Homogenization of alloying elements is desired during sintering of powder metallurgy components. The redistribution processes such as penetration of liquid phase into the interparticle/grain boundaries of solid particles and subsequent solid-state  diffusion of alloy element(s) in the base powder, are important for the effective homogenization of alloy element(s) during liquid phase sintering of the mixed powders. The aim of this study is to increase the understanding of alloy element redistribution processes and their effect on the dimensional properties of the compact by means of numerical and experimental techniques. The phase field model coupled with Navier-Stokes equations is used for the simulations of dynamic wetting of millimeter- and micrometer-sized metal drops and liquid phase penetration into interparticle boundaries. The simulations of solid particle rearrangement under the action of capillary forces exerted by the liquid phase are carried out by using the equilibrium equation for a linear elastic material. Thermodynamic and kinetic calculations are performed to predict the phase diagram and the diffusion distances respectively. The test materials used for the experimental studies are three different powder mixes; Fe-2%Cu, Fe-2%Cu-0.5%C, and Fe-2%(Cu-2%Ni-1.5%Si)-0.5%C. Light optical microscopy, energy dispersive X-ray spectroscopy and dilatometry are used to study the microstructure, kinetics of the liquid phase penetration, solid-state diffusion of the Cu, and the dimensional changes during sintering. The wetting simulations are verified by matching the spreading experiments of millimeter-sized metal drops and it is observed that wetting kinetics is much faster for a micrometer-sized drop compared to the millimeter-sized drop. The simulations predicted the liquid phase penetration kinetics and the motion of solid particles during the primary rearrangement stage of liquid phase sintering in agreement with the analytical model. Microscopy revealed that the C addition delayed the penetration of the Cu rich liquid phase into interparticle/grain boundaries of Fe particles, especially into the grain boundaries of large Fe particles, and consequently the Cu diffusion in Fe is also delayed. We propose that the relatively lower magnitude of the sudden volumetric expansion in the master alloy system could be due to the continuous melting of liquid forming master alloy particles. / <p>QC 20140515</p>

The size and morphology of the dendrite growth patterns are simulated for laser powder deposition of Ti-Nb alloys under steady-state and transient growth conditions. A phase field model using an adaptive grid technique was employed to simulate the steady-state growth of dendrites on rather small domains, in which fixed local solidification conditions are present. For simulation of dendrite growth patterns at transient conditions, a cellular automaton model was used along with a virtual front tracking technique on larger domains, containing various initial orientations of the solid-liquid (SL) interface. To obtain the required input thermal data, i.e., the temporal distribution of temperature, a finite element analysis was performed along with a novel numerical approach for the real-time addition of new deposition material in each time step, thus building the deposition geometry momentarily. Using the output of the thermal model, the motion and morphology of the SL interface was determined through tracking the isotherm of the solidification temperature. First, in this study, the appropriate set of processing parameters was found through an optimization process using a new concept, laser supplied energy Es, which combines the effects of the energy and powder density in the process. With the developed analytical/experimental procedure, crack and pore-free coatings of Ti-Nb with continuous beads were produced by examining the effects of a few sets of processing parameters, including laser power, laser scan velocity, laser beam diameter and powder feed rate. The results of the thermal model for the optimized set of parameters matched with the thermocouple temperature measurements with only ~5% deviation. The thermal model was able to predict realistic profiles for the temporal development of deposition geometry, thus predicting meaningful morphologies of the SL interface. The model output was easily treated for extraction of local processing parameters, such as the temperature gradient and solidification velocity. These data are very useful when simulating the dendrite growth patterns at steady-state conditions in directional solidification of selected regions in the microstructure. In order to define transient growth conditions, the simulated distribution of temperature can be also directly fed into the microstructure model at each solution time step. Phase field simulations of steady-state growth of dendrites during directional solidification showed a remarkable agreement with the experimental observations for the local dendrite arm spacing across the microstructure. Also qualitatively agreeing with the experiment, the simulated dendrite spacing exhibited a minimum around the mid-height region of the microstructure, which is explained by the counter effect of the temperature gradient and solidification velocity along the height of the sample. On a large domain containing different initial orientations of the SL interface, cellular automaton simulations for transient growth patterns of dendrites could reproduce most qualitative features observed in the microstructure. The dendrite arm spacing gradually decreased from the top of the microstructure. The competition was won by the dendrites growing in areas with higher cooling rates, i.e., in the regions closer to the top of the microstructure. The secondary arms of the primary dendrites, which are initially inclined on the vertical axis, grew extensively only along the overall growth direction and eventually became primary arms in some cases.

<p>This dissertation addresses interface problems simulated with the finite element method (FEM) with mesh adaptivity. More specifically, we concentrate on the strategies that adaptively modify the mesh and the associated data transfer issues. </p><p>In finite element simulations there often arises the need to change the mesh and continue the simulation on a new mesh. Analysts encounter such an issue when they adaptively refine the mesh to reduce the computational cost, smooth distorted elements to improve system conditioning, or introduce new surfaces and change the domain in simulations of fracture problems. In such circumstances, the transfer of data from the old mesh to the new one is of crucial importance, especially for nonlinear problems. We are concerned in this work with contact problems with adaptive re-meshing and fracture problems modeled with the eXtended finite element method (X-FEM). For the former ones, the transfer of surface data is built upon the technique of parallel transport, and the error of such a transfer strategy is investigated through classic benchmark tests. A transfer scheme based on a least squares problem is also proposed to transfer the bulk data when nearly incompressible hyperelastic materials are employed. For the latter type of problems, we facilitate the transfer of internal variables by making partial elements utilize the same quadrature points from the uncut parent elements and meanwhile adjusting the quadrature weights via the solution of moment fitting equations. The proposed scheme helps avoid the complicated remapping procedure of internal variables between two different sets of quadrature points. A number of numerical examples are presented to demonstrate the robustness and accuracy of our proposed approaches.</p><p>Another renowned technique to simulate fracture problems is based upon the phase-field formulation, where a set of coupled mechanics and phase-field equations are solved via FEM without modeling crack geometries. However, losing the ability to model distinct surfaces in the phase-field formulation has drawbacks, such as difficulties simulating contact on crack surfaces and poorly-conditioned stiffness matrices. On the other hand, using the pure X-FEM in fracture simulations mandates the calculation of the direction and increment of crack surfaces at each step, introducing intricacies of tracing crack evolution. Thus, we propose combining phase-field and X-FEM approaches to utilize their individual benefits based on a novel medial-axis algorithm. Consequently, we can still capture complex crack geometries while having crack surfaces explicitly modeled by modifying the mesh with the X-FEM.</p> / Dissertation

Submitted by Daniella Sodre (daniella.sodre@ufpe.br) on 2015-04-08T13:19:43Z No. of bitstreams: 2 TESE Sérgio Henrique Lira.pdf: 10473188 bytes, checksum: ad39baf570ad4b641f94987468e9d1d0 (MD5) license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) / Made available in DSpace on 2015-04-08T13:19:43Z (GMT). No. of bitstreams: 2 TESE Sérgio Henrique Lira.pdf: 10473188 bytes, checksum: ad39baf570ad4b641f94987468e9d1d0 (MD5) license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Previous issue date: 2014-02-21 / CNPq; INCT-FCx. / Nesta Tese são empregadas técnicas analíticas e numéricas para investigar o fenômeno de formação de dedos viscosos entre fluidos imiscíveis confinados quando um destes fluidos é um fluido magnético complexo. Diferentes tipos de esquemas geométricos efetivamente bidimensionais foram investigados. Duas situações distintas são tomadas com relação à natureza da amostra de fluido magnético: um fluido newtoniano usual, e um fluido magneto-reológico que apresenta um yield stress dependente da intensidade do campo magnético. Equações governantes adequadas são derivadas para cada um dos casos. Para obter um entendimento analítico dos estágios iniciais da evolução temporal da interface foi empregada uma análise fracamente não-linear de modos acoplados. Este tipo de análise acessa a estabilidade de uma interface inicialmente perturbada e também revela a morfologia dos dedos emergentes. Em algumas circunstâncias soluções estacionárias podem ser encontradas mesmo na ordem não-linear mais baixa. Nesta situação é feita uma comparação de algumas destas soluções com soluções estáticas totalmente não-lineares obtidas através de um formalismo de vortex-sheet na condição de equilíbrio. Em seguida foi desenvolvido um modelo de phase-field aplicado a fluidos magnéticos que é capaz de simular numericamente a dinâmica totalmente não-linear do sistema. O modelo consiste em introduzir uma função auxiliar que reproduz uma interface difusa de espessura finita. Utilizando esta ferramenta também é possível estudar um complexo problema de dedos viscosos de origem biológica: o fluxo de actina como um fluido ativo dentro de um fragmento lamelar.

Le comportement mécanique des alliages métalliques industriels, notamment ceux utilisés dans le domaine de l’aéronautique, est contrôlé par la présence de différents types de précipités et par la nucléation et propagation de défauts cristallins tels que les dislocations. La compréhension du comportement de ces matériaux nécessite des modèles continus afin d’accéder à l’échelle macroscopique. Cependant, même aujourd’hui, les théories conventionnelles de la plasticité utilisent des variables mésoscopique et des équations d’évolution qui ne reposent pas sur la notion de transport de dislocations. En conséquence, ces théories sont basées sur des lois phénoménologiques qu’il est nécessaire de calibrer pour chaque matériau et chaque application. Il est donc souhaitable d’établir le lien entre les échelles micro et macro afin de générer une théorie continue de la plasticité déduite analytiquement des équations fondamentales de la dynamique des dislocations. L’objet de cette thèse est précisément de contribuer à l’élaboration d’une telle théorie. La première étape a consisté à établir rigoureusement la procédure de changement d’échelle dans une situation simplifiée. Nous avons alors abouti à un système d’équations de transport hyperboliques sur des densités de dislocations contrôlées par des contraintes locales de friction et de backstress qui émergent du changement d’échelle. Nous avons ensuite développé une procédure numérique pour calculer ces termes et analyser leur comportement. Finalement, nous avons développé un schéma numérique efficace pour intégrer les équations de transport ainsi qu’un schéma spectral multi-grille pour résoudre l’équilibre élastique associé à un champ de déformation propre quelconque dans un milieu élastiquement anisotrope et inhomogène. / The mechanical behavior of industrial metallic alloys, in particular those used in the aerospace industry, is controlled by the existence of several types of precipitates and by the nucleation and propagation of crystalline defects such as dis- locations. The understanding of this behavior requires continuous models to access the macroscopic scale. However, even today, conventional plasticity theories use mesoscopic variables and evolution equations that are not based on the transport of dislocations. Therefore, these theories are based on phenomenological laws that must be calibrated for each material, or, for each specific applications. It is therefore highly desirable to make link between the micro and macro scales, in order to derive a continuous theory of plasticity from the fundamental equations of the dislocation dynamics. The aim of this thesis is precisely to contribute the elaboration of such a theory. The first step has consisted to rigorously establish a coarse graining procedure in a simplified situation. We have then obtained a set of hyperbolic transport equations on dislocation densities, controlled by a local friction stress and a local back-stress that emerge from the scale change. We have then developed a numerical procedure to compute these local terms and analyze their behavior. Finally, we have developed an efficient numerical scheme to integrate the transport equations as well as a multigrid spectral scheme to solve elastic equilibrium associated to an arbitrary eigenstrain in an elastically heterogeneous and anisotropic medium.

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

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.

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.

<div> <div> <div> <p>The material responses and the deformation pattern of crystals are strongly influ- enced by their microstructure, crystallographic texture and the presence of defects of various types. </p> <p>In electronics, Sn coatings are widely used in circuits to protect conductors, reduce oxidation and improve solderability. However, the spontaneous growth of whiskers in Sn films causes severe system failures. Based on extensive experimental results, whiskers are observed to grow from surface grains with shallow grain boundaries. The underlying mechanism for these surface grains formation is crucial to predict potential whisker sites. A phase field model is coupled with a single crystal plasticity model and applied to simulate the grain boundary migration as well as the grain rotation process in Sn thin film, which are two possible mechanisms for surface grain formation. The grain boundary migration of three columnar grains is modeled and no surface grain is formed due to large plastic dissipation. In polycrystal Sn thin film, the nucleation of subgrains with shallow grain boundaries is observed for certain grain orientations on the film surface and the location of which corresponds to the regions with high strain energy density. From these simulations, it can be concluded that the grain rotation is the mechanism for whisker grain formation and the nucleated subgrains may be the potential whisker sites. </p> <p>Sn-based solders are also widely used in electronics packaging. The reliability and the performance of SAC (Sn-Ag-Cu) solders are of key importance for the miniaturiza- tion of electronics. The interfacial reaction between Cu substrates and Sn-based sol- ders forms two types of brittle intermetallic compounds (IMCs), Cu6Sn5 and Cu3Sn. </p> </div> </div> <div> <div> <p>During the operation, the interconnecting solders usually experience thermal loading and electric currents. These environmental conditions result in the nucleation of voids in Cu3Sn layer and the growth of the IMCs. A phase field damage model is applied to model the fracture behavior in Cu/Sn system with different initial void densities and different Cu3Sn thickness. The simulation results show the fracture location is dependent on the Cu3Sn thickness and the critical stress for fracture can be increased by lowering the void density and Cu3Sn thickness.<br></p></div></div></div><div><div><div> <p>In alloys, the stacking fault energy varies with the local chemical composition. The effects of the stacking fault energy fluctuation on the strengthening of alloys are studied using phase field dislocation method (PFDM) simulations that model the evolution of partial dislocations in materials at zero temperature. Some examples are shown to study the dependency of the yield stress on the stacking fault energy, the decorrelation of partial dislocations in the presence of impenetrable and penetrable particles. Simulations of the evolution of partial dislocations in a stacking fault energy landscape with local fluctuations are presented to model the responses of high entropy alloys. A strong size dependency is observed with a maximum strength when the mean region size approaches the average equilibrium stacking fault width. The strength of high entropy alloys could be improved by controlling the disorder in the chemical misfit. </p> </div> </div> </div>

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