Download or read book A Grand Potential Based Multi phase Field Model for Alloy Solidification written by Kaushik Shampur and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "The ability to model phase transitions in complex (i.e. multi-component and multi- phase) alloys, accurately, efficiently, and in an accessible manner, is important in material science. This thesis derives a new model that extends the quantitative model of polycrystalline solidification of Ofori-Opoku et al [3] to the case of multiple components and alloy phases through a grand potential functional description. Here, solidification is described by a set of order parameters describing solid phases and a set chemical potentials describing solute components. Solidification of a solid phase is driven by the grand potential difference between it and the liquid, expanded here to quadratic order in the chemical potential difference (relative to equilibrium) of each solute, i.e., its supersaturation. This allows us to model both near and far- from equilibrium solidification conditions, and to easily make contact with previous quantitative single-crystal phase field theories in the literature. Thermal fluctuations in the theory are treated via stochastic noise, a feature important for modelling multi-phase nucleation self-consistently. Working in the grand canonical ensemble treats the evolution of order parameter and chemical potential as a coupled process, unique compared to the traditional methods. As a result, complete decoupling of all diffusion fields and order parameter fields is achieved at equilibrium, making it possible to easily set solid-liquid or solid- solid interface energy independently of solute distribution across an an interface, an important feature for quantitative meso-scale calculations. Chemical diffusion equations in the model are augmented by a non-variational, so-called anti-trapping flux in each solute species. These fictitious fluxes are used in the literature in some phase field theories to correct for spurious solute trapping effects caused by the use of a diffuse interface, which is done solely for numerical expediency.We demonstrate its workings of our model in the limit of a two-component eutectic alloy system simulated with 2D dynamic adaptive mesh refinement. Benchmark eutectic lamellar simulations and measurements are first performed. Following that, two-phase homogenous nucleation and growth are examined. In the limit of near- equilibrium interfaces (zero interface kinetics), we illustrate two-phase grain growth scaling that is independent of nucleation barrier." --
Download or read book Quantitative Phase Field Modelling of Solidification written by Nikolas Provatas and published by CRC Press. This book was released on 2021-10-12 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a study of phase field modelling of solidification in metal alloy systems. It is divided in two main themes. The first half discusses several classes of quantitative multi-order parameter phase field models for multi-component alloy solidification. These are derived in grand potential ensemble, thus tracking solidification in alloys through the evolution of the chemical potentials of solute species rather than the more commonly used solute concentrations. The use of matched asymptotic analysis for making phase field models quantitative is also discussed at length, and derived in detail in order to make this somewhat abstract topic accessible to students. The second half of the book studies the application of phase field modelling to rapid solidification where solute trapping and interface undercooling follow highly non-equilibrium conditions. In this limit, matched asymptotic analysis is used to map phase field evolution equations onto the continuous growth model, which is generally accepted as a sharp-interface description of solidification at rapid solidification rates. This book will be of interest to graduate students and researchers in materials science and materials engineering. Key Features Presents a clear path to develop quantitative multi-phase and multi-component phase field models for solidification and other phase transformation kinetics Derives and discusses the quantitative nature of the model formulations through matched interface asymptotic analysis Explores a framework for quantitative treatment of rapid solidification to control solute trapping and solute drag dynamics
Download or read book Phase field simulations of multi component solidification and coarsening based on thermodynamic datasets written by Schulz, Sebastian and published by KIT Scientific Publishing. This book was released on 2017-02-22 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: The utilization of thermodynamic and mobility data plays a major role in phase-field modeling. This work discusses different formulations for the thermodynamic quantities of a grand potential model along with practices to determine parameters from datasets. The framework is used to study solidification of Al-Si-Mg for a variation of composition, diffusivities and surface energy anisotropies. To verify the simulations, they are compared with solidification theories.
Download or read book Quantitative Phase field Model for Phase Transformations in Multi component Alloys written by Abhik Narayan Choudhury and published by Karlsruher Institut Fur Technologie. This book was released on 2014-05-13 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Phase-field modeling has spread to a variety of applications involving phase transformations.While the method has wide applicability, derivation of quantitative predictions requires deeper understanding of the coupling between the system and model parameters. The book highlights a novel phase-field model based on a grand-potential formalism allowing for an elegant and efficient solution to problems in phase transformations.
Download or read book Phase Field Methods in Materials Science and Engineering written by Nikolas Provatas and published by John Wiley & Sons. This book was released on 2011-07-26 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive and self-contained, one-stop source discusses phase-field methodology in a fundamental way, explaining advanced numerical techniques for solving phase-field and related continuum-field models. It also presents numerical techniques used to simulate various phenomena in a detailed, step-by-step way, such that readers can carry out their own code developments. Features many examples of how the methods explained can be used in materials science and engineering applications.
Download or read book A Phase field Model for Technical Alloy Solidification written by Janin Eiken and published by . This book was released on 2010 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book TMS 2020 149th Annual Meeting Exhibition Supplemental Proceedings written by The Minerals, Metals & Materials Society and published by Springer Nature. This book was released on 2020-02-13 with total page 2046 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection presents papers from the 149th Annual Meeting & Exhibition of The Minerals, Metals & Materials Society.
Download or read book TMS 2019 148th Annual Meeting Exhibition Supplemental Proceedings written by & The Minerals, Metals Materials Society and published by Springer. This book was released on 2019-02-26 with total page 1631 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection features papers presented at the 148th Annual Meeting & Exhibition of The Minerals, Metals & Materials Society.
Download or read book Treatise on Process Metallurgy written by Roderick Guthrie and published by Elsevier. This book was released on 2024-01-25 with total page 818 pages. Available in PDF, EPUB and Kindle. Book excerpt: Treatise on Process Metallurgy: Volume One, Process Fundamentals provides academics with the fundamentals of the manufacturing of metallic materials, from raw materials into finished parts or products. In these fully updated volumes, coverage is expanded into four volumes, including Process Fundamentals, encompassing process fundamentals, structure and properties of matter; thermodynamic aspects of process metallurgy, and rate phenomena in process metallurgy; Processing Phenomena, encompassing interfacial phenomena in high temperature metallurgy, metallurgical process phenomena, and metallurgical process technology; Metallurgical Processes, encompassing mineral processing, aqueous processing, electrochemical material and energy processes, and iron and steel technology, non-ferrous process principles and production technologies, and more. The work distills the combined academic experience from the principal editor and the multidisciplinary four-member editorial board. Provides the entire breadth of process metallurgy in a single work Includes in-depth knowledge in all key areas of process metallurgy Approaches the topic from an interdisciplinary perspective, providing broad range coverage on topics
Download or read book Phase field Simulations of Multi component Solidification and Coarsening Based on Thermodynamic Datasets written by Sebastian Schulz and published by . This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Thermodynamics of Flowing Systems written by Antony N. Beris and published by Oxford University Press. This book was released on 1994-05-26 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: This much-needed monograph presents a systematic, step-by-step approach to the continuum modeling of flow phenomena exhibited within materials endowed with a complex internal microstructure, such as polymers and liquid crystals. By combining the principles of Hamiltonian mechanics with those of irreversible thermodynamics, Antony N. Beris and Brian J. Edwards, renowned authorities on the subject, expertly describe the complex interplay between conservative and dissipative processes. Throughout the book, the authors emphasize the evaluation of the free energy--largely based on ideas from statistical mechanics--and how to fit the values of the phenomenological parameters against those of microscopic models. With Thermodynamics of Flowing Systems in hand, mathematicians, engineers, and physicists involved with the theoretical study of flow behavior in structurally complex media now have a superb, self-contained theoretical framework on which to base their modeling efforts.
Download or read book Derivation and Analysis of a Phase Field Model for Alloy Solidification written by Björn Stinner and published by . This book was released on 2005 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Quantitative Phase Field Modelling of Solidification written by Nikolas Provatas and published by CRC Press. This book was released on 2021-10-13 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a study of phase field modelling of solidification in metal alloy systems. It is divided in two main themes. The first half discusses several classes of quantitative multi-order parameter phase field models for multi-component alloy solidification. These are derived in grand potential ensemble, thus tracking solidification in alloys through the evolution of the chemical potentials of solute species rather than the more commonly used solute concentrations. The use of matched asymptotic analysis for making phase field models quantitative is also discussed at length, and derived in detail in order to make this somewhat abstract topic accessible to students. The second half of the book studies the application of phase field modelling to rapid solidification where solute trapping and interface undercooling follow highly non-equilibrium conditions. In this limit, matched asymptotic analysis is used to map phase field evolution equations onto the continuous growth model, which is generally accepted as a sharp-interface description of solidification at rapid solidification rates. This book will be of interest to graduate students and researchers in materials science and materials engineering. Key Features Presents a clear path to develop quantitative multi-phase and multi-component phase field models for solidification and other phase transformation kinetics Derives and discusses the quantitative nature of the model formulations through matched interface asymptotic analysis Explores a framework for quantitative treatment of rapid solidification to control solute trapping and solute drag dynamics
Download or read book Solidification written by Michel Rappaz and published by EPFL Press. This book was released on 2009-08-21 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solidification is one of the oldest processes for producing useful implements and remains one of the most important modern commercial processes. This text describes the fundamentals of the technology in a coherent way, using consistent notation.
Download or read book Phase Equilibria Phase Diagrams and Phase Transformations written by Mats Hillert and published by Cambridge University Press. This book was released on 2007-11-22 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational tools allow material scientists to model and analyze increasingly complicated systems to appreciate material behavior. Accurate use and interpretation however, requires a strong understanding of the thermodynamic principles that underpin phase equilibrium, transformation and state. This fully revised and updated edition covers the fundamentals of thermodynamics, with a view to modern computer applications. The theoretical basis of chemical equilibria and chemical changes is covered with an emphasis on the properties of phase diagrams. Starting with the basic principles, discussion moves to systems involving multiple phases. New chapters cover irreversible thermodynamics, extremum principles, and the thermodynamics of surfaces and interfaces. Theoretical descriptions of equilibrium conditions, the state of systems at equilibrium and the changes as equilibrium is reached, are all demonstrated graphically. With illustrative examples - many computer calculated - and worked examples, this textbook is an valuable resource for advanced undergraduates and graduate students in materials science and engineering.
Download or read book High Performance Computing in Science and Engineering 20 written by Wolfgang E. Nagel and published by Springer Nature. This book was released on 2022-01-01 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the state-of-the-art in supercomputer simulation. It includes the latest findings from leading researchers using systems from the High Performance Computing Center Stuttgart (HLRS) in 2020. The reports cover all fields of computational science and engineering ranging from CFD to computational physics and from chemistry to computer science with a special emphasis on industrially relevant applications. Presenting findings of one of Europe’s leading systems, this volume covers a wide variety of applications that deliver a high level of sustained performance. The book covers the main methods in high-performance computing. Its outstanding results in achieving the best performance for production codes are of particular interest for both scientists and engineers. The book comes with a wealth of color illustrations and tables of results.
Download or read book Multiscale Modeling of Solidification of Multi component Alloys written by Lijian Tan and published by . This book was released on 2007 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modeling solidification in the micro-scale is computationally intensive. To overcome this difficulty, a method combining features of front-tracking methods and fixed-domain methods is developed. To explicitly track the interface growth and shape of the solidifying crystals, a front-tracking approach based on the level set method is implemented. To easily model the heat and momentum transport, a fixed-domain method is implemented assuming a diffused freezing front where the liquid fraction is defined in terms of the level set function. The fixed-domain approach, by avoiding the explicit application of essential boundary conditions on the freezing front, leads to an energy conserving methodology that is not sensitive to the mesh size. Techniques including fast marching, narrow band computing and adaptive meshing are utilized to speed up computations. The model is used to investigate various phenomena in solidification including two- and three-dimensional dendrite growth of pure material and alloys, eutectic and peritectic solidification, convection effects on crystal and dendrite growth, planar/cellular/dendritic transition, interaction between multiple dendrites, columnar/equiaxed transition and etc. Interaction between thousands or even millions of crystals gives the overall behavior of the solidification process and defines the properties of the final product. A multiscale model based on a database approach is developed to investigate alloy solidification. Appropriate assumptions are introduced to describe the behavior of macroscopic temperature, macroscopic concentration, liquid volume fraction and microstructure features. These assumptions lead to a macroscale model with two unknown functions: liquid vol- ume fraction and microstructure features. These functions are computed using information from microscale solutions of selected problems. A computationally efficient model, which is different from the microscale and macroscale models, is utilized to find relevant sample problems. The microscale solution of the relevant sample problems is then utilized to evaluate the two unknown functions (liquid volume fraction and microstructure features) in the macroscale model. The temperature solution of the macroscale model is further used to improve the estimation of the liquid volume fraction and microstructure features. Interpolation is utilized in the feature space to greatly reduce the number of required sample problems. The efficiency of the proposed multiscale framework is demonstrated with numerical examples that consider a large number of crystals. A computationally intensive fully-resolved microscale analysis is also performed to evaluate the accuracy of the multiscale framework. (Abstract).
