Three-dimensional Multiscale Modeling of Dendritic Spacing Selection During Al-Si Directional Solidification PDF Download
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Languages : en
Pages : 10
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Book Description
We present a three-dimensional extension of the multiscale dendritic needle network (DNN) model. This approach enables quantitative simulations of the unsteady dynamics of complex hierarchical networks in spatially extended dendritic arrays. We apply the model to directional solidification of Al-9.8 wt.%Si alloy and directly compare the model predictions with measurements from experiments with in situ x-ray imaging. The focus is on the dynamical selection of primary spacings over a range of growth velocities, and the influence of sample geometry on the selection of spacings. Simulation results show good agreement with experiments. The computationally efficient DNN model opens new avenues for investigating the dynamics of large dendritic arrays at scales relevant to solidification experiments and processes.
Author:
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Category :
Languages : en
Pages : 10
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Book Description
We present a three-dimensional extension of the multiscale dendritic needle network (DNN) model. This approach enables quantitative simulations of the unsteady dynamics of complex hierarchical networks in spatially extended dendritic arrays. We apply the model to directional solidification of Al-9.8 wt.%Si alloy and directly compare the model predictions with measurements from experiments with in situ x-ray imaging. The focus is on the dynamical selection of primary spacings over a range of growth velocities, and the influence of sample geometry on the selection of spacings. Simulation results show good agreement with experiments. The computationally efficient DNN model opens new avenues for investigating the dynamics of large dendritic arrays at scales relevant to solidification experiments and processes.
Author: Lijian Tan
Publisher:
ISBN:
Category :
Languages : en
Pages : 438
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Book Description
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).
Author: Kunal Pratap Bhagat
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Languages : en
Pages : 0
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Book Description
Microstructure evolution in metal additive manufacturing (AM) is a complex multi-physics and multi-scale problem. Understanding the impact of AM process conditions on the microstructure evolution and the resulting mechanical properties of the printed part is an active area of research. The investigation into understanding the microstructure evolution under AM conditions, at different length scales, is done as a three-part research program that is presented in this thesis. In the first part, a high-fidelity numerical method at the mesoscale to model varied dendritic solidification morphologies is developed. A numerical framework encompassing the modeling of Stefan problem formulations relevant to dendritic evolution using a phase-field approach and a finite element method implementation is presented. Using this framework, numerous complex dendritic morphologies that are physically relevant to the solidification of pure melts and binary alloys are modeled. To the best of our knowledge, this is a first-of-its-kind study of numerical convergence of the phase-field equations of dendritic growth in a finite element method setting. Further, using this numerical framework, various types of physically relevant dendritic solidification patterns like single equiaxed, multi-equiaxed, single-columnar, and multi-columnar dendrites are modeled in two-dimensional and three-dimensional computational domains. In the second part, the complex dynamics of meltpool formation during metal additive manufacturing are modeled using a thermo-fluidic numerical model. Statistical-based method of least-squares is exploited to characterize the role of dimensional numbers in the microstructure evolution process. A novel strategy using dimensional analysis and the method of linear least-squares regression to numerically investigate the thermo-fluidic governing equations of the Laser Powder Bed Fusion AM process is presented. First, the governing equations are solved using the finite element method, and the model predictions are validated with experimental and numerical results from the literature. Then, through dimensional analysis, an important dimensionless quantity - interpreted as a measure of heat absorbed by the powdered material and the meltpool, is identified. Key contributions of this work include the demonstration of the correlation between the dimensionless measure of heat absorbed, and classical dimensionless quantities such as Peclet, Marangoni, and Stefan numbers, with advective transport in the meltpool for different alloys, meltpool morphologies, and microstructure evolution-related variables In the third part, the influence on the morphology of evolving dendritic microstructure due to the rapid thermal cycle and fluid convection in the meltpool during metal additive manufacturing is investigated. A finite-element formulation that solves a coupled Navier-Stokes flow model and a phase-field model of dendritic solidification is developed. Microstructure evolution modeled using purely heat and mass diffusion process may not capture the entire spectrum of the dendrite morphology observed in metal additive manufacturing. The impact of flow dynamics on the thermal gradients and momentum transfer that modulate dendritic shapes, along with the associated remelting are modeled using a coupled phase-field model of solidification. Further, the morphological changes to dendrites in the solidifying region beneath the meltpool fusion line are modeled by accounting for convective effects in the mass and heat diffusion process in equiaxed, aligned equiaxed, and columnar dendrite growth for a pure metal and binary alloys. It is observed that for a meltpool formed under high laser power and scan speed conditions, where Marangoni convection is significant, enhanced growth of the secondary arms of columnar dendrite occurs as compared to dendrite growth observed in low convection regions of the meltpool.
Author: Yili Lu
Publisher:
ISBN:
Category :
Languages : en
Pages : 428
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Book Description
Author: Michael C. Sukop
Publisher: Springer Science & Business Media
ISBN: 3540279822
Category : Science
Languages : en
Pages : 178
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Book Description
Here is a basic introduction to Lattice Boltzmann models that emphasizes intuition and simplistic conceptualization of processes, while avoiding the complex mathematics that underlies LB models. The model is viewed from a particle perspective where collisions, streaming, and particle-particle/particle-surface interactions constitute the entire conceptual framework. Beginners and those whose interest is in model application over detailed mathematics will find this a powerful 'quick start' guide. Example simulations, exercises, and computer codes are included.
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Category : Aeronautics
Languages : en
Pages : 1032
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Category : Metallurgy
Languages : en
Pages : 762
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Book Description
Author: Martin Eden Glicksman
Publisher: Springer Science & Business Media
ISBN: 1441973443
Category : Technology & Engineering
Languages : en
Pages : 517
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Book Description
“Principles of Solidification” offers comprehensive descriptions of liquid-to-solid transitions encountered in shaped casting, welding, and non-biological bulk crystal growth processes. The book logically develops through careful presentation of relevant thermodynamic and kinetic theories and models of solidification occurring in a variety of materials. Major topics encompass the liquid-state, liquid-solid transformations, chemical macro- and microsegregation, purification by fractional crystallization and zone refining, solid-liquid interfaces, polyphase freezing, and rapid solidification processing. Solid-liquid interfaces are discussed quantitatively both as sharp and diffuse entities, with supporting differential geometric descriptions. The book offers: • Detailed mathematical examples throughout to guide readers • Applications of solidification and crystal growth methodologies for preparation and purification of metals, ceramics, polymers and semiconductors • Appendices providing supporting information on special topics covered in the chapters. Readers in materials, metallurgical, chemical, and mechanical engineering will find this to be a useful source on the subjects of solidification and crystal growth. Chemists, physicists, and geologists concerned with melting/freezing phenomena will also find much of value in this book.
Author: Eric S. Huron
Publisher: John Wiley & Sons
ISBN: 1118516400
Category : Technology & Engineering
Languages : en
Pages : 952
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Book Description
A superalloy, or high-performance alloy, is an alloy that exhibits excellent mechanical strength at high temperatures. Superalloy development has been driven primarily by the aerospace and power industries. This compilation of papers from the Twelfth International Symposium on Superalloys, held from September 9-13, 2012, offers the most recent technical information on this class of materials.
Author: Nikolas Provatas
Publisher: John Wiley & Sons
ISBN: 3527632379
Category : Computers
Languages : en
Pages : 323
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Book Description
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.
