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Modeling and Simulation of Microstructure Evolution in Solidifying Alloys (Mathematics and Its Applications) PDF

304 Pages·2004·17.92 MB·English
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MODELING AND SIMULATION OF MICROSTRUCTURE EVOLUTION IN SOLIDIFYING ALLOYS This page intentionally left blank MODELING AND SIMULATION OF MICROSTRUCTURE EVOLUTION IN SOLIDIFYING ALLOYS by Laurentiu Nastac KLUWER ACADEMIC PUBLISHERS NEW YORK,BOSTON, DORDRECHT, LONDON, MOSCOW CD-ROM available only in print edition eBookISBN: 1-4020-7832-3 Print ISBN: 1-4020-7831-5 ©2004 Kluwer Academic Publishers NewYork, Boston, Dordrecht, London, Moscow Print ©2004 Kluwer Academic Publishers Boston All rights reserved No part of this eBook maybe reproducedortransmitted inanyform or byanymeans,electronic, mechanical, recording, or otherwise,withoutwritten consent from the Publisher Created in the United States of America Visit Kluwer Online at: http://kluweronline.com and Kluwer's eBookstoreat: http://ebooks.kluweronline.com Dedication To my lovely wife, Mihaela To my fantastic kids, Gabriel and Michael To others... KLUWER ACADEMIC PUBLISHERS NEW YORK,BOSTON, DORDRECHT, LONDON, MOSCOW This page intentionally left blank Contents 1. Length-Scales and Generations ofModelingMethodologies for Predicting the Evolution of the Solidification Structure 1 1.1Introduction 1 1.2Length Scales in Modeling of the Solidification Structures 1 1.3 Generations of Modeling Techniques, Modeling Capabilities andLimitations 2 2. Deterministic Macro-Modeling: Transport ofEnergy, Momentum, Species, Mass, and Hydrodynamics Duringthe Solidification Processes 5 2.1 Introduction 5 2.2A Macroscopic Model forCalculatingEnergy, Momentum, Mass and Species Transport 6 2.3References 11 Appendix: Methods forCouplingHT-SKModels 13 A2.1 Introduction 13 A2.2 HT-SK Model 13 A2.2.1 HT Model 13 A2.2.2 SolidificationKineticsModel 15 A2.2.3 Stability Criterion 15 A2.2.4 Coupling ofHT-SK Models 16 3. Deterministic Micro-Modeling: Mathematical Models forEvolution of Dendritic and Eutectic Phases 23 3.1 Introduction viii Modeling and Simulation of Microstructure Evolution in Solidifying Alloys 3.2 A Microscopic Model for Predicting the Evolution of the Fraction of Solid 23 3.3 Theoretical Analysis 26 3.3.1 Comparison between Hemispherical and Parabolic Growth 26 3.3.2 Comparison between Calculated and Experimental Growth Velocities of Dendrite Tip for Succinitrile 26 3.4 References 28 4. Stochastic/Mesoscopic Modeling of Solidification Structure 29 4.1Introduction 29 4.2Mesoscale Model for Dendritic Growth 32 4.3Solution Methodology 34 4.4Algorithm 40 4.5Results and Discussion 41 4.6References 51 5. Solute Transport Effects on Macrosegregation and Solidification Structure 53 5.1 Analytical Modeling of Solute Redistribution during Unidirectional Solidification 53 5.1.1 Introduction 53 5.1.2 Mathematical Formulation and Analytical Solution 54 5.1.3 Model Validation 58 5.1.4 Size of Initial Transient Region 60 5.1.5 Solid/Liquid Interface Instability of Dilute Binary Alloys 61 5.2 Numerical Modeling of Segregation 65 5.3 References 72 6. Micro-Solute Transport Effects on Microstructure and Microsegregation 75 6.1Introduction 75 6.2Dendrite Coherency and Grain Size Evolution 75 6.3Deterministic Modeling of Microsegregation 78 6.3.1Introduction 78 6.3.2Models based on the “Closed System” Assumption 79 6.3.3An analytical Model for Estimation of Microsegregation in Open and Expanding Domains 82 6.3.4Partition Coefficient Evaluation 91 6.3.5Predictions of Microsegregation in commercial alloys 95 6.3.6Microsegregation Index (MSI) 97 6.4 Deterministic Modeling of Secondary Phases 99 Modeling and Simulation of Microstructure Evolution in Solidifying ix Alloys 6.5 References 107 7. Probabilistic (Monte Carlo) Modeling of Solidification Structure 109 7.1Fourth Generation of Solidification Modeling 109 7.2Results and Discussion 111 7.3References 112 Appendix: Monte Carlo Program 113 8. Modeling and Simulation of Solidification Structure in Shaped and Centrifugal Castings 115 8.1Shaped Castings 115 8.1.1Prediction of Grain Structure and of Columnar-to- Equiaxed Transition in Steel Castings 115 8.1.2 Gray-to-White Transition in Cast Iron 117 8.1.3 Modeling of Solidification Structure in Al-based Alloy Castings 128 8.1.4 Modeling of Solidification Structure in RS5 Alloys 128 8.2 Centrifugal Castings 136 8.2.1Introduction 136 8.2.2Model Description 138 8.2.3Results and Discussion 143 8.2.4Summary of the Parametric Studies 145 8.3 References 148 9. Modeling and Simulation of IngotSolidification Structure in Primary and Secondary Remelt Processes 151 9.1Introduction 151 9.2Description of a Modeling Approach for Simulation of Remelt Ingots 153 9.2.1 A Deterministic Macroscopic Model for Calculation of Mass and EnergyTransport in Cast Ingots 153 9.2.2 AStochastic Mesoscopic Model for Simulation of Structure Evolution in Solidifying Ingots 156 9.2.3 Computational Aspects for Modeling of Remelt Ingots 164 9.2.4 Primary and Secondary Dendrite Arm Spacings in Commercial alloys (Deterministic Modeling) 165 9.2.5 A Stochastic Model for Modeling Secondary Phases During Solidification of Alloy 718 Ingots 166 9.3 Simulation Results for Some Commercial Applications 170 9.3.1Modeling Parameters 170 9.3.2Global Comparison of VAR, ESR, and PAM Processes 173

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