The Theory of Laser Materials Processing

Transcription

1 John Dowden (Ed.) The Theory of Laser Materials Processing Heat and Mass Transfer in Modern Technology Springer

2 Contents 1 Mathematics in Laser Processing John Dowden Mathematics and its Application Formulation in Terms of Partial Differential Equations Length Scales Conservation Equations and their Generalisations Governing Equations of Generalised Conservation Type Gauss's Law Boundary and Interface Conditions Generalised Conservation Conditions The Kinematic Condition in Fluid Dynamics Fick's Laws Electromagnetism Maxwell's Equations Ohm's Law 18 References 19 2 Simulation of Laser Cutting Wolfgang Schulz, Markus Nießen, Urs Eppelt, Kerstin Kowalick Introduction Physical Phenomena and Experimental Observation Mathematical Formulation and Analysis The One-Phase Problem The Two-Phase Problem Three-Phase Problem Outlook Acknowledgements 65 References 65

3 x Contents 3 Keyhole Welding: The Solid and Liquid Phases Alexander Kaplan Heat Generation and Heat Transfer Absorption Heat Conduction and Convection Surface Convection and Radiation Phase Transformations Transient and Pulsed Heat Conduction Geometry of the Liquid Pool Melt Flow Melt Flow Passing Around the Keyhole Marangoni Flow Driven by Surface Tension Gradients Uncontrolled Violent Melt Motion and Drop Ejection Behind the Keyhole Humping Caused by Accumulating Downstream Flow Stagnation Point for Accelerated Flow, Causing Undercuts and a Central Peak Interior Eddies, Driven by Vertical Downstream Flow at the Keyhole's Rear Wall Root Drop-out by Gravity and the Keyhole Front Film Ejected by Ablation Pressure Concluding Remarks 92 References 92 4 Laser Keyhole Welding: The Vapour Phase John Dowden Notation The Keyhole The Keyhole Wall The Knudsen Layer Fresnel Absorption The Role of Convection in the Transfer of Energy to the Keyhole Wall Fluid Flow in the Keyhole General Aspects Turbulence in the Weld Pool and the Keyhole Ill 4.6 Further Aspects of Fluid Flow Simplifying Assumptions for an Analytical Model Lubrication Theory Model Boundary Conditions Solution Matched to the Liquid Region Electromagnetic Effects Self-Induced Currents in the Vapour The Laser Beam as a Current Guide 123 References 126

4 Contents xi 5 Basic Concepts of Laser Drilling Wolfgang Schulz, Urs Eppelt Introduction Technology and Laser Systems Diagnostics and Monitoring for /is Pulse Drilling Phenomena of Beam-Matter Interaction Physical Domains - Map of Intensity and Pulse Duration Beam Propagation Refraction and Reflection Absorption and Scattering in the Gaseous Phase Kinetics and Equation of State Phenomena of the Melt Expulsion Domain Mathematical Formulation of Reduced Models Spectral Decomposition Applied to Dynamics in Recast Formation Analysis Initial Heating and Relaxation of Melt Flow Widening of the Drill by Convection Narrowing of the Drill by Recast Formation Melt Closure of the Drill Hole Drilling with Inertial Confinement - Helical Drilling Outlook Acknowledgements 161 References Arc Welding and Hybrid Laser-Arc Welding Ian Richardson The Structure of the Welding Arc Macroscopic Considerations Arc Temperatures and the plte Assumption Multi-Component Plasmas The Arc Electrodes The Cathode The Anode Molten Metal Flow The Arc Generated Weld Pool Metal Transfer Unified Arc and Electrode Models Arc Plasma - Laser Interactions Absorption Scattering Laser-Arc Welding 203 References 210

5 > xii Contents 7 Metallurgy of Welding and Hardening Alexander Kaplan Thermal Cycle and Cooling Rate Resolidification Metallurgy Diffusion Fe-Based Alloys Model of the Metallurgy During Transformation Hardening of Low Alloy Steel Non-Fe-based Alloys Defects 227 References Laser Cladding Dietrich Lepski and Frank Brückner Introduction Beam-Particle Interaction Powder Mass Flow Density Effect of Gravity on the Mass Flow Distribution Beam Shadowing and Particle Heating Formation of the Weld Bead Particle Absorption and Dissolution Shape of the Cross Section of a Weld Bead Three-Dimensional Model of the Melt Pool Surface Temperature Field Calculation using Rosenthal's Solution Self-Consistent Calculation of the Temperature Field and Bead Geometry Role of the Thermocapillary Flow Thermal Stress and Distortion Fundamentals of Thermal Stress Phase Transformations FEM Model and Results Simplified Heuristic Model Crack Prevention by Induction Assisted Laser Cladding Conclusions and Future Work 274 References Laser Forming Thomas Pretorius History of Thermal Forming Forming Mechanisms Temperature Gradient Mechanism Residual Stress Point Mechanism 292

6 Contents xiii Upsetting Mechanism Buckling Mechanism Residual Stress Relaxation Mechanism Martensite Expansion Mechanism Shock Wave Mechanism Applications Plate Bending Tube Bending/Forming High Precision Positioning Using Actuators Straightening of Weld Distortion Thermal Pre-Stressing 311 References Femtosecond Laser Pulse Interactions with Metals Bernd Hüttner Introduction What is Different Compared to Longer Pulses? The Electron-Electron Scattering Time The Nonequilibrium Electron Distribution Material Properties Under Exposure to Femtosecond Laser Pulses Optical Properties Thermal Properties Electronic Thermal Diffusivity Determination of the Electron and Phonon Temperature Distribution The Two-Temperature Model The Extended Two-Temperature Model Summary and Conclusions 334 References Comprehensive Numerical Simulation of Laser Materials Processing Markus Gross Motivation - The Pursuit of Ultimate Understanding Review Correlation, the Full Picture Introduction to Numerical Techniques The Method of Discretisation Meshes Explicit versus Implicit Discretisation of Transport pde's Schemes of Higher Order The Multi Phase Problem 356 t

7 xiv Contents 11.5 Solution of the Energy Equation and Phase Changes Gas Dynamics Beam Tracing and Associated Difficulties Program Development and Best Practice when Using Analysis Tools Introduction to High Performance Computing MPI openmp Performance Visualisation Tools Summary and Concluding Remarks 375 References 375 Index 381