Dowden / Schulz The Theory of Laser Materials Processing

Heat and Mass Transfer in Modern Technology
2. Auflage 2017
ISBN: 978-3-319-56711-2
Verlag: Springer Nature Switzerland
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 119, 442 Seiten

Reihe: Springer Series in Materials Science

The revised edition of this important reference volume presents an expanded overview of the analytical and numerical approaches employed when exploring and developing modern laser materials processing techniques. The book shows how general principles can be used to obtain insight into laser processes, whether derived from fundamental physical theory or from direct observation of experimental results. The book gives readers an understanding of the strengths and limitations of simple numerical and analytical models that can then be used as the starting-point for more elaborate models of specific practical, theoretical or commercial value.Following an introduction to the mathematical formulation of some relevant classes of physical ideas, the core of the book consists of chapters addressing key applications in detail: cutting, keyhole welding, drilling, arc and hybrid laser-arc welding, hardening, cladding and forming. The second edition includes a new a chapter on glass cutting with lasers, as employed in the display industry.A further addition is a chapter on meta-modelling, whose purpose is to construct fast, simple and reliable models based on appropriate sources of information. It then makes it easy to explore data visually and is a convenient interactive tool for scientists to improve the quality of their models and for developers when designing their processes. As in the first edition, the book ends with an updated introduction to comprehensive numerical simulation. Although the book focuses on laser interactions with materials, many of the principles and methods explored can be applied to thermal modelling in a variety of different fields and at different power levels. It is aimed principally however at academic and industrial researchers and developers in the field of laser technology.

Prof. John Dowden was educated at Bedford School and Cambridge University, UK, where he graduated with a First Class degree in Mathematics in 1962. He became the first student of the new University of Essex obtaining a PhD in Mathematical Oceanography in 1967. He was appointed to the staff of the Mathematics Department of the university and subsequently changed his main research interests to the mathematics and physics of laser technology while retaining interests in mathematically related applications of heat and mass transfer. Before retirement he was Head of the university's Department of Mathematical Sciences, a member of the Institute of Physics and of the Laser Institute of America. He is still a Fellow of the Institute of Mathematics and its Applications and is now an Emeritus Professor of the University.  Prof. Dr. Wolfgang Schulz studied physics at Braunschweig University of Technology. He graduated from the Institute for Theoretical Physics and received a postgraduate scholarship in 1986 on the topic of 'Hot electrons in metals'. In 1987, he accepted an invitation to the department Laser Technology at RWTH Aachen University. He received the 'Borchers Medal' award in 1992 in recognition of his PhD thesis. In 1997, he joined the Fraunhofer Institute for Laser Technology in Aachen and, in 1999, received the 'Venia Legendi' in the field 'Principles of Continuum Physics applied to Laser Technology'. His postdoctoral lecture qualification (habilitation) was awarded with distinction in 1999 with the prize of the Friedrich-Wilhelm Foundation at RWTH Aachen University. Since March 2005, he has represented the newly founded department 'Nonlinear Dynamics of Laser Processing' at RWTH Aachen University and is the head of the newly founded department of 'Modelling and Simulation' at the Fraunhofer Institute for Laser Technology in Aachen. Since 2007, he is the coordinator of the Excellence Cluster Domain 'Virtual Production' at RWTH Aachen University. His current work is focused on developing and improving laser systems and their industrial applications by combination of mathematical, physical and experimental methods. In particular, he applies the principles of optics, continuum physics and thermodynamics to analyse the phenomena involved in laser processing. The mathematical objectives are modelling, analysis and dynamical simulation of Free Boundary Problems, which are systems of nonlinear partial differential equations. Analytical and numerical methods for model reduction are developed and applied. The mathematical analysis yields approximate dynamical systems of small dimensions in the phase space and is based on asymptotic properties such as the existence of inertial manifolds.

Autoren/Hrsg.

Dowden, John

Schulz, Wolfgang

Inhaltsverzeichnis

1;Preface;6
2;Contents;9
3;Contributors;16
4;1 Mathematics in Laser Processing;17
4.1;Abstract;17
4.2;1.1 Mathematics and Its Application;17
4.3;1.2 Formulation in Terms of Partial Differential Equations;19
4.3.1;1.2.1 Length Scales;19
4.3.2;1.2.2 Rectangular Cartesian Tensors;20
4.3.3;1.2.3 Conservation Equations and Their Generalisations;23
4.3.4;1.2.4 Governing Equations of Generalised Conservation Type;25
4.3.4.1;1.2.4.1 Flow of a Viscous Fluid;25
4.3.4.2;1.2.4.2 Viscous Heat Flow;27
4.3.4.3;1.2.4.3 Conservation of Electric Charge;28
4.3.4.4;1.2.4.4 Linear Thermo-Elasticity in a Moving Frame of Reference;28
4.3.5;1.2.5 Gauss’s Law;29
4.4;1.3 Boundary and Interface Conditions;30
4.4.1;1.3.1 Generalised Conservation Conditions;30
4.4.2;1.3.2 The Kinematic Condition in Fluid Dynamics;35
4.5;1.4 Fick’s Laws;36
4.6;1.5 Electromagnetism;37
4.6.1;1.5.1 Maxwell’s Equations;37
4.6.2;1.5.2 Ohm’s Law;39
4.7;References;40
5;2 Simulation of Laser Cutting;41
5.1;2.1 Introduction;42
5.1.1;2.1.1 Physical Phenomena and Experimental Observation;44
5.2;2.2 Mathematical Formulation and Analysis;47
5.2.1;2.2.1 The One-Phase Problem;49
5.2.2;2.2.2 The Two-Phase Problem;62
5.2.3;2.2.3 Three-Phase Problem;70
5.3;2.3 Outlook;84
5.4;References;85
6;3 Glass Cutting;89
6.1;Abstract;89
6.2;3.1 Introduction;90
6.3;3.2 Phenomenology of Glass Processing with Ultrashort Laser Radiation;90
6.4;3.3 Modelling the Propagation of Radiation and the Dynamics of Electron Density;92
6.5;3.4 Radiation Propagation Solved by BPM Methods;93
6.6;3.5 The Dynamics of Electron Density Described by Rate Equations;93
6.7;3.6 Properties of the Solution with Regard to Ablation and Damage;95
6.8;3.7 Electronic Damage Versus Thermal Damage;98
6.9;3.8 Glass Cutting by Direct Ablation or Filamentation?;102
6.10;Acknowledgements;103
6.11;References;103
7;4 Keyhole Welding: The Solid and Liquid Phases;105
7.1;Abstract;105
7.2;4.1 Heat Generation and Heat Transfer;105
7.2.1;4.1.1 Absorption;105
7.2.2;4.1.2 Heat Conduction and Convection;107
7.3;4.2 Steady State 3D-Solutions Based on Moving Point Sources of Heat;108
7.4;4.3 Steady State 2D-Heat Conduction from a Moving Cylinder at Constant Temperature;110
7.5;4.4 Sophisticated Quasi-3D-Model Based on the Moving Line Source of Heat;112
7.5.1;4.4.1 Surface Convection and Radiation;113
7.5.2;4.4.2 Phase Transformations;114
7.5.3;4.4.3 Transient and Pulsed Heat Conduction;115
7.6;4.5 Model for Initiation of Laser Spot Welding;115
7.6.1;4.5.1 Geometry of the Liquid Pool;117
7.7;4.6 Mass Balance of a Welding Joint;118
7.8;4.7 Melt Flow;119
7.8.1;4.7.1 Melt Flow Passing Around the Keyhole;120
7.8.2;4.7.2 Numerical 2D-Simulation of the Melt Flow Around a Prescribed Keyhole Shape;121
7.8.3;4.7.3 Marangoni Flow Driven by Surface Tension Gradients;123
7.8.4;4.7.4 Flow Redirection, Inner Eddies, Spatter and Stagnation Points;124
7.8.5;4.7.5 Humping Caused by Accumulating Downstream Flow;125
7.8.6;4.7.6 Keyhole Front Melt Film Flow Downwards, Driven by Recoil Pressure;125
7.9;4.8 Concluding Remarks;126
7.10;References;127
8;5 Laser Keyhole Welding: The Vapour Phase;129
8.1;Abstract;129
8.2;5.1 Notation;129
8.3;5.2 The Keyhole;131
8.4;5.3 The Keyhole Wall;135
8.4.1;5.3.1 The Knudsen Layer;135
8.4.1.1;5.3.1.1 Ablation Through the Knudsen Layer;135
8.4.1.2;5.3.1.2 Thermal Flux and Viscous Slip in the Knudsen Layer;138
8.4.2;5.3.2 Fresnel Absorption;139
8.5;5.4 The Role of Convection in the Transfer of Energy to the Keyhole Wall;140
8.6;5.5 Fluid Flow in the Keyhole;144
8.6.1;5.5.1 General Aspects;144
8.6.2;5.5.2 Turbulence in the Weld Pool and the Keyhole;145
8.6.3;5.5.3 Stability of the Keyhole Wall;147
8.6.4;5.5.4 Stability of Waves of Acoustic Type;147
8.6.5;5.5.5 Elongation of the Keyhole;151
8.7;5.6 Further Aspects of Fluid Flow;152
8.7.1;5.6.1 Simplifying Assumptions for an Analytical Model;152
8.7.2;5.6.2 Lubrication Theory Model;152
8.7.3;5.6.3 Boundary Conditions;153
8.7.4;5.6.4 Solution Matched to the Liquid Region;157
8.8;5.7 Electromagnetic Effects;158
8.8.1;5.7.1 Self-induced Currents in the Vapour;158
8.8.2;5.7.2 The Laser Beam as a Current Guide;163
8.8.2.1;5.7.2.1 Note on Cooling by Thermal Convection;165
8.9;References;165
9;6 Basic Concepts of Laser Drilling;168
9.1;6.1 Introduction;169
9.2;6.2 Technology and Laser Systems;169
9.3;6.3 Diagnostics and Monitoring for s Pulse Drilling;171
9.4;6.4 Phenomena of Beam-Matter Interaction;173
9.4.1;6.4.1 Physical Domains---Map of Intensity and Pulse Duration;174
9.4.2;6.4.2 Beam Propagation;180
9.4.3;6.4.3 Refraction and Reflection;182
9.4.4;6.4.4 Absorption and Scattering in the Gaseous Phase;183
9.4.5;6.4.5 Kinetics and Equation of State;184
9.5;6.5 Phenomena of the Melt Expulsion Domain;186
9.6;6.6 Mathematical Formulation of Reduced Models;188
9.6.1;6.6.1 Spectral Decomposition Applied to Dynamics in Recast Formation;189
9.7;6.7 Analysis;190
9.7.1;6.7.1 Initial Heating and Relaxation of Melt Flow;190
9.7.2;6.7.2 Widening of the Drill by Convection;192
9.7.3;6.7.3 Narrowing of the Drill by Recast Formation;193
9.7.4;6.7.4 Melt Closure of the Drill Hole;195
9.7.5;6.7.5 Drilling with Inertial Confinement---Helical Drilling;197
9.8;6.8 Outlook;199
9.9;References;200
10;7 Arc Welding and Hybrid Laser-Arc Welding;204
10.1;Abstract;204
10.2;7.1 The Structure of the Welding Arc;204
10.2.1;7.1.1 Macroscopic Considerations;205
10.2.2;7.1.2 Arc Temperatures and the PLTE Assumption;215
10.2.3;7.1.3 Multi-component Plasmas;221
10.3;7.2 The Arc Electrodes;224
10.3.1;7.2.1 The Cathode;224
10.3.2;7.2.2 The Anode;226
10.4;7.3 Fluid Flow in the Arc-Generated Weld Pool;227
10.5;7.4 Unified Arc and Electrode Models;230
10.6;7.5 Arc Plasma-Laser Interactions;233
10.6.1;7.5.1 Absorption;234
10.6.2;7.5.2 Scattering;239
10.6.3;7.5.3 Absorption Measurements;241
10.7;7.6 Laser-Arc Hybrid Welding;242
10.8;References;250
11;8 Metallurgy and Imperfections of Welding and Hardening;255
11.1;Abstract;255
11.2;8.1 Thermal Cycle and Cooling Rate;255
11.3;8.2 Resolidification;258
11.4;8.3 Metallurgy;259
11.4.1;8.3.1 Diffusion;259
11.4.2;8.3.2 Fe-Based Alloys;261
11.4.2.1;8.3.2.1 Low Alloy Steel;261
11.4.3;8.3.3 Model of the Metallurgy During Transformation Hardening of Low Alloy Steel;263
11.4.4;8.3.4 Non-Fe-Based Alloys;265
11.5;8.4 Imperfections;266
11.5.1;8.4.1 Large Geometrical Imperfections;267
11.5.2;8.4.2 Cracks;268
11.5.3;8.4.3 Spatter;269
11.5.4;8.4.4 Pores and Inclusions;270
11.6;References;274
12;9 Laser Cladding;276
12.1;Abstract;276
12.2;9.1 Introduction;276
12.3;9.2 Beam-Particle Interaction;283
12.3.1;9.2.1 Powder Mass Flow Density;283
12.3.2;9.2.2 Effect of Gravity on the Mass Flow Distribution;284
12.3.3;9.2.3 Beam Shadowing and Particle Heating;286
12.4;9.3 Formation of the Weld Bead;289
12.4.1;9.3.1 Particle Absorption and Dissolution;290
12.4.2;9.3.2 Shape of the Cross Section of a Weld Bead;291
12.4.3;9.3.3 Three-dimensional Model of the Melt Pool Surface;293
12.4.4;9.3.4 Temperature Field Calculation Using Rosenthal’s Solution;294
12.4.5;9.3.5 Self-consistent Calculation of the Temperature Field and Bead Geometry;296
12.4.6;9.3.6 Role of the Thermocapillary Flow;297
12.5;9.4 Thermal Stress and Distortion;300
12.5.1;9.4.1 Fundamentals of Thermal Stress;300
12.5.2;9.4.2 Phase Transformations;302
12.5.3;9.4.3 FEM Model and Results;304
12.5.4;9.4.4 Simplified Heuristic Model;305
12.5.5;9.4.5 Crack Prevention by Induction Assisted Laser Cladding;311
12.6;9.5 Conclusions and Future Work;314
12.7;References;316
13;10 Laser Forming;320
13.1;Abstract;320
13.2;10.1 History of Thermal Forming;322
13.3;10.2 Forming Mechanisms;323
13.3.1;10.2.1 Temperature Gradient Mechanism;324
13.3.2;10.2.2 Residual Stress Point Mechanism;331
13.3.3;10.2.3 Upsetting Mechanism;333
13.3.4;10.2.4 Buckling Mechanism;338
13.3.5;10.2.5 Residual Stress Relaxation Mechanism;342
13.3.6;10.2.6 Martensite Expansion Mechanism;343
13.3.7;10.2.7 Shock Wave Mechanism;344
13.4;10.3 Applications;345
13.4.1;10.3.1 Plate Bending;346
13.4.2;10.3.2 Tube Bending/Forming;347
13.4.3;10.3.3 High Precision Positioning Using Actuators;348
13.4.4;10.3.4 Straightening of Weld Distortion;349
13.4.5;10.3.5 Thermal Pre-stressing;350
13.5;References;351
14;11 Femtosecond Laser Pulse Interactions with Metals;354
14.1;Abstract;354
14.2;11.1 Introduction;354
14.3;11.2 What Is Different Compared to Longer Pulses?;356
14.3.1;11.2.1 The Electron-Electron Scattering Time;356
14.3.2;11.2.2 The Nonequilibrium Electron Distribution;359
14.4;11.3 Material Properties Under Exposure to Femtosecond Laser Pulses;361
14.4.1;11.3.1 Optical Properties;361
14.4.2;11.3.2 Thermal Properties;363
14.4.3;11.3.3 Electronic Thermal Diffusivity;365
14.5;11.4 Determination of the Electron and Phonon Temperature Distribution;366
14.5.1;11.4.1 The Two-Temperature Model;366
14.5.2;11.4.2 The Extended Two-Temperature Model;369
14.6;11.5 Summary and Conclusions;372
14.7;References;373
15;12 Meta-Modelling and Visualisation of Multi-dimensional Data for Virtual Production Intelligence;375
15.1;Abstract;375
15.2;12.1 Introduction;375
15.3;12.2 Implementing Virtual Production Intelligence;377
15.4;12.3 Meta-Modelling Providing Operative Design Tools;378
15.5;12.4 Meta-Modelling by Smart Sampling with Discontinuous Response;384
15.6;12.5 Global Sensitivity Analysis and Variance Decomposition;389
15.7;12.6 Reduced Models and Emulators;392
15.8;12.7 Summary and Advances in Meta-Modelling;393
15.9;Acknowledgements;393
15.10;References;394
16;13 Comprehensive Numerical Simulation of Laser Materials Processing;396
16.1;13.1 Motivation---The Pursuit of Ultimate Understanding;397
16.2;13.2 Review;398
16.3;13.3 Correlation, The Full Picture;404
16.4;13.4 Introduction to Numerical Techniques;405
16.4.1;13.4.1 The Method of Discretisation;405
16.4.2;13.4.2 Meshes;406
16.4.3;13.4.3 Explicit Versus Implicit;407
16.4.4;13.4.4 Discretisation of Transport pde's;408
16.4.5;13.4.5 Schemes of Higher Order;411
16.4.6;13.4.6 The Multi Phase Problem;413
16.5;13.5 Solution of the Energy Equation and Phase Changes;416
16.5.1;13.5.1 Gas Dynamics;419
16.5.2;13.5.2 Beam Tracing and Associated Difficulties;421
16.6;13.6 Program Development and Best Practice When Using Analysis Tools;423
16.7;13.7 Introduction to High Performance Computing;425
16.7.1;13.7.1 MPI;425
16.7.2;13.7.2 openMP;427
16.7.3;13.7.3 Hybrid;428
16.7.4;13.7.4 Performance;429
16.8;13.8 Visualisation Tools;430
16.9;13.9 Summary and Concluding Remarks;431
16.10;References;432
17;Index;437