahead of the crack tip. This dissertation is an attempt to provide a kinetic-based model for tetragonal to monoclinic transformation in zirconia. We used the phase field technique to capture the temporal and spatial evolution of monoclinic phase. In addition to morphological patterns, we were able to calculate the developed internal stresses during tetragonal to monoclinic transformation. The model was started form the two dimensional single crystal then was expanded to the two dimensional polycrystalline and finally to the three dimensional single crystal. The model is able to predict the most physical properties associated with tetragonal to monoclinic transformation in zirconia including: morphological patterns, transformation toughening, shape memory effect, pseudoelasticity, surface uplift, and variants impingement. The model was benched marked with several experimental works. The good agreements between simulation results and experimental data, make the model a reliable tool for predicting tetragonal to monoclinic transformation in the cases we lack experimental observations.

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