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| 1 Mathematics in Laser Processing | ||
| John Dowden | 1 | |
| 1.1 | Mathematics and its Application | 1 |
| 1.2 | Formulation in Terms of Partial Differential Equations | 3 |
| 1.2.1 | Length Scales | 3 |
| 1.2.2 | Conservation Equations and their Generalisations | 4 |
| 1.2.3 Governing Equations of Generalised | ||
| Conservation Type | 7 | |
| 1.2.4 | Gauss's Law | 10 |
| 1.3 | Boundary and Interface Conditions | 11 |
| 1.3.1 | Generalised Conservation Conditions | 11 |
| 1.3.2 | The Kinematic Condition in Fluid Dynamics | 13 |
| 1.4 | Fick's Laws | 15 |
| 1.5 | Electromagnet ism | 15 |
| 1.5.1 | Maxwell's Equations | 15 |
| 1.5.2 | Ohm's Law | 18 |
| References | 19 | |
| 2 Simulation of Laser Cutting | ||
| Wolfgang Schulz, Markus Niefien, Urs Eppelt, Kerstin Kowalick | 21 | |
| 2.1 | Introduction | 22 |
| 2.1.1 | Physical Phenomena and Experimental Observation | 23 |
| 2.2 | Mathematical Formulation and Analysis | 26 |
| 2.2.1 | The One-Phase Problem | 29 |
| 2.2.2 | The Two-Phase Problem | 42 |
| 2.2.3 | Three-Phase Problem | 51 |
| 2.3 | Outlook | 64 |
| 2.4 | Acknowledgements | 65 |
| References | 65 | |
| 3 Keyhole Welding: The Solid and Liquid Phases | ||
| Alexander Kaplan | 71 | |
| 3.1 | Heat Generation and Heat Transfer | 71 |
| 3.1.1 | Absorption | 71 |
| 3.1.2 | Heat Conduction and Convection | 73 |
| 3.1.3 | Surface Convection and Radiation | 79 |
| 3.1.4 | Phase Transformations | 80 |
| 3.1.5 | Transient and Pulsed Heat Conduction | 80 |
| 3.1.6 | Geometry of the Liquid Pool | 82 |
| 3.2 | Melt Flow | 84 |
| 3.2.1 | Melt Flow Passing Around the Keyhole | 86 |
| 3.2.2 | Marangoni Flow Driven by Surface Tension Gradients | 89 |
| 3.2.3 Uncontrolled Violent Melt Motion and Drop Ejection | ||
| Behind the Keyhole | 89 | |
| 3.2.4 | Humping Caused by Accumulating Downstream Flow | 90 |
| 3.2.5 Stagnation Point for Accelerated Flow, Causing | ||
| Undercuts and a Central Peak | 90 | |
| 3.2.6 Interior Eddies, Driven by Vertical Downstream Flow | ||
| at the Keyhole's Rear Wall | 91 | |
| 3.2.7 Root Drop-out by Gravity and the Keyhole Front Film | ||
| Ejected by Ablation Pressure | 91 | |
| 3.2.8 | Concluding Remarks | 92 |
| References | 92 | |
| 4 Laser Keyhole Welding: The Vapour Phase | ||
| John Dowden | 95 | |
| 4.1 | Notation | 95 |
| 4.2 | The Keyhole | 95 |
| 4.3 | The Keyhole Wall | 101 |
| 4.3.1 | The Knudsen Layer | 101 |
| 4.3.2 | Fresnel Absorption | 104 |
| 4.4 The Role of Convection in the Transfer of Energy to the | ||
| Keyhole Wall | 106 | |
| 4.5 | Fluid Flow in the Keyhole | 109 |
| 4.5.1 | General Aspects | 109 |
| 4.5.2 Turbulence in the Weld Pool and the Keyhole..........Ill | ||
| 4.6 | Further Aspects of Fluid Flow | 113 |
| 4.6.1 | Simplifying Assumptions for an Analytical Model | 113 |
| 4.6.2 | Lubrication Theory Model | 113 |
| 4.6.3 | Boundary Conditions | 114 |
| 4.6.4 | Solution Matched to the Liquid Region | 118 |
| 4.7 | Electromagnetic Effects | 119 |
| 4.7.1 | Self-Induced Currents in the Vapour | 119 |
| 4.7.2 | The Laser Beam as a Current Guide | 123 |
| References | 126 | |
| 5 Basic Concepts of Laser Drilling | ||
| Wolfgang Schulz, Urs Eppelt | 129 | |
| 5.1 | Introduction | 129 |
| 5.2 | Technology and Laser Systems | 130 |
| 5.3 | Diagnostics and Monitoring for /xs Pulse Drilling | 132 |
| 5.4 | Phenomena of Beam-Matter Interaction | 134 |
| 5.4.1 Physical Domains - Map of Intensity and Pulse | ||
| Duration | 135 | |
| 5.4.2 | Beam Propagation | 142 |
| 5.4.3 | Refraction and Reflection | 143 |
| 5.4.4 | Absorption and Scattering in the Gaseous Phase | 145 |
| 5.4.5 | Kinetics and Equation of State | 146 |
| 5.5 | Phenomena of the Melt Expulsion Domain | 148 |
| 5.6 | Mathematical Formulation of Reduced Models | 149 |
| 5.6.1 Spectral Decomposition Applied to Dynamics in Recast | ||
| Formation | 150 | |
| 5.7 | Analysis | 151 |
| 5.7.1 | Initial Heating and Relaxation of Melt Flow | 152 |
| 5.7.2 | Widening of the Drill by Convection | 152 |
| 5.7.3 | Narrowing of the Drill by Recast Formation | 154 |
| 5.7.4 | Melt Closure of the Drill Hole | 156 |
| 5.7.5 | Drilling with Inertial Confinement - Helical Drilling | 159 |
| 5.8 | Outlook | 160 |
| 5.9 | Acknowledgements | 161 |
| References | 162 | |
| 6 Arc Welding and Hybrid Laser-Arc Welding | ||
| Ian Richardson | 167 | |
| 6.1 | The Structure of the Welding Arc | 167 |
| 6.1.1 | Macroscopic Considerations | 172 |
| 6.1.2 | Arc Temperatures and the pLTE Assumption | 176 |
| 6.1.3 | Multi-Component Plasmas | 182 |
| 6.2 | The Arc Electrodes | 185 |
| 6.2.1 | The Cathode | 186 |
| 6.2.2 | The Anode | 188 |
| 6.3 | Molten Metal Flow | 189 |
| 6.3.1 | The Arc Generated Weld Pool | 189 |
| 6.3.2 | Metal Transfer | 191 |
| 6.4 | Unified Arc and Electrode Models | 193 |
| 6.5 | Arc Plasma - Laser Interactions | 196 |
| 6.5.1 | Absorption | 197 |
| 6.5.2 | Scattering | 202 |
| 6.6 | Laser-Arc Welding | 203 |
| References | 210 | |
| 7 Metallurgy of Welding and Hardening | ||
| Alexander Kaplan | 217 | |
| 7.1 | Thermal Cycle and Cooling Rate | 217 |
| 7.2 | Resolidification | 219 |
| 7.3 | Metallurgy | 220 |
| 7.3.1 | Diffusion | 220 |
| 7.3.2 | Fe-Based Alloys | 221 |
| 7.3.3 Model of the Metallurgy During Transformation | ||
| Hardening of Low Alloy Steel | 224 | |
| 7.3.4 | Non-Fe-based Alloys | 226 |
| 7.4 | Defects | 227 |
| References | 233 | |
| 8 Laser Cladding | ||
| Dietrich Lepski and Frank Brückner | 235 | |
| 8.1 | Introduction | 235 |
| 8.2 | Beam-Particle Interaction | 241 |
| 8.2.1 | Powder Mass Flow Density | 241 |
| 8.2.2 | Effect of Gravity on the Mass Flow Distribution | 243 |
| 8.2.3 | Beam Shadowing and Particle Heating | 244 |
| 8.3 | Formation of the Weld Bead | 247 |
| 8.3.1 | Particle Absorption and Dissolution | 248 |
| 8.3.2 | Shape of the Cross Section of a Weld Bead | 249 |
| 8.3.3 | Three-Dimensional Model of the Melt Pool Surface | 251 |
| 8.3.4 Temperature Field Calculation using Rosenthal's | ||
| Solution | 253 | |
| 8.3.5 Self-Consistent Calculation of the Temperature Field | ||
| and Bead Geometry | 255 | |
| 8.3.6 | Role of the Thermocapillary Flow | 256 |
| 8.4 | Thermal Stress and Distortion | 259 |
| 8.4.1 | Fundamentals of Thermal Stress | 259 |
| 8.4.2 | Phase Transformations | 261 |
| 8.4.3 | FEM Model and Results | 263 |
| 8.4.4 | Simplified Heuristic Model | 265 |
| 8.4.5 Crack Prevention by Induction Assisted Laser | ||
| Cladding | 270 | |
| 8.5 | Conclusions and Future Work | 274 |
| References | 276 | |
| 9 Laser Forming | ||
| Thomas Pretorius | 281 | |
| 9.1 | History of Thermal Forming | 281 |
| 9.2 | Forming Mechanisms | 284 |
| 9.2.1 | Temperature Gradient Mechanism | 285 |
| 9.2.2 | Residual Stress Point Mechanism | 292 |
| 9.2.3 | Upsetting Mechanism | 294 |
| 9.2.4 | Buckling Mechanism | 299 |
| 9.2.5 | Residual Stress Relaxation Mechanism | 303 |
| 9.2.6 | Martensite Expansion Mechanism | 304 |
| 9.2.7 | Shock Wave Mechanism | 305 |
| 9.3 | Applications | 306 |
| 9.3.1 | Plate Bending | 307 |
| 9.3.2 | Tube Bending/Forming | 308 |
| 9.3.3 | High Precision Positioning Using Actuators | 309 |
| 9.3.4 | Straightening of Weld Distortion | 310 |
| 9.3.5 | Thermal Pre-Stressing | 311 |
| References | 312 | |
| 10 Femtosecond Laser Pulse Interactions with Metals | ||
| Bernd Huttner | 315 | |
| 10.1 | Introduction | 315 |
| 10.2 | What is Different Compared to Longer Pulses? | 317 |
| 10.2.1 | The Electron-Electron Scattering Time | 317 |
| 10.2.2 | The Nonequilibrium Electron Distribution | 320 |
| 10.3 Material Properties Under Exposure to Femtosecond Laser | ||
| Pulses | 322 | |
| 10.3.1 | Optical Properties | 322 |
| 10.3.2 | Thermal Properties | 325 |
| 10.3.3 | Electronic Thermal Diffusivity | 327 |
| 10.4 Determination of the Electron and Phonon Temperature | ||
| Distribution | 328 | |
| 10.4.1 | The Two-Temperature Model | 328 |
| 10.4.2 | The Extended Two-Temperature Model | 330 |
| 10.5 | Summary and Conclusions | 334 |
| References | 335 | |
| 11 Comprehensive Numerical Simulation of Laser Materials | ||
| Processing | ||
| Markus Gross | 339 | |
| 11.1 | Motivation - The Pursuit of Ultimate Understanding | 339 |
| 11.2 | Review | 341 |
| 11.3 | Correlation, the Full Picture | 348 |
| 11.4 | Introduction to Numerical Techniques | 348 |
| 11.4.1 | The Method of Discretisation......• | 349 |
| 11.4.2 | Meshes | 349 |
| 11.4.3 | Explicit versus Implicit | 350 |
| 11.4.4 | Discretisation of Transport pde's | 351 |
| 11.4.5 | Schemes of Higher Order | 354 |
| 11.4.6 | The Multi Phase Problem | 356 |
| 11.5 Solution of the Energy Equation and | ||
| Phase Changes | 359 | |
| 11.5.1 | Gas Dynamics | 362 |
| 11.5.2 | Beam Tracing and Associated Difficulties | 364 |
| 11.6 Program Development and Best Practice when Using Analysis | ||
| Tools | 367 | |
| 11.7 | Introduction to High Performance Computing | 368 |
| 11.7.1 | MPI | 369 |
| 11.7.2 | openMP | 371 |
| 11.7.3 | Performance | 372 |
| 11.8 | Visualisation Tools | 374 |
| 11.9 | Summary and Concluding Remarks | 375 |
| References | 375 | |
| Index | 381 | |
Ablation, 99-101, 108-117, 129-138, 146-150, 159, 161, 306, 315, 317, 334, 346
Cold, 134-136
Hot, 134-136, 138
absorptance, 71-73, 81, 218
absorption, 71-82, 95, 97, 105-108, 117-129, 136-150, 180, 196-210, 217, 246, 248, 315-324, 375
absorption coefficient, 145, 180, 197, 199-201, 208, 210, 287, 288, 296, 301, 328, 329
absorptivity, 73, 82, 247, 256, 306
aerofoil, 51
Ampère's Circuit Law, 17
annealing, 223, 274, 303
anode, 173-196, 204, 206, 210
ansatz, 31, 36, 37, 40, 43, 151
definition: 2
arc, 38, 60, 89, 119-126, 143, 156, 167,
172-210, 228, 251
ASCII, 367
assumed kerf, 341
attenuation, 347
attractor, 21, 26, 27
austenite, 80, 223-225, 260-263, 305
autonomous machine, 22
bainite, 262
Beam-Propagation-Method, 142, 143
Beam Tracing, 364
Beer's law (Lambert-Beer Law), 332
Bénard Problem, 28
bending, 24, 236, 262-275, 282-311
longitudinal, 290, 291
bending angle, 285-296, 300-305,
308-310
Bernoulli equation, 231
Biberman-Holstein constants, 179
blanketing, 347
Boltzmann constant, 178, 325
Boltzmann distribution, 178-181
Boltzmann equation, 147, 321, 322, 332
boundary condition, 41, 48, 79, 80, 106,
114, 116, 151, 156, 189, 341, 357
Boundary Element Method (BEM), 254
boundary layer, 21, 26, 31-54, 114, 190, 344
boundary temperature, 287, 288
bremsstrahlung
inverse, 95, 97, 106, 107, 117-124, 197, 206, 208
butt joint, 228
butt weld, 83
capillarity parameter, 251
capillary, 21, 30, 44, 47, 71, 142, 156, 206
cast iron, 222
cathode, 123, 172-196, 208, 209
non-thermionic, 187
Cauchy dispersion relation, 144
causality, 348
cementite, 223
Chaffee-Infante reaction-diffusion equation, 28
Chapman-Jouguet case, 147
cladding, 235-275
coating materials, 235
collision
electron-electron, 136
electron-phonon, 136
collisional-radiative model, 179, 180
compressible gas dynamics, 362
concentration, 15, 183, 188, 206, 220, 225
conductivity, 18, 30, 52, 98, 104, 121, 124, 174-193, 208, 210, 255, 287, 323, 325
thermal, 7, 79, 86, 89, 99, 109, 174, 175, 207, 255, 275, 288, 292-302, 316, 319, 325-333
conservation equations, 4, 5, 175, 183
generalised, 5, 10
conservation of mass, 83-89, 99, 102,
113, 118, 362
continuity equation, see also conserva- tion of mass 193-195
continuum approximation, 4, 101
continuum hypothesis, see continuum
approximation 4
contraction, 27, 71, 90, 208, 230-232, 262, 270
thermal, 236, 259, 269-274
convection, 8, 44, 50, 73, 79-84, 99, 106, 108, 124, 125, 150, 152, 185, 247, 254, 256, 295, 351, 358
surface, 79
convective cooling, 344
convective kinematics, 355
correlation, 45, 341, 348, 375
Couette flow, 48
counter-bending, 286-293, 303, 305
Courant-Friedrichs-Lewy number, 350
crack, 155, 226-229, 270
cracks
hot, 227
Curie point, 271
current, 2, 17, 18, 119-125, 172-175, 181-210, 271, 281, 284, 351, 361-367
intrinsic, 120, 123
cutting
laser, 21, 23, 64, 104, 341, 358
cutting front, 22-26, 35-64, 142
de Broglie wavelength, 142
Debye length, 145
delamination, 129-131, 236, 259, 274
dendrite growth, 223
deposition, 235, 270, 365, 366
deviatoric stress, 8
diffusion
ambipolar, 183, 188, 193
species, 173
diffusivity
thermal, 30, 34, 76, 139, 155, 207, 255, 287, 319-328
electronic, 319, 327
discretisation, 77, 78, 254, 349, 351, 359
dispersive systems, 356
displacement current, 9
distortion, 228-241, 259, 262, 274-281, 303, 310-312
thermal, 241, 259
distortion potential, 312
drill, 59, 71, 132, 133, 148-161
drill base, 134, 148-161
drill wall, 142, 148-161
drilling
helical, 131, 159, 160
laser, 146
percussion, 129, 130, 155-159
pulse, 129, 132
dross, 21-23, 43-47, 51, 62, 64
Drude conductivity, 323
Drude's relaxation time, 329
eddies, 85, 89, 91
electromagnet ism, 3, 15, 17
Emissivity, 194
energy
Conservation of, 4, 5, 17, 79
interatomic, 223
energy balance, 341, 361
energy dispersive X-ray spectroscopy
(EDX), 258
enthalpy, 30, 52, 53, 80, 100, 125,
156, 174, 175, 219, 220, 246, 247, 254
formulation, 361
of evaporation, 362
Euler's equation, 250
explicit time integration scheme, 351
fall zone, 172
anode, 172, 173
cathode, 172, 173
Faraday's law, 3, 17
femtosecond, 315-322, 327-334
pulses, 319, 320
Fermi energy, 188, 318, 321, 325
Fermi liquid theory, 317
Fermi velocity, 328, 330
Fermi-Dirac distribution, 320-325, 334
ferrite, 80, 225, 262, 305
ferritic steel, 224
ferromagnetics, 271
Fick's Laws, 15
filler wire, 84, 228
fillet
joint, 228
Finite Control Volume (FCV), 85, 86, 360
Finite-Difference-Time-Domain
FDTD-method, 142
Finite Element Analysis (FEA), 219
finite element models (FEM), 241
Flash lamp pumped laser systems, 131
forming, 54, 129, 143, 178, 227, 235, 270, 281-308, 361
laser assisted, 285
forming mechanisms direct thermal, 281
indirect thermal, 281
non-thermal, 281, 285, 305
Fourier diffusion flux, 192
Fourier's Law, 7, 9, 139, 330
fracture, 222, 227, 228, 270
Free Boundary Problem, 21, 28, 29, 38, 42
Fresnel absorption, 95, 97, 104, 108,
117, 341
Fresnel formulae, 105, 142
Galileo, 1
gas dynamics, 344
Gas Metal Arc (GMA) welding, 196
Gaunt factor, 197, 198
Gauss's Law, 10, 17
Gauss's Theorem, 6, 9
Gaussian distribution, 34, 50
Gaussian pulse, 328
Gladstone-Dale constant, 365
GMA welding, 191, 203
gold, 318-333
gravitational force, 91, 243
Green's function, 74
grid independence, 350
hardness, 222, 225, 241, 262
heat affected zone (HAZ), 205, 225, 317
heat exchange coefficient, 328, 329
heat transport, 21, 40-48, 206, 334
heating
resistive, 271
helical drilling, 131, 159, 160
Hook's tensor, 260
hot-cracking, 131
humping, 85-91, 119, 228
hybrid welding, 84, 85, 91, 167, 202, 210, 228
hypereutectoid, 224, 225
hypoeutectoid, 224, 225
hypre, 351
induction assisted laser cladding, 241, 251, 270
intensity, 23-51, 97, 105, 130-144, 157-161, 177-180, 197, 210, 246, 253, 317, 321-334, 360
interaction
beam-matter, 129-140
interface conditions, 2, 11, 13, 118
intermetallic FeAl-needles, 226
intermetallic phase layer, 226
inversion
Abel, 177
inviscid fluid, 14
Ionisation
Above-Threshold, 140, 141
Field, 141
Tunnel, 141
ionisation potential, 140, 195
ionised vapour, 95-106, 120-122, 124, 139
joints
butt, 84, 228
overlap, 84
Keldysh-parameter, 141
kerf, 21-26, 38, 42, 45, 55-62, 341
keyhole, 71-95, 97-123, 185, 203-207, 229-233, 340, 347, 364
effect, 347
keyhole collapse, 85, 230
keyhole welding, 85, 95, 101
kinematic condition, 13
kinetic theory, 7, 27
Kirchhoff's transformation, 255
Knudsen layer, 15, 95, 101-106,
135-147, 161
Knudsen number, 4, 7, 9, 146
Koistinen-Marburger formula, 263
Krylov-Subspace solvers, 351
Kuramoto-Sivashinsky equation, 157
Lambert-Beer law, see Beer's law 138
Lamé constants, 8
Langmuir probe, 189
laser
attosecond, 132
C02, 95-123, 196-209, 245, 283, 306, 308
excimer, 306, 316
free electron, 316
Nd:YAG, 106, 120, 145, 196-207, 308, 316
sapphire, 316, 319
laser cutting, 21, 23, 64, 104, 105, 341, 358
one phase problem, 21
Three-phase problem, 51
two phase problem, 21
two-phase problem, 42
laser welding
pw, 71, 80, 85, 217
single pulse, 81, 85
laser-arc welding, 203, 204
latent heat, 361
Leibnitz, 3
Level-Set method, 42
limiter, 355
line source
moving, 73-76, 217
line source solution, see Rosenthal 117
local thermal equilibrium (LTE, see also pLTE) 139, 175, 179, 182, 315-334
Lorentz force, 189
Lorenz gas, 18
lubrication theory, 113, 114, 157
Mach disc, 55
Mach number, 102, 103, 147
magnetohydrodynamic, 175, 176
manifold central, 27
finite dimensional, 21, 27
inertial, 21, 27, 28, 149, 150
Marangoni flow, 85, 89, 191, 256
Marangoni number, 258
martensite, 219-225, 261-264, 269-272, 305
martensite expansion mechanism
(MEM), 281, 284, 304
mass balance, 53, 63, 83, 84, 223, 341, 351
Maxwell's equations, 9, 15, 142, 143, 174
Maxwellian distribution, 198
melt expulsion, 129-139, 148, 151
melt film, 21, 23, 43-64, 86, 91, 148-157, 340
melt flow, 21-23, 29, 40-47, 51-63, 71-92, 136, 148-159, 340, 357
melt pool, 71-91, 110, 112, 220, 235, 240, 241, 248-259, 263, 274, 275
melting front, 24-26, 29-47, 51, 136
mesh, 263, 350, 351, 355, 365, 366
message passing information, 368
metallurgy, 217, 219-222, 224, 227
methods explicit, 350
implicit, 350
Mie scattering, 202, 203, 245
mirror sources
method of, 81
molten pool, 83
monotonicity, 356, 364
moving boundary
free, 150
moving source, 341
multi phase, 222, 356
Multi-photon ionisation, 139, 140
multiphase, 356
Navier-Stokes equation, 99, 174, 175
Needleman potential, 223
Neumann, 39
Newton's Laws of Motion, 1, 3
Newton's theory of gravitation, 9, 17
nozzle, 22, 23, 54-65, 235, 241-247, 345, 355
Laval/Laval-Venturi, 61, 62
nozzle geometry, 240
number density, 18, 139, 178-183, 200, 209
numerical model (BM, RSPM, TGM,
UM), 284, 292
numerical modelling, 284-301, 312, 339
Ockham's razor, 332
Ohm's law, 18, 120, 124
generalised, 120, 174
ohmic heating, 124, 194, 208
one-phase model, 26, 29, 47
Three-dimensional, 38
ordinary differential equations (ODE,
ode), 246, 366
overshoots, 356
partial differential equations, 48, 108
particle heating, 235, 244
Pauli's exclusion principle, 317
pearlite, 221, 224, 225, 262
Peclet-number, 31-40, 41, 48, 153
penetration depth, 31, 34, 139, 146, 150,
151, 257, 271, 319
permeability dielectric, 210
magnetic, 271
phase change, 101, 103, 146, 361
phase space, 26-28, 33, 43, 64, 130, 137, 138, 318
phase transformation, 80, 262-267, 305
phenomelogical evaporation, 345
phonon, 135-139, 317, 319, 328, 329,
331-349
Planck's constant, 178
Planck's radiation law, 79
plasma, 18, 71, 79, 108, 120-124, 133-148, 154, 161, 167-188, 193-202, 206-210, 251, 282, 283, 306, 315, 334
plasmas, 183, 185, 197
multi-component, 182, 195
plastic deformation, 222, 262, 270, 272, 282-298, 309
plastic strain, 260-262, 267-275, 286, 287, 296
plasticity, 223, 241, 259-261, 269, 288,
297, 302
pLTE assumption, 176, 182
point source
moving, 73, 74, 217, 253
Poiseuille flow, 111
polarisation, 29, 131, 135, 160, 179
polarised light, 105
pores, 91, 227, 229, 230
powder, 235, 240-245, 249-252, 256,
274, 275
power law scheme, 351
Poynting vector, 29, 142
Prandtl boundary layer equations, 52, 53
Prandtl number, 52, 109, 110, 190, 208, 258
pre-stressing, 311, 312
preheating, 39, 240, 241, 262, 270-275
pressure
ablation, 85-91, 112-117
electron, 120, 123, 198
recoil, 86, 91, 136, 206, 230
pressure equation, 351, 352
probe laser, 203, 319
process chain, 304, 311, 312
propagation
beam, 142, 161, 349
pulse duration, 47, 129, 131-138, 145,
147, 157-159, 316-323
pump laser, 319
quasi-neutrality approximation, 98
QUICK, 355, 363
Quotidian Equation of State, 148
radiation, 25, 58, 64, 71-79, 97, 124, 129-145, 148-161, 167, 174-188, 196-203, 209, 245, 247, 254, 295, 344, 360, 367
thermal, 79, 132, 134
radiation heat transfer, 344
radiative surface losses, 79
ray tracing, 143, 360, 364-367
Rayleigh length, 30, 131
reaction kinetics, 344
recast, 59, 131, 148-159
recast formation, 129, 130, 148-157
reflection, 24, 58, 71, 134, 139-247, 322,
324, 334
reflection coefficient, 105
refractive index, 197-202, 210, 323, 365, 366
Representative Volume Element (RVE), 223
Residual Stress Point Mechanism
(RSPM), 284, 292
Residual Stress Relaxation Mechanism
(RSRM), 284, 303
resistivity, 18, 122, 271, 319
resolidification, 29, 51, 76-90, 150-157,
217-232
Reynolds number, 46, 109-113
Reynolds stress, 190
Rice criterion, 222
Richardson effect, 139
Richardson's constant, 123
Richardson-Dushman equation, 123, 186
Richardson-Schottky expression, 187
Riemann solver, 364
ring source, 81, 82
ripple, 21-26, 43, 44, 58
Root drop-out, 83, 85, 91, 227
Rosenthal, 117, 253, 255, 267, 271
Runge-Kutta methods, 366
Rydberg electrons, 141
Saha's equation, 97
scattering, 71, 145, 181, 202, 203, 207, 242, 318
electron-electron, 315, 317-327, 334
Thomson, 189, 202
Schlieren method, 23, 26
Schlieren photography, 22, 51, 55, 56, 58
Schottky effect, 123
shadowing, 148, 149, 152, 157, 365
beam, 235, 244, 275
shear stress, 21, 23, 43-55, 61, 63, 156,
189-194, 256, 344
sheath, 187-196
shielding gas, 79, 84, 90, 91, 112, 122,
182, 185, 230-233
shock capturing, 364
shock wave, 55, 281, 285, 305
SIMPLE, 349
simulation, 22, 55-63, 74, 90, 129-135, 151-161, 222, 223, 255, 262, 263, 270, 281-302, 339-358, 365-375
numerical, 22, 23, 42, 86, 205, 284, 339, 348
singular perturbation analysis, 41, 42
slag, 227, 229
Slowly-Varying-Envelope SVE-
approximations, 142
spallation, 129, 134, 137, 138
spatter, 85, 90, 91
specific heat, 30, 52, 100, 109, 219, 263, 288-302, 325, 330, 332, 362
electronic, 319, 329, 330
spectral decomposition, 49, 150
spectroscopy
emission, 176
spot welding, 81, 230
stagnation point, 54, 85, 89, 90, 107,
108, 119, 228
stagnation pressure, 44, 53, 88
stainless steel, 190, 195, 220-228, 309
Stefan condition, 14, 154, 219
Stefan number, 32
Stefan-Boltzmann constant, 124, 247
Stefan-Boltzmann law, 79, 360
Stellite, 271, 272
stents, 51
stirring, 119
Stokes's Theorem, 9
straightening, 281, 283, 310, 311
stress
residual, 227, 228, 264, 271, 281, 300,
302-304, 310, 311
thermal, 235, 241, 259, 261, 282-293, 299, 304
striations, 23
substrate, 190, 206, 235-275
superconductivity, 329
supercooling, 219
superposition, 41, 74, 81, 82, 217, 242,
253, 287
supersonic flow, 55, 144
supersonic gas jet, 22, 23, 26, 54
surface tension, 14, 44, 63, 71, 87,
89-91, 112-116, 156, 189-195, 206, 230, 232, 248-258
surface tension gradient, 191, 195, 256
temperature
electron, 97, 135, 139, 145, 180, 315-334
phonon, 136, 139, 315-319, 323, 324-328
temperature gradient, 7, 76, 80, 183, 219, 220, 281-305, 312, 328, 332, 333
tensile stress, 228, 271, 274, 295
thermal barrier coatings, 129, 130
thermal cycle, 217, 222-228, 259
thermalisation, 135-139, 320
thermionic emitters, 186
Thermo-Elasticity
Linear, 9
thermocapillary flow, see also
Marangoni flow 79, 89, 256-258, 274, 275
thermography, 258
Three-Phase Problem, 51
time-temperature-transformation
(TTT), 219
transformation hardening, 221-225
transient conditions, 80, 85
transition
interband, 316, 319, 323
transpiration
thermionic, 194
transportiveness, 355
trepanning, 22, 58, 59, 129
tungsten inert gas (TIG), 175
turbulence, 109-112, 118, 157, 190, 340, 349
two-temperature model, 138, 139, 315, 319, 328, 330, 334
undercut/undercutting, 83, 84, 228
Upsetting Mechanism (UM), 284,
294-297
upwind, 355
vapour plume, 347
viscosity, 7, 52, 63, 83, 87, 111, 113-115, 175
bulk, 7, 176
dynamic, 109, 174
kinematic, 110, 152, 258
turbulent, 190
viscous flow, 53
viscous heat flow, 7, 9
visualisation, 241, 374
von Karman's coefficient, 191
wave
continuous, 71, 217
pulsed, 71, 217
Weber number, 44, 45, 47, 63, 156
Weibull type distributions, 245
weld
butt, 83
weld bead, 240, 247-258, 264
weld pool, 79, 89, 90, 95, 108-111,
120-123, 182, 189-196, 204-210
weld seam, 83, 90, 91
welding
hybrid laser-arc, 196
Wiedemann-Franz law, 325
work function, 123, 186, 317
work piece, 9, 24, 71-85, 98-123, 133, 159, 208, 235-247, 263, 268, 270, 281, 283, 341
X-ray imaging, 91
Young's modulus, 263, 288-302, 317
Young-Laplace equation, 230
