Multi-scale Modeling of Dendritic Alloy Solidification PDF Download
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Author: Johannes Dagner
Publisher:
ISBN:
Category :
Languages : en
Pages : 202
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Author: Johannes Dagner
Publisher:
ISBN:
Category :
Languages : en
Pages : 202
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Author: Chaoyang Wang
Publisher:
ISBN:
Category : Dendritic crystals
Languages : en
Pages : 494
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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:
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Category :
Languages : en
Pages : 10
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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: Kunal Pratap Bhagat
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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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: Yi Zhang
Publisher: Elsevier
ISBN: 0128225599
Category : Technology & Engineering
Languages : en
Pages : 252
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Book Description
Multiscale Modeling of Additively Manufactured Metals: Application to Laser Powder Bed Fusion Process provides comprehensive coverage on the latest methodology in additive manufacturing (AM) modeling and simulation. Although there are extensive advances within the AM field, challenges to predictive theoretical and computational approaches still hinder the widespread adoption of AM. The book reviews metal additive materials and processes and discusses multiscale/multiphysics modeling strategies. In addition, coverage of modeling and simulation of AM process in order to understand the process-structure-property relationship is reviewed, along with the modeling of morphology evolution, phase transformation, and defect formation in AM parts. Residual stress, distortion, plasticity/damage in AM parts are also considered, with scales associated with the spatial, temporal and/or material domains reviewed. This book is useful for graduate students, engineers and professionals working on AM materials, equipment, process, development and modeling. Includes the fundamental principles of additive manufacturing modeling techniques Presents various modeling tools/software for AM modeling Discusses various design methods and how to optimize the AM process using these models
Author: K. C. Mills
Publisher: Woodhead Publishing
ISBN: 9780871707536
Category : Alloys
Languages : en
Pages : 288
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Author: Badrinarayan Athreya
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Alexander Mielke
Publisher: Springer Science & Business Media
ISBN: 3540356576
Category : Mathematics
Languages : en
Pages : 704
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Book Description
This book reports recent mathematical developments in the Programme "Analysis, Modeling and Simulation of Multiscale Problems", which started as a German research initiative in 2006. Multiscale problems occur in many fields of science, such as microstructures in materials, sharp-interface models, many-particle systems and motions on different spatial and temporal scales in quantum mechanics or in molecular dynamics. The book presents current mathematical foundations of modeling, and proposes efficient numerical treatment.
Author: Nikolas Provatas
Publisher: CRC Press
ISBN: 1000435008
Category : Science
Languages : en
Pages : 186
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Book Description
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
