Science and Engineering of Casting Solidification

Science and Engineering of Casting Solidification

by Doru Michael Stefanescu

Paperback(Softcover reprint of the original 3rd ed. 2015)

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Product Details

ISBN-13: 9783319330631
Publisher: Springer International Publishing
Publication date: 10/22/2016
Edition description: Softcover reprint of the original 3rd ed. 2015
Pages: 556
Product dimensions: 6.10(w) x 9.25(h) x 0.05(d)

About the Author

Professor Doru Michael Stefanescu graduated with a Dipl. Eng. degree in Metallurgical Engineering from the University Politehnica Bucharest, Romania in 1965 and obtained a Ph.D. in Physical Metallurgy from the same institution in 1973. In 1980 he served as a Visiting Professor at the University of Wisconsin, Madison and then joined the University of Alabama where he taught and did research until 2005 when he retired. He continued his scholarly activity as Ashland Designated Research Professor at the Ohio State University till 2010. Professor Stefanescu has conducted 39 Master of Science theses and 17 Philosophy Doctor dissertations. He has authored and co-authored 397 publications. He is a Doctor Honoris Causa of the Technical University of Cluj-Napoca, Romania (1998), the University Transilvania, Brasov, Romania (2001) and Jonkoping University, Sweden (2012). He is a Honorary Professor, University Politehnica, Bucharest, Romania (2006)

Prof. Stefanescu’s research interests include experimental and numerical aspects of solidification processing, influence of low-gravity on solidification, processing of metal-matrix composites, processing of ceramic superconductors, manufacturing technologies and physical metallurgy of cast iron, steel and nonferrous alloys, and cast metals technology. He is recognized as a world expert in cast iron.

Dr. Stefanescu honors and awards include Fellow of the ASM International (1997), the Award for Scientific Merit of the American Foundry Society (2000), the Joseph Seaman Gold Medal of the American Foundry Society (2011), Honorary Member of the Romanian Academy of Technical Sciences (2012), the John Campbell Medal from the Institute of Cast Metals Engineers, United Kingdom (2012).

Dr. Stefanescu is currently Cudworth Professor of Engineering Emeritus, The University of Alabama, and Professor Emeritus, The Ohio State University.

Table of Contents

1 Length-scale in solidification analysis 1

References 4

2 Equilibrium and non-equilibrium during solidification 5

2.1 Equilibrium 5

2.2 The undercooling requirement 6

2.3 Curvature undercooling 9

2.4 Thermal undercooling 11

2.5 Constitutional undercooling 12

2.6 Pressure undercooling 15

2.7 Kinetic undercooling 15

2.8 Departure from equilibrium 17

2.8.1 Local interface equilibrium 19

2.8.2 Interface non-equilibrium 20

2.9 Applications 23

References 23

3 Macro-scale phenomena - general equations 25

3.1 Relevant Transport Equations 25

3.2 Introduction to diffusive transport 29

3.2.1 Flux laws 29

3.2.2 The differential equation for macroscopic heat transport 30

References 31

4 Macro-mass transport 33

4.1 Solute diffusion controlled segregation 33

4.1.1 Equilibrium solidification 36

4.1.2 No diffusion in solid, complete diffusion in liquid (the Gulliver-Scheil model) 38

4.1.3 No diffusion in solid, limited diffusion in liquid 39

4.1.4 Limited diffusion in solid, complete diffusion in liquid 41

4.1.5 Limited diffusion in solid and liquid 44

4.1.6 Partial mixing in liquid, no diffusion in solid 44

4.1.7 Zone melting 47

4.2 Fluid dynamics during mold filling 49

4.2.1 Fluidity of molten metals 49

4.2.2 Capillary flow 49

4.2.3 Gating systems for castings 51

4.3 Fluid dynamics during solidification 54

4.3.1 Shrinkage flow 55

4.3.2 Natural convection 55

4.3.3 Surface tension driven (Marangoni) convection 58

4.3.4 Flow through the mushy zone 58

4.4 Macrosegregation 60

4.4.1 Fluid flow controlled segregation 61

4.4.2 Fluid flow/solute diffusion controlled segregation 62

4.5 Fluid dynamics during casting solidification- macroshrinkage formation 64

4.5.1 Metal shrinkage and feeding 65

4.5.2 Shrinkage defects 68

4.6 Applications 69

References 74

5 Macro-energy transport 75

5.1 Governing equation for energy transport 76

5.2 Boundary conditions 77

5.3 Analytical solutions for steady-state solidification of castings 79

5.4 Analytical solutions for non-steady-state solidification of castings 81

5.4.1 Resistance in the mold 84

5.4.2 Resistance at the mold/solid interface 86

5.4.3 The heat transfer coefficient 89

5.4.4 Resistance in the solid 92

5.5 Applications 93

References 96

6 Numerical Macro-modeling of solidification 97

6.1 Problem formulation 97

6.1.1 The Enthalpy Method 98

6.1.2 The Specific Heat Method 99

6.1.3 The Temperature Recovery Method 99

6.2 Discretization of governing equations 100

6.2.1 The Finite Difference Method - Explicit formulation 100

6.2.2 The Finite Difference Method - implicit formulation 105

6.2.3 The Finite Difference Method - general implicit and explicit formulation 105

6.2.4 Control-volume formulation 106

6.3 Solution of the discretized equations 107

6.4 Macrosegregation modeling 107

6.5 Macroshrinkage modeling 111

6.5.1 Thermal models 112

6.5.2 Thermal/volume calculation models 114

6.5.3 Thermal/fluid flow models 115

6.6 Applications of macro-modeling of solidification 118

6.7 Applications 121

References 125

7 Micro-scale phenomena and interface dynamics 127

7.1 Nucleation 128

7.1.1 Heterogeneous nucleation models 131

7.1.2 Dynamic nucleation models 135

7.2 Micro-solute redistribution in alloys and microsegregation 135

7.3 Interface stability 142

7.3.1 Thermal instability 143

7.3.2 Solutal instability 144

7.3.3 Thermal, solutal, and surface energy driven morphological instability 148

7.3.4 Influence of convection on interface stability 153

7.4 Applications 154

References 155

8 Cellular and dendritic growth 157

8.1 Morphology of primary phases 157

8.2 Analytical tip velocity models 160

8.2.1 Solute diffusion controlled growth (isothermal growth) of the dendrite tip 160

8.2.2 Thermal diffusion controlled growth 163

8.2.3 Solutal, thermal, and capillary controlled growth 164

8.2.4 Interface anisotropy and the dendrite tip selection parameter 171

8.2.5 Effect of fluid flow on dendrite tip velocity 172

8.2.6 Multicomponent alloys 174

8.3 Dendritic array models 175

8.4 Dendritic arm spacing and coarsening 177

8.4.1 Primary spacing 177

8.4.2 Secondary arm spacing 179

8.5 The columnar-to-equiaxed transition 183

8.6 Applications 188

References 193

9 Eutectic solidification 195

9.1 Classification of eutectics 195

9.2 Cooperative eutectics 197

9.2.1 Models for regular eutectic growth 199

9.2.2 Models for irregular eutectic growth 205

9.2.3 The unified eutectic growth model 207

9.3 Divorced eutectics 211

9.4 Interface stability of eutectics 214

9.5 Equiaxed eutectic grain growth 218

9.6 Solidification of cast iron 219

9.6.1 Nucleation and growth of austenite dendrites 219

9.6.2 Crystallization of graphite from the liquid 222

9.6.3 Eutectic solidification 226

9.6.4 The gray-to-white structural transition 231

9.7 Solidification of aluminum-silicon alloys 233

9.7.1 Nucleation and growth of primary aluminum dendrites 233

9.7.2 Eutectic solidification 233

9.8 Applications 240

References 244

10 Peritectic solidification 247

10.1 Classification of peritectics 247

10.2 Peritectic microstructures and phase selection 249

10.3 Mechanism of peritectic solidification 254

10.3.1 The rate of the peritectic reaction 255

10.3.2 The rate of the peritectic transformation 257

10.3.3 Growth of banded (layered) peritectic structure 259

10.4 Applications 261

References 262

11 Monotectic solidification 265

11.1 Classification of monotectics 266

11.2 Mechanism of monotectic solidification 266

References 270

12 Microstructures obtained through rapid solidification 271

12.1 Rapidly solidified crystalline alloys 272

12.2 Metallic glasses 276

References 280

13 Solidification in the presence of a third phase 283

13.1 Interaction of solid inclusions with the solid/liquid interface 283

13.1.1 Particle interaction with a planar interface 285

13.1.2 Material properties models 287

13.1.3 Kinetic models 288

13.1.4 Mechanism of engulfment (planar S/L interface) 300

13.1.5 Particle interaction with a cellular/dendritic interface 301

13.2 Shrinkage porosity 303

13.2.1 The physics of shrinkage porosity formation 303

13.2.2 Analytical models including nucleation and growth of gas pores 310

13.2.3 Analysis of shrinkage porosity models and defect prevention 312

References 313

14 Numerical micro-modeling of solidification 317

14.1 Deterministic models 318

14.1.1 Problem formulation 318

14.1.2 Coupling of MT and TK codes 322

14.1.3 Models for dendritic microstructures 323

14.1.4 Microporosity models 333

14.2 Stochastic models 341

14.2.1 Monte-Carlo models 342

14.2.2 Cellular automaton models 346

14.3 Phase field models 355

References 358

15 Atomic scale phenomena - Nucelation and growth 361

15.1 Nucleation 361

15.1.1 Steady-state nucleation - homogeneous nucleation 362

15.1.2 Steady-state nucleation - Heterogeneous Nucleation 368

15.1.3 Time-dependent (transient) nucleation 373

15.2 Growth Kinetics 374

15.2.1 Types of interfaces 377

15.2.2 Continuous growth 378

15.2.3 Lateral growth 379

15.3 Applications 379

References 382

Appendix A 383

Appendix B 385

Appendix C 391

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