Metallurgical Modelling of Welding

Metallurgical Modelling of Welding SECOND EDITION 0YSTEIN GRONG Norwegian University of Science and Technology, Departme...

Author: Oystein Grong

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Metallurgical Modelling of Welding SECOND EDITION 0YSTEIN GRONG Norwegian University of Science and Technology, Department of Metallurgy, N-7034 Trondheim, Norway

MATERIALS MODELLING SERIES

Editor: H. K. D. H. Bhadeshia The University of Cambridge Department of Materials Science and Metallurgy

T H E INSTITUTE OF MATERIALS

Book 677 First published in 1997 by The Institute of Materials 1 Carlton House Terrace London SWlY 5DB First edition (Book 557) Published in 1994 The Institute of Materials 1997 All rights reserved ISBNl 86125 036 3

Originally typeset by PicA Publishing Services Additional typesetting and corrections by Fakenham Photosetting Ltd Printed and bound in the UK at The University Press, Cambridge

TO TORHILD, TORBJ0RN AND HAVARD without your support, this book would never have been finished.

Preface to the second edition

Besides correcting some minor linguistic and print errors, I have in the second edition included a collection of different exercise problems which have been used in the training of students at NTNU. They illustrate how the models described in the previous chapters can be used to solve practical problems of more interdisciplinary nature. Each of them contains a 'problem description' and some background information on materials and welding conditions. The exercises are designed to illuminate the microstructural connections throughout the weld thermal cycle and show how the properties achieved depend on the operating conditions applied. Solutions to the problems are also presented. These are not complete or exhaustive, but are just meant as an aid to the reader to develop the ideas further. Trondheim, 28 October, 1996 0ystein Grong

Preface to the first edition

The purpose of this textbook is to present a broad overview on the fundamentals of welding metallurgy to graduate students, investigators and engineers who already have a good background in physical metallurgy and materials science. However, in contrast to previous textbooks covering the same field, the present book takes a more direct theoretical approach to welding metallurgy based on a synthesis of knowledge from diverse disciplines. The motivation for this work has largely been provided by the need for improved physical models for process optimalisation and microstructure control in the light of the recent advances that have taken place within the field of materials processing and alloy design. The present textbook describes a novel approach to the modelling of dynamic processes in welding metallurgy, not previously dealt with. In particular, attempts have been made to rationalise chemical, structural and mechanical changes in weldments in terms of models based on well established concepts from ladle refining, casting, rolling and heat treatment of steels and aluminium alloys. The judicious construction of the constitutive equations makes full use of both dimensionless parameters and calibration techniques to eliminate poorly known kinetic constants. Many of the models presented are thus generic in the sense that they can be generalised to a wide range of materials and processing. To help the reader understand and apply the subjects and models treated, numerous example problems, exercise problems and case studies have been worked out and integrated in the text. These are meant to illustrate the basic physical principles that underline the experimental observations and to provide a way of developing the ideas further. Over the years, I have benefited from interaction and collaboration with numerous people within the scientific community. In particular, I would like to acknowledge the contribution from my father Professor Tor Grong who is partly responsible for my professional upbringing and development as a metallurgist through his positive influence on and interest in my research work. Secondly, I am very grateful to the late Professor Nils Christensen who first introduced me to the fascinating field of welding metallurgy and later taught me the basic principles of scientific work and reasoning. I will also take this opportunity to thank all my friends and colleagues at the Norwegian Institute of Technology (Norway), The Colorado School of Mines (USA), the University of Cambridge (England), and the Universitat der Bundeswehr Hamburg (Germany) whom I have worked with over the past decade. Of this group of people, I would particularly like to mention two names, i.e. our department secretary Mrs. Reidun 0stbye who has helped me to convert my original manuscript into a readable text and Mr. Roald Skjaerv0 who is responsible for all line-drawings in this textbook. Their contributions are gratefully acknowledged. Trondheim, 1 December, 1993 0ystein Grong

Contents

Preface to the Second Edition ........................................................

xiii

Preface to the First Edition .............................................................

xiv

1. Heat Flow and Temperature Distribution in Welding ...........

1

1.1

Introduction ...............................................................................

1

1.2

Non-steady Heat Conduction ....................................................

1

1.3

Thermal Properties of Some Metals and Alloys ........................

2

1.4

Instantaneous Heat Sources .....................................................

4

1.5

Local Fusion in Arc Strikes ........................................................

7

1.6

Spot Welding .............................................................................

10

1.7

Thermit Welding ........................................................................

14

1.8

Friction Welding ........................................................................

18

1.9

Moving Heat Sources and Pseudo-steady State ......................

24

1.10 Arc Welding ...............................................................................

24

1.10.1 Arc Efficiency Factors ..................................................

26

1.10.2 Thick Plate Solutions ................................................... 1.10.2.1 Transient Heating Period ............................. 1.10.2.2 Pseudo-steady State Temperature Distribution ................................................... 1.10.2.3 Simplified Solution for a Fast-moving High Power Source ..............................................

26 28

1.10.3 Thin Plate Solutions ..................................................... 1.10.3.1 Transient Heating Period ............................. 1.10.3.2 Pseudo-steady State Temperature Distribution ................................................... This page has been reformatted by Knovel to provide easier navigation.

31 41 45 48 49

vi

Contents

vii

1.10.3.3 Simplified Solution for a Fast Moving High Power Source ..............................................

56

1.10.4 Medium Thick Plate Solution ....................................... 1.10.4.1 Dimensionless Maps for Heat Flow Analyses ...................................................... 1.10.4.2 Experimental Verification of the Medium Thick Plate Solution ..................................... 1.10.4.3 Practical Implications ...................................

59

1.10.5 Distributed Heat Sources ............................................. 1.10.5.1 General Solution .......................................... 1.10.5.2 Simplified Solution .......................................

77 77 80

1.10.6 Thermal Conditions during Interrupted Welding ..........

91

1.10.7 Thermal Conditions during Root Pass Welding ...........

95

61 72 75

1.10.8 Semi-empirical Methods for Assessment of Bead Morphology .................................................................. 1.10.8.1 Amounts of Deposit and Fused Parent Metal ............................................................ 1.10.8.2 Bead Penetration .........................................

96 99

1.10.9 Local Preheating ..........................................................

100

References .........................................................................................

103

Appendix 1.1: Nomenclature ............................................................

105

Appendix 1.2: Refined Heat Flow Model for Spot Welding ..............

110

Appendix 1.3: The Gaussian Error Function ....................................

111

Appendix 1.4: Gaussian Heat Distribution .......................................

112

96

2. Chemical Reactions in Arc Welding ...................................... 116 2.1

Introduction ...............................................................................

116

2.2

Overall Reaction Model .............................................................

116

2.3

Dissociation of Gases in the Arc Column ..................................

117

2.4

Kinetics of Gas Absorption ........................................................

120

2.4.1

Thin Film Model ...........................................................

120

2.4.2

Rate of Element Absorption .........................................

121

This page has been reformatted by Knovel to provide easier navigation.

viii

Contents 2.5

The Concept of Pseudo-equilibrium ..........................................

122

2.6

Kinetics of Gas Desorption ........................................................

123

2.6.1

Rate of Element Desorption .........................................

123

2.6.2

Sievert’s Law ...............................................................

124

Overall Kinetic Model for Mass Transfer during Cooling in the Weld Pool ............................................................................

124

Absorption of Hydrogen ............................................................

128

2.8.1

Sources of Hydrogen ...................................................

128

2.8.2

Methods of Hydrogen Determination in Steel Welds ...........................................................................

128

2.8.3

Reaction Model ............................................................

130

2.8.4

Comparison between Measured and Predicted Hydrogen Contents ...................................................... 2.8.4.1 Gas-shielded Welding .................................. 2.8.4.2 Covered Electrodes ..................................... 2.8.4.3 Submerged Arc Welding .............................. 2.8.4.4 Implications of Sievert’s Law ....................... 2.8.4.5 Hydrogen in Multi-run Weldments ............... 2.8.4.6 Hydrogen in Non-ferrous Weldments ..........

131 131 134 138 140 140 141

Absorption of Nitrogen ..............................................................

141

2.9.1

Sources of Nitrogen .....................................................

142

2.9.2

Gas-shielded Welding ..................................................

142

2.9.3

Covered Electrodes .....................................................

143

2.9.4

Submerged Arc Welding ..............................................

146

2.10 Absorption of Oxygen ................................................................

148

2.10.1 Gas Metal Arc Welding ................................................ 2.10.1.1 Sampling of Metal Concentrations at Elevated Temperatures ............................... 2.10.1.2 Oxidation of Carbon ..................................... 2.10.1.3 Oxidation of Silicon ...................................... 2.10.1.4 Evaporation of Manganese .......................... 2.10.1.5 Transient Concentrations of Oxygen ...........

148

2.7 2.8

2.9


149 149 152 156 160

Contents

ix

2.10.1.6 Classification of Shielding Gases ................ 2.10.1.7 Overall Oxygen Balance .............................. 2.10.1.8 Effects of Welding Parameters ....................

166 166 169

2.10.2 Submerged Arc Welding .............................................. 2.10.2.1 Flux Basicity Index ....................................... 2.10.2.2 Transient Oxygen Concentrations ...............

170 171 172

2.10.3 Covered Electrodes ..................................................... 2.10.3.1 Reaction Model ............................................ 2.10.3.2 Absorption of Carbon and Oxygen .............. 2.10.3.3 Losses of Silicon and Manganese ............... 2.10.3.4 The Product [%C] [%O] ...............................

173 174 176 177 179

2.11 Weld Pool Deoxidation Reactions .............................................

180

2.11.1 Nucleation of Oxide Inclusions .....................................

182

2.11.2 Growth and Separation of Oxide Inclusions ................. 2.11.2.1 Buoyancy (Stokes Flotation) ........................ 2.11.2.2 Fluid Flow Pattern ........................................ 2.11.2.3 Separation Model .........................................

184 185 186 188

2.11.3 Predictions of Retained Oxygen in the Weld Metal ...... 2.11.3.1 Thermodynamic Model ................................ 2.11.3.2 Implications of Model ...................................

190 190 192

2.12 Non-metallic Inclusions in Steel Weld Metals ...........................

192

2.12.1 Volume Fraction of Inclusions ......................................

193

2.12.2 Size Distribution of Inclusions ...................................... 2.12.2.1 Effect of Heat Input ...................................... 2.12.2.2 Coarsening Mechanism ............................... 2.12.2.3 Proposed Deoxidation Model .......................

195 196 196 201

2.12.3 Constituent Elements and Phases in Inclusions .......... 2.12.3.1 Aluminium, Silicon and Manganese Contents ...................................................... 2.12.3.2 Copper and Sulphur Contents ..................... 2.12.3.3 Titanium and Nitrogen Contents .................. 2.12.3.4 Constituent Phases ......................................

202


202 202 203 204

x

Contents 2.12.4 Prediction of Inclusion Composition ............................. 2.12.4.1 C-Mn Steel Weld Metals .............................. 2.12.4.2 Low-alloy Steel Weld Metals ........................

204 204 206

References .........................................................................................

212


215

Appendix 2.2: Derivation of Equation (2-60) ....................................

219

3. Solidification Behaviour of Fusion Welds ............................ 221 3.1

Introduction ...............................................................................

221

3.2

Structural Zones in Castings and Welds ...................................

221

3.3

Epitaxial Solidification ...............................................................

222

3.3.1

Energy Barrier to Nucleation ........................................

225

3.3.2

Implications of Epitaxial Solidification ..........................

226

Weld Pool Shape and Columnar Grain Structures ....................

228

3.4.1

Weld Pool Geometry ....................................................

228

3.4.2

Columnar Grain Morphology ........................................

229

3.4.3

Growth Rate of Columnar Grains ................................. 3.4.3.1 Nominal Crystal Growth Rate ...................... 3.4.3.2 Local Crystal Growth Rate ...........................

230 230 234

3.4.4

Reorientation of Columnar Grains ............................... 3.4.4.1 Bowing of Crystals ....................................... 3.4.4.2 Renucleation of Crystals ..............................

239 240 242

Solidification Microstructures ....................................................

251

3.5.1

Substructure Characteristics ........................................

251

3.5.2

Stability of the Solidification Front ................................ 3.5.2.1 Interface Stability Criterion ........................... 3.5.2.2 Factors Affecting the Interface Stability .......

254 254 256

3.5.3

Dendrite Morphology ................................................... 3.5.3.1 Dendrite Tip Radius ..................................... 3.5.3.2 Primary Dendrite Arm Spacing .................... 3.5.3.3 Secondary Dendrite Arm Spacing ...............

260 260 261 264

3.4

3.5


Contents 3.6

3.7

3.8

xi

Equiaxed Dendritic Growth .......................................................

268

3.6.1

Columnar to Equiaxed Transition .................................

268

3.6.2

Nucleation Mechanisms ...............................................

272

Solute Redistribution .................................................................

272

3.7.1

Microsegregation .........................................................

272

3.7.2

Macrosegregation ........................................................

278

3.7.3

Gas Porosity ................................................................ 3.7.3.1 Nucleation of Gas Bubbles .......................... 3.7.3.2 Growth and Detachment of Gas Bubbles .... 3.7.3.3 Separation of Gas Bubbles ..........................

279 279 281 284

3.7.4

Removal of Microsegregations during Cooling ............ 3.7.4.1 Diffusion Model ............................................ 3.7.4.2 Application to Continuous Cooling ...............

286 286 286

Peritectic Solidification ..............................................................

290

3.8.1

Primary Precipitation of the γp-phase ...........................

290

3.8.2

Transformation Behaviour of Low-alloy Steel Weld Metals .......................................................................... 3.8.2.1 Primary Precipitation of Delta Ferrite ........... 3.8.2.2 Primary Precipitation of Austenite ................ 3.8.2.3 Primary Precipitation of Both Delta Ferrite and Austenite ...................................

290 290 292 292

References .........................................................................................

293


296

4. Precipitate Stability in Welds ................................................. 301 4.1

Introduction ...............................................................................

301

4.2

The Solubility Product ...............................................................

301

4.2.1

Thermodynamic Background .......................................

301

4.2.2

Equilibrium Dissolution Temperature ...........................

303

4.2.3

Stable and Metastable Solvus Boundaries .................. 4.2.3.1 Equilibrium Precipitates ............................... 4.2.3.2 Metastable Precipitates ...............................

304 304 308


xii

Contents 4.3

Particle Coarsening ...................................................................

314

4.3.1

Coarsening Kinetics .....................................................

314

4.3.2

Application to Continuous Heating and Cooling ........... 4.3.2.1 Kinetic Strength of Thermal Cycle ............... 4.3.2.2 Model Limitations .........................................

314 315 315

Particle Dissolution ....................................................................

316

4.4.1

Analytical Solutions ...................................................... 4.4.1.1 The Invariant Size Approximation ................ 4.4.1.2 Application to Continuous Heating and Cooling ........................................................

316 319

Numerical Solution ....................................................... 4.4.2.1 Two-dimensional Diffusion Model ................ 4.4.2.2 Generic Model ............................................. 4.4.2.3 Application to Continuous Heating and Cooling ........................................................ 4.4.2.4 Process Diagrams for Single Pass 6082T6 Butt Welds ..............................................

325 326 328

References .........................................................................................

334


334

4.4

4.4.2

322

329 332

5. Grain Growth in Welds ........................................................... 337 5.1

Introduction ...............................................................................

337

5.2

Factors Affecting the Grain Boundary Mobility ..........................

337

5.2.1

Characterisation of Grain Structures ............................

337

5.2.2

Driving Pressure for Grain Growth ...............................

339

5.2.3

Drag from Impurity Elements in Solid Solution ............

340

5.2.4

Drag from a Random Particle Distribution ...................

341

5.2.5

Combined Effect of Impurities and Particles ................

342

Analytical Modelling of Normal Grain Growth ...........................

343

5.3.1

Limiting Grain Size .......................................................

343

5.3.2

Grain Boundary Mobility ...............................................

345

5.3


Contents

xiii

Grain Growth Mechanisms .......................................... 5.3.3.1 Generic Grain Growth Model ....................... 5.3.3.2 Grain Growth in the Absence of Pinning Precipitates .................................................. 5.3.3.3 Grain Growth in the Presence of Stable Precipitates .................................................. 5.3.3.4 Grain Growth in the Presence of Growing Precipitates .................................................. 5.3.3.5 Grain Growth in the Presence of Dissolving Precipitates .................................

345 345

Grain Growth Diagrams for Steel Welding ................................

360

5.4.1

Construction of Diagrams ............................................ 5.4.1.1 Heat Flow Models ........................................ 5.4.1.2 Grain Growth Model ..................................... 5.4.1.3 Calibration Procedure .................................. 5.4.1.4 Axes and Features of Diagrams ..................

360 360 361 361 363

5.4.2

Case Studies ............................................................... 5.4.2.1 Titanium-microalloyed Steels ....................... 5.4.2.2 Niobium-microalloyed Steels ....................... 5.4.2.3 C-Mn Steel Weld Metals .............................. 5.4.2.4 Cr-Mo Low-alloy Steels ................................ 5.4.2.5 Type 316 Austenitic Stainless Steels ...........

364 364 367 370 372 375

Computer Simulation of Grain Growth ......................................

380

5.3.3

5.4

5.5

5.5.1

347 348 351 356

Grain Growth in the Presence of a Temperature Gradient .......................................................................

380

Free Surface Effects ....................................................

382

References .........................................................................................

382


384

5.5.2

6. Solid State Transformations in Welds ................................... 387 6.1

Introduction ...............................................................................

387

6.2

Transformation Kinetics ............................................................

387

6.2.1

387

Driving Force for Transformation Reactions ................


xiv

Contents

6.3

6.2.2

Heterogeneous Nucleation in Solids ............................ 6.2.2.1 Rate of Heterogeneous Nucleation .............. 6.2.2.2 Determination of ∆Ghet.* and Qd ................... 6.2.2.3 Mathematical Description of the C-curve .....

389 389 390 392

6.2.3

Growth of Precipitates .................................................. 6.2.3.1 Interface-controlled Growth ......................... 6.2.3.2 Diffusion-controlled Growth .........................

396 396 397

6.2.4

Overall Transformation Kinetics ................................... 6.2.4.1 Constant Nucleation and Growth Rates ...... 6.2.4.2 Site Saturation .............................................

400 400 402

6.2.5

Non-isothermal Transformations .................................. 6.2.5.1 The Principles of Additivity ........................... 6.2.5.2 Isokinetic Reactions ..................................... 6.2.5.3 Additivity in Relation to the Avrami Equation ...................................................... 6.2.5.4 Non-additive Reactions ................................

402 403 404

High Strength Low-alloy Steels .................................................

406

6.3.1

Classification of Microstructures ..................................

406

6.3.2

Currently Used Nomenclature ......................................

406

6.3.3

Grain Boundary Ferrite ................................................ 6.3.3.1 Crystallography of Grain Boundary Ferrite .......................................................... 6.3.3.2 Nucleation of Grain Boundary Ferrite .......... 6.3.3.3 Growth of Grain Boundary Ferrite ................

408 408 408 422

6.3.4

Widmanstätten Ferrite ..................................................

427

6.3.5

Acicular Ferrite in Steel Weld Deposits ........................ 6.3.5.1 Crystallography of Acicular Ferrite ............... 6.3.5.2 Texture Components of Acicular Ferrite ...... 6.3.5.3 Nature of Acicular Ferrite ............................. 6.3.5.4 Nucleation and Growth of Acicular Ferrite ..........................................................

428 428 429 430

Acicular Ferrite in Wrought Steels ...............................

444

6.3.6


404 405

432

6.4

6.5

Contents

xv

6.3.7

Bainite .......................................................................... 6.3.7.1 Upper Bainite ............................................... 6.3.7.2 Lower Bainite ...............................................

444 444 447

6.3.8

Martensite .................................................................... 6.3.8.1 Lath Martensite ............................................ 6.3.8.2 Plate (Twinned) Martensite ..........................

448 448 448

Austenitic Stainless Steels ........................................................

453

6.4.1

Kinetics of Chromium Carbide Formation ....................

456

6.4.2

Area of Weld Decay .....................................................

456

Al-Mg-Si Alloys ..........................................................................

458

6.5.1

459

6.5.2

Quench-sensitivity in Relation to Welding .................... 6.5.1.1 Conditions for β’(Mg2Si) Precipitation during Cooling .............................................. 6.5.1.2 Strength Recovery during Natural Ageing .........................................................

459 461

Subgrain Evolution during Continuous Drive Friction Welding ...........................................................

464

References .........................................................................................

467


471

Appendix 6.2: Additivity in Relation to the Avrami Equation ............

475

7. Properties of Weldments ........................................................ 477 7.1

Introduction ...............................................................................

477

7.2

Low-alloy Steel Weldments .......................................................

477

7.2.1

477 478

Weld Metal Mechanical Properties .............................. 7.2.1.1 Weld Metal Strength Level ........................... 7.2.1.2 Weld Metal Resistance to Ductile Fracture ....................................................... 7.2.1.3 Weld Metal Resistance to Cleavage Fracture ....................................................... 7.2.1.4 The Weld Metal Ductile to Brittle Transition .....................................................


480 485 486

xvi

Contents 7.2.1.5

Effects of Reheating on Weld Metal Toughness ...................................................

491

7.2.2

HAZ Mechanical Properties ......................................... 7.2.2.1 HAZ Hardness and Strength Level .............. 7.2.2.2 Tempering of the Heat Affected Zone .......... 7.2.2.3 HAZ Toughness ...........................................

494 495 500 502

7.2.3

Hydrogen Cracking ...................................................... 7.2.3.1 Mechanisms of Hydrogen Cracking ............. 7.2.3.2 Solubility of Hydrogen in Steel ..................... 7.2.3.3 Diffusivity of Hydrogen in Steel .................... 7.2.3.4 Diffusion of Hydrogen in Welds ................... 7.2.3.5 Factors Affecting the HAZ Cracking Resistance ...................................................

509 509 513 514 514

H2S Stress Corrosion Cracking .................................... 7.2.4.1 Threshold Stress for Cracking ..................... 7.2.4.2 Prediction of HAZ Cracking Resistance .......

524 524 525

Stainless Steel Weldments .......................................................

527

7.3.1

HAZ Corrosion Resistance ..........................................

527

7.3.2

HAZ Strength Level .....................................................

529

7.3.3

HAZ Toughness ...........................................................

530

7.3.4

Solidification Cracking ..................................................

532

Aluminium Weldments ..............................................................

536

7.4.1

Solidification Cracking ..................................................

536

7.4.2

Hot Cracking ................................................................ 7.4.2.1 Constitutional Liquation in Binary Al-Si Alloys ........................................................... 7.4.2.2 Constitutional Liquation in Ternary Al-MgSi Alloys ....................................................... 7.4.2.3 Factors Affecting the Hot Cracking Susceptibility ................................................

540

7.2.4

7.3

7.4

7.4.3

HAZ Microstructure and Strength Evolution during Fusion Welding ............................................................


518

541 542 544 547

Contents 7.4.3.1 7.4.3.2 7.4.3.3 7.4.3.4 7.4.4

Effects of Reheating on Weld Properties ..... Strengthening Mechanisms in Al-Mg-Si Alloys ........................................................... Constitutive Equations ................................. Predictions of HAZ Hardness and Strength Distribution ....................................

HAZ Microstructure and Strength Evolution during Friction Welding ........................................................... 7.4.4.1 Heat Generation in Friction Welding ............ 7.4.4.2 Response of Al-Mg-Si Alloys and Al-SiC MMCs to Friction Welding ............................ 7.4.4.3 Constitutive Equations ................................. 7.4.4.4 Coupling of Models ...................................... 7.4.4.5 Prediction of the HAZ Hardness Distribution ...................................................

xvii 547 548 548 550 556 556 557 558 558 560

References .........................................................................................

564


567

8. Exercise Problems with Solutions ......................................... 571 8.1

Introduction ...............................................................................

571

8.2

Exercise Problem I: Welding of Low Alloy Steels ......................

571

8.3

Exercise Problem II: Welding of Austenitic Stainless Steels .....

583

8.4

Exercise Problem III: Welding of Al-Mg-Si Alloys ......................

587

Index .............................................................................................. 595 Author Index ................................................................................. 602


1 Heat Flow and Temperature Distribution in Welding

1.1 Introduction Welding metallurgy is concerned with the application of well-known metallurgical principles for assessment of chemical and physical reactions occurring during welding. On purely practical grounds it is nevertheless convenient to consider welding metallurgy as a profession of its own because of the characteristic non-isothermal nature of the process. In welding the reactions are forced to take place within seconds in a small volume of metal where the thermal conditions are highly different from those prevailing in production, refining and fabrication of metals and alloys. For example, steel welding is characterised by: High peak temperatures, up to several thousand 0 C. High temperature gradients, locally of the order of 103 0C mm"1. Rapid temperature fluctuations, locally of the order of 103 0C s 1 . It follows that a quantitative analysis of metallurgical reactions in welding requires detailed information about the weld thermal history. From a practical point of view the analytical approach to the solution of heat flow problems in welding is preferable, since this makes it possible to derive relatively simple equations which provide the required background for an understanding of the temperature-time pattern. However, because of the complexity of the heat flow phenomena, it is always necessary to check the validity of such predictions against more reliable data obtained from numerical calculations and in situ thermocouple measurements. Although the analytical models suffer from a number of simplifying assumptions, it is obvious that these solutions in many cases are sufficiently accurate to provide at least a qualitative description of the weld thermal programme. An important aspect of the present treatment is the use of different dimensionless groups for a general outline of the temperature distribution in welding. Although this practice involves several problems, it is a convenient way to reduce the total number of variables to an acceptable level and hence, condense general information about the weld thermal programme into two-dimensional (2-D) maps or diagrams. Consequently, readers who are unfamiliar with the concept should accept the challenge and try to overcome the barrier associated with the use of such dimensionless groups in heat flow analyses.

1.2 Non-Steady Heat Conduction The symbols and units used throughout this chapter are defined in Appendix 1.1.

Since heat losses from free surfaces by radiation and convection are usually negligible in welding, the temperature distribution can generally be obtained from the fundamental differential equations for heat conduction in solids. For uniaxial heat conduction, the governing equation can be written as:1

(i-D where T is the temperature, t is the time, x is the heat flow direction, and a is the thermal diffusivity. The thermal diffusivity is related to the thermal conductivity X and the volume heat capacity pc through the following equation:

(1-2) For biaxial and triaxial heat conduction we may write by analogy:1

d-3) and

(1-4) The above equations must clearly be satisfied by all solutions of heat conduction problems, but for a given set of initial and boundary conditions there will be one and only one solution.

1.3 Thermal Properties of Some Metals and Alloys A pre-condition for obtaining simple analytical solutions to the differential heat flow equations is that the thermal properties of the base material are constant and independent of temperature. For most metals and alloys this is a rather unrealistic assumption, since both X, a, and pc may vary significantly with temperature as illustrated in Fig. 1.1. In addition, the thermal properties are also dependent upon the chemical composition and the thermal history of the base material (see Fig. 1.2), which further complicates the situation. By neglecting such effects in the heat flow models, we impose several limitations on the application of the analytical solutions. Nevertheless, experience has shown that these problems to some extent can be overcome by the choice of reasonable average values for X, a and pc within a specific temperature range. Table 1.1 contains a summary of relevant thermal properties for different metals and alloys, based on a critical review of literature data. It should be noted that the thermal data in Table 1.1 do not include a correction for heat consumed in melting of the parent materials. Although the latent heat of melting is temporarily removed during fusion welding, experience has shown this effect can be accounted for by calibrating the equations against a known isotherm (e.g. the fusion boundary). In practice, such corrections are done by adjusting the arc efficiency factor Tq until a good correlation is achieved between theory and experiments.

Hx-H0 = PC(T-T0 ),J/mm3

Carbon steel

Temperature, 0C Fig. 1.1. Enthalpy increment H7-H0 2-4.

referred to an initial temperature T0 = 200C. Data from Refs.

Table 1.1 Physical properties for some metals and alloys. Data from Refs 2 - 6 .

Material

(WrTIm-10C-1)

(mm2 s"1)

(Jmnr 3 0C"1)

(0C)

(J mnr 3 )

(J mnr 3 )

Carbon Steels

0.040

8

0.005

1520

7.50

2.0

Low Alloy Steels

0.025

5

0.005

1520

7.50

2.0

High Alloy Steels

0.020

4

0.005

1500

7.40

2.0

Titanium Alloys

0.030

10

0.003

1650

4.89

1.4

Aluminium (> 99% Al)

0.230

85

0.0027

660

1.73

0.8

Al-Mg-Si Alloys

0.167

62

0.0027

652

1.71

0.8

Al-Mg Alloys

0.149

55

0.0027

650

1.70

0.8

Does not include the latent heat of melting (AH1n).

X9 W/mm 0C

(a)

Temperature, 0C

(b)

X, W/mm 0C

High alloy steel

Temperature, 0C Fig. 1.2. Factors affecting the thermal conductivity X of steels; (a) Temperature level and chemical composition, (b) Heat treatment procedure. Data from Refs. 2-4.

1.4 Instantaneous Heat Sources The concept of instantaneous heat sources is widely used in the theory of heat conduction.1 It is seen from Fig. 1.3 that these solutions are based on the assumption that the heat is released instantaneously at time t - 0 in an infinite medium of initial temperature T0, either across a plane (uniaxial conduction), along a line (biaxial conduction), or in a point (triaxial conduction). The material outside the heat source is assumed to extend to x = + °° for a plane source in a long rod, to r = °° for a line source in a wide plate, or to R = °° for a point source in a heavy slab. The initial and boundary conditions can be summarised as follows:

T-T0 = oo for t = O and x = O (alternatively r = O or R = O) T-J 0 = O for t = O and x * O (alternatively r > O or 7? > O) 7-T 0 = O for O < t < oo when x = ± oo (alternatively r = oo or R = oo). It is easy to verify that the following solutions satisfy both the basic differential heat flow equations (1-1), (1-3) and (1-4) and the initial and boundary conditions listed above: (i)

Plane source in a long rod (Fig. 1.3a): d-5)

where Q is the net heat input (energy) released at time t = O, and A is the cross section of the rod. (ii)

Line source in a wide plate (Fig. 1.3b): (1-6)

where d is the plate thickness. (iii)

Point source in a heavy slab (Fig. 1.3c): (1-7)

Equations (1-5), (1-6) and (1-7) provide the required basis for a comprehensive theoretical treatment of heat flow phenomena in welding. These solutions can either be applied directly or be used in an integral or differential form. In the next sections a few examples will be given to illustrate the direct application of the instantaneous heat source concept to problems related to welding.

(a)

T

Fig. 1.3. Schematic representation of instantaneous heat source models; (a) Plane source in a long rod.

T

(b)

X

y

T

R (C)

Fig. 1.3.Schematic representation of instantaneous heat source models (continued); (b) Line source in a wide plate, (c) Point source in a heavy slab.

1.5 Local Fusion in Arc Strikes The series of fused metal spots formed on arc ignition make a good case for application of equation (1-7). Model

The model considers a point source on a heavy slab as illustrated in Fig. 1.4. The heat is assumed to be released instantaneously at time t = 0 on the surface of the slab. This causes a temperature rise in the material which is exactly twice as large as that calculated from equation (1-7): (1-8) In order to obtain a general survey of the thermal programme, it is convenient to write equation (1-8) in a dimensionless form. The following parameters are defined for this purpose: — Dimensionless temperature: (1-9) where Tc is the chosen reference temperature. — Dimensionless time: d-10) where tt is the arc ignition time. — Dimensionless operating parameter:

(1-11) where qo is the net arc power (equal to Qlt(), and (Hc-Ho) is the heat content per unit volume at the reference temperature. — Dimensionless radius vector: (1-12) By substituting these parameters into equation (1-8), we obtain:

(1-13)

Heat source

Isotherms

3-D heat flow Fig. 1.4. Instantaneous point source model for assessment of temperatures in arc strikes.

0Zn1

e/n

Linear time scale

T1

î Fig. 1.5. Calculated temperatures in arc strikes. Equation (1-13) has been solved numerically for different values ofCT1and T1. The results are presented graphically in Fig. 1.5. Due to the inherent assumption of instantaneous release of heat in a point, it is not possible to use equation (1-13) down to very small values OfCT1 and T1. However, at some distance from the heat source and after a time not much shorter than the real (assumed) time of heating, the calculated temperature-time pattern will be reasonably correct. Note that the heavy broken line in Fig. 1.5 represents the locus of the peak temperatures. This locus is obtained by setting 3In(OAi1VdT1 = 0:

from which

Substituting this into equation (1-13) gives:

(1-14) where Qp is the peak temperature, and e is the natural logarithm base number. Example (1.1)

Consider a small weld crater formed in an arc strike on a thick plate of low alloy steel. Calculate the cooling time from 800 to 5000C (Af875), and the total width of the fully transformed region adjacent to the fusion boundary. The operational conditions are as follows:

where r| is the arc efficiency factor. Relevant thermal data for low alloy steel are given in Table 1.1. Solution

In the present case it is convenient to use the melting point of the steel as a reference temperature (i.e. 0 = 0m = 1 when Tc = TJ. The corresponding values OfZi1 and 9 (at 800 and 5000C, respectively) are:

Cooling time At8/5

Since the cooling curves in Fig. 1.5 are virtually parallel at temperatures below 800 0 C, Af875 will be independent of Cr1 and similar to that calculated for the centre-line ((J1 = 0). By rearranging equation (1-13) we get:

and

Total width offully transformed region Zone widths can generally be calculated from equation (1-14), as illustrated in Fig. 1.6. Taking the Ac3-temperature equal to 8900C for this particular steel, we obtain:

and

Alternatively, the same information could have been read from Fig. 1.5. Although it is difficult to check the accuracy of these predictions, the calculated values for Ats/5 and ARlm are considered reasonably correct. Thus, because the cooling rate is very large, in arc strikes a hard martensitic microstructure would be expected to form within the transformed parts of the HAZ, in agreement with general experience.

1.6 Spot Welding Equation (1-6) can be used for an assessment of the temperature-time pattern in spot welding of plates. Model

The model considers a line source which penetrates two overlapping plates of similar thermal properties, as illustrated in Fig. 1.7. The heat is assumed to be released instantaneously at time Heat source

Fig. 1.6. Definition of isothermal zone width in Example (1.1).

Electrode

Heat source

d

Fig. 1.7. Idealised heat flow model for spot welding of plates.

t = 0. If transfer of heat into the electrodes is neglected, the temperature distribution is given by equation (1-6). This equation can be written in a dimensionless form by introducing the following group of parameters: — Dimensionless time: (1-15) where th is the heating time (i.e. the duration of the pulse). — Dimensionless operating parameter: (1-16) where dt is the total thickness of the joint. — Dimensionless radius vector: (1-17) By substituting these parameters into equation (1-6), we get: (1-18) where 6 denotes the dimensionless temperature (previously defined in equation (1-9)).

6/n2

e/n2

Linear time scale

T

2

T2 Fig. 1.8. Calculated temperature-time pattern in spot welding. Figure 1.8 shows a graphical representation of equation (1-18) for a limited range of a 2 and T2. A closer inspection of the graph reveals that the temperature-time pattern in spot welding is similar to that observed during arc ignition (see Fig. 1.5). The locus of the peak temperatures in Fig. 1.8 is obtained by setting d\n{^ln7}ldx2 - 0.

which gives and (1-19)

Example (1.2)

Consider spot welding of 2 mm plates of low alloy steel under the following operational conditions:

Calculate the cooling time from 800 to 5000C (Af8/5) in the centre of the weld, and the cooling rate (CR.) at the onset of the austenite to ferrite transformation. Assume in these calculations that the total voltage drop between the electrodes is 1.6 V. The M^-temperature of the steel is taken equal to 475°C. Solution

If we use the melting point of the steel as a reference temperature, the parameters n2 and 6 (at 800 and 5000C, respectively) become:

Cooling time Atg/5

The parameter A%5 can be calculated from equation (1-18). For the weld centre-line (CT2 = 0), we get:

and

Cooling rate at 475 0C

The cooling rate at a specific temperature is obtained by differentiation of equation (1-18) with respect to time. When (J2 = 0 the cooling rate at 9 = 0.3 (475°C) becomes:

and

Since the cooling curves in Fig. 1.8 are virtually parallel at temperatures below 8000C (i.e. for QZn2 < 0.15), the computed values of Ar8/5 and CR. are also valid for positions outside the weld centre-line. In the present example the centre-line solutions can be applied down to (°"2m)2 ~ 2. According to equation (1-19), this corresponds to a lower peak temperature of:

which is equivalent with:

It should be emphasised that the present heat flow model represents a crude oversimplification of the spot welding process. In a real welding situation, most of the heat is generated at the interface between the two plates because of the large contact resistance. This gives rise to the development of an elliptical weld nugget inside the joint as shown in Fig. 1.9. Moreover, since the model neglects transfer of heat into the electrodes, the mode of heat flow will be mixed and not truly two-dimensional as assumed above. Consequently, equation (1-18) cannot be applied for reliable predictions of isothermal contours and zone widths. Nevertheless, the model may provide useful information about the cooling conditions during spot welding if the efficiency factor if] and the voltage drop between the electrodes can be estimated with a reasonable degree of accuracy. A more refined heat flow model for spot welding is presented in Appendix 1.2.

1.7 Thermit Welding Thermit welding is a process that uses heat from exothermic chemical reactions to produce coalescence between metals and alloys. The thermit mixture consists of two components, i.e. a metal oxide and a strong reducing agent. The excess heat of formation of the reaction product provides the energy source required to form the weld. Model

In thermit welding the time interval between the ignition of the powder mixture and the completion of the reduction process will be short because of the high reaction rates involved. Assume that a groove of width 2L1 is filled instantaneously at time t = 0 by liquid metal of an initial temperature Tt (see Fig. 1.10). The metal temperature outside the fusion zone is T0. If heat losses to the surroundings are neglected, the problem can be treated as uniaxial conduction where the heat source (extending from -L 1 to +L1) is represented by a series of elementary sources, each with a heat content of: (1-20) At time t this source produces a small rise of temperature at position JC, given by equation (1 -5):

(1-21)

The final temperature distribution is obtained by substituting u = (x-xy(4at)m (i.e. dx'- du(4at)m) into equation (1-21) and integrating between the limits JC'= -L 1 and x'- +L1. This gives (after some manipulation): (1-22)

Isl'srau*'*'=]

Fusion

zone

Fig. 1.9. Calculated peak temperature contours in spot welding of steel plates (numerical solution). Operational conditions: / = 23kA, 64 cycles. Data from Bently et al1

Fusion

zone

Fig. 1.10. Idealised heat flow model for thermit welding of rails. where erf(u) is the Gaussian error function. The error function is defined in Appendix 1.3*. Because of the complex nature of equation (1-22), it is convenient to present the different solutions in a dimensionless form by introducing the following groups of parameters: *The error function is available in tables. However, in numerical calculations it is more convenient to use the Fortran subroutine given in Appendix 1.3.

Dimensionless temperature: (1-23) Dimensionless time: (1-24) Dimensionless jc-coordinate: (1-25) Substituting these parameters into equation (1-22) gives: (1-26) Equation (1-26) has been solved numerically for different values of Q and T3. The results are presented graphically in Fig. 1.11. As would be expected, the fusion zone itself (Q < 1) cools in a monotonic manner, while the temperature in positions outside the fusion boundary (Q > 1) will pass through a maximum before cooling. The locus of the HAZ peak temperatures in Fig. 1.11 is defined by 3673T3 = 0. Referring to Appendix 1.3, we may write:

which gives (1-27) The peak temperature distribution is obtained by solving equation (1-27) for different combinations of Qm and T3m and inserting the roots into equation (1-26).

Example (1.3)

Consider thermit welding of steel rails (i.e. reduction of Fe2O3 with Al powder) under the following operational conditions:

Calculate the cooling time from 800 to 5000C in the centre of the weld, and the total width of the fully transformed region adjacent to the fusion boundary. The Ac3-temperature of the steel is taken equal to 8900C.

91

Definition of parameters:

T

3

Fig. 1.11. Calculated temperature-time pattern in thermit welding. Solution

For positions along the weld centre-line (Q. = 0) equation (1-26) reduces to:

Cooling time At 8/5

From the above relation it is possible to calculate the cooling time from Tt = 22000C to 800 and 5000C, respectively:

and

By rearranging equation (1-24), we obtain the following expression for Ar875:

The computed value for A/8/5 is also valid for positions outside the weld centre-line, since the cooling curves at such low temperatures are reasonably parallel within the fusion zone. Total width of fully transformed region The fusion boundary is defined by:

The locus of the 8900C isotherm in temperature-time space can be read from Fig. 1.11. Taking the ordinate equal to 0.40, we get:

By inserting this value into equation (1-27), we obtain the corresponding coordinate of the isotherm:

The total width of the fully transformed HAZ is thus:

Unfortunately, measurements are not available to check the accuracy of these predictions. Systematic errors would be expected, however, because of the assumption of instantaneous release of heat immediately after powder ignition and the neglect of heat losses to the surroundings. Nevertheless, the present example is a good illustration of the versatility of the concept of instantaneous heat sources, since these solutions can easily be added in space as shown here or in time for continuous heat sources (to be discussed below).

1.8 Friction Welding Friction welding is a solid state joining process that produces a weld under the compressive force contact of one rotating and one stationary workpiece. The heat is generated at the weld interface because of the continuous rubbing of the contact surfaces, which, in turn, causes a temperature rise and subsequent softening of the material. Eventually, the material at the interface starts to flow plastically and forms an up-set collar. When a certain amount of upsetting has occurred, the rotation is stopped and the compressive force is maintained or slightly increased to consolidate the weld. Model (after Rykalin et al.5j

The model considers a continuous (plane) heat source in a long rod as shown in Fig. 1.12(a). The heat is liberated at a constant rate q'o in the plane x = 0 starting at time / = 0. If we subdivide the time t during which the source operates into a series of infinitesimal elements dt/ (Fig. 1.12b), each element will have a heat content of: (1-28)

(a) Continuous heat source

(b) q

t Fig. 1.12. Idealised heatflowmodel for friction welding of rods; (a) Sketch of model, (b) Subdivision of time into a series of infinitesimal elements dt'. At time / this heat will cause a small rise of temperature in the material, in correspondance with equation (1-5): (1-29)

If we substitute t"=t-1'into equation (1 -29), the total temperature rise at time t is obtained by integrating from t"= t (t'= 0) to /"= 0 (t'= t):

(1-30) In order to evaluate this integral, we will make use of the following mathematical transformation:

where

and

Hence, we may write:

The latter integral can be expressed in terms of the complementary error function* erfc{u) by substituting:

and integrating between the limits u = x I (4at)l/2 and w = . This gives (after some manipulation):

(1-31) If the temperature of the contact section at the end of the heating period is taken equal to Th, equation (1-31) can be rewritten as: (1-32)

where t'h denotes the duration of the heating period (t < t'h). Measured contact section temperatures for different metal/alloy combinations are given in Table 1.2. Equation (1-32) may be presented in a dimensionless form by the use of the following groups of parameters: Dimensionless temperature: (1-33) Dimensionless time: (1-34) The complementary error function is defined in Appendix 1.3.

Table 1.2 Measured contact section temperatures during friction welding of some metals and alloys. Data from Tensi et al.10 Metal/Alloy Combination

Measuring Method

Temperature Level [0C]

Partial Melting

Steel

Thermocouples

1080-1340

No

1260-1400

No/Yes

1080

No

Direct readings

1

548

Yes

Copper-Nickel

Direct readings

1

1083

Yes

Al-Cu-2Mg

Thermocouples

506

Yes

Al-4.3Cu

Thermocouples

562

Yes

Al-12Si

Thermocouples

575

Yes

Al-5Mg

Thermocouples

582

Yes

1

Steel-Nickel

Direct readings

Steel-Titanium

Direct readings1

Copper-Al

Based on direct readings of the voltage drop between the two work-pieces.

— Dimensionless .^-coordinate: (1-35)

By substituting these parameters into equation (1-32), we obtain: (1-36)

Equation (1-36) describes the temperature in different positions from the weld contact section during the heating period. However, when the rotation stops, the weld will be subjected to free cooling, since there is no generation of heat at the interface. As shown in Fig. 1.13(a) this can be accounted for by introducing an imaginary heat source of power +qo at time t = t'h which acts simultaneously with an imaginary heat sink of negative power -q o. It follows from the principles of superposition (see Fig. 1.13b) that the temperature during the cooling period is given by:9 (1-37) where 6"(x4) and 6"(T 4 - 1) are the temperatures calculated for the heat source and the heat sink, respectively, using equation (1-36). Equations (1-36) and (1-37) have been solved numerically for different values of Q'and T4. The results are presented graphically in Fig. 1.14. Considering the contact section (Q'= 0), the temperature increases monotonically with time during the heating period, in correspondance with the relationship: (1-38)

q (a) Imaginary heat source Real heat source t Imaginary heat sink

e" (b)

Heating period

$ffl9 \

Fig. 1.13. Method for calculation of transient temperatures during friction welding; (a) Sketch of imaginary heat source/heat sink model, (b) Principles of superposition.

Similarly, for the cooling period we get: (1-39) Outside the contact section (Q / > 0), the temperature rise will be smaller and the cooling rate lower than that calculated from equations (1-38) and (1-39).

Heating

e"

Cooling

\ Fig. 1.14. Calculated temperature-time pattern in friction welding.

Example (1.4)

Consider friction welding of 026mm aluminium rods (Al-Cu-2Mg) under the following conditions:

Calculate the peak temperature distribution across the joint. Assume in these calculations that the thermal diffusivity of the Al-Cu-2Mg alloy is 70mm2 s"1. Solution Readings from Fig. 1.14 give:

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In this particular case, it is possible to check the accuracy of the calculations against in situ thermocouple measurements carried out on friction welded components made under similar conditions. A comparison with the data in Fig. 1.15 shows that the model is quite successful in predicting the HAZ peak temperature distribution. In contrast, the weld heating and cooling cycles cannot be reproduced with the same degree of precision. This has to do with the fact that the present analytical solution omits a consideration of the plastic straining occurring during friction welding, which displaces the coordinates and alters the heat balance for the system.

1.9 Moving Heat Sources and Pseudo-Steady State In most fusion welding processes the heat source does not remain stationary. In the following we shall assume that the source moves at a constant speed along a straight line, and that the net power supply from the source is constant. Experience shows that such conditions lead to a fused zone of constant width. This is easily verified by moving a tungsten arc across a sheet of steel or aluminium, or by moving a soldering iron across a piece of lead or tin. Moreover, zones of temperatures below the melting point also remain at constant width, as indicated by the pattern of temper colours developed on welding ground or polished sheet. It follows from the definition of pseudo-steady state that the temperature will not vary with time when observed from a point located in the heat source. Under such conditions the temperature field around the source can be described as a temperature 'mountain' moving in the direction of welding (e.g. see Fig. 15 in Ref. 11). For points along the weld centre-line, the temperature at different positions away from the heat source (which for a constant welding speed becomes a time axis) may be presented in a two-dimensional plot as indicated in Fig. 1.16. Specifically, this figure shows a schematic representation of the temperature in steel welding from the base plate ahead of the arc to well into the solidified weld metal trailing the arc. If we consider a fixed point on the weld centre-line, the temperature will increase very rapidly during the initial period, reaching a maximum of about 2000-22000C for positions immediately beneath the root of the arc.11 When the arc has passed, the temperature will start to fall, and eventually (after long times) approach that of the base plate. In contrast, an observer moving along with the heat source will always see the same temperature landscape, since this will not change with time according to the presuppositions. It will be shown below that the assumption of pseudo-steady state largely simplifies the mathematical treatment of heat flow during fusion welding, although it imposes certain restrictions on the options of the models.

1.10 Arc Welding Arc welding is a collective term which includes the following processes*: - Shielded metal arc (SMA) welding. - Gas tungsten arc (GTA) welding. - Gas metal arc (GMA) welding. *The terminology used here is in accordance with the American Welding Society's recommendations. 12

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In this particular case, it is possible to check the accuracy of the calculations against in situ thermocouple measurements carried out on friction welded components made under similar conditions. A comparison with the data in Fig. 1.15 shows that the model is quite successful in predicting the HAZ peak temperature distribution. In contrast, the weld heating and cooling cycles cannot be reproduced with the same degree of precision. This has to do with the fact that the present analytical solution omits a consideration of the plastic straining occurring during friction welding, which displaces the coordinates and alters the heat balance for the system.

1.9 Moving Heat Sources and Pseudo-Steady State In most fusion welding processes the heat source does not remain stationary. In the following we shall assume that the source moves at a constant speed along a straight line, and that the net power supply from the source is constant. Experience shows that such conditions lead to a fused zone of constant width. This is easily verified by moving a tungsten arc across a sheet of steel or aluminium, or by moving a soldering iron across a piece of lead or tin. Moreover, zones of temperatures below the melting point also remain at constant width, as indicated by the pattern of temper colours developed on welding ground or polished sheet. It follows from the definition of pseudo-steady state that the temperature will not vary with time when observed from a point located in the heat source. Under such conditions the temperature field around the source can be described as a temperature 'mountain' moving in the direction of welding (e.g. see Fig. 15 in Ref. 11). For points along the weld centre-line, the temperature at different positions away from the heat source (which for a constant welding speed becomes a time axis) may be presented in a two-dimensional plot as indicated in Fig. 1.16. Specifically, this figure shows a schematic representation of the temperature in steel welding from the base plate ahead of the arc to well into the solidified weld metal trailing the arc. If we consider a fixed point on the weld centre-line, the temperature will increase very rapidly during the initial period, reaching a maximum of about 2000-22000C for positions immediately beneath the root of the arc.11 When the arc has passed, the temperature will start to fall, and eventually (after long times) approach that of the base plate. In contrast, an observer moving along with the heat source will always see the same temperature landscape, since this will not change with time according to the presuppositions. It will be shown below that the assumption of pseudo-steady state largely simplifies the mathematical treatment of heat flow during fusion welding, although it imposes certain restrictions on the options of the models.

1.10 Arc Welding Arc welding is a collective term which includes the following processes*: - Shielded metal arc (SMA) welding. - Gas tungsten arc (GTA) welding. - Gas metal arc (GMA) welding. *The terminology used here is in accordance with the American Welding Society's recommendations. 12

- Flux cored arc (FCA) welding. - Submerged arc (SA) welding. The main purpose of this section is to review the classical models for the pseudo-steady state temperature distribution around moving heat sources. The analytical solutions to the differential heat flow equations under conditions applicable to arc welding were first presented (a) Cooling period

Temperature, 0C

Heating period

Predicted heating and cooling cycles for the contact section (x=0)

Time, s

Peak temperature, 0C

(b)

Observed relationship

Predicted relationship

Distance from contact section, mm Fig. 1.15. Comparison between measured and predicted temperatures in friction welding of Al-Cu-2Mg alloys; (a) Temperature-time pattern, (b) Peak temperature distribution. Data from Tensi et al.10

by Rosenthal,1314 but the theory has later been extended and refined by a number of other inve stigators .9'n*15"20 1.10.1 Arc efficiency factors In arc welding heat losses by convection and radiation are taken into account by the efficiency factor r\, defined as: (1-40) where qo is the net power received by the weldment (e.g. measured by calorimetry), / is the welding current (amperage), and U is the arc voltage. For submerged arc (SA) welding the efficiency factor (r\) has been reported in the range from 90 to 98%, for SMA and GMA welding from 65 to 85%, and for GTA welding from 22 to 75%, depending on polarity and materials.11 A summary of ranges is given in Table 1.3. 7.70.2 Thick plate solutions Model (after Rykalin9) According to Fig. 1.17, the general thick plate model consists of an isotropic semi-infinite body at initial temperature T0 limited in one direction by a plane that is impermeable to heat. At time t = 0 a. point source of constant power qo starts on the surface at position O moving in the positive x-direction at a constant speed U The rise of temperature T- T0 in point P at time t is sought. During a very short time interval from ^'to t'+ dt'the amount of heat released at the surface is dQ = qodt'. According to equation (1-7) this will produce an infinitesimal rise of temperature in P at time t:

(1-41)

where

is the time available for conduction of heat over the distance

to point P. For a convenient presentation of the pseudo-steady state solution, the position P should be referred to that of the moving heat source. This is achieved by changing the coordinate system from O to O'(see Fig. 1.17):

and

Hence, we may write:

T

Solidified weld metal

Root of arc

Weld pool

X=Vt Relative position along weld centre-line Fig. 1.16. Schematic diagram showing weld centre-line temperature in different positions from the heat source during steel welding at pseudo-steady state.

Table 1.3 Recommended arc efficiency factors for different welding processes. Data from Refs 11,21. Arc efficiency factor j] Welding Process

Range

Mean

SA welding (steel)

0.91-O.99

0.95

SMA welding (steel)

0.66-0.85

0.80

GMA welding (CO2-steel)

0.75-0.93

0.85

GMA welding (Ar-steel)

0.66-0.70

0.70

GTA welding (Ar-steel)

0.25-0.75

0.40

GTA welding (He-Al)

0.55-0.80

0.60

GTA welding (Ar-Al)

0.22-0.46

0.40

(1-42)

where The total rise of temperature at P is obtained by substituting:

and

into equation (1-42), and integrating between the limits u = (R2l4af)m and u = o°.This gives (after some manipulation): (1-43) It is well-known that:

Hence, the general thick plate solution can be written as:

(1-44)

If u is sufficiently small (i.e. when welding has been performed over a sufficient period), we obtain the pseudo-steady state temperature distribution:

(1-45) This equation is often referred to as the Rosenthal thick plate solution,1314 in honour of D. Rosenthal who first derived the relation by solving the differential heat flow equation directly for the appropriate boundary conditions. 1.10.2.1 Transient heating period It follows from the above analysis that the pseudo-steady state temperature distribution is

Fig. 1.17. Moving point source on a semi-infinite slab. attained after a transient heating period. The duration of this heating period is determined by the integral in equation (1-44). Taking the ratio between the real and the pseudo-steady state temperature equal to K1, we have: (1-46) Equation (1-46) can be expressed in terms of the following parameters: Dimensionless radius vector: (1-47) Dimensionless time: (1-48) Substituting these into equation (1-46) gives: (1-49)

where

and

Equation (1-49) has been solved numerically for a limited range of cr3 and x. The results are presented graphically in Fig. 1.18. A closer inspection of Fig. 1.18 reveals that the duration of the transient heating period depends on the dimensionless radius vector a 3 . In practice this means that the Rosenthal equation is not valid during the initial period of welding unless the distance from the heat source to the observation point is very small. It should be noted, however, that a dimensionless distance o~3 may be 'short' for one combination of welding speed and thermal diffusivity, while the same position may represent a 'long' distance for another combination of V and a. Similarly, the dimensionless time T may be 'short' or 'long' at a chosen number of seconds, depending on the ratio v/2a. Example (1.5)

Consider stringer bead deposition on a thick plate of aluminium at a constant welding speed of 5 mm s"1. Calculate the duration of the heating period when the distance from the heat source to the point of observation is 17 mm. Solution

Ki = (T-T0)/(T-T0)p.s.

Taking a = 85 mm2 s"1, the dimensionless radius vector becomes:

T = v2t/2a Fig. 1.18. Ratio between real and pseudo-steady state temperature in thick plate welding for different combinations ofCT3and T.

It is seen from Fig. 1.18 that the pseudo-steady state temperature distribution is approached when T ~ 3, which gives:

This corresponds to a total bead length of:

The above calculations show that the Rosenthal equation is not valid if the ratio between R and L2 exceeds a certain critical value (typically 0.15 to 0.30 for aluminium welds and 0.4 to 0.6 for steel welds). This important point is often overlooked when discussing the relevance of the thick plate solution in arc welding. 1.10.2.2 Pseudo-steady state temperature distribution The Rosenthal equation gives, with the limitations inherent in the assumptions, full information on the thermal conditions for point sources on heavy slabs. Accordingly, in order to obtain a general survey of the pseudo-steady state temperature distribution, it is convenient to present the different solutions in a dimensionless form. The following parameters are defined for this purpose:11 — Dimensionless operating parameter: (1-50) Dimensionless jc-coordinate: (1-51) Dimensionless ^-coordinate: (1-52) Dimensionless z-coordinate: (1-53) By substituting these parameters into equation (1-45), we obtain: (1-54) where 6 and a 3 are the dimensionless temperature and radius vector, respectively (previously defined in equations (1-9) and (1-47)). Equation (1-54) has been solved numerically for chosen values of a 3 and £. A graphical presentation of the different solutions is shown in Fig. 1.19. These maps provide a good

e/n3

(a)

% Fig, /./P.Dimensionless temperature maps for point sources on heavy slabs; (a) Vertical sections parallel to the ^-axis. overall indication of the thermal conditions during thick plate welding, but are not suitable for precise readings. Consequently, for quantitative analyses, the following set of equations can be used:11 Isothermal zone widths The maximum width of an isothermal enclosure is obtained by setting 3ln(0M3)/9a3 = 0:

From the definition of a 3 we have:

(b)

%

V

%

V Fig. /.iP.Dimensionless temperature maps for point sources on heavy slabs (continued): (b) Isothermal contours in the £-\}/-plane for different ranges of 0/n3. Partial differentiation of the Rosenthal equation gives:

and (1-55) Equation (1-55) can be used for calculations of isothermal zone widths V|/w and cross sectional areas A1. From Fig. 1.20 we have: (1-56) and (1-57) A graphical presentation of equations (1-55), (1-56), and (1-57) is shown in Fig. 1.21. Length of isothermal enclosures Referring to Fig. 1.20, the total length of an isothermal enclosure £r is given by: (1-58) where £' and £"are the distance from the heat source to the front and the rear of the enclosure, respectively.

x,S Heat source

y.v

z, C

Fig. 1.20.Three-dimensional graphical representation of Rosenthal thick plate solution (schematic).

Vm,O3m,Al

1

V9P

Fig. 1.21. Dimensionless distance a3m, half width \|/m and cross sectional area A1 vs n3 /Qp. The coordinates £' and £" are found by setting a 3 = ± ^ in equation (1-54). This gives: (1-59)

and (1-60)

Volume of isothermal enclosures Since the assumption of a point heat source involves semi-circular isotherms in the \|/-£ plane, the volume of an isothermal enclosure is obtained by integration over the total length from £" tor: (1-61) The former integral is readily evaluated by substituting:

which follows from a differentiation of equation (1-54). Hence, we may write:

(1-62)

Noting that IaIv1), it is a fair approximation to set K0 (x)« exp(-x)Vrc/2x (see Fig. 1.27). Hence, equation (1-83) reduces to: (1-91) Equation (1-91) provides a basis for calculating the cooling time within a specific temperature interval (e.g. from O1 to 02):

(1-92)

The dimensionless cooling time from 800 to 5000C is thus given by:

(1-93) from which the real cooling time is obtained: (1-94) Taking as average values X = 0.025 W mm"1 0C"1, pc = 0.005 J mm"3 0C"1, and T0 = 200C for welding of low alloy steels, we have:

d-95) Similarly, the cooling rate at a specific temperature is obtained by differentiating equation (1-91) with respect to time: (1-96)

By multiplying equation (1-96) with the appropriate conversion factor, we get:

(1-97)

For welding of low alloy steels, the cooling rate becomes:

(1-98)

Example (LlO)

Consider GTA butt welding of a 2mm thick sheet of cold-rolled aluminium (Al-Mg alloy) under the following conditions:

Sketch the contours of the fusion boundary and the Ar-isotherm in the £-\|/ (x-y) plane at pseudo-steady state. The recrystallisation temperature Ar of the base material is taken equal to 2750 C. Calculate also the cross sectional area of the fully recrystallised HAZ and the cooling rate at 2750C for points located within this region. Solution Referring to Fig. 1.22(a) (Example (1.6)) it is sufficient to calculate the coordinates in four different (characteristic) positions to sketch the contour of the fusion boundary. If we neglect the latent heat of melting, the n3/68 ratio at the melting point becomes:

End-points The end-points can be read from Fig. 1.32:

and

Maximum widths The maximum width of an isothermal enclosure can generally be calculated from equations (1-86) and (1-87) or read from Fig. 1.31. When n3/QpS = 0.84, we obtain:

and

Intersection point with y/(y)-axis In this case £ = 0 and cr5 = \j/. Hence, equation (1-83) reduces to:

which gives

Similarly, the contour of the Ar-isotherm can be determined by inserting n3/db = 2.08 into the same set of equations. Figure 1.33 shows a graphical representation of the calculated isothermal contours.

V

§ x(mm)

y(mm) Fig. 1.33. Calculated contours of fusion boundary and Ar-isotherm in GTA butt welding of a 2mm thick aluminium plate (Example 1.10).

Cross sectional area of fully recrystallised HAZ In general, cross sectional areas can be read from Fig. 1.31. Taking the n3/OpS ratio equal to 0.84 (Qp= 1) and 2.08 (8 p = 0.48), respectively, we have:

which gives

Cooling rate at 275 0C The cooling rate at a specific temperature can be calculated from equation (1-97). In the present case, we obtain:

1.10.3.3 Simplified solution for a fast moving high power source Model (after Rykalin9) It follows from Fig. 1.29 that the isotherms behind the heat source become increasingly elongated as the 08M3 ratio decreases. In the limiting case the isotherms will degenerate into surfaces which are parallel to the welding x direction, as shown in Fig. 1.34. In a short time interval dt the amount of heat released per unit length of the weld is equal to:

(1-99) According to the assumptions this amount of heat will remain in a rod of constant cross sectional area due to the lack of a temperature gradient in the welding direction. Under such conditions the mode of heat flow becomes essentially one-dimensional, and the temperature distribution is given by equation (1-5): (1-100) Equation (1-100) represents the simplified solution for a fast moving high power source* in a thin sheet, and is valid within a limited range of the more general Rosenthal equation for twodimensional heat flow (equation (1-81)). By substituting the appropriate dimensionless parameters into equation (1-100), we obtain:

* Since the shape of a given isotherm in the x-y plane is determined by the qjd ratio, the minimum welding speed which is required to maintain 1-D heat flow increases with decreasing qjVd ratios. Hence, the term 'fast moving high power source' is also appropriate in the case of the thin plate welding.

Fig. 1.34. Fast moving high power source in a thin plate.

(1-101) The locus of the peak temperatures is readily evaluated from equation (1-101) by setting 3ln(e8M3)/3T = 0:

which gives

and (1-102) It is evident from the plot in Fig. 1.35 that the predicted width of the isotherms is always greater than that inferred from the general thin plate solution (equation (1-83)) due to the assumption of one-dimensional heat flow. However, such deviations become negligible at very small Qpb/n3 ratios because of a small temperature gradient in the welding x direction compared to the transverse y direction of the plate. A general graphical representation of the weld thermal programme (similar to that shown in Fig. 1.25 for a fast moving high power source on a heavy slab) can be obtained by combining equations (1-101) and (1-102):

¥m(1-D)/¥m(a-D)

Asymptote

0 p 8/n 3

e/ep

Fig. 1.35. Theoretical width of isotherms under 1-D and 2-D heat flow conditions, respectively at pseudosteady state (thin plate welding).

2t/(vm)2 Fig. 1.36. Temperature-time pattern in thin plate welding at high arc power and high welding speed.

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(1-103) Equation (1-103) has been plotted in Fig. 1.36. Example (LU) Consider butt welding of a 2mm thin plate of austenitic stainless steel with covered electrodes (SMAW) under the following conditions:

Calculate the retention time within the critical temperature range for chromium carbide precipitation (i.e. from 650 to 8500C) for points located at the 8500C isotherm. Solution

If we use the melting point of the steel as a reference temperature, the parameter n3/5 becomes:

A comparison with Fig. 1.35 shows that the assumption of 1-D heat flow is justified when Qp< 1. Hence, the total time spent in the thermal cycle from 6 = 0.43 (T = 6500C) to 0p = 0.56 (Tp = 8500C) and down again to 0 = 0.43 can be read from Fig. 1.36. Taking the ordinate 0/0p equal to 0.76, we obtain:

which gives

and

1.10.4 Medium thick plate solution In a real welding situation the assumption of three-dimensional or two-dimensional heat flow inherent in the Rosenthal equations is not always met because of variable temperature gradients in the through thickness z direction of the plate. Model (after Rosenthal14)

The general medium thick plate model considers a point heat source moving at constant speed across a wide plate of finite thickness d. With the exception of certain special cases (e.g. watercooling of the back side of the plate), it is a reasonable approximation to assume that the

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(1-103) Equation (1-103) has been plotted in Fig. 1.36. Example (LU) Consider butt welding of a 2mm thin plate of austenitic stainless steel with covered electrodes (SMAW) under the following conditions:

Calculate the retention time within the critical temperature range for chromium carbide precipitation (i.e. from 650 to 8500C) for points located at the 8500C isotherm. Solution

If we use the melting point of the steel as a reference temperature, the parameter n3/5 becomes:

A comparison with Fig. 1.35 shows that the assumption of 1-D heat flow is justified when Qp< 1. Hence, the total time spent in the thermal cycle from 6 = 0.43 (T = 6500C) to 0p = 0.56 (Tp = 8500C) and down again to 0 = 0.43 can be read from Fig. 1.36. Taking the ordinate 0/0p equal to 0.76, we obtain:

which gives

and

1.10.4 Medium thick plate solution In a real welding situation the assumption of three-dimensional or two-dimensional heat flow inherent in the Rosenthal equations is not always met because of variable temperature gradients in the through thickness z direction of the plate. Model (after Rosenthal14)

The general medium thick plate model considers a point heat source moving at constant speed across a wide plate of finite thickness d. With the exception of certain special cases (e.g. watercooling of the back side of the plate), it is a reasonable approximation to assume that the

plate surfaces are impermeable to heat. Thus, in order to maintain the net flux of heat through both boundaries equal to zero, it is necessary to account for mirror reflections of the source with respect to the planes of z = 0 and z = d. This can be done on the basis of the 'method of images' as illustrated in Fig. 1.37. By including all contributions from the imaginary sources ...2q__2 , 2g_i , 2q\ , 2q2 ,...located symmetrically at distances ± 2id below and above the upper surface of the plate, the pseudo-steady state temperature distribution is obtained in the form of a convergent series*:

(1-104)

where Note that equation (1-104) is simply the general Rosenthal thick plate solution (equation (1-45)) summed for each source.

Fig. 1.37. Real and imaginary point sources on a medium thick plate. *The number of imaginary heat sources necessary to achieve the required accuracy depends on the chosen values of R0 and vd/2a.

By substituting the dimensionless parameters defined above into equation (1-104), we obtain: (1-105) where

It follows from equation (1-104) that the thermal conditions will be similar to those in a thick plate close to the centre of the weld. Moreover, Rosenthal1314has shown on the basis of a Fourier series expansion that equation (1-104) converges to the general thin plate solution (equation (1-81) for points located sufficiently far away from the source. However, at intermediate distances from the heat source, the pseudo-steady state temperature distribution will deviate significantly from that observed in thick plate or thin plate welding because of variable temperature gradients in the through-thickness direction of the plate. Within this 'transition region', the thermal programme is only defined by the medium thick plate solution (equation (1-104)). 1.10.4.1 Dimensionless maps for heat flow analyses Based on the models described in the previous sections, it is possible to construct a series of dimensionless maps which provide a general outline of the pseudo-steady state temperature distribution during arc welding.20 Construction of the maps The construction of the maps is done on the basis of the medium thick plate solution (equation (1-105)). This model is generally applicable and allows for the plate thickness effect in a quantitative manner. Since the other solutions are only valid within specific ranges of this equation, they will have their own characteristic fields in the temperature-distance or the temperature-time space. The extension of the different fields can be determined from numerical calculations of the temperature distribution by comparing each of these models with the medium thick plate solution, using a conformity of 95% as a criterion. Similarly, when the 95% conformity is not met between the respective solutions, the fields are marked 'transition region'. Since any combination of dimensionless temperature, operating parameter, and plate thickness locates a point in a field, it means that the dominating heat flow mechanism can readily be read off from the maps. Peak temperature distribution The variation of peak temperature with distance in the \j/(^j-direction has been numerically evaluated from equation (1-105) for different values of the dimensionless plate thickness (8 = vdlla). The results are shown graphically in Fig. 1.38(a) and (b) for the two extreme cases of £ = 0 (z = 0) and £ = 8 (z = d), respectively. An inspection of the maps reveals that the temperature-time pattern in stringer bead weldments can be classified into three main categories:

(a)

VV

Thin plate solution (2-D heat flow) (1-D heat flow)

¥

%

Y

m

(b) Thin plate solution 1-D heat flow

V"3

(2-D heat flow)

Y

m

Fig. 1.38. Peak temperature distribution in transverse direction (\|/ = \\fm) of plate; (a) Upper plate surface (^ = 0), (b) Lower plate surface (J = 8).

1. Close to the heat source, the thermal programme will be similar to that in a thick plate (Fig. 1.38(a)), which means that the temperature distribution is determined by equation (154). For large values of the dimensionless plate thickness, the mode of heat flow may become essentially two-dimensional. This corresponds to the limiting case of a fast moving high power source in a thick plate (equation (1-74)). Under such conditions the slope of the Qp/n3-\ym curves in Fig. 1.38(a) attains a constant value of-2. 2. With increasing distance from the heat source, a transition from three-dimensional to two-dimensional heat flow may occur, depending on the dimensionless plate thickness and the operational conditions applied. Considering the upper surface of the plate (Fig. 1.38(a)), the extension of the transition region is seen to decrease with increasing values of 8 as the conditions for thick plate welding are approached. The opposite trend is observed for the bottom plate surface (Fig. 1.38(b)), since a small dimensionless plate thickness generally results in a more rapid equalisation of the temperature gradients in the t,(z) direction. When the curves in Fig. 1.38(b) become parallel with the jc-axis, the temperature at the bottom of the plate reaches its maximum value. Note that within the transition region, reliable predictions of the pseudo-steady temperature distribution can only be made from the medium thick plate solution (equation (1-105)). 3. For points located sufficiently far away from the heat source, the temperature gradients in the through-thickness direction of the plate become negligible. This implies that the temperature distribution at the upper and lower surface of the plate is similar, and can be computed from the thin plate solution (equation (1-83)). When the conditions for onedimensional heat flow are approached (equation (1-101)), the slope of the dp/n3-\\fm curves in Fig. 1.38(a) and (b) attains a constant value o f - 1 . Cooling conditions close to weld centre-line Figure 1.39 contains a plot of the cooling programme for points located on the weld centre-line (\j/ = £ = 0), as calculated from equation (1-105). A closer inspection of Fig. 1.39 reveals that the slope of the cooling curves increases gradually from -1 to -0.5 with increasing distance from the heat source. This corresponds to a change from three-dimensional to one-dimensional heat flow. From Fig. 1.39 it is possible to read-off the cooling time within specific temperature intervals for a wide range of operational conditions. These results are also valid for positions outside the weld centre-line, since the cooling curves are virtually parallel in the transverse \|/ direction of the plate. A requirement is, however, that the peak temperature of the thermal cycle is significantly higher than the actual temperature interval under consideration. Retention times at elevated temperatures The retention time, Axn is defined as the total time spent in a thermal cycle from a chosen reference temperature 0 to the peak temperature dp and down again to 9. This parameter can readily be computed from equation (1-105) by means of numerical methods. The results of such calculations (carried out in position £ = 0) are shown graphically in Fig. 1.40 for 9 = 0.5 An inspection of Fig. 1.40 reveals a complex temperature-time pattern. In this case it is not possible to determine the exact field boundaries between the respective solutions, since the

e/n3

e/n3

Thin plate solution (2-D heat flow) (1-D heat flow)

T= ^

e/n 3

X Fig. 1.39. Cooling programme for points located on the weld centre-line (\\f = £ =0).

6

T

AXf

Fig. 1.40. Total time spent in a thermal cycle from 9 through 9p to 9 for a chosen reference temperature of 9 = 0.59p.

mode of heat flow may vary within a single thermal cycle. Hence, the extension of the different fields is not indicated in the graph. The results in Fig. 1.40 provide a systematic basis for calculating the retention time within specific temperature intervals under various welding conditions. Isothermal contours Because of the number of variables involved, it is not possible to present a two-dimensional plot of the isotherms without first specifying the dimensionless plate thickness. Examples of calculated isotherms in different planes are shown in Figs. 1.41 and 1.42 for 8 equal to 0.5 and 5, respectively. It is evident that an increase in the dimensionless plate thickness from 0.5 to 5 has a dramatic effect on the shape and position of the isothermal contours. However, in order to explain these observations in an adequate manner, it is necessary to condense the results into a two-dimensional diagram. As shown in Fig. 1.43, this can be done by plotting the calculated field boundaries in Fig. 1.38(a) at maximum width of the isotherms vs the parameters Qp/n3

and vdlla. It is seen from Fig. 1.43 that a large plate thickness generally will favour three-dimensional heat flow. With decreasing values of Qp/n3, the conditions for a fast moving high power source are approached before the transition from the thick plate to the thin plate solution occurs. In such cases the isotherms at the bottom of the plate will be strongly elongated in the welding £ direction and shifted to positions far behind the heat source. The opposite trend is observed at small values of vdlla, since a rapid equalisation of the temperature gradients in the throughthickness direction of the plate will result in elliptical isotherms at both plate surfaces, located in an approximately equal distance from the heat source. In either case the temperature at which the cross-sectional isotherms approach a semi-circle or become parallel with the XXz)axis can be obtained from Fig. 1.43 by reading-off the intercept between the line for the dimensionless plate thickness and the respective field boundaries. Limitations of the maps Since the maps have been constructed on the basis of the analytical heat flow equations, it is obvious that they will apply only under conditions for which these equations are valid. The simplifying assumptions inherent in the models can be summarised as follows: (a)

The parent material is isotropic and homogeneous at all temperatures, and no phase changes occur on heating.

(b)

The thermal conductivity, density, and specific heat are constant and independent of temperature.

(c)

The plate is completely insulated from its surroundings, i.e. there are no heat losses by convection or radiation from the boundaries.

(d)

The plate is infinite except in the directions specifically noted.

(e)

The electrode is not consumed during welding, and all heat is concentrated in a zero-volume point or line.

(a)

¥

C

(b)

%

C

(C)

V

C Fig. 1.41. Computed isothermal contours in different sections for 8 = 0.5; (a) Front view (\j/ = \|/m), (b) Side view (\|/ = 0), (c) Top view (£ = 0) and bottom view (£ = 8).

(a)

¥

C

(b)

%

C

(C)

v

V

\Fig. 1.42.Computed isothermal contours in different sections for 8 = 5; (a) Front view (\|/ = \|/m); (b) Side view (\|/ = 0); (c) Top view (£ = 0) and bottom view (£ = 8).

ep/n3

Thick plate solution (3-D heat flow)

Thin plate solution

1-D heat flow Thick plate solution (2-D heat flow)

5 = vd/2a Fig. 1.43. Heat flow mechanism map showing calculated field boundaries in transverse direction (i|/ = i|/m) of plate vs Qp/n3 and 8 = vdlla.

(f)

Pseudo-steady state, i.e. the temperature does not vary with time when observed from a point located in the heat source.

In general, the justification of these assumptions relies on a good correlation between theory and experiments. However, since the analytical solutions ignore the important role of arc energy distribution and directed metal currents in the weld pool, predictions of the weld thermal programme should be restricted to positions well outside the fusion zone where such effects are of less importance (to be discussed below). Example (1.12)

Consider stringer bead welding (GMAW) on a 12mm thick plate of aluminium (> 99% Al) under the following conditions:

Based on Fig. 1.43, sketch the peak temperature contours in the transverse section of the weld at pseudo-steady state.

Solution If we neglect the latent heat of melting, the parameter n3 at the chosen reference temperature (Tc = Tm) becomes:

Similarly, when v = 3mm s l and a = 85mm2 s"1 we obtain the following value for the dimensionless plate thickness:

Readings from Fig. 1.43 give: ep

^, (0C)

Model System

Comments

0.50 —• 1.0

340 —• 660

Medium thick plate solution

Heat flow in x and y directions, partial heat flow in z direction

0.17 -> 0.50

130 -> 340

Thin plate solution (2-D heat flow)

Heat flow in x and y directions, negligible heat flow in z direction

< 0.17

< 130

Thin plate solution (1 -D heat flow)

Heat flow in y direction, negligible heat flow in x and z directions

A sketch of the HAZ peak temperature contours in the transverse section of the weld is shown in Fig. 1.44. Case Study (Ll) Consider stringer bead GMA welding on 12.5mm thick plates of low alloy steel and aluminium (i.e. a Al-Mg-Si alloy), respectively under the conditions E = 1.5 kJ mm"1 and r\ = 0.8. Details of welding parameters for the four series involved are given in Table 1.4. Computed peak temperature contours in the transverse section of the welds are given in Figs. 1.45 and 1.46.

Arrows indicate heat flow directions

Fusion zone

Fig. 1.44. Schematic diagram showing specific peak temperature contours within the HAZ of an aluminium weld at pseudo-steady state (Example 1.12).

WELD A1 y(mm)

(b)

WELD A2

z(mm)

(a)

z(mm)

y(mm)

Fig. 1.45. Computed peak temperature contours in aluminium welding at pseudo-steady state (Case study 1.1); (a) Weld Al, (b) Weld A2. Black regions indicate fusion zone.

Aluminium welding In general, the maximum width of the isotherms at the upper and lower surface of the plate can be obtained from Fig. 1.38(a) and (b), although these maps are not suitable for precise readings. A comparison with the computed peak temperature contours in Fig. 1.45(a) and (b) reveals a strong influence of the welding speed on the shape and position of the cross-sectional isotherms at a constant gross heat input of 1.5 kJ mm"1. It is evident that the extension of the fusion zone and the neighbouring isotherms becomes considerably larger when the welding speed is increased from 2.5 to 5 mm s"1. This effect can be attributed to an associated shift from elliptical to more elongated isotherms at the plate surfaces (e.g. see Fig. 1.43), which reduces heat conduction in the welding direction. It follows from Fig. 1.43 that the upper left corner of the map represents the typical operating region for aluminium welding. Because of the pertinent differences in the heat flow conditions, the temperature-time pattern will also vary significantly between the respective series as indicated by the maps in Figs. 1.39 and 1.40. Hence, in the case of aluminium welding the usual procedure of reporting arc power and travel speed in terms of an equivalent heat input per unit length of the bead is highly questionable, since this parameter does not define the weld thermal programme. In general, the correct course would be to specify both qo, v and d, and compare the weld thermal history on the basis of the dimensionless parameters n3 and 8. Steel welding If welding is performed on a steel plate of similar thickness, the operating region will be shifted to the lower right corner of Fig. 1.43. Under such conditions, the isotherms adjacent to the fusion boundary will be strongly elongated in the x-direction even at very low welding speeds (see Fig. 1.42). This implies that the thermal programme approaches a state where the temperature distribution is uniquely defined by the net heat input r\E, corresponding to the

(a)

W E L D S1

z(mm)

y(mm)

(b)

WELD S2

z(mm)

y(mm)

Fig. 7.46.Computed peak temperature contours in steel welding at pseudo-steady state (Case study 1.1); (a) Weld Sl, (b) Weld S2. Black regions indicate fusion zone.

Table 1.4 Operational conditions assumed in Case study (1.1). qo

V

d

E

Series

(W)

(mras"1)

(mm)

(kJmrrr 1 )

Al-Mg-Si alloy

Al A2

6000 3000

5 2.5

12.5 12.5

Low alloy steel

Sl S2

9600 4800

8 4

12.5 12.5

Material

n3

8

1.5 1.5

0.36 0.09

0.50 0.25

1.5 1.5

32.6 8.2

10 5

limiting case of a fast moving high power source. As a result, the calculated shape and width of the fusion boundary and neighbouring isotherms are seen to be virtually independent of choice of qo and v as illustrated in Fig. 1.46(a) and (b). 1.10.4.2 Experimental verification of the medium thick plate solution It is clear from the above discussion that the medium thick plate solution provides a systematic basis for calculating the temperature distribution within the HAZ of stringer bead weldments under various welding conditions. In the following, the accuracy of the model will be checked against extensive experimental data, as obtained from in situ thermocouple measurements and numerical analyses of a large number of bead-on-plate welds. Weld thermal cycles Examples of measured and predicted weld thermal cycles in aluminium welding are presented in Fig. 1.47. It is evident that the medium thick plate solution predicts adequately the HAZ temperature-time pattern under different heat flow conditions for fixed values of the peak temperature. This, in turn, implies that the model is also capable of predicting the total time spent in a thermal cycle within a specific temperature interval as shown in Fig. 1.48. Weld cooling programme At temperatures representative of the austenite to ferrite transformation in mild and low alloy steel weldments, the conditions for a fast moving high power source are normally approached before the transition from thick plate to thin plate welding occurs (see Fig. 1.39). In such cases, it is possible to present the different solutions for Ax875 (at \|/ = £ = 0) in a single graph by introducing the following groups of variables*:

Ordinate:

Abscissa: Relevant literature data for the cooling time between 800 and 5000C are given in Fig. 1.49. A closer inspection of the figure reveals a reasonable agreement between observed and predicted values in all cases. For welding of thick plates, the ordinate attains a constant value of 1. Similarly, in thin sheet welding, the slope of the curve becomes equal to 1. In aluminium welding, the thermal conditions will be much more complex because of the resulting higher base plate thermal diffusivity (see Fig. 1.39). Hence, it is not possible to describe the weld cooling programme in terms of equations (1-74) and (1-101), which apply to fast moving high power sources. The plot in Fig. 1.50 confirms, however, that the medium thick plate solution is also capable of predicting the cooling time within specific temperature intervals (e.g. from 300 to 1000C) in aluminium weldments.

These groups of variables can be obtained from equations (1-74) and (1-101).

Measured Predicted

Temperature (0C)

GMAW: q 0 = 3872 W, v = 8.8 mm/s, d =8 mm

Time (sec)

A tr(s), observed

Fig. 1.47. Comparison between measured and predicted weld thermal cycles in aluminium welding for fixed values of Tp. Data from Myhr and Grong.20

T

P t

A tr(s), predicted Fig. /.4#. Comparison between measured and predicted retention times in aluminium welding for fixed values of Tp. Data from Myhr and Grong.20

8/5 AT

n 3 [-i--4-

1

SMAW SMAW SAW SAW THICK PLATE SOLUTION

THIN PLATE SOLUTION

-2Hr + Ir 1 5 6SOO 6SOO Fig. 1.49. Comparison between observed and predicted cooling times from 800 to 5000C in steel welding (solid lines represent theoretical calculations). Data from Myhr and Grong.20

At

(sec), observed

GMAW (Al+2.5 wt% Mg)

T(0C)

t(sec)

At

(sec), predicted

Fig. 1.50. Comparison between observed and predicted cooling times from 300 to 1000C in aluminium welding. Data from Myhr and Grong.20

Peak temperatures and isothermal contours Figure 1.51 shows a comparison between measured and predicted HAZ peak temperatures in aluminium welding. It is evident that the relative positions of the HAZ isotherms can be calculated with a reasonable degree of accuracy from the medium thick plate solution, provided that the equation is precalibrated against a known isotherm (i.e. the fusion boundary). Additional information on the HAZ peak temperature distribution in aluminium welding can be obtained from the data of Koe and Lee21 reproduced in Fig. 1.52. These numerical calculations* showed a good correlation with experimental measurements. A comparison with the medium thick plate solution in Fig. 1.52 reveals a fair agreement between numerically and analytically computed isothermal contours. It is interesting to note that even though the plate thickness is small (i.e. 3.2mm), the mode of heat flow becomes essentially three-dimensional close to the fusion boundary. This important point is often overlooked when discussing the relevance of the analytical heat flow models in thin sheet welding. LlOAJ Practical implications The following important conclusions can be drawn from the results presented in Figs. 1.381.52:

Tp, 0C , observed

GMAW (Al +2.5 wt% Mg)

Tp, 0C , predicted Fig. 1.51. Comparison between observed and predicted HAZ peak temperatures in aluminium welding. Data from Myhr and Grong.20 Based on the finite difference method (FDM).

Z (mm)

y (mm)

Fig. 1.52. Comparison between numerically and analytically computed peak temperature contours in GTA welding of a 3.2mm thin aluminium sheet. (Broken lines: numerical model; solid lines: analytical model.) Data for welding parameters and material properties are given in Ref. 21.

1. Considering heat flow and temperature distribution in fusion welding, there exists no defined plate thickness which can be regarded as 'thick' or 'thin'. Accordingly, in a real welding situation, the mode of heat flow will vary continuously with increasing distance from the heat source. 2. Close to the centre of the weld, the thermal conditions will be similar to those in a heavy slab. This means that the temperature distribution is approximately described by the Rosenthal thick plate solution. 3. At intermediate distances from the heat source, the temperature distribution will deviate significantly from that observed in thick plate welding because of variable temperature gradients in the through-thickness direction of the plate. Within this transition region, reliable predictions of the pseudo-steady state temperature distribution can only be made from the medium thick plate solution. 4. For points located sufficiently far away from the heat source, the temperature gradients in the through-thickness direction of the plate become negligible. Under such conditions, the weld thermal programme is approximately defined by the Rosenthal thin plate solution. 5. In general, a full description of the weld thermal history requires that both the arc power qo, the travel speed V, and the plate thickness d are explicitly specified. Hence, the usual procedure of reporting welding variables in terms of an equivalent heat input per unit length of the bead, £(kJ mm"1), is highly questionable, since this parameter does not define the weld thermal programme. An exception is welding of thick steel plates, where the temperature distribution approaches that of a fast moving high power source because of a low thermal diffusivity of the base metal. 6. A comparison between theory and experiments shows that the medium thick plate solution predicts adequately both the peak temperature distribution and the temperaturetime pattern within the HAZ of stringer bead weldments for a wide range of operational conditions (including aluminium and steel welding). A requirement is, however, that the equation is calibrated against a known isotherm (e.g. the fusion boundary) due to the simplifying assumptions inherent in the model.

1.10.5 Distributed heat sources In some cases it is also necessary to consider the important influence of filler metal additions, arc energy distribution, and convectional heat flow in the weld pool on the resulting bead morphology to obtain a good agreement between theory and experiments. Of particular interest in this respect is the formation of the so-called weld crater/weld finger, frequently observed in GMA and SA stringer bead weldments (see Fig. 1.53). Although the nature of these phenomena is very complex, they can readily be accounted for by applying an empirical correction for the effective heat distribution in the weld pool. 1.10.5.1 General solution Model (after Myhr and Grong22) The heat distribution used to simulate the weld crater/weld finger formation is shown schematically in Fig. 1.54(a). Here we consider two discreate distributions of elementary point sources, which extend in the y- and z-direction of the plate, respectively. The contribution from each source to the temperature rise in an arbitrary point P located within the plate is calculated on the basis of the "method of images", as shown in Fig. 1.54(b) and (c). For a heat source displaced in the y-direction (Fig. 1.54(b)), the temperature field is given by equation (1 104):

(1-106) where

y Crater

HAZ"

Finger Fusion line

Z Fig. 1.53. Schematic diagram showing the weld crater/weld finger formation during stringer bead welding.

(a)

y

X

Z

(b)

y

Z Fig. 1.54. General heat flow model for welding on medium thick plates; (a) Physical representation of the heat distribution by elementary point sources, (b) Method for calculating the temperature field around an elementary point source displaced along the y-axis.

(C)

y

Z Fig. 1.54. General heat flow model for welding on medium thick plates(continued): (c) Method for calculating the temperature field around an elementary (submerged) point source displaced along the z-axis. Similarly, for a submerged point source located along the z-axis (Fig. 1.54(c))> we obtain:

(1-107)

where and

Note that equation (1-107) correctly reduces to equation (1-106) when A approaches zero. The total temperature rise in point P is then obtained by superposition of the temperature fields from the different elementary heat sources, i.e.: (1-108) where

In practice, we can subdivide the heat distributions into a relatively small number of elementary point sources, and usually a total number of 8 to 10 sources is sufficient to obtain good results (i.e. smooth curves). However, the relative strength of each heat source and their distribution along the y- and z-axes must be determined individually by trial and error by comparing the calculated shape of the fusion boundary with the real (measured) one. Figure 1.55 shows the results from such calculations, carried out for a single pass (bead-ingroove) GMA steel weld. It is evident that the important effect of the weld crater/weld finger formation on the HAZ peak temperature distribution is adequately accounted for by the present model. A weakness of the model is, of course, that the shape and location of the fusion boundary must be determined experimentally before a prediction can be made. 1.10.5.2 Simplified solution Similar to the situation described above, the point heat source will clearly not be a good model when the heat is supplied over a large area. Welding with a weaving technique and surfacing with strip electrodes are prime examples of this kind. Model (after Grong and Christensen19)

As a first simplification, the Rosenthal thick plate solution is considered for the limiting case of a high arc power qo and a high welding speed D, maintaining the ratio qo Iv within a range applicable to arc welding. Consider next a distributed heat source of net power density qo I2L extending from -L to +L on either side of the weld centre-line in the y-direction*, as shown schematically in Fig. 1.56. It follows from equation (1-73) that an infinitesimal source dqy located between y and y + dy will cause a small rise of temperature in point P at time f, as: (1-109) where

and

Alternatively, we can use a Gaussian heat distribution, as shown in Appendix 1.4.

z (mm)

Shaded region indicates fusion zone

y (mm) Fig. 1.55. Calculated peak temperature contours in the transverse section of a GMA steel weldment (Operational conditions: / = 450A, U - 30V, v = 2.6mm s"1, d = 50mm).

2-D heat flow

Fig. 1.56. Distributed heat source of net power density qJ2L on a semi-infinite body (2-D heat flow).

(1-110)

where erf(u) is the Gaussian error function (previously defined in Appendix 1.3). Peak temperature distribution Because of the complex nature of equation (1-110), the variation of peak temperature with distance in the y-z plane can only be obtained by numerical or graphical methods. Accordingly, it is convenient to present the different solutions in a dimensionless form. The following parameters are defined for this purpose: — Dimensionless operating parameter:

(1-111)

Dimensionless time: (1-112) Dimensionless y-coordinate: (1-113) Dimensionless z-coordinate: (1-114) By substituting these parameters into equation (1-110), we obtain:

(1-115)

where 0 is the dimensionless temperature (previously defined in equation (1-9)).

The variation of peak temperature Qp with distance in the y-z plane has been numerically evaluated from equation (1-115) for chosen values of P and 7 (i.e. P = 0, (3 = 3/4, P = I , and 7 = 0). The results are presented graphically in Figs. 1.57 and 1.58 for the through thickness (z = zm) and the transverse (y = ym) directions, respectively. These figures provide a systematic basis for calculating the shape of the weld pool and neighbouring isotherms under various welding conditions. In Fig. 1.59 the weld width to depth ratio has been computed and plotted for different combinations of nw and 9p. It is evident that the predicted width of the isotherms generally is much greater, and the depth correspondingly smaller than that inferred from the point source model. Such deviations tend to become less pronounced with decreasing peak temperatures (i.e. increasing distance from the heat source). At very large value of nw, the theoretical shape of the isotherms approaches that of a semi-circle, which is characteristic of a point heat source. Example (1.13)

Consider GMA welding with a weaving technique on a thick plate of low alloy steel under the following conditions:

Sketch the contours of the fusion boundary and the Ac r isotherm (71O0C) in the y-z plane. Compare the shape of these isotherms with that obtained from the point heat source model. Solution If we neglect the latent heat of melting, the operating parameter at the chosen reference temperature (Tc = Tm) becomes:

Fusion boundary Here we have:

Readings from Figs. 1.57 and 1.58 give:

Ac j-temperature In this case the peak temperature should be referred to 7200C, i.e.:

ep/nw

V -

ep/nw

Fig. /.57. Calculated peak temperature distribution in the through-thickness direction of the plate at different positions along the weld surface.

y m /L Fig. 1.58. Calculated peak temperature distribution in the transverse direction of the plate at position y (Z) = 0.

y m /z m

nw Fig. 1.59. Effects of nw and dp on the weld width to depth ratio.

from which

Readings from Figs. 1.57 and 1.58 give:

Similarly, equation (1-75) provides a basis for calculating the width of the isotherms in the limiting case where all heat is concentrated in a zero-volume point. By rearranging this equation, we obtain:

which gives 6.3 mm when Bp = 1(Tp = 15200C)

and when Figure 1.60 shows a graphical presentation of the calculated peak temperature contours. Implications of model

It is evident from Fig. 1.60 that the predicted shape of the isotherms, as evaluated from equation (1-110), departs quite strongly from the semi-circular contours required by a point heat source. Moreover, a closer inspection of the figure shows that inclusion of the heat distribution also gives rise to systematic variations in the weld thermal programme along a specific isotherm, as evidenced by the steeper temperature gradient in the v-direction compared with the z-direction of the plate. This point is more clearly illustrated in Fig. 1.61, which compares the HAZ temperature-time programme for the two extreme cases of z = 0 and y = 0, respectively. It is obvious from Fig. 1.61 that the retention time within the austenite regime is considerably longer in the latter case, although the cooling time from 800 to 5000C, Af8/5, is reasonably similar. These results clearly underline the important difference between a point heat source and a distributed heat source as far as the weld thermal programme is concerned. Model limitations

In the present model, we have used the simplified solution for a fast moving high power source (equation 1-73)) as a starting point for predicting the temperature-time pattern. Since the equations derived later are obtained by integrating equation (1-73), they will, of course, apply only under conditions for which this solution is valid. Moreover, a salient assumption in the model is that the heat distribution during weaving can be represented by a linear heat source orientated perpendicular to the welding direction. Although this is a rather crude approximation, experience shows that the assumed heat dis-

z, mm Fig. /.60. Predicted shape of fusion boundary and Acpisotherm during GMA welding of steel with an oscillating electrode (Example 1.13). Solid lines: Distributed heat source; Broken lines: Point heat source.

Temperature, 0C

Time, s Fig. L61. Calculated HAZ thermal cycles in positions y = 0 and z = 0 (Example 1.13). tribution is not critical unless the rate of weaving is kept close to the travel speed. However, for most practical applications weaving at such low rates would be undesirable owing to an unfavourable bead morphology. Case Study (1.2)

Surfacing with strip electrodes makes a good case for application of equation (1-110). Specifically, we shall consider SA welding of low alloy steel with 60mm X 0.5mm stainless steel electrodes. The operational conditions employed are listed in Table 1.5. It is evident from the metallographic data presented in Fig. 1.62 that neither the bead penetration nor the HAZ depth (referred to the plate surface) can be predicted readily on the basis of the present heat flow model when welding is carried out with a consumable electrode, owing to the formation of a reinforcement. This situation arises from the simplifications made in deriving equation (1-110). The problem, however, may be eliminated by calculating the depth of the Ac3 and Ac1 regions relative to the fusion boundary, i.e. Azm = zm(Qp) - zm (Qp = 1), or Aym = ym (8p) - ym (6p = 1), for specific positions along the weld fusion line, as shown by the solid curves in Fig. 1.62 for Qp = 0.54 and 0.45, respectively. An inspection of the graphs reveals satisfactory agreement between theory and experiments in all three cases, which implies that the model is quite adequate for predicting the HAZ thermal programme as far as strip electrode welding is concerned. This result is to be expected, since the assumption of twodimensional heat flow is a realistic one under the prevailing circumstances. Case Study (1.3)

As a second example we shall consider GTA welding (without filler wire additions) at various heat inputs and amplitudes of weaving within the range from 1 to 2.5 kJ mm"1 and 0 to 15mm, respectively. Data for welding parameters are given in Table 1.6.

Stainless steel! y, mm

Weld S3

Fusion line

z, mm

Stainless steel y, mm

Weld S4

z, mm Stainless steel! y, mm Weld S5

z, mm Fig. 1.62. Comparison between observed and predicted Ac3 and Ac1 contours during strip electrode welding (Case study 1.2). Data from Grong and Christensen.19 Table 1.5 Operational conditions used in strip electrode welding experiments (Case study 1.2). Base metal/ filler metal combination

Weld No.

S3 Low alloy steel/ stainless steel

/ (A)

730

S4

73

S5

730

°

U (V)

27 27

27

v (mms"1)

2L (mm)

nw Cn = 0.7)

1.8

60

0.34

2 2

-

2.5

60 60

0.28 0.24

Table 1,6 Operational conditions used in GTA welding experiments (Case study 1.3). I

U

v

2L 1

nw "V=O-

12

WeIdNo.

(A)

(V)

(mms" )

(mm)

T] = 0.23

Bl

200

13.5

2.6

9.5

0.20

0.40

B2

200

14.0

1.1

15.0

0.20

0.40

B3

200

13.5

2.5

-

B4

200

12.5

1.0

Calibration procedure In general, a comparison between theory and experiments requires that the arc efficiency factor can be established with a reasonable degree of accuracy. Unfortunately, the arc efficiency factor for GTA welding has not yet been firmly settled, where values from 0.25 up to 0.75 have been reported in the literature (see Table 1.3). Additional problems result from the fact that only a certain fraction of the total amount of heat transferred from the arc to the base plate is sufficiently intense to cause melting. This has led to the introduction of the melting efficiency factor T]m, which normally is found to be 30-70% lower than the total arc efficiency of the process, depending on the latent heat of melting, the applied amperage, voltage, shielding gas composition, or electrode vertex angle.23 Consequently, since these parameters cannot readily be obtained from the literature, the following reasonable values for r\m and r\ have been assumed to calculate nw in Table 1.6, based on a pre-evaluation of the experimental data: j \ m = 0.12 (fusion zone), TI = 0.23 (HAZ). It should be noted that the above values also include a correction for three-dimensional heat flow, since the assumption of a fast moving high power source during low heat input GTA welding is not valid. Hence, both the arc efficiency factor and the melting efficiency factor used in the present case study are seen to be lower than those commonly employed in the literature. Full weaving (welds Bl and B2) The results from the metallographic examination of the two GTA welds deposited under full weaving conditions are presented graphically in Fig. 1.63. Note that the shape of the fusion boundary as well as the Ac3 and the Ac1 isotherms can be predicted adequately from the present model for both combinations of E and L (an exception is the HAZ end points in position z = 0), provided that proper adjustments of i\m and Tj are made. The good correlation obtained in Fig. 1.63 between the observed and the calculated peak temperature contours justifies the adaptation of the model to low heat input processes such as GTA welding, despite the fact that the assumption of two-dimensional heat flow is not valid under the prevailing circumstances. No weaving (welds B3 and B4) For the limiting case of no weaving (Fig. 1.64), the concept of an equivalent amplitude of weaving has been used in order to calculate the peak temperature contours from the model. This parameter (designated Leq) takes into account the effects of convectional heat flow in the weld pool on the resulting bead geometry, and is evaluated empirically from measurements of the actual weld samples. At low heat inputs (Fig. 1.64(a)), the agreement between theory and

y, mm

Weld B1

z, mm Fusion line

y, mm

Weld B2

z, mm

Fig. 1.63. Comparison between observed and predicted fusion line, Ac3 and Ac1 contours during GTA welding under full weaving conditions (Case study 1.3). Data from Grong and Christensen.19 experiments is largely improved by inserting 2Leq = 7.5mm into equation (1-110), when comparison is made on the basis of the point source model. In contrast, at a heat input of 2.5 kJ mm"1 (Fig. 1.64(b)), the measured shape of the HAZ isotherms is seen to approach that of a semi-circle, and hence the deviation between the present model and the simplified solution for a fast moving high power point source is less apparent. Intermediate weaving At intermediate amplitudes of weaving (2L = 5 and 7.5mm, respectively), convectional heat flow in the weld pool will also tend to increase the bead width to depth ratio beyond the theoretical value predicted from the present model, as shown in Fig. 1.65. The plot in Fig. 1.65

Weld B3 y, mm

z, mm

Fusion line

y, mm

Weld B4

z, mm Fig. 1.64. Comparison between observed and predicted fusion line, Ac3 and Ac1 contours during GTA welding with a stationary arc (Case study 1.3). Solid lines: Distributed heat source, Broken lines: Point heat source. Data from Grong and Christensen.19 includes all data obtained in the GTA welding experiments with an oscillating arc, as reported by Grong and Christensen.19 These results suggest that the applied amplitude of weaving must be quite large before such effects become negligible. Consequently, adaptation of the model to the weld series considered above would require an empirical calibration of the weaving amplitude similar to that performed in Fig. 1.64 for stringer bead weldments to ensure satisfactory agreement between theory and experiments. 1.10.6 Thermal conditions during interrupted welding Rapid variations of temperatures as a result of interruption of the welding operation can have an adversely effect on the microstructure and consequently the mechanical properties of the weldment.

Width

Width to depth ratio

Depth

Theoretical curve

n

w

Fig. 1.65.Comparison between observed and predicted weld width to depth ratios during GTA welding with an oscillating arc (Case study 1.3). Data from Grong and Christensen.19

T,e

t,t

Fig. 1.66. Idealised heat flow model for prediction of transient temperatures during interrupted welding.

Model (after Rykalin9)

The situation existing after arc extinction may be described as shown in Fig. 1.66. From time t = t* there is no net heat supply to the weldment. This condition is satisfied if the real source q0 is considered maintained by adding an imaginary source +qo and sink -qo of the same strength at t*. The temperature at some later time t** in a given position R0 (measured from the origin 0") is then equal to the difference of temperatures due to the positive heat sources qo and +qo and the negative heat sink -qo. Each of these temperature contributions will be a product of a pseudo-steady state temperature Tps, and a correction factor K1 or K2 (given by equations (1-49) and (1-82), respectively). Hence, for 3-D heat flow, we have: (1-116) where and Similarly, for 2-D heat flow, we get: (1-117) where

(ro is the position of the weld with respect to the imaginary heat source at time f* in the x —y plane). Example (1.14)

Consider repair welding of a heavy steel casting with covered electrodes under the following conditions:

Suppose that a 50mm long bead is deposited on the top of the casting. Calculate the temperature in the centre of the weld 5 s after arc extinction. Solution

The pseudo-steady state temperature for points located on the weld centre-line (i|/ = £= 0) can be obtained from equation (1-65). When t** - t* = 5 s, we get:

Referring to Fig. 1.67, the position of the weld with respect to the imaginary heat source at time f* is 10mm, which gives:

Fig. 1.67. Sketch of weld bead in Example 1.14.

(a) 3-D heat flow

(b) 3-D heat flow

(C) 3-D heat flow

Fig. /.6#. Recommended correction factor/for some joint configurations; (a) Single V-groove, (b) Double V-groove, (c) T-joint.

Moreover, the dimensionless times T** and T** - x* are:

and At these coordinates, the correction factor K1 is seen to be 1 and 0.62, respectively (Fig. 1.18). The temperature in the centre of the weld 5 s after arc extinction is thus: which is equivalent to

LlOJ

Thermal conditions during root pass welding

During conventional bead-on-plate welding the angle of heat conduction is equal to 180° due to symmetry effects (e.g. see Fig. 1.23). In order to apply the same heat flow equations during root pass welding, it is necessary to introduce a correction factor,/, which takes into account variations in the effective heat diffusion area due to differences in the joint geometry. Taking /equal to 1 for ordinary bead-on-plate welding (b.o.p.), we can define the net heat input of a groove weld as:9 (1-118) Recommended values of the correction factor/for some joint configurations are given in Fig. 1.68. Example (Ll5)

Consider deposition of a root pass steel weld in a double-V-groove with covered electrodes (SMAW) under the following conditions:

Calculate the cooling time from 800 to 5000C (Ar875), and the cooling rate (CR.) at 6500C in the centre of the weld when the groove angle is 60°. Solution

The cooling time, Ar875, and the cooling rate, CR., can be obtained from equation (1-68) and (1-71), respectively: Cooling time, Atm

Cooling rate at 6500C

The above calculations show that the thermal conditions existing in root pass welding may deviate significantly from those prevailing during ordinary stringer bead deposition due to differences in the effective heat diffusion area. These results are in agreement with general experience (see Fig. 1.69). 1.10.8 Semi-empirical methods for assessment of bead morphology In fusion welding fluid flow phenomena will have a strong effect on the shape of the weld pool. Since flow in the weld pool is generally driven by a combination of buoyancy, electromagnetic, and surface tension forces (e.g. see Fig. 3.10 in Chapter 3), prediction of bead morphology from first principles would require detailed consideration of the current and heat flux distribution in the arc, the interaction of the arc with the weld pool free surface, convective heat transfer due to fluid flow in the liquid pool, heat of fusion, convective and radiative losses from the surface, as well as heat and mass loss due to evaporation. Over the years, a number of successful studies have been directed towards numerical weld pool modelling, based on the finite difference, the finite element, or the control volume approach.24"31 Although these studies provide valuable insight into the mechanisms of weld pool development, the solutions are far too complex to give a good overall indication of the heatand fluid-flow pattern. The present treatment is therefore confined to a discussion of factors affecting the nominal composition of single-bead fusion welds. This composition can be obtained from an analysis of the amount of deposit D and the fused part of the base material B, from which we can calculate the mixing ratio BI(B + D) or DI(B + D). Methods have been outlined in the preceding sections for handling such problems by means of point or line source models. The following section gives a brief description of procedures which can be used for predictions of the desired quantities in cases where the classic models break down, or where the calculation will be too tedious. 1.10.8.1 Amounts of deposit and fused parent metal The heat conduction theory does not allow for the presence of deposited metal. The rate of deposition, dMwldt, is roughly proportional to the welding current /, and is often reported as a coefficient of deposition, defined as: (1-119) Since the area of deposited metal D is frequently wanted, we may write: (1-120) where p is the density, and v is the welding speed.

Groove angle: | = 60°

Cooling time, AtQ/5(s)

Plate thickness:

Heat input, E (kJ/mm) Fig. 1.69. Comparison between observed and predicted cooling times from 800 to 5000C in root pass welding of steel plates (groove preparation as in Fig. 1.68(b)). Data from Akselsen and Sagmo.34 Recommended values of k'/p for some arc welding processes are given in Table 1.7. In practice, the deposition coefficient k'/p will also vary with current density and electrode stickout due to resistance heating of the electrode. Consequently, the numbers contained in Table 1.7 are estimated averages, and should therefore be used with care. Example (1.16)

Consider stringer bead deposition (S AW) on a thick plate of low alloy steel under the following conditions:

Table 1.7 Average rates of volume deposition in arc welding. Data from Christensen.32 Welding Process

k'/p (mm3 A"1 s l)

SMAW

0.3-0.5

GMAW, steel

0.6-0.7

GMAW, aluminium

-0.9

SAW, steel

-0.7

Calculate the mixing ratio Bf(B + D) at pseudo-steady state. Solution

The amount of fused parent material can be obtained from equation (1-75). If we include an empirical correction for the latent heat of melting, the dimensionless radius vector a4m becomes:

This gives:

Similarly, the amount of deposited metal can be calculated from equation (1-120). Taking ifc'/p equal to 0.7mm3 A"1 s"1 for SAW (Table 1.7), we get:

The mixing ratio is thus:

Example (L 17)

Consider stringer bead deposition with covered electrodes (SMAW) on a thick plate of low alloy steel under the following conditions:

Calculate the mixing ratio BI(B + D) at pseudo-steady state. Solution

In this particular case the conditions for a fast moving high power source are not met. Thus, in order to eliminate the risk of systematic errors, the amount of fused parent metal should be calculated from the general Rosenthal thick plate solution (equation (1-45)) or read from Fig. 1.21. When Tc = Tm (i.e. 8^ = 1), we obtain:

Reading from Fig. 1.21 gives:

and

Moreover, the amount of deposited metal can be calculated from equation (1-120). Taking k'/p equal to 0.4mm3 A"1 s~l for SMAW (Table 1.7), we get:

and

The above calculations indicate a small difference in the mixing ratio between SA and SMA welding, but the data are not conclusive. In practice, a value of BI(B + D) between 1/3 and 1/2 is frequently observed for SMAW, while the mixing ratio for SAW is typically 2/3 or higher. The observed discrepancy between theory and experiments arises probably from difficulties in estimating the amount of fused parent metal from the point heat source model. 1.10.8.2 Bead penetration It is a general experience in arc welding that the shape of the fusion boundary will depart quite strongly from that of a semi-circle due to the existence of high-velocity fluid flow fields in the weld pool.24"31 For combinations of operational parameters within the normal range of arc welding, a fair prediction of bead penetration h can be made from the empirical equation derived by Jackson et al.:33 (1-121) A summary of Jackson's data is shown in Table 1.8. It is seen that the constant C in equation (1-121) has a value close to 0.024 for SAW and SMAW with E6015 type electrodes, and about 0.050 for GMAW with CO2 -shielding gas. Penetration measurements of GMA/Ar + O2, GMA/Ar, and GMA/He welds, on the other hand, show a strong dependence of polarity, and shielding gas composition, to an extent which makes the equation useless for a general prediction. Such data have therefore not been included in Table 1.8. Example (1.18)

Based on the Jackson equation (equation (1-121)), calculate the bead penetration for the two specific welds considered in Examples (1.16) and (1.17). Use these results to evaluate the applicability of the point heat source model under the prevailing circumstances. Solution

From equation (1-121) and Table 1.8, we have:

Table 1.8 Recommended bead penetration coefficients for some arc welding processes. Data from Jackson.33 Welding Process

C

Comments

SAW, steel

-0.024

Various types of fluxes (Zz from 3 to 15 mm)

SMAW, steel (E6015)

-0.024

Wide range of /, U, and v (h from 0.7 to 5mm)

GMAW, steel (CO2 - shielding)

-0.050

Electrode positive (h from 6.5 to 8mm)

and

The corresponding values predicted from the point heat source model are:

and

Provided that the Jackson equation gives the correct numbers, it is obvious from the above calculations that the point heat source model is not suitable for reliable predictions of the bead penetration during arc welding. This observation is not surprising. 1.10.9 Local preheating So far, we have assumed that the ambient temperature T0 remains constant during the welding operation (i.e. is independent of time). The use of a constant value of T0 is a reasonable approximation if the work-piece as a whole is subjected to preheating. In many cases, however, the dimensions of the weldment allow only preheating of a narrow zone close to the weld. This, in turn, will have a significant influence on the predicted weld cooling programme, particularly in the low temperature regime where the classic models eventually break down when T approaches T0. Model (after Christensen n)

The idealised preheating model is shown in Fig. 1.70. Here it is assumed that the weld centreline temperature is equal to the sum of the contributions from the arc and from the field of preheating. The former contribution is given by equation (1-45) for R = -x = Vt, provided that the plate thickness is sufficiently large to maintain 3-D heat flow. Similarly, the temperature field due to preheating can be calculated as shown in Section 1.7 for uniaxial heat conduction from extended sources (thermit welding). By combining equations (1-45) and (1-22), we obtain the following relation for the weld centre-line: (1-122)

T

Temperature profile att = 0

Weld Preheated zone

z Fig. 1.70. Sketch of preheating model. where T* is the local preheating temperature, and L* is the half width of the preheated zone. Equation (1-122) can be written in a general form by introducing the following groups of parameters: — Dimensionless temperature: (1-123)

Time constant: (1-124)

Dimensionless time: (1-125)

Dimensionless half width of preheated zone: (1-126) By inserting these parameters into equation (1-122), we obtain: (1-127)

It is evident from the graphical representation of equation (1-127) in Fig. 1.71 that the predicted weld cooling programme falls within the limits calculated for Q"-^ 0 (no preheating) and Q /7 -> oo (global preheating). The controlling parameter is seen to be the dimensionless half width of the preheated zone Q", which depends both on the actual width L*, the base plate thermal properties a, X, and the net heat input qo Iv. Example (1.19)

Consider stringer bead deposition with covered electrodes (SMAW) on a thick plate of low alloy steel under the following conditions:

Calculate the cooling time from 800 to 50O0C (A%5), and the cooling time £1Oo measured from the moment of arc passage to the temperature in the centre of the weld reaches 10O0C. Solution First we calculate the time constant to from equation (1-124):

e*-

from which we obtain

^6

Fig. 1.71. Graphical representation of equation (1-127).

Next Page Cooling time, At8/5

The dimensionless temperatures conforming to 800 and 5000C are:


from which

This cooling time is only slightly longer than that calculated from equation (1-68) for T0 = 200C (6.9s), showing that moderate preheating up to 1000C is not an effective method of controlling Ar875. Cooling time, t]00

When T=T0* = 1000C, the dimensionless temperature 9* = 1. Reading from Fig. 1.71 gives T 6 - 10, from which:

The above value should be compared with that evaluated from the numerical data of Yurioka et al.,35 replotted in Fig. 1.72 (see p.104). It follows from Fig. 1.72 that the weld cooling programme in practice is also a function of the plate thickness d, an effect which cannot readily be accounted for in a simple analytical treatment of the heat diffusion process. For the specific case considered above the parameter ^100 varies typically from 500 to 900s, depending on the chosen value of d. This cooling time is significantly shorter than that calculated from equation (1-127), indicating that the analytical model is only suitable for qualitative predictions.

References 1. 2. 3. 4. 5. 6.

H.S. Carslaw and J.C. Jaeger: Conduction of Heat in Solids; 1959, Oxford, Oxford University Press. British Iron and Steels Research Association: Physical Constants of some Commercial Steels at Selected Temperatures; 1953, London, Butterworths. R. Hultgren, R.L. Orr, RD. Anderson and K.K. Kelly: Selected Values of Thermodynamic Properties of Metals and Alloys; 1963, New York, J. Wiley & Sons. E. Griffiths (ed.): J. Iron and Steel Inst., 1946,154, 83-121. J.E. Hatch (ed.): Aluminium — Properties and Physical Metallurgy; 1984, Metals Park (Ohio), American Society for Metals. Metals Handbook, 9th edn., Vol. 2, 1979, Metals Park (Ohio), American Society for Metals.

Previous Page Cooling time, At8/5

The dimensionless temperatures conforming to 800 and 5000C are:


from which

This cooling time is only slightly longer than that calculated from equation (1-68) for T0 = 200C (6.9s), showing that moderate preheating up to 1000C is not an effective method of controlling Ar875. Cooling time, t]00

When T=T0* = 1000C, the dimensionless temperature 9* = 1. Reading from Fig. 1.71 gives T 6 - 10, from which:

The above value should be compared with that evaluated from the numerical data of Yurioka et al.,35 replotted in Fig. 1.72 (see p.104). It follows from Fig. 1.72 that the weld cooling programme in practice is also a function of the plate thickness d, an effect which cannot readily be accounted for in a simple analytical treatment of the heat diffusion process. For the specific case considered above the parameter ^100 varies typically from 500 to 900s, depending on the chosen value of d. This cooling time is significantly shorter than that calculated from equation (1-127), indicating that the analytical model is only suitable for qualitative predictions.

References 1. 2. 3. 4. 5. 6.

H.S. Carslaw and J.C. Jaeger: Conduction of Heat in Solids; 1959, Oxford, Oxford University Press. British Iron and Steels Research Association: Physical Constants of some Commercial Steels at Selected Temperatures; 1953, London, Butterworths. R. Hultgren, R.L. Orr, RD. Anderson and K.K. Kelly: Selected Values of Thermodynamic Properties of Metals and Alloys; 1963, New York, J. Wiley & Sons. E. Griffiths (ed.): J. Iron and Steel Inst., 1946,154, 83-121. J.E. Hatch (ed.): Aluminium — Properties and Physical Metallurgy; 1984, Metals Park (Ohio), American Society for Metals. Metals Handbook, 9th edn., Vol. 2, 1979, Metals Park (Ohio), American Society for Metals.

Cooling time, t100(s)

Heat input: E=1.7 kJ/mm

Preheating temperature, T^ (0C) Fig. 1.72. Cooling time to 1000C, tm, in steel welding for different combinations of T0*, L*, d and E. Data from Yurioka et a/.35

7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.

K.P. Bentley, J.A. Greenwood, R McKnowlson and R.G. Bakes: Brit. Weld. J., 1963,10, 613619. N.N. Rykalin, A.I. Pugin and V.A. Vasil'eva: Weld. Prod., 1959, 6, 42-52. N.N. Rykalin: Berechnung der Warmevorgdnge beim Schweissen; 1953, Berlin, VEB Verlag Technik. H.M. Tensi, W. Welz and M. Schwalm: Aluminium, 1981, 58, 515-518. N. Christensen, V. de L. Davis and K. Gjermundsen: Brit. Weld. J., 1965,12, 54-75. Welding Handbook, 8th edn., Vol. 2, 1991, Miami (Florida), American Welding Society. D. Rosenthal: Weld. / , 1 9 4 1 , 20, 220s-234s. D. Rosenthal: Trans. ASME, 1946, 68, 849-866. CM. Adams: Weld. J., 1958, 37, 210s-215s. RS. Myers, O.A. Uyehara and G.L. Borman: Weld. Res. Bull., 1967, 123, 1-46. T.W Eagar and N.S. Tsai: Weld. J., 1983, 62, 346s-355s. M.F. Ashby and K.E. Easterling: Ada Metall, 1984, 32, 1935-1948. 0. Grong and N. Christensen: Mater. ScL Tech., 1986, 2, 967-973. O.R. Myhr and 0 . Grong: Acta Metall. Mater., 1990, 38, 449-460. S. Kou and Y. Le: Metall. Trans., 1983,14A, 2245-2253.

22. 23. 24. 25. 26. 27. 28. 29. 30. 32. 33. 34. 35.

O.R. Myhr and 0. Grong: Unpublished work, 1990, University of Trondheim, The Norwegian Institute of Technology. R.W. Niles and CE. Jackson: Weld. J., 1975, 54, 25s-32s. G.M. Oreper, T.W. Eagar and J. Szekely: Weld J., 1983, 62, 307s-312s. Y.H. Wang and S. Kou: Proc. Int. Conf. on Trends in Welding Research, Gatlinburg, TN, May, 1986, pp. 65-69, Publ. ASM International. S.A. David and J.M Vitek: Int. Mater. Rev., 1989, 34, 213-245. K.C. Mills and BJ. Keene: Int. Mater. Rev., 1990, 35, 185-216. R.L. UIe, Y. Joshi and E.B. Sedy: Metall. Trans., 1990, 21B, 1033-1047. T. Zacharia, S.A. David, J.M. Vitek and H.G. Kraus: Metall. Trans., 1991, 22B, 243-257. A. Matsunawa: Proc. 3rd Int. Conf. on Trends in Welding Research, Gatlinburg, TN, 1992, pp.3-16, Publ. ASM International. N. Christensen: Welding Metallurgy Compendium, 1985, University of Trondheim, The Norwegian Institute of Technology. CE. Jackson: Weld. J., 1960, 39, 226s-230s. O.M. Akselsen and G. Sagmo: Technical Report STF34 A89147, 1989, Trondheim (Norway), Sintef-Division of Metallurgy. N. Yurioka, M. Okumura, S. Ohshita and S. Saito: HW Doc. XII-E-10-81, 1981.

Appendix 1.1 Nomenclature General symbols thermal diffusivity (mm2 s"1)

finite difference method heat content per unit volume at Tc (J mm"3)

cross section (mm2) start temperature of ferrite to austenite transformation (0C) end temperature of ferrite to austenite transformation (0C) recrystallisation temperature (0C)

enthalpy increment referred to an initial temperature T0 (J mm' 3 ) latent heat of melting (J mm"3) amperage (A) modified Bessel function of second kind and zero order

cooling rate (0C s"1) plate thickness (mm)

modified Bessel function of second kind and first order

natural logarithm base number

integration parameter

Gaussian error function


complementary Gaussian error function

start temperature of austenite to martensite transformation (0C)


y-axis/transverse direction (mm)

net power (W)

z-axis/through thickness direction (mm)

net heat input (J) efficiency factor two-dimensional radius vector (mm)

dimensionless temperature

locus of peak temperature in T-r space (mm)

dimensionless temperature conforming to 8000C

three-dimensional radius vector (mm)

dimensionless temperature conforming to 5000C

locus of peak temperature in T-R space (mm)

dimensionless temperature conforming to the melting point

isothermal zone width (mm)

dimensionless peak temperature

temperature (0C)

volume heat capacity (J mm-3 0C-1)

reference temperature (0C) ambient temperature (0C)

thermal conductivity (W mm"1 0C-1)

melting point (0C)

dimensionless time

peak temperature (0C)

dimensionless cooling time

time (s)

dimensionless cooling time from 800 to 5000C

time variable (s) dimensionless cooling time from 300 to 1000C

time variable (s) cooling time (s)

Specific symbols 0

cooling time from 800 to 500 C (s)

Local Fusion in Arc Strikes

0

cooling time from 300 to 100 C (s) integration parameter voltage (V) integration parameter x-axis/welding direction (mm)

dimensionless operating parameter arc ignition time (s) isothermal zone width (mm) dimensionless R-vector locus of peak temperature in G-CT1 space

dimensionless isothermal zone width

locus of peak temperature in 0'-£2 space (star denotes a specific peak temperature)

dimensionless time dimensionless time locus of peak temperature in 0-T1 space

dimensionless cooling time from ^ to 5000C

dimensionless cooling time locus of peak temperature in (T-T3 space

Spot Welding thickness of overlapping plates (mm) dimensionless operating parameter

Friction Welding integral in equation (1-30)

heating time (s)

net power generation at weld interface (W)

dimensionless r-vector

duration of heating period (s)

locus of peak temperature in 0-cr2 space

contact section temperature at the end of heating period (0C)

dimensionless time

dimensionless temperature

locus of peak temperature in 0-T2 space

dimensionless peak temperature

dimensionless cooling time

Thermit Welding

dimensionless jc-coordinate locus of peak temperature in 6"Q.' space dimensionless time

half width of groove (mm) initial temperature of liquid metal (0C) distance from reference point to infinitesimal source (mm) dimensionless temperature dimensionless peak temperature dimensionless .^-coordinate

Arc Welding amount of fused parent metal (mm2) constant in Jackson equation amount of deposited metal (mm2) gross heat input per unit length of weld (kJ mm"1) correction factor for the net heat input during root pass welding

FCAW

flux cored arc welding

imaginary heat source of net arc power qo, qa, or qb (W)

GMAW gas metal arc welding GTAW

maximum intensity of distributed (Gaussian) heat source (W mm"1)

gas tungsten arc welding bead penetration (mm)

power density of distributed (Gaussian) heat source (W mm"1)

integer variables.... -1,0, L... infinitesimal heat source (W) constant in heat distribution function (mm"2)

two-dimensional radius vector in y-z plane (mm)

coefficient of weld metal deposition (g A"1 s"1)

locus of peak temperature in T-r* space (mm)

amplitude of weaving or half width of strip electrode (mm)

distance from infinitesimal heat source to point P in x-y or y-z plane (mm)

half width of preheated zone (mm)

position of weld end-crater with respect to imaginary heat source at time t** in x-y plane (mm)

equivalent amplitude of weaving (mm) half width of linear source in Gaussian heat distribution model (mm)

distance from infinitesimal heat source to point P in x-y-z space (mm)

length of weld bead (mm) k

mass of weld metal (g)

distances from real and imaginary heat sources to point P in x-y-z space (mm)

dimensionless operating parameter position of weld with respect to imaginary heat source at time f** in x-y-z space (mm)

dimensionless operating parameter in weaving model reference point in stationary coordinate system reference point in moving coordinate system

SAW

submerged arc welding

SMAW

shielded metal arc welding time at moment of arc extinction (s)

arbitrary reference point time constant in preheating model arbitrary point of observation strength of elementary heat sources (W)

(S)

cooling time to 1000C (s)

time constant in heat distribution function (s)

displacement of elementary heat source in z-direction (mm)

time referred to moment of arc ignition (s)

groove angle

retention time (s)

ratio between real and pseudo-steady state temperature (thick plate welding)

preheating temperature (0C) welding speed (mm s"1) volume of isothermal enclosure (mm3) welding direction in stationary coordinate system (mm) ^-coordinate at maximum width of isotherm (mm) transverse direction in stationary coordinate system (mm) distance from infinitesimal heat source to point P in j-direction (mm) ^-coordinate at maximum width of isotherm (mm)

ratio between real and pseudosteady state temperature (thin plate welding) dimensionless temperature in preheating model dimensionless cross sectional area of isothermal enclosure (thick plate welding) dimensionless cross sectional area of isothermal enclosure (thin plate welding) density of weld metal (g mm 3 ) dimensionless distance from real and imaginary heat sources to point P dimensionless /^-vector

isothermal zone width (mm) dimensionless R0-vector through-thickness direction in stationary coordinate system (mm) z-coordinate at maximum width of isotherms (mm) isothermal zone width (mm) dimensionless y-coordinate in weaving model dimensionless z-coordinate in weaving model dimensionless plate thickness

locus of peak temperature in 0-a3 space dimensionless r*-vector locus of peak temperature in 0-04 space dimensionless r-vector dimensionless r^-vector locus of peak temperature in 8-CT5 space

dimensionless jc-axis

dimensionless zo -axis

dimensionless xo -axis

dimensionless z-coordinate at maximum depth of isotherm

dimensionless jc-coordinate at maximum width of isotherm

melting efficiency factor

dimensionless length of isothermal enclosure

dimensionless volume of isothermal enclosure

dimensionless distance from heat source to front of isothermal enclosure

dimensionless half width of preheated zone

dimensionless distance from heat source to rear of isothermal enclosure

dimensionless time in weaving model dimensionless time in preheating model

dimensionless y-axis dimensionless yo -axis dimensionless ^-coordinate at maximum width of isotherm dimensionless isothermal zone width dimensionless z-axis

locus of peak temperature in 6-x space dimensionless retention time dimensionless time at moment of arc extinction dimensionless time referred to moment of arc ignition

Appendix 1.2 Refined Heat Flow Model for Spot Welding The refined model is based on the assumption that all heat is released instantaneously at time t = 0 in a point located at the interface between the two overlapping plates, which implies that equation (1-7) is valid. However, in order to maintain the net flux of heat through both plate surfaces equal to zero, it is necessary to account for mirror reflections of the source with respect to the planes z = dt/2 and z = - dt/2. This can be done on the basis of the method of images, as illustrated in Fig. A 1.1. By including all contributions from the imaginary sources "Q-2 >Q-i ,Q\,Qi >••• located symmetrically at distances ± idt below and above the centre-axis of the joint, the temperature distribution is obtained in the form of a convergent series:

(Al-I) where

y

Z Fig. Al.l.Refined heat flow model for spot welding of plates. and i is an integer variable (...-1, 0, 1...)A numerical solution of equation (Al.l) gives a peak temperature distribution similar to that shown in Fig. 1.9.

Appendix 1.3 The Gaussian Error Function The eiTor function erf(u) and the complementary error function erfc(u) are special cases of the incomplete gamma function. Their definitions are:

and

The functions have the following limiting values and symmetries:

and

The following Fortran subroutine can be used for calculations of the error functions with a fractional error less than 1.2 X 10~7: FUNCTION ERFC(U) Z=ABS(U) T=l./(l.+0.5*Z) ERFC=T*EXP(-Z*Z-1.26551223+T*(1.00002368+T*(.37409196+ *

T%09678418+T*(-.18628806+T%27886807+T*(-l.13520398+

*

T*(1.48851587+T*(-.82215223+T*.17O87277)))))))))

IF (U.LT.O.) ERFC=2.-ERFC RETURN END

Appendix 1.4 Gaussian Heat Distribution Following the treatment of Rykalin,9 the situation may be described as shown in Fig. Al.2. Here we consider a distributed heat source of net power density (in W mm"1): (Al-2) The total power of the source qo is obtained by integration of equation (Al-2). Substituting and integrating from u = -©© to u = +, gives:

from which

(Al-3)

It follows from equation (1-73) that an infinitesimal source dqy> located between j ' a n d will cause a small rise of temperature dTy> in point P at time t, as:

(Al-4) where

and

Integration of equation (Al-4) between the limits y'= -°o and >>'= +00 gives:

(Al-5)

q(y)

P

2-D heat flow

z Fig, Al.2. Distributed heat source of net power density q(y) on a semi-infinite body.

where

is a time constant)and n = Aat.

The latter integral can be evaluated by substituting:

from which

and integrating between the limits w = -°° and This gives (after some manipulation):

(Al-6) If we replace the Gaussian heat distribution by a linear source of the same strength, which extends from -L0 to +L0 on either side of the weld centre-line in the y-direction (see Fig. A1.3), we may write:

By rearranging this equation, we obtain:

(Al-7) In practice, the parameter L0 has the same physical significance as the weaving amplitude L in equation (1-110). Consequently, these solutions are equivalent in the sense that they predict a similar temperature-time pattern.

q(y)

Fig. Al.3. Physical representation of a Gaussian heat distribution by a linear source of width 2LO.

2 Chemical Reactions in Arc Welding

2.1 Introduction The weld metal composition is controlled by chemical reactions occurring in the weld pool at elevated temperatures, and is therefore influenced by the choice of welding consumables (i.e. combination of filler metal, flux, and/or shielding gas), the base metal chemistry, as well as the operational conditions applied. In contrast to ladle refining of metals and alloys where the reactions occur under approximately isothermal conditions, a characteristic feature of the arc welding process is that the chemical interactions between the liquid metal and its surroundings (arc atmosphere, slag) take place within seconds in a small volume where the metal temperature gradients are of the order of 1000°C mm"1 with corresponding cooling rates up to 1000°C s"1. The complex thermal cycle experienced by the liquid metal during transfer from the electrode tip to the weld pool in GMA welding of steel is shown schematically in Fig. 2.1. As a result of this strong non-isothermal behaviour, it is very difficult to elucidate the reaction sequences during all stages of the process. Consequently, a complete understanding of the major controlling factors is still missing, which implies that fundamentally based predictions of the final weld metal chemical composition are limited. Additional problems result from the lack of adequate thermodynamic data for the complex slag-metal reaction systems involved. However, within these restrictions, the development of weld metal compositions can be treated with the basic principles of thermodynamics and kinetic theory considered in the following sections.

2.2 Overall Reaction Model The symbols and units used throughout this chapter are defined in Appendix 2.1. In ladle refining of metals and alloys, the reaction kinetics are usually controlled by mass transfer between the liquid metal and its surroundings (slag or ambient atmosphere). Examples of such kinetically controlled processes are separation of non-metallic inclusions from a deoxidised steel melt or removal of hydrogen from liquid aluminium. In welding, the reaction pattern is more difficult to assess because of the characteristic non-isothermal behaviour of the process (see Fig. 2.1). Nevertheless, experience shows that it is possible to analyse mass transfer in welding analogous to that in ladle refining by considering a simple two-stage reaction model, which assumes:1 (i)

A high temperature stage, where the reactions approach a state of local pseudo-equilibrium.

(ii)

A cooling stage, where the concentrations established during the initial stage tend to readjust by rejection of dissolved elements from the liquid.

Gas nozzle Shielding gas Filler wire

Contact tube

Arc plasma temperature~10000°C

Electrode tip droplet (1600-20000C) Falling droplet (24000C) Hot part of weld pool (1900-22000C)

Cold part of weld pool (< 19000C)

Weld pool retention time 2-1Os

Base plate

Fig. 2.1. Schematic diagram showing the main process stages in GMA welding. Characteristic average temperature ranges at each stage are indicated by values in parenthesis.

As indicated in Fig. 2.2 the high temperature stage comprises both gas/metal and slag/metal interactions occurring at the electrode tip, in the arc plasma, or in the hot part of the weld pool, and is characterised by extensive absorption of elements into the liquid metal. During the subsequent stage of cooling following the passage of the arc, a supersaturation rapidly increases because of the decrease in the element solubility with decreasing temperatures. The system will respond to this supersaturation by rejection of dissolved elements from the liquid, either through a gas/metal reaction (desorption) or by precipitation of new phases. In the latter case the extent of mass transfer is determined by the separation rate of the reaction products in the weld pool. It should be noted that the boundary between the two stages is not sharp, which means that phase separation may proceed simultaneously with absorption in the hot part of the weld pool. In the following sections, the chemistry of arc welding will be discussed in the light of this two-stage reaction model.

2.3 Dissociation of Gases in the Arc Column As shown in Table 2.1, gases such as hydrogen, nitrogen, oxygen, and carbon dioxide will be widely dissociated in the arc column because of the high temperatures involved (the arc plasma temperature is typically of the order of 10 0000C or higher). From a thermodynamic standpoint, dissociation can be treated as gaseous chemical reactions, where the concentrations of the reactants are equal to their respective partial pressures. Hence, for dissociation of diatomic gases, we may write: (2-1) where X denotes any gaseous species.

'Cold' part of weld pool

Solid weld metal

Solid weld metal

Peak temperature

Grey j zonei

Rejection of dissolved elements

Peak concentration

Solid weld metal

Concentration

Absorption of elements

Solid weld metal

Temperature

'Hot1 part of weld pool

Equilibrium concentration at melting point

Time Fig. 2.2. Idealised two-stage reaction model for arc welding (schematic). Table 2.1 Temperature for 90% dissociation of some gases in the arc column. Data from Lancaster.2 Gas

Dissociation Temperature (K)

CO 2

3800

H2

4575

O2

5100

N2

8300

Next, consider a shielding gas which consists of two components, i.e. one inert component (argon or helium) and one active component X2. When the fraction dissociated is close to unity, the partial pressure of species X in the gas phase px is equal to:

(2-2) where H1 and nx are the total number of moles of components / (inert gas) and X, respectively in the shielding gas, andptot is the total pressure (in atm). It follows from equation (2-1) that two moles of X form from each mole of X2 that dissociates. Hence, equation (2-2) can be rewritten as:

(2-3)

where nXl is the total number of moles of component X2 which originally was present in the shielding gas. If nXl and H1 are proportional to the volume concentrations of the respective gas components in the shielding gas, equation (2-3) becomes:

(2-4)

Taking vol% / = (100 - vol% X2) andp,ot = 1 atm, we obtain the following expression for Px(2-5)

Similarly, if X2 is replaced by another gas component of the type YX2, we get: (2-6) and (2-7)

It is evident from the graphical representations of equations (2-5) and (2-7) in Fig. 2.3 that the partial pressure of the dissociated component X increases monotonically with increasing concentrations of X2 and YX2 in the shielding gas. The observed non-linear variation of px arises from the associated change in the total number of moles of constituent species in the gas phase due to the dissociation reaction. Moreover, it is interesting to note that the partial pressure px is also dependent on the nature of the active gas component in the arc column (i.e. the stoichiometry of the reaction). This means that the oxidation capacity of for instance CO2 is only half that of O2 when comparison is made on the basis of equal concentrations in the shielding gas (to be discussed later).

Px

Vol%)^ f VoRGYX2 Fig. 2.3. Graphical representation of equations (2-5) and (2-7).

2.4 Kinetics of Gas Absorption In general, mass transfer between a gas phase and a melt involves:3 (i)

Transport of reactants from the bulk phase to the gas/metal interface.

(ii)

Chemical reaction at the interface.

(iii)

Transport of dissolved elements from the interface to the bulk of the metal.

2.4.1 Thin film model In cases where the rate of element absorption is controlled by a transport mechanism in the gas phase (step one), it is a reasonable approximation to assume that all resistance to mass transfer is confined to a stagnant layer of thickness 8 (in mm) adjacent to the metal surface, as shown in Fig. 2.4. Under such conditions, the overall mass transfer coefficient is given by:2

(2-8) where Dx is the diffusion coefficient of the transferring species X (in mm2 s~*). Although the validity of equation (2-8) may be questioned, the thin film model provides a simple physical picture of the resistance to mass transfer during gas absorption.

Partial pressure

Distance Fig. 2.4. Film model for mass transfer (schematic).

2.4.2 Rate of element absorption Referring to Fig. 2.5, the rate of mass transfer between the two phases (in mol s"1) can be written as: (2-9) where A is the contact area (in mm 2 ), R is the universal gas constant (in mm3 atm K"1 mol"1), T is the absolute temperature (in K), px is the partial pressure of the dissociated species X in the bulk phase (in atm), and px is the equilibrium partial pressure of the same species at the gas/ metal interface (in atm). Based on equation (2-9) it is possible to calculate the transient concentration of element X in the hot part of the weld pool. Let m denote the total mass of liquid weld metal entering/ leaving the reaction zone per unit time (in g s"1). If Mx represents the atomic weight of the element (in g mol"1), we obtain the following relation w h e n / ? x » p°x:

(2-10)

It follows from equation (2-10) that the transient concentration of element X in the hot part of the weld pool is proportional to the partial pressure of the dissociated component X in the plasma gas. Since this partial pressure is related to the initial content of the molecular species X2 or YX2 in the shielding gas through equations (2-5) and (2-7), we may write:

Arc column

Bulk gas phase

Stagnant gaseous boundary layer Gas/metal interface Metal phase Hot part of weld pool Fig. 2.5. Idealised kinetic model for gas absorption in arc welding (schematic). (2-11) and (2-12)

where C1 and C2 are kinetic constants which are characteristic of the reaction systems under consideration.

2.5 The Concept of Pseudo-Equilibrium Although the above analysis presupposes that the element absorption is controlled by a transport mechanism in the gas phase, the transient concentration of the active component X in the hot part of the weld pool can alternatively be calculated from chemical thermodynamics by considering the following reaction: X(gas)

X (dissolved)

(2-13)

By introducing the equilibrium constant K{ for the reaction and setting the activity coefficient to unity, we get: (2-14) This equation should be compared with equation (2-10) which predicts a linear relationship

between wt% X and px. If the above analysis is correct, one would expect that the partial pressure px at the gas/metal interface is directly proportional to the partial pressure of the dissociated component in the bulk phase. Unfortunately, the proportionality constant is difficult to establish in practice.

2.6 Kinetics of Gas Desorption During the subsequent stage of cooling following the passage of the arc, the concentrations established at elevated temperatures will tend to readjust by rejection of dissolved elements from the liquid. When it comes to gases such as hydrogen and nitrogen, this occurs through a desorption mechanism, where the driving force for the reaction is provided by the decrease in the element solubility with decreasing metal temperatures. 2.6.1 Rate of element desorption Consider a melt which first is brought in equilibrium with a monoatomic gas of partial pressure px at a high temperature T1, and then is rapidly cooled to a lower temperature T2 and immediately brought in contact with diatomic X2 of partial pressure pXl (see Fig. 2.6). Under such conditions, the rate of element desorption (in mol s"1) is given by:

(2-15)

where k'd is the mass transfer coefficient (in mm s 1X and p°x is the equilibrium partial pressure of component X2 at the gas/metal interface (in atm).

Bulk gas phase

Stagnant gaseous boundary layer Gas/metal interface Metal phase Cold part of weld pool Fig. 2.6. Idealised kinetic model for gas desorption in arc welding (schematic).

The partial pressure pX2 can be calculated from chemical thermodynamics by considering the following reaction: 2X(dissolved) = X2 (gas) (2-16) from which (2-17) where K2 is the equilibrium constant, and [wt% X] is the concentration of element X in the liquid metal (in weight percent). Note that the activity coefficient has been set to unity in the derivation of equation (2-17). The equilibrium constant K2 may be expressed in terms of the solubility of element X in the liquid metal at 1 atm total pressure Sx. Hence, equation (2-17) transforms to:

(2-18)

By combining equations (2-15) and (2-18), we get:

(2-19) Data for the solubility of hydrogen and nitrogen in some metals up to about 22000C are given in Figs. 2.7 and 2.8, respectively. It is evident that the element solubility decreases steadily with decreasing metal temperatures down to the melting point. This implies that the desorption reaction is thermodynamically favoured by the thermal conditions existing in the cold part of the weld pool. 2.6.2. Sievert's law It follows from equation (2-19) that desorption becomes kinetically unfeasible when Px2 ~ Px2' corresponding to: (2-20) Equation (2-20) is known as the Sievert's law. This relation provides a basis for calculating the final weld metal composition in cases where the resistance to mass transfer is sufficiently small to maintain full chemical equilibrium between the liquid metal and the ambient (bulk) gas phase.

2.7 Overall Kinetic Model for Mass Transfer during Cooling in the Weld Pool Because of the complexity of the rate phenomena involved, it would be a formidable task to derive a complete kinetic model for mass transfer in arc welding from first principles. How-

(b)

Aluminium

ml H2/100 g fused metal

ml H2/100 g fused metal

(a)

Temperature, 0C

Solid Cu

Temperature, 0C

Iron

Temperature, 0C

ml H2/100g fused metal

(d)

(C)

ml H2/100g fused metal

Copper

Nickel

Temperature, 0C

Fig. 2.7. Solubility of hydrogen in some metals; (a) Aluminium, (b) Copper, (c) Iron, (d) Nickel. Data compiled by Christensen.4 ever, for the idealised system considered in Fig. 2.9, it is possible to develop a simple mathematical relation which provides quantitative information about the extent of element transfer occurring during cooling in the weld pool. Let [%X]eq denote the equilibrium concentration of element X in the melt. If we assume that the net flux of element X passing through the phase boundary A per unit time is proportional to the difference ([%X] - [%X]eqX the following balance is obtained:3 (2-21) where V is the volume of the melt (in mm 3 ), kd is the overall mass transfer coefficient (in mm s"1), and A is the contact area between the two phases (in mm 2 ).

Temperature, 0C

log (wt% N)

Iron

104AT1 K Fig. 2.8. Solubility of nitrogen in iron. Data from Turkdogan.5

Phase I i

Phase i

Distance

Net flux of X

Contact area (A)

Volume (V)

Concentration Fig. 2.9. Idealised kinetic model for mass transfer in arc welding (schematic). By rearranging equation (2-21) and integrating between the limife [%X]( (att = O) and [%X] (at an arbitrary time t\ we get:

(2-22)

where to is a time constant (equal to VI kjA).

It is evident from the graphical representation of equation (2-22) in Fig. 2.10 that the rate of mass transfer depends on the ratio Vl kji, i.e. the time required to reduce the concentration of element X to a certain level is inversely proportional to the mass transfer coefficient kd. This type of response is typical of a first order kinetic reaction. Although the above model refers to mass transfer under isothermal conditions, it is also applicable to welding if we assume that the weld cooling cycle can be replaced by an equivalent isothermal hold-up at a chosen reference temperature. Thus, by rearranging equation (222), we get: (2-23) It follows that the final concentration of element X in the weld metal depends both on the cooling conditions and on the intrinsic resistance to mass transfer, combined in the ratio t/to. When [%X]eq is sufficiently small, equation (2-23) predicts a direct proportionality between [%X] and [%X\t (i.e. the initial concentration of element X in the weld pool). This will be the case during deoxidation of steel weld metals where separation of oxide inclusions from the weld pool is the rate controlling step. Moreover, when t/t0 » 1 (small resistance to mass transfer), equation (2-23) reduces to: (2-24)

(X-X^)Z(X1-Xeq)

Under such conditions the final weld metal composition can be calculated from simple chemical thermodynamics. Because of this flexibility, equation (2-23) is applicable to a wide range of metallurgical problems at the same time as it provides a simple physical picture of the resistance to mass transfer during cooling in the weld pool.

t,s Fig. 2.10. Graphical representation of equation (2-22).

2.8 Absorption of Hydrogen Some of the well-known harmful effects of hydrogen discussed in Chapters 3 and 7 (i.e. weld porosity and HAZ cold cracking) are closely related to the local concentration of hydrogen established in the weld pool at elevated temperatures due to chemical interactions between the liquid metal and its surroundings. 2.8.1 Sources of hydrogen Broadly speaking, the principal sources of hydrogen in welding consumables are:6 (i) Loosely bound moisture in the coating of shielded metal arc (SMA) electrodes and in the flux used in submerged arc (SA) or flux-cored arc (FCA) welding. Occasionally, moisture may also be introduced through the shielding gas in gas metal arc (GMA) and gas tungsten arc (GTA) welding. (ii) Firmly bound water in the electrode coating or the welding flux. This can be in the form of hydrated oxides (e.g. rust on the surface of electrode wires and iron powder), hydrocarbons (in cellulose), or crystal water (bound in clay, astbestos, binder etc.). (iii) Oil, dirt and grease, either on the surface of the work piece itself, or trapped in the surface layers of welding wires and electrode cored wires. It is evident from Fig. 2.11 that the weld metal hydrogen content may vary strongly from one process to another. The lowest hydrogen levels are usually obtained with the use of lowmoisture basic electrodes or GMA welding with solid wires. Submerged arc welding and fluxcored arc welding, on the other hand, may give high or low concentrations of hydrogen in the weld metal, depending on the flux quality and the operational conditions applied (note that the former process is not included in Fig. 2.11). The highest hydrogen levels are normally associated with cellulosic, acid, and rutile type electrodes. This is due to the presence of large amounts of asbestos, clay and other hydrogen-containing compounds in the electrode coating. Table 2.2 (shown on page 132) gives a summary of measured arc atmosphere compositions in GMA and SMA welding. Included are also typical ranges for the weld metal hydrogen content. 2.8.2 Methods of hydrogen determination in steel welds Hydrogen is unlike other elements in weld metal in that it diffuses rapidly at normal room temperatures, and hence, some of it may be lost before an analysis can be made. This, coupled with the fact that the concentrations to be measured are usually at the parts per million level, means that special sampling and analysis procedures are needed. In order that research results may be compared between different laboratories and can be used to develop hydrogen control procedures, some international standardisation of these sampling and analysis methods is necessary. Three methods are currently being used, as defined in the following standards:

Potential hydrogen level

FCAW

Very Low Medium low Weld hydrogen level

High

Fig. 2.11. Ranking of different welding processes in terms of hydrogen level (schematic). The diagram is based on the ideas of Coe.6 (i) The Japanese method (JIS Z 313-1975), which has been adopted with important adjustments from the former ASTM designation A316-48T. This method involves collection of released hydrogen from a single pass weld above glycerine for 48h at 45 0 C. The total volume of hydrogen is reported in ml per 10Og deposit. Only 5 s of delay are allowed from extinction of the arc to quenching. (ii) The French method (N.F.A. 81-305-1975) where two beads are deposited onto core wires placed in a copper mould. Hydrogen released from this bead is collected above mercury, and the volume is reported in ml per 10Og fused metal (including the fused core wire metal). (iii) The International Institute of Welding (HW) method (ISO 3690-1977), where a single bead is deposited on previously degassed and weighed mild steel blocks clamped in a quickrelease copper fixture. The weldment is quenched and refrigerated according to a rigorously specified time schedule. Hydrogen released from the specimens is collected above mercury for 72 h at 25°C, and the results are reported in ml per 10Og deposit, or in g per ton fused metal. To avoid confusion, it is recommended to use the symbol HDM for the content reported in terms of deposited metal (ml per 10Og deposit), and HFM for the content referred to fused metal (ml per 100 g or g per ton fused metal). The relationship between HDM and HFM is shown in Fig. 2.12. As would be expected, these three methods do not give identical results when applied to a given electrode. Approximate correlations have been established between the HW criteria HDM and HFM and the numbers obtained by the Japanese and the French methods (designated HJIS and HFR, respectively). For covered electrodes tested at various hydrogen levels, we have:7

Fig. 2.12. The relation between HDM and HFM (0.9 is the conversion factor from ml per 10Og to g per ton). (2-25) (2-26) The conversion factor from HFR to HFM applies to a ratio of deposited to fused metal, DI(B + D), equal to 0.6, which is a reasonable average for basic electrodes. The use of HFM in preference of HDM is normally recommended, because it is a more rational criterion of concentration. Moreover, HDM values would be grossly unfair, if applied to high penetration processes like submerged arc welding. In GTA welds made without filler wire HDM cannot be used at all, since there is no deposit. It should be noted that the present HW procedure gives the amount of 'diffusible hydrogen'. For certain purposes the total hydrogen content may be wanted. It is obtained by adding the content of 'residual hydrogen' determined on the same samples by vacuum or carrier gas extraction at 6500C. A very small additional amount may be observed on vacuum fusion of the sample, tentatively labelled 'fixed hydrogen'. There is no clear line of demarcation between these categories of hydrogen. As will be discussed later, the extent of hydrogen trapping depends both on the weld metal constitution and the thermal history of the metal. In singlebead basic electrode deposits the diffusible fraction is usually well above 90%. 2.8.3 Reaction model Normally, measurements of hydrogen in weld metals are carried out on samples from solidified beads. Due to the rapid migration of hydrogen at elevated temperatures, such data do not represent the conditions in the hot part of the weld pool. Quenched end crater samples would be better in this respect, but they are not representative of normal welding. Further complications arise from the presence of hydrogen in different states (e.g. diffusible or residual hydrogen) and the lack of consistent sampling methods. Nevertheless, experience has shown that pick-up of hydrogen in arc welding can be interpreted on the basis of the simple model outlined in Fig. 2.13. According to this model, two zones are considered: (i) An inner zone of very high temperatures which is characterised by absorption of atomic hydrogen from the surrounding arc atmosphere.

Electrode Hot part of weld pool Absorption of atomic hydrogen (controlled by pH in the arc column)

Cold part of weld pool Desorption of hydrogen (controlled by pH2 in ambient gas phase)

Hydrogen trapped in weld metal Weld pool

Fig. 2.13. Idealised reaction model for hydrogen pick-up in arc welding. (ii) An outer zone of lower temperatures where the resistance to hydrogen desorption is sufficiently small to maintain full chemical equilibrium between the liquid weld metal and the ambient (bulk) gas phase. Under such conditions, the final weld metal hydrogen content should be proportional to the square root of the initial partial pressure of diatomic hydrogen in the shielding gas, in agreement with Sievert's law (equation (2-20)). 2.8.4 Comparison between measured and predicted hydrogen contents It is evident from the data in Table 2.2 that the reported ranges for hydrogen contents in steel weld metals are quite wide, and therefore not suitable for a direct comparison of prediction with measurement. For such purposes, the welding conditions and consumables must be more precisely defined. 2.8.4.1 Gas-shielded welding In GTA and GMA welds the hydrogen content is usually too low to make a direct comparison between theory and experiments. An exception is welding under controlled laboratory conditions where the hydrogen content in the shielding gas can be varied within relatively wide limits. The results from such experiments are summarised in Fig. 2.14, from which it is seen that Sievert's law indeed is valid. A closer inspection of the data reveals that the weld metal hydrogen content falls within the range calculated for chemical equilibrium at 1550 and 20000C, depending on the applied welding current. This shows that the effective reaction temperature is sensitive to variations in the operational conditions. An interesting effect of oxygen on the weld metal hydrogen content has been reported by Matsuda et al.9 Their data are reproduced in Fig. 2.15. It is evident that the hydrogen level is significantly higher in the presence of oxygen. This is probably due to the formation of a thin (protective) layer of slag on the top of the bead, which kinetically suppresses the desorption of hydrogen during cooling.

Table 2.2 Measured arc atmosphere compositions in steel welding. Also included are typical ranges for the weld metal hydrogen content. Data compiled by Christensen.4 Arc Atmosphere Composition (vol%) Method

Primary Source of Hydrogen

Weld Metal Hydrogen Content (ppm)

CO2

CO

H 2 +H 2 O

Range

Average

98-80

2-20

2 gas mixtures, (b) Ar-CC>2 gas mixtures. Data from Grong and Christensen.1

Carbon control

Silicon control

Pco>

atm

the former case. Normally, homogeneous nucleation of CO gas within the liquid metal is considered impossible, which means that the CO nucleation in practice must take place heterogeneously. However, the most probable site for CO evolution during droplet formation at the electrode tip will be the gas/metal interface itself, which allows carbon to be oxidised simultaneously with silicon and manganese. It is reasonable to assume that most of the observed carbon oxidation is located to the hot layers facing the arc, where the reaction is thermodynamically favoured. At other surface positions Si and Mn are expected to prevent carbon from reacting due to a rather low metal temperature, stated to be only slightly above the melting point at the time of detachment.21 It is evident from the data in Fig. 2.24(a) and (b) that the carbon losses increase with increasing O2 or CO2 contents in the shielding gas up to a certain critical level. Hence, supply of oxygen to the tip droplet surface is the rate controlling step for oxidation of carbon at low oxygen potentials. This conclusion is also consistent with calculations made by Corderoy et al.,22 who found that transport of atomic oxygen through a stagnant gaseous boundary layer close to the metal surface controls the oxidation rate of alloying elements at this stage of the process. The carbon oxidation will gradually decline with increasing oxygen concentrations in the shielding gas, probably as a result of build-up of carbon monoxide in the surrounding atmosphere. When the critical CO gas pressure is reached, the carbon reaction is blocked, silicon (and manganese) now exercising control of the oxygen level, as indicated in Fig. 2.25. For ArO 2 gas mixtures this critical pco pressure is attained at about 10 to 15 vol% O 2 in the shielding gas, corresponding roughly to 0.05 wt% C oxidised in chilled metal. When welding is performed in Ar-CO 2 mixtures the reaction is blocked at a much earlier stage of carbon oxidation (equal to about 0.02 wt% C lost in chilled metal), since dissociation of CO2 in this case will produce an additional amount of CO to concentrate in the surrounding gas phase.

Temperature, 0C Fig. 2.25. Break even equilibrium partial pressure of CO vs temperature for silicon control of oxygen level at 0.8 wt% Si and silica saturation. Data from Elliott et al. 23

The mechanism indicated above is supported by the data presented in Fig. 2.26, which show that a CO2-rich atmosphere even may act carburising if the initial carbon content of the electrode wire is sufficiently low. Moreover, it is interesting to note that the carbon-oxygen reaction is also influenced by the rate of droplet detachment. Since the highest carbon oxidation losses are normally associated with a coarse globular droplet transfer mode, this suggests that the reaction time is more important than the effective contact area available for interaction which depends on the droplet size. 2.10.1.3 Oxidation of silicon It is evident from the data in Fig. 2.27 that loss of silicon mainly take place in the weld pool, as indicated by the difference between the measured silicon content in chilled and multi-layer weld metal. In Ar-O 2 mixtures the Si loss increases steadily with increasing oxygen potential of the shielding gas. Thus, at 30 vol% O2 in Ar it amounts to 0.59 wt% Si (or 0.67 wt% O) removed from the weld pool as a result of deoxidation reactions. A similar situation exists in the case of CO2-shielded welding up to about 20 vol% CO2 in Ar. At higher CO2 contents, the Si loss tends to drop off, finally attaining an upper limit of approximately 0.30 wt% Si corresponding to 0.34 wt% O removed from the weld pool. In comparison, the amount of Si lost in the two preceding stages (i.e. electrode tip and arc column) is much smaller, as shown by the data for the chilled metal Si content. Since no slag is formed under the conditions of rapid cooling, silicon must escape in the form of a gaseous

Weld metal carbon content, wt%

GMAW (low-alloy steel)

(Gain)

(Loss)

Filler wire carbon content, wt% Fig. 2.26. Correlation between filler wire and weld metal carbon contents in CO2-shielded welding. Data from Ref.24.

(a) Chilled metal (falling droplet) Multi-layer weld metal

Wt% Si

Electrode wire

Vol% O 2 in Ar

(b) Chilled metal (falling droplet) Multi-layer weld metal

Wt% Si

Electrode wire

Vol% CO 2 in Ar

Fig. 2.27. Measured silicon contents in chilled and multi-layer weld metals vs the oxygen potential of the shielding gas; (a) Ar-02 gas mixtures, (b) Ar-CC>2 gas mixtures. Data from Grong and Christensen.1

product. Evaporation losses can in this case be excluded due to a very low vapour pressure of silicon at the prevailing temperatures. It is therefore reasonable to assume that SiO(g) forms as a result of chemical reactions occurring at the electrode tip. The observed decrease in chilled metal Si content with increasing O2 and CO2 contents in the shielding gas is probably caused by the presence of CO at the gas/metal interface, which facilitates SiO formation according to the reaction: (slag) (gas) (gas) (gas) (2-36)

PSiO,10-3atm

Figure 2.28 shows a plot of the equilibrium partial pressure of SiO vs temperature at silica saturation for three different CO levels. Note that stoichiometric amounts of CO2 have been assumed to form in order to calculate psi0. It is evident from the thermodynamical data presented in Fig. 2.28 that the formation of SiO is strongly dependent on the CO partial pressure at the slag/metal interface. Thus, from a thermodynamic standpoint the silicon loss at the electrode tip should be most pronounced during CO2-shielded welding due to the resulting higher CO pressure. The data shown in Fig. 2.27(a) and (b) support this assumption. It is seen that the silicon loss is increased by a factor of 3 to 5 in presence of CO2 when comparison is made on the basis of equal oxygen potential of the shielding gas (i.e. equal loss of deoxidants in the weld pool). Similar observations have also been made by Heile and Hill27 from determination of silicon in collected GMA welding fumes. The recorded chilled metal Si loss in Fig. 2.27(a) and (b) is in good agreement with the reported fume formation rates of silicon. Since all CO consumed in reaction (2.36) is expected to be regenerated immediately by decomposition of CO2 at the metal surface, the high CO partial pressure required for SiO formation at the electrode tip is maintained even in the case of extensive silicon losses. Consequently, the net reaction can be written as:

Temperature, 0C Fig. 2.28. Equilibrium partial pressure of SiO vs temperature at different CO levels. Data from Refs. 25 and 26.

(slag)

(dissolved)

(gas)

(2-37)

When welding is performed in Ar-O 2 gas mixtures, pSiO andpco may be taken proportional to the recorded loss of silicon and carbon in chilled metal (see data in Fig. 2.29). It is evident from this plot that the silicon loss is directly proportional to the corresponding loss of carbon up to a certain critical level. Thus, during the initial period of carbon oxidation at the electrode tip the SiO formation is probably controlled by the resulting partial pressure of CO at the slag/ metal interface, according to reaction (2-36). When the carbon reaction is blocked, the chilled metal silicon loss becomes independent of the CO partial pressure (see reaction (2-37)), since all CO consumed in the SiO formation will immediately be recirculated within the system. However, at the break even point for silicon control of the oxygen level at the electrode tip, the CO pressure in the surrounding gas phase will be the same for both Ar-O 2 and Ar-CO 2 gas mixtures. Hence, the recorded loss of silicon in chilled metal at 20 vol% CO2 in Ar is seen to be similar to that in Ar + 10 vol% O2, as indicated by the heavy broken line in Fig. 2.29. At the temperatures where liquid steel is normally deoxidised, silicon and manganese have a strong affinity to oxygen. Their ability to form stable oxides decreases rapidly with increasing temperature, and above approximately 180O0C silicon and manganese do no longer act as efficient deoxidation agents. Precipitation of manganese silicate slags is therefore favoured by the lower metal temperatures prevailing at the electrode tip and in the cold part of the weld pool. At higher temperatures, these oxides become unstable. Consequently, as a result of the metal superheating occurring during droplet transfer through the arc column, the macroscopic slag phase formed earlier at the electrode tip surface (as reported by Corderoy et ah12) will redissolve in the metal. This gives rise to a relatively high chilled metal oxygen content (to be discussed below).

Loss of silicon (%)

Ar+20 vol% CO2

Ar+10vol%O2

Loss of carbon (%) Fig. 2.29. Correlation between loss of carbon and silicon in chilled metal at different O 2 levels in the shielding gas. The corresponding loss of silicon at 20 vol% CO2 in Ar is indicated by the heavy broken line in the graph. Data from Grong and Christensen.1

Example (2.5)

Consider CO2-shielded welding on a thin sheet of low-alloy steel with a 0.8mm dia. electrode wire under the following conditions:

Based on the data presented in Fig. 2.27(b), calculate the fume formation rate (FFR) of silicon (in mg per min) due to SiO formation at the electrode tip. The wire feed rate is 125mm s"1. Solution

The total loss of silicon due to SiO formation may be taken equal to the observed difference between the filler wire and the chilled metal silicon contents. For welding in pure CO2, we get:

The corresponding fume formation rate of silicon (in mg min"1) can readily be calculated when the wire feed rate (WFR) is known. Taking the density of the steel equal to 7.85mg mm"3, we obtain:

A comparison with the measured FFR of silicon in Table 2.6 (at / = 13OA) shows that the calculated value is reasonable correct. Moreover, these data support our previous conclusion that the SiO formation is favoured by a high CO2 content in the shielding gas due to the dissociation reaction. In fact, more detailed studies of the reaction kinetics have confirmed that the rate of SiO formation is proportional to the resulting partial pressure of CO at the gas/metal interface,28 in agreement with equation (2-36). 2.10.1.4 Evaporation of manganese It is seen from the data in Fig. 2.30(a) and (b) that the amount of manganese lost in chilled metal is virtually independent of the oxygen potential of the shielding gas, as indicated by the constant difference of about 0.35 wt% between the filler wire and the chilled metal Mn contents in both graphs. This implies that significant amounts of manganese are lost during droplet transfer through the arc column as a result of evaporation. At the prevailing temperatures, the vapour pressure of iron is also high due to the almost unity activity of Fe. If the average arc metal temperature is taken equal to about 24000C,29 the data in Fig. 2.31 indicate that the vapour pressures of iron and manganese (at 1.27 wt% Mn) are nearly identical and close to 0.05 atm. In the hot surface layers of liquid metal facing the arc the temperature will be even higher, which means that iron vapour will dominate. Measurements of collected GMA welding fume reported by Heile and Hill27 (see data in Table 2.6) show a substantial higher loss of iron than that derived from simple thermodynamical calculations taking the rate of element loss proportional to the vapour pressure. From their results a reasonable value of the average mass ratio Fe to Mn in dust is about 5. Consequently, as a preliminary estimate the loss of iron may be taken 5 times the amount of manganese lost

Table 2.6 Measured fume formation rates in GMA welding of ferrous materials. Data from Heile and Hill.27

Shielding Gas

Argon

Ar+ 2 % O 2

Ar+ 5% O 2

Ar + 25% CO2

Pure CO2

Current

Voltage

(A)

(V)

Fume Formation Rate (mg min"1) Mn

Si

Fe

250

29

1

1

22

300 350

31 35

1 5

0 4

12 51

150 200 300 400

28 28 29 34

15 12 5 18

8 10 4 16

134 75 35 86

100 200 300

28 28 28

29 16 10

33 22 23

273 129 76

100

23

11

20

75

150 300

27 35

13 29

35 62

105 191

130 150 200 250 300

27 30 30 30 30

13 14 19 31 36

59 63 73 112 125

86 120 126 216 214

in chilled metal, corresponding to a total loss of 1.7 wt% (Fe + Mn) or 500mg (Fe + Mn) per min. The reported fume formation rate of Fe and Mn under nearly similar conditions is only one half of that stated above, which indicates that the calculated flux of metal vapour may be somewhat overestimated. However, if these two values are considered to represent borderline cases, the volume of metal vapour is in the range from 300 to 500 times that of the droplets and will therefore be more than sufficient to protect the metal from arc atmosphere oxidation at this stage of the process. This conclusion is consistent with statements made by Distin et al?1 who claim that iron vapour acts as an effective oxygen getter already at about 19000C. Very large amounts of manganese are also lost in the weld pool stage, as shown by the difference between the measured Mn contents in chilled and multi-layer weld metals. This situation appears to be quite similar to that of silicon. For Ar-O 2 mixtures the manganese loss increases steadily with increasing oxygen contents in the shielding gas, and reaches a value of about 1.08 wt% Mn (or 0.31 wt% O) removed from the weld pool at 30 vol% O2 in Ar. In the case OfAr-CO2 shielded welding the Mn oxidation loss starts to drop off at a CO2 content of about 20 vol%, finally attaining an upper limit of about 0.50 wt% Mn corresponding to 0.15 wt% O removed from the weld pool. A more detailed discussion of oxidation reactions in GMA welding is given in Section 2.10.1.5. Example (2.6)

Consider GMA welding low-alloy of steel under conditions similar to those in Example 2.5.

(a)

Wt% Mn

Chilled metal (falling droplet)

Multi-layer weld metal Electrode wire

Vol% O 2 in Ar

Wt% Mn

(b)

Chilled metal (falling droplet) Multi-layer weld metal Electrode wire

Vol%CO 2 inAr Fig. 2.30. Measured manganese contents in chilled and multi-layer weld metals vs the oxygen potential of the shielding gas; (a) Ar-02 gas mixtures, (b) Ar-CO2 gas mixtures. Data from Grong and Christensen.1 Based on the data presented in Fig. 2.30(b), calculate the fume formation rate (FFR) of manganese due to evaporation losses occurring during droplet transfer through the arc column. Estimate also the effective mass transfer coefficient for manganese evaporation under the prevailing circumstances by utilising the vapour pressure data in Fig. 2.31. The surface temperature of the falling droplets is assumed constant and equal to 26000C.

PMr/PFe

LogpMn,atm

Temperature, 0C Fig. 2.31. Equilibrium manganese vapour pressure and corresponding vapour pressure ratio pMn to PFe vs temperature at 1.27 wt% Mn in iron. Data from Kubaschewski and Alcock. 30 Solution

The total loss of manganese due to evaporation may be taken equal to the observed difference between the filler wire and the chilled metal manganese contents. For welding in pure CO2, we have:

The corresponding fume formation rate of manganese (in mg min"1) can readily be calculated when the wire feed rate (WFR) is known. Taking the density of the steel equal to 7.85mg mm~3, we obtain:

A comparison with the data in Table 2.6 reveals that the reported fume formation rate of manganese (at / = 13OA) is much lower than computed in the present example. This discrepancy can probably be attributed to differences in the filler wire manganese content. Assuming that the evaporation loss of manganese is controlled by a transport mechanism in the gas phase, we can estimate the effective mass transfer coefficient from equation (2-15) by inserting a reasonable average value for the manganese vapour pressure at the gas/metal interface (pMn in the bulk phase is taken equal to zero). Reading from Fig. 2.31 (at T= 26000C) gives:

If the diameter of the falling droplets is taken equal to the diameter of the filler wire, it is possible to calculate the total loss of manganese associated with one droplet (in mol):

Since the average flight time of large, globular droplets through the arc column is of the order of one second, the corresponding flux of manganese vapour per unit time is close to 9.97 X 10~8 mol s"1. Thus, by rearranging equation (2-15), we obtain the following value for the effective mass transfer coefficient:

Although the above value is rather uncertain, the calculated mass transfer coefficient is of the expected order of magnitude. This supports our previous conclusion that the evaporation kinetics are controlled by a transport mechanism in the gas phase. 2.10.1.5 Transient concentrations of oxygen It is evident from the data summarised in Fig. 2.32 that the oxygen content in both chilled and multi-layer weld metal increases with increasing oxygen potential of the shielding gas. The chilled metal analysis is representative of the oxygen absorption occurring at the electrode tip due to the lack of gas/metal interaction in the arc column. Measurements of manganese oxidation losses during droplet formation have been performed by Corderoy et al.22 From the curve presented for 20ms tip melting cycles, a reasonable estimate for the manganese oxidation loss in Ar-O 2 shielding gas mixtures may be: (2-38) Taking the Si to Mn mass ratio in precipitated slag equal to 0.66,22 the corresponding loss of silicon is equal to: (2-39) Based on equations (2-38) and (2-39) it is possible to calculate the oxygen absorption at the electrode tip which is associated with the MnO and the SiO2 slag formation. If corrections also are made for the amount of oxygen simultaneously removed as iron oxide*, we obtain: (2-40)

*An approximate correction can be made from an analysis of the Fe to Mn mass ratio in precipitated slag, which under the prevailing circumstances is close to 0.16.22

(a)

Wt% O


Vol%O2inAr (b)

Wt% O


Vol% CO2 in Ar Fig. 2.32. Measured oxygen contents in chilled and multi-layer weld metals vs the oxygen potential of the shielding gas; (a) Ar-C>2 gas mixtures, (b) Ar-CO2 gas mixtures. Data from Grong and Christensen.1 At 30 vol% O2 in Ar the absorption of oxygen is roughly 0.27 wt% O, which is reasonably close to that recorded in the chilled metal analysis (about 0.23 wt% O). The rate controlling step for metal oxidation at this stage of the process is believed to be transport of atomic oxygen through a stagnant gaseous boundary layer of Ar and/or CO adjacent to the metal surface.22 On the other hand, the measured chilled metal oxygen contents are much too low to account for the heavy oxidation losses of deoxidants observed in multi-layer welds. This indicates that

considerable amounts of oxygen are introduced in the hot part of the weld pool immediately beneath the root of the arc. Although the gas/metal interfacial contact area available for reaction is much smaller than that of the electrode tip (or falling) droplets, the strong turbulence existing in the hot part of the pool will provide an effective circulation of the liquid metal through the reaction zone.32 Moreover, absorption of oxygen at this stage of the process will be favoured by the increased time available for gas/metal interaction. If the diameter of the reaction zone is taken equal to about 3mm, the time available for oxygen absorption in the weld pool is of the order of one second for a typical welding speed of 3mm s"1. In comparison, the corresponding reaction time during droplet formation at the electrode tip is only 20 to 50 ms. Calculations of the total oxygen absorption can be done on the basis of the measured difference between silicon and manganese contents in chilled and multi-layer weld metals, designated A[%S7] and A[%Mn], respectively*. Moreover, corrections should be made for the amount of oxygen simultaneously removed as iron oxide from the weld pool. For deoxidation with silicon and manganese the mass ratio wt% Fe to wt% Mn in precipitated slag is equal to about O.I.1 This leads to the following balance: (2-41) At 30 vol% O2 in Ar the total oxygen absorption amounts to:

It is seen from the graphical representation of equation (2-41) in Fig. 2.33(a) and (b) that most of the oxygen pick-up takes place in the weld pool. However, at present it is not clear whether the calculated values represent a real transient concentration in the hot part of the weld pool or a number in concentration units representing precipitation of manganese silicate slags. According to Fischer and Schumacher33 the solubility of oxygen in liquid iron is 0.94 wt% at 19000C and 1.48 wt% at 20000C This temperature range is probably relevant with respect to the hot part of the weld pool, although the surface metal temperature will be even higher.34 However, in steel weld metals the oxygen concentrations should be well below this solubility limit in the presence of silicon and manganese. Taking the average weld pool silicon content equal to 0.50 wt%, the corresponding oxygen content in equilibrium with a silicasaturated slag is roughly 0.10 and 0.20 wt% at 1900 and 20000C, respectively.23 On the other hand, under the prevailing circumstances there will be no solid/liquid interface available for nucleation of oxide particles, and hence homogeneous nucleation is the only possibility. According to Sigworth and Elliott35 this requires a relatively high degree of supersaturation, which means that the oxygen concentration most likely will exceed the Si-Mn-O equilibrium value before slag precipitation occurs. The data in Fig. 2.33(a) and (b) indicate that the weld pool oxygen absorption is controlled by a complex transport mechanism in the gas phase. However, since mass transfer in gas-jet/ liquid systems is not fully understood,3 we shall only consider the limiting case where the resistance to mass transfer is confined to a stagnant gaseous boundary layer adjacent to the metal surface. Under such conditions equation (2-10) predicts that the transient oxygen concentration is determined by the partial pressure of atomic oxygen in the plasma gas, as shown *Oxygen consumed in CO and SiO formation is not included.

(a)

Wt% O

Calculated total oxygen absorption Analytical weld metal oxygen content

Vol% O2 in Ar

(b)

Wt% O

Calculated total oxygen absorption Analytical weld metal oxygen content

Vol% CO2 in Ar Fig. 2.33. Calculated total oxygen absorption in GMA welding at different oxygen potentials of the shielding gas; (a) Ar-O 2 gas mixtures, (b) Ar-CO 2 gas mixtures. The analytical weld metal oxygen content is indicated by the broken lines in the graphs. Data from Grong and Christensen.1

by the plots in Fig. 2.34. If we as a borderline case assume that all oxygen present in the plasma gas is immediately absorbed in the liquid metal, the slope of the curve in Fig. 2.34 for Ar-O 2 gas mixtures (equal to about 2.67 wt% dissolved oxygen at one atmosphere total pressure of atomic oxygen) is representative of the total amount of gas passing through the arc column. Taking the mass of liquid metal leaving/entering the reaction zone equal to 3Og min"1 under the prevailing circumstances,1 the following gas flow rate is obtained (in Nl min"1).

This value corresponds to about 6 per cent of the total shielding gas flow rate. In contrast to the situation described in Fig. 2.34 for Ar-O 2 gas mixtures, a large deviation from the expected relationship is observed for welding in CO2-rich atmospheres. At present, the reason for this shift in the reaction kinetics is not known. However, it is evident from the data presented in Fig. 2.34 that the effective mass transfer coefficient decreases by a factor of about 2.5 when the CO2 content in the shielding gas increases from 10 to 100 vol%. This implies that the oxidation capacity of pure CO2 is comparable with that of Ar + 13 vol% O2, although the partial pressure of atomic oxygen in the plasma gas is equivalent with an oxygen content of about 33 vol%. Example (2.7)

[%O]t0t,wt%

Consider GMA welding of low-alloy steel in Ar + 20 vol% CO2 and pure CO2, respectively. Based on the results in Figs. 2.27(b) and 2.30(b), calculate the total weight of top bead slag (in gram per 100 gram weld deposit) which forms as a result of deoxidation reactions. Assume in these calculations that the iron to manganese mass ratio in precipitated slag is equal to 0.1.

Pure CO2

P0, atm Fig. 2.34. Calculated total oxygen absorption in GMA welding at different partial pressures of atomic oxygen in the plasma gas. Data from Grong and Christensen.1

Solution

The amount of silicon and manganese lost as a result of deoxidation reactions is equal to the observed difference in the chilled and multi-layer weld metal Si and Mn contents. Assuming that these elements are removed from the weld pool as SiO2 and MnO, respectively, the following balance is obtained:

Thus, for welding in Ar + 20 vol% CO2, the total weight of slag amounts to:

Similarly, for CO2-shielded welding, we get:

A comparison with the experimental data in Fig. 2.35 shows that there is a fair agreement between the amount of slag recorded by weighing and that calculated from a simple mass balance of silicon, manganese and iron.

g slag/10Og deposit

Calculated weight of slag Measured weight of slag

Vol% CO2 in Ar Fig. 2.35. Comparison between measured and calculated weight of top bead slag in CO2-shielded welding. Data from Grong and Christensen.1

2.10.1.6 Classification of shielding gases The data in Fig. 2.34 provide a basis for evaluating the oxidation capacity of various shielding gases. For welding in Ar + O2 and Ar+CO2 gas mixtures up to 10 vol% CO2 in argon, the total oxygen absorption is approximately given by the following equation:

(2-42) Similarly, for welding with CO2-rich shielding gases (i.e. between 10 and 100 vol% CO2), we obtain: (2-43) Equal oxidation capacity means that the total weld metal oxygen absorption is the same for both shielding gas mixtures. Hence, we may write:

(2-44) when the CO2 content in the shielding gas is less than 10 vol%, and

(2-45)

when welding is performed with CO2-rich shielding gases (more than 10 vol% CO2 in Ar). Based on equations (2-44) and (2-45) it is possible to compare the oxidation capacity of various shielding gases (see Table 2.7). Included in Table 2.7 is also a slightly modified version of the International Institute of Welding (HW) classification system,36 which is based on an evaluation of retained (analytical) oxygen in the weld deposit. It is evident from these data that both systems are applicable and mutual consistent, although the former one utilises a more rational criterion for the shielding gas oxidation capacity. 2.10.1.7 Overall oxygen balance In GMA welding with solid wires, the CO content in the exhaust gas provides a direct measure of the extent of gas/metal interaction. This CO content should be compatible with that calculated from an overall oxygen balance for the reaction system.37 Example (2.8)

Consider GMA welding of low-alloy steel under the following conditions:

Table 2.7 Proposed shielding gas classification scheme for GMA welding of low-alloy steel according to equations (2-44) and (2-45). Included is also a modified version of the corresponding IIW's classification system.36 Shielding Gas Composition

[%O] tot

Vol%CO2

Vol%O 2

Vol%Ar

(wt%)

IIW's Terminology*

0-4 0-2

0-2 0-1

balance balance balance

0.60

Extremely oxidising (> 0.07)

The analytical weld metal oxygen content (in wt%) is given by the values in brackets. The shielding gas is pure CO2 and is supplied at a constant rate of 15Nl min *. Based on the composition data in Table 2.8 calculate the resulting CO content in the welding exhaust gas. Solution First we calculate the nominal weld metal chemical composition by neglecting oxidation loss of alloying elements due to chemical reactions:

The dilution ratios BI(B + D) and DI(B + D) can be estimated from the classic heat flow theory presented in Chapter 1. From equations (1-75) and (1-120), we have:

Table 2.8 Chemical composition of filler wire, base plate and weld metal used in Example 2.8. C (wt%)

O (wt%)

Si (wt%)

Mn (wt%)

Filler wire

0.10

0.01

0.93

1.52

Baseplate

0.14

0.007

0.40

1.30

Weld metal

0.09

0.065

0.35

0.81

Element

and

This gives:

The extent of gas/metal interaction can then be evaluated from the observed concentration displacements:

Calculated values for the concentration displacements of carbon, oxygen, silicon and manganese utilising the composition data in Table 2.8 are given below. Element \-%X\nom.

[A%X]

C 0

-

1 2

-0.03

O 0

-

0 0 8

0.057

0

'

Si

Mn

6 3

L 3 9

-0.28

-0.58

The total CO evolution (in mol min l) can now be computed from an overall oxygen balance for the reaction system. In these calculations we shall assume that Si and Mn lost as SiO(g) and Mn(vap.) immediately react with CO2 to form SiO2 and MnO, respectively*. Taking the density of steel equal to 7.85 X 10~3 g mm"3, the total mass of weld metal produced per unit time amounts to:

Overall oxygen balance (i.e. consumption of CO2) Oxidation of carbon:

Oxidation of silicon:

:

CO 2 consumed in oxidation of iron vapour is disregarded.

Oxidation of manganese:

Increase in oxygen content:

Total CO evolution (sum):(13.4 + 53.5 + 28.3 + 9.6) X 10~3 mol CO min - 1 = 104.8 X 10~3 mol CO min' 1 Based on this information it is possible to calculate the resulting CO content in the welding exhaust gas:

A comparison with the data in Table 2.2 shows that a CO content of about 15 vol% is reasonably close to that determined by analysis. 2.10.1.8 Effects of welding parameters So far, gas/metal interactions in GMA welding has mainly been discussed in terms of the oxygen potential of the shielding gas. In the following, some consideration will be given to the effects of welding parameters on the weld metal chemistry. Amperage

When the welding current is raised, the time available for interaction decreases due to the more rapid detachment of the electrode tip droplets. At the same time the interfacial contact area increases as the average droplet size becomes smaller. From measurements of fume formation rates in GMA welding,27 it has been shown that these two counteracting effects will almost cancel, i.e. the total amount of emitted dust (in mg per g deposit) is found to be constant and nearly independent of the applied amperage. On the other hand, the total fume formation rate is probably not a reliable index for the burn-off of Si and Mn, since the evolution of iron vapour during droplet transfer will tend to conceal the corresponding loss of alloying elements. The effect of amperage (or more correct the droplet detachment frequency) on the burn-off of carbon, silicon, and manganese in CO2-shielded welding has been investigated by Smith et al.38 They found that the recovery of alloying elements in the weld deposit increased with increasing welding current (i.e. droplet detachment frequency). In view of the previous discussion, it is reasonable to assume that the higher weld metal carbon and silicon contents reported by Smith et al3S are a result of a reduced CO and SiO gas evolution at the electrode tip due to the shorter time available for chemical interaction. In the case of manganese reduced evaporation losses because of a more rapid transfer of the droplets through the arc column offers a

reasonable explanation to the increased element recovery. This shows that the weld metal chemistry is sensitive to variations in the welding current. Arc voltage

Since the arc voltage neither affects the melting rate nor the droplet size to any great extent,39 variations in the arc voltage should only have a minor effect on the weld metal chemistry. This conclusion is apparently in conflict with observations made by Lindborg,40 who found that the oxidation reactions in GMA welding were strongly voltage dependent and at the same time independent of the welding current, the droplet detachment frequency, and the mode of metal transfer (spray or short-circuiting). Consequently, further investigations are required to explain these discrepancies. Welding speed

It can be inferred from the data of Grong and Christensen1 that the analytical weld metal carbon and oxygen contents are virtually independent of the welding speed v within the normal range of GMAW (i.e. from 0.4 to 6 mm s"1). However, the intensified losses of silicon and manganese observed at low welding speeds indicate that more oxygen is absorbed in the weld pool under such conditions. This point is more clearly illustrated in Fig. 2.36 which shows a plot of [%O]tot vs v for a series of multi-pass GMA welds deposited under the shield of Ar + 10 vol% O2. It is evident that the total oxygen absorption increases nearly by a factor of two when the welding speed decreases from 6 to 0.4mm s"1. This shows that the welding speed has a marked effect on the transient oxygen pick-up in the hot part of the weld pool during GMA welding, since it controls the time available for element absorption. 2.10.2 Submerged arc welding In flux-shielded processes the reaction pattern is much more difficult to assess because of the

[%O]tot,wt%

Calculated total oxygen absorption

Travel speed, mm/s Fig. 2.36. Calculated total oxygen absorption in GMA welding at different travel speeds. Data from Grong and Christensen.1

complicating presence of the slag. For this reason most investigators have chosen to analyse empirically slag/metal reactions in SA welding. Nevertheless, some authors have been able to interpret their results on more theoretical grounds in spite of the complex reaction systems involved.41"*5 Unfortunately, these thermodynamic approaches give, at best, only a qualitative description of the compositional changes occurring during the welding operation. Recently, a kinetic model has been developed by Mitra and Eagar46 to account for variations in the element recovery in both single-pass and multi-pass SA steel weldments. From their work it is evident that the transfer of alloying elements between the slag phase and the weld metal cannot be adequately described by means of a primitive model of pseudo-equilibrium without including a more detailed analysis of the reaction kinetics. This shows that the conditions existing in SA welding are quite similar to those prevailing during GMA welding, although the experimental and theoretical challenges are much greater in the former case due to the complicating presence of a macroscopic slag phase. 2.10.2.1 Flux basicity index During SA welding of steel, oxygen may be transferred from the slag to the weld metal due to decomposition of easily reduced oxides at elevated temperatures according to the overall reaction: MxOy = xM (dissolved) + y O (dissolved)

(2-46)

where MxOy denotes any oxide component in the slag phase (e.g. SiO2, MnO or FeO). The basicity index (B.I.), originally adopted from steel ladle refining practice, is most frequently employed for assessment of oxygen pick-up in SA welding, since it gives an approximate measure of the flux oxidation capacity. A number of different expressions exists in the literature, but for the purpose of convenience the basicity index defined by Eagar47 has been adopted here: basic oxides" non- basic oxides

(2-47) where the concentration of each flux component is given in weight percent. It is evident from Fig. 2.37, which shows a typical correlation between the weld metal oxygen content and B.L, that the oxygen level of welds produced under acid fluxes (i.e. low B.I.) is strongly dependent on the basicity index. In contrast, the oxygen concentrations of welds deposited under basic fluxes are seen to be essentially independent of B.I., as indicated by the horizontal part of the curve in Fig. 2.37. It should be noted that this analysis gives no information about the extent of slag/metal interaction, since it is based on data for retained oxygen in the weld deposit. Consequently, because of the empirical nature and limited applicability of the basicity index, its role in the choice of welding fluxes for SA welding is a keenly debated question.

Oxygen content, wt%

Basic fluxes

Acid fluxes

Flux basicity index Fig. 2.37. Correlation between retained oxygen and flux basicity in SA welding. Data from Eagar.47

2.10.2.2 Transient oxygen concentrations In SA welding of C-Mn steels, the transient flux of oxygen passing through the weld pool can be estimated from the observed concentration displacements of silicon and manganese, which may be taken equal to the difference between absorbed and rejected Si and Mn, respectively: (2-48) and (2-49) If we assume that rejection of Si and Mn in the weld pool occurs as a result of MnSiO3 microslag precipitation and subsequent phase separation, [%Mn]rej^ is bound to [%Si]rej. through the following stoichiometric relationship: (2-50) Taking the ratio between absorbed Mn and Si in the weld metal equal to k, a combination of equations (2-48), (2-49) and (2-50) gives:

(2-51) The value of k is difficult to evaluate in practice, but in view of the reported mass transfer coefficients for Mn and Si a reasonable estimate would be about 0.5 in the case of manganese silicate fluxes.46 Under such conditions the total oxygen absorption, [%O]abs is given by:

(2-52) where [A%O] is the observed concentration displacement of oxygen in the weld metal, and [%O]rej. is the amount of oxygen rejected from the weld pool as a result of deoxidation reactions. Based on equation (2-52) it is possible to estimate the total oxygen absorption during SA welding of C-Mn steels from an analysis of measured concentration displacements of oxygen, silicon, and manganese in the weld metal. The results of such calculations are shown graphically in Fig. 2.38, using data from Indacochea et a/.44 It is evident from this plot that the total oxygen absorption during SA welding is much larger than that inferred from an analysis of retained oxygen in the weld deposit. The situation is thus quite similar to that observed experimentally in GMA welding (see Fig. 2.33). It should be noted that the calculated values for [%O]abs. in Fig. 2.38 may be encumbered by systematic errors due to the number of simplifying assumptions inherent in equation (2-52). However, this does not affect our main conclusion regarding the significance of the oxygen absorption, since more refined calculations give a pattern similar to that observed above (see Fig. 2.39). 2.10.3 Covered electrodes Chemical reactions during SMA welding have been studied by several investigators in the

Oxygen content, wt%

Experimental MnO-FeO-SiO2 fluxes

Retained oxygen

[A% Si]0.5 - [A%Mn] Fig. 2.38. Calculated total oxygen absorption in SA welding with experimental MnO-FeO-SiO2 fluxes. Data from Indacochea et al.AA

Oxygen content, wt%

Flux Type CS: Bead on Plate » — : Two Wires Filled Symbols: Flux FB

Absorbed oxygen Retained oxygen

Silicon content, wt% Fig. 2.39. Calculated total oxygen absorption in SA welding with commercial calcium silicate (CS) and fluoride-basic (FB) fluxes. Data from Christensen and Grong.45 past.47"51 Most of these investigators have interpreted their results as a high-temperature equilibrium between the slag and the weld metal, but a verified quantitative understanding of the transfer of elements during welding is lacking. This situation arises mainly from the lack of adequate thermodynamic data for the complex slag/metal systems involved. 2.10.3.1 Reaction model The reaction model presented here is restricted to welding with basic covered electrodes. During SMA welding gases are generated by decomposition of compounds present in the electrode coating. In the case of basic covered electrodes, the decomposition of limestone results in an atmosphere consisting predominantly of carbon monoxide and carbon dioxide, containing only small amounts OfH2 and H2O (see data in Table 2.2). The characteristic high concentrations of CO and CO2 in the arc atmosphere would be expected to lead to extensive absorption of carbon and oxygen in the weld metal. Under the prevailing circumstances, it is reasonable to assume that these reactions approach a state of local pseudo-equilibrium during droplet transfer through the arc column. During the subsequent stage of cooling in the weld pool, a supersaturation with respect to the various deoxidation reactions is initially increasing, which is released when the conditions for nucleation of the respective reaction products are reached. Since carbon is a much stronger deoxidant than silicon and manganese at temperatures above about 17000C,23 it is reasonable to assume that carbon will be in control of the oxygen level during the initial stage of cooling*, in accordance with the reaction: C (dissolved) + O (dissolved) = CO(gas)

(2-53)

* Although gases such as CO and CO2 are widely dissociated and ionised in the arc column, from a thermodynamic standpoint, there is no objection to the choice of molecular species as components for the system, provided that equilibrium is maintained down to temperatures where such species are stable.

Oxygen content, wt%

Carbon boil in the weld pool has been detected experimentally during welding with covered electrodes,49 which implies that heterogeneous nucleation of CO is kinetically feasible under the prevailing circumstances. Possible nucleation sites for CO are gas bubbles present in the macroscopic slag layer covering the metal, created by the vigorous stirring action of the arc plasma jet. It should be noted that this behaviour is in sharp contrast to experience with GMA welding, where little or no oxidation of carbon takes place in the weld pool, as shown previously in Section 2.10.1.2. It is tentatively suggested that the apparent difference between SMA and GMA welding regarding the possibilities for CO nucleation in the weld pool arises from the lack of a macroscopic slag layer in the latter case. Unlike carbon, the deoxidation capacity of silicon (and manganese) increases rapidly with decreasing metal temperatures (se Fig. 2.40), which means that carbon oxidation becomes gradually suppressed during cooling in the weld pool. Upon reaching the critical temperature indicated in Fig. 2.40, the carbon reaction is blocked, silicon and manganese now control the oxygen level. An unknown but significant fraction of the manganese silicate inclusions precipitated in the hot part of the weld pool beneath the root of the arc are brought by convection currents to the interface between the macroslag and the metal, where they are readily absorbed. The remaining fraction formed in the cold and unstirred part of the weld pool is trapped in the metal solidification front in the form of finely dispersed oxide particles. This results in a high and rather unpredictable weld metal oxygen content. The above reaction model has been tested experimentally against data obtained from a series of hyperbaric welding experiments carried out in a remotely controlled pressure chamber with basic covered electrodes containing various levels of ferrosilicon in the electrode coating (see Table 2.9). Welding under hyperbaric conditions offer the special advantage of assessing the reactions through variations in the ambient pressure without changing the composition of the electrode coating or the core wire. Consequently, if the proposed reaction model

0.1 wt%Cat10bar.

0.1 wt% C at 1 bar

Temperature,°C Fig. 2.40. The break even equilibrium temperature for silicon control of oxygen level at 0.1 wt% C and 0.3 wt% Si. Data from Elliott et al.23

Table 2.9 Contents of ferrosilicon and iron powder in the electrode coating of experimental consumables used in the hyperbaric welding experiments. Electrode

FeSi (76 wt% Si)

Iron Powder

R*

4.5 wt%

31wt%

A

5.5 wt%

30 wt%

B

6.5 wt%

29 wt%

C

7.5 wt%

28 wt%

Carbon content, wt%

^Reference electrode (E8018-C1 type electrode).

Electrode R A B C

Low FeSi levels

Total pressure, bar

Fig. 2.41. Carbon absorption in hyperbaric SMA welding. Data from Grong et al.51 is at least qualitatively correct would expect a correlation between the weld metal carbon content and the concentrations of oxygen, silicon and manganese, both under atmospheric and hyperbaric welding conditions. The main effect of pressure on weld metal chemistry is thus to suppress the carbon-oxygen reaction in the weld pool at the expense of intensified oxidation losses of silicon and manganese, as indicated by the thermodynamic data in Fig. 2.40. 2.103.2 Absorption of carbon and oxygen It is evident from the data presented Fig. 2.41 that the weld metal carbon content increases monotonically with pressure from 1 to 31 bar for all four electrodes involved. This indicates that the carbon oxidation in the weld pool is systematically suppressed under hyperbaric welding conditions. Moreover, Fig. 2.41 reveals a small but important effect of electrode deoxidation capacity on the weld metal carbon content. Since ferrosilicon itself is an insignificant source of carbon, the observed increase in the carbon concentrations with increasing additions of ferrosilicon to the electrode coating is an indication that carbon oxidation in the weld pool is blocked at an earlier stage of the process at high silicon levels, according to the reaction:

Si (dissolved) + 2CO(gas) = 2 C (dissolved) + SiO2 (slag)

(2-54)

This interpretation is further supported by the results from the oxygen determination contained in Fig. 2.42. Although there is considerable scatter in the data in this figure, it is evident that the recorded enhancement of the weld metal carbon content at high ferrosilicon levels in the electrode coating is accompanied by a corresponding reduction in the oxygen concentrations. 2.10.3.3 Losses of silicon and manganese Suppression of carbon oxidation in the weld pool at elevated pressures gives rise to intensified oxidation losses of silicon and manganese, as shown in Figs. 2.43 and 2.44. Moreover, it is apparent that increased additions of ferrosilicon to the electrode coating result in a corresponding increase in both the silicon and the manganese concentrations. This finding suggests that the final weld metal content of the deoxidants is controlled by the reaction: Si (dissolved) + 2MnO (slag) = 2 Mn (dissolved) + SiO2 (slag)

(2-55)

Assuming the activity ratio (tf Mn0 ) / (aSio2 )in precipitated slag to be constant and independent of pressure, equation (2-55) may be rewritten as: (2-56)

Oxygen content, ppm

In Fig. 2.45 the weld metal manganese content has been plotted versus the square root of the silicon content by inserting data from Figs. 2.43 and 2.44. As it appears from Fig. 2.45, the

Electrode R

A B C

Total pressure, bar Fig. 2.42. Oxygen absorption in hyperbaric SMA welding. Data from Grong et al.51

Silicon content, wt%

Electrode R A B C

Total pressure, bar

Manganese content, wt%

Fig. 2.43. Silicon oxidation in hyperbaric SMA welding. Data from Grong et al.51

Electrode R A B C

High FeSi levels

Low FeSi levels

Total pressure, bar Fig. 2.44. Manganese oxidation in hyperbaric SMA welding. Data from Grong et al.51 experimental data cluster around a straight line passing through the origin, which confirms that the silicon and manganese concentrations are balanced by a reaction according to equation (2-55).

Manganese content, wt%

Electrode R A B C

1/2 [Silicon content, wt%] Fig. 2.45. Correlation between weld metal manganese and silicon contents. Data from Grong et a/.51

2.103.4 The product [%C] [%O] From steelmaking practice, the product [%C] [%O] is generally accepted as an adequate index of the interaction between carbon and oxygen during the refining stage. This product is related to the equilibrium content of dissolved carbon and oxygen in contact with carbon monoxide of a partial pressure pco: (2-57) Here K5 is the equilibrium constant for reaction (2-53) (equal to about 2.0 X 10"3 at 16000C and 2.6 X 10~3 at 20000C),23 Nco is the mole fraction of CO in the reaction product (equal to the partial pressure of CO at 1 bar), andptotis the total ambient pressure. During the initial stage of cooling in the weld pool, the oxygen content in an assumed equilibrium with carbon would be expected to be higher than the analytical values. This situation applies in particular to welds made under hyperbaric conditions, where significant quantities of oxygen clearly are removed from the weld pool in the form of oxide inclusions after the completion of the carbon oxidation. The concentration of dissolved oxygen at the break even temperature for silicon control of the oxygen level can be estimated from the measured concentration displacements of oxygen, silicon and manganese in the weld deposit with increasing pressures, relative to 1 bar (designated A[%(9], A[%Si] and A[%Mrc], respectively). If the total amount of oxygen which reacts with silicon and manganese at 1 bar, as a first approximation, is taken equal to the analytical weld metal oxygen content, the following balance is obtained:

(2-58)

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Here [%0]eq. is the oxygen concentration in an assumed equilibrium with carbon at a given pressure, and [%O]anaL is the analytical weld metal oxygen content. For this correlation, minor vaporisation losses of manganese as well as possible reactions between oxygen and liquid iron have been neglected. In Fig. 2.46 the product m = [%C] [%O] is plotted vs the total ambient pressure. Calculations of m have been done both on the basis of [%O]anaL and [%O]eq. It can be seen from Fig. 2.46 that the former set of data (i.e. open symbols in the graph) cannot be represented by a straight line passing through the origin, which should apply to a true equilibrium reaction. However, when proper corrections are made for the amount of oxygen removed from the weld pool after the completion of the carbon oxidation, such a correlation may be obtained as shown by the solid line in Fig. 2.46. No clear effect of the electrode deoxidation capacity (i.e. ferrosilicon content) on the product m = [%C] [%O] can be observed within the precision of measurements. This result is to be expected if the weld metal carbon content is controlled by a local equilibrium with oxygen established at elevated temperatures in the weld pool. Also, inspection of the slope of the curve (i.e. heavy solid line in Fig. 2.46) indicates that the product K5Nco is about 1.14 X 10~3 under the prevailing circumstances. If a reasonable average value for the equilibrium constant K5 of 2.3 X 10~3 is assumed within the specific temperature range of the reaction, we get: Nco~0.5 (2-59) The above calculations suggest that the controlling partial pressure of CO in the reaction product is significantly lower than the ambient pressure under hyperbaric welding conditions. This probably arises from an extensive infiltration of helium in the nucleating bubbles at the slag/metal interface which, thermodynamically, will enhance the deoxidation capacity of carbon according to Le Chatelier's Principle. The conditions existing in hyperbaric SMA welding thus appear to be similar to OBM/Q-BOP steelmaking, where simultaneous injection of oxygen and inert gas from the bottom of the convenor during the decarburisation stage results in a steel carbon content which is typically below the value calculated for equilibrium between oxygen and carbon at 1 atm partial pressure of CO.52

2.11 Weld Pool Deoxidation Reactions During cooling, the metal concentrations established at high temperatures due to dissolution of oxygen tend to readjust by precipitation of new phases. Accordingly, a supersaturation with respect to the various deoxidation reactants initially increases and thus provides the driving force for nucleation of oxides. Subsequently, the deoxidation reactions will proceed rapidly through growth of nuclei above a critical size. Equilibrium conditions will finally establish the limits for the degree of deoxidation that can be achieved. In spite of the fact that large amounts of oxygen are removed from the weld pool during the deoxidation stage, the analytical weld metal oxygen content exceeds by far the value predicted from chemical thermodynamics, assuming that equilibrium conditions are maintained down to the solidification temperature (see data in Table 2.5). This situation cannot be ascribed to a large deviation from chemical equilibrium, but is mainly a result of an incomplete phase separation. Consequently, due consideration must be given to the kinetics. The three basic consecutive steps in steel deoxidation are shown in Fig. 2.47.

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Here [%0]eq. is the oxygen concentration in an assumed equilibrium with carbon at a given pressure, and [%O]anaL is the analytical weld metal oxygen content. For this correlation, minor vaporisation losses of manganese as well as possible reactions between oxygen and liquid iron have been neglected. In Fig. 2.46 the product m = [%C] [%O] is plotted vs the total ambient pressure. Calculations of m have been done both on the basis of [%O]anaL and [%O]eq. It can be seen from Fig. 2.46 that the former set of data (i.e. open symbols in the graph) cannot be represented by a straight line passing through the origin, which should apply to a true equilibrium reaction. However, when proper corrections are made for the amount of oxygen removed from the weld pool after the completion of the carbon oxidation, such a correlation may be obtained as shown by the solid line in Fig. 2.46. No clear effect of the electrode deoxidation capacity (i.e. ferrosilicon content) on the product m = [%C] [%O] can be observed within the precision of measurements. This result is to be expected if the weld metal carbon content is controlled by a local equilibrium with oxygen established at elevated temperatures in the weld pool. Also, inspection of the slope of the curve (i.e. heavy solid line in Fig. 2.46) indicates that the product K5Nco is about 1.14 X 10~3 under the prevailing circumstances. If a reasonable average value for the equilibrium constant K5 of 2.3 X 10~3 is assumed within the specific temperature range of the reaction, we get: Nco~0.5 (2-59) The above calculations suggest that the controlling partial pressure of CO in the reaction product is significantly lower than the ambient pressure under hyperbaric welding conditions. This probably arises from an extensive infiltration of helium in the nucleating bubbles at the slag/metal interface which, thermodynamically, will enhance the deoxidation capacity of carbon according to Le Chatelier's Principle. The conditions existing in hyperbaric SMA welding thus appear to be similar to OBM/Q-BOP steelmaking, where simultaneous injection of oxygen and inert gas from the bottom of the convenor during the decarburisation stage results in a steel carbon content which is typically below the value calculated for equilibrium between oxygen and carbon at 1 atm partial pressure of CO.52

2.11 Weld Pool Deoxidation Reactions During cooling, the metal concentrations established at high temperatures due to dissolution of oxygen tend to readjust by precipitation of new phases. Accordingly, a supersaturation with respect to the various deoxidation reactants initially increases and thus provides the driving force for nucleation of oxides. Subsequently, the deoxidation reactions will proceed rapidly through growth of nuclei above a critical size. Equilibrium conditions will finally establish the limits for the degree of deoxidation that can be achieved. In spite of the fact that large amounts of oxygen are removed from the weld pool during the deoxidation stage, the analytical weld metal oxygen content exceeds by far the value predicted from chemical thermodynamics, assuming that equilibrium conditions are maintained down to the solidification temperature (see data in Table 2.5). This situation cannot be ascribed to a large deviation from chemical equilibrium, but is mainly a result of an incomplete phase separation. Consequently, due consideration must be given to the kinetics. The three basic consecutive steps in steel deoxidation are shown in Fig. 2.47.

[%C][%O]x102

Electrode R A B C

Total pressure, bar

Separation Stage Buoyancy Surface tension Stirring

Growth Stage Diffusion of reactants in the melt to the oxide nuclei Particle coalescence

Nucleation Stage Homogeneous nucleation Heterogeneous nucleation

Average particle size

Fig. 2.46. The product [%C][%0] in hyperbaric SMA welding. Solid symbols: calculations based on [%O]eq.. Open symbols: calculations based on [%O]anai.- Data from Grong et al. 51

Reaction time

Fig. 2.47. The three major consecutive steps in steel deoxidation (schematic).

Although rate phenomena in ladle refining of liquid steel are extensively investigated and reported in the literature,53"55 only recently attempts have been made to include such effects in an analysis of deoxidation reactions in arc welding. 1 ' 56 ' 57 2.11.1 Nucleation of oxide inclusions During ladle-refining of liquid steel, it is well established that homogeneous nucleation of oxide inclusions may occur in certain regions of the melt where the supersaturation is sufficiently high.55'58 Over the composition range normally applicable to deoxidation of steel, the number of nuclei formed at the time of addition of deoxidisers is approximately 105 mirr 3 . 55 However, in steel weld metals, the number of oxide nuclei formed during the initial stage of deoxidation must be considerably higher to account for the observed inclusion number density of about 107 mm~3 to 108 mm"3.56'57 This implies that the supersaturation established in the weld pool on cooling as a result of rapid temperature fluctuations (~103 0C s"1) exceeds by far that obtained by additions of deoxidisers to a liquid steel melt under approximately isothermal conditions. There are several theories available for treating nucleation phenomena, but for the purpose of convenience, a simplified version of the model of Turpin and Elliott58 has been adopted here. Consider a steel melt which is brought to a state of supersaturation by first equilibrating it with pure MxOy at a high temperature T\ and then rapidly cooling it to a lower temperature T2, as shown schematically in Fig. 2.48. It follows from the classical theory of homogeneous nucleation that the required temperature difference T1-T2 necessary to achieve spontaneous precipitation of MxOy is approximately given by the following relationship:

(2-60) where AH° is the standard enthalpy of reaction, G is the oxide-steel interfacial energy (assumed to be constant and independent of temperature), and Vm is the molar volume of the nucleus. The derivation of equation (2-60) is shown in Appendix 2.2. Example (2.9)

Assume that precipitation of manganese silicates in the weld pool occurs according to the following reaction: Si (dissolved) + Mn (dissolved) + 3 O (dissolved) = MnSiO3 (slag)

(2-61)

where AG°(J) = 858620 + 3457. Based on equation (2-60), calculate the critical temperature interval of subcooling for homogeneous nucleation OfMnSiO3. Typical physical data for liquid steel and manganese silicate slags are given in Table 2.10.

£

Time

Fig. 2.48. Idealised model for homogeneous nucleation of oxide inclusions in steel weld metals (schematic). Table 2.10 Physical data for liquid steel and manganese silicate slags at 16000C. Data from Refs. 3 and 53.

Property

Density (kgnr 3 )

Viscosity (kgm^s- 1 )

Steel

6900

4.3 X 10~3

Silicate slag

2300

-

Interfacial Energyt (Jm" 2 )

0.8

1

In contact with liquid steel.

Solution

First we estimate the molar volume of the nucleus:

By inserting the appropriate values for Vm, AH°, and a in equation (2-60), we obtain:

from which

If we assume that the supersaturation is released at T2 = 16000C (1873K), the initial temperature of the liquid T1 becomes:

The critical temperature interval of subcooling is thus:

Critical temperature interval, AT (0C)

Similar calculations can also be carried out for other types of oxide inclusions, e.g. FeO(I), SiO2(s), and Al2O3(S). The results of such computations are presented graphically in Fig. 2.49, using data from Refs 55 and 58. It is evident from these plots that the critical temperature interval of subcooling depends on the interfacial energy, G. Although data for oxide-steel interfacial energies are scarce, the following average values are frequently used in the literature, 5558 i.e. a(FeO-Fe) = 0.3 J m"2; G(SiO2-Fe) = 0.9 J m~2; and G(Al2O3-Fe) - 1.5 J mr2. If these values are accepted, the results in Fig. 2.49 indicate that the critical temperature interval of subcooling for homogeneous nucleation of FeO (1), SiO2(s), and Al2O3(S) is of the order of 200 to 30O0C. Considering the fact that the liquid weld metal spans a temperature range of about 2200 to 15000C,34 it is not surprising to find that nucleation of oxide inclusions occurs readily in the weld pool during cooling. It should be noted that the quoted data for G are representative of ladle-refined steel deoxidised at 16000C. At higher metal temperatures, in the presence of large amounts of dissolved oxygen, the oxide-steel interfacial energies would be expected to be significantly lower.59 Hence, it is reasonable to assume that the actual temperature interval of subcooling required for spontaneous oxide precipitation in a weld pool is well below 2000C.

Interfacial energy,o(J/m2) Fig. 2.49. Critical temperature interval of subcooling for homogeneous nucleation of oxide inclusions in steel weld metals at 16000C as a function of the interfacial energy a.

2.11.2 Growth and separation of oxide inclusions In practice, there are three major growth processes in steel deoxidation:55

(i) Collision (ii) Diffusion (iii) Ostwald ripening. From deoxidation and ladle refining of liquid steel it is well established that the flotation rate of the oxides generally depends on their growth rates, since large inclusions separate much more rapidly than small ones, in agreement with Stokes law.55 Growth of the oxides can proceed either through diffusion of reactants in the melt to the oxide nuclei or by collision and coalescence of ascending inclusions, and is therefore influenced by factors such as the number density of the nuclei, interfacial tensions, and the extent of melt stirring.53"55 The last factor is of particular importance in welding, because the stirring action will increase the possibilities for collision and coalescence of inclusions and, depending on the direction of flow, can give rise to circulation of inclusion-laden metal to the surface. As a result, the separation of small oxide particles, i.e. microslag, is strongly favoured by the turbulent conditions existing in the hot part of the weld pool immediately beneath the root of the arc. 2.11.2.1 Buoyancy (Stokes flotation) Assessment of the role of buoyancy (Stokes flotation) in the separation of deoxidation products from the weld pool can be done on the basis of the experimental data of Grong et ai56 reproduced in Fig. 2.50. It is evident that a change in the welding position (i.e. from flat to overhead position) has no significant effect on the weld metal oxygen content. This shows that the buoyancy effect does not play an important role in the separation process of oxide inclusions during welding.

Oxygen content, wt%

Upward welding Downward welding

Horizontal

Welding orientation, degrees Fig. 2.50. Effect of welding position on retained oxygen in GMA steel weld deposits. Data from Grong et a/. 56

The above conclusion is also in agreement with predictions based on the Stokes law, which gives the terminal velocity of the ascending particles (u) relative to the liquid:55 (2-62) where g is the gravity constant, dv is the particle diameter, Ap is the difference in densities between the liquid steel and the inclusions, and |x is the steel viscosity. Taking the Stokes parameter, gAp/18|ji, equal to 0.6 jjinr1 s"1 for manganese silicate slags in steel (Table 2.10), equation (2-62) becomes: (2-63) Generally, the majority of non-metallic inclusions in steel weld metals are of a diameter below 2 jxm.56'57 According to equation (2-63), such particles have a relative velocity less than 2.4 |xm s"1. This implies that the buoyancy effect alone is far too insignificant to promote flotation of the inclusions out of the weld pool before solidification, when it is recognised that the average fluid flow velocity in the weld pool is four to five orders of magnitude higher (to be discussed later). Stokes law is based on the assumption that the inclusions are completely wetted by the liquid steel, i.e. there is no slip at the oxide/metal interface.55 Normally, interfacial tension effects promote slip at the particle/metal interface, which, in turn, enhances the flotation rate of the ascending oxides (often referred to as the Plockinger effect).60 The concept of a wetting angle has been used in this context. But, the slip phenomenon is probably perceived better in terms of a secondary flow in the interfacial region between the liquid metal and the solid precipitate, which is produced by gradients in interfacial tension. In the rare case of no wetting (0 = 180°), it has been shown that the average terminal velocity of the inclusions is approximately 50% higher than that given by equation (2-62).55 For silica slags, the wetting angle (in the presence of air) is close to 115°,54 indicating that the correction in the particle terminal velocity due to the slip at the oxide/metal interface in less than about 30%. Consequently, interfacial tension effects between the slag and the steel do not significantly affect the flotation rate of the particles, and, therefore, can be ignored. 2.11.2.2 Fluid flow pattern It is evident from the above discussion that the separation of deoxidation products during arc welding is controlled by the fluid flow fields set up within the weld pool. The typical flow pattern in a submerged arc weld pool is shown in Fig. 2.51. It can be seen from the figure that a depression is formed at the forward edge of the pool, which forces the melted metal to flow underneath and on either side of the depression, following the arrows in Fig. 2.51. At the rear of the weld pool the flow direction is reversed, and the metal streams back along the pool surface. A similar flow pattern has also been observed in GMA weld pools.61 As a result, the inclusions precipitated in the turbulent part of the weld pool are rapidly brought to the upper surface behind the arc due to the high-velocity flow field created within the liquid metal, and disengaged by the surface tension effects in the pool. The drag force exerted on the particles because of the liquid flow-field velocity can be estimated from published data for weld pool flow velocities following electromagnetic fluid mechanics theory. Normally, for weld pools the Peclet number for heat transfer lies within the

range from 10 to 5000, which indicates that the heat flow is predominately convectional.62 The limits quoted above for the Peclet number correspond to a range in the average weld pool fluid velocity from about 0.025 to 0.4 m s"1 in the case of SA welding.6364 Unfortunately, specific information about the fluid flow velocity gradients in the weld pool are lacking, which prevents a more complete analysis of variations in the flow pattern with increasing distance from the root of the arc. Generally, the drag force, Fd, acting on a spherical particle in relative motion to a fluid can be expressed as:3 (2-64) where Cd is the drag coefficient, p is the fluid density, u is the bulk velocity of the fluid relative to the particle, and dv is the particle diameter. The drag coefficient is, in turn, a function of the particle Reynolds number, A^,:3 (2-65) where |x is the fluid viscosity. Typical physical-property data for liquid steel are given in Table 2.10. By inserting the values for p and JJL from Table 2.10, then using the relative velocity calculated in equation (2-63) (2.4 |xm s"1) as one extreme and the fluid flow velocity (0.4 m s"1) as the other (i.e. assuming a stationary particle), one can demonstrate that the particle Reynolds numbers obtained never exceed 1.3 for most weld metal inclusions. The limit calculated above for the Reynolds number is within the so-called creeping flow region where Stokes law is indeed valid. Under such conditions, the ratio between the particle drag force Fd and the corresponding gravity force Fg is given by the expression:3 (2-66) Note that equation (2-66) is the basis for obtaining Stokes law (equation (2-62)). For steady motion of the particle, Fd and Fg are, of course, equal. However, the significance of Fd can also be interpreted in a transient sense, by considering the limiting case where the particle is stationary and its instantaneous motion is governed by the forces acting on it. In this case, the ratio of Fd (max) acting on the particle relative to the net gravity force (given by Electrode

Pulsating cavity

Base plate

Fig. 2.51. Typical flow pattern in SA weld pools. For clarity, the arc, slag and flux have been omitted. The sketch is based on the ideas of Lancaster.32

equation (2-66)) can determine the dominant force responsible for the particle's trajectory. In Fig. 2.52 the above ratio has been calculated and plotted against the particle diameter, dv, for values of u' equal to 0.025 and 0.4 m s"1, which represent the typical velocities reported for SA steel weld pools. 63 ' 64 It can be seen from the figure that the drag force is always several orders of magnitude greater than the gravity force for particles within the typical size range of weld metal inclusions (i.e. less than 2 |xm in diameter). This result is to be expected, since the relative velocity, based on Stokes law and calculated in equation (2-63), is negligible compared with the liquid velocities in the weld pool (2.4 \xm s"1 vs 0.02 to 0.4 m s"1). This calculation thus supports our previous conclusion that the separation of the oxide inclusions is controlled solely by the fluid flow behaviour in the weld pool. The fact that the phase separation proceeds under strongly turbulent conditions is also evidenced by the large number of iron droplets being mechanically dispersed in the top bead slag of GMA steel welds, as shown by the optical micrographs in Fig. 2.53. In the case of GMA welding, the non-metallic inclusions that are brought to the upper surface behind the arc coalesce rapidly to form large slag clusters that float on the top of the bead. Generally, re-entrapment of the slag does not occur owing to the decrease in the total surface free energy of the system, which is caused by the emergence of the inclusions from the weld metal.54 Consequently, the slag will remain floating on the top of the bead even when welding is performed in the overhead position, as shown previously in Fig. 2.50.

*ci(max/Fg

2.11.2.3 Separation model Based mainly on experience with the GMA welding process, a simple model for the assessment of the sequence of deoxidation reactions in arc welding has been proposed,1 and is shown schematically in Fig. 2.54. The model is based on the assumption that equilibrium between the reacting elements and precipitated slag is maintained down to low metal temperatures, and divides the weld pool into the following two main reaction zones:

Inclusion diameter, |i.m Fig. 2.52. The ratio between maximum particle drag force, Fornax) and the corresponding gravity force, F8, vs the inclusion diameter at two different flow velocities in the weld pool. Calculations are based on equation (2-66).

(a)

(b)

Fig. 2.53. Optical micrographs showing characteristic "comet's tails" of trapped iron droplets (light areas) in collected top bead slags of GMA steel welds; (a) Ar + 5vol%O2, (b) Ar + 5vol%CO2.

Electrode (a)

Cold part of weld pooN

Arc

Hot part of weld pool Base plate

S e c t i o n A-A

Cold part of weld pool: Hot part of weld pool: Deoxidation/phase Deoxidation/incomplete separation phase separation

Temperature

(b)

Final weld metal, oxygen concentration

Oxygen content Fig. 2.54. Schematic diagrams showing the sequence of reactions occurring during weld metal deoxidation; (a) Longitudinal section of weld pool, (b) Cross section of weld pool along A-A. The diagrams are based on the ideas of Grong and Christensen.1

(i) The hot part of the weld pool, characterised by simultaneous oxidation and deoxidation of the metal, where the separation of microslag takes place continuously as a result of highly turbulent flow conditions. (ii) The cold part of the weld pool, where precipitated slag will largely remain in the metal as finely dispersed particles as a result of inadequate melt stirring. Under such conditions equation (2-23) predicts a direct correlation between absorbed and retained (analytical) oxygen in the weld metal, i.e.:

(2-67) in agreement with experimental observations (see plots in Figs. 2.33, 2.38, and 2.39). Typically, the proportionality constant C4 varies between 0.1 to 0.2, which corresponds to a range in the t/to ratio from 2.3 to 1.6. This shows that the boundary between 'hot' and 'cold' parts of the weld pool is not well defined, but depends on the welding system under consideration as well as on the operational conditions applied. 2.11.3 Predictions of retained oxygen in the weld metal Although the weld metal oxygen content is controlled by a transport mechanism in the weld pool, the concept of pseudo-equilibrium can still be used for an assessment of slag/metal reactions in arc welding. 2.11.3.1 Thermodynamic model In the case of silicon deoxidation of steel weld metals, we may write: Si (dissolved) + 2 O (dissolved) = SiO2 (slag)

(2-68)

On introduction of the equilibrium constant for the reaction, we obtain: (2-69) To allow for the decrease in the silica activity with increasing manganese-to-silicon ratios, it is essential to establish a correlation that links the activity of silica to the concentrations of the deoxidation elements in the weld metal. A semi-empirical corr61ation of this kind has been presented by Walsh and Ramachandran,65 derived from a re-analysis of activity data for silica in the Fe-Mn-Si-O system previously published by Hilty and Crafts.66 Within the temperature range from 1550 to 16500C, they showed that the silica activity in the deoxidation product can be approximately expressed as: (2-70) where K1 represents the manganese-to-silicon ratio at which the activity of silica becomes

unity for a given temperature. A check of this equation against more recent data for silica activities in MnO-SiO2 slags reported by Turkdogan67 supports the findings of Walsh and Ramachandran65 that the activity of silica is approximately given by equation (2-70) for a wide range in the steel manganese-to-silicon ratio (i.e. from 0.1 to 50). By combining equations (269) and (2-70), it is possible to obtain an expression for the equilibrium oxygen content, solely in terms of the silicon and manganese concentrations: (2-71) where K^ is a temperature-dependent parameter equal to (K1I K6)05. The temperature dependence of the Si-O reaction (equation (2-68)) is well established and is approximately given by the relationship:23 (2-72) when pure SiO2 is used as the standard state for the silica activity. For a rough estimate of the temperature dependence of equation (2-70), the results of Turkdogan55 can be used. It should be noted that Walsh and Ramachandran65 did calculate the temperature dependence of K1 within the range from 1550 to 16500C. However, because equation (2-70) is empirical, the function cannot be extrapolated beyond these temperature limits. The data quoted in Ref. 55 are derived directly from the Si-Mn reaction (equation (2-55)) and activity data for MnO at silica saturation. On introduction of the equilibrium constant for equation (2-55), we obtain: (2-73) By using data from Ref.55, the initial [%Mn]2/[%Si] ratio for precipitation of silica saturated slags (equal to K9(aMnO)2) at 1500,1550,1600 and 16500C has been recorded and replotted against temperature, as shown in Fig. 2.55. The figure shows that the critical [%Mn]2/[%Si] ratio for precipitation of silica saturated slags is temperature dependent and decreases from about 5 at 15000C to below 1.5 at 16500C. On the basis of a crude extrapolation of the data to higher metal temperatures, it can, however, be argued that the ratio would approach a constant value of approximately 0.75 at temperatures beyond about 17500C (indicated by the broken horizontal line in Fig. 2.55). The above observation reflects the fact that the Si-Mn-O reaction equilibrium (equation (2-55)) is not very sensitive to a change in temperature (i.e. the enthalpy for the reaction is small). Over the composition range normally applicable to Si-Mn deoxidation of steel weld metals the observed threshold for the critical [%Mn]2/[%Si] ratio for precipitation of silica-saturated slags in Fig. 2.55 corresponds to a manganese-to-silicon ratio closely equal to unity. Consequently, at temperatures higher than about 17500C, K1 can, as a first approximation, be taken constant and independent of temperature (i.e. K1- Y). The temperature dependence of equation (2-71) is thus simply (1/^ 6 ) 05 or: (2-74)

for temperatures higher than about 17500C (2023K).

[%Mn]2/[%Si]

Temperature, 0C Fig. 2.55. The critical [%Mn]2/ [%Si] ratio for precipitation of silica-saturated slags as a function of temperature. Data from Turkdogan.55

2.11.3.2 Implications of model Figure 2.56 shows plots of retained (analytical) oxygen in GMA and SMA steel weld metals vs the theoretical deoxidation parameter ([%Si][%Mn])~°25, using relevant literature data. 5668 This parameter allows for the inherent decrease in the silica activity with increasing weld metal Mn to Si ratios. A closer inspection of the slopes of the curves reveals that the effective reaction temperature falls within the range calculated for chemical equilibrium between silicon, manganese, and oxygen at 1800 to 19000C. Although the boundary between 'hot' and 'cold' parts of the weld pool for possible inclusion removal in practice is not sharp, the results in Fig. 2.56 literally suggest that all oxides precipitated above 1800 to 19000C are simultaneously removed from the weld pool under the prevailing turbulent flow conditions. At lower temperatures, the degree of melt stirring is too low to promote separation of the deoxidation products out of the pool before solidification and hence, they are trapped in the metal solidification front in the form of finely dispersed inclusions. Moreover, the observed difference in the effective reaction temperature between GMA and SMA welding supports our previous conclusion that any change in welding parameters, flux or shielding gas composition, which alters the fluid flow pattern in the weld pool, will often have a stronger influence on the weld metal oxygen content than variations in the deoxidation practice. This implies that control of the weld metal oxygen level through additions of deoxidants, in practice, is difficult to achieve.

2.12 Non-Metallic Inclusions in Steel Weld Metals Inclusions commonly found in steel weldments will either be exogenous or indigenous, dependent on their origin. The first type arises from entrapment of welding slags and surface scale, while indigenous inclusions are formed within the system as a result of deoxidation reactions (oxides) or precipitation reactions (nitrides, sulphides). The latter group is almost always seen to be heterogeneous in nature both with respect to chemistry (multiphase parti-

Oxygen content, wt%

GMA Welding SMA Welding

([%SI] [%Mn]f°"25 Fig. 2.56. Examples of pseudo-equilibrium in GMA and SMA welding of C-Mn steels. The solid lines in the graph represent thermodynamical calculations at indicated temperatures. Data from Refs. 56 and 68. cles), shape (angular or spherical particles), and crystallographic properties as a result of the complex alloying systems involved69 (see Fig. 2.57). An exception may be C-Mn steel welds, where the oxide inclusions will be predominately glassy, spherical, manganese silicates.1 A survey of important weld metal inclusion characteristics is given in Table 2.11. 2.12.1 Volume fraction of inclusions It is evident from Table 2.11 that the volume fraction of non-metallic inclusions in steel weld metals normally falls within the range from 2 X 10~3 to 8 X 10~3, depending on the type of weld under consideration. Based on simple stoichiometric calculations it is possible to convert the analytical weld metal oxygen and sulphur contents to an equivalent inclusion volume fraction when the chemical composition of the reaction products is known. This is shown below. Table 2.11 Summary of weld metal inclusion characteristics. The data are compiled from miscellaneous sources. Size Distribution*

Chemical Composition

Type of Weld

C-Mn steel weld metals Low-alloy steel weld metals

Constituent elements

Reported phases

10-50

Si, Mn, O, S (traces of Al, Ti, and Cu)

SiO2, MnOSiO2, MnS, (CuxS)

10-40

Al, Ti, Si, Mn, O, S, N (Cu)

MnOAl2O3, 7-Al2O35TiN, MnOSiO2, SiO2, a-MnS, (3-MnS, (Cu^S)

Vv X 10"3

dv

NvX 107

Sv

3-8

0.3-0.6

1-10

2-6

0.3-0.7

0.5-5

*Vy: volume fraction; dv: arithmetic mean (3-D) particle diameter (jxm); Nv: number of particles per unit volume (mm"3); Sv\ total particle surface area per unit volume (mm2 per mm3).

Fig. 2.57. Digital STEM brightfield image and Si, Al, S, Mn and Ti X-ray images of a multiphase weld metal inclusion. After Kluken and Grong.57

Solution

First we calculate the total weight of retained MnOSiO2 per 100 g weld metal:

This corresponds to an equivalent volume fraction of:

Similarly, we can calculate the weight and volume fraction of MnS in the weld metal:

and

The total volume fraction of MnOSiO2 and MnS is thus:

In practice, the stoichiometric conversion factors for oxygen and sulphur are virtually constant for a wide spectrum of inclusions70 and hence, they can be regarded as independent of composition. Taking the solubility of sulphur in solid steel equal to 0.003 wt%, the following relationship is obtained for steel weld metals:57'70 (2-75) The validity of equation (2-75) has been confirmed experimentally by comparison with microscopic assessment methods.5771 In steel weld metals the majority of the inclusions will be in the submicroscopic range owing to the limited time available for growth of the oxides. From the histogram in Fig. 2.58 it is seen that particles with diameters between 0.3 to 0.8 |xm contribute to nearly 50 percent of the total inclusion volume fraction. This trend is not significantly changed by additions of strong deoxidisers, such as aluminium and titanium, or by a moderate increase/decrease in the heat input.57 2.12.2 Size distribution of inclusions As shown in Fig. 2.59 the majority of the three-dimensional (3-D) inclusion diameters fall within the range of 0.05 to 1.5 |xm, with a characteristic peak in the particle frequency at about 0.4 to 0.5 |jim. These data obey the log-normal law, since a plot of the frequencies against the logarithms of the diameters approximately gives a symmetrical curve. Considering specific inclusion size classes, deoxidation with aluminium generally results in a higher fraction of coarse particles (> 1 |xm) due to incipient clustering of Al2O3.57' 69 However, the observed particle clustering has no significant influence on the arithmetic mean 3-D inclusion diameter, as shown by the data in Fig. 2.59.

Relative volume fraction (%)

Particle diameter (jim) Fig. 2.58. Percental contribution of different size classes to the total volume fraction of non-metallic inclusions in a low-alloy steel weld metal. Data from Kluken and Grong.57

2.12.2.1 Effect of heat input In contrast to the situation described above, the 3-D inclusion size distribution is strongly affected an increase in the heat input (see Fig. 2.60). At 1 kJ mm"1, the measured 3-D inclusion diameters fall within the range from 0.05 to 1 |xm, with a well-defined peak in the particle frequency at about 0.3 |xm. When the heat input is increased to 8 kJ mm"1, the content of coarse inclusions will dominate (>0.5 |xm), which results in a broader distribution curve and a shift in the peak frequency towards larger particle diameters. A comparison with Fig. 2.61 reveals that the arithmetic mean 3-D inclusion diameter is approximately a cube-root function of the heat input. This result is to be expected if Ostwald ripening is the dominating coarsening mechanism in the cold part of the weld pool (to be discussed below). 2.12.2.2 Coarsening mechanism As already mentioned in Section 2.11.2 there are three major growth processes in steel deoxidation, i.e. (i) collision, (ii) diffusion, and (iii) Ostwald ripening. In the cold part of the weld pool, particle growth by collision can be excluded in the absence of adequate melt stirring because of a low collision probability of inclusions while ascending in the molten steel within the regime of Stokes law.72 In addition, the diffusion-controlled part of the deoxidation reaction (which involves diffusion of reactants in the melt to the oxide nuclei) would be expected to be essentially complete within a fraction of a second when the number of nuclei is greater than 107 mm"3.55 This implies that the observed increase in the inclusion diameter with increasing heat inputs (Fig. 2.61) can be attributed solely to Ostwald ripening effects. Before discussing details of the inclusion growth kinetics, it is essential to clarify the temperature level in the 'cold' part of the weld pool. As shown by the results in Fig. 2.62, the liquid metal temperature in the trailing edge of the weld pool is fairly constant and slightly above the melting point of the steel. Accordingly, inclusion growth in welding (at a fixed volume fraction) can be treated as an isothermal process, where the time dependence of the mean particle diameter dv is approximately given by the Wagner equation:

(a)

Frequency (%)

Low Al (0.018 wt%) Low Ti (0.005 wt%)

Particle diameter (fxm)

(b) High Al (0.053 wt%) Frequency (%)

High Ti (0.053 wt%)

Particle diameter, p,m Fig. 2.59. Three-dimensional (3-D) size distribution of non-metallic inclusions in two different lowalloy steel weld metals; (a) Low weld metal aluminium and titanium levels, (b) High weld metal aluminium and titanium levels. Data from Kluken and Grong.57

(2-76)

Here do is the initial particle diameter, a is the oxide-steel interfacial energy, Dm is the element diffusivity, Cm is the element bulk concentration, V'm is the molar volume of the oxide per mole of the diffusate, and t is the retention time.

Frequency (%)

Particle diameter, p,m

Particle diameter, u,m

Fig. 2.60. Effect of heat input on the 3-D inclusion size distribution in low-alloy steel weld metals. Data from Kluken and Grong.57

Heat input, kJ/mm

Fig. 2.61. Variation of arithmetic mean 3-D inclusion diameter with heat input during SA welding. Data from Kluken and Grong.57 For welding of thick plates, the time available for growth of particles in the 'cold' part of the weld pool can be estimated from the Rosenthal equation, i.e. equation (1-45) in Section 1.10.2 (Chapter 1). If the characteristic length of the cooling zone is taken equal to the weld ripple lag (defined in Fig. 2.63), the retention time t is approximately given by the following relationship:

Temperature, C°

"Tpeak = 1538°C (about 8 mm from edge of weld pool)

Time, seconds Fig. 2.62. Measured temperature level in the trailing edge of the weld pool during GMA welding. Data from Kluken and Grong.57

Top view of weld crater (z = 0)

Max. width

Retention time Weld ripple lag Welding speed Heat source

Fusion boundary

Fig. 2.63. Definition of weld ripple lag xm, and retention time t.

(2-77) where J\ is the arc efficiency (equal to about 0.95 for SAW and 0.80 for GMAW /SMAW), and E is the gross heat input (kJ mm"1). Note that equation (2-77) assumes constant values for the steel thermal diffusivity and volume heat capacity (5 mm2 s"1 and 0.0063 J mm"3 0C"1, respectively), and no preheating (T0* = 200C). In Fig. 2.64 the Ostwald ripening theory has been tested against relevant literature data, which may be considered representative of the 3-D particle size distribution. Although there is some scatter in the data, the observed inclusion growth rates fall within the range calculated for oxygen diffusion-controlled coarsening of SiO2 and Al2O3 at 15500C, using the Wagner equation. In these calculations, a reasonable average value for the bulk diffusivity of oxygen has been assumed (i.e. 10~2 mm2 s"1).55 If the effective inclusion growth rate constant for lowalloy steel weld metals is taken equal to the slope of the curve in Fig. 2.64, the following relationship is achieved:

GMAW SAW

dv,jLim

SMAW

•1/3 i i sJ/3 Fig. 2.64. Relation between arithmetic mean (3-D) inclusion diameter dv and retention time t for different arc welding processes. Data compiled by Kluken and Grong.57 CoId1 part of weld pool

Deoxidation Phase separation Deoxidation Incomplete phase; separation Homogeneous nucleation

Growth of inclusions

Oxidation

Solid weld metal

Temperature

Gas/metalslag/metal reactions

Solid weld metal

1

'Hot' part of weld pool

Ostwald ripening

Time Fig. 2.65. Proposed deoxidation model for steel weld metals (schematic). The diagram is based on the ideas of Kluken and Grong.57

(2-78) By substituting equation (2-77) into equation (2-78), we obtain a direct correlation between the arithmetic mean 3-D inclusion diameter dv and the net heat input T\E: (2-79)

Equation (2-79) predicts that dv is a simple cube root function of E, in agreement with the experimental data in Fig. 2.61. It should be noted that the measured shape of the particle distributions (see Figs. 2.59 and 2.60) deviates somewhat from that required by the Wagner equation, which assumes a quasistationary distribution curve, and that the maximum stable particle diameter is about 1.5 times the mean diameter of the system.73 Although the origin of this discrepancy remains to be resolved, this suggests that particle clustering is also a significant process in steel weld metals as it is in other metallurgical systems. In fact, such effects would be expected to be most pronounced at high aluminium levels because of a large interfacial energy between Al2O3 and liquid steel, in agreement with experimental observations.57'69 2.12.2.3 Proposed deoxidation model Referring to Fig. 2.65, the sequence of reactions occurring during weld metal deoxidation can be summarised as follows. In general, nucleation of oxide inclusions occurs homogeneously as a result of the supersaturation established during cooling in the weld pool. The diffusioncontrolled deoxidation reactions (i.e. diffusion of reactants to the oxide nuclei) will be essentially complete when the liquid metal temperature attains a constant level of about 15500C at some distance behind the root of the arc. Growth of the particles may then proceed under approximately isothermal conditions at a rate controlled by the Wagner equation until the temperature reaches the melting point of the steel. Since retention times in welding generally depend on the heat input, it follows that choice of operating parameters will finally determine the degree of particle coarsening to be achieved. Example (2.11)

Consider SA welding with a basic flux on a thick plate of low-alloy steel under the following conditions:

Previous experience has shown that this steel/flux combination gives a weld metal oxygen and sulphur content of 0.035 and 0.008 weight percent, respectively. Based on the stereometric relationships given below, calculate the total number of particles per unit volume Nv, the total number of particles per unit area Na, the total particle surface area per unit volume Sv, and the mean particle centre to centre volume spacing Xv in the weld deposit:74'75

(2-80) (2-81)

(2-82)

(2-83)

Solution

First we calculate the total volume fraction of oxide and sulphide inclusions from equation (2-75): Vv = 10-2 [5.0(0.035) + 5.4(0.008 -0.003)] = 2.0 X 10~3 The arithmetic mean (3-D) inclusion diameter can then be evaluated from equation (2-79):

This gives: particles per mm3

particles per mm 2 mm 2 per mm3

particles per mm3

particles per mm 2 mm 2 per mm3

2.123 Constituent elements and phases in inclusions It is evident from Table 2.11 that non-metallic inclusions commonly found in low-alloy steel weld metals may contain a considerable number of constituent elements and phases. 2.12.3.1 Aluminium, silicon and manganese contents Figure 2.66 shows examples of measured X-ray intensity histograms for silicon, manganese, and aluminium in inclusions extracted from a low-alloy steel weld metal. These results have been converted into arbitrary elemental weight concentrations by normalising the collected Xray data for all preselected elements (i.e. Al, Si, Mn, Ti, Cu, and S) to 100%. The characteristic normal distribution curves recorded for silicon, manganese, and aluminium show that the content of each oxide phase may vary significantly from one particle to another. This observation is not surprising, considering the complex chemical nature of the weld metal inclusions (see Fig. 2.57). 2.12.3.2 Copper and sulphur contents In addition, the inclusions may contain significant levels of both copper and sulphur in addition to aluminium, silicon, manganese and titanium. Sulphide shells around extracted inclusions have frequently been observed in SA and SMA steel welds, often in combination with copper. This has been taken as an indication of copper sulphide formation. However, based on the wavelength dispersive X-ray (WDX) data reported by Kluken and Grong,57 it can be argued that copper sulphide is a rather unlikely reaction product in steel weld metals as it is in ordinary ladle-refined steel.76 From their data it is evident that the total

Silicon

Manganese

Aluminium

Frequency (%)

26 wt%

20 wt%

28 wt%

Arbitrary elemental weight concentrations, wt% Fig. 2.66. Measured X-ray intensity histograms for silicon, manganese and aluminium in inclusions extracted from a low-alloy steel weld metal. Arrows indicate average composition. Data from Kluken and Grong.57 number of counts recorded for copper in discrete particles is not significantly higher than the corresponding matrix value, which shows that the copper content of the inclusions is low. Since these measurements were carried out on mechanically polished specimens and not on carbon extraction replicas, as done in the EDX analysis, the indications are that the higher inclusion copper level observed in the latter case mainly results from surface copper contamination inherent from the extraction process. In contrast, the WDX analysis of sulphur revealed evidence of sulphur enrichment in most of the particles. Considering the fact that these particles also contained significant amounts of manganese, it is reasonable to assume that most of the sulphur is present in the form of MnS (possibly with some copper in solid solution).76 2.12.3.3 Titanium and nitrogen contents From the literature reviewed, it is apparent that conflicting views are held about the role of titanium in weld metal deoxidation. From a thermodynamic standpoint, Ti2O3 is the stable reaction product in titanium deoxidation,76 but this phase has not yet been detected experimentally in steel weldments (only in continuous cast steel).77 However several authors have reported the presence of crystalline patches containing titanium toward the edges of inclusions.78"80 This constituent has a cubic crystal structure with a lattice parameter close to 0.42 nm, conforming to either 7-TiO, TiN, or TiC (note that the 7-T1O phase is the hightemperature modification of the titanium monoxide).81 In general, formation of titanium monoxide requires strongly reducing conditions, which

implies that the 7-TiO constituent is not an equilibrium reaction product in steel deoxidation.55'76 Hence, it is reasonable to assume that the titanium-rich crystalline patches observed toward the edges of weld metal inclusions are titanium nitride. This conclusion has later been confirmed experimentally by Kluken and Grong.57 2.12.3.4 Constituent phases Based on the above discussion, it is possible to rationalise the formation of primary and secondary reaction products (i.e. oxides, sulphides and nitrides) during cooling in the weld pool, as shown in Fig. 2.67. In general, the inclusions will consist of an oxide core which is formed during the primary deoxidation stage. The chemical composition of the deoxidation product can vary within wide limits, depending on the activities of Al, Ti, Si, Mn, and O in the weld metal. The surface of the oxides will partly be covered by MnS and TiN (see also STEM micrograph in Fig. 2.57). Precipitation of these phases occurs after the completion of the weld metal deoxidation, probably during solidification, where the reactions are favoured by solute enrichment in the interdendritic liquid. Additional precipitation of TiN may occur in the solid state as a result of diffusion of titanium and nitrogen to the surface of the inclusions. 2.12.4 Prediction of inclusion composition Since the diffusion-controlled deoxidation reactions are completed within a fraction of a second when the number of nuclei is of the order of 107 mm"3 or higher,55 the average chemical composition of the inclusions should be compatible with that calculated for chemical equilibrium at temperatures close to the melting point (e.g. 15500C). 2.12.4.1 C-Mn steel weld metals Over the composition range normally applicable to silicon-manganese deoxidation of steel weld metals (i.e. between 0.4 to 0.7 wt% Si and 0.8 to 1.5 wt% Mn) the equilibrium reaction product at 15500C should be silica-saturated slags with a mole fraction of SiO2 close to 0.55. 5565 Since the two other slag components are MnO and FeO, we may write: (2-84) The activity coefficients for MnO and FeO in the ternary system SiO 2 -MnO-FeO can be computed from the equations presented by Sommerville et al.:S2 (2-85) and (2-86) For the specific case of silica-saturated slags, we obtain: (2-87) and (2-88)

TiN (secondary reaction product) Oxide Core (primary reaction product] MnS (secondary reaction product) Fig. 2.67. Schematic diagram showing the presence of primary and secondary phases in weld metal inclusions. Under such conditions the activity ratio aMnO/aFeO in the slag is given by:

(2-89)

The activity ratio aMnO/aFeO can also be estimated from the equilibrium constant for the FeMn reaction at 15500C,23 i.e.: (2-90)

The corresponding mole fractions of MnO and FeO in the slag phase are then obtained by combining equations (2-89) and (2-90): (2-91) and (2-92)

Equations (2-91) and (2-92) provide a basis for calculating the chemical composition of the inclusions under different deoxidation conditions. A requirement is, however, that the weld metal Si to Mn ratio is sufficiently high to promote precipitation of silica-saturated slags at 15500C.

and

This gives the following chemical composition of the inclusions (in wt%):

The above calculations should be compared with the composition data presented in Fig. 2.68. It is evident from this plot that the agreement between predictions and experiments is reasonably good both at high and low weld metal manganese levels. This justifies the simplifications made in deriving equations (2-91) and (2-92). 2.12.4.2 Low-alloy steel weld metals In principle, a procedure similar to that described above could also be used to establish a theoretical basis for predicting the chemical composition of the inclusions in the case lowalloy steel weld metals. Unfortunately, adequate activity data for the Fe-Al-Ti-Si-Mn-O system are not available in the literature. An alternative approach would be to calculate the average inclusion composition from simple mass balances, assuming that all oxygen combines stoichiometrically with the various deoxidation elements to form stable oxides in the order Al2O3, Ti2O3, SiO2, and MnO, according to their oxygen affinity in liquid steel (see Fig. 2.69). If reasonable average values for the inclusion and steel densities are used (i.e. 4.2 and 7.8 g cm"3, respectively), the following set of equations* can be derived from a balance of O, Al, Ti, S, Si, and Mn and data for acid soluble aluminium and titanium in the weld metal:57 Aluminium

The average aluminium content of the inclusions, [%Al]inch can be estimated from the measured difference between total and acid soluble aluminium in the weld metal, (k%Al)we[d. This difference is, in turn, equal to the total mass of aluminium in the inclusions: (2-93) where mind and Vv (cal) are the total mass and volume fraction of non-metallic inclusions in the weld deposit, respectively. *The numerical constants in the constitutive equations given below could alternatively be expressed in terms of atomic weights etc. to bring out more clearly their physical significance (e.g. see the treatment of Bhadeshia and Svensson83).

Mole fraction

Ar - O2 gas mixtures Ar - CO2 gas mixtures

Manganese content, wt% Fig. 2.68. Comparison between measured and predicted microslag composition in GMA welding of C-Mn steels. Solid lines represent theoretical calculations based on equations (2-91) and (2-92). Data from Grong and Christensen.1

Oxygen in solution, wt%

Iron oxide in solution at 16000C Mn

Si Ti

Al

Deoxidizer in solution, wt% Fig. 2.69.Deoxidation equilibria in liquid steel at 1600°C.Data from Turkdogan.55

By rearranging equation (2-93), we get:

(2-94)

However, since data for acid soluble aluminium (and titanium), in practice, may contain large inherent errors, the following restriction applies: (2-95) where [%O]anaL is the analytical weld metal oxygen content. Titanium

Similarly, the average titanium content of the inclusions, [%Ti]incl, can be estimated from the measured difference between total and acid soluble titanium, (A%Ti)weld. However, since TiN dissolves readily in strong acid, it is necessary to include an empirical correction for the amount of titanium nitride which simultaneously forms at the surface of the inclusions during solidification. This can be done on the basis of published data for the solubility product of TiN in liquid steel.84 If we assume that the nitrogen content of the inclusions is proportional to the calculated difference between total and dissolved nitrogen at the melting point (15200C), the following relationship is obtained:

(2-96)

where [%N]anai is the analytical weld metal nitrogen content, and [%Ti]soL is acid soluble titanium. Note that the correction term for TiN, in practice, neither can be negative nor exceed [%Ti]soh

In this case, the maximum amount of titanium which can be bound as Ti2O3 is determined by the overall oxygen balance: (2-97) Sulphur

If the solubility of sulphur in solid steel is taken equal to 0.003 wt%,70 the average sulphur content of the inclusions, [%S]ind is given by:

(2-98) where [%S]anai is the analytical weld metal sulphur content. Silicon and manganese

From the experimental data of Saggese et al.S5 reproduced in Fig. 2.70, it is evident that the mass ratio between SiO2 and MnO in the oxide phase may be considered constant and virtually independent of composition (i.e. equal to about 0.94). This implies that the average silicon content of the inclusions, [%Si]ind, can be calculated from a balance of oxygen:

SiO2

Al2O3

MnO wt% AI2O3

Fig. 2.70. Measured inclusion compositions in low-alloy steel weld metals. Data from Saggese et alP

(2-99) Considering manganese, proper adjustments should also be made for the amount of MnS formed at the surface of the inclusions during solidification. Hence, the average manganese content of the inclusions, [%Mn]inci, is given by the sum of the oxygen and the sulphur contributions:

(2-100)

Experimental verification of model

In Fig. 2.71, the accuracy of the model has been tested against the experimental SA/GMA inclusion data reported by Kluken and Grong,57 taking the sum (%A1 + %Ti + %S + %Si + %Mn) equal to 100%. A closer inspection of the graphs reveals a reasonable agreement between calculated and measured average inclusion compositions in all cases, which confirms that the model is sound. Included in Fig. 2.71 is also a collection of data for SMA low-alloy steel weld metals (3 kJ mm"1 — basic electrodes). Since these results follow the same pattern, it implies that the model is generally applicable and, therefore, can be adopted to all relevant arc welding processes.

Measured composition, wt%

Aluminium Sulphur

Marked symbols: SMAW

Measured composition, wt%

Calculated composition, wt%

Titanium Manganese Silicon

Marked symbols: SMAW

Calculated composition, wt% Fig. 2.71. Comparison between measured and predicted inclusion compositions; (a) Aluminium and sulphur, (b) Titanium, manganese and silicon. Data from Kluken and Grong57'86 Implications of model

It can be inferred from equations (2-94) and (2-95) that the chemical composition of the inclusion oxide core is directly related to the aluminium to oxygen ratio in the weld metal. Referring to Fig. 2.72, the fraction of MnOAl2O3 and 7-Al2O3 in the inclusions is seen to increase steadily with increasing (A%Al)wdJ[%O]anal ratios until the stoichiometric composition for precipitation of aluminium oxide is reached at 1.13. At higher ratios, the deoxidation product will be pure Al2O3, since aluminium is present in an over-stoichiometric amount with respect to oxygen. When titanium is added to the weld metal, titanium oxide (in the form of Ti2O3) may also enter the reaction product. At the same time both TiN and a-MnS form epitaxially on the surface of the inclusions during solidification. Consequently, in Al-Ti-Si-Mn deoxidised steel weld metals the total number of constituent phases within the inclusions may approach six. The kinetics of inclusion formation are further discussed in Ref. 87.

SiO2

MnO

Fig. 2.72. Coexisting phases in inclusions at different weld metal aluminium-to-oxygen ratios. Shaded region indicates the approximate composition range for the oxide phase. The diagram is constructed on the basis of the model of Kluken and Grong57 and relevant literature data.

Example (2.13)

Consider SA welding of low-alloy steel with two different basic fluxes. Data for the weld metal chemical compositions are given in Table 2.12. Based on Fig. 2.72, estimate the total number of constituent phases in the inclusions in each case. Solution

It follows from Fig. 2.72 that the chemical composition of the deoxidation product is determined by the aluminium to oxygen ratio in the weld metal. For weld A, we have:

Since this ratio is higher than the stoichiometric factor of 1.13, all oxygen is probably tied up as aluminium oxide. In addition, weld A contains small amounts of titanium and sulphur, which may give rise to precipitation of TiN and MnS at the surface of the inclusions during solidification. Hence, the three major constituent phases in the weld metal inclusions are 7-Al2O3, TiN, and ot-MnS.

Table 2.12 Chemical composition of SA steel weld metals considered in Example 2.13. Weld No.

C (wt%)

O (wt%)

Si (wt%)

Mn (wt%)

S (wt%)

N (wt%)

Al* (wt%)

Ti* (wt%)

A

0.09

0.021

0.45

1.52

0.01

0.006

0.028 (0.003)

0.010 (0.009)

B

0.09

0.045

0.45

1.52

0.01

0.006

0.028 (0.003)

0.028 (0.010)

*Data for acid soluble Al and Ti are given by the values in brackets.

In the case of weld B the situation is much more complex due to a higher content of oxygen and titanium. From Table 2.12, we have:

and

These calculations show that Al and Ti are not present in sufficient amounts to tie-up all oxygen. Under such conditions Fig. 2.72 predicts that the total number of constituent phases in the inclusions is six, i.e.: SiO2, MnOAl2O3, 7-Al2O3, Ti2O3, a-MnS and TiN. References 1 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

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52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85.

86. 87.

P. Nilles, P. Dauby and J. Claes: Proc. Int. Conf. Basic Oxygen Steelmaking —A New Technology Emerges, London, 1978, 60-72, The Metals Society (England). U. Lindborg and K. Torsell: Trans. TMS-AIME, 1968, 242, 94-102. N.F. Grevillius: Jernkont. Ann., 1969,153, 547-572. E.T. Turkdogan: Proc. Int. Conf. on Chem. Metall. of Iron and Steel, Sheffield, July 1971,153170, Publ. The Iron and Steel Institute (England). 0 . Grong. T.A. Siewert, G.P. Martins and D.L. Olson: Metall. Trans. A, 1986,17A, 1797-1807. A.O. Kluken and 0 . Grong: Metall. Trans. A, 1989, 2OA, 1335-1349. M.L. Turpin and J.F. Elliott: J. Iron Steel Inst., 1966, 204, 217-225. E.T. Turkdogan: Physicochemical Properties of Molten Slags and Glasses, 1983, London, The Metals Society. E. Plockinger and M. Wahlster: Stahl und Eisen, 1960, 80, 659-669. BJ. Bradstreet: HW Doc. 212-138-68, 1968. J.F. Lancaster: Phys. Technol, 1984,15, 73-79 F. Eickhorn and A. Engel: HW Doc. 212-201-70, 1970. N. Mori and Y. Horii: HW Doc. 212-188-70, 1970. R.A. Walsh and S. Ramachandran: Trans. TMS-AIME, 1963, 227, 560-562. D.C. Hilty and W. Crafts: Trans.-AIME, 1950,188, 425-436. E.T. Turkdogan: Trans. TMS-AIME, 1965, 233, 2100-2112. G.M. Evans: HW Doc. IIA-630-84, 1984. 0 . Grong and D.K Matlock: Int. Met. Rev., 1986, 31, 27-48. A.G. Franklin: J. Iron Steel Inst., 1969, 207, 181-186. A.O. Kluken, 0. Grong and J. Hjelen: Mat. ScL Technol., 1988, 4, 649-654. L.M. Hocking: Quart. J. Royal Meterol. Soc, 1959, 85, 44-50. C. Wagner: Z Electrochemie, 1961, 65, 581-591. E.E. Underwood: Quantitative Stereology, 1970, London, Addison-Wesley Publ. Co. M.F. Ashby and R. Ebeling: Trans. TMS-AIME, 1966, 236, 1396-1404. R. Kiessling: Non-Metallic Inclusions in Steel, 1978, London, The Metals Society (TMS). H. Homma, S. Ohkita, S. Matsuda and K. Yamamoto: Weld. J., 1987, 66, 301s-309s. G. Thewlis: HW Doc. IIA-736-88, 1988. J.M. Dowling, J.M. Corbett and H.W. Kerr: Metall. Trans. A, 1986,17A, 1611-1623. G.M. Evans: Metal Constr., 1986,18, 631R-636R. J.L. Murray and H.A. Wriedt: Bull. Alloy Phase Diagr., 1987, 8, 148-165. LD. Sommerville, I. Ivanchev and H.B. Bell: Proc. Int. Conf Chem. Metall of Iron and Steel, Sheffield, July 1971, 23-25, Publ. The Iron and Steel Inst. (1973). H.K.D.H. Bhadeshia and L.E. Svensson: Mathematical Modelling of Weld Phenomena (Eds H. Cerjak and K.E. Easterling), 1993, London, The Institute of Materials, 109-180. S. Matsuda and N. Okumura: Trans. ISIJ, 1978,18, 198-205. M.E. Saggese, A.R. Bhatti, D.N. Hawkins and J.A. Whiteman: Proc. Int. Conf on the Effect of Residual, Impurity and Micro-Alloy ing Elements on Weldability and Weld Properties, London, Nov. 1983, Paper 15, Publ. The Welding Institute (England). A.O. Kluken and 0 . Grong: Report No. STF34 F87125, 1987, Sintef, Trondheim, Norway. S.S. Babu, S.A. David, J.M. Vitek, K. Mundra and T. DebRoy: Mater. ScL Technol., 1995,11,186199.

Appendix 2.1 Nomenclature contact area (mm2)

activity coefficient of element X

difference between total and acid soluble Al in weld metal (wt%)

gravity constant (9.81ms- 2 )

thermal diffusivity (mm2 s 1 )

standard free energy of reaction (J mol"1 or kJ mol-1)

activity of arbitrary slag component

energy barrier for homogeneous nucleation (kJ mol-1)

cross section of fused parent metal (mm2)

driving force for precipitation of oxide inclusions (J nr 3 )

flux basicity index kinetic constants GMAW

gas metal arc welding

GTAW

gas tungsten arc welding

drag coefficient molar concentration of element X in the liquid (mol m~3) cross section of deposited metal (mm2) element diffusivity in liquid phase (m2 s"1 or mm2 s"1) diffusivity of element X in gas phase (mm2 s"1) gross heat input (kJ mm"1) FCAW

standard enthalpy of reaction (J mol-1 or kJ mol-1) hydrogen content related to deposited metal (ml per 10Og deposit) hydrogen content related to fused metal (ml per 10Og or g per ton)

flux cored arc welding

hydrogen content related to French practice (g per ton)

drag force acting on spherical particle in relative motion to a fluid (N)

heat content per unit volume at the melting point (J mm"3)

gravity force acting on a spherical particle in relative motion to a fluid (N)

hydrogen content related to Japanese practice (ml per 10Og deposit)

fume formation rate (mg miir 1 )

amperage (A)

nucleation rate of oxide inclusions in the weld pool (nuclei nr 3 s"1) constant in equation (A2-1) (nuclei rrrV 1 ) ratio between absorbed Si and Mn in the weld metal coefficient of weld metal deposition (g A-1S"1) mass transfer coefficient for gas absorption (mm s"1) mass transfer coefficient for gas desorption (mm s"1) overall mass transfer coefficient (mm s"1) equilibrium constants

total mass of liquid metal leaving/entering the reaction zone per unit time (g s-1) arbitrary flux or slag component concentration displacement of manganese referred to different standard states (wt%) total manganese absorption in the weld metal due to slag/metal interactions (wt%) rejected manganese during cooling in the weld pool (wt%) oxidation loss of manganese at electrode tip (wt%)

the product [%C][%O] atomic weight of element X mass of CO2 per 100 g of electrode coating (g or wt%)

dimensionless operating parameter

total mass of inclusions per 100 g weld deposit (g)

total number of moles of component /

mass of H2O per 100 g of electrode coating (g or wt%)

absorption/desorption rate of element X in the weld pool (mol s"1)

total weight of retained MnOSiO2 (g per 100 g weld deposit)

total number of moles of component X

total weight of precipitated microslag (in g per 100 g weld deposit) total weight of precipitated MnS (g per 100 g weld deposit)

total number of moles of component X2 number of particles per unit area (mm"2) Avogadro constant (6.022 X 1023 mor 1 )

mole fraction of arbitrary slag component

combined partial pressure of H2 and H2O (atm)

analytical weld metal nitrogen content (wt%)

post weld heat treatment parts per million (g per ton)

mole fraction of CO in gas phase Reynolds number number of particles per unit volume (No. per mm"3) calculated oxygen absorption in electrode tip or falling droplets (wt%) analytical weld metal oxygen content (wt%)

net arc energy (W) universal gas constant (J K-1 mol-1) relative humidity (%) analytical weld metal sulphur content (wt%) standard entropy of reaction (J K -1 mol"1)

equilibrium weld metal oxygen content (wt%)

concentration displacement of silicon referred to different standard states (wt%)

rejected oxygen during cooling in the weld pool (wt%)

total silicon absorption in the weld metal due to slag/ metal interactions (wt%)

total oxygen absorption in hot part of weld pool (wt%)

rejected silicon during cooling in the weld pool (wt%)

total pressure (atm or bar) partial pressure of component X in bulk gas phase (atm) equilibrium partial pressure of component X at gas/ metal interface (atm) partial pressure of component X2 in bulk gas phase (atm) equilibrium partial pressure of component X2 at gas/ metal interface (atm)

oxidation loss of silicon at electrode tip (wt%) solubility of element X at 1 atm total pressure (ml per 10Og, ppm or wt%) total particle surface area per unit volume (mm2 per mm3) modified solubility of hydrogen at 1 atm total pressure (ml per 100 g, ppm or wt%)

SAW

submerged arc welding

SMAW

shielded metal arc welding

STEM

scanning transmission electron microscope

volume fraction of inclusions concentration of component / (vol%) concentration of component X2 (vol%)

time (s) time constant (s) acid soluble titanium in weld metal (wt%) difference between total and acid soluble Ti in weld metal (wt%) temperature (0C or K)

concentration of component YX2 (vol%) WDX

wavelength dispersive Xray analysis

WFR

wire feed rate (mm s -1 or m min"1) arbitrary element or gaseous species

ambient temperature (0C or K)

weld ripple lag (mm)

preheating temperature (0C or K)

concentration of element X in the weld metal (wt%)

reference temperatures (0C or K)

concentration displacement of element X referred to nominal weld metal composition (wt%)

rising velocity of ascending particles relative to the liquid (|jLms-1) bulk velocity of the fluid relative to the particles (ms- 1 )

equilibrium concentration of element X in the weld pool (wt%)

voltage (V)

initial concentration of element X in the weld pool (wt%)

welding (travel) speed (mm s"1)

average content of element X in inclusions (wt%)

volume of melt (mm3)

nominal concentration of element X in weld metal (wt%)

molar volume of nucleus (m3 mol-1) molar volume of oxide per mole of the diffusate (m3 mol-1)

concentration of element X in base plate (wt%)

concentration of element X in filler wire (wt%) arbitrary element or gaseous species density (kg irr 3 or g mm"3)

thickness of stagnant gaseous boundary layer (mm) wetting angle mean particle centre to centre volume spacing (jxm)

difference in density between liquid steel and inclusion (kg irr 3 or g mm"3)

dimensionless y-coordinate at maximum width of isotherm

slag/metal interfacial energy (J nr 2 )

activity coefficient for MnO in slag phase

arc efficiency factor

activity coefficient for SiO2 in slag phase

viscosity (kg nr 1 s"1)

Appendix 2.2 Derivation of equation (2-60) The nucleation rate / as a function of temperature can be expressed as: (A2-1) where J0 is a constant (with the unit nuclei per m3 and s) and AG* is the energy barrier for nucleation. By rearranging equation (A2-1) and inserting reasonable values for J and J0 for the specific case of homogeneous nucleation of oxide inclusions in liquid steel,55 we obtain:

(A2-2)

From the classic theory of homogeneous nucleation AG* is given by:

(A2-3) where NA is the Avogadro constant, o is the interfacial energy between the nucleus and the liquid (in J nr 2 ) and AGV is the driving force for the precipitation reaction (in J nr 3 ).

The parameter AGV can be expressed as:

(A2-4) where AH° and AS° are the standard entalpy and entropy of the precipitation reaction, respectively and Vm is the molar volume of the nucleus (in m3 mol"1). It is evident from Fig. 2.48 that AGV = 0 when T=Tu which gives \S° = A//7 T\. Hence, equation (A2-4) may be rewritten as: (A2-5)

By combining equations (A2-2), (A2-3) and (A2-5), we obtain the following relationship between T\ and T^-

(A2- 6)

3 Solidification Behaviour of Fusion Welds

3.1 Introduction Inherent to the welding process is the formation of a pool of molten metal directly below the heat source. The shape of this molten pool is influenced by the flow of both heat and metal, with melting occurring ahead of the heat source and solidification behind it. The heat input determines the volume of molten metal and, hence, dilution and weld metal composition, as well as the thermal conditions under which solidification takes place. Also important to solidification is the crystal growth rate, which is geometrically related to weld travel speed and weld pool shape. Hence, weld pool shape, weld metal composition, cooling rate, and growth rate are all factors interrelated to heat input which will affect the solidification microstructure. Some important points regarding interpretation of weld metal microstructure in terms of these four factors will be discussed below. Since the properties and integrity of the weld metal depend on the solidification microstructure, a verified quantitative understanding of the weld pool solidification behaviour is essential. At present, our knowledge of the chemical and physical reactions occurring during solidification of fusion welds is limited. This situation arises mainly from a complex sequence of reactions caused by the interplay between a number of variables which cannot readily be accounted for in a mathematical simulation of the process. Nevertheless, the present treatment will show that it is possible to rationalise the development of the weld metal solidification microstructure with models based on well established concepts from casting and homogenising treatment of metals and alloys.

3.2 Structural Zones in Castings and Welds The symbols and units used throughout this chapter are defined in Appendix 3.1. During ingot casting, three different structural zones can generally be observed, as shown schematically in Fig. 3.1. The chill zone is produced by heterogeneous nucleation in the region adjacent to the mould wall as a result of the pertinent thermal undercooling. These grains rapidly become dendritic, and dendrites having their direction (preferred easy growth direction for cubic crystals) parallel to the maximum temperature gradient in the melt will soon outgrow those grains that do not have this favourable orientation. Competitive growth occurring during the initial stage of the solidification process leads to an alignment of the crystals in the heat flow direction and eventually to the formation of a columnar zone. 12 Finally, an equiaxed zone may develop in the centre of the casting, mainly as a result of growth of detached dendrite arms within the remaining, slightly undercooled liquid. A similar situation also exists in welding, as indicated in Fig. 3.2 However, in this case the chill zone is absent, since the partly melted base metal grains at the fusion boundary act as seed crystals for the growing columnar grains.3 In addition, the growth direction of the columnar

Shrinkage pipe

Chill zone Columnar zone Equiaxed zone Mould

Fig. 3.1. Transverse section of an ingot showing the chill zone, the columnar zone and the equiaxed zone (schematic). grains will change continuously from the fusion line towards the centre of the weld due to a corresponding shift in the direction of the maximum temperature gradient in the weld pool. This change in orientation may result in a curvature of the columnar grains (Fig. 3.2(a)). Alternatively, new grains can nucleate and grow in a columnar manner, producing a so-called 'stray' structure as shown schematically in Fig. 3.2(b). Finally, if the conditions for nucleation of new grains are favourable, an equiaxed zone will form near the weld centreline similar to that observed in ingots or castings (see Fig. 3.2(b)). Although the process of weld pool solidification is frequently compared with that of an ingot in 'miniature', a number of basic differences, already mentioned, exist which strongly influence the microstructure and properties of the weld metal. Of particular importance is also the disparity in cooling rate between a fusion weld and an ingot (see Fig. 3.3). For conventional processes such as shielded metal arc (SMA), gas metal arc (GMA), submerged arc (SA) or gas tungsten arc (GTA) welding the cooling rate may vary from 10 to 103 0 C s"1, while for modern high energy beam processes such as electron beam (EB) and laser welding the cooling rate is typically of the order of 103 to 106 0 C s"1.4 Consequently, to appreciate fully the implications of these differences in general solidification behaviour between a weld pool and an ingot, it is necessary to consider in detail the sequence of events taking place in the solidifying weld metal beginning with the initiation of crystal growth at the fusion boundary.

3.3 Epitaxial Solidification It is well established that initial solidification during welding takes place epitaxially, where the partly melted base metal grains at the fusion boundary act as seed crystals for the columnar grains. This process is illustrated schematically in Fig. 3.4.

(a) Welding direction

(b) Columnar zone Welding direction

Equiaxed zone Columnar zone •

Rapid solidification technology

SMAW, SAW, GMAW, GTAW

Electron beam welding Laser welding

Cooling rate, °C/s

Fig. 3.2. Examples of structural zones in fusion welds (schematic); (a) Curved columnar grains, (b) Stray grain structure.

Process Fig. 3.3. Disparity in cooling conditions between casting, welding and rapid solidification.

Fusion boundary HAZ

Weld metal

Fig. 3.4. Schematic illustration showing epitaxial growth of columnar grains from partly melted base metal grains at fusion boundary. Liquid (L)

Substrate (S)

Fig. 3.5. Schematic representation of heterogeneous nucleation.

3.3.1 Energy barrier to nucleation During epitaxial solidification, a solid embryo (nucleus) of the weld metal forms at the meltedback surface of the base metal grain. Assuming that the interfacial energy between the embryo and the liquid is isotropic, it can be shown, for a given volume of the embryo, that the interfacial energy of the whole system is minimised if the embryo has the shape of a spherical cap. Under such conditions, the following relationship exists between the interfacial energies (see Fig. 3.5): (3-1) where (3 is the wetting angle. The change in free energy, AGhet, accompanying the formation of a solid nucleus with this configuration is given by:5 (3-2)

where VE is the volume of the solid embryo, AGV is the free energy change associated with the embryo formation, AEL and AES are the areas of the embryo-liquid and embryo-substrate interfaces, respectively, and/(P) is the so-called shape factor, defined as:

(3-3)

The critical radius of the stable nucleus, r / , is found by differentiating equation (3-2) with respect to rs and equating to zero: (3-4)

By substituting equation (3-4) into equation (3-2), we obtain the following expression for the energy barrier to heterogeneous nucleation (AG^ r ):

(3-5)

where AHm is the latent heat of melting, Tm is the melting point, and AJT is the undercooling. It is easy to verify that the first term in equation (3-5) is equal to the energy barrier to homogeneous nucleation, AGôm. Hence, we may write: (3-6) Equation (3-6) shows that AG^ is a simple function of the wetting angle O). Since the

chemical composition and the crystal structure of the two solid phases are usually very similar, we have:6

Under such conditions equation (3-1) predicts that the wetting angle 3 ~ 0 (cos(3 ~ 1), which implies that there is a negligible energy barrier to solidification of the weld metal (№}*het ~ 0), i.e. no undercooling of the melt is needed, and solidification occurs uniformly over the whole grain of the base metal. This is in sharp contrast to conventional casting of metals and alloys where some undercooling of the melt is always required to overcome the inherent energy barrier to solidification (see Fig. 3.6). 3.3.2 Implications of epitaxial solidification Since the initial size of the weld metal columnar grains is inherited directly from the grain growth zone adjacent to the fusion boundary, the solidification microstructure depends on the grain coarsening behaviour of the base material. This is particularly a problem in high energy processes such as submerged arc and gas metal arc welding, where grain growth of the base metal can be considerable. In such cases the size of the columnar grains at the fusion boundary will be correspondingly coarse, as indicated by the data in Fig. 3.7. Moreover, during multipass welding the columnar grains can renucleate at the boundary between for instance the first and the second weld pass and subsequently grow across the entire fusion zone, as illustrated in Fig. 3.8. This type of behaviour is usually observed in weldments which do not undergo transformations in the solid state (e.g. aluminium, certain titanium alloys, stainless steel etc.). In practice, the problem can be eliminated by additions of inoculants via the filler wire, which facilitates a refinement of the columnar grain structure through heterogeneous nucleation of new (equiaxed) grains ahead of the advancing interface (to be discussed later).

AG

r

s

Welding

Casting Homogeneous nucleation

Fig. 3.6. The free energy change associated with heterogeneous nucleation during casting and weld metal solidification, respectively (schematic). The corresponding free energy change associated with homogeneous nucleation is indicated by the broken curve in the graph.

Weld metal prior austenite grain size (jim)

Fusion line

HAZ

Weld metal

GMAW (low-alloy steel)

HAZ prior austenite grain size (jim) Fig. 3.7. Correlation between HAZ prior austenite grain size at the fusion boundary and the corresponding weld metal prior austenite grain size. Data from Grong et al?

2. pass

1. pass HAZ

Base metal

Fig. 3.8. Optical micrograph showing renucleation of columnar grains during multipass GMA welding of a P-titanium alloy.

3.4 Weld Pool Shape and Columnar Grain Structures Growth of the columnar grains always proceeds closely to the direction of the maximum thermal gradient in the weld pool, i.e. normal to the fusion boundary. This implies that the columnar grain morphology depends on the weld pool geometry. 3.4.1 Weld pool geometry The weld pool geometry is a function of the welding speed and the balance between the heat input and the cooling conditions, as influenced by the base plate thermal properties. At pseudosteady state, these conditions establish a dynamic equilibrium between heat supply and heat extraction so that the shape of the weld pool remains constant for any given speed. Following the treatment in Chapter 1, the weld pool geometry depends on the dimensionless operating parameter n3, defined as: (3-7) where qo is the net arc power, v is the welding speed, a is the thermal diffusivity of the base plate, and Hm-Ho is the heat content per unit volume at the melting point. As shown in Fig. 3.9(a), a tear-shaped weld pool is favoured by a high n3 value, which is characteristic of fast moving high power sources. In contrast, at a low arc power and a low welding speed the shape of the weld pool becomes more elliptical because of a shift in the mode of heat flow (see Fig. 3.9(b)). Note, however, that the thermal properties of the base metal is also of importance in this respect, since the n3 parameter is a function of both a and Hm-Ho. Consequently, a tear-shaped weld pool is usually observed in weldments of a low thermal diffusivity (e.g. austenitic stainless steel), whereas an elliptical or spherical weld pool is more likely to form during aluminium welding owing to the resulting higher thermal diffusivity of the base metal. In addition to the factors mentioned above, the geometry of the weld pool is also affected by convectional heat transfer due to the presence of buoyancy, electromagnetic or suface tension gradient forces. Recently, attempts have been made to include such effects in heat flow models for welding.8"11 Referring to Fig. 3.10(a) the buoyancy force will promote the formation of a shallow, wide weld pool because of transport of 'hot' metal to the surface and 'cold' metal to the bottom of the pool. In the presence of the electromagnetic force the flow pattern is reversed, since the latter force will tend to push the liquid metal in the central part of the pool downward to the root of the weld. This makes the weld pool deeper and more narrow, as shown in Fig. 3.10(b). Moreover, it is generally accepted that surface tension gradients can promote circulation of liquid metal within the weld pool from the region of low surface tension to the region of higher surface tension.9 In the absence of surface active elements such as oxygen and sulphur, the surface tension decreases with increasing temperature as illustrated in Fig. 3.10(c), which forces the metal to flow outwards towards the fusion boundary. This results in the formation of a relatively wide and shallow weld pool. However, if oxygen or sulphur is present in sufficient quantities a positive temperature coefficient of the surface tension may develop, which facilitates an inward fluid flow pattern and an increased weld penetration (see Fig. 3.10(d)). The important influence of surface active elements on the resulting bead morphology is well docu-

HAZ isotherms Fusion boundary

V

Weld pool

(a) HAZ isotherms Fusion boundary

Weld pool

V

(b) Fig. 3.9. Theoretical shape of fusion boundary and neighbouring isotherms under different operational conditions; (a) High n3 values, (b) Low ^-values. merited for ordinary GTA austenitic stainless steel welds. 1 2 1 3 The indications are that such effects become even more important under hyperbaric welding conditions. 14

3.4.2 Columnar grain morphology It is evident from the above discussion that a change in the weld pool geometry, caused by variations in the operational conditions, may strongly alter the weld metal solidification microstructure. In fact, more than nine different grain morphologies have been observed during fusion welding.15 The two most important are shown in Fig. 3.11. Referring to Fig. 3.11(a) a spherical or elliptical weld pool will reveal curved and tapered columnar grains owing to a shift in the direction of the maximum thermal gradient in the liquid from the fusion boundary towards the weld centre-line. In contrast, a tear-shaped weld pool yields straight and broad

Electrode

Weld pool

Arc

(a)

Electrode

Weld pool

Arc

(b)

Fig. 3.10. Schematic diagrams illustrating the major fluid flow mechanisms operating in a weld pool; (a) Buoyancy force (b) Electromagnetic force. columnar grains as shown in Fig. 3.11(b), since the direction of the maximum temperature gradient in the melt does not change significantly during the solidification process. The latter condition is known to promote formation of centre-line cracking because of mechanical entrapment of inclusions and enrichment of eutectic liquid at the trailing edge of the weld pool. 3.4.3 Growth rate of columnar grains The growth rate of the columnar grains is geometrically related to the weld travel speed and the weld pool shape. 3.4.3.1 Nominal crystal growth rate Since the shape of the weld pool remains constant during steady state welding, the growth rate of the columnar grains must vary with position along the fusion boundary. This point is more clearly illustrated in Fig. 3.12 which shows a sketch of a single columnar grain growing parallel with the steepest temperature gradient in the weld pool. Taking the angle between the

Surface tension Temperature Electrode

Weld pool

Arc

Surface tension

(C)

Temperature

Electrode

Arc Weld pool

(d)

Fig. 3.10. Schematic diagrams illustrating the major fluid flow mechanisms operating in a weld pool (continued); (c) Surface tension gradient force (negative gradient); (d) Surface tension gradient force (positive gradient).

Heat source

v

Heat source

v

(a)

(b)

Fig. 3.11. Schematic comparison of columnar grain structures obtained under different welding conditions; (a) Elliptical weld pool (low n3 values), (b) Tear-shaped weld pool (high n3 values). Open arrows indicate the direction of the maximum temperature gradient in the weld pool.

Fusion boundary

Heat source Crystal Fig. 3.12. Definition of the nominal crystal growth rate RN. growth direction and the welding direction equal to a, the steady state growth rate, R N , becomes: (3-8) where v is the welding speed. Considering spherical or elliptical weld pools, the nominal crystal growth rate is lowest at the edge of the weld pool (a—>90°, cosa-^0) and highest at the weld centre-line where R N approaches v (a->0, c o s a ^ l ) . In contrast, columnar grains trailing behind a tear-shaped weld pool will grow at an approximately constant rate which is significantly lower than the actual welding speed (a » 0), since the direction of the maximum temperature gradient in the weld pool does not change during the solidification process. This is also in agreement with practical experience (see Fig. 3.13).

(a) Nominal growth rate (RN), mm/s

Niobium (1 mm plate thickness)

Relative position from edge of weld pool (%)•

(b)

Equiaxed zone

Nominal growth rate (RN), mm/s

Stainless steel (1 mm plate thickness)

Relative position from edge of weld pool (%) Fig. 3.13. Measured crystal growth rates in thin sheet electron beam welding; (a) Niobium, (b) Stainless steel. Data from Senda et al.16

Example (3.1)

Consider electron beam (EB) welding of a lmm thin sheet of austenitic stainless steel under the following conditions:

Estimate on the basis of the Rosenthal thin plate solution (equation 1-83) the steady state growth rate of the columnar grains trailing the weld pool. Solution

The contour of the fusion boundary can be calculated from the Rosenthal thin plate solution according to the procedure shown in Example (1.10). If we include a correction for the latent heat of melting, the QbZn3 ratio at the melting point becomes:

Substitution of the above value into equation (1-83) gives the fusion boundary contour shown in Fig. 3.14. It is evident from Fig. 3.14 that the weld pool is very elongated under the prevailing circumstances due to a constrained heat flow in the ^-direction. This implies that the angle a will not change significantly during the solidification process. Taking a as an average, equal to about 70°, the steady-state crystal growth rate R N becomes:

This value is in reasonable agreement with the measured crystal growth rates in Fig. 3.13(b). 3.4.3.2 Local crystal growth rate Equation (3-8) does not take into account the inherent anisotropy of crystal growth. For faceted materials the dendrite growth directions are always those that are 'capped' by relatively slow-growing (usually low-index) crystallographic planes.1 Figure 3.15 shows examples of faceted cubic crystals delimited by {100} and {111} planes, respectively. If the {111} planes are the slowest growing ones, the {100} planes will grow out, leaving the {111} facets and a new crystal growing in the directions as shown schematically in Fig. 3.15(b). Although most metals and alloys do not form faceted dendrites, the anisotropy of crystal growth is still maintained during solidification.2 In fact, experience has shown that the major dendrite growth direction is normally the axis of a pyramid whose sides are the most closely packed planes with which a pyramid can be formed.1 These directions are thus for body- and face-centred cubic structures, < 1010 > for hexagonal close-packed structures, and for body-centred tetragonal structures. Because of the existence of preferred growth directions, the local growth rate of the crystals RL will always be higher than the nominal growth rate R N defined in equation (3-8). Consider now a cubic crystal which grows along the steepest temperature gradient in the weld pool, as shown schematically in Fig. 3.16. If § denotes the angle between the interface normal and the direction, the following relationship exists between RN and RL:

-y(mm) Columnar zone

Heat source

Equiaxed zone +x(mm)

Columnar zone

+yjmm)

Fusion boundary

Fig. 3.14. Predicted shape of fusion boundary during electron beam welding of austenitic stainless steel (Example (3.1)).

(a)

(b)

Fig. 3.25.Examples of faceted cubic crystals; (a) Crystal delimited by {100} planes, (b) Crystal delimited by {111} planes.

Columnar grain

Welding direction (x)

Tip temperature, 0C

Fig. 3.16. Definition of the local crystal growth rate RL.

Liquidus temperature

Tip velocity, mm/sFig. 3.17. Calculated dendrite tip temperature vs dendrite growth velocity for an Fe-15Ni-15Cr alloy. The undercooling of the dendrite tip is given by the difference between the liquidus temperature and the solid curve in the graph. Data from Rappaz et alP

(3-9) which gives:

(3-10) Equation (3-10) shows that the local growth rate increases with increasing misalignment of

the crystal with respect to the direction of the maximum temperature gradient in the weld pool. Since such crystals cannot advance without a corresponding increase in the undercooling ahead of the solid/liquid interface (see Fig. 3.17), they will soon be outgrowed by other grains which have a more favourable orientation. Fusion welds of the fee and bcc type will therefore develop a sharp solidification texture in the columnar grain region, similar to that documented for ingots and castings. The weld metal columnar grains may nevertheless be separated by 'high-angle' boundaries, as shown in Fig. 3.1&, due to a possible rotation of the grains in the plane perpendicular to their length axes. Example (3.2)

Consider electron beam welding of a 2mm thick single crystal disk of Fe-15Ni-15Cr under the following conditions:

The orientation of the disk with respect to the beam travel direction is shown in Fig. 3.19. Calculate on the basis of the minimum velocity (undercooling) criterion the growth rate of the dendrites trailing the weld pool under steady state welding conditions (assume 2-D heat flow). Make also schematic drawings of the solidification microstructure in different sections of the weld. Relevant thermal properties for the Fe-15Ni-15Cr single crystal are given below:

Solution

Since the base metal is a single crystal, separate columnar grains will not develop. Nevertheless, under 2-D heat flow conditions growth of the dendrites can occur both in the [100] and the [010] (alternatively the [010]) direction. Referring to Fig. 3.20 the growth rate of the [100] and the [010] deridrites is given by:

and

Fig. 3.18. Spatial misorientation between two columnar grains growing in the direction (schematic).

Heat source

Weld

Fig. 3.19. Orientation of the single crystal Fe-15Ni-15Cr disk with respect to beam travel direction (Example (3.2)).

Welding direction

Fig. 3.20. Schematic diagram showing the pertinent orientation relations between the fusion boundary interface normal and the dendrite growth directions (Example (3.2)). From this it is seen that the velocity of the [100] dendrites is always equal to that of the heat source v. In contrast, the growth rate of the [010] dendrites depends both on v and a, and will therefore vary with position along the fusion boundary. It follows from minimum velocity criterion that the [100] dendrites will be selected when the interface normal angle a is less than 45°, while the [010] dendrites will develop at larger angles. This is shown graphically in Fig. 3.21. At pseudo-steady state the fusion boundary can be calculated from the Rosenthal thin plate solution (equation (1-83)) according to the procedure shown in Example (1.10). If we include

R

hk ,

/V

dendrites

a, degrees Fig. 3.21.Normalised minimum dendrite tip velocity vs interface normal angle a (Example 3.2)).

a correction for the latent heat of melting, the QbIn3 ratio at the melting point becomes:

Substitution of this value into equation (1-83) gives the fusion boundary contour shown in Fig. 3.22(a). Included in Fig. 3.22 are also schematic drawings of the predicted solidification microstructure in different sections of the weld. The results in Fig. 3.22 should be compared with the reconstructed 3-D image of the solidification microstructure in Fig. 3.23, taken form Rappaz et al.17 Due to partial heat flow in the z-direction, [001] dendrite trunks will also develop. Nevertheless, these data confirm the general validity of equations (3-8) and (3-10) relating crystal growth rate to welding speed and weld pool shape. 3.4.4 Reorientation of columnar grains In principle, there are two different ways a columnar grain can adjust its orientation during solidification in order to accommodate a shift in the direction of the maximum temperature gradient in the weld pool, i.e.: (i) (ii)

Through bowing Through renucleation.

-y (mm)

(a)

dendrites

Heat source

dendrites

+x (mm)

dendrites +y (mm) Fusion boundary (b)

Fusion zone (4.4 mm)

Base plate

dendrites

dendrites

dendrites

Fig. 3.22. Schematic representation of the weld metal solidification micro structure (Example 3.2)); (a) Top view of fusion zone, (b) Transverse section of fusion zone.

3.4.4.1 Bowing of crystals A continuous change in the crystal orientation due to bowing will result in curved columnar grains, as shown previously in Fig. 3.2(a). This type of grain morphology has been observed in for instance electron beam welded aluminium and iridium alloys.34 Normally, the adjustment of the crystal orientation is promoted by multiple branching of dendrites present within the grains. Alternatively, the reorientation can be accommodated by the presence of surface defects at the solid/liquid interface, e.g. screw dislocations, twin boundaries, rotation boundaries, etc. The latter process presumes, however, a faceted growth morphology, and is therefore of minor interest in the present context. Example (3.3)

Consider a curved columnar grain of iridium which grows from the fusion boundary towards the weld centre-line along a circle segment of length L, as shown schematically in Fig. 3.24. Based on the assumption that the bowing is accommodated solely by branching of [010] dendrites in the [100] direction, calculate the maximum local growth rate of the crystal during solidification.

y X

2 Fig. 3.23. Reconstructed 3-D image of solidification microstructure in an electron beam welded Fe-15Ni15Cr single crystal. The letters (a), (b) and (c) refer to [100], [010] and [001] type of dendrites, respectively. After Rappaz et al.17 Weld centre-line

Fusion line

Fig. 3.24. Sketch of curved columnar grain in Example (3.3). Solution In principle, the solution to this problem is identical to that presented in Example (3.2). Referring to Fig. 3.24 the growth rate of [100] and the [010] dendrite stems is given by:

and

It follows from Fig. 3.21 that growth will occur preferentially in the [010] direction as long as the interface normal angle a is larger than 45°, while the [100] direction is selected at smaller angles. This means that the local growth rate of the dendrites, in practice, never will exceed the welding speed v. 3.4.4.2 Renucleation of crystals In ingots and castings, three different mechanisms for nucleation of new grains ahead of the advancing interface are operative:12 (i) (ii) (iii)

Heterogeneous nucleation Dendrite fragmentation Grain detachment.

The former mechanism is of particular importance in welding, since the weld metal often contains a high number of second phase particles which form in the liquid state. These particles can either be primary products of the weld metal deoxidation or stem from reactions between specific alloying elements which are deliberately introduced into the weld pool through the filler wire. The latter process is also known as inoculation. Nucleation potency of second phase particles In general, the effectiveness of individual particles to act as heterogeneous nucleation sites can be evaluated from a balance of interfacial energies, analogous to that described in Section 3.3.1 for epitaxial nucleation. It follows from the definition of the wetting angle (3 in Fig. 3.5 that the energy barrier to heterogeneous nucleation is a function of both the substrate/liquid interfacial energy ySL, the substrate/embryo interfacial energy yES, and the embryo/liquid interfacial energy yEL. Complete wetting is achieved when: (3-11) Under such conditions, the nucleus will readily grow from the liquid on the substrate. Unfortunately, data for interfacial energies are scarce and unreliable, which makes predictions based on equation (3-11) rather fortuitous.18 In pure metals, experience has shown that the solid/liquid interfacial energies are roughly proportional to the melting point, as shown by the data in Fig. 3.25. On this basis, it can be expected that the higher melting point phases will reveal the highest ySL values, and thus be nucleants for lower melting phases. A similar situation also exists in the case of non-metallic inclusions in liquid steel, where the high-melting point phases are seen to exhibit the highest solid/liquid interfacial energies (see Fig. 3.26). In contrast, very little information is available on the substrate/embryo interfacial energy yES. For fully incoherent interfaces, yES would be expected to be of the order of 0.5 to 1 J m~2.5 However, this value will be greatly reduced if there is epitaxy between the inclusions and the nucleus, which results in a low lattice disregistry between the two phases. In general, assessment of the degree of atomic misfit between the nucleus n and the substrate s can be done on

Melting point, K

Interfacial energy, J / m 2

lnterfacial energy, J/m2

Fig. 3.25. Values of solid/liquid interfacial energy ySL of various metals as function of their melting points. Data from Mondolfo.18

Melting point, 0 C Fig. 3.26. Values of interfacial energy 7 5L for different types of non-metallic inclusions in liquid steel at 16000C as function of their melting points. Data compiled from miscellaneous sources.

the basis of the Bramfitt's planar lattice disregistry model :19

(3-12)

a low-index a low-index a low-index a low-index

where

plane of the substrate; direction in (hkl)s plane in the nucleated solid; direction in (hkl)n;

the interatomic spacing along [wvw]n; the interatomic spacing along [WVH>]5; and the angle between the [wvw]^ and the [wvw]w.

Undercooling, 0C

In practice, the undercooling Ar (which is a measure of the energy barrier to heterogeneous nucleation) increases monotonically with increasing values of the planar lattice disregistry, as shown by the data in Fig. 3.27. This means that the most potent catalyst particles are those which also provide a good epitaxial fit between the substrate and the embryo. Examples of such catalyst particles are TiAl3 in aluminium 18 and TiN in steel.19 Nucleation of delta ferrite at titanium nitride will be considered below.

« „ « > Fig. 3.27. Relationship between planar lattice disregistry and undercooling for different nucleants in steel. Data compiled from miscellaneous sources.

Example (3.4)

In low-alloy steel weld metals, titanium nitride can form in the melt due to interactions between dissolved titanium and nitrogen. Assume that the TiN particles are faceted and delimited by {100} planes. Calculate on the basis of equation (3-12) the minimum planar lattice disregistry between TiN and the nucleating delta-ferrite phase under the prevailing circumstances. Indicate also the plausible orientation relationship between the two phases. The lattice parameters of delta ferrite and TiN at 15200C may be taken equal to 0.293 and 0.43 lnm, respectively. Solution

Titanium nitride has the NaCl crystal structure, while delta ferrite is body-centred cubic, as shown in Fig. 3.28(a) and (b). It is evident from Fig. 3.29(a) that a straight cube-to-cube orientation relationship between TiN and 8-Fe will not result in a small lattice disregistry. However, the situation is largely improved if the two phases are rotated 45° with respect to each other (see Fig. 3.29(b)), conforming to the following orientation relationship:

The resulting crystallographic relationship at the interface is shown schematically in Fig. 3.29(c). Since the lattice arrangements are similar in this case, equation (3-12) reduces to:

A comparison with the data in Fig. 3.27 shows that the calculated lattice disregistry conforms to an undercooling of about 1 to 2°C. This value is sufficiently small to facilitate heterogeneous nucleation of new grains ahead of the advancing interface during solidification. Considering other inclusions with more complex crystal structures, the chances of obtaining a small planar lattice disregistry between the substrate and the delta ferrite nucleus are

Fe- atoms

N-atoms

Ti- atoms (a)

(b)

Fig. 3.28. Crystal structures of phases considered in Example (3.4); (a) Titanium nitride, (b) Delta ferrite.

TiN

(a)

TiN

(C) (b)

Ti atoms

N atoms

8-Fe atoms

Fig. 3.29. Possible crystallographic relationships between titanium nitride and delta ferrite (Example (3.4)); (a) Straight cube-to-cube orientation, (b) Twisted cube-to-cube orientation, (c) Details of lattice arrangement along coherent TiN/d-Fe interface.

rather poor (see Fig. 3.27). Nevertheless, such particles can act as favourable sites for heterogeneous nucleation if 7 ^ is sufficiently large compared with yEL and 7 ^ . This is illustrated by the following example: Example (3.5)

In low-alloy steel weld metals 7-Al2O3 inclusions can form during the primary deoxidation stage as discussed in Section 2.12.4.2 (Chapter 2). Based on the classic theory of heterogeneous nucleation, evaluate the nucleation potency of such inclusions with respect delta ferrite.

Solution

It is readily seen from Fig. 3.27 that the planar lattice disregistry between delta ferrite and Al2O3 is very large, which indicates of a fully incoherent interface (i.e. yES « 0.75 J m" 2 ). Moreover, readings from Figs. 3.25 and 3.26 give the following average values for the delta ferrite/liquid and the inclusion/liquid interfacial energies:

and

According to equation (3-11) complete wetting is achieved when ySL > yES + yEL. This requirement is clearly met under the prevailing circumstances. Similar calculations can also be performed for other types of non-metallic inclusions in steel weld metals. The results are presented graphically in Fig. 3.30. It is evident that the nucleation potency of the inclusions increases in the order SiO2-MnO, Al 2 O 3 -Ti 2 O 3 -SiO 2 MnO, Al2O3, reflecting a corresponding increase in the inclusion/liquid interfacial energy ySL. The resulting change in the weld metal solidification microstructure is shown in Fig. 3.31, from which it is seen that both the average width and length of the columnar grains decrease with increasing Al2O3-contents in the inclusions. This observation is not surprising, considering the characteristic high solid/liquid interfacial energy between aluminium oxide and steel (see Fig. 3.26). The important effect of deoxidation practice on the weld metal solidification microstructure is well documented in the literature.320"22 Rate of heterogeneous nucleation It can be inferred from the classic theory of heterogeneous nucleation that the nucleation rate

Complete wetting

No wetting

Embryo'

A

G*he/AGhom

p (degrees)

Inclusion

(Y sf Y ES )/7 EL Fig. 3.30. Nucleation potency of different weld metal oxide inclusions with respect to delta ferrite.

AI2O3 content (wt%)

(a)

Average width of grains, î m

95% confidence limit

Pure AI2O3

(A%AI)weld/[%O]anaL AI2O3 content (wt%)

(b)

Average length of grains, ^m

95% confidence limit Pure AI2O3

* will, in turn, depend on the nucleation potency of the catalyst particles and can be estimated for different types of welds. If growth of the columnar grains is assumed to occur along a circle segment of length L (see Fig. 3.33), the critical cell/dendrite alignment angle is given by: (3-15)

Average width of grains, (x m

where co is the total grain rotation angle, and / is the average length of the columnar grains (in mm).

Titanium content, wt% Fig. 3.32. Effect of titanium on the columnar grain structure in 1100 aluminium welds. The value Y is the fractional distance from fusion line to top surface of weld metal. Data from Yunjia et alP

Weld metal

Fig. 3.33. Characteristic growth pattern of columnar grains in bead-on-plate welds (schematic). By introducing reasonable average values for co and / in the case of SA welding of lowalloy steel,22 we obtain: (3-16) Calculated values for 4>* in steel weld metals are presented in Fig. 3.34, using data from Kluken et al.22 An expected, the critical cell/dendrite alignment angle in fully aluminium deoxidised steel welds is seen to be very small (of the order of 2°), reflecting the fact that nucleation of delta ferrite occurs readily at Al2O3 inclusions. The value of 4>* increases gradually with decreasing Al2O3 contents in the inclusions and reaches a maximum of about 4° for Si-Mn deoxidised steel weld metals. This situation can be attributed to less favourable nucleating opportunities for delta ferrite at silica-containing inclusions, which reduces the possibilities of obtaining a change in the crystal orientation during solidification through a nucleation and growth process. Dendrite fragmentation In principle, nucleation of new grains ahead of the advancing interface can also occur from random solid dendrite fragments contained in the weld pool. Although the source of these solid fragments has yet to be investigated, it is reasonable to assume that they are generated by some process of interface fragmentation due to thermal fluctuations in the melt or mechanical disturbances at the solid/liquid interface.3 At present, it cannot be stated with certainty whether grain refinement by dendrite fragmentation is a significant process in fusion welding.26 Grain detachment Since the partially melted base metal grains at the fusion boundary are loosely held together by liquid films between them, there is also a possibility that some of these grains may detach themselves from the base metal and be trapped in the solidification front.26 Like dendrite fragments, such partially melted grains can act as seed crystals for the formation of new grains in the weld metal during solidification if they are able to survive sufficiently long in the melt.

R L / v cos a

Next Page

Calculated from equation (3-10)

Critical cell/dendrite alignment angle ($*) Fig. 3.34. Critical cell/dendrite alignment angle ()>* for reorientation of delta ferrite columnar grains during solidification of steel weld metals. Data from Kluken et al.22

3.5 Solidification Microstructures So far, we have discussed growth of columnar grains without considering in detail the weld metal solidification microstructure. In general, each individual grain will exhibit a substructure consisting of a parallel array of dendrites or cells. This substructure can readily be revealed by etching, also in cases where it is masked by subsequent solid state transformation reactions (as in ferrous alloys).2224 3.5.1 Substructure characteristics A cellular substructure within a single grain consists of an array of parallel (hexagonal) cells which are separated from each other by 'low-angle' grain boundaries, as shown schematically in Fig. 3.35. In the presence of solute, these boundaries respond to etching even in the absence of segregation. When the cellular to dendritic transition occurs, the cells become more distorted and will finally take the form of irregular cubes, as indicated by the optical micrograph in Fig. 3.36. This is actually a dendritic type of substructure, where the formation of secondary and tertiary dendrite arms is suppressed because of a relatively small temperature gradient in the transverse direction compared with the longitudinal (growth) direction. Fully branced dendrites may, however, develop in the centre of the weld if the thermal conditions are favourable. Branching will then occur in specific crystallographic directions, e.g. along the three easy growth directions for bcc and fee crystals, as illustrated in Fig. 3.37. Besides the difference in morphology, the distinction between cells and dendrites lies primarily in their sensitivity to crystalline alignment. Cells do not necessarily have the axis orientation, while dendrites do.2 Hence, cells can grow with their axes parallel to the heat flow direction, regardless of the crystal orientation. This important point is often overlooked when discussing competitive grain growth in fusion welding.

R L / v cos a

Previous Page

Calculated from equation (3-10)

Critical cell/dendrite alignment angle ($*) Fig. 3.34. Critical cell/dendrite alignment angle ()>* for reorientation of delta ferrite columnar grains during solidification of steel weld metals. Data from Kluken et al.22

3.5 Solidification Microstructures So far, we have discussed growth of columnar grains without considering in detail the weld metal solidification microstructure. In general, each individual grain will exhibit a substructure consisting of a parallel array of dendrites or cells. This substructure can readily be revealed by etching, also in cases where it is masked by subsequent solid state transformation reactions (as in ferrous alloys).2224 3.5.1 Substructure characteristics A cellular substructure within a single grain consists of an array of parallel (hexagonal) cells which are separated from each other by 'low-angle' grain boundaries, as shown schematically in Fig. 3.35. In the presence of solute, these boundaries respond to etching even in the absence of segregation. When the cellular to dendritic transition occurs, the cells become more distorted and will finally take the form of irregular cubes, as indicated by the optical micrograph in Fig. 3.36. This is actually a dendritic type of substructure, where the formation of secondary and tertiary dendrite arms is suppressed because of a relatively small temperature gradient in the transverse direction compared with the longitudinal (growth) direction. Fully branced dendrites may, however, develop in the centre of the weld if the thermal conditions are favourable. Branching will then occur in specific crystallographic directions, e.g. along the three easy growth directions for bcc and fee crystals, as illustrated in Fig. 3.37. Besides the difference in morphology, the distinction between cells and dendrites lies primarily in their sensitivity to crystalline alignment. Cells do not necessarily have the axis orientation, while dendrites do.2 Hence, cells can grow with their axes parallel to the heat flow direction, regardless of the crystal orientation. This important point is often overlooked when discussing competitive grain growth in fusion welding.

Cell wall'

Fig. 3.35. Schematic representation of the cellular substructure.

Fig. 3.36. Optical micrograph showing the characteristic cellular-dendritic substructure in a low-alloy steel weld. The metallographic section is normal to the columnar grain growth direction. After Kluken etal.22

Fig. 3.37. Schematic representation of the development of primary, secondary and tertiary dendrite arms along directions in cubic crystals.

A characteristic feature of cellular and cellular-dendritic growth is also that the boundary between two adjacent columnar grains will closely follow the contours of the original cell boundaries. An illustration of this point is contained in Fig. 3.38. Consequently, since all cell walls are preferential sites for segregation during solidification (see ion micrograph in Fig. 3.39), the presence of solute at the columnar grain boundaries can strongly alter the kinetics of subsequent solid state transformation reactions. The indications are that for instance phosphorus segregations at prior austenite grain boundaries will promote the formation of grain boundary ferrite in low-alloy steel weld metals during the 7 to a transformation because of the associated increase in the A

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