No description available.

In this thesis, we have used a phase field model for studying the effect of atomic mobility inside the precipitate phase on coarsening behaviour in two dimensional (2D) systems. In all the available coarsening theories, the diffusivity inside the precipitate phase is not explicitly taken into account; this would imply that there is no chemical potential gradient inside the precipitate. This assumption is valid if (a) the atomic mobility inside the precipitate is much higher than that in the matrix, or (b) the precipitate volume fraction is small (i.e. the interparticle spacing is far higher than the average particle size). We undertook this study to evaluate the potential effect of diffusivity in the precipitate on coarsening in situations where conditions (a) and (b), above, do not hold, by studying systems with moderate volume fractions (20% and 30%) and with low atomic mobilities in the precipitate. In our study, we have fixed the atomic mobility in the matrix at a constant value. We have used the well known Cahn-Hilliard model in which the microstructure is described in terms of a composition field variable. The evolution of microstructure is studied by numerically solving a non-classical diffusion equation known as the Cahn-Hilliard equation. We have used a semi-implicit Fourier spectral technique for solving the CH equation using periodic boundary conditions. The coarsening behaviour is tracked and analyzed using number density of particles, their average size and their size distribution. The main conclusion from this study is that, contrary to expectations, the atomic mobility in the precipitate phase has only a small effect on coarsening behavior. Specifically, with decreasing atomic mobility in the precipitate phase, we report a small increase in the number density, a slightly wider size distribution and a slightly smaller coarsening rate. We also add that these effects are too small to allow experimental verification. These results indicate that the need for chemical potential equilibration within each precipitate is not an important factor during coarsening.

No description available.

No description available.

Numerous efforts have contributed to the study of phase-change problems for over a century|both analytical and numerical. Among those numerical approximations applied to solve phase-transition problems, phase-field models attract more and more attention because they not only capture two important effects, surface tension and supercooling, but also enable explicitly labeling the solid and liquid phases and the position of the interface. In the research of this dissertation, a phase-field model has been employed to simulate 2-D dendrite growth of pure nickel without a flow, and 2-D ice crystal growth in a high-Reynolds-number lid-driven-cavity flow. In order to obtain the details of ice crystal structures as well as the flow field behavior during freezing for the latter simulation, it is necessary to solve the phase-field model without convection and the equations of motion on two different scales. To accomplish this, a heterogeneous multiscale method is implemented for the phase-field model with convection such that the phase-field model is simulated on a microscopic scale and the equations of motion are solved on a macroscopic scale. Simulations of 2-D dendrite growth of pure nickel provide the validation of the phase-field model and the study of dendrite growth under different conditions, e.g., degree of supercooling, interface thickness, kinetic coefficient, and shape of the initial seed. In addition, simulations of freezing in a lid-driven-cavity flow indicate that the flow field has great effect on the small-scale dendrite structure and the flow eld behavior on the large scale is altered by freezing inside it.

abstract: Miniaturization of microdevices comes at the cost of increased circuit complexity and operating current densities. At high current densities, the resulting electron wind imparts a large momentum to metal ions triggering electromigration which leads to degradation of interconnects and solder, ultimately resulting in circuit failure. Although electromigration-induced defects in electronic materials can manifest in several forms, the formation of voids is a common occurrence. This research aims at understanding the morphological evolution of voids under electromigration by formulating a diffuse interface approach that accounts for anisotropic mobility in the metallic interconnect. Based on an extensive parametric study, this study reports the conditions under which pancaking of voids or the novel void ‘swimming’ regimes are observed. Finally, inferences are drawn to formulate strategies using which the reliability of interconnects can be improved. / Dissertation/Thesis / Masters Thesis Materials Science and Engineering 2020

We introduce a continuous modeling approach which combines elastic response of the trabecular bone structure with the concentration of signaling molecules within the bone and a mechanism for concentration dependent local bone formation and resorption. In an abstract setting bone can be considered as a shape changing structure. For similar problems in materials science phase field approximations have been established as an efficient computational tool. We adapt such an approach for trabecular bone remodeling. It allows for a smooth representation of the trabecular bone structure and drastically reduces computational costs if compared with traditional micro finite element approaches. We demonstrate the advantage of the approach within a minimal model. We quantitatively compare the results with established micro finite element approaches on simple geometries and consider the bone morphology within a bone segment obtained from micro-CT data of a sheep vertebra with realistic parameters.

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第19991号 / 工博第4235号 / 新制||工||1655(附属図書館) / 33087 / 京都大学大学院工学研究科機械理工学専攻 / (主査)教授 北村 隆行, 教授 田畑 修, 教授 鈴木 基史 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

The diffuse-interface phase-field model is a powerful method to simulate and predict mesoscale microstructure evolution in materials using fundamental properties of thermodynamics and kinetics. The objective of this dissertation is to develop phase-field model for simulation and prediction of interdiffusion behavior and evolution of microstructure in multiphase binary and ternary systems under composition and/or temperature gradients. Simulations were carried out with emphasis on multicomponent diffusional interactions in single-phase system, and microstructure evolution in multiphase systems using thermodynamics and kinetics of real systems such as Ni-Al and Ni-Cr-Al. In addition, selected experimental studies were carried out to examine interdiffusion and microstructure evolution in Ni-Cr-Al and Fe-Ni-Al alloys at 1000°C. Based on Onsager’s formalism, a phase-field model was developed for the first time to simulate the diffusion process under an applied temperature gradient (i.e., thermotransport) in single- and two-phase binary alloys. Development of concentration profiles with uphill diffusion and the occurrence of zeroflux planes were studied in single-phase diffusion couples using a regular solution model for a hypothetical ternary system. Zero-flux plane for a component was observed to develop for diffusion couples at the composition that corresponds to the activity of that component in one of the terminal alloys. Morphological evolution of interphase boundary in solid-to-solid two-phase diffusion couples (fcc-γ vs. B2-β) was examined in Ni-Cr-Al system with actual thermodynamic data and concentration dependent chemical mobility. With the instability introduced as a small initial compositional fluctuation at the interphase boundary, the evolution of the interface morphology was found to vary largely as a function of terminal alloys and related composition-dependent chemical mobility. In a binary Ni-Al system, multiphase diffusion couples of fcc-γ vs. L12-γ′, γ vs. γ+γ′ and γ+γ′ vs. γ+γ′ were simulated with alloys of varying compositions and volume fractions of second phase (i.e., γ′). Chemical mobility as a function of composition was employed in the study with constant gradient energy coefficient, and their effects on the final interdiffusion microstructure was examined. Interdiffusion microstructure was characterized by the type of boundaries formed, i.e. Type 0, Type I, and Type II boundaries, following various experimental observations in literature and thermodynamic considerations. Volume fraction profiles of alloy phases present in the diffusion couples were measured to quantitatively analyze the formation or dissolution of phases across the boundaries. Kinetics of dissolution of γ′ phase was found to be a function of interdiffusion coefficients that can vary with composition and temperature. The evolution of interdiffusion microstructures in ternary Ni-Cr-Al solid-to-solid diffusion couples containing fcc-γ and γ+β (fcc+B2) alloys was studied using a 2D phase-field model. Alloys of varying compositions and volume fractions of the second phase (β) were used to simulate the dissolution kinetics of the β phase. Semi-implicit Fourier-spectral method was used to solve the governing equations with chemical mobility as a function of compositions. The simulation results showed that the rate of dissolution of the β phase (i.e., recession of β+γ twophase region) was dependent on the composition of the single-phase γ alloy and the volume fraction of the β phase in the two-phase alloy of the couple. Higher Cr and Al content in the γ alloy and higher volume fraction of β in the γ+β alloy lower the rate of dissolution. Simulated results were found to be in good agreement with the experimental observations in ternary Ni-CrAl solid-to-solid diffusion couples containing γ and γ+β alloys. For the first time, a phase-field model was developed to simulate the diffusion process under an applied temperature gradient (i.e., thermotransport) in multiphase binary alloys. Starting from the phenomenological description of Onsager’s formalism, the field kinetic equations are derived and applied to single-phase and two-phase binary system. Simulation results show that a concentration gradient develops due to preferential movement of atoms towards the cold and hot end of an initially homogeneous single-phase binary alloy subjected to a temperature gradient. The temperature gradient causes the redistribution of both constituents and phases in the two-phase binary alloy. The direction of movement of elements depends on their atomic mobility and heat of transport values.

The continual research and development of nickel-based superalloys is driven by the global demand to improve efficiency and reduce emissions in the aerospace and power generation industries. Integrated Computational Material Engineering (ICME) is a valuable tool for reducing the cost, time, and resources necessary for the development and optimization of the mechanical properties of materials. In this work, an ICME approach for understanding the microstructure development and optimizing the mechanical properties in nickel-based superalloys is employed. Most nickel-based superalloys are precipitate strengthened by either the γ’ phase, γ” phase, or both. Therefore, understanding the precipitation kinetics and morphological evolution of these phases is critical for evaluating their hardening effects during heat treatment and degradation of the microstructure during high temperature service. To this end, a phase-field model has been developed to analyze the nucleation, growth and coarsening kinetics during isothermal and non-isothermal aging conditions. Utilizing the phase-field model, the γ” phase microstructure development and its coherency strengthening effect in Inconel 625 is studied. A novel multistage aging strategy to optimize the γ” phase strengthening effect and reduce aging times for Inconel 625 is proposed. Secondly, the coarsening kinetic and microstructure development of γ’ strengthening phase in nickel-based superalloys is studied, with the goal of understanding the effect of elastic inhomogeneity on the microstructure evolution at high volume fractions of the γ’ phase. The result shows deviation of the coarsening kinetics from the classical Lifshitz-Slyozov-Wagner (LSW) due to the effect of elastic inhomogeneity, highlighting the need for incorporating elastic energy into coarsening theories.