Solidification:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
[Lausanne]
EPFL Press
2009
|
| Edition: | 1. ed. |
| Series: | Engineering sciences : materials
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XXI, 621 S. Ill., graph. Darst. |
| ISBN: | 9782940222179 9780849382383 |
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| 245 | 1 | 0 | |a Solidification |c J. A. Dantzig and M. Rappaz |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a [Lausanne] |b EPFL Press |c 2009 | |
| 300 | |a XXI, 621 S. |b Ill., graph. Darst. | ||
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| 490 | 0 | |a Engineering sciences : materials | |
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| 650 | 4 | |a Metals |x Rapid solidification processing | |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
PREFACE v
NOMENCLATURE AND DIMENSIONLESS GROUPS
xiii
1
OVERVIEW
1
1.1
Introduction
............................ 1
1.1.1
Organization of the text
................. 4
1.2
Solidification processes
...................... 5
1.2.1
Shape casting
....................... 5
1.2.2
Continuous and semi-continuous casting
....... 13
1.2.3
Crystal growth processes
................. 16
1.2.4
Welding
........................... 19
1.3
Summary
.............................. 22
1.4
References
............................. 22
1 Fundamentals and Macroscale Phenomena
23
2
THERMODYNAMICS
27
2.1
Introduction
............................ 27
2.2
Thermodynamics of unary systems
............... 28
2.2.1
Single phase systems
................... 28
2.2.2
Equilibrium of phases
.................. 32
2.3
Binary alloys
............................ 37
2.3.1
Thermodynamics of a single phase solution
...... 37
2.3.2
Ideal and regular solutions
............... 40
2.3.3
Equilibrium of two phases
................ 44
2.3.4
Multi-component alloys and Gibbs phase rule
.... 47
2.4
Departure from equilibrium
................... 49
2.4.1
Interfacial
equilibrium
.................. 50
2.4.2
True departure from equilibrium
............ 51
2.5
Summary
.............................. 64
2.6
Exercises
.............................. 64
2.7
References
............................. 66
viii Contents
PHASE DIAGRAMS
69
3.1 Motivation............................. 69
3.2
Binary systems
.......................... 70
3.2.1
Isomorphous systems: preliminary concepts
..... 71
3.2.2
Isomorphous systems: construction from Gibbs
free energy curves
..................... 75
3.2.3
Eutectic systems
..................... 78
3.2.4
Peritectic systems
..................... 83
3.2.5
Other binary systems
................... 84
3.2.6
Calculation of binary alloy phase diagrams
...... 86
3.3
Ternary systems
.......................... 90
3.3.1
Ternary isomorphous systems
.............. 91
3.3.2
Ternary three-phase equilibrium
............ 95
3.3.3
Ternary four-phase equilibrium: ternary eutectic
... 99
3.4
Summary
.............................. 102
3.5
Exercises
.............................. 102
3.6
References
............................. 104
BALANCE EQUATIONS
105
4.1
Introduction
............................ 105
4.1.1
Reference frames and definitions
............ 105
4.1.2
Control volumes
...................... 109
4.2
Mass balance
............................ 114
4.3
Momentum balance
........................ 119
4.3.1
Linear elastic solids
.................... 122
4.3.2
Plastic deformation
.................... 123
4.3.3
Newtonian fluids
..................... 127
4.3.4
Average form of the momentum balance
........ 127
4.4
Energy balance
.......................... 132
4.5
Solute balance in multicomponent systems
.......... 137
4.6
Scaling
............................... 141
4.7
Summary
.............................. 148
4.8
Exercises
.............................. 148
4.9
References
............................. 150
ANALYTICAL SOLUTIONS FOR SOLIDIFICATION
151
5.1
Introduction
............................ 151
5.2
Solidification in a superheated melt
.............. 151
5.2.1
Pure materials
....................... 151
5.2.2
Planar front solidification of a binary alloy
...... 158
5.2.3
Transient solidification of a binary alloy at
constant velocity
...................... 164
5.3
Solidification in an undercooled melt
.............. 172
5.3.1
Planar front growth
.................... 172
5.3.2
Solidification of a paraboloid
............... 177
5.4
The effect of curvature
...................... 182
5.4.1
Solidification of a sphere in an undercooled melt
. . . 182
5.5
Summary and conclusions
.................... 186
Contents
5.6
Exercises
.............................. 187
5.7
References
............................. 190
NUMERICAL METHODS FOR SOLIDIFICATION
191
6.1
Introduction
............................ 191
6.2
Heat conduction without phase change
............. 192
6.2.1
Finite difference method
................. 192
6.2.2
Finite volume method
.................. 199
6.2.3
Finite element method
.................. 202
6.3
Heat conduction with phase change
.............. 209
6.3.1
Fixed grid: Enthalpy methods
.............. 209
6.3.2
Fixed grid: Temperature recovery methods
...... 215
6.3.3
Front tracking methods
................. 216
6.3.4
Level set methods
..................... 220
6.4
Fluid flow
.............................. 222
6.4.1
Finite difference method on staggered grids
...... 224
6.4.2
Finite element methods for CFD
............ 228
6.4.3
Example: Melting of pure Ga
.............. 230
6.5
Optimization and inverse methods
............... 233
6.6
Summary
.............................. 240
6.7
Exercises
.............................. 241
6.8
References
............................. 244
II
Microstructure
245
7
NUCLEATION
249
7.1
Introduction
............................ 249
7.2
Homogeneous nucleation
..................... 249
7.2.1
Embryos and nuclei
.................... 249
7.2.2
Nucleation rate
...................... 253
7.3
Heterogeneous nucleation
.................... 258
7.3.1
Motivation
......................... 258
7.3.2
Basic theory
........................ 261
7.3.3
Instantaneous or athermal nucleation
......... 268
7.4
Mechanisms for grain refinement
................ 276
7.5
Summary
.............................. 281
7.6
Exercises
.............................. 282
7.7
References
............................. 284
8
DENDRITIC GROWTH
287
8.1
Introduction
............................ 287
8.2
Free growth
............................ 287
8.2.1
General observations
................... 287
8.2.2
Stability and scale selection for a freely growing
sphere of a pure material
................ 293
8.2.3
Extension to binary alloys
................ 298
Contents
8.3
Constrained growth
........................ 300
8.3.1
General observations
................... 300
8.3.2
Length scales and pattern selection in constrained
growth
........................... 303
8.3.3
Stability of planar front growth in binary alloys
. . . 305
8.4
Growth of a needle crystal
.................... 312
8.4.1
General observations
................... 312
8.4.2
Approximate models for growth at the
dendrite tip
. 318
8.4.3
Primary
dendrite
arm spacing in constrained
growth
........................... 323
8.4.4
Secondary
dendrite
arm spacing: Coarsening
..... 325
8.5
Convection and dendritic growth
................ 329
8.5.1
Convection and free growth
............... 329
8.5.2
Convection and columnar growth
............ 331
8.6
Phase-field methods
........................ 332
8.7
Summary
.............................. 338
8.8
Exercises
.............................. 338
8.9
References
............................. 342
9
EUTECTICS, PERITECTICS AND
MICROSTRUCTURE
SELECTION
345
9.1
Introduction
............................ 345
9.2
Eutectics
.............................. 346
9.2.1
General considerations
.................. 346
9.2.2
Coupled eutectic growth morphologies
......... 349
9.2.3
Jackson-Hunt analysis for regular eutectics
...... 353
9.2.4
Operating point and stability of regular eutectic
. . . 359
9.2.5
Irregular eutectics
.................... 363
9.2.6
Other eutectic morphologies
............... 366
9.3
Peritectics
............................. 373
9.3.1
General considerations
.................. 373
9.3.2
Nucleation
......................... 374
9.3.3
Solidification of peritectics at normal speed
...... 376
9.3.4
Solidification of peritectics at low speed
........ 379
9.4
Phase selection and coupled zone
................ 381
9.4.1
Phase competition
..................... 381
9.4.2
Coupled zone
........................ 385
9.5
Summary
.............................. 389
9.6
Exercises
.............................. 389
9.7
References
............................. 393
10
MICROSEGREGATION AND HOMOGENIZATION
395
10.1
Introduction
............................ 395
10.2
1-D microsegregation models for binary alloys
........ 396
10.2.1
Microsegregation with diffusion in the solid state
. . 401
10.2.2
Peritectic alloys
...................... 407
10.2.3
Volume averaged model
................. 410
Contents
10.3 Homogenization and
solution
treatment............
413
10.3.1 Homogenization...................... 414
10.3.2
Solution heat treatment
................. 417
10.4
Multicomponent alloys
...................... 420
10.5
Summary
.............................. 425
10.6
Exercises
.............................. 425
10.7
References
............................. 427
11
MACRO- AND
MICROSTRUCTURES
429
11.1
Introduction
............................ 429
11.2
Equiaxed grains growing in a uniform temperature field
. . 431
11.2.1
Nucleation and growth of equiaxed eutectic grains
. . 432
11.2.2
Transition from globular to dendritic grain
morphologies
........................ 436
11.2.3
Nucleation and growth of equiaxed dendritic grains
. 438
11.3
Grains nucleating and growing in a thermal gradient
.... 442
11.4
Columnar grains
.......................... 446
11.5
Columnar-to-Equiaxed Transition
............... 452
11.5.1
Hunt s criterion
...................... 452
11.5.2
Microsegregation and cooling curves
.......... 455
11.6
Micro-macroscopic models
.................... 456
11.6.1
Thermal conditions
.................... 456
11.6.2
Analytical models of
microstructure
formation
.... 459
11.6.3
Stochastic models of
microstructure
formation
.... 460
11.6.4
Influence of convection
.................. 464
11.7
Summary
.............................. 469
11.8
Exercises
.............................. 470
11.9
References
............................. 472
III Defects
475
12
POROSITY
479
12.1
Introduction
............................ 479
12.2
Governing equations
....................... 483
12.3
Interdendritic fluid flow and pressure drop
.......... 485
12.3.1
Darcy equation
...................... 485
12.3.2
Niyama criterion
..................... 486
12.4
Thermodynamic of gases in solution
.............. 490
12.5
Nucleation and growth of pores
................. 496
12.5.1
Pore Nucleation
...................... 499
12.5.2
The role of curvature during growth
.......... 501
12.5.3
Contribution of gas diffusion during growth
...... 503
12.5.4
Summary of the coupling between pressure and
pore fraction
........................ 504
12.6
Boundary conditions
....................... 505
12.7
Application of the concepts
.................... 508
xii Contents
12.8
Summary
.............................. 513
12.9
Exercises
.............................. 514
12.10
References
............................ 516
13
DEFORMATION DURING SOLIDIFICATION AND
HOT TEARING
519
13.1
Introduction
............................ 519
13.2
Thermomechanics of castings
.................. 520
13.2.1
Origins of thermal stresses
............... 520
13.2.2
General formalism for a fully solid material
...... 523
13.2.3
Examples
.......................... 524
13.3
Deformation of the mushy zone
................. 528
13.3.1
Rheological measurements on semi-solid alloys
. . . . 530
13.3.2
Coherency
......................... 538
13.3.3
Two-phase approach
................... 542
13.4
Hot tearing
............................. 546
13.4.1
Characteristics of hot tears
............... 546
13.4.2
Hot tearing tests and hot tear sensitivity
....... 551
13.5
Hot tearing criteria and models
................. 554
13.6
Summary
.............................. 561
13.7
Exercises
.............................. 562
13.8
References
............................. 563
14
MACROSEGREGATION
567
14.1
Introduction
............................ 567
14.2
Macrosegregation during planar front solidification
..... 569
14.2.1
Thermal convection in a pure material
......... 569
14.2.2
Convection during directional solidification
of a binary alloy
...................... 571
14.3
Composition field and governing equations
.......... 575
14.4
Macrosegregation induced by solidification shrinkage
.... 578
14.4.1
Initial solidification at the mold surface
........ 579
14.4.2
Steady state
........................ 580
14.4.3
Final transient
...................... 581
14.5
Macrosegragation induced by fluid flow
............ 583
14.5.1
Analysis based on Flemings criterion
......... 583
14.5.2
General approach
..................... 585
14.5.3
Freckle formation
..................... 589
14.6
Macrosegregation induced by solid movement
......... 594
14.6.1
Macrosegregation induced by grain movement
.... 595
14.6.2
Macrosegregation induced by solid deformation
. . . 597
14.7
Summary
.............................. 603
14.8
Exercises
.............................. 603
14.9
References
............................. 606
INDEX
609
SOLIDIFICATION
Solidification
applications
ranging
from art to industry, and remains as one of the
important commercial pro<
·
the
198
fundamenta]
develop solidification
and
microstructure
formation have come from both
pplication of computational
techñii
nonly
available powerful computers. This book integrates these new
deve
in a compreht hem in
ti
of more classical theor
The three
nal
engineers. Th
part, Fundamentals an< Phenon
-
the thermo
ind
then builds on that subject to motivate and describe
equilibrium phase diagrams. Transport phenomena are discussed next, focu
lies of most importance to liquid-solid phase transformations,
then; odescrib
η
detail both analytical and
r
ι
kal
appi
ches
i g
such problems. The second part, Microstructure, em
fundamental
cont
he treatment of nucleation, dendritic gi
microsegregation, eutectic and peritectic solidification, and microstructure
competition. This part
c s
with a chapter describing the coupling of
macro- and microscopic phenomena in microstructure development. The
third and final part describes various types of Defects that may occur, with
empi
segregation, presented usinj; the
modeling tools and microstructure desc;
і
earlier.
|
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| id | DE-604.BV035844530 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:05:57Z |
| institution | BVB |
| isbn | 9782940222179 9780849382383 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018702758 |
| oclc_num | 432402558 |
| open_access_boolean | |
| owner | DE-29T DE-703 |
| owner_facet | DE-29T DE-703 |
| physical | XXI, 621 S. Ill., graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | EPFL Press |
| record_format | marc |
| series2 | Engineering sciences : materials |
| spelling | Dantzig, Jonathan A. Verfasser aut Solidification J. A. Dantzig and M. Rappaz 1. ed. [Lausanne] EPFL Press 2009 XXI, 621 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Engineering sciences : materials Metals Solidification Metals / Rapid solidification processing Metals Rapid solidification processing Erstarrung (DE-588)4140191-8 gnd rswk-swf Erstarrung (DE-588)4140191-8 s DE-604 Rappaz, Michel Verfasser aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018702758&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018702758&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Dantzig, Jonathan A. Rappaz, Michel Solidification Metals Solidification Metals / Rapid solidification processing Metals Rapid solidification processing Erstarrung (DE-588)4140191-8 gnd |
| subject_GND | (DE-588)4140191-8 |
| title | Solidification |
| title_auth | Solidification |
| title_exact_search | Solidification |
| title_full | Solidification J. A. Dantzig and M. Rappaz |
| title_fullStr | Solidification J. A. Dantzig and M. Rappaz |
| title_full_unstemmed | Solidification J. A. Dantzig and M. Rappaz |
| title_short | Solidification |
| title_sort | solidification |
| topic | Metals Solidification Metals / Rapid solidification processing Metals Rapid solidification processing Erstarrung (DE-588)4140191-8 gnd |
| topic_facet | Metals Solidification Metals / Rapid solidification processing Metals Rapid solidification processing Erstarrung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018702758&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018702758&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT dantzigjonathana solidification AT rappazmichel solidification |