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Phase Field Modeling Of Microstructure Evolution In Elastically Inhomogeneous Polycrystalline Materials
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Book Synopsis Phase-field Modeling of Microstructure Evolution in Elastically Inhomogeneous Polycrystalline Materials by : Tae Wook Heo
Download or read book Phase-field Modeling of Microstructure Evolution in Elastically Inhomogeneous Polycrystalline Materials written by Tae Wook Heo and published by . This book was released on 2012 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Phase-field Models of Microstructure Evolution in a System with Elastic Inhomogeneity and Defects by : Shenyang Hu
Download or read book Phase-field Models of Microstructure Evolution in a System with Elastic Inhomogeneity and Defects written by Shenyang Hu and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Phase-field Models of Microstructure Evolution and New Numerical Strategies by : Weiming Feng
Download or read book Phase-field Models of Microstructure Evolution and New Numerical Strategies written by Weiming Feng and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A basic interest in materials science is the determination of microstructures of materials in order to understand why materials have the properties they exhibit and how these properties can be controlled to serve technological uses. In this dissertation, the phase-field approach is combined with other models and algorithms to study the effect of elastic energy, anisotropic mobility and structural defects on phase separation kinetics and morphological evolution in bulk systems. A multi-dimensional general phase-field model has been developed by combining the iteration method for calculating the elastic energy and a semi-implicit spectral method for solving the Cahn?Hilliard equation. The model can efficiently calculate the microstructure evolution for systems with rather general elastic anisotropies, arbitrarily large elastic inhomogeneity, general misfit strain, and large anisotropic mobility. The microstructure and structure functions have been studied to show the effect of large anisotropic mobility together with the elastic energy. To address the challenge of large scale simulations of microstructures which are still computationally expensive to date, an adaptive semi-implicit Fourier spectral (AFSIM) method is developed to solve Allen-Cahn equation by making grid points spatially adaptive in the physical domain via a moving mesh strategy, while maintaining a uniform grid in the computational domain for the spectral implementation. The moving mesh method is adopted since it is particularly efficient among recent efforts in developing advanced numerical algorithms. The newly developed approach not only provides more accurate treatment at the interfaces requiring higher resolution, but also retains the numerical efficiency of the semi-implicit Fourier spectral method. Numerical examples using the adaptive moving mesh semi-implicit Fourier spectral method are presented for both two and three space dimensional microstructure simulations, and they are compared with those obtained by other methods. By maintaining similar accuracy, the proposed method is shown to be far more efficient than the existing methods for microstructures with small ratios of interfacial width to the domain size. The AFSIM is further implemented to solve Cahn-Hilliard equation with inhomogeneous, anisotropic elasticity. Numerical implementations and test examples in both two and three dimensions are considered with a particular illustration using the well-studied example of mis-fitting particles in a solid as they approach to their equilibrium shapes. It is shown that significant savings in memory and computational time is achieved while accurate solutions are preserved. The dynamics of the structure defects such as dislocations generally control the material properties during non-equilibrium processing. In phase-fields description, the dislocations exist only along the dislocations lines parallel to the slip planes. The total dislocation line length to volume ratio in dislocation motion is expected to be significantly smaller than the total area to volume ratio for interface motion. Therefore, AFSIM is extended to study the dislocation motion. By comparing the results with analytical solutions for accuracy and with results from the uniform Fourier-spectral semi-implicit method (UFSIM) for efficiency, it is shown that AFSIM yields much more accurate results for the dislocation stress field and is an order magnitude more efficient than the UFSIM for the same accuracy.
Book Synopsis Theory and Modeling of Microstructural Evolution in Polycrystalline Materials by : Ning Ma
Download or read book Theory and Modeling of Microstructural Evolution in Polycrystalline Materials written by Ning Ma and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: To accurately predict microstructure evolution and, hence, to synthesis metal and ceramic alloys with desirable properties involves many fundamental as well as practical issues. In the present study, novel theoretical and phase field approaches have been developed to address some of these issues including solute drag and segregation transition at grain boundaries and dislocations, grain growth in systems of anisotropic boundary properties, and precipitate microstructure development in polycrystalline materials. The segregation model has allowed for the prediction of a first-order segregation transition, which could be related to the sharp transition of solute concentration of grain boundary as a function of temperature. The incorporating of interfacial energy and mobility as functions of misorientation and inclination in the phase field model has allowed for the study of concurrent grain growth and texture evolution. The simulation results were analyzed using the concept of local grain boundary energy density, which simplified significantly the development of governing equations for texture controlled grain growth in Ti-6Al-4V. Quantitative phase field modeling techniques have been developed by incorporating thermodynamic and diffusivity databases. The models have been validated against DICTRA simulations in simple 1D problems and applied to simulate realistic microstructural evolutions in Ti-6Al-4V, including grain boundary a and globular a growth and sideplate development under both isothermal aging and continuous cooling conditions. The simulation predictions agree well with experimental observations.
Book Synopsis Phase-field Modeling of Displacive Phase Transformations in Elastically Anisotropic and Inhomogeneous Polycrystals by :
Download or read book Phase-field Modeling of Displacive Phase Transformations in Elastically Anisotropic and Inhomogeneous Polycrystals written by and published by . This book was released on 2014 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Spectral Methods for Modeling Microstructure Evolution in Deformation Processing of Cubic Polycrystalline Metals by : Hari Kishore Duvvuru
Download or read book Spectral Methods for Modeling Microstructure Evolution in Deformation Processing of Cubic Polycrystalline Metals written by Hari Kishore Duvvuru and published by . This book was released on 2007 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mechanical properties of engineering materials are directly controlled by the underlying microstructure, which in turn is governed by the processing methods. The complete description of microstructure is extremely complex and is also not required for many microstructure-properties relationships of interest. The relevant details of the microstructure that influence strongly the elastic-plastic properties of the material include the lattice orientation distribution (texture), the grain size and shape distribution, and the arrangement and distribution of dislocation networks on the various slip systems in the constituent crystals. Of these, the crystallographic texture is perhaps the most important aspect of microstructure that has a strong influence on the elastic and the initial yield properties of most polycrystalline materials used in the manufacture of engineering components. It should also be noted that crystallographic texture is likely to have the dominant effect on the inherent anisotropy exhibited by these materials.The objective of this thesis is to provide a mathematical framework for the development of material databases; capturing the relevant details of the microstructure, while paying attention to inherent anisotropy of properties associated with them. Here crystallographic texture is the only microstructural parameter that is considered. This work is motivated by a new design paradigm called microstructure sensitive design (MSD) which employs statistical description of microstructure and its core feature is the efficient spectral representations of microstructure-property-processing linkages. Using the MSD framework as the basis, novel computational methodologies were developed in this work to build material spectral databases in single phase cubic polycrystalline materials. These databases were critically evaluated in three different cases: 1) To predict the effective macroscale elastic properties in perfectly disordered copper polycrystals 2) Evolution of the microstructure and the concomitant anisotropic stress-strain response during deformation processes in FCC polycrystals and (3) in developing a processing recipe to obtain a targeted texture using selected processing techniques.
Book Synopsis Phase-Field Methods in Materials Science and Engineering by : Nikolas Provatas
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.
Book Synopsis Incorporating Physically-based Microstructures in Materials Modeling by :
Download or read book Incorporating Physically-based Microstructures in Materials Modeling written by and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Here, the mechanical properties of materials systems are highly influenced by various features at the microstructural level. The ability to capture these heterogeneities and incorporate them into continuum-scale frameworks of the deformation behavior is considered a key step in the development of complex non-local models of failure. In this study, we present a modeling framework that incorporates physically-based realizations of polycrystalline aggregates from a phase field (PF) model into a crystal plasticity finite element (CP-FE) framework. Simulated annealing via the PF model yields ensembles of materials microstructures with various grain sizes and shapes. With the aid of a novel FE meshing technique, FE discretizations of these microstructures are generated, where several key features, such as conformity to interfaces, and triple junction angles, are preserved. The discretizations are then used in the CP-FE framework to simulate the mechanical response of polycrystalline [alpha]-iron. It is shown that the conformal discretization across interfaces reduces artificial stress localization commonly observed in non-conformal FE discretizations. The work presented herein is a first step towards incorporating physically-based microstructures in lieu of the overly simplified representations that are commonly used. In broader terms, the proposed framework provides future avenues to explore bridging models of materials processes, e.g. additive manufacturing and microstructure evolution of multi-phase multi-component systems, into continuum-scale frameworks of the mechanical properties.
Book Synopsis Phase-field Modeling of Microstructure and Fracture Evolution in Magneto-electro-mechanics by : Ashish Sridhar
Download or read book Phase-field Modeling of Microstructure and Fracture Evolution in Magneto-electro-mechanics written by Ashish Sridhar and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Fundamental and Practical Applications of Phase Field Method to the Study of Alloy Microstructure Evolutions by : Weiqi Luo
Download or read book Fundamental and Practical Applications of Phase Field Method to the Study of Alloy Microstructure Evolutions written by Weiqi Luo and published by . This book was released on 2005 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: The microstructure of a material has a great influence on its properties. Therefore, understanding underlying mechanisms of microstructural evolution is critical for developing desired properties. However, microstructural evolution is highly non-linear and, at this stage, fundamental quantitative understanding of it is limited. There has been an increasing demand lately for modeling and simulating microstructural evolution. That is not only because they have a relatively lower cost than experiment, and can be performed for arbitraries conditions, but also they can provide fundamental understanding of experimental observations, and its ability to predict the evolution. Moreover, a quantitative predictive model will be very usefully to guide process design in various industry applications. For this reason, many computer models have been developed. Among them, the phase field method has become a rigorous approach to simulating complex microstructural evolution, such as martensitic transformation, dendritic growth, dislocation movement and grain growth. The effect of nucleating ordered precipitates at dislocations and the subsequent growth on particle morphology in Ni-Al and Al-Li through phase field method study is presented in this thesis. Results show that this process yields the splitting pattern that is observed experimentally. In particular, the structural discontinuity associated with an edge dislocation may lead to the formation of an antiphase domain boundary within an ordered phase particle. At this stage, the application of phase field methods in industry is still limited because many phase field models are qualitative in nature. The development of a quantitative phase field model for the Fe-Cr-C system by designing an appropriate energy expression and linking the thermodynamic and kinetics parameters to quantitative databases is presented in this thesis. This model is validated and its capability is shown in the corresponding chapter.
Book Synopsis A Numerical Algorithm for the Solution of a Phase-Field Model of Polycrystalline Materials by :
Download or read book A Numerical Algorithm for the Solution of a Phase-Field Model of Polycrystalline Materials written by and published by . This book was released on 2008 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: We describe an algorithm for the numerical solution of a phase-field model (PFM) of microstructure evolution in polycrystalline materials. The PFM system of equations includes a local order parameter, a quaternion representation of local orientation and a species composition parameter. The algorithm is based on the implicit integration of a semidiscretization of the PFM system using a backward difference formula (BDF) temporal discretization combined with a Newton-Krylov algorithm to solve the nonlinear system at each time step. The BDF algorithm is combined with a coordinate projection method to maintain quaternion unit length, which is related to an important solution invariant. A key element of the Newton-Krylov algorithm is the selection of a preconditioner to accelerate the convergence of the Generalized Minimum Residual algorithm used to solve the Jacobian linear system in each Newton step. Results are presented for the application of the algorithm to 2D and 3D examples.
Book Synopsis The Fundamentals and Applications of Phase Field Method in Quantitative Microstructural Modeling by : Chen Shen
Download or read book The Fundamentals and Applications of Phase Field Method in Quantitative Microstructural Modeling written by Chen Shen and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: The key to predicting and therefore controlling properties of materials is the knowledge of microstructure. As computer modeling and simulation is becoming an important part of materials science and engineering, there is an ever-increasing demand for quantitative models that are able to handle microstructures of realistic complexity at length and time scales of practical interest. The phase field approach has become the method of choice for modeling complicated microstructural evolutions during various phase transformations, grain growth and plastic deformation. Using gradient thermodynamics of non-uniform systems and Langevin dynamics, the method characterizes arbitrary microstructures and their spatial-temporal evolution with field variables, and is capable of simulating microstructures and their evolution under various realistic conditions. However, the adoption of the phase field method in practical applications has been slow because the current phase field microstructure modeling is qualitative in nature. In this thesis, recent efforts in developing the phase field method for quantitative microstructure modeling are presented. This includes extension of the phase field method to situations where nucleation, growth and coarsening occur concurrently, incorporation of anisotropic elastic energy into the nucleation activation energy, and comparison of phase field kinetics for diffusion-controlled phase transformations with Johnson-Mehl-Avrami-Kolmogorov (JMAK) theory. The recent extensions of the phase field method to modeling dislocation networks, dislocation core structures and partial dislocations, and dislocation interactions with $\gamma$/$\gamma'$ microstructures in superalloys are also presented. The length scale limitations and practical approaches to increase simulation length scales for quantitative modeling are discussed for a quite general category of phase field applications. These extensions enable various new understandings of microstructure. For example, coherent precipitates are found to behave similar to dislocations and grain boundaries, causing solute segregation, correlated nucleation and autocatalytic effect. The overall kinetics in diffusion-controlled precipitation agrees with the JMAK prediction only at early stages, and due to soft-impingement and the Gibbs-Thomson effect the later kinetics could deviate considerably. The modified formulations in phase field dislocation model allow studying complex dislocation structures, including networks and dissociated nodes, in a self-consistent way. The introduction of $\gamma$-surfaces enables treating dislocation motion in multi-phase microstructure in one model.
Book Synopsis Phase-field Simulation of Microstructural Development Induced by Interdiffusion Fluxes Under Multiple Gradients by : Rashmi Ranjan Mohanty
Download or read book Phase-field Simulation of Microstructural Development Induced by Interdiffusion Fluxes Under Multiple Gradients written by Rashmi Ranjan Mohanty and published by . This book was released on 2009 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 multi-phase 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 zero-flux 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-[gamma] vs. B2-[beta]) 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-[gamma] vs. L12-[gamma prime], [gamma] vs. [gamma]+[gamma prime] and [gamma]+[gamma prime] vs. [gamma]+[gamma prime] were simulated with alloys of varying compositions and volume fractions of second phase (i.e., [gamma prime]). 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 [gamma prime] 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-[gamma] and [gamma]+[beta] (fcc+B2) alloys was studied using a 2D phase-field model. Alloys of varying compositions and volume fractions of the second phase ([beta]) were used to simulate the dissolution kinetics of the [beta] 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 [beta] phase (i.e., recession of [beta]+[gamma] two-phase region) was dependent on the composition of the single-phase [gamma] alloy and the volume fraction of the [beta] phase in the two-phase alloy of the couple. Higher Cr and Al content in the [gamma] alloy and higher volume fraction of [beta] in the [gamma]+[beta] alloy lower the rate of dissolution. Simulated results were found to be in good agreement with the experimental observations in ternary Ni-Cr-Al solid-to-solid diffusion couples containing [gamma] and [gamma]+[beta] 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.
Book Synopsis Diffraction Analysis of the Microstructure of Materials by : Eric J. Mittemeijer
Download or read book Diffraction Analysis of the Microstructure of Materials written by Eric J. Mittemeijer and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 557 pages. Available in PDF, EPUB and Kindle. Book excerpt: Overview of diffraction methods applied to the analysis of the microstructure of materials. Since crystallite size and the presence of lattice defects have a decisive influence on the properties of many engineering materials, information about this microstructure is of vital importance in developing and assessing materials for practical applications. The most powerful and usually non-destructive evaluation techniques available are X-ray and neutron diffraction. The book details, among other things, diffraction-line broadening methods for determining crystallite size and atomic-scale strain due, e.g. to dislocations, and methods for the analysis of residual (macroscale) stress. The book assumes only a basic knowledge of solid-state physics and supplies readers sufficient information to apply the methods themselves.
Book Synopsis Crystal Plasticity Finite Element Methods by : Franz Roters
Download or read book Crystal Plasticity Finite Element Methods written by Franz Roters and published by John Wiley & Sons. This book was released on 2011-08-04 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by the leading experts in computational materials science, this handy reference concisely reviews the most important aspects of plasticity modeling: constitutive laws, phase transformations, texture methods, continuum approaches and damage mechanisms. As a result, it provides the knowledge needed to avoid failures in critical systems udner mechanical load. With its various application examples to micro- and macrostructure mechanics, this is an invaluable resource for mechanical engineers as well as for researchers wanting to improve on this method and extend its outreach.
Book Synopsis Microdynamics Simulation by : Paul Bons
Download or read book Microdynamics Simulation written by Paul Bons and published by Springer Science & Business Media. This book was released on 2007-11-21 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete starting package for students and researchers of the earth science community interested in numerical modeling of microstructures. This excellent book deals with the numerical simulation of such microstructures in rocks. It starts with an introduction to existing methods and techniques for optical and electron microscopic analysis. The main part of the book contains examples of numerical modeling of processes and microstructures in rocks, using the software package "ELLE".
Book Synopsis Continuum Scale Simulation of Engineering Materials by : Dierk Raabe
Download or read book Continuum Scale Simulation of Engineering Materials written by Dierk Raabe and published by John Wiley & Sons. This book was released on 2006-03-06 with total page 885 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book fills a gap by presenting our current knowledge and understanding of continuum-based concepts behind computational methods used for microstructure and process simulation of engineering materials above the atomic scale. The volume provides an excellent overview on the different methods, comparing the different methods in terms of their respective particular weaknesses and advantages. This trains readers to identify appropriate approaches to the new challenges that emerge every day in this exciting domain. Divided into three main parts, the first is a basic overview covering fundamental key methods in the field of continuum scale materials simulation. The second one then goes on to look at applications of these methods to the prediction of microstructures, dealing with explicit simulation examples, while the third part discusses example applications in the field of process simulation. By presenting a spectrum of different computational approaches to materials, the book aims to initiate the development of corresponding virtual laboratories in the industry in which these methods are exploited. As such, it addresses graduates and undergraduates, lecturers, materials scientists and engineers, physicists, biologists, chemists, mathematicians, and mechanical engineers.
