Metallurgical Modelling of Welding 2nd Edition (1997)

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

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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

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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

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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

Appendix 2.1: Nomenclature ............................................................

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

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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

Appendix 3.1: Nomenclature ............................................................

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

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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

Appendix 4.1: Nomenclature ............................................................

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

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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

Appendix 5.1: Nomenclature ............................................................

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 ................

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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

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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

Appendix 6.1: Nomenclature ............................................................

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 .....................................................

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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 ............................................................

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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

Appendix 7.1: Nomenclature ............................................................

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

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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

^i 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:

Next Page

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

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

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, ^i 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.

4 Precipitate Stability in Welds

4.1 Introduction Precipitate stability is an important aspect of welding metallurgy. Normally, modern structural steels and aluminium alloys derive their balanced package of high strength, ductility and toughness via optimised thermomechanical processing to produce a fine-grained, precipitation strengthened matrix. This delicate balance of microalloy precipitation and microstructure, however, is significantly disturbed by the heat of welding processes, which, in turn, affects the mechanical integrity of the weldment. When a commercial alloy is subjected to welding or heat treatment several competitive processes are operative which may contribute to a change in the volume fraction and size distribution of the base metal precipitates. The two most important are:1 (i) (ii)

Particle coarsening (Ostwald ripening) Particle dissolution (reversion)

Referring to Fig. 4.1, particle coarsening occurs typically at temperatures well below the equilibrium solvus Te of the precipitates, while particle dissolution is the dominating mechanism at higher temperatures. On the other hand, there exists no clear line of demarcation between these two processes, which means that particle coarsening can take place simultaneously with reversion in certain regions of the weld where the peak temperature of the thermal cycle falls within the 'gray zone' in Fig. 4.1. Nevertheless, it is important to regard them as separate processes, since the reaction kinetics are so different (coarsening is driven by the surface energy alone, whereas dissolution, which involves a change in the total volume fraction, is driven by the free energy change of transformation).

4.2 The Solubility Product The symbols and units used throughout this chapter are defined in Appendix 4.1. The solubility product is a basic thermodynamic quantity which determines the stability of the particles under equilibrium conditions. Because of its simple nature, the solubility product is widely used for an evaluation of the response of grain size-controlled and dispersion-hardened materials to welding and thermal processing.23 4.2.1 Thermodynamic background In general, the solubility product can be derived from an analysis of the Gibbs free energy AG° of the following dissolution reaction:

'Grey zone1

Particle coarsening |

Increasing heating rate

Temperature

Particle dissolution

%B Fig. 4.1. Schematic diagram showing the characteristic temperature ranges where specific physical reactions occur during reheating of grain size-controlled and dispersion-hardened materials.

(4-1) At equilibrium, we have:

(4-2) where AH° and AS° are the standard enthalpy and entropy of reaction, respectively. The other symbols have their usual meaning (see Appendix 4.1). When pure An Bm is used as a standard state, the activity of the precipitate {aAn Bm) is equal to unity. In addition, for dilute solutions it is a fair approximation to set aA~[%A] and aB~[%B], where the matrix concentrations of elements A and B are either in wt% or at%*. Hence, the solubility product can be written as: (4-3)

*For the solute, the standard state is usually a hypothetical 1 % solution. This implies that the activity coefficient is equal to unity as long as Henry's law is obeyed.

Table 4.1 gives a summary of equilibrium solubility products for a wide range of precipitates in low-alloy steels and aluminium alloys. In addition to the compounds listed in Table 4.1, different types of mixed precipitates may form within systems which contain more than two alloying elements.3"6 However, since the presence of such multiphase particles largely increases the complexity of the analysis, only pure binary intermetallics will be considered below. 4.2.2 Equilibrium dissolution temperature Based on equation (4-3) it is possible to calculate the equilibrium dissolution temperature Td of the precipitates. By rearranging this equation, we get:

(4-4) where [%A]o and [%B]o refer to the analytical content of elements A and B in the base metal, respectively. Equation (4-4) shows that the equilibrium dissolution temperature increases with increasing concentrations of solute in the matrix. This is in agreement with the Le Chatelier's principle. Table 4.1 Equilibrium solubility products for different types of precipitates in low-alloy steels and aluminium alloys. Data compiled from miscellaneous sources. Material/ phase

log [%A]n [%B]m

Type of Precipitate

C* = AS°/R'

D* = Mi0IR'

TiN

0.32

8000

TiC

5.33

10475

NbN

4.04

10230

Low-alloy steel

NbC

2.26

6770

(austenite)t

VN

3.02

7840

VC

6.72

9500

AIN

1.79

7184

Mo2C

5.0

7375

Al-Mg-Si^

Mg2Si

5.85

5010

Al-Cu-Mg$

CuMg

6.64

4005

MgZn

5.33

2985

Zn2Mg

7.72

4255

Al-Zn-Mgij:

All concentrations in wt% All concentrations in at.%

Example (4.1)

Consider a low-alloy steel with the following chemical composition:

Calculate on the basis of the reported solubility products in Table 4.1 the equilibrium dissolution temperature of each of the following three nitride precipitates, i.e. NbN, AlN, and TiN.

Solution

The equilibrium dissolution temperature of the precipitates can be computed from equation (44) by inserting the correct values for C* and D* from Table 4.1:

It is evident from these calculations that precipitates of the NbN and the AlN type will dissolve readily at temperatures above 1050 to 11000C, while TiN is thermodynamically stable up to about 14500C. In practice, however, a certain degree of superheating is always required to overcome the inherent kinetic barrier against dissolution, particularly if the heating rate is high. Consequently, in a real welding situation the actual dissolution temperature of the precipitates may be considerably higher than that inferred from simple thermodynamic calculations based on the solubility product (to be discussed later). 4.2.3 Stable and metastable solvus boundaries Due to the lack of adequate phase diagrams for the complex alloy systems involved, thermodynamic calculations based on the solubility product represent in many cases the only practical means of estimating the solid solubility of alloying elements in commercial low-alloy steels and aluminium alloys. 4.2.3.1 Equilibrium precipitates In the case of large, incoherent precipitates (where the Gibbs-Thomson effect can be neglected), the concentration of element A in equilibrium with pure An Bm at different temperatures can be inferred directly from equation (4-3). If we replace / ^ by R (i.e. switch from common to natural logarithms), this equation yields: (4-5)

Equation (4-5) describes the solvus surface within the solvent-rich corner of the phase diagram. However, when a pure binary compound dissolves the concentration of elements A and B in solid solution is fixed by the stoichiometry of the reaction. The following relationship exists between [%B] and [%A]:

(4-6) or

where MA and MB are the atomic weight of elements A and B, respectively. Figure 4.2 shows a graphical representation of equations (4-5) and (4-6), and the corresponding change in the matrix concentrations during dissolution of pure AnBm for a given set of starting conditions. Alternatively, we can express T as function of the product [%A]n [%B]m by utilising equations (4-3) and (4-6). The combination of these equations provides a mathematical description of the 'solvus boundary' of an equilibrium precipitate in a multi-component alloy system. It is evident from the graphical representation in Fig. 4.3 that the solid solubility will always in-

[%B]

[%A]0

[%B]o

Excess B [%A] Fig. 4.2. Concentration displacements during dissolution of binary intermetallics (equilibrium conditions).

Increased additions _of element B

Nominal alloy composition

Reduced solid solubility of element A

Temperature

I Increased dissolution temperature

Concentration of element A Fig. 4.3. Factors affecting the solid solubility of a binary intermetallic compound in a multi-component alloy system (schematic).

crease with increasing temperature when AH° is positive. This type of behaviour is characteristic of intermetallics in metals and alloys, since the dissolution process in such systems is endothermic.7 As a result, increased additions of a second alloying element B will also reduce the solubility of the first alloying element A by shifting the 'solvus boundary' towards higher temperatures when an intermetallic compound between A and B is formed. With the aid of Fig. 4.3 it is easy to verify that the equilibrium volume fraction of the precipitates/^ at a fixed temperature is given by:

(4-7)

where fmax is the maximum possible volume fraction precipitated at absolute zero. Equation (4-7) provides a basis for estimating the equilibrium volume fraction of binary intermetallics in complex alloy systems at different temperatures in cases where the concentration of element B is sufficiently high to tie-up all A in the form of precipitates. Similarly, if A is present in an overstoichiometric amount with respect to B, we may write:

(4-8)

Example (4.2)

In Al-Mg-Si alloys the equilibrium Mg2Si phase may form during prolonged high temperature annealing. Consider a pure ternary alloy which contains 0.75 wt% (0.83 at.%) Mg and 1.0 wt% (0.96 at.%) Si. Estimate on the basis of the solubility product the equilibrium volume fraction of Mg2Si at 4000C. Make also a sketch of the Mg2Si solvus in a vertical section through the ternary Al-Mg-Si phase diagram. Relevant physical data for the Al-Mg-Si system are given below:

Solution

The maximum possible volume fraction of Mg2Si precipitated at absolute zero (fmax) can be estimated from a simple mass balance by considering the stoichiometry of the reaction:

Moreover, the solubility product [at.% Mg]2 [at.% Si] at 4000C (673K) can be obtained from equation (4-3) by utilising data from Table 4.1:

from which

If we also take into account the stoichiometry of the reaction, the solubility product can be expressed solely in terms of the Mg-concentration. Substituting

into the above equation gives [at.% Mg] ~ 0.20. The equilibrium volume fraction OfMg2Si at 4000C is thus:

Similarly, the equilibrium Mg2Si solvus can be calculated from the solubility product by substituting

into equation (4-3). By inserting data from Table 4.1 and rearranging this equation, we get:

It is seen from the graphical representation of the above equation in Fig. 4.4 that the Mg2Si compound is thermodynamically stable up to about 3000C. At higher temperatures the phase will start to dissolve until the process is completed at 5600C. It is obvious from these calculations that the microstructure of overaged Al-Mg-Si alloys should be very persistent to the heat of welding processes. In practice, only a narrow solutionised zone forms adjacent to the fusion boundary. However, within this zone significant strength recovery may occur after welding due to reprecipitation of hardening phases from the supersaturated solid solution. Consequently, in such weldments the ultimate HAZ strength level is usually higher than that of the base metal, as illustrated in Fig. 4.5. 4.2.3.2 Metastable precipitates In practice, the solid solubility is also affected by the size of the particles. If, for instance, a

Nominal alloy composition

Temperature, 0C

Dissolution temperature: 5600C

at% Mg at%Mg Si Fig. 4.4. Solubility of Mg2Si in aluminium (Example (4.2)).

Strength level

After artificial ageing After natural ageing Immediately after welding

HAZ

Unaffected base metal Distance from fusion line

Fig. 4.5. Response of overaged Al-Mg-Si alloys to welding and subsequent heat treatment (schematic). spherical precipitate is acted on by an external pressure of say 1 atm, the same precipitate is also subjected to an extra pressure AP due to the curvature of the particle/matrix interface, just as a soap bubble exerts an extra pressure on its content (see Fig. 4.6(a)). The pressure AP is given as:8 (4-9) where 7 is the particle/matrix interfacial energy, and r is the radius of the precipitate. Because of this extra pressure, the Gibbs energy of a small precipitate will be higher than that of a large one, which, in turn, increases its solubility (see Fig. 4.6(b)). The important influence of particle curvature on the solid solubility has been extensively investigated and reported in the literature.18 Usually, the phenomenon is referred to as the capillary or the Gibbs-Thompson effect. In the following we shall assume that the thermodynamic and crystallographic properties of the metastable precipitates are similar to those of the equilibrium phase and that the reduced thermal stability is only associated with capillary effects. For single phase precipitates in binary alloy systems, it is fairly simple to show that the concentration of solute across a curved interface, [%A]r, is interrelated to the equilibrium concentration of solute across a planar interface, [%A], through the following equation:8

(4-10) where Vn is the molar volume of the precipitate (in m3 mol"1), and Q is the contribution of the interface curvature to the reaction enthalpy (equal to IyVJr).

(a)

Atmospheric pressure

Matrix

(b)

Gibbs energy

Small precipitate

Matrix

Large precipitate

[%A]

[%A] r Concentration

Fig. 4.6. Effect of interfacial energy on the solubility of small particles; (a) Schematic representation of spherical particles embedded in a metal matrix, (b) Integral molar Gibbs energy of matrix and precipitates at a constant temperature. Assuming that this relationship also holds in the case of binary intermetallics, a combination of equations (4-5) and (4-10) gives:

(4-11)

where (4-12)

or

Alternatively, we can express T as a function of the product [%A]rn [%B]rm. This gives the following expression for the solvus temperature of metastable precipitates T'eq: (4-13) It is evident from the graphical representation of equation (4-13) in Fig. 4.7 that the solid solubility at a given temperature is significantly increased at small particle radii. Taking as an example 7 = 0.5 J n r 2 , Vm = 10~5 m3 moH, R = 8.314 J Kr1 moH, T = 500 K, we obtain from equation (4-10):

or

where r is the particle radius in nm. From this it is seen that quite large solubility differences can arise for particles in the range from r = 1 - 50nm.

Temperature

Large (equilibrium) precipitates

Small (metastable) precipitates

Concentration Fig. 4.7. Graphical representation of equation (4-13) (schematic).

Example (4.3)

In Al-Mg-Si alloys metastable (hardening) p"(Mg2Si)-precipitates m a y form during artificial ageing in the temperature range from 160-2000C. Consider a T6 heat treated ternary alloy which contains 0.75 wt% (0.83 at.%) Mg and 1.0 wt% (0.96 at.%) Si. Based on equation (413) make a sketch of the metastable P "(Mg2Si) solvus in a vertical section through the ternary Al-Mg-Si phase diagram. In these calculations we shall assume that the thermodynamic properties of the metastable (3"(Mg2Si) phase are similar to those of the equilibrium (3 (Mg2Si) phase, i.e. the reduced thermal stability is only related to the Gibbs-Thomson effect. Relevant physical data for the Al-Mg-Si system are given below:

Solution

First we estimate the molar volume of the precipitate:

The contribution of the particle curvature to the reaction enthalpy is thus:

The metastable [3"(Mg2Si) solvus can now be calculated from the solubility product by substituting

into equation (4-13). By inserting data from Table 4.1 and rearranging this equation, we get:

It is evident from the graphical representation of the above equation in Fig. 4.8 that the particle curvature has a dramatic effect on the solid solubility. A comparison with Fig. 4.4 shows that the dissolution temperature drops from about 5600C in the case of the equilibrium Mg2Si phase to approximately 225°C for the metastable |3"(Mg2Si)-phase. On this basis it is not surprising to find that artificially aged (T6 heat treated) Al-Mg-Si alloys suffer from severe softening in the HAZ after welding, as shown schematically in Fig. 4.9. Moreover, it is

Nominal alloy composition A

Temperature, 0C

Dissolution temperature: 225 0C

Metastable solvus boundary

at% Mg at% Mg 2 Si

Strength level

Fig. 4.8. Solubility of (3"(Mg2Si) in aluminium (Example (4.3)).

After artificial ageing After natural ageing Immediately after welding

HAZ Distance from fusion line Fig. 4.9. Response of artificially aged Al-Mg-Si alloys to welding and subsequent heat treatment (schematic).

evident that the characteristic low dissolution temperature of the precipitates also gives rise to the formation of a heat affected zone which is significantly wider than that observed during welding of overaged Al-Mg-Si alloys.9 This shows that the response of age-hardenable aluminium alloys to welding and thermal processing depends strongly on the initial base metal temper condition. With the aid of equation (4-11) it is also possible to calculate an average (apparent) metastable solvus boundary enthalpy for hardening |3"(Mg2Si)-precipitates in Al-Mg-Si alloys. A closer evaluation of the exponent gives:

This value is in close agreement with the reported solvus boundary enthalpy for (3"(Mg2Si)precipitates in 6082-T6 aluminium alloys. 910

4.3 Particle Coarsening When dispersed particles have some solubility in the matrix in which they are contained, there is a tendency for the smaller particles to dissolve and for the material in them to precipitate on larger particles. The driving force is provided by the consequent reduction in the total interfacial energy and ultimately, only a single large particle would exist within the system. 4.3.1 Coarsening kinetics The classical theory for particle coarsening was developed independently by Lifshitz and Slyovoz11 and by Wagner.12 The kinetics are generally controlled by volume diffusion through the matrix. At steady state, the time dependence of the mean particle radius r is found to be:11'12 (4-14) where ro is the initial particle radius, 7 is the particle-matrix interfacial energy, Dm is the element diffusivity, Cm is the concentration of solute in the matrix, Vm is the molar volume of the precipitate per mole of the diffusate, and t is the retention time. Although the classic Lifshitz-Wagner theory suffers from a number of simplifying assumptions, experimental observations usually reveal a cubic growth law of the form given by equation (4-14).13 4.3.2 Application to continuous heating and cooling Ion, Easterling and Ashby14 have shown how equation (4-14) can be applied to continuous heating and cooling. In their analysis equation (4-14) was used in a more general form: (4-15)

where c{ is a kinetic constant, and Qs is the activation energy for the coarsening process (for binary intermetallics Qs may be taken equal to the activation energy for diffusion of the less mobile constituent atom of the precipitates in the matrix). 4.3.2.1 Kinetic strength of thermal cycle It follows that the extent of particle coarsening occurring during a weld thermal cycle can be calculated by integration of equation (4-15) between the limits t = t{ and t = t2:

(4-16) The integral on the right-hand side of equation (4-16) represents the kinetic strength of the thermal cycle with respect to particle coarsening, and can be determined by means of numerical methods when the weld thermal (T-t) programme is known. The resulting radius of the precipitates may then be evaluated from equation (4-16) by inserting representative values for the constants ro and C1 (e.g. obtained from quantitative particle measurements). 4.3.2.2 Model limitations A salient assumption in the classic Lifshitz-Wagner theory is that the particles coarsen at almost constant volume fraction, i.e. no solute is lost to the surrounding matrix during the coarsening process. Consequently, equation (4-16) should only be applied in cases where the peak temperature of the thermal cycle is well below the equilibrium solvus of the precipitates. Example (4.4)

Consider stringer bead deposition (GMAW) on a thick plate of a Ti-microalloyed steel under the following conditions:

Assume that the base metal contains a fine dispersion of TiN precipitates in the as-received condition. Calculate on the basis of equation (4-16) and the Rosenthal thick plate solution (equation (1-45)) the extent of particle coarsening occurring within the fully transformed heat affected zone during welding. Relevant physical data for titanium-microalloyed steels are given below:

(activation energy for diffusion of Ti in austenite) Solution

In the present example the problem is to calculate the size of the TiN precipitates in different

positions from the fusion boundary. This requires detailed information about the weld thermal programme, as shown in Fig. 4.10(a). By substituting the appropriate values for qo, X, a and v into the Rosenthal thick plate solution, the governing heat flow equation becomes:

where /?* refers to the three-dimensional radius vector in the moving coordinate system (designated R in equation (1-45)), while x is the welding direction (equal to vt at pseudo-steady state). Since titanium nitride is thermodynamically stable up to the melting point of the steel, equation (4-16) can be used to calculate the extent of particle coarsening occurring within the transformed parts of the HAZ. In the present example, we may write:

where the times tx and t2 are defined in Fig. 4.10(a). The kinetic strength of the weld thermal cycle with respect to particle coarsening can now be evaluated from these two equations by utilising the numerical integration procedure shown in Fig. 4.10(b). The results from such computations are presented graphically in Fig. 4.11. It is evident from this figure that significant coarsening of the precipitates occurs within the HAZ during welding, particularly in regions close to the fusion boundary where the peak temperature of the thermal cycle is high. A comparison with the experimental data of Ion et al.l4 (reproduced in Fig. 4.12) shows that the theory gives a fairly good prediction of particle size as a function of the peak temperature, provided that the kinetic constant C1 in equation (416) can be estimated with a reasonable degree of accuracy. In practice, however, the numerical value of C1 will vary significantly with the chemical composition and thermal history of the base metal (see Fig. 4.13). This means that empirical calibration of equation (4-16) to experimental data is always required to avoid systematic deviations between theory and experiments.

4.4 Particle Dissolution During welding, the thermal pulse experienced by the heat affected zone adjacent to the fusion boundary can result in complete dissolution of the base metal precipitates. Since this may give rise to subsequent strength loss and grain growth, it is important to understand how variations in welding parameters and operational conditions affect the dissolution rate. In the following, the kinetics of particle dissolution will be discussed from a more fundamental point of view. 4.4.1 Analytical solutions Over the years, several analytical models have been developed which describe the kinetics of particle dissolution in metals and alloys at elevated temperatures.16 None of these solutions are exact, since they represent different approximations to the diffusion field around the dissolv-

(a) Weld metal

Temperature

HAZ

Y~ regime

Time

(i/r)exp(-Qs/RT)

(b)

Time

Fig. 4.10. Kinetic strength of weld thermal cycle with respect to particle coarsening (Example (4.4)); (a) HAZ temperature-time programme (schematic), (b) Numerical integration procedure (schematic).

Weld metal

Partly transformed HAZ

Particle radius, nm

Fully transformed HAZ •

Peak temperature, 0C Fig. 4.11. Coarsening of TiN during steel welding (Example (4.4)).

Frequency, %•

Rosenthal thick plate heat cycle:

Particle radius, nm

Fig. 4.12. Measured size distribution of TiN before (broken lines) and after (full lines) weld thermal simulation. Operational conditions as in Example (4.4). Data from Ion et al.14 ing precipitates. Nevertheless, it will be shown below that at least some of them are sufficiently accurate to capture the essential physics of the problem and to give valuable quantitative information on the extent of particle dissolution occurring during the weld thermal cycle.

Particle radius, nm

Annealing temperature: 1350 0C

Steel A Steel B Steel C

Annealing time, s Fig. 4.13. Effects of annealing time and steel chemical composition on the mean particle size of TiN. Data from Matsuda and Okumura.15

4.4. L1 The invariant size approximation The model described here is due to Whelan.17 Consider a spherical particle embedded in an infinite matrix, as shown schematically in Fig. 4.14. The corresponding matrix concentration profile is plotted in the lower part of the figure. In this case the concentration of the constituent element A is higher close to the particle/matrix interface than in the bulk. Hence, there is a tendency for the element to diffuse away from the particle and into the surrounding matrix (i.e. the particle dissolves). Based on the assumption that the particle/matrix interface is stationary (i.e. the diffusion field has no memory of the past position of the interface), Whelan17 arrived at the following expression for the dissolution rate of a spherical precipitate at a constant temperature: (4-17) where r is the particle radius, a is the dimensionless supersaturation (defined in Fig. 4.14), and Dm is the element bulk diffusivity. The term Hr on the right-hand side of equation (4-17) stems from the steady-state part of the diffusion field, while the (1 A/7) term arises from the transient part. Because of the complex form of equation (4-17) it cannot be integrated analytically and hence, numerical methods must be applied. However, if the transient part of equation (4-17) is neglected (conforming to the solution after long times), it is possible to obtain a simple expression for the particle radius as a function of time: (4-18) where ro is the initial particle radius. Equation (4-18) is identical with the so-called invariant-field solution developed independ-

Concentration

Distance Fig. 4J4. Schematic representation of the concentration profile around a dissolving spherical particle in an infinite matrix. ently by Aaron et al.16 and is valid after a certain period of time, provided that there is no impingement of diffusion fields from neighbouring precipitates. As shown in Fig. 4.15, this simplified solution gives a reasonable description of the dissolution kinetics of small spherical precipitates in steel during reheating above the AC1 -temperature. Following the treatment of Agren,18 the time required for complete dissolution of a spherical precipitate td can be obtained from equation (4-18) by setting r = 0:

(4-19) Moreover, the volume fraction of the precipitates/as a function of time is given by:

(4-20) where fo is the initial particle volume fraction. The former equation shows that the dissolution time td depends strongly on the initial particle size rQ. Example (4.5)

The following example illustrates the direct application of equations (4-18) and (4-19). Consider a niobium-microalloyed steel which contains a fine dispersion of NbC precipitates. Provided that impingement of diffusion fields from neighbouring particles can be neglected, calculate the total time required for complete dissolution of a 100 nm large NbC precipitate at

Particle radius, jam

Numerical solution (Agren)

Simplified analytical solution (Whelan)

Time, s Fig. 4.15. Dissolution kinetics of spherical cementite particles in austenite at 8500C. Data from Agren.18 135O°C. Data for the steel chemical composition and the diffusivity of Nb in austenite at 13500C are given below: Steel chemical composition:

Diffusivity of Nb in austenite at 13500C:

Atomic weight of Nb: Atomic weight of C : Solution

In the present example it is reasonable to assume that the dissolution rate of the precipitate is controlled by diffusion of Nb in austenite. For a single NbC precipitate embedded in a Nbdepleted matrix, the dimensionless supersaturation becomes:

The equilibrium concentration of niobium at the particle/matrix interface can be estimated

from the solubility product by utilising data from Table 4.1. If we assume that the carbon concentration at the interface is constant and equal to the nominal value of 0.12 wt% (i.e. the stoichiometry of the dissolution reaction is neglected), equation (4-5) reduces to:

Moreover, the concentration of Nb in the precipitate is equal to:

This gives:

The dissolution time td can now be calculated from equation (4-19) by inserting the appropriate values for ro, aNt)J and Dm\

A comparison with Fig. 4.16 shows that the predicted value is off by a factor of about 4 compared with that obtained from more sophisticated numerical calculations. This degree of accuracy is acceptable and justifies the use of equation (4-18) for prediction of the dissolution rate of spherical precipitates under different thermal conditions provided that the model is calibrated against experimental data points. 4.4.1.2 Application to continuous heating and cooling Application of the model to continuous heating and cooling requires numerical integration of equation (4-18) over the weld thermal cycle:

(4-21)

Under such conditions the volume fraction of the precipitates is given by:

(4-22)

Equations (4-21) and (4-22) provide a basis for predicting the extent of particle dissolution occurring within the HAZ during welding in the absence of impingement of diffusion fields from neighbouring precipitates.

Dissolution time, s

Particle diameter, nm Fig. 4.16. The dissolution time of NbC in austenite at 13500C as function of initial particle diameter lro for different Nb and C levels (numerical solution). Data from Suzuki et al.6 Example (4.6)

Consider stringer bead deposition (SAW) on a thick plate of a Nb-microalloyed steel (0.10 wt% C - 0.03 wt% Nb) under the following conditions:

Assume that the base metal contains a fine dispersion of NbC precipitates in the as-received condition. Calculate on the basis of equation (4-22) and the Rosenthal thick plate solution (equation (1-45)) the extent of particle dissolution occurring within the fully transformed HAZ during welding. Relevant physical data for Nb-microalloyed steels are given below:

Solution

In the present example the problem is to calculate the variation in the//fo ratio across the fully transformed HAZ. By substituting the appropriate values for qo, X, a, and v into the Rosenthal thick plate solution, the governing heat flow equation becomes:

Since it is reasonable to assume that the dissolution rate of the precipitates is controlled by diffusion of Nb in austenite, the dimensionless supersaturation reduces to:

As shown in example (4.5), the equilibrium concentration of niobium at the particle/matrix interface (in wt%) can be estimated from the solubility product by utilising data from Table 4.1. If we assume that the carbon concentration at the interface is constant and equal to the nominal value of 0.10 wt%, equation (4-5) becomes:

Moreover, the concentration of Nb in the precipitate is equal to:

This gives:

By substituting the appropriate expressions for aNb and DNb into equation (4-22), we obtain:

Here the lower and upper integration limits refer to the total time spent in the thermal cycle from Ac3 to T and down again to Ac3. The extent of particle dissolution occurring within the HAZ during welding can now be calculated in an iterative manner by numerical integration of the above equation over the weld thermal cycle. The results from such computations are presented graphically in Fig. 4.17. It is evident from these data that NbC starts to dissolve when the peak temperature of the thermal cycle T exceeds the equilibrium dissolution temperature Td of the precipitate. The process is completed when T approaches 13300C, conforming to a temperature interval of 1900C. This shows that considerable superheating is required in order to overcome the inherent kinetic barrier against particle dissolution under the prevailing circumstances. 4.4.2 Numerical solution In the previous treatment, no consideration is given to impingement of diffusion fields from neighbouring precipitates or the position of the particle/matrix interface during the dissolution process. In certain cases, however, such phenomena will have a marked effect on the dissolution kinetics.18"22 A good example is Al-Mg-Si alloys where the hardening P"(Mg2Si)-phase forms a very fine distribution of needle-shaped precipitates along directions in the aluminium matrix. These precipitates are closely spaced and will therefore interact strongly with each other during dissolution (coupled reversion).

f/fo

No dissolution-

Complete dissolution Peak temperature, 0C Fig. 4.17. Dissolution of NbC during steel welding (Example (4.6)).

4.4.2.1 Two-dimensional diffusion model For rod or needle-shaped precipitates in a finite, depleted matrix, the rate of dissolution can be calculated by numerical methods from a simplified two-dimensional diffusion model. Assuming that the precipitates are mainly aligned in one crystallographic direction, it is reasonable to approximate their distribution by that of a face-centered cubic (close-packed) space lattice, as shown in Fig. 4.18(a). If planes are placed midway between the nearest-neighbour particles, they enclose each particle in a separate cell. Since symmetry demands that the net flux of solute through the cell boundaries is zero, the dissolution zone is approximately defined by an inscribed cylinder whose volume is equivalent to that of the hexagonal cell. The modelling principles outlined in Fig. 4.18(a) and (b) have previously been used by a number of other investigators to describe particle dissolution during isothermal heat treatment.18"22 Consequently, readers who are unfamiliar with the concept should consult the original papers for further details. It follows from Fig. 4.18(b) that the rate of reversion can be reported as: (4-23)

where ro is the initial cylinder (particle) radius. (a)

Concentration

(b)

Distance Fig. 4.18. Numerical model for dissolution of rod-shaped particles in a finite, depleted matrix; (a) Dissolution cell geometry, (b) Particle/matrix concentration profile (moving boundary).

For a specific alloy, the ratio between ro and L (the mean interparticle spacing) can be calculated from a simple mass balance, assuming that all solute is tied-up in precipitates. Taking this ratio equal to 0.06 for rod-shaped precipitates in diluted alloys,9 the kinetics of particle dissolution during isothermal heat treatment have been examined for a wide range of operational conditions. These results are presented in a general form in Fig. 4.19 by the use of the following groups of dimensionless parameters: Dimensionless time

(4-24)

Dimensionless supersaturation

(4-25)

(a is defined previously in Fig. 4.14). The data in Fig. 4.19 suggest that the reaction kinetics during the initial stage of the process are approximately described by the relation: (4-26)

log 0) or impurity elements in solid solution (n < 0.5).

5.3 Analytical Modelling of Normal Grain Growth By substituting V = V2 (dD/dt) and M = M0 exp (- QappIRT) into equation (5-18), it is possible to obtain a simple differential equation which describes the variation in the average grain size D with time t and temperature T in the presence of impurities and grain boundary pinning precipitates: (5-19) Equation (5-19) can be written in a more general form by setting

and (5-20)

From this it is seen that the parameters M0 and k are true physical constants which are related to the grain boundary mobility and the pinning efficiency of the precipitates, respectively. 5.3.1 Limiting grain size Equation (5-20) shows that the grain structure is stabilised when (d D ldi) - 0. The stable (limiting) grain size is given by: (5-21) The parameter k (which in the following is referred to as the Zener coefficient) is defined as the ratio between the numerical constants in equations (5-7) and (5-16), respectively. In the original Zener's model k = 4/3, while other investigators have arrived at different results.811"14 As shown in Fig. 5.4, the limiting grain size may vary by over one order of magnitude, depending upon the assumptions of the models. This makes it difficult to apply equations (5-20) and (5-21) for quantitative grain size analyses without further background information on the Zener coefficient.

Diim.nm

Gladman

r/f, um Fig. 5.4. Relation between limiting grain size Dum., particle radius r, and volume fraction/predicted by different models. Example (5. J)

Consider multipass GMA welding on a thick steel plate under the following conditions:

Based on the models of Zener,10 Hellman and Hillert,8 and Gladman13 estimate the limiting austenite grain size Dlim in the transformed parts of the weld HAZ when the oxygen and sulphur contents of the as-deposited weld metal are 0.04 and 0.01 wt%, respectively. Solution

As shown in Chapter 2 of this textbook the volume fraction of oxide and sulphide inclusions can be calculated from equation (2-75):

Similarly, the average radius of the grain boundary pinning inclusions can be obtained from equation (2-79):

This gives the following values for the limiting austenite grain size:

Zener:

Hellman and Hillert:

Gladman: and As expected, the limiting austenite grain size is seen to vary by more than one order of magnitude, depending on the assumptions of the models. In practice, the Zener coefficient in low-alloy steel weld metals falls within the range from 0.32 to 0.93, as shown in Fig. 5.5. The average value of A: is close to 0.52, which is the same as that inferred from the Gladman model (upper limit). When it comes to intermetallic compounds such as titanium nitride, the Zener coefficient varies typically between 0.75 and 0.25 during grain growth in the austenite regime. 1617 This suggests that k ~ 0.50 is a reasonable estimate of the grain boundary pinning efficiency of oxides and nitrides in steel. 5.3.2 Grain boundary mobility Direct application of equation (5-20) requires also reliable information on the time exponent n and the grain boundary mobility M. When n = 0.5 and/= 0, the classic impurity drag theories predict that the activation energy Qapp, should be close to the value for boundary self diffusion in the matrix material.2'3 This borderline case is approximately attained in steel welding, as shown in Fig. 5.6(a) and (b), since the driving pressure for austenite grain growth immediately following the dissolution of the pinning precipitates is usually so large that the grain boundary migration rate approaches the higher velocity limit defined in equation (5-9).18 On this basis it is not surprising to find that Qapp falls within the range reported for lattice self diffusion (284 kJ mol"1) and boundary self diffusion (170 kJ mol~l) in pure 7-iron19 during welding.18 In most cases, however, the activation energy will be different from the theoretical one due to complex interactions between impurity atoms and grain boundaries (characterised by a time exponent n < 0.5). Under such conditions, the value of Qapp has no physical meaning.1 5.3.3 Grain growth mechanisms Equation (5-20) provides a basis for evaluating the grain growth inhibiting effect of impurity elements and second phase particles under different thermal conditions. This also includes situations where the grain boundary pinning precipitates either coarsen or dissolve during the heat treatment process. 5.3.3.1 Generic grain growth model Equation (5-20) can readily be integrated to give the average grain size D as a function of time. In the general case we may write: (5-22)

(a) Austenite grain size, Jim

SA steel weld metal

Annealing temperature, 0 C

(b)

D||m. Hm

GMA and SA steel weld metals

r/f, urn

Fig. 5.5. Evaluation of the Zener coefficient in steel weld metals containing stable oxide and sulphide inclusions; (a) Determination of Dum. from isothermal grain growth data (holding time: 30 min), (b) Variation in Dum. with the inclusion rlf ratio. Data from Skaland and Grong.15 where D{im is the limiting grain size (defined in equation (5-21)). The integral I1 on the right-hand side of equation (5-22) represents the kinetic strength of the thermal cycle with respect to grain growth and can be determined by numerical methods when the temperature-time programme is known. In practice, however, it is not necessary to solve this integral to evaluate the grain growth mechanisms. Consequently, the left-hand side of equation

(a) Steel A Log (DxZD1)

Slope: n = 0.4

Log [number of cycles]

(b)

LogD7

Steel A Steel B

Fig. 5.6. Evaluation of the time exponent n and the activation energy Q for austenite grain growth in steel under thermal conditions applicable to welding; (a) Time exponent n, (b) Activation energy Qapp. Data from Akselsen et ah18

(5-22) can be solved explicitly for different values of DUm, n, and Z1. The results may then be presented in the form of novel diagrams which show the competition between the various processes that lead to grain growth during heat treatment of metals and alloys. A more thorough documentation of the predictive power of the model and its applicability to welding is given in Section 5.4. 5.3.3.2 Grain growth in the absence ofpinning precipitates In the absence of grain boundary pinning precipitates, we have:/= 0, Dlim —> ~ , and (1/ DlitrL) = 0. Under such conditions, equation (5-22) reduces to:

(5-23)

After integration this equation yields: (5-24) Referring to Fig. 5.7, the average grain size D becomes a simple cube root function of Z1 when n = 0.5 and D 0 = 0. In other situations (n < 0.5), the grains will coarsen at a slower rate due to drag from alloying and impurity elements in solid solution. This is seen as a general reduction in the slope of the D-Ix curves in Fig. 5.7. The important austenite grain growth inhibiting effect of phosphorus and free nitrogen in steel following particle dissolution is shown in Fig. 5.8. 5.3.3.3 Grain growth in the presence of stable precipitates

If grain growth occurs in the presence of stable precipitates, the limiting grain size {Dlim) in equation (5-22) becomes constant and independent of the thermal cycle. In the specific case when n = 0.5 the integral on the left-hand side of equation (5-22) has the following analytical solution:

D, ^m

(5-25)

I1W" Fig. 5.7. Predicted variation in average grain size D with /, and n f o r / = 0 and D0 = 0 ('free' grain growth).

(a)

D Y ,fim

Steel A

Number of cycles (b)

D y ,um

Steel B

Number of cycles Fig. 5.8. Illustration of the austenite grain growth inhibiting effect of phosphorus and free nitrogen in low-alloy steel during reheating above the Ac^ temperature (multi-cycle weld thermal simulation); (a) Steel A (50ppm P, 20ppm N), (b) Steel B (180ppm P, 80ppm N). Data from Akselsen et a/.18

from which the average grain size D is readily obtained. In other cases, numerical methods must be employed to evaluate D. It is evident from the graphical representation of equation (5-25) in Fig. 5.9 that the grain growth inhibiting effect of the precipitates is very small during the initial stage of the process when D « D lim. Under such conditions the grains will coarsen at a rate which is comparable with that observed for free grain growth (n = 0.5,/= 0). The grain coarsening process becomes gradually retarded as the average grain size increases because of the associated reduction in the effective driving pressure APG until it comes to a complete stop when AP0 = 0 (i.e. D = D Hm)-

D, jim

I 1 ^m 2

D, (im

Fig. 5.9. Predicted variation in average grain size D with Z1 and Dnm. for n = 0.5 and D0 = 0 (stable precipitates).

I 1 , [nm]1/n

Fig. 5.10. Predicted variation in average grain size D with Z1 and n for Dum. = 250|Jin and D0 = 0 (stable precipitates). Dotted curves correspond to grain growth in the absence of pinning precipitates.

If grain growth at the same time occurs under the action of a constant drag from impurity elements in solid solution, the situation becomes more complex. As shown in Fig. 5.10, a decrease in the time exponent from say 0.5 to 0.2 gives rise to a marked reduction in the slope of the D-I 1 curves, similar to that observed in Fig. 5.7 for particle-free systems (/= 0). However, the predicted grain coarsening rate is lower than that evaluated from equation (5-24) due to the extra drag exerted by the grain boundary pinning precipitates. This leads ultimately to a stabilisation of the microstructure when D = DUm. 5.3.3.4 Grain growth in the presence of growing precipitates Very little information is available in the literature on the matrix grain growth behaviour of metals and alloys in the presence of growing second phase particles. So far, virtually all modelling work has been carried out on two phase a-(3 titanium alloys.14 Unfortunately, none of these models can be extended to more complex alloy systems such as steels or aluminium alloys. When grain growth occurs in the presence of growing second phase particles, Dum. will no longer be constant due to the associated increase in the particle rlf ratio with time. As shown in Chapter 4 of this textbook, the Lifshitz-Wagner theory2021 provides a basis for modelling particle growth during welding and heat treatment of metals and alloys in cases where the peak temperature of the thermal cycle is kept well below the equilibrium solvus of the precipitates. Under such conditions, the particles will coarsen at almost constant volume fraction (f=fo), in accordance with equation (4-16): (5-26) where Qs is the activation energy for the coarsening process, C5 is a kinetic constant, and I2 is the kinetic strength of the thermal cycle with respect to particle coarsening. The other symbols have their usual meaning. If the base metal contains particles of an initial radius ro and volume fraction/^, the limiting grain size at I2 = 0 (D° lim) can be defined as:

(5-27) from which (5-28) Similarly, when I2 > 0, we may write: (5-29) By combining equations (5-26), (5-28), and (5-29), we arrive at the following relationship between (D Um ) and I2: (5-30)

It is seen from equation (5-30) that the limiting grain size in the presence of growing particles depends on the product (k/fo)3I1. In practice, the grain boundary pinning effect of the precipitates is determined by the relative rates of particle coarsening and grain growth in the material, i.e. whether the grain boundary mobility is sufficiently high to keep pace with the increase in DUm during heat treatment. Generally, the pinning conditions are defined by the (k/fo)3 I1IIx ratio, which after substitution and rearranging yields:

(5-31)

In cases where the parameters c5 ,Qs, M0*, and Qapp are known, the average grain size D can readily be evaluated from equations (5-22), (5-30), and (5-31) by utilising an appropriate integration procedure. However, since Qs normally differs from Qapp^ the (klfo)3I1I Ix ratio will depend on the thermal path during continuous heating and cooling. Consequently, solution of these coupled equations generally requires stepwise integration in temperature-time space via a fourth heat flow equation. This problem will be dealt with in Section 5.4. The situation becomes much simpler if heat treatment is carried out isothermally. Under such conditions the product (k/fo)311 will only differ from Ix by a proportionality constant m, which is characteristic of the system under consideration. Accordingly, equation (5-30) can be rewritten as: (5-32) From this we see that the two coupled equations (5-22) and (5-32) can be solved explicitly for different values of D°nm., n, m, and Z1. Hence, it is possible to present the results in the form of novel 'mechanism maps' which show the competition between particle coarsening and grain growth during isothermal heat treatment for a wide range of operational conditions. Examples of such diagrams are given in Figs. 5.11 and 5.12. It is evident from these figures that the grain coarsening behaviour during isothermal heat treatment is very sensitive to variations in the proportionality constant m. For large values of m, the matrix grains will coarsen at a rate which is comparable with that observed in Fig. 5.7 for particle-free systems (f = 0). This corresponds to a situation where the grain boundary pinning precipitates will completely outgrow the matrix grains. It is interesting to note that particle outgrowing is more likely to occur if the time exponent n is small, as shown in Fig. 5.12, because of the associated reduction in the grain boundary mobility in the presence of impurity elements in solid solution. In other systems, where the proportionality constant m is closer to unity, the reduced coarsening rate of the precipitates gives rise to a higher Zener retardation pressure and ultimately to a stagnation in the matrix grain growth. In the limiting case, when m = 0, the grain growth behaviour becomes idential to that observed in Figs. 5.9 and 5.10 for stable precipitates.

D.jim

Time exponent n = 0.5

I 1 ,^m 2 Fig. 5.11. Predicted variation in average grain size D with Ix and m for D°um. = 50jLim, n = 0.5, and D0 =0 (growing precipitates).

D,fxm

Time exponent n = 0.3

I1^m1'" Fig. 5.12. Predicted variation in average grain size D with I1 and m for D°um. - 50|im, n = 0.3, and D0 = 0 (growing precipitates).

Example (5.2)

Consider a titanium-microalloyed steel with the following chemical composition: Ti(total): 0.016 wt%, Ti(soluble): 0.009 wt%, N: 0.006 wt% Assume that the base metal contains an uniform dispersion of TiN precipitates in the asreceived condition, conforming to a limiting austenite grain size T>°um. of 50 |iim. Provided that boundary drag from impurity elements in solid solution can be neglected (i.e. n ~ 0.5), estimate on the basis of Fig. 5.11 the average austenite grain size D1 in the material after 25 s of isothermal annealing at 13000C. Relevant physical data for titanium-microalloyed steels are given below: (activation energy for diffusion of Ti in austenite)

Solution

The initial volume fraction of TiN in the material can be estimated from simple stoichiometric calculations by considering the difference between total and soluble titanium. Taking the atomic weight of Ti and N equal to 47.9 and 14.0 g mol"1, respectively, we obtain:

From this we see that the initial radius of the TiN precipitates in the base metal is close to:

Since heat treatment is carried out under isothermal conditions, the parameters m and Z1 can be obtained directly from equations (5-31) and (5-22) without performing a numerical integration:

Similarly, in the case of Z1 we get:

The average austenite grain size can now be read from Fig. 5.11 by linear interpolation between the curves for m = 10 and 100 Jim. This gives:

Although experimental data are not available for a direct comparison, the predicted grain size is of the expected order of magnitude. From this it is obvious that considerable austenite grain growth may occur in titanium-microalloyed steels because of particle coarsening, in spite of the fact that TiN, from a thermodynamic standpoint, is stable up to the melting point of the steel. The process can, to some extent, be counteracted by the use of a finer dispersion of TiN precipitates in the material. For example, if the initial particle radius is reduced by a factor of five (conforming to a change in I W from 50 to 10 Jim), the austenite grain size of the annealed material decreases from 75 to 65 jLim, as shown in Fig. 5.13. Nevertheless, since particle coarsening is a physical phenomenon occurring during high temperature heat treatment of metals and alloys, austenite grain growth cannot be avoided. This explains why, for instance, conventional titanium-microalloyed steels are not suitable for high heat input welding due to their tendency to form brittle zones of Widmanstatten ferrite and upper bainite in the coarse grained HAZ region adjacent to the fusion boundary.22

D,jim

Time exponent n = 0.5

Stable particles I1-Hm2 Fig. 5.13. Predicted variation in average grain size D with Z1 and m for D°Hm. = 10 um, n = 0.5, and Do = 0 (growing precipitates).

5.3.3.5 Grain growth in the presence of dissolving precipitates Little information is available in the literature on the matrix grain growth behaviour of metals and alloys in the presence of dissolving precipitates. As shown in Chapter 4, the model of Whelan23 provides a basis for calculating the dissolution rate of single precipitates embedded in an infinite matrix. If the transient part of the diffusion field is neglected, the variation in the particle radius r with time t at a constant temperature is given by equation (4-18): (5-33) where a is the dimensionless supersaturation (defined in Fig. 4.14), and Dm is the element diffusivity. Application of the model to continuous heating and cooling requires numerical integration of equation (5-33) over the weld thermal cycle: (5-34)

where I3 is the kinetic strength of the thermal cycle with respect to particle dissolution. From this relation the following expression for the particle volume fraction can be derived (see equation (4-22), Chapter 4):

(5-35) where fo is the initial particle volume fraction. By substituting Dlim - k(rlf) and D°nm. = Kr0If0) into equations (5-34) and (5-35), it is possible to obtain a simple mathematical relation which describes the variation in the limiting grain size with I3 during particle dissolution. After some manipulation, we obtain:

(5-36)

It is seen from equation (5-36) that the limiting grain size increases from D°um. at I3 = 0 to infinite when I3 = (fo Ik)2 (D°um. )2 • Since the magnitude of the Zener drag, in practice, depends on the relative rates of grain growth and particle dissolution in the material, the pinning conditions are defined by the (klfo)2131 Ix ratio:

(5-37)

Equation (5-37) shows that the (k/fo)2I3111 ratio is contingent upon the thermal path during continuous heating and cooling. Consequently, application of the model to welding generally requires numerical integration of the coupled equations (5-22), (5-36), and (5-37) over the weld thermal cycle. However, the integration procedure is largely simplified if heat treatment is carried out isothermally. In such cases the product (k/fo)213 will only differ from Ix by a proportionality constant m*, which is characteristic of the system under consideration. By substituting m*Ix into equation (5-36), we obtain:

(5-38) From this we see thaUhe two coupled equations (5-22) and (5-38) can be solved explicitly for different values of Dun., n,m*, and I1. Hence, it is possible to present the results in the form of novel 'mechanism maps' which show the competition between particle dissolution and grain growth during isothermal heat treatment for a wide range of operational conditions. Examples of such diagrams are given in Figs. 5.14 and 5.15. As expected, the stability of the second phase particles is sensitive to variations in the proportionality constant m*. Normally, the precipitates will exert a drag on the grain boundaries as long as they are present in the metal matrix. However, when the dissolution process is completed, the matrix grains are free to grow without any interference from precipitates. This

Time exponent n = 0.5

D,jim

Complete particle dissolution

Stable particles

I 1 ,nm 2 Fig. 5.14. Predicted variation in average grain size D with Z1 and ra* for D°um. = 50 um, n = 0.5, and D0 =0 (dissolving precipitates).

D,jim

Time exponent n = 0.3 Complete particle dissolution

I 1 ^m 1 ' 0 Fig. 5.15. Predicted variation in average grain size D with I1 and m* for D°um. - 50 Jim, n - 0.3, and Do =0 (dissolving precipitates). means that the grains, after prolonged high temperature annealing, will coarsen at a rate which is comparable with that observed in Fig. 5.7 for particle-free systems. In the limiting case, when m* = 0, the grain growth behaviour becomes identical to that shown in Figs. 5.9 and 5.10 for stable precipitates. Example (5.3)

Consider a niobium-microalloyed steel with the following composition: Nb(total): 0.025 wt%, Nb(soluble): 0.010 wt%, C: 0.10 wt% Assume that the base metal contains a fine dispersion of NbC precipitates in the as-received condition, conforming to a limiting austenite grain size Dnm. of 50 jim. Provided that the boundary drag from impurity elements in solid solution can be neglected (i.e. n ~ 0.5), estimate on the basis of Fig. 5.14 the average austenite grain size D 7 in the material after 25 s of isothermal annealing at 13000C. Relevant physical data for niobium-microalloyed steels are given below:

Solution

The initial volume fraction of NbC in the material can be estimated from simple stoichiometric calculations by considering the difference between total and soluble niobium. Taking the atomic weight of Nb and C equal to 92.9 and 12.0 g mol"1, respectively, we obtain:

From this we see that the radius of the NbC precipitates in the base metal is close to:

As shown in Example 4.6 (Chapter 4), the dimensionless supersaturation of niobium a ^ adjacent to the particle/matrix interface during dissolution can be written as:

By substituting this value into the expression for the proportionality constant m*, we obtain:

Moreover, at 1300°C the value OfZ1 becomes:

The average austenite grain size can now be read from Fig. 5.14 by interpolation between the curves for m* = 1 and/= 0 (free grain growth). This gives:

Since the calculated value of D1 is reasonably close to that observed for a particle-free system, it means that the presence of a fine dispersion of NbC in the base metal has no significant effect on the resulting austenite grain size under the prevailing circumstances. Other

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types of niobium microalloyed steels may reveal a different grain coarsening behaviour, depending on the chemical composition, size distribution, and initial volume fraction of the base metal precipitates. However, the pattern remains essentially the same, i.e. the growth inhibition is always succeeded by grain coarsening as long as the precipitates are thermally unstable.

5.4 Grain Growth Diagrams for Steel Welding In welding the temperature will change continuously with time, which makes predictions of the HAZ grain coarsening behaviour rather complicated. The method adopted from Ashby et ^ 24,25 j s b asec i o n m e jd e a o f integrating the elementary kinetic models over the weld thermal cycle where the unknown kinetic constants are determined by fitting the integrals at certain fixed points to data from real or simulated welds. Although the introduction of the Zener drag in the grain growth equation largely increases the complexity of the problem, the methodology and calibration procedure remain essentially the same. This means that the results from such complex computations can be presented in the form of simple grain growth diagrams which show contours of constant grain size in temperature-time space. 5.4.1 Construction of diagrams A grain growth model for welding consists of two components, i.e. a heat flow model, and a structural (kinetic) model. 5.4.1.1 Heat flow models As a first simplification, the general Rosenthal equations26 are considered for the limiting case of a high net power qo and a high welding speed v, maintaining the ratio qo/v within a range applicable to arc welding. It has been shown in Chapter 1 that under such conditions, where no exchange of heat occurs in the .^-direction, the following equations apply: Thick plate welding (2-D heat flow) (5-39) Thin plate welding (1-D heat flow)

6 Solid State Transformations in Welds

6.1 Introduction The majority of phase transformations occurring in the solid state take place by thermally activated atomic movements. In welding we are particularly interested in transformations that are induced by a change in temperature of an alloy with a fixed bulk composition. Such transformations include precipitation reactions, eutectoid transformations, and massive transformations both in the weld metal and in the heat affected zone. Since welding metallurgy is concerned with a number of different alloy systems (including low and high alloy steels, aluminium alloys, titanium alloys etc.), it is not possible to cover all aspects of transformation behaviour. Consequently, the aim of the present chapter is to provide the background material necessary for a verified quantitative understanding of phase transformations in weldments in terms of models based on thermodynamics, kinetics, and simple diffusion theory. These models will then be applied to specific alloy systems to illuminate the basic physical principles that underline the experimental observations and to predict behaviour under conditions which have not yet been studied.

6.2 Transformation Kinetics In order to understand the extent and direction of a transformation reaction, it is essential to know how far the reaction can go and how fast it will proceed. To answer the first question we need to consider the thermodynamics, whereas kinetic theory provides information about the reaction rate. 6.2.1 Driving force for transformation reactions The symbols and units used throughout this chapter are defined in Appendix 6.1. In practice, solid state transformations require a certain degree of undercooling, which is essential to accommodate the surface and strain energies of the new phase.1 Generally, this minimum molar free energy of transformation, AG, can be written as a balance between the following four contributions: (6-1) Here AGy (the volume free energy change associated with the transformation) and AGD (free energy donated to the system when the nucleation takes place heterogeneously) are negative, since they assist the transformation, while AGS (increase in surface energy between the two phases) and AGE (increase in strain energy resulting from lattice distortion) are both positive because they represent a barrier against nucleation. It follows that the transformation

Molar free energy

Stable (B)

Stable (a)

Temperature Fig. 6.1. Schematic representation of the molar free energies of two solid a and P phases as a function of temperature (allotrophic transformation — no compositional change).

Temperature

reaction can proceed when the driving force AG becomes greater than the right-hand side of equation (6-1). For an allotropic transformation, in which there is no compositional change, AG will be a simple function of temperature, as illustrated in Fig.6.1. For alloys the situation is slightly more complex, since there is an additional variable, i.e. the composition. In such cases the temperature at which the a-phase becomes thermodynamically unstable (Teq) corresponds to a fixed point on the a-(3 solvus boundary in the equilibrium phase diagram, as shown schematically in Fig. 6.2. Since phase diagrams are available for many of the important industrial alloy systems, it means that the driving force for a transformation reaction can readily be obtained from such diagrams in the form of a characteristic undercooling (AT).

%B Fig. 6.2. Schematic representation of the a-(3 solvus boundary in a simple binary phase diagram.

6.2.2 Heterogeneous nucleation in solids In general, solid state transformations in metals and alloys occur heterogeneously by nucleation at high energy sites such as grain corners, grain boundaries, inclusions, dislocations and vacancy clusters. The potency of a nucleation site, in turn, depends on the energy barrier against nucleation (AG*^) which is a function of the 'wetting' conditions at the substrate/ nucleus interface.1 It can be seen from Fig. 6.3 that nucleation at for instance inclusions or dislocations is always energetically more favourable than homogeneous nucleation (AG*het < tsG*hom ) but less favourable than nucleation at grain boundaries or free surfaces. As a result, the transformation behaviour is strongly influenced by the type and density of lattice defects and second phase particles present within the parent material. 6.2.2.1 Rate of heterogeneous nucleation Whereas every atom is a potential nucleation site during homogeneous nucleation, only those associated with lattice defects or second phase particles can take part in heterogeneous nucleation. In the latter case the rate of nucleation (Nhet) is given by:1'2

(6-2) where v is a vibration frequency factor, Nv is the total number of heterogeneous nucleation sites per unit volume, AG^, is the energy barrier against nucleation, and Qd is the activation energy for atomic migration across the nucleus/matrix interface.

Grain boundary

Vacancy clusters

Dislocations/stacking faults

Inclusions

Grain boundaries

Inclusion

Grain corners

Free surfaces

AG* /AG* het. horn.

Free surface

Nucleation site Fig. 6.3 Schematic diagram showing the most potent sites for heterogeneous nucleation in metals and alloys.

It follows from the graphical representation of equation (6-2) in Fig. 6.4 that the nucleation rate Nhet is highest at an intermediate temperature due to the competitive influence of undercooling (driving force) and diffusivity on the reaction kinetics. This change in Nhet with temperature gives rise to corresponding fluctuations in the transformation rate, as shown schematically in Fig. 6.5. Note that the peak in transformation rate is due to two functions, growth and nucleation (which peak at different T) whereas peak in Nhet is due to nucleation only. 6.2.2.2 Determination

of AGhet and Qd

During the early stages of a precipitation reaction, the reaction rate may be controlled by the nucleation rate Nhet. Under such conditions, the time taken to precipitate a certain fraction of the new phase t* is inversely proportional to Nhet\

(6-3) where C1 and C2 are kinetic constants. By taking the natural logarithm on both sides of equation (6-3), we obtain:

(6-4) If the complete C-curve is known for a specific transformation reaction, it is possible to evaluate AG*het and Qd from equation (6-4) according to the procedure described by Ryum.3 In general, a plot of In t* vs HT will yield a distorted C-curve with well-defined asymptotes, as shown in Fig. 6.6. At high undercoolings, when &G*het is negligible, the slope of the curve becomes constant and equal to QdIR. The mathematical expression for this asymptote is: T

T

Low undercooling High diffusivity

High undercooling Low diffusivity %B

Nhet.

Fig. 6.4. Schematic diagram showing the competitive influence of undercooling (driving force) and diffusivity on the heterogeneous nucleation rate.

T

Fraction transformed

logt

logt Fig. 6.5. Fraction transformed as a function of time referred to the C-curve (schematic). (6-5) At the chosen reference temperature Tr the time difference between the real C-curve and the extension of the lower asymptote amounts to (see Fig. 6.6): (6-6) from which (6-7) It follows that equations (6-5) and (6-7) provide a systematic basis for obtaining quantitative information about Qd and AGhet from experimental microstructure data through a simple graphical analysis of the shape and position of the C-curve in temperature-time space.

T

1/r

lnt Fig. 6.6. Determination of AG*het and Qd from the C-curve (schematic).

6.2.2.3 Mathematical description of the C-curve In order to obtain a full mathematical description of the C-curve, we need to know the variation in the energy barrier AG*het with undercooling AT. For heterogeneous nucleation of precipitates above the metastable solvus, the strain energy term entering the expression for AG*het can usually be ignored. In such cases the energy barrier is simply given as:1 (6-8)

where TV4 is the Avogadro constant, ^ n is the interfacial energy per unit area between the nucleus and the matrix, AGV is the driving force for the precipitation reaction (i.e. the volume free energy change associated with the transformation), and 5(0) is the so-called shape factor which takes into account the wetting conditions at the nucleus/substrate interface. For a particular alloy, AGV is for small Ar proportional to the degree of undercooling:l (6-9) where C3 is a kinetic constant. This equation follows from the definition of AGv in diluted alloy systems and the mathematical expression for the solvus boundary in the binary phase diagram. By substituting equation (6-9) into equation (6-8), we get: (6-10) It follows that A0 is a characteristic material constant which is related to the potency of the heterogeneous nucleation sites in the material. The value of A0 is, in turn, given by equations (6-7) and (6-10): (6-11)

In cases where A0 is known, it is possible to obtain a more general expression for t* by substituting equation (6-10) into equation (6-3):

(6-12)

Equation (6-12) can further be modified to allow for compositional and structural variations in the parent material by using the calibration procedure outlined in Fig. 6.7. Let tr denote the time taken to precipitate a certain fraction of (3 at a chosen reference temperature T= Tr in an alloy containing Nv nucleation sites per unit volume. If we take the corresponding solvus temperature of the (3-phase equal to T*q , the expression for t* becomes:

(6-13)

A combination of equations (6-12) and (6-13) then yields:

(6-14)

Equation (6-14) provides a basis for predicting the displacement of the C-curve in temperature-time space due to compositional or structural variations in the parent material. In genT

C-cun/e(Nv=N^)

logt Fig. 6.7. Method for eliminating unknown kinetic constant in expression for t*.

eral, an increase in Nv will shift the nose of the C-curve to the left in the diagram (i.e. towards shorter times), as shown schematically in Fig. 6.8, because of the resulting increase in the nucleation rate. Moreover, in solute-depleted alloys the critical undercooling for nucleation will be reached at lower absolute temperatures where the diffusion is slower. This results in a marked drop in Nhet, which displaces the C-curve towards lower temperatures and longer times in the IT-diagram, as indicated in Fig. 6.9. Example (6.1)

Isothermal transformation (IT) or continuous cooling transformation (CCT) diagrams are available for many of the important alloy systems.4 In the case of aluminium, so-called temperature-property diagrams exist for different types of wrought alloys.45 Suppose that the C-curve in Fig. 6.10 conforms to incipient precipitation of [3'(Mg2Si) particles at manganese-containing dispersoids in 6351 extrusions. Use this information to estimate the values of A0 and Qd in equation (6-3) when the solvus temperature of (3'(Mg2Si) is 5200C. Solution

The parameters A0 and Qd can be evaluated from the C-curve according to the procedure shown in Fig. 6.6. Referring to Fig. 6.11, the value of AG^ at the chosen reference temperature Tr = 35O°C (623K) is equal to:

When AGhet is known, the parameter A0 can be obtained from equation (6-11): T

iogt Fig. 6.8. Effect of Nv on the shape and position of C-curve in temperature-time space (schematic).

T

T

T

logt \e, Fig. 6.9. Effect of solute content on the shape and position of C-curve in temperature-time space (schematic). %B

Similarly, Qd can be read from Fig. 6.11 by considering the slope of the lower asymptote:

This value is in good agreement with the reported activation energy for diffusion of magnesium in aluminium.6

Temperature, 0C

AA 6351 - T6

Time, s Fig. 6.10. C-curve for 99.5% maximum yield strength of an AA6351-T6 extrusion. After Staley.5

103/T, K"1

Solvus temperature: 520 0C

lnt Fig. 6.11. Determination of kG*heU and Qd from the C-curve in Fig. 6.10 (Example 6.1).

6.2.3 Growth of precipitates If the embryo is larger than some critical size, it will grow by a transport mechanism which involves diffusion of solute atoms from the bulk phase to the matrix/nucleus interface. 6.2.3.1 Interface-controlled growth When transfer of atoms across the a/(3-interface becomes the rate-controlling step, the reaction is said to be interface-controlled. This growth mode is therefore observed during the initial stage of a precipitation reaction before a large, solute-depleted zone has formed around the particles. In the case of incoherent precipitates, the variation in the particle radius r with time is given by:7 (6-15)

where M1 is a mobility term, C0 is the concentration of solute in matrix, Ca is the concentration of solute at the particle/matrix interface, and Cp is the concentration of solute inside the precipitate. In general, the mobility of incoherent interfaces is high, since the solute atoms can easily 'jump' across the interface and find a new position in the particle lattice, as shown schematically in Fig. 6.12(a). In contrast, a coherent interface is essentially inmobile because transfer in this case involves trapping of atoms in an intermediate lattice position, as indicated in Fig. 6.12(b). As a result, semi-coherent precipitates are forced to grow by lateral movement of ledges along a low energy interface in a direction where the matrix is incoherent with respect to the particle lattice (see Fig. 6.13). In such cases the thickening rate of the precipitates U*aj^ is given by:3'7

Incoherent Interface

Coherent interface

(a) (b)

U

a/p

Fig. 6J2. Schematic illustration of atom transfer across different kinds of interfaces; (a) Incoherent interface, (b) Coherent interface.

Lateral movement of incoherenf interface

Fig. 6.13. Thickening of plate-like precipitates by the ledge mechanism (schematic).

(6-16)

where M1* is a new mobility term, and / is the interledge spacing. 6.2.3.2 Diffusion-controlled growth For growth of incoherent precipitates above the metastable solvus, the rate-controlling step will be diffusion of solute in the matrix. If precipitation of the P-phase occurs from a

supersaturated a, the reaction proceeds by diffusion of solute to the growing p-particle, as shown schematically in Fig. 6.14. On the other hand, when the (3-phase is formed by rejection of solute from the a-phase, the transformation occurs by diffusion of atoms away from the Pparticle, as indicated in Fig. 6.15. Aron et al.s have presented general solutions for diffusion-controlled growth of both flat plates and spheres under such conditions. In the former case the half thickness AZ of the plate is given by: (6-17) The parameter E1 in equation (6-17) is frequently referred to as the one-dimensional parabolic thickening constant, and is defined as:

Temperature

Liquid

Concentration

%B

Diffusion of solute

Distance Fig. 6.14. Schematic representation of concentration profile ahead of advancing interface during precipitation of (B from a supersaturated a-phase.

Temperature Concentration

%B

Diffusion of solute

Distance Fig. 6.15. Schematic representation of concentration profile ahead of advancing interface during growth of solute-depleted P into a metastable a-phase.

(6-18)

where Dm is the diffusivity of the solute in the matrix, and erfc(u) is the complementary error function (defined previously in Appendix 1.3, Chapter 1). Similarly, for growth of spherical precipitates, the variation in the radius r with time can be written as:8 (6-19) where e 2 *s t n e corresponding parabolic thickening constant for a spherical geometry, defined as:

(6-20)

The parabolic relations in equations (6-17) and (6-19) imply that the growth rate slows down as the (3-phase grows. This is due to the fact that the total amount of solute partitioned during growth decreases with time when the diffusion distance increases. Moreover, the form of equations (6-18) and (6-20) suggests that the maximum in the growth rate is achieved at an intermediate temperature because of the competitive influence of undercooling (driving force) and diffusivity on the reaction kinetics. Consequently, a plot of E1 or £2 vs temperature will reveal a pattern similar to that shown in Fig. 6.4 for the nucleation rate, although the thickening constants generally are less temperature-sensitive. In addition to the models presented above for plates and spheres, approximate solutions also exist in the literature for thickening of needle-shaped precipitates, based on the Trivedi theory for diffusion-controlled growth of parabolic cylinders.9 However, because of space limitations, these solutions will not be considered here. 6.2.4 Overall transformation kinetics The progress of an isothermal phase transformation may be conveniently represented by an ITdiagram of the type shown in Fig. 6.5. Among the factors that determine the shape and position of the C-curve are the nucleation rate, the growth rate, the density and the distribution of the nucleation sites as well as the physical impingement of adjacent transformed volumes. Due to the lack of adequate kinetic models for diffusion-controlled precipitation, we shall assume that the overall microstructural evolution with time can be described by an Avramitype of equation:10 (6-21) where X is the fraction transformed, n is a time exponent, and k is a kinetic constant which depends on the nucleation and growth rates. The exponential growth law summarised in the Avrami equation is valid for linear growth under most circumstances, and approximately valid for the early stages of diffusion-controlled growth.10 Table 6.1 gives information about the value of the time exponent for different experimental conditions. In general, the value of n will not be constant, but change due to transient effects until the steady-state nucleation rate is reached and n attains its maximum value. Subsequently, the nucleation rate starts to decrease as the sites become filled with nuclei and eventually approach zero when complete saturation occurs. This is because the heterogeneous nucleation sites are not randomly distributed in the volume, but are concentrated near other nucleation sites leading to an overall reduction in n. From then on, the transformation rate is solely controlled by the growth rate. 6.2.4.1 Constant nucleation and growth rates For a specific transformation reaction, the value of k in equation (6-21) can be estimated from

Table 6.1 Values of the time exponent n in the Avrami equation. After Christian.10 Polymorphic changes, discontinuous precipitation, eutectoid reactions, interface controlled growth, etc. Increasing nucleation rate Constant nucleation rate Decreasing nucleation rate Zero nucleation rate (saturation of point sites) Grain edge nucleation after saturation Grain boundary nucleation after saturation Diffusion controlled growth All shapes growing from small dimensions, increasing nucleation rate All shapes growing from small dimensions, constant nucleation rate All shapes growing from small dimensions, decreasing nucleation rate All shapes growing from small dimensions, zero nucleation rate Growth of particles of appreciable initial volume Needles and plates of finite long dimensions, small in comparison with their separation Thickening of long cylinders (needles) (e.g. after complete end impingement) Thickening of very large plates (e.g. after complete edge impingement) Precipitation on dislocations (very early stages)

kinetic theory, using the classic models of nucleation and growth described in the previous sections. In practice, however, this is a rather cumbersome method, particularly if the base metal is of a heterogeneous chemical nature. Alternatively, we can calibrate the Avrami equation against experimental microstructure data, e.g. obtained from generic IT-diagrams. A convenient basis for such a calibration is to write equation (6-21) in a more general form: (6-22) where k* is a new kinetic constant (equal to kr1/n). In the latter equation the parameter k* can be regarded as a time constant, which is characteristic of the system under consideration. Note that this form of the Avrami equation is mathematically more appropriate, as the dimensions of the k* constant are not influenced by the value of the time exponent n. During the early stages of a transformation reaction, the reaction rate is controlled by the nucleation rate. Let f denote the time taken to precipitate a certain fraction of P (X = Xc) at an arbitrary temperature T (previously defined in equation (6-14)). It follows from equation (6-22) that the value of k* in this case is given as: (6-23) A combination of equations (6-22) and (6-23) then gives:

(6-24)

from which (6-25) Equation (6-25) represents an alternative mathematical description of the Avrami equation, and is valid as long as the nucleation and growth rates do not change during the transformation. It has therefore the following limiting values and characteristics: X=O when t = 0, X = Xc when t = t*, and X—>1 when r—> . 6.2.4.2 Site saturation If the nucleation rate is considered to be zero by assuming early site saturation, the subsequent phase transformation simply involves the reconstructive thickening of the p-layer. In the onedimensional case, the process can be modelled in terms of the normal migration of a planar a/p interface, as shown schematically in Fig. 6.16. Let Aa/^ denote the interfacial area between a and (3 per unit volume and Ua/^ the growth rate of the incoherent a/p-interface. From Fig. 6.16 we see that the volume fraction of the transformed (3-phase is given as: (6-26) By using the standard Johnson-Mehl correction for physical impingement of adjacent transformation volumes, we may write in the general case: (6-27) which after integration yields: (6-28) This specific form of the Avrami equation is valid under conditions of early site saturation where the a/p-interface is completely covered by P nuclei at the onset of the transformation. 6.2.5 Non-isothermal transformations So far, we have assumed that the phase transformations occur isothermally. This is, of course, a rather unrealistic assumption in the case of welding where the temperature varies continuously with time. From the large volume of literature dealing with solid state transformations in

Fig. 6.16, Schematic illustration of the planar geometry assumed in the site saturation model.

metals and alloys, it appears that the bulk of the research has been concentrated on modelling of microstructural changes under predominantly isothermal conditions.1"411 In contrast, only a limited number of investigations has been directed towards non-isothermal transformations. 51012 " 18 However, these studies have clearly demonstrated the advantage of using analytical modelling techniques to describe the microstructural evolution during continuous cooling, instead of relying solely on empirical CCT-diagrams. 6.2.5.1 The principles of additivity From the literature reviewed it appears that there is considerable confusion regarding the application of isothermal transformation theory for prediction of non-isothermal transformation behaviour. These difficulties are mainly due to the independent variations of the nucleation and growth rate with temperature. In fact, it can be shown on theoretical grounds that the problem is only tractable when the instantaneous transformation rate is a unique function of the fraction transformed and the temperature.10 This leads to the additivity criterion described below. The principles of additivity are based on the theory advanced by Scheil.12 He proposed that the start of a transformation under non-isothermal conditions could be predicted by calculating the consumption of fractional incubation time at each isothermal temperature, with the transformation starting when the sum is equal to unity. The Scheil theory has later been extended to phase transformations to predict continuous cooling transformation kinetics from isothermal microstructure data.10'17'18 Let t* again denote the time taken to precipitate a certain fraction of P (X - Xc) at an arbitrary temperature T. If the reaction is additive, the total time to reach Xc under continuous cooling conditions is obtained by adding the fractions of time to reach this stage isothermally until the sum is equal to unity. Noting that t* varies with temperature, we may write in the general case: (6-29)

A schematic illustration of the Scheil theory is contained in Fig. 6.17. T

Cooling curve

Subdivision of time into infinitesimal steps of isothermal heat treatments.

logt Fig. 6.17. Schematic illustration of the Scheil theory.

6.2.5.2 Isokinetic reactions The concept of an isokinetic reaction has previously been introduced in Section 4.4.2.3 (Chapter 4). A reaction is said to be isokinetic if the increments of transformation in infinitesimal isothermal time steps are additive, according to equation (6-29). Christian10 defines this mathematically by stating that a reaction is isokinetic if the evolution equation for some state variable X may be written in the form: (6-30) where G(X) and H(T) are arbitrary functions of X and T, respectively. For a given thermal history, T(t), this essentially means that the differential equation contains separable variables of X and T. 6.2.5.3 Additivity in relation to the Avrami equation The concept of an isokinetic reaction can readily be applied to the Avrami equation. Differentiation of equation (6-22) with respect to time leads to the following expression for the rate of transformation: (6-31)

In a typical diffusion-controlled nucleation and growth process, the fraction transformed X will not be independent of temperature, since the equilibrium volume fraction of the precipitates decreases with temperature (e.g. see equation (4-7) in Chapter 4). However, for dilute alloys it is a fair approximation to neglect this variation as the solvus boundary becomes increasingly steeper and in the limiting case approaches that of a straight (vertical) line. Thus, if n is constant and k* depends only on the transformation temperature, the reaction will be isokinetic in the general sense defined by Christian.10 Because of the independent variations of the nucleation and growth rate with temperature, the transformation rate will not be a simple function of temperature. However, by considering the form of the constitutive equations, it is obvious that the change in the nucleation rate with temperature is far more significant than the corresponding fluctuations in the growth rate. This point is more clearly illustrated in Fig. 6.18, which shows the temperature-dependency of the nucleation and growth rates of grain boundary ferrite in a C-Mn steel. It is evident from these data that the change in the parabolic thickening constant £, is negligible compared with the fluctuations in the nucleation rate. Consequently, in transformations that involve continuous cooling it is sufficient to allow for the variation of Nhet with temperature, provided that site saturation has not been reached. Thus, if n is constant we can apply the Scheil theory directly and rewrite equation (6-25) in an integral form: (6-32) In equation (6-32) Z1 represents the kinetic strength of the thermal cycle with respect to Pprecipitation. This parameter is generally defined by the integral:

Thickening constant Ce1),|ims"

-2 -1 Nucleation rate (N*het), cm s

Temperature, 0C Fig. 6.18. Predicted variation in N*het and E1 with temperature during the austenite to ferrite transformation in a C-Mn steel (0.15 wt% C, 0.40 wt% Mn). Data from Umemoto et al.19

(6-33)

where dt is the time increment at T, and f is the corresponding hold time required to reach Xc at the same temperature (given by equation (6-14)). The derivation of equation (6-32) is shown in Appendix 6.2 The principles of additivity are also applicable under conditions of early site saturation. If only U^p varies with temperature, it is possible to rewrite equation (6-28) in an integral form:

(6-34)

This equation can readily be integrated by numerical methods when the temperature-time programme is known. 6.2.5.4 Non-additive reactions If the additivity condition is not satisfied, it means that the fraction transformed is dependent on the thermal path, and the differential equation has no general solution. This, in turn, implies that the C-curve concept breaks down and cannot be applied to non-isothermal transforma-

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tions. Solution of the differential equation then requires stepwise integration in temperature-time space, using an appropriate numerical integration procedure. As already pointed out, this will generally be the case for diffusion-controlled precipitation reactions, since the evolution parameter X is a true function of temperature. Under such conditions, experimentally based continuous cooling transformation (CCT) diagrams must be employed.

6.3 High Strength Low-Alloy Steels High-strength low-alloy steels are typically produced with a minimum yield strength in the range 300-500 MPa, depending on the plate thickness.2021 During welding microstructural changes take place both within the heat affected zone (HAZ) and the fusion region, which, in turn, affect the mechanical integrity of the weldment.2122 In the HAZ, for instance, nitrides and carbides coarsen and dissolve, and grain growth occurs to an extent that depends on the distance from the fusion boundary and the exposure time characteristic of the welding process. This can have a profound effect on the subsequent structure and properties of the weld by displacing the CCT curve to longer times, thereby producing more Widmanstatten ferrite, or increasing the possibility of bainite and martensitic transformation products on cooling. The formation of such microstructures may reduce the toughness of the weld and increase the risk of hydrogen cracking.2122 6.3.1 Classification of microstructures It is appropriate to start this section with a detailed classification of the various microstructural constituents commonly found in low-alloy steel weldments. During the austenite to ferrite transformation, a large variety of microstructures can develop, depending on the cooling rate and the steel chemical composition. Normally, the microstructure formed within each single austenite grain after transformation will be a complex mixture of two or more of the following constituents, arranged in approximately decreasing order of transformation temperature: (i) (ii) (iii) (iv) (v) (vi) (vii)

grain boundary (or allotriomorphic) ferrite (GF) polygonal (or equiaxed) ferrite (PF) Widmanstatten ferrite (WF) acicular ferrite (AF) upper bainite (UB) lower bainite (LB) martensite (M).

The microstructural constituents listed above are indicated in Fig. 6.19, which shows photomicrographs of typical regions within low-alloy steel weldments. 6.3.2 Currently used nomenclature Quantification of microstructures in steel welds is most commonly done by means of optical microscopy. Several systems have been introduced throughout the years for the classification of the various constituents, with each system reflecting different investigator's views and

7 Properties of Weldments

7.1 Introduction Weldments are prime examples of components where the properties obtained depend upon the characteristics of the microstmcture. Since failure of welds often can have dramatic consequences, a wealth of information is available in the literature on structure-property relationships. However, in order to fit some of the apparently conflicting results into a more consistent picture, a theoretical approach is adopted here rather than a review of the literature. This procedure also involves the use of phenomenological models for the quantitative description of structure-property relationships in cases where a full physical treatment is not possible.

7.2 Low-Alloy Steel Weldments The symbols and units used throughout the chapter are defined in Appendix 7.1. The major impetus for developments in high-strength low-alloy (HSLA) steels has been provided by the need for: (i) higher strength, (ii) improved toughness, ductility, and formability, and (iii) increased weldability. In order to meet these contradictory requirements, the steel carbon contents have been progressively lowered to below 0.10 wt% C. The desired strength is largely achieved through a refinement of the ferrite grain size, produced by the additions of microalloying elements such as aluminium, vanadium, niobium, and titanium in combination with various forms for thermomechanical processing.1 This procedure has made it possible to improve the resistance of steels to hydrogen-assisted cold cracking, stress corrosion cracking, and brittle fracture initiation in the weld heat-affected zone (HAZ) region, without sacrificing base metal strength, ductility, or low-temperature toughness.2 Controlled rolled HSLA steels are currently produced with a minimum yield strength in the range from 350-550 MPa. Above this strength level, quenched and tempered steels are commonly employed. 72.1 Weld metal mechanical properties The recent progress in steel plate manufacturing technology has, in turn, called for new developments in welding consumables to produce weld metal deposits with mechanical properties essentially equivalent to the base metal.3 From the large volume of literature dealing with HSLA steel filler metals, it appears that the bulk of weld metal research over the past decade has been concentrated on the achievement of a maximum toughness and ductility for a given strength level by control of the weld metal microstructure.34 There seems to be general agreement that microstructures primarily consisting of acicular ferrite provide optimum weld metal mechanical properties, both from a strength and toughness point of view, by virtue of its high

dislocation density and small lath size. The formation of large proportions of upper bainite, Widmanstatten ferrite, or grain boundary ferrite, on the other hand, are considered detrimental to toughness, since these structures provide preferential crack propagation paths, especially when continuous films of carbides are present between the ferrite laths or plates. Attempts to control the weld metal acicular ferrite content have led to the introduction of welding consumables containing complex deoxidisers (Si, Mn, Al, Ti) and balanced additions of various alloying elements (Nb, V, Cu, Ni, Cr, Mo, B). The final weld metal microstructure will depend on complex interactions between several important variables such as:3"5 (i) (ii)

The total alloy content. The concentration, chemical composition, and size distribution of non-metallic inclusions. (iii) The solidification microstructure. (iv) The prior austenite grain size, (v) The weld thermal cycle. Although the microstructural changes taking place within the weld metal on cooling through the critical transformation temperature range in principle are the same as those occurring during rolling and heat treatment of steel, the conditions existing in welding are significantly different from those employed in steel production because of the characteristic strong nonisothermal behaviour of the arc welding process. For example, in steel weld deposits the volume fraction of non-metallic inclusions is considerably higher than that in normal cast steel products because of the limited time available for growth and separation of the particles. Oxygen is of particular interest in this respect, since a high number of oxide inclusions is known to influence strongly the austenite to ferrite transformation both by restricting the growth of the austenite grains as well as by providing favourable nucleation sites for various types of microstructural constituents (e.g. acicular ferrite). Moreover, during solidification of the weld metal, alloying and impurity elements tend to segregate extensively to the centre parts of the interdendritic or intercellular spaces under the conditions of rapid cooling.67 The existence of extensive segregations further alters the kinetics of the subsequent solid state transformation reactions. Accordingly, the weld metal transformation behaviour is seen to be quite different from that of the base metal, even when the nominal chemical composition has not been significantly changed by the welding process.3"5 This, in turn, will affect the mechanical integrity of the weldment. 7.2.1.1 Weld metal strength level In low-alloy steel weld metals there are at least four different strengthening mechanisms which may contribute to the final strength achieved. These are: (i) (ii) (iii) (iv)

Solid solution strengthening, Dislocation strengthening, Grain boundary strengthening, Precipitation strengthening.

The relative contribution from each is determined by the steel chemical composition and

the weld thermal history. Because of the number of variables involved, a full physical treatment of the problem is not possible. Consequently, the simplified treatment of Gladman and Pickering8 has been adopted here. Figure 7.1 shows the individual strength contributions in low-carbon bainite, which is the dominating microconstituent in as-deposited steel weld metals (includes both upper and lower bainite as well as acicular ferrite). Firstly, there are the solid solution strengthening increments from alloying and impurity elements such as manganese, silicon and uncombined nitrogen, which in the present example correspond to a matrix strength of about 165 MPa. Secondly, the grain size contribution to the yield stress is shown as a very substantial component, the magnitude of which is determined by the bainite lath size. Finally, a typical increment for dispersion strengthening is indicated. This contribution is negligible at large lath sizes typical of upper bainite, but becomes significant at small grain sizes because of a finer intralath carbide dispersion.8 Hence, in steel weld deposits containing high proportions of acicular ferrite or lower bainite carbides will make a direct contribution to strength, even at relatively low carbon levels. The results in Fig. 7.1 are of significant practical importance, since they show the inherent limitations of the system with regard to the maximum strength that can be achieved through control of the microstructure. As shown in Section 6.3.5.4 (Chapter 6), the typical lath size (width) of acicular ferrite in low-alloy steel weld metals is about 2 jam. According to Fig. 7.1, this corresponds to a maximum yield strength of approximately 650 MPa, which is in good agreement with the observed threshold strength of acicular ferrite containing steel weld deposits.9 If higher strength levels are required, it is necessary to decrease the grain (lath) size through a refinement of the microstructure, i.e. by replacing acicular ferrite with either lower

Yield strength, MPa

p 1/4 -f/o Number of carbides per mm Nv (mm" )

Dispersion

Grain size

Matrix strength

-1/2 Bainitic ferrite grain size, mm

Fig. 7.1. Contributions to strength in low-carbon bainite. Data from Gladman and Pickering.8

bainite or martensite. Development along these lines has led to the introduction of a new generation of high strength steel weld metals with a yield strength in the range from 650 to 900 MPa.10'11 7.2.1.2 Weld metal resistance to ductile fracture It is well established that the weld metal resistance to ductile fracture is strongly influenced by the volume fraction, shape, and size distribution of non-metallic inclusions.12"15 Although a verified quantitative understanding of the fracture process is still lacking, there seems to be general agreement that it involves the following three basic steps:16 (i)

Nucleation of internal cavities during plastic flow, preferentially at non-metallic inclusions. (ii) Growth of these cavities with continued deformation, (iii) Final coalescence of the cavities to produce complete rupture. Details of these three stages may vary widely in different materials and with the state of stress existing during deformation. Similarly, the fractographic appearance of the final fracture surface is also influenced by the same factors. Effect of inclusion volume fraction The primary variables affecting the true strain at fracture 8/ are the inclusion diameter dv, and the inclusion volume fraction Vv. The relation between Ef and Vv has been determined experimentally for a wide variety of materials, and can most simply be expressed as:17 (7-1) where c\ is an empirical constant. The tensile test data of Widgery12 reproduced in Fig. 7.2 reveal a strong dependence of £/ on Vv, but the relationship appears to be linear rather than non-linear, as predicted by equation (7-1). Due to a similar fracture mechanism, a correlation also exists between the Charpy Vnotch (CVN) upper shelf energy and the true fracture strain in tensile testing, as shown in Fig. 7.3. For this reason, the weld metal impact properties are normally seen to decrease with increasing oxygen concentrations when testing is performed in the upper shelf region. From Fig. 7.4 we see that the CVN upper shelf energy is a linear function of the weld metal oxygen content. This observation is not surprising, considering the fact that the inclusion volume fraction is directly proportional to the oxygen level (see equation (2-75) in Chapter 2). Effect of inclusion size distribution Void nucleation may occur both by cracking of the inclusions and by interface decohesion. In the former case, the critical stress for particle cracking ap is given by:16

(7-2)

where 7^ is the surface energy of the particle, Ep is the Young's modulus of the particle, A is the stress concentration factor at the particle, and dv is the particle diameter.

True fracture strain

GMAW (E=1.6kJ/mm)

Inclusion volume fraction

CVN upper shelf energy, J

Fig. 7.2. Variation of true fracture strain £/with inclusion volume fraction Vv. Data from Widgery.12

SAW and FCAW

True fracture strain Fig. 7.3. Correlation of CVN upper shelf energy with true fracture strain in tensile testing. Data from Akselsen and Grong.20 Equation (7-2) predicts that large inclusions will tend to form voids first as the stress required for initiation is proportional to (l/dv )1/2. This result is also in agreement with experimental observations. As shown in Fig. 7.5, the size distribution of inclusions located in the centre of voids at the fracture surface is significantly coarser than the corresponding particle size distribution in the material. In particular, large, angular shaped aluminium oxide (AI2O3)

CVN upper shelf energy, J

SAW

Oxygen content, wt% Fig. 7.4. Correlation of CVN upper shelf energy with analytical weld metal oxygen content. Data from Devillers et aL 13

inclusions appear to be preferential nucleation sites for microvoids in low-alloy steel weld metals (see Fig. 7.5(b)). Although the combined effect of particle size and local stress concentration on the ductile fracture behaviour cannot readily be accounted for in a mathematical simulation of the process, the CVN data in Fig. 7.6 suggest that the content of large inclusions (e.g. of a diameter greater than about 1.5 Jim) should be minimised in order to maintain a high resistance against dimpled rupture. In practice, this requires careful control of the weld metal aluminium-oxygen balance and the heat input applied during welding (see Section 2.12 in Chapter 2). Effect of strength level The toughness of a material reflects its ability to absorb energy in the plastic range. One way of looking at toughness is to assume that it scales with the total area Uj under the stress-strain curve. Several mathematical expressions for this area have been suggested. For ductile materials we may write:19 (7-3) where Rm is the ultimate tensile strength (UTS). If Uj is regarded as a material constant, one would expect that Rm and £y are reciprocal

Total inclusion population

SAW

Frequency, %

Frequency, %

Inclusions associated with dimples

Inclusion diameter, jum

Frequency, %

Total inclusion population

(b)

SAW

Inclusions associated with dimples

Frequency, %

(a)

Inclusion diameter, jum

Fig. 7.5. Histograms showing the size distribution of non-metallic inclusions in the weld metal and in the centre of microvoids at the fracture surface, respectively; (a) Low aluminium level (Al-containing manganese silicate inclusions), (b) High aluminium level (AI2O3 inclusions). Data from Andersen.18

High Ti levels CVN upper shelf energy, J

Medium Ti levels Low Ti levels

SAW

Nv (d v >1.5 um)-105 Fig. 7.6. Correlation of CVN upper shelf energy with number of particles per mm3 greater than 1.5 urn, Nv(dv > 1.5 um). Data from Grong and Kluken.15

True fracture strain

SAW and FCAW

Ultimate tensile strength, MPa Fig. 7.7. Correlation of true fracture strain with ultimate tensile strength (low-alloy steel weld metals). Data from Akselsen and Grong.20 quantities, i.e. an increase in Rm is always associated with a corresponding decrease in Ef, according to the equation: (7-4) where c^ is a constant which is characteristic of the alloy system under consideration.

It is evident from the tensile test data in Fig. 7.7 that the fracture strain is a true function of Rm, although the relationship appears to be linear rather than non-linear, as predicted by equation (7-4). These results are of considerable practical importance, since they imply that the upper shelf energy absorption, and hence, the shape of the CVN transition curve is strongly affected by the weld metal strength level. Accordingly, control of the weld metal microstructure becomes particularly urgent at high strength levels to avoid problems with the cleavage fracture resistance (to be discussed below). 7.2.1.3 Weld metal resistance to cleavage fracture Cleavage fracture is characterised by very little plastic deformation prior to the crack propagation, and occurs in a crystallographic fashion along planes of low indicies, i.e. of high atomic density.1 Body-centred cubic (bcc) iron cleaves typically along {100} planes, which implies that the cracks must be deflected at high angle grain (or packet) boundaries, as shown schematically in Fig. 7.8. Consequently, in steel weld metals the ferrite grain size and the bainite packet width are the main microstructural features controlling the resistance to cleavage crack propagation. Since the microstructure which forms within each single austenite grain will not be uniform but a complex mixture of two or more constituent phases, it is difficult, in practice, to define a meaningful grain size or packet width. For this reason, most investigators have attempted to correlate toughness with the presence of specific microconstituents in the weld metal.3"5 For example, an increase in the volume fraction of acicular ferrite will result in a corresponding increase in toughness (i.e. decrease in the CVN transition temperature), as shown in Fig. 7.9.

(a)

(b) Fig. 7.8. Schematic diagrams showing cleavage crack deflection at interfaces; (a) High angle ferriteferrite grain boundaries, (b) High angle packet boundaries (bainitic microstructures).

Transition temperature, 0C

SAW (E = 5.2-6.2 kJ/mm)

Al: 0.018-0.062 wt% Ti: 0.005 - 0.065 wt% O: 0.018-0.058 wt%

Acicular ferrite content, vol% Fig. 7.9. Correlation between the weld metal 35J CVN transition temperature and the acicular ferrite content. Data from Grong and Kluken.15 This observation is not surprising, considering the extremely fine lath size of the acicular ferrite microstructure (typically less than 5jim). Moreover, results obtained from fractographic examinations of SMA and FCA steel weld metals have demonstrated that large non-metallic inclusions (> l|im) can strongly influence the cleavage fracture resistance, either by acting as cleavage cracks themselves of by providing internal sites of stress concentration which facilitate carbide-initiated cleavage in the adjacent matrix.21'22 In the former case, the critical stress required for crack propagation in the matrix, Cf(M), is given by the Griffith's equation:19

(7-5)

where En is the Young's modulus of the matrix, ye^ is the effective surface energy (equal to the sum of the ideal surface energy and the plastic work), and c is the half crack length. Since c is proportional to the particle diameter dv, equation (7-5) predicts that welds containing large inclusions should be more prone to cleavage cracking than others. This result is also in agreement with general observations. For example, in self-shielded FCA steel weld metals it has been demonstrated that cleavage crack initiation is usually associated with large aluminium-containing inclusions which form in the molten pool before solidification (see Fig. 7.10). Consequently, control of the inclusion size distribution is essential in order to ensure an adequate low-temperature toughness. 7.2.1.4 The weld metal ductile to brittle transition In addition to the parameters mentioned above, there are several other factors, some interrelated, which play an important part in the initiation of cleavage fracture. These are:1 (i)

The temperature dependence of the yield stress.

(a)

(b)

(C)

Fig. 7.10. Initiation of cleavage fracture in a self-shielded FCA steel weld from an aluminium-containing inclusion; (a) Initiation site short distance ahead of the notch, (b) Detail of initiation site showing cracked inclusion, (c) Detail of cracked inclusion (remnants of particle are left in the hole). (ii) (iii) (iv)

Dislocation locking effects caused by interstitials or alloying elements in solid solution (e.g. nitrogen and silicon), Nucleation of cracks at twins, Nucleation of cracks at carbides.

In general, this picture is too complicated to establish a physical framework within which the various theoretical models for the ductile to brittle transition in steel can be embedded. We are therefore forced to base our judgement and understanding of how key parameters affect the position and shape of the CVN transition curve solely on scattered phenomenological observations and empirical models (e.g. see the reviews of Grong and Matlock3 or Abson and Pargeter4). An example of how far the latter approach has been developed is given below. Akselsen and Grong20 have established a series of empirical equations which relates toughness to the weld metal acicular ferrite content and the ultimate tensile strength (UTS). Figures 7.11 and 7.12 show how each of these parameters influences the CVN transition curve. It is evident from the diagrams that control of the weld metal acicular ferrite content becomes particularly important at high strength levels to avoid problems with the fracture toughness. In cases where undermatch is aimed at (i.e. a weld metal to base plate strength ratio less than unity), the weld metal tensile strength is typically of the order of 450 to 550 MPa. Within this range a volume fraction of acicular ferrite beyond 25 vol% will generally be sufficient to meet current toughness requirements (35 J at -40 0 C). If overmatch is desired, the volume fraction of acicular ferrite becomes more critical, partly because of a higher weld metal strength level and partly because of more stringent toughness requirements (e.g. 45 J rather than 35 J at -40 0 C). Process diagrams of the type shown in Figs. 7.11 and 7.12 can therefore serve as a basis for proper selection of consumables for welded steel structures. It should be noted that Akselsen and Grong20 in their analysis omitted a consideration of the important influence of free (uncombined) nitrogen and non-metallic inclusions on the CVN transition curve. Based on the experimental data in Fig. 7.13 it can be argued that such compositional variations can be equally detrimental to toughness as a decrease in the acicular ferrite content. Consequently, further refinements of the models are required if a verified quantitative understanding of the ductile to brittle transition in low-alloy steel weld metals is to be obtained. Example (7.1)

Consider multipass FCA steel welding with two different electrode wires, one with titanium additions and one without. Table 7.1 contains a summary of weld metal chemical compositions. Provided that the microstructure and the inclusion size distribution are similar in both cases, use this information to evaluate the low-temperature toughness of the welds, as revealed by CVN testing. Solution

Since the nitrogen content of both welds is quite high (0.011 wt%), the risk of a toughness deterioration due to strain ageing is imminent, particularly at low Ti levels. Taking the atomic weight of titanium and nitrogen equal to 47.9 and 14.0 g mol"1, respectively, the stoichiometric amount of titanium that is necessary to tie-up all nitrogen as TiN can be calculated as follows:

WeIdA In weld A most of the nitrogen is free (uncombined) due to an unbalance in the titanium content. This means that the risk of a toughness deterioration due to strain ageing is high.

(a)

Absorbed energy, J

Tensile strength: 600 MPa Vol% acicular ferrite

35 Joules

Test temperature, 0C

(b)

Absorbed energy, J

Tensile strength: 800 MPa

Vol% acicular ferrite

35Joules.

Test temperature, 0C Fig. 7.11. Predicted effect of weld metal acicular ferrite content on the CVN transition curve at two different tensile strength levels; (a) Rm = 600 MPa, (b) Rm = 800 MPa. Data from Akselsen and Grong.20

WeIdB Weld B contains 0.030 wt% Ti, which is not far from the stoichiometric amount of titanium necessary to tie-up all nitrogen. Although some titanium also is bound as Ti2O3, it is reasonable to assume that the free nitrogen content in this case is sufficiently low to eliminate problems with strain ageing. Consequently, weld B would be expected to exhibit the highest toughness (i.e. the lowest CVN transition temperature) of the two, as indicated in Fig. 7.14.

(a) 25 vol% acicular ferrite Absorbed energy, J

UTS

35 Joules

Test temperature, 0C

(b)

Absorbed energy, J

75 v o l % acicular ferrite

UTS

-..35J.Q.ute$-

Test temperature, 0 C

Fig. 7.12. Predicted effect of weld metal ultimate tensile strength (UTS) on the CVN transition curve at two different volume fractions of acicular ferrite; (a) 25 vol% AF, (b) 75 vol% AF. Data from Akselsen and Grong.20 Table 7.1 Chemical composition of FCA steel weld metals considered in Example (7.1). Element Weld

wt% C

wt% Si

wt% Mn

wt% Al

wt% Ti

wt% S

wt% N

wt% O

A

0.10

0.40

1.50

0.005

0.006

0.008

0.011

0.031

B

0.10

0.40

1.50

0.005

0.030

0.008

0.011

0.031

(a) SMAW (basic electrodes) Absorbed energy, J

95% confidence interval

Testing temperature: -400C

Nitrogen content, ppm (b)

Absorbed energy, J

Low content of coarse inclusions

High content of coarse inclusions ( > 1}im )

Self-shielded FCA steel weld metals Test temperature, 0C Fig. 7.13. Effect of impurities on weld metal CVN toughness; (a) Nitrogen content, (b) Inclusion level. Data from ESAB AB (Sweden) and Grong et al. 22

7.2.1.5 Effects of reheating on weld metal toughness In principle, improvement of weld properties can be achieved through a post-weld heat treatment (PWHT). This may have the benefits of:3 (i)

Enhancing the fatigue strength through a general reduction of welding residual stresses.

Absorbed energy

WeIdB

WeIdA

35 J

Test temperature, 0C Fig. 7.14. Schematic drawings of the CVN transition curves for welds A and B (Example (7.1)).

(a)

(b)

Fig. 7.15. Typical low-temperature fracture modes of Ti-B containing steel weld metals; (a) Quasicleavage (as-welded condition), (b) Intergranular fracture (after PWHT).

(ii)

Increasing the toughness by recovery (i.e. removal of strain-aged damage) and martensite tempering.

For these reasons local PWHTs are commonly required for all structural parts above a specified plate thickness (e.g. 50 mm according to current North Sea offshore specifications). Post-weld heat treatment is usually carried out in the temperature range from 550 to 6500C. In practice, however, the toughness achieved will depend on the weld metal chemical composition, and in some cases deterioration rather than improvement of the impact properties is observed after PWHT. In such cases the reduction in toughness can be ascribed to:3'4 (i)

Precipitation hardening reactions. Present experience indicates that elements such as vanadium, niobium, and presumably titanium can produce a marked deterioration in toughness because of precipitation of carbonitrides in the ferrite, provided that these elements are present in the weld metal in sufficiently high concentrations.

(ii)

Segregation of impurity elements (e.g. P, Sn, Sb and As) to prior austenite grain boundaries, which, in turn, can give rise to intergranular fracture. The indications are that this type of embrittlement is strongly enhanced by the presence of second phase particles at the grain boundaries.

Experience shows that Ti-B containing steel weld metals often fail by intergranular fracture in the columnar grain region after PWHT,23 as evidenced by the SEM fractographs in Fig. 7.15. The observed shift in the fracture mode is associated with a significant drop in toughness (Fig. 7.16) and arises from the combined action of solidification-induced phosphorus segregations and borocarbide precipitation along the prior columnar austenite grain bounda-

ACVN, J

SAW

Open symbols: 5 - 8 ppm B Filled symbols: 20 - 25 ppm B

Base line

Titanium content, wt% Fig. 7.16. Observed displacement in the CVN toughness after PWHT (ACVN) as a function of the weld metal boron and titanium contents. Negative values indicate loss of toughness. Data from Kluken and Grong.23

Fig. 7.17. TEM micrograph showing precipitation of borocarbides, Fe23(B,C)6, along prior austenite grain boundaries in a Ti-B containing steel weld metal after PWHT (600 0 C-Ih).

ries (Fig. 7.17). Since borocarbides are brittle and partly incoherent with the matrix, they can be regarded as microcracks (of length dp) ready to propagate. In such cases there is virtually no plastic deformation occurring before crack propagation, which implies that the intergranular fracture stress is given by the Griffith's equation:24 (7-6)

where 7 ^ is again the effective surface energy (equal to the sum of the ideal surface energy and the plastic work), and dp is the particle diameter. Although the value of yeg_ would be expected to be low in the presence of solidificationinduced phosporus segregations,24 this alone is not sufficient to initiate intergranular fracture in the weld metal. However, during PWHT the borocarbides will start to grow from an initially small value to a maximum size of about 0.1 to 0.2jim (Fig. 7.17), following the classic growth law for grain boundary precipitates dpatl/4?5 This implies that the intergranular fracture stress, Oj(I), will gradually decrease with increasing annealing times, as indicated in Fig. 7.18. When the matrix fracture strength, Cj(M), is reached, the fracture mode shifts from predominantly quasi-cleavage in the as-welded condition (Fig. 7.15(a)) to intergranular rupture after PWHT (Fig. 7.15(b)). This is observed as a marked reduction in the CVN toughness, as shown previously in Fig. 7.16. 7.2.2 HAZ mechanical properties The last twenty years have seen a revolution in the metallurgical design of steel. Whereas old steels relied on the use of carbon for strength, the trend today is to rely more on grain refinement in combination with microalloy precipitation to meet the current demand for an improved weldability. This includes both the sensitivity to weld cracking and the HAZ mechanical properties required by service conditions and test temperatures. The latter aspect is of particular interest in the present context and will be discussed later.

Stress

Intergranular fracture mode

Quasi-cleavage fracture mode Particle diameter

[Annealing time]174 Fig. 7.18. Schematic illustration of the mechanisms of temper embrittlement in Ti-B containing steel weld metals (Gf(M): matrix fracture strength, (*/(/): intergranular fracture strength).

p0.2> R nv M P a R

HV 5 ,kp/mm 2

Martensite content, vol%

7.2.2.1 HAZ hardness and strength level The HAZ hardness and strength level is of significant practical importance, since it influences both the cracking resistance and the toughness. Although the peak strength is mainly controlled by the martensite content (see Fig. 7.19), the relationship is generally too complicated to allow reliable predictions to be made from first principles. This implies that our understanding of the HAZ strength evolution, at best, is semi-empirical.

Cooling time, At 8 / 5 , s Fig. 7.19. Structure-property relationships in the grain coarsened HAZ of low-carbon microalloyed steels (vol% M: martensite content, Rp : 0.2% proof stress, Rm: ultimate tensile strength, HV5: Vickers hardness, A%5.* cooling time from 800 to 5000C). Data from Akselsen et al.26

A number of different empirical models exist in the literature for prediction of HAZ peak hardness and strength.26"31 However, the aptness of some of these models is surprisingly good, which justifies construction of iso-hardness and iso-strength diagrams for specific grades of steels.32 Examples of such diagrams are given in Fig. 7.20. It is evident from Fig. 7.20 that the HAZ peak strength is controlled by two main variables, i.e. the steel chemical composition and the weld cooling programme. The compositional effect is allowed for by the use of an empirical carbon equivalent, which ranks the influence of the various alloying elements on the steel hardenability. According to Yurioka et al.,2* the CEn-equivalent is given as:

(7-7) where all compositions are given in wt%. Moreover, the cooling time from 800 to 5000C, Af8/5, is used as an abscissa in Fig. 7.20. This parameter is widely accepted as an adequate index for the weld cooling programme, and can be read from nomograms of the type shown in Fig. 1.49 (Chapter 1). The axes of Fig. 1.49 are dimensionless, but they can readily be converted into real numbers through the use of the following conversion factors:33 Ordinate: (7-8)

Abscissa: (7-9) The different parameters in equations (7-8) and (7-9) are defined in Appendix 7.1. The results in Fig. 1.49 are interesting, since they show that the cooling time, A%5, depends on the mode of heat flow during welding. In this case the transition from 'thick' to 'thin' plates, corresponding to an abscissa of about 0.64, is clearly not represented by a single plate thickness d, but will be a function of both the net heat input r\E and the ambient temperature T0. Accordingly, the HAZ strength level is seen to vary between wide limits, depending on the steel chemical composition and the operational conditions applied (Fig. 7.20). Example (7.2)

Consider stringer bead deposition (GMAW) on two low-alloy steel plates of similar composition but different thickness under the following conditions: I = 250A, U = 30V, v = 5mm s"1, r| = 0.8, T0 = 200C According to the steel mill certificate the CEn carbon equivalent is equal to 0.46 wt%. Use this information together with the diagrams in Figs. 1.49 and 7.20 to estimate the peak HAZ strength level when the plate thickness is 10 and 30 mm, respectively.

CEn, wt%

(a)

Cooling time, A t 8 / 5 , s

CE||f wt%

(b)

Cooling time, At 8 7 5 , s Fig. 7.20. HAZ iso-property diagrams for HSLA steels; (a) Iso-hardness contours, (b) Iso-yield strength contours. Data from Kluken et al.32

Solution

First we calculate the net heat input per unit length of the weld r\E:

From equation (7-9) we have:

Readings from Fig. 1.49 then give: d = 10 mm:

from which

d = 30 mm:

from which

We can now use the diagrams in Fig. 7.20(a) and (b) to obtain the peak HAZ hardness and yield strength, respectively. This gives: d = 10 mm:

d = 30 mm:

It is evident from the above calculations that the HAZ strength level is sensitive to variations in the welding conditions. Normally, the HAZ hardenability is high enough to facilitate

a local strength increase adjacent to the fusion boundary, as shown in Fig. 7.21. An exception is high heat input welding on quenched and tempered steels (Fig. 7.2l(b)), where the presence of large amounts of Widmanstatten ferrite and polygonal ferrite within the grain coarsened and grain refined region, respectively can lead to a severe HAZ softening. This type of mechanical impairment represents a problem in engineering design, since it puts a restriction on the use of high strength steels in welded structures.

BM"

IR"

JfL Gf[R. GCR

BM

High strength steels.

GCR GRR

Medium strength steels

R p02 and R m ,

(a)

Low heat input welding: E^ 1 -2 kJ/mm

Medium strength steels

High strength steels

SR" BM"

TR"

GCR "GRR

,BM [SR JfL, ^GRR. QQR.

R

p0.2 and R m> MPa

(b)

High heat input welding: E^4 kJ/mm Fig. 7.21. Effects of steel chemical composition and welding conditions on the HAZ strength level (BM: base metal, SR: subcritical region, IR: intercritical region, GRR: grain refined region, GCR: grain coarsened region); (a) Low heat input, (b) High heat input. Data from Akselsen and R0rvik.34

7.2.2.2 Tempering of the heat affected zone Certain regulations for offshore structures require that no part of the welded joint shall be harder than a specified limit, e.g. 280, 300 or 325 VPN, to reduce the risk of hydrogen cracking. Such requirements cannot always be met by a suitable choice of preheating and welding conditions. In practice, a reduction in the HAZ strength level can be achieved by applying a PWHT. The tempering effect of different temperature-time combinations can be described by the Hollomon-Jaffe parameter:35 (7-10) where T is in K (absolute temperature). In Fig. 7.22 the isothermal hardness data reported by Olsen et al.36 have been plotted against the empirical Hollomon-Jaffe parameter. In this particular case the best fit is obtained if the constant B* in equation (7-10) is equal to 16.5 (with t in seconds). It is evident from Fig. 7.22 that tempering at, say, 6000C for 1 h is more than sufficient to reduce the HAZ peak hardness to values below 280 VPN. This implies that PWHT is an effective (but expensive) way of reducing the HAZ strength level. Deposition of temper weld beads has been suggested as an alternative means of reducing the hardness of the HAZ.36"38 This procedure is indicated schematically in Fig. 7.23, showing two temper beads (black) in the lower sketch. If the beads are properly positioned with respect to the fusion line, the outer Ac\ contour of the HAZ produced by the temper bead should just touch the fusion line of the last filler pass, as indicated in the upper sketch of Fig. 7.23. The material reaustenitised by the temper bead would then be weld metal, while the HAZ remaining from the last filler pass would be tempered below the transformation range.

Vickers hardness, VPN

Filled symbols: t = 10 seconds

Steel chemical composition (wt%)

F> = T(16.5 + logt) Fig. 7.22. Hollomon-Jaffe type plot of isothermal hardness data. After Olsen et al.36

Temper bead

Last filler pass

Fusion line Ac3 line Ac1 line

Fig. 7.23. Schematic illustration of weld bead tempering. Since the Hollomon-Jaffe parameter is an empirical criterion developed for isothermal tempering of medium and high carbon steels, it cannot readily be applied to pulsed tempering. A better approach would be to use the so-called Dorn parameter,39 which in an integral form can be written as:39'40 (7-11)

where Qapp. is the apparent activation energy for the controlling diffusion reaction. The Dorn parameter has proved useful to compare isothermal and pulsed tempering data on the assumption that the kinetics of softening, in the actual range of hardness, are controlled by diffusion of carbon in ferrite. Qualitatively, the aptness of equation (7-11) can be illustrated in a plot of measured hardness against the diffusional parameter P^ ( s e e Fig- 7.24). It is evident from Fig. 7.24 that the isothermal data points can be represented by a smooth curve which coincides with the upper boundary of the scatter band obtained in pulsed tempering. The slightly higher hardness observed after isothermal tempering arises probably from a brief period of heating that makes the effective time somewhat less than 10 s. Case Study (7.1)

As an illustration of principles, Fig. 7.25 shows a case of identical welding parameters for the last filler pass and the temper bead, the latter one being positioned so as to give a peak temperature of 7200C at the fusion line of the former one. The temperature field around the two

^s

1

'

Vickers hardness. VPN

Hardness ratio HV/HVmax, %

Isothermal 10 s Series 1 " 2 " 3 " 4 Double pulse

2

Fig. 7.24. Measured hardness ratio HVIHVmax. vs the Dorn parameter P2 (Qapp. = 83.14 kJ mol *). Data fromOlsentf/tf/.36

beads is clearly the same. In Fig. 7.25 an estimate has been based on the simplified Rykalin thick plate solution, which applies to a fast moving high power source on a semi-infinite body (see equation (1-73) in Chapter 1). At T-T0 ~ 15000C, a fusion line radius of about 4.4 mm is obtained for a net heat input of 0.8 kJ mm"1. The corresponding Ac\ radius is 6.5 mm. The temperature-time pattern is shown in the lower left graphs of Fig. 7.25 for three different positions in the HAZ, i.e. y = 0 (former fusion line), y = 1 mm, and y = 2 mm (z = 0). The corresponding plots of dP2 ldt vs t are shown to the right. Taking the area P2 under each curve and reading the hardness ratio at TJP^ from Fig. 7.24, an expected hardness profile is obtained, as shown in the upper diagram of Fig. 7.25. The expected effect of tempering is seen to range from a hardness of about 65% (HV « 265 VPN) at the fusion line to about 80% (HV « 340 VPN) close to the outer boundary of the HAZ (y = 2 mm). If the centre-line displacement had been different from the chosen optimum of 2.1 mm (e.g. say 3 mm), the predicted hardness curve would be shifted to about 75% and 90% of the peak hardness at y = 0 and y = 2 mm, respectively. On the other hand, if the centre-line distance had been shorter, say 1 mm, a narrow zone of the original HAZ would be re-austenitised and therefore about as hard as before deposition of the temper bead. The results from the above modelling exercise show that the HAZ hardness of weld toes and cap layers can be reduced by applying an appropriate temper bead technique. However, this requires an extremely good process control, since the temper beads must be positioned very precisely for a successful result. Consequently, the use of temper beads for improvement of the HAZ properties has not found a wide application in the industry.3641 7.2.2.3 HAZ toughness In spite of the recent developments in steel plate manufacturing technology, there is still concern about the HAZ toughness of low-carbon microalloyed steels because of their tendency to

max

HV/HV

last filter pass

temper bead

y, mm

HA2

Parent plate

106exp(-10000/T)

T, 0C

We d metal

t,s

t,s

Fig. 7.25. Application of Dorn parameter to weld bead tempering (Case Study (7.1)). form brittle microstructures within specific thermal regions of the weld. 4142 Moreover, improvement of the HAZ toughness through PWHT is sometimes found to be difficult in contrast to experience with more traditional C-Mn steels.41'43 Consequently, the increasing use of lowcarbon microalloyed steels in various welded structures has introduced new problems related to the HAZ brittle fracture resistance which formerly did not appear to be of particular concern.44 Fully transformed region Specific effects of peak temperature on HAZ toughness, as assessed on the basis of thermally cycled CVN specimens, are shown in Fig. 7.26. It is apparent from the graph that embrittlement in the fully transformed part of the HAZ is often located in the grain coarsened region adjacent

I SR R

G C R

G R R

-3

(D

c O

I

Sn igel cycel 0

Peak e tmperau tre,C Fig. 7.26. Effects of peak temperature on the CVN energy absorption at -400C (SR: subcritical region, IR: intercritical region, GRR: grain refined region, GCR: grain coarsened region). Data from Akselsen et a/.45 to the fusion boundary where the peak temperature of the thermal cycle has been above about 12000C. The problem can mainly be ascribed to the presence of low-toughness microstructures such as upper bainite and Widmanstatten ferrite which form typically at intermediate and slow cooling rates (see Fig. 6.55 in Chapter 6). In contrast, the grain refined region will almost always exhibit a satisfactory low-temperature toughness owing to the characteristic fine polygonal ferrite microstructure.41 An exception is low heat input welds produced from steels with a heavily banded pearlite/ferrite microstructure, where the risk of a toughness deterioration is imminent due to martensite formation along the prior base metal pearlite bands.45'46 In recent years a new class of low-carbon microalloyed steels has emerged which is characterised by an excellent low temperature HAZ toughness, even at high heat inputs (see Fig. 7.27). This particular grade is frequently referred to as Ti-O steels due to their content of indigenous titanium oxide inclusions (presumably Ti2O3). Although the mechanisms involved are not yet fully understood, it is reasonable to assume that the improved toughness at high heat inputs arises from a refinement of the HAZ microstructure, as discussed previously in Section 6.3.6 (Chapter 6). It is interesting to note that the major effect of the titanium oxide inclusions in this case appears not to be control of the austenite grain size (which in some cases can exceed 500 |im at the fusion boundary), but is rather to act as favourable nucleation sites for acicular ferrite intragranularly.4748 Similar phenomena are well known from transformation kinetics of low-alloy steel weld deposits, where non-metallic inclusions play an important role in the development of the acicular ferrite microstructure.3"5 Intercritical region The microstructural evolution in the intercritical HAZ of low-carbon steels has previously been discussed in Section 6.3.8.2 (Chapter 6). In order to understand the origin of embrittlement in the intercritical region, consideration must be given to the stress fields and the transformation strains developed in the ferrite matrix

Transition temperature, 0C

Ti-O steel Ti-N steel

Peak temperature, 0C Fig. 7.27. Response of modern Ti-O steels and traditional Ti-N steels to CVN testing following weld thermal simulation. Data from Homma et al.41 as a result of the martensite formation.49 It follows from Fig. 7.28 that the hard martensiteaustenite (M-A) islands will give rise to significant stress concentrations at the martensite/ ferrite interface owing to the pertinent difference in the yield strength (stiffness) between the two phases. At the same time, the volume expansion associated with the austenite to martensite transformation leads to significant elastic and plastic straining of the ferrite.50 At moderately high temperatures and deformation strains, many of the matrix dislocations will be mobile, which means that the ferrite will maintain its ductility, while the stiffer M-A islands are exposed to cracking and debonding. With increasing strain, the cracks can grow into voids and further develop into deep holes, until final rupture occurs by hole/void coalescence due to internal necking.49 However, when mechanical testing is performed at subzero temperatures under high strain rate conditions (> 102 s"1 for CVN testing), the flow strength of the ferrite increases significantly because of the reduced mobility of the screw dislocations.51 In addition, strain partitioning between the M-A islands and the ferrite may also occur, which further enhances the stress concentrations at the M-A/ferrite interface.52 Accordingly, the local stress level at the interface will eventually exceed the cleavage strength of the ferrite, with consequent initiation of brittle fracture. This conclusion is consistent with observations made from tensile testing of dual-phase steels, showing that failure of dual-phase microstructures often is caused by fracture in the ferrite region.52"54 Because the intercritical HAZ toughness is closely related to the volume fraction of the M-A constituent in the matrix, 4 5 5 1 5 5 embrittlement can normally be avoided by decreasing the cooling rate through the critical transformation temperature range to facilitate pearlite formation (see Fig. 7.29). An exception is boron-containing steels, where the HAZ hardenability is high enough to stabilise the M-A constituent, even at slow cooling rates (see CVN data for steel B in Fig. 7.29).

Normalized stress Stiff particle Normalized distance

Absorbed energy, J

Fig. 7.28. Stress distribution in matrix caused by stiff inclusion (or: radial stress, (5$: tangential stress, tmax.' maximum shear stress). Data from Chen et al.49

Open symbols: Filled symbols:

Steel A (T-L)

(L-T) Steel B

(T-L)

Cooling time, At 6 / 4 , s Fig. 7.29. Effect of cooling time Ar674 on the intercritical HAZ toughness at -20 0 C (thermally cycled specimens). Steel A: 11 ppm B, Steel B: 26 ppm B. Data from Ramberg et al.55

Effect of PWHT Considering the intercritical HAZ, a significant improvement of the CVN toughness can be achieved by applying a PWHT, as shown by the data of Akselsen et al51 This effect arises partly from a reduction of the stress concentrations at the M-A/ferrite interface as a result of martensite tempering and partly from relaxation of transformation strains within the ferrite matrix.51 Such recovery reactions will start to occur when the temperature is raised above about100 0 C.

(a)

CTOD at -1O0C, mm

(b)

P content, wt% Fig. 7.30. Effects of PWHT on the grain coarsened HAZ toughness; (a) Example of intergranular fracture along prior austenite grain boundaries after PWHT (6000C - 1 h), (b) Measured CTOD vs base plate phosphorus content for post weld heat treated specimens (6000C - 4 h). Data quoted by Grong and Akselsen.41

In contrast to the behaviour described above for the intercritical HAZ, the reported effect of PWHT on the grain coarsened HAZ toughness is much more complicated and rather confusing. However, experience has shown that particularly niobium-vanadium containing steels are sensitive to PWHT due to the strong precipitation hardening potential of Nb(C,N) and V(C,N).43'56 In addition, a toughness deterioration may occur as a result of segregation of impurity elements such as phosphorus, tin, and antimony to prior austenite grain boundaries. This, in combination with a tempered martensitic microstructure, can lead to intergranular

fracture when testing is performed at subzero temperatures (see Fig. 7.30(a)). The detrimental effect of phosphorus on the HAZ toughness of low carbon microalloyed steels after PWHT is shown in Fig. 7.30(b). Example (7.3)

Consider procedure test SA welding on a thick plate of a Nb-microalloyed steel under the following conditions: / = 500A, U = 30V, v = 6mm s"1, r\ = 0.95, T0 = 200C Table 7.2 contains data from CVN testing of the base plate and thermally cycled specimens. The weld thermal simulation experiments were carried out at three different peak temperatures (i.e. 13500C, 10000C, and 7800C) under cooling conditions similar to those employed in the SA welding trial. Based on the data in Table 7.2 and the simplified Rykalin thick plate solution (equation (1-73) in Chapter 1), estimate the locations of the brittle zones (referred to the fusion boundary) within the HAZ of the SA procedure test weld considered above. Solution

It is evident from the CVN data in Table 7.2 that the HAZ toughness would be expected to be low in positions of the weld where the peak temperature has been close to 780 and 13500C, conforming to the intercritical and grain coarsened region, respectively. Based on the simplified Rykalin thick plate solution, the following expression can be derived for an arbitrary isothermal zone width, Ar*m, referred to the fusion boundary (see equation (5-47) in Chapter 5):

Taking pc and Tm equal to 0.005 J mm"3 0C"1 and 15200C, respectively for low-alloy steels (from Table 1.1 in Chapter 1), we obtain: Table 7.2 Results from CVN testing of base metal, thermally cycled specimens, and procedure test weld (Example (7.3)) Test results

Absorbed energy at -40 0 C (J)

Base metal Thermally cycled specimens Weld HAZ* 1

320, 310, 305; average: 312 0

Tp = 780 C T = 10000C 7;= 13500C

40, 36, 34; average: 37 225, 220, 219; average: 221 50, 46, 40; average: 46

GCR: 63, GRR: 225, IR: 53

GCR: grain coarsened region; GRR: grain refined region; IR: intercritical region.

Next Page

Intercritical HAZ (Tp « 7800C):

Grain coarsened HAZ (Tp « 13500C):

From this we see that the brittle zones are located 3.5 and 0.5 mm from the fusion boundary, respectively. A comparison with the procedure test results in Table 7.2 shows that the measured CVN toughness after welding at these locations is slightly higher than that inferred from the weld thermal simulation experiments. This observation is not surprising, considering the fact the CVN specimens extracted from the procedure test weld, in practice, include a wide spectrum of thermal regions which have undergone highly different temperature-time programmes, whereas the microstructure within the thermally cycled CVN specimens is more homogeneous due to a similar temperature-time pattern across the whole gauge length (see Fig. 7.31). Hence, weld thermal simulation cannot replace procedure testing carried out on real welds. Nevertheless, it is a useful method of evaluating the microstructural stability and mechanical response of materials to reheating, as experienced in welding. 7.2.3 Hydrogen cracking Hydrogen embrittlement as a problem is mainly associated with ferritic steels and the risk of crack initiation in the grain coarsened HAZ following welding.5758 As shown in Fig. 7.32, these cracks are usually situated at weld toes, weld root, or in an underbead position. Occationally, hydrogen cracks can also develop in the weld metal. A characteristic feature of hydrogen-induced cracking is that the process is time-dependent, i.e. the crack may first appear after several minutes or hours from the time of arc extinction. Consequently, the phenomenon is also referred to delayed cracking or cold cracking in the scientific literature. 7.2.3.1 Mechanisms of hydrogen cracking Hydrogen embrittlement in steels in characterised by:59'60 (i)

The crystal structure dependence Hydrogen embrittlement is mainly associated with materials which exhibit a bcc or a bet crystal structure, i.e. ferritic and martensitic steels. Austenitic stainless steels and aluminium alloys with a fee crystal structure are usually not sensitive to hydrogen.

(ii)

The microstructure dependence A martensitic steel is generally more prone to hydrogen cracking than a ferritic steel, but a martensitic microstructure is not a requirement for crack initiation.

8 Exercise Problems with Solutions

8.1 Introduction This chapter contains a collection of different exercise problems which the author has adopted in his welding metallurgy course for graduate (mature) students. 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.

8.2 Exercise Problem I: Welding of Low Alloy Steels Problem description Consider gas metal arc (GMA) welding of low allow steels under the following conditions: (i) (ii) (iii) (iv)

Tack welding of a T-joint (Fig. 8.1) Root pass deposition in a single V-groove (Fig. 8.2) Root pass deposition in a X-groove (Fig. 8.3) Deposition of cap layer during multipass welding (Fig. 8.4)

The materials to be welded are a C-Mn steel and a Nb-microalloyed low carbon steel with chemical compositions and properties as listed in Tables 8.1 and 8.2. Details of welding parameters and operational conditions are given in Table 8.3 and 8.4, respectively. Table 8.1 Exercise problem I: Base plate chemical compositions (in wt%). Steel C-Mn

1

LC-Nb 1

1

C

Si

Mn

P

S

Nb

Al

0.20

0.35

1.46

0.003

0.002

-

0.037

0.08

0.26

1.44

0.003

0.003

0.020

0.025

Ti: -0.008, N: 0.0027, Ca: 0.0040, B: 0.0002.

Table 8.2 Exercise problem I: Mechanical properties of base materials. Steel

1

Rp02 (MPa)

I

Rm (MPa)

I

El. (%)

I

CVN - 4 0 (J)

C-Mn

328

525

33

150

LC-Nb

430

525

32

225

Table 8.3 Exercise problem I: Welding parameters. Parameter

/ (A)

U (V)

v (mm s"1)

Value

150

21

4

f

The arc efficiency factor may be taken equal to 0.85 (see Table 1.3). No preheating is applied (T0 = 20 0C).

Table 8.4 Exercise problem I: Operational conditions and filler wire characteristics K Shielding gas:

Pure CO2

Gas flow rate:

15 Nl per min

Wire diameter:

1.0 mm

Wire feed rate:

6.0 m per min

Wire composition:

C: 0.1 wt%, Si: 1.0 wt%, Mn: 1.7 wt%

Weld metal* composition:

C: 0.09 wt%, Si: 0.7 wt%, Mn: 1.2 wt%

Weld metal* properties:

Rp02: 460 MPa, Rm: 560 MPa, El.: 26%, CVN _40: 50 J

f

Data compiled from dedicatedfillerwire catalogues and welding manuals. * Values refer to all weld metal deposit.

Fig. 8.1. Tack welding of a T-joint.

Fig. 8.2. Root pass deposition in a single V-groove.

Fig. 8.3. Root pass deposition in a X-groove.

Fig. 8.4. Deposition of cap layer during multipass welding.

Analysis: The students should work in groups (3 to 4 persons) where each group select a specific combination of base material and welding conditions (e.g. deposition of a cap layer on the top of a thick multipass C-Mn steel weld). The problem here is to evaluate the response of the base material to heat released by the welding arc. The analysis should be quantitative in nature and based on sound physical principles. The following points shall be considered: (a) Select an appropriate heat flow model for the system under consideration. (b) Estimate the minimum bead length which is required to achieve pseudo-steady state (i.e. a temperature field that does not vary with position when observed from a point located in the heat source). (c) Estimate the value of the deposition coefficient kx (in gA " 1 S" 1 ), the weld cross section areas D and B (in mm2), and the mixing ratio DI(B + D) during welding. (d) Estimate the weld metal chemical composition. Calculate then the following quantities: - Total loss of Si and Mn in the arc column - Total oxygen pick-up in the weld pool - Residual oxygen level and total amount of oxygen rejected from the weld pool during deoxidation - Total amount of slag formed during welding (in g per 100 gram weld metal) (e) Carry out a total oxygen balance for the system, and estimate the resulting CO content in the welding exhaust gas. (f) Estimate the chemical composition, volume fraction, and mean size (diameter) of the

oxide inclusions which form in the cold part of the weld pool. Calculate then the following inclusion characteristics: -

Number of particles per unit volume Number of particles per unit area Total surface area of particles per unit volume Mean particle centre to centre volume spacing

(g) Estimate the weld metal solidification mode and the resulting columnar grain morphology. Indicate also the type of substructure which form at different positions from the weld centre line. (h) Evaluate the thermal stability of the base metal grain boundary pinning precipitates. At which temperature will these precipitates dissolve? (i) Calculate the austenite grain size profile across the HAZ. Estimate also the size of the columnar austenite grains in the weld metal. (j) Estimate the primary reaction products which form in the weld metal and the HAZ after the austenite to ferrite transformation. (k) Estimate the maximum hardness in the HAZ after welding. Use this information to evaluate the risk of hydrogen cracking and H2S stress corrosion cracking during service. (1) Estimate the CVN toughness both in the weld metal and the HAZ after welding. (m) Based on the results obtained explain why the carbon content of modern structural steels has been gradually lowered to values below 0.1 wt% in step with the progress in steel manufacturing technology. Solution: In all cases we can use stringer bead deposition on thick plates as a model system. It follows from the analysis in Section 1.10.7 (Chapter 1) that the pertinent difference in the effective heat diffusion area between a bead-on-plate weld and a groove weld may conveniently be accounted for by introducing a correction factor/, which depends on the geometry of the groove (see Fig. 1.68). Thus, in the general case the net (effective) power of the heat source can be written as:

In the following, we shall only consider deposition of a cap layer on a thick plate where / = 1, but the analysis can readily be applied to other combinations of steels and welding conditions as well (e.g./< 1). In the former case, we get:

Table 1.1 (Chapter 1) contains relevant input data for the steel thermal properties. (a) The problem of interest is whether we must use the general (but complex) Rosenthal

thick plate solution (equation (1-45)) or can adopt the simplified solution for a fast moving high power source (equation (1-73)). Fig 1.24 provides a basis for such an evaluation. The most critical position will be the fusion line. If we neglect the latent heat of melting, the QJn3 ratio at the melting point becomes:

Readings from Fig. 1.24 suggest that the error introduced by neglecting the contribution from heat flow in the welding direction is sufficiently small that it can be disregarded in the calculations of the HAZ thermal programme. This means that equation (1-73) can be used in replacement of equation (1-45) if that is desirable. (b) The duration of the transient heating period depends on the actual point of observation (i.e. the distance from the heat source). If we, as an illustration of principles, would like to apply the pseudo-steady state solution down to a peak temperature of, say, 7000C, the corresponding nJQ ratio at that temperature becomes:

From Fig. 1.21 we see that this ratio corresponds to a dimensionless radius vector a3m of about 5. The duration of the transient heating period may now be read from Fig. 1.18. A crude extrapolation gives:

from which

The minimum bead length is thus 25 mm, which is surprisingly short, (c) The value of the deposition coefficient may be estimated from the data in Table 8.4.

This value corresponds to a kVp ratio of about 0.65 mm 3A 1 S \ which is in excellent agreement with the data quoted in Table 1.7. The area D of deposited metal thus becomes (see equation (1-120)):

The corresponding area of fused parent metal is most conveniently read from Fig. 1.21. Taking the n3/Q ratio at the melting point equal to (1/0.22) ~ 4.5, we obtain:

from which

The mixing ratio is thus:

This value is somewhat lower than the expected mixing ratio, which for low heat input welding is close to 0.67. (d) The composition data in Table 8.4 refer to all weld metal deposit. Since the dilution with respect to the base material in this case is small, the weld metal composition would be expected to be close to that given in Table 8.4. An estimate of the total burn-off of alloying elements during welding can be obtained by considering the difference in chemical composition between the filler wire and the weld metal. In the present case we get:

Loss of silicon As shown in Section 2.10.1.3 (Chapter 2), the silicon loss can partly be ascribed to SiO(g) formation in the arc column (with consequent fume formation), and partly to reactions with oxygen in the weld pool during the deoxidation stage (with consequent silicate slag formation). The former loss can be estimated from the fume formation data presented in Table 2.6. Taking the fume formation rate (FFF) of silicon equal to 63 mg min"1, the total loss of silicon in the arc column amounts to:

The corresponding oxidation loss of silicon in the weld pool is thus:

Loss of manganese As shown in Section 2.10.1.4 (Chapter 2), manganese is partly lost in the arc column due evaporation and partly in the weld pool due to deoxidation reactions. Taking the fume formation rate of manganese equal to 14 mg min"1 (from Table 2.6), the total loss of Mn in the arc column amounts to:

The corresponding oxidation loss of manganese in the weld pool is thus:

Oxygen pick-up in the weld pool When the oxidation losses of silicon and manganese in the weld pool are known, it is possible to calculate the total oxygen pick-up in the hot spot of the pool immediately beneath the root of the arc, according to the procedure outlined in Section 2.10.1.5 (Chapter 2). However, first we need to estimate the residual weld metal oxygen content on the basis of the thermodynamic model presented in Fig. 2.56. In the present example, the numerical value of the deoxidation parameter is:

Reading from Fig. 2.56 gives a residual oxygen content of about 0.07 wt%. The total oxygen pick-up in the weld pool is thus:

Rejected oxygen from the weld pool The amount of rejected oxygen is equal to the difference between the total and the residual oxygen level:

From this we see that most of the oxygen which is picked up at elevated temperatures is rejected again during cooling in the weld pool due to deoxidation reactions and subsequent phase separation. Manganese silicate slag formation The weld pool deoxidation reactions give rise to the formation of a top bead slag, as shown in Section 2.10.1.5 (Chapter 2). In the present example the amount of slag per 10Og weld metal is equal to:

A comparison with Fig. 2.35 shows that the calculated weight of slag is in reasonable agreement with experimental observations. (e) The oxygen balance is carried out in accordance with the procedure outlined in Section 2.10.1.7 (Chapter 2). First we need to estimate the total mass of weld metal produced per unit time:

The total CO2 consumption is thus: Oxidation of carbon:

Oxidation of silicon:

Oxidation of manganese:

Increase in the weld metal oxygen content:

The total CO evolution is equal to the sum of these four contributions:

The resulting CO content in the welding exhaust gas is thus:

A comparison with the experimental data in Table 2.2 shows that the calculated CO content is of the expected order of magnitude. (f) The deoxidation model in Section 2.12.4.1 (Chapter 2) can be used to estimate the inclusion composition. From Fig. 2.68 we see that the inclusions are essentially pure manganese silicates with an overall composition close to MnSiO3. When the inclusion composition is known, it is possible to convert the residual weld metal oxygen content into an equivalent inclusion volume fraction according to the procedure outlined in Section 2.12.1.Taking the stoichiometric conversion factor equal to 5.0 X 10~2 for manganese silicate slags, we obtain:

Moreover, we can use equation (2-79) in Section 2.12.2.2 to calculate the mean diameter of the inclusions:

The different inclusion characteristics may now be estimated from equations (2-80) to (2-83): Number of particles per mm3:

Number of particles per mm2:

Total surface area of particles per mm3:

Mean particle centre to centre volume spacing:

A comparison with Table 2.11 shows that the calculated inclusion characteristics are in reasonable agreement with those reported for C-Mn steel weld metals. (g) The characteristic growth pattern of columnar grains in bead-on-plate welds is shown schematically in Fig. 3.33. The first phase to form will be delta ferrite which subsequently decomposes to austenite via a peritectic transformation (see Fig. 3.72). The important question is whether re-nucleation of the grains will occur during solidification. In practice, this depends on the interplay between a number of variables which cannot readily be accounted for in a simplified analysis, including the weld pool geometry, the cooling rate and the nucleation potency of the non-metallic inclusions. Broadly speaking, the energy barrier associated with nucleation of delta ferrite at manganese silicates is rather high (e.g. see Fig. 3.30), which suggests that formation of new grains ahead of the advancing solid/liquid interface is not very likely under the prevailing circumstances. Hence, the columnar grain zone would be expected to extend entirely from the fusion line towards the centre of the weld, as frequently observed in this type of welds. Moreover, Fig. 3.43 provides a basis for estimating the substructure of the weld metal columnar grains. Close to weld centre-line the local crystal growth rate will approach the welding speed (i.e. RL ~ 4 mm s"1). At the same time a simple analytical solution exists for the thermal gradient in the weld pool (equation (3-28)):

From this we see that a cellular-dendritic type of substructure is likely to form within the central parts of the fusion zone, in agreement with general experience (see Fig. 3.36). (h) Fig. 5.25 shows the location of the cap layer. Since the base plate is a Nb-microalloyed steel, the important grain boundary pinning precipitates within the HAZ are either NbC, NbN or a mixture of these. In the former case the equilibrium dissolution temperature may be estimated from the solubility product of the pure binary compounds. From equation (4-4) and Table 4.1, we have:

and

This shows that NbC is thermodynamically more stable than NbN. In practice, the real dissolution temperature may be significantly higher than that predicted from equation (4-4) because of the kinetic superheating (see discussion in Section 4.4, Chapter 4). The grain growth diagram in Fig. 5.21 (a) provides a basis for estimating the effect of heating rate (heat input) on the dissolution kinetics. Taking the ordinate qo /v equal to 2678/4000 = 0.67 kJ mm"1, we obtain:

This corresponds to a kinetic superheating of about 2000C in the case of NbC. In the HAZ on the weld metal side (see Fig. 5.25), oxide inclusions may act as effective grain boundary pinning precipitates. These will be thermodynamically stable up to the melting point of the steel. (i) The austenite grain size profile across the base plate HAZ can be read from Fig. 5.21(a). Taking the ordinate q/v equal to 0.67 kJ mm"1, we see that the maximum austenite grain size at the fusion boundary will exceed 100 /mm because of dissolution of the base metal grain boundary pinning precipitates. In the HAZ on the weld metal side, the situation is different. Here the stable weld metal oxide inclusions will impede austenite grain growth to a much larger extent.The limiting austenite grain size may be calculated from equation (5-21).Taking the Zener coefficient equal to 0.5 for oxide inclusions in steel (Fig. 5.4), we obtain:

Because of the phenomenon of epitaxial grain growth (see Section 3.3, Chapter 3), the initial size of the weld metal delta ferrite/austenite columnar grains would be expected to be comparable to the size of the HAZ austenite grains adjacent to the fusion boundary. Since the latter varies along the periphery of the fusion boundary at the same time as competitive grain growth leads to a general coarsening of the solidification microstructure with increasing distance from the fusion boundary, an average columnar austenite grain size of about 50 /mm seems reasonable under the prevailing circumstances. (j) As an illustration of principles, we shall assume that the CCT diagram in Fig. 6.27(a) provides an adequate description of the base plate transformation behaviour during welding. The cooling time from 800 to 500 0C can be calculated from equation (1-67):

from which

Readings from Fig. 6.27(a) give the following microstructures within the grain coarsened and grain refined region of the HAZ, respectively: Grain coarsened region (T ~ 13500C): Microstructure : 100% lath martensite Transformation start temperature: ~ 470 0C Grain refined region (Tp «10000C): Microstructure : ferrite + pearlite Transformation start temperature: ~ 600 0C It follows that the observed difference in the HAZ transformation behaviour can mainly be attributed to a corresponding difference in the prior austenite grain size, which according to Fig. 5.21(a) is about 50 /im at Tp « 1350 0C and below 10 ^m at Tp « 10000C. In addition, small islands of plate martensite will form within the intercritical (partly transformed) HAZ, where the peak temperature of the thermal cycle has been between Ac1 and Ac3 (see discussion in Section 6.3.8.2, Chapter 6). Just above the Ac1 temperature the volume fraction of the M-A (martensite-austenite) constituent is approximately equal to the base plate pearlite content (Fig. 6.66), which in the present case is about 8 vol%, as judged from the steel carbon content. Considering the weld metal, the situation is different. Here the oxide inclusions will strongly affect the microstructure evolution by promoting intragranular nucleation of acicular ferrite (see discussion in Section 6.3.5, Chapter 6). In practice, the role of inclusions in weld metal transformation kinetics is difficult to assess and hence, we will take a more simplistic (pragmatic) approach to this problem by just comparing the total surface area available for nucleation of ferrite at prior austenite grain boundaries and inclusions, respectively (SJGB) versus SJI)). The following three regions of the weld are considered: As-deposited weld metal:

Reheated weld metal (close to fusion line):

Reheated weld metal (far from fusion line): In this case an estimate will be made for dy = 10 /mi.

From the above calculations it is apparent that the conditions for acicular ferrite formation are particularly favourable within the as-deposited weld metal (Sx(I) > SJGB)), and somewhat less favourable within the high peak temperature region of the weld HAZ (SJGB) > SJI)). In contrast, acicular ferrite would not be expected to form within the low peak temperature region of the HAZ, since nucleation of ferrite at austenite grain boundaries in this case will completely override nucleation at inclusions (SJGB) » SJI)).This is also in agreement with general experience (e.g. see photographs of typical microstructures in Fig. 6.19(c) and (d)). (k) The maximum hardness/strength level within the grain coarsened region of the HAZ can be estimated from the diagrams presented in Section 7.2.2 (Chapter 7) if the steel composition and welding parameters fall within the specified range. Alternatively, we can use Fig. 7.19, which applies to low carbon microalloyed steels. Taking the cooling time from 800 to 500 0C, Ar8/5, equal to 3.3 s, we obtain: HVmax = ~ 380 VPN and Rp02 (max) = ~ 980 MPa In general, a hardness rather than a strength criterion is used as a basis for evaluation of the risk of hydrogen cracking and H2S stress corrosion cracking during service. In the former case an upper limit of about 300 to 325 VPN is incorporated in many welding specifications to avoid problems with hydrogen cracking, but this restriction can be relaxed if specific precautionary actions are taken during the welding operation to reduce the supply of hydrogen as shown in Section 7.2.3 (Chapter 7). Considering the H2S stress corrosion cracking resistance a maximum hardness level of 248 VPN is strictly enforced in many welding specifications, as discussed previously in Section 7.2.4 (Chapter 7). Hence, significant tempering of the martensite would be required if the weldment is going to be used in environments containing sour oil or gas. (1) In general, the toughness requirements vary with the type of application, but for offshore structures a minimum CVN toughness of 35J at — 400C is frequently specified. From the CVN data in Tables 8.2 and 8.4 it apparent that both the base plate and the weld metal meet this requirement. Moreover, auto-tempered low carbon martensite and polygonal ferrite, which form within the grain coarsened and grain refined region of the HAZ, respectively are known to have an adequate cleavage resistance.This means that the intercritical HAZ is the most critical region of the joint when it comes to toughness due to the presence of high carbon plate martensite within the ferrite matrix (see Figs. 6.61 through 6.65 and discussion in Section 7.2.2.3, Chapter 7). In practice, the problem may be solved by applying an appropriate post weld heat treatment (PWHT). (m) Since the properties of martensite depend on the carbon content, C-Mn steel weldments will generally be more prone to hydrogen cracking, H2S stress corrosion cracking and brittle fraction initiation in the HAZ than low carbon microalloyed steel weldments. This explains

why the base plate carbon content has been gradually lowered to values well below 0.1 wt% in step with the progress in steel plate manufacturing technology.

8.3 Exercise Problem II: Welding of Austenitic Stainless Steels Problem

description:

Consider GTA welding of 2 mm thin sheets of AISI 316 austenitic stainless steel with chemical composition as listed in Table 8.5. The base plate has an average grain size of 18 /xm in the fully annealed condition, which conforms to a tensile yield strength of about 300 MPa. The sheets shall be butt welded in one pass, using a simple I-groove with 3 mm root gap. In this case the addition of filler wire is adjusted so that the area of the weld reinforcement amounts to 50% of the groove cross section. Details of welding parameters and operational conditions are given in Table 8.6 and 8.7, respectively. Table 8.5 Exercise problem II: Base plate chemical composition (in wt%). Steel

C

Mn

Cr

Ni

AISI316

0.03

2.0

16

12

Table 8.6 Exercise problem II: Welding parameters*. Parameter Value

/ (A)

U (V)

200

15

+

v (mm s"1) 5 0

The arc efficiency factor may be taken equal to 0.4. No preheating is applied (T0 = 20 C).

Table 8.7 Exercise problem II: Operational conditions and filler wire characteristics1. Shielding gas:

Argon

Wire composition: Weld metal* properties: Data compiled from dedicatedfillerwire catalogues and welding manuals. Values refer to all weld metal deposit.

Analysis: The problem here is to evaluate the response of the base material to welding under the conditions described above. The analysis should be quantitative in nature and based on sound physical principles. The following input data are recommended:

Specific questions: (a) Select an appropriate heat flow model for the system under consideration. (b) Estimate the minimum bead length which is required to achieve pseudo-steady state down to a peak temperature of 1000 0C. (c) Estimate the deposition rate (in gA^s" 1 ), the weld cross section areas D and B (in mm2), and the dilution ratio B/(B + D) during welding. (d) Estimate the weld metal chemical composition for the given combination of base plate, filler wire and dilution ratio. (e) Sketch the contour of the weld pool and the resulting columnar grain morphology in the x-y plane after solidification. Estimate also the weld metal delta ferrite content. (f) Evaluate the risk of solidification cracking during welding. (g) Calculate the austenite grain size profile across the HAZ. Estimate also the size of the columnar grains in the weld metal. (h) Evaluate the risk of chromium carbide formation in the HAZ during welding. (i) Estimate on the basis of the Hall-Petch relation the maximum load bearing capacity of the joint during service. Solution: (a) The problem of interest is whether we must use the general (but complex) Rosenthal thin plate solution (equation (1-81)) or can adopt the simplified solution for a fast moving high power source (equation (1-100)). Fig 1.43 provides a basis for such an evaluation. The most critical position will be the fusion line. If we neglect the latent heat of melting, the BJn^ ratio at the melting point becomes:

Similarly, the dimensionless plate thickness is equal to:

Readings from Fig. 1.43 show that we are outside the validity range of the simplified 1-D model close to the fusion line, but that this solution is a good approximation within the low peak temperature region of the HAZ. Here equation (1-100) may be used in replacement of equation (1-81). (b) The duration of the transient heating period depends on the actual point of observation (i.e. the distance from the heat source). If we would like to apply the pseudo-steady state solution down to a peak temperature of 1000 0C, the corresponding nJ8B ratio becomes:

From Fig. 1.31 we see that this ratio corresponds to a dimensionless radius vector a5m of about 5. The duration of the transient heating period may now be read from Fig. 1.28. A crude extrapolation gives:

from which

(c) First we need to calculate D:

This gives the following deposition rate:

The total area of fused metal can be read from Fig. 1.31. At the melting point the n3/0p8 ratio is close to 2, which gives:

and

This gives:

Note that in these calculations we have assumed that A2 is equal to the sum of (B+D) in order to achieve realistic numbers. (d) The weld metal composition can be calulated from a simple 'rule of mixtures':

By using input data from Tables 8.5 and 8.7, we get:

(e) The bead morphology can be read from Fig. 1.29. Taking the 68In3 ratio at the melting point equal to 0.5, it is easy to verify that the geometry of the weld pool in this case is tearshaped. The columnar grain structure is therefore similar to that shown in Fig. 3.11(b). When the composition is known the weld metal microstructure can be read from Fig. 7.53 by considering the resulting chromium and nickel equivalents:

This gives a delta ferrite content of about 7 vol%. (f) Normally, a minimum delta ferrite content of about 5 to 10 vol% is specified to avoid problems with solidification cracking in the weld metal (see discussion in Section 7.3.4, Chapter 7). This requirement is clearly met under the prevailing circumstances. (g) The HAZ austenite grain size in different positions from the fusion boundary can be read from Fig. 5.30(b). In the present example the net heat input per mm2 of the weld is equal to:

This corresponds to a maximum austenite grain size of about 60/mi close to the fusion boundary, which also is a reasonable estimate of the weld metal columnar grain size. (h) The most critical position is the low peak temperature region of the weld HAZ where Tp is between 800 and 1000 0C, as shown in Section 6.4.2 (Chapter 6). However, it is evident from Fig. 6.69 that the risk of chromium carbide formation in this case is negligible because of the low base plate carbon content. Hence, the corrosion resistance will not be significantly affected by the welding operation. (i) The minimum HAZ strength level may conveniently be calculated from equation (7-21), using input data from Example 7.5 (page 530):

This gives the following strength reduction factor for the joint:

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

description:

Consider G M A welding of 5 mm A A 6082 extrusions with chemical composition as listed in Table 8.8. The base material has a Vickers hardness and tensile yield strength of 110 VPN and 280 MPa, respectively in the T6 temper condition. The extrusions shall be butt welded in one pass, using a simple I-groove with no root gap. Two different filler wires are available, one Al-Si wire and one Al-Mg wire (in the following designated wire I and II, respectively). Details of welding parameters and operational conditions are given in Table 8.9 and 8.10, respectively. Table 8.8 Exercise problem III: Base plate chemical composition (in wt%). Alloy AA 6082

Si

Mg

Mn

Fe

0.98

0.64

0.52

0.19

Table 8.9 Exercise problem III: Welding parameters1. Parameter Value

/(A)

(/(V)

200

28

v (mm s"1) 10 0

|The arc efficiency factor may be taken equal to 0.8. No preheating is applied (T = 20 C).

Table 8.10 Exercise problem III: Operational conditions and filler wire characteristics1. Shielding gas:

Argon

Gasflowrate:

20 Nl per min

Wire diameter:

1.6 mm

Wire feed rate:

5.5 m per min

Wire composition:

Wire I : Al + 5 wt% Si Wire II: Al +5 wt% Mg

Weld metal* properties:

Wire I: Rp02 : 55 MPa, Rn; 165 MPa, El.: 18% Wire II: Rp02 : >130 MPa, Rn;. >280 MPa, El.: >17%, CVN+20: >30 J

Data compiled from dedicated filler wire catalogues and welding manuals. Values refer to all weld metal deposit.

Analysis: The problem here is to evaluate the response of the base material to welding under the conditions described above. The analysis should be quantitative in nature and based on sound physical principles. The following input data are recommended:

Specific questions:

Temperature, 0C

Atomic percent silicon

Weight percent silicon Fig. 8.5. The binary Al-Si phase diagram.

Temperature, 0C

Atomic percent magnesium

Weight percent magnesium Fig. 8.6. The binary Al-Mg phase diagram.

(a) Select an appropriate heat flow model for the system under consideration. (b) Estimate the minimum bead length which is required to achieve pseudo-steady state down to a peak temperature of 200 0C. (c) Estimate the value of the deposition coefficient k' (in gA^s" 1 ), the weld cross section areas B and Z) (in mm2), and the dilution ratio BI(B + D) during welding. (d) Estimate the content of Mg and Si in the weld metal. (e) Sketch the weld metal columnar grain structure and the segregation pattern during solidification. Indicate also the type of substructure which forms at different positions along the periphery of the fusion boundary. Relevant binary phase diagrams are given in Figs. 8.5 and 8.6. (f) Evaluate the risk of solidification cracking during welding. (g) Evaluate the risk of liquation cracking in the HAZ during welding. (h) Sketch the sequence of reactions occurring within the HAZ during welding. Then estimate the following quantities: - The temperature for incipient dissolution of /3". - The total width of the HAZ (referred to the fusion boundary). - The temperature for full dissolution of /3". - The total width of the fully reverted HAZ (referred to the fusion boundary). (i) Estimate for each combination of filler wire and parent material an overall strength reduction factor which determines the load bearing capacity of the joint. (j) Imagine now that the same extrusion instead is used in the fully annealed (O- temper) condition with a Vickers hardness and tensile yield strength of 50 VPN and 100 MPa, respectively. To what extent will the temper condition affect the microstructure and strength evolution during welding? Solution: (a) The problem of interest is whether we must use the general (but complex) Rosenthal thin plate solution (equation (1-81)) or can adopt the simplified solution for a fast moving high power source equation (1-100)). Fig 1.43 provides a basis for such an evaluation. The most critical position will be the fusion line. If we neglect the latent heat of melting, the 6 In3 ratio at the melting point becomes:

Similarly, the dimensionless plate thickness is equal to:

Readings from Fig. 1.43 show that we are outside the validity range of the simplified 1-D solution close to the fusion line, but that equation (1-100) may be used (with some reservations) within the low peak temperature region of the HAZ. (b) The duration of the transient heating period depends on the actual point of observation (i.e. the distance from the heat source). If we would like to apply the pseudo-steady state solution down to a peak temperature of 200 0C, the corresponding n/86p ratio becomes:

From Fig. 1.31 we see that this ratio corresponds to a dimensionless radius vector 130 MPa, Base metal: Rp02 - 100 MPa Strength reduction factor (base metal control): / = 100/100 = 1

Index Index terms

Links

A absorption of elements see hydrogen, nitrogen, oxygen acicular ferrite in low-alloy steels

428

crystallography of

428

nature of

430

nucleation and growth of

432

texture components of

429

acicular ferrite in wrought steels

444

aluminium as alloying element in steel effect on inclusion composition

202

206

effect on solidification microstructure

246

272

effect on weld properties

481

486

solubility product of precipitates

303

aluminium weldments

458

age-hardenable alloys

458

quench sensitivity

459

precipitation conditions during cooling

459

strength recovery during natural ageing

461

subgrain evolution in friction welding

464

characteristics

293

536

536

constitutional liquation in Al-Mg-Si alloys

542

in Al-Si alloys

541

example (7.9) – minimum HAZ strength level

554

example (7.8) – weld metal hot cracking

544

example (7.7) – weld metal solidification cracking

537

example (7.10) – minimum HAZ hardness level

562

HAZ microstructure evolution

547

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595

596

Index terms

Links

aluminium weldments (Continued) constitutive equations

548

during friction welding

555

during fusion welding

547

hot cracking

540

factors affecting

544

solidification cracking

536

strength evolution during welding

547

constitutive equations

548

during friction welding

555

hardness and strength distribution

550

strengthening mechanisms in alloys

547

amplitude of weaving – definition arc atmosphere composition

80 132

see also shielding gases arc efficiency factors

26

definition

26

selected values

27

arc welding

24

definition of processes

24

austenite grain size in low-alloy steels

409

primary precipitation in fusion welds

292

austenite formation in low-alloy steels conditions for austenitic stainless steels

558

449 450 453

see also stainless steel weldments characteristics of

527

chromium carbide formation

456

grain growth diagrams for steel welding

375

weld decay area

456

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

558 560

597

Index terms

Links

Avrami equation in solid state transformations see also solid state transformation and transportation kinetics additivity in

404

exponents in

401

475

B Bain orientation region

436

bainite in low-alloy steels

444

lower

447

upper

444

bead morphology

96

bead penetration

99

deposit and fused parent metal

96

example (1.16) – SA welding of steel

97

example (1.17) – SMAW welding of steel

98

example (1.18) – Jackson equation

99

Bessel functions – modified

46

47

boron in steel effect on transformation behaviour

413

segregation of

294

weld properties

493

bowing of crystal

240

Bramfitt’s planar lattice disregistry model

244

505

see also solidification of welds

C carbon equivalents

496

carbon as alloying element in steel austenitic stainless steels

453

weld deposits

424

carbon-manganese steel weld metals, grain growth in

370

casting, structural zones

221

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

521

49

598

Index terms cell/dendrite alignment angle

Links 249

see also solidification of welds cellular substructure

251

see also solidification of welds chemical reaction model – overall

116

chromium carbide formation in austenitic stainless steels

456

chromium-molybdenum steel welds, grain growth in

372

columnar grains

228

see also solidification of welds columnar to equiaxial transition

268

see also solidification of welds competitive grain growth

234

see also solidification of welds concentration displacements during welding see oxygen, absorption of cooling condition during solidification

221

cooling rate, C.R. thick plate welding

37

thin plate welding

53

cooling time, ∆t8/5 thick plate welding

36

thin plate welding

53

cooling time, t100

103

D Delong diagram

535

delta ferrite, primary precipitation of

290

dendrite arm spacing

261

primary

261

secondary

264

dendrite fragmentation

250

see also solidification of welds

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

292

599

Index terms dendrite substructure

Links 252

see also solidification of welds dendrite tip radius

260

see also solidification of welds deoxidation reactions in weld pools

180

example (2.9) – homogeneous nucleation of MnSiO3

182

growth and separation of oxide inclusions

184

buoyancy (Stokes flotation)

185

fluid flow pattern

186

separation model

188

nucleation model

182

nucleation of inclusions

182

overall deoxidation model

201

deposit – amount of weld metal

96

deposition rate

96

dissociation of gases in arc column

117

distributed heat sources

77

general solution

77

simplified solution (Gaussian heat distribution) simplified solution (planar heat distribution)

112 80

case study (1.2) – surfacing with strip electrodes

87

case study (1.3) – GTA welding with a weaving technique

87

dimensionless operating parameter

82

dimensionless time

82

dimensionless y- and z-coordinates

82

example (1.13) – effect of weaving on temperature distribution

83

implications of model

86

model limitations

86

2-D heat flow model

80

see also heat flow models Dorn parameter

219

501

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

112

600

Index terms

Links

duplex stainless steels

531

HAZ toughness

532

HAZ transformation behaviour

532

E energy barrier to solidification

225

see also solidification of welds enthalpy of reaction

302

definition of

302

values

303

entropy of reaction

302

definition

302

values

303

epitaxial solidification

222

equiaxed dentritic growth

268

equilibrium dissolution temperature of precipitates

303

see also solidification of welds error functions see Gaussian error functions

F fluid flow pattern in weld pools

186

flux basicity index

171

friction welding

18

see also aluminium weldments dimensionless temperature

20

dimensionless time

20

dimensionless x-coordinate

21

example (1.4) – peak temperature distribution

23

heat flow model

18

temperature-time pattern

23

Fritz equation

281

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

228

601

Index terms

Links

fume formation, rate of iron

157

manganese

156

silicon

152

fused parent metal – amount of

98

G gas absorption, kinetics of

120

rate of element absorption

121

thin film model

120

gas desorption, kinetics of

123

rate of element desorption

123

Sievert’s law

124

gas porosity in fusion welds

279

growth and detachment of gas bubbles

281

nucleation of gas bubbles

279

separation of gas bubbles

283

Gaussian error functions, definition

112

Gaussian heat distribution

112

see also distributed heat sources Gibbs-Thomson law

309

Gladman equation

344

grain boundary ferrite

408

crystallography of

408

growth of

422

nucleation of

408

grain detachment

250

see also solidification of welds grain growth computer simulation

337 380

diagrams construction of

360

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

602

Index terms

Links

grain growth (Continued) axes and features of

363

calibration procedures

361

heat flow models

360

for steel welding

360

case studies

364

C-Mn steel weld metals

370

Cr-Mo low alloy steels

372

niobium-microalloyed steels

367

titanium-microalloyed steels

364

type 316 austenitic stainless steels

375

driving pressure for

339

example (5.3) – austenite grain size in niobium-microalloyed steels

358

example (5.2) – austenite grain size in Ti microalloyed steels

354

example (5.1) – limiting austenite grain size in steel weld metals

344

grain boundary mobility

337

drag from impurities

340

drag froma random particle distribution

341

driving pressure for growth

339

grain structures, characteristics

337

growth mechanisms

345

nomenclature

384

normal grain growth

343

size, limiting

343

Griffith’s equation

486

gross heat input – definition growth rate of crystals

37 230

local

234

nominal

230

see also solidification of welds

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

342

494

603

Index terms

Links

H Hall-Petch relation

529

heat flow models distributed heat sources

77

grain growth diagrams

360

instantaneous heat sources local preheating

5 100

medium thick plate solution

59

thermal conditions during interrupted welding

91

thermal conditions during root pass welding

95

thick plate solutions

26

thin plate solutions

45

heat input see heat flow models Hellman and Hillert equation

344

Hollomon-Jaffe parameter

500

hydrogen, absorption of

128

content in welds

132

covered electrodes

134

combined partial pressure of

134

example (2.1) – hydrogen absorption in GTAW

133

example (2.2) – hydrogen absorption in SMAW

136

in gas-shielded welding

131

hydrogen determination

128

implications of Sievert’s law

140

reaction model

130

sources of hydrogen

128

in submerged arc welding

138

effect of water content in flux

138

example (2.3) – hydrogen absorption in SAW

139

hydrogen cracking in low-alloy steel weld metals

509

diffusion in welds

514

diffusivity in steel

514

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

112

604

Index terms

Links

hydrogen cracking in low-alloy steel weld metals (Continued) HAZ cracking resistance

518

mechanisms of

509

solubility in steel

513

hydrogen in multi-run weldments

140

hydrogen in non-ferrous weldments

141

hydrogen sulphide corrosion cracking in low-alloy steel weld metals

524

prediction of

525

threshold stress for

524

hyperbaric welding

176

I implant testing

520

see also hydrogen cracking inclusions in welds – origin

192

constituent elements and phases in inclusions

202

example (2.10) – computation of inclusion volume fraction

194

example (2.12) – computation of total number of constituent phases in inclusions

211

prediction of inclusion composition

204

size distribution of inclusions

195

coarsening mechanism

196

effect of heat input

196

example (2.11) – computation of number density and size distribution of inclusions volume fraction stoichiometric conversion factors

201 193 194

instantaneous heat sources

5

line source

5

plane source

5

point source

5

interface stability

254

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

605

Index terms interfacial energies

Links 242

see also solidification of welds interrupted welding, thermal conditions

91

example (1.14) – repair welding of steel casting

93

heat flow models

93

K Kurdjumow-Sachs orientation relationship

408 444

L latent heat of melting

3

lattice disregistry see Bramfitt’s planar lattice disregistry model local fusion in arc strikes

7

dimensionless operating parameter

7

dimensionless radius vector

7

dimensionless temperature

7

dimensionless time

7

example (1.1) – weld crater formation and cooling conditions

9

heat flow model

7

temperature-time pattern

8

low-alloy steel weldments

477

acicular ferrite in

428

crystallography of

428

nature of

430

nucleation and growth in

432

texture components of

429

austenite formation in

449

conditions for

450

bainite in

444

lower

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

427 448

429

606

Index terms

Links

low-alloy steel weldments (Continued) upper

444

case study (7.1) – weld bead tempering

501

example (7.1) – low-temperature toughness of welds

488

example (7.2) – peak HAZ strength level

496

example (7.3) – location of brittle zones

508

HAZ mechanical properties

494

hardness and strength level

495

tempering

500

toughness

502

hydrogen cracking

509

diffusion in welds

514

diffusivity in steel

514

example (7.4) – hydrogen cracking under hyperbaric welding conditions

521

HAZ cracking resistance

518

implant testing

520

mechanisms of

509

solubility in steel

513

hydrogen sulphide corrosion cracking

524

prediction of

525

threshold stress for

524

martensite in

447

austenite formation, kinetics of

449

lath

447

M-A formation, conditions for

450

plate (twinned)

447

mechanical properties

477

ductile to brittle transition

486

reheating

491

resistance to cleavage fracture

485

resistance to ductile fracture

480

strength level

478

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

607

Index terms

Links

low-alloy steel weldments (Continued) transformation behaviour

290

406

solidification primary precipitation of austenite

292

primary precipitation of delta ferrite

290

solid state acicular ferrite

428

bainite

444

grain boundary ferrite

408

martensite

447

microstructure classification

406

nomenclature for

406

Widmanstatten ferrite

427

Ludwik equation

524

M magnesium in aluminium alloys solubility product of precipitates

303

martensite in low-alloy steels

447

austenite formation, kinetics of

449

lath

447

M-A formation, conditions for

450

plate (twinned)

447

martensitic stainless steels, characteristics of

527

mass transfer in weld pool, overall kinetic model of

124

medium thick plate solution

59

see also heat flow models dimensionless maps for heat flow analysis

61

case study (1.1) – temperature distribution in steel and aluminium weldments

69

construction of maps

61

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

292

608

Index terms

Links

medium thick plate solution (Continued) cooling conditions close to weld centre line

63

example (1.12) – aluminium welding

68

isothermal contours

65

limitation of maps

65

peak temperature distribution

61

retention times at elevated temperatures

63

experimental verification

72

peak temperature and isothermal contours

75

weld cooling programme

72

weld thermal cycles

72

general heat flow model

59

practical implications

75

melting efficiency factor

89

mixing ratio

98

moving heat sources

24

see also heat flow models net arc power, definition

26

niobium-microalloyed steels, grain growth in

367

nitrogen, absorption of

141

content in welds

143

covered electrodes

143

gas-shielded welding

142

nominal composition

147

sources of

142

submerged arc welding

146

example (2.4) – nitrogen content in weld metal deposit

146

N non-isothermal transformations additivity principle and Avrami equation

403 404

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

609

Index terms

Links

non-isothermal transformations (Continued) isokinetic reactions

404

non-additive reactions

405

non-steady heat conduction biaxial conduction

2

triaxial conduction

2

uniaxial conduction

2

nucleation, energy barrier to

225

nucleation, homogeneous

182

219

see also deoxidation reactions in weld pools nucleation, potency of particles

242

see also solidification of welds nucleation, rate of heterogeneous during solidification

248

nucleation in solid state transformation kinetics

389

in C-curve modeling

390

nucleation of gas bubbles in fusion welds

279

nucleation of grain boundary ferrite in low-alloy steels

408

austenite grain size

409

boron alloying

413

factors affecting ferrite grain size

420

solidification-induced segregation

417

O operating parameter, dimensionless point and line heat source models

31

weaving model

82

Ostwald ripening see particle coarsening oxygen, absorption of

148

classification of shielding gases

166

overall oxygen balance

166

content in welds

148

covered electrodes

173

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

272

610

Index terms

Links

oxygen, absorption of (Continued) absorption of carbon and oxygen

176

loss of silicon and manganese

177

the product [%C] [%O]

179

reaction model

174

effects of welding parameters

169

amperage

169

voltage

170

welding speed

170

example (2.8) – oxygen consumption and total CO evolution during GMAW gas arc metal welding

166 148

manganese evaporation

156

example (2.6) – fume formation rate of manganese

157

sampling of elevated concentrations

149

carbon oxidation

149

silicon oxidation

152

example (2.5) – fume formation rate of silicon

156

SiO formation

154

total oxygen absorption

162

transient oxygen concentrations

160

example (2.7) – slag formation in GMAW

164

submerged arc welding

170

concentration displacements

172

flux basicity index

171

total oxygen absorption

173

transient oxygen absorption

172

oxygen, retained in weld metal

190

implications of model

192

thermodynamic model of

190

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

173

611

Index terms

Links

P particle coarsening

314

applications to continuous heating and cooling

314

example (4.4) – coarsening of titanium nitride in steel

315

kinetics

314

particle dissolution

316

analytical solution

316

case study (4.1) – solute distribution across HAZ

330

example (4.5) – isothermal dissolution of NbC in steel

320

example (4.6) – dissolution of NbC within fully transformed HAZ

323

numerical solution

325

application to continuous heating and cooling

329

process diagrams for aluminium butt welds

332

Peclet number for weld pools

186

peritectic solidification in welds

290

see also low alloy steel weldments primary precipitation of γp-phase

290

transformation behaviour

290

precipitate growth mechanisms liquid state

196

solid state

395

diffusion-controlled

397

interface-controlled

396

precipitate stability

301

see also particle coarsening and particle dissolution example (4.1) – equilibrium dissolution temperature of nitride precipitates

304

example (4.2) – equilibrium volume fraction of Mg2Si

307

example (4.3) – metastable β”(Mg2Si) solvus

312

nomenclature

334

solubility product

301

equilibrium dissolution temperature

303

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

612

Index terms

Links

precipitate stability (Continued) stable and metastable solvus boundaries

304

thermodynamic background

301

preheating, local heat flow model

100 100

dimensionless half width of preheated zone

101

dimensionless temperature

101

dimensionless time

101

example (1.19) – cooling conditions during steel welding

102

time constant

101

pseudo-equilibrium, concept of pseudo-steady state temperature distribution, definition

122 24

R reversion see particle dissolution example (1.15) – cooling conditions during root pass welding

95

heat flow model

95

Reynold number definition

187

of gas bubbles

284

of particles

187

root pass welding, thermal conditions in

95

Rosenthal equations see thick and thin plate solutions

S Scheil equation

272

modified

276

original

272

separation of gas bubbles in fusion welds

283

shielding gases see oxygen, hydrogen and nitrogen, absorption of CO-evolution

166

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

613

Index terms Sievert’s law

Links 124

140

silicon in aluminium solubility product of precipitates

303

solid state transformations in welds

387

Al-Mg-Si alloys

458

austenitic stainless steels

453

Avrami equation in, additivity in

404

high strength low-alloy steels

406

kinetics see transformation kinetics nomenclature solid state transformation kinetics

471 387

see also transformation kinetics driving force for

387

non-isothermal transformations

402

nucleation in solids

389

overall

400

precipitates, growth of

395

solidification cracking in weldments aluminium

536

stainless steel

532

solidification microstructures

251

columnar to equiaxed transition

268

dendrite tip radius

260

equiaxed dendritic growth

268

example (3.12) – equiaxed dendritic growth in Al-Si welds

270

example (3.13) – application of Scheil equation

276

interface stability criterion

254

example (3.6) – critical temperature gradient for planar solidification front in Al-Si welds example (3.7) – substructure characteristics of Al-Mg welds primary dendrite arm spacing

256 258 261

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

475

614

Index terms

Links

solidification microstructures (Continued) example (3.8) – effect of heat input on primary dendrite arm spacing in welds

262

example (3.9) – variation of primary dendrite arm spacing across fusion zone secondary dendrite arm spacing example (3.10) – secondary dendrite arm spacing in thick plate GTA Al-Si welds

263 264 266

example (3.11) – secondary dendrite arm spacing in thin plate GTA Al-Si butt welds

267

local solidification time

265

substructure characteristics

251

cellular

251

dendritic

252

solidification of welds

221

columnar grain structures and morphology

228

epitaxial solidification

222

energy barrier to solidification

225

implications of

226

growth rate of columnar grains

230

example (3.1) – nominal crystal growth rate in thin sheet welding of austenitic stainless steels

234

example (3.2) – local dendrite growth rate in single crystal welds

237

local crystal growth rate

234

nominal crystal growth rate

230

renucleation of crystals

242

critical cell-dendrite alignment angle

249

dendrite fragmentation

250

example (3.4) – nucleation potency of TiN with respect to delta ferrite

245

example (3.5) – nucleation potency of γ-Al2O3 with respect to delta ferrite

246

grain detachment

250

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615

Index terms

Links

solidification of welds (Continued) nucleation potency of second phase particles rate of heterogeneous nucleation reorientation of columnar grains

242 247 239

bowing of crystal

240

example (3.3) – bowing by dendritic branching

240

structural zones solubility of gases in liquids and solids

221 125

hydrogen in Al

125

hydrogen in Cu

125

hydrogen in Fe

125

hydrogen in Ni

125

nitrogen in Fe

126

see also gas absorption and gas desorption solubility product

301

equilibrium dissolution temperature

303

stable and metastable solvus boundaries

304

thermodynamic background

301

solute redistribution in welds

272

example (3.14) – formation of hydrogen bubbles in weld pools

282

example (3.15) – separation of hydrogen bubbles in weld pools

284

example (3.16) – solute redistribution during cooling in austenite regime

287

gas porosity

279

homogenisation of microsegregations

286

macrosegregation

277

microsegregation

272

spot welding

10

dimensionless operating parameter

11

dimensionless radius vector

11

dimensionless time

11

example (1.2) – cooling conditions

12

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

513

616

Index terms

Links

spot welding (Continued) heat flow model

11

refined model for

110

temperature-time pattern

12

stainless steel weldments

527

see also austenitic stainless steels austenitic characteristics of

527

chromium carbide formation

456

grain growth diagrams for steel welding

375

example (7.5) – variation in HAZ austenite grain size and strength level

530

example (7.6) – weld metal solidification cracking

533

HAZ corrosion resistance

527

HAZ strength level

529

HAZ toughness

530

solidification cracking

532

weld decay area

456

duplex HAZ toughness

532

HAZ transformation behaviour

532

stereometric relationships (number of particles per unit volume, number of particles per unit area, total surface area per unit volume, and mean particle volume spacing)

201

Stokes law

185

substructure of welds

251

187

see also solidification of welds

T texture in welds solidification

221

solid state

429

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

290

284

617

Index terms

Links

thermal properties of metal and alloys

3

conductivity

3

diffusivity

3

heat content at melting point

3

latent heat of melting

3

melting point

3

volume heat capacity

3

thermit welding

14

dimensionless temperature

16

dimensionless time

16

dimensionless x-coordinate

16

example (1.3) – cooling conditions

16

heat flow model

14

temperature-time pattern

17

thick plate solutions

26

see also heat flow models pseudo-steady state temperature distribution

31

cooling conditions close to weld centre line

36

dimensionless operating parameter

31

dimensionless x-coordinate

31

dimensionless y-coordinate

31

dimensionless z-coordinate

31

distribution of temperatures

31

example (1.5) – duration of transient heating period in aluminium welding

30

example (1.6) – thermal contours

37

example (1.7) – weld geometry

39

isothermal zone widths

32

length of isothermal enclosures

34

simplified solution

41

example (1.8) – retention time in steel welding

44

temperature-time pattern

41

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618

Index terms

Links

thick plate solutions (Continued) 2-D heat flow model volume of isothermal enclosures transient heating period thin plate solutions

41 35 29 45

see also heat flow models example (1.9) – duration of transient heating period in aluminium welding

48

pseudo-steady state temperature distribution

49

cooling conditions close to weld centre line

53

example (1.10) – weld geometry and cooling rate

54

isothermal zone widths

49

length of isothermal enclosures

51

simplified solution

56

example (1.11) – retention time in steel welding

59

1-D heat flow model

56

temperature-time pattern

57

transient heating period

29

titanium as alloying element in steel effect on inclusion composition

203

208

effect on solidification microstructure

244

272

effect on grain growth

354

364

effect on transformation behaviour

435

444

effect on weld properties

488

solubility product of precipitates

303

titanium-microalloyed steels, grain growth in

364

see also low alloy steel weldments transformation kinetics

387

Avrami equation

400

475

additivity in

404

475

exponents in

401

driving force for

387

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

619

Index terms

Links

transformation kinetics (Continued) example (6.1) – C-curve analysis

394

example (6.2) – conditions for ferrite formation within HAZ

410

example (6.3) – volume fraction of grain boundary ferrite in HAZ

412

example (6.4) – ferrite/martensite formation in HAZ

416

example (6.5) – displacement of ferrite C-curve due to segregation

418

example (6.6) – variation in ferrite grain size across HAZ

421

example (6.7) – volume fraction of allotriomorphic ferrite in weld deposit

425

example (6.8) – volume of acicular ferrite plate

440

example (6.9) – conditions for acicular ferrite formation

442

example (6.10) – conditions for chromium carbide formation

456

example (6.11) – conditions for β’(Mg2Si) precipitation

460

example (6.12) – ageing characteristics of aluminium weldments

463

non-isothermal transformations

402

nucleation in solids

389

overall

400

precipitates, growth of

395

type 316 austentitic stainless steels, grain growth in

375

see also stainless steel weldments

V volume of weld metal volume fraction of inclusions

36 193

volume heat capacity

3

W Wagner-Lifshitz equation

196

water content

137

in electrode coating

137

in welding flux

138

see also hydrogen absorption This page has been reformatted by Knovel to provide easier navigation.

314

351

620

Index terms weld pool shape and geometry

Links 228

elliptical weld pool

229

tear-shaped weld pool

229

see also solidification of welds welding processes, definitions

24

see also arc welding processes wetting conditions

222

242

interfacial energies

242

247

wetting angle

225

see also solidification of welds Widmanstätten ferrite in low-alloy steels

427

Z Zener drag, definition of in grain growth

341 341

Zener equation

342

Zener-Hollomon parameter

465

zinc in aluminium solubility product of precipitates

303

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

344

Author Index

A Aaron, H.B. 320, 326, 398-9 Aaronson, H.I. 408, 429 Abson, DJ. 407, 428, 440, 477-8, 485,493, 504 Adams, CM. 26 Adrian, H. 301,303 Agren, J. 320-1,326 Akselsen, O.M. 97, 345, 347, 349, 367,406,414-15,419,444,446, 448-54, 481, 484, 488-90, 4956, 499, 502-7, 525 Alberry, RJ. 374, 500, 502 Alcock, CB. 159 AIi, A. 427-8 American Society for Testing Materials (ASTM) 364 Andersen, I. 483 Anderson, M.P. 380 Anderson, RD. 3 Ankem, S. 343,351 Apold,A. 174-5 Araki, T. 505-6 Ardeil, AJ. 494 Ashby, M.F. 26, 201, 314, 318, 329, 360, 363-4, 375, 377-8, 459, 461,464 Asthana, R. 326 Atlas of isothermal transformation and cooling transformation diagrams 403 Avrami, M. 403, 422

B Babu, S.S. 210,408,443-4 Bach, H. 138 Bain, E.C 408, 427, 436 Bakes, R.G. 15 Baldwin, W.M. 509,511 Balliger, N.K. 452 Bannister, S.R. 441,443 Barbara, FJ. 435-6, 441-4 Barin, I. 154 Barrie, G.S. 441,443 Barritte, G.S. 434-6,441 Baskes, M.I. 277-8 Beachem,CD. 512 Beaven, RA. 440 Bell, H.B. 171,204-5 Bentley, K.R 15

Berge, J.O. 229 Bernstein, LM. 512 Betzold,J. 413 Bhadeshia, H.K.D.H. 147, 206, 292, 408-9, 413, 422-9, 431, 4 3 3 ^ , 436,441,443-4 Bhatti,A.R. 208-10 Biloni, H. 229 Bjornbakk, B. 486,491 Blander, M. 171,173 Boiling, G.F. 290 Bonnet, C 435, 440 Bradstreet, BJ. 186 Bramfitt, B.L. 244 Bratland, D.H. 459-62, 556-8, 562 British Iron and Steels Research Association 3 Brody, H.D. 272, 276 Brooks, J.A. 277-8, 533 Brown, A.M. 345 Brown, LT. 509, 511 Brown, L.C. 314 Burck, R 289 Burgardt, R 229

C Cahn, J.W. 337, 340-1, 345 Cai, X.-L. 450 Cameron, T.B. 413 Camping, M. 556-8, 562 Capes, J.F. 251,292-3,412 Carslaw, H.S. 2, 4 Chai,CS. 171 Challenger, K.D. 434, 480 Chan, J.W. 403 Charpentier, F.R 435, 440 Chen, J.H. 505-6 Chew, B. 132, 135 Chipman, J. 414 Choi, H.S. 450 Christensen, N. 24, 26-7, 31-2, 80, 88,90-1,97,100, 116, 125, 132, 143,148-50,153,155,158,162, 170-1, 173-4, 176-9, 181-2, 186,189,193,207,345,347,349, 367,500,502,515-17,520-2 Christian, J.W. 329, 400-1, 403-4, 429,431 Cisse, J. 290 Claes, J. 180

Cochrane, R.C. 292-3, 407, 428 Coe,F.R. 128-9,509-10,515 Coleman, M.C 259, 263-4 Collins, F.R. 537 Corbett, J.M. 203, 428 Corderoy, DJ.H. 151, 155, 160-1 Cotton, H J.U. 496 Cottrell, CL.M. 496 Crafts, W. 190 Craig, I. 171 Cross, CE. 251,259,292-3,412,538 Crossland, B. 556 D Dallam, CM. 441 D'annessa, A.T. 280 Das. G. 452 Dauby, P. 180 David, S. A. 96,99,105,210,222,228, 236, 239-41, 250, 260, 272, 278, 290,478 Davis, GJ. 221, 240, 247, 250, 278, 279,292,478 Davis, V. deL. 162 DeArdo, AJ. 290 Deb, P. 434, 480 DebRoy,T.210 Delong,WT.533 Demarest, V. A. 449-50 Devillers, L. 435,440,480, 482 Devletian,J.H.279,285,413 Dieter, G.E. 482,486, 524-5, 529 Distin, PA. 157 Doherty,R.D.301,309,396 Dolby, R.E. 407,444 Dons, A.L. 438,459, 541 Dorn, XE. 501-2 Dowling, J.M. 203,428 Dube, CA. 408 Dudas, J.H. 537 Dumolt, S.D. 547 E Eagar, T.W. 26, 96, 99, 105, 171-2, 174,228 Easterling, K.E. 26, 226, 247, 301, 303, 309, 314, 318, 345, 360, 363-4, 367, 375, 377-8, 380, 389, 392, 403, 408, 427, 429, 435-6, 441-4, 448, 500, 502

Ebeling, R. 201 Edmonds, D.V. 409 Edwards, G.R. 227,259,422-3,425, 428,441 Eickhorn,F. 187-8 Elliott, J.F. 151, 162, 174-5, 179, 182, 184, 191 Engel,A. 187-8 Enjo, T. 547 Es-Souni, M. 440 European Recommendations for Aluminium Alloy Structures 552 Evans, G.M. 137-8, 192-3, 203, 420-1,435,440

F Fainstein, D. 320, 398-9 Farrar, R.A. 435, 441, 443,480 Fast, J.D. 513 Ferrar, R.A. 428,435,444,478,485, 504 Fine, M.E. 389, 403 Fischer, W. A. 162 Fisher, DJ. 221, 234, 242, 251, 259, 261,265-6,270,274 Fleck, N.A. 422-3, 428, 441 Flemings, M.C. 221, 234, 242, 265, 272,275-6 Fortes, M.A. 374-5, 380-1 Fountain, R.W. 414 Fradkov, V.E. 380 Franklin, A.G. 195,208 Fredriksson, H. 290 Frost, HJ. 380 Fruehan, RJ. 156 Fujibayashi, K. 146

G Garcia, C.I. 290 Garland, J. 505 Garland, J.G. 221,240,247,250,278, 279, 292-3, 478 Garret-Reed, AJ. 450 Gergely, M. 501-2 Giovanola, B. 260 Gittos, N.F. 544-5 Gjermundsen, K. 162, 516 Gjestland, H. 541 Gladman, T. 343-5, 452, 479 Gleiser,M. 151,162,174-5,179,191 Goldak,J.A. 515 Goolsby, R.D. 306 Greenwood, J.A. 15 Grest, G.S. 380 Gretoft, B. 147, 422-8 Grevillius, N.F. 182, 185, 188

Grewal, G. 343,351 Griffiths, E. 3,4 Grong, 0 , 26, 61, 73-5, 77, 80, 88, 90-2,116, 149-50,153,155,158, 161, 163-6, 170, 174, 176-9, 181-2, 185-6, 189, 192-204, 206-7, 209-11, 227, 247-8, 250-4, 256, 290, 292-4, 314, 327-30,345-7,349,355,360,364, 367-8, 371-2, 406, 412-15, 419, 422-3, 425, 428, 430-2, 435-6, 438, 440-1, 444, 446-54, 458-62, 464, 465-6, 477-8, 480-1, 484-6, 488-91, 493, 496, 502-7, 547-9, 551-8,560-3 Gunleiksrud, A. 503 Guo, Z.H. 405,420-1

H Habrekke, T. 229 Halmoy,E. 151 Hannertz, N.E. 507 Harris, D.R. 414 Harrison, P.L. 428, 435, 444, 478, 485, 504 Hatch, J.E. 3, 458, 547 Hawkins, D.N. 208-10, 435, 440 Hazzledine, P.M. 342-3 Heckel, R.W. 326 Hehemann, R.F. 429,452 Heile, R.F. 154, 156-7, 169 Heintze, G.N. 244, 247 Heiple, CR. 229 Hellman, P. 339, 343-5 Hemmer,H. 371-2 Hilbert, M. 339, 343-5 Hill,D.C. 154, 156-7, 169 Hillert, M. 290 Hilty, D.C. 190 Hjelen, J. 195, 292, 430-3, 438 Hocking, L.M. 196 Hollomon, J.H. 465, 500 H6llrigl-Rosta,F.413 Homma, H. 203, 444-5, 504-5 Hondros,E.D. 414 Honeycombe, R.W.K. 406,408,420, 429, 431, 444, 447-8, 453, 486 Horii,Y. 187-8 Houghton, D.C. 303, 323 Howden, D.G. 141 Howell, PR. 434-6, 441 Hu, H. 337-8, 342-3, 345,430 Hultgren, R. 3 Hunderi, O. 337, 341-2, 380

I Ibarra, S. 497 Indacochea, J.E. 171,173 International Institute of Welding 129, 152 Ion, J.C. 314, 318, 360, 3 6 3 ^ , 368 Ivanchev, I. 204-5

J Jackobs, F.A. 418 Jackson, CE. 89, 99, 100 Jaeger, J.C. 2, 4 Jaffe, L.D. 500 Janaf, ?. 154 Jelmorini, G. 156 Jonas, JJ. 464 Jones, W.K.C 374 Jordan, M.F. 143, 145, 259, 263-4 Joshi, Y. 96, 99, 105 Just, E. 413

K Kaplan, D. 435, 440, 480, 482 Kasuya, T. 496 Kato, M. 233 Kawasaki, K. 380 Keene, BJ. 96, 99, 105,228 Kelly, A. 548 Kelly, K.K. 3 Kern, A. 380 Kerr, H.W. 203, 247, 273, 290, 428 Kiessling, R. 202^4 Kihara,H. 131, 133, 134 Kikuchi, T. 1 4 2 ^ Kikuta, Y. 505-6 Kim, B.C. 444 Kim, LS. 450 Kim, NJ. 444,451,505 Kim, YG. 451 Kinsman, K.R. 429, 452 Kirkwood, RR. 292-3 Kluken, A.O. 182, 186, 194-204, 206,209-11,247-8,250-4,256, 290, 292-4, 371-2, 430-3, 4356,438,440,446-7,479-80,484, 486,491,493,497 Knacke, O. 154 Knagenhjem, H.O. 229 Knott, J.F. 486 Kobayashi, T. 1 4 2 ^ Kotler, G.R. 320, 326, 398-9 Kou, S. 27, 75-6, 96, 99, 105, 228, 250, 264-5, 272, 377, 453, 455, 458 Krauklis, P. 435-6, 441-4 Kraus, H.G. 228

Krauss, G. 418 Kubaschewski, O. 159 Kuroda, T. 547 Kurz, W. 221, 234, 242, 251, 259, 260-1,265-6,270,274 Kuwabara, M. 146 Kuwana, T. 142-4 Kvaale, FE. 414-15, 419, 504

L Lancaster, J.F. 118, 120, 162, 187 Lanzillotto, C.A.N. 452, 505 Le, Y. 27, 75-6, 265 Lee, D.Y. 444 Lee, J.-L. 504 Lei, T.C. 505 Li, W.B. 345, 367 Lifshitz, J.M. 314, 351 Lindborg,U. 170, 182-3, 185 Liu, J.Z. 505 Liu, S. 251, 292-3,412,422-3,428, 435-6,441,497 Liu, Y. 339 Loberg, B. 303 Lohne, O. 380,459,541 Long, CJ. 533, 535 Lucke,K. 337, 340-1,345 Lutony, MJ. 380

M Maitrepierre, Ph. 414 Marandet, B. 435, 440, 480, 482 Marder,A.R.451 Marthinsen, K. 380 Martins, G.P. 182, 185-6, 192-3 Martukanitz, R.P. 459 Matlock, D.K. 193, 195, 201, 413, 422-3, 428, 432, 435, 440-1, 477-8, 480, 485, 488, 491, 493, 504 Matsuda, F. 131, 133, 134, 233, 271 Matsuda, S. 203, 208, 319, 444-5, 504-5 Matsuda, Y. 505-6 Matsunawa, A. 96, 99, 105 Mazzolani, F.M. 458 McKnowlson, P 15 McMahon, CJ. 418 McPherson, R. 244, 247 McQueen, HJ. 464 McRobie, D.E. 486 Mehl, R.F. 408, 436-7 Metals Handbook 3, 545 Midling, O.T. 465-6, 556-8, 560-3 Miller, R.L. 449-50 Mills, A.R. 435, 440

Mills, K.C. 96, 99,105,228 Milner, D.R. 141 Miranda, R.M. 374-5 Mitra, U. 171-2 Mizuno, M. 284 Moisio, T. 290 Mondolfo, L.F. 2A2-A Mori, N. 187-8 Morigaki, 0.146 Morral, J.E. 413 Mossinger, R. 554 Mundra, K. 210 Munitz, A. 267 Murray, J.L. 203 Muzzolani, F.M. 547,550,552 Myers, RS. 26 Myhr, O.R. 26, 61, 73-5, 77, 314, 327-30, 360, 458-62, 464, 496, 547-9,550-5 N Naess, OJ. 503 Nagai, T. 380 Nakagawa,H. 131, 133, 134 Nakata, K. 271 Nes,E. 337, 341-2, 380 Nicholson, R.B. 548 Niles, R.W. 89 Nilles,P. 180 Nordgren, A. 303 North, T.H. 171 Nowicki,A. 171 Nylund, H.K. 438 O O'Brien, J.E. 143, 145 Odland, PT. 480 Ohkita, S. 203, 444-5, 504-5 Ohno, S. 143 Ohshita, S. 103, 104,496,515 Ohta, S. 380 Okumura, M. 103, 104 Okumura, N. 208, 319 Olsen, K. 500, 502 Olson, D.L. 171,173-4,176-9,1812, 185-6, 192-3, 422-3, 428, 436,441,480,497,500,502 Onsoien, M.I. 479, 448-9, 495-6, 525 Oreper, G.M. 96, 99, 105, 228 Oriani, R.A. 514 Orr, R.L. 3 Ostrom, G. 533 0verlie, H.G. 541 Owen, W.S. 450 Ozturk,B. 156

P Paauw, AJ. 446, 503 Pabi, S.K. 326 Pakrasi, S. 413 Pan, Y-T. 504 Pande, C S . 339 Pardo, E. 247, 273 Pargeter, RJ. 428, 440, 477-8, 485, 493, 504 Patterson, B.R. 339 Pepe,JJ. 541 Petch,NJ. 512 Petty-Galis, J.L. 306 Phillip, R.H. 444 Phillips, H.W.L. 543 Pickering, RB. 301, 303, 452, 479, 505 Pitsch, W. 436-7 Plockinger, E. 186 Porter, D.A. 247,309,389,392,403, 408,413,427,429,435,448 Pottore,N.S.290 Priestner, R. 451 Pugin, A.I. 556-7

R Ramachandran, S. 190-1, 204 Ramakrishna, V. 151, 162, 174-5, 179, 191 Ramberg, M. 450-1, 505-6 Ramsay, CW. 480 Rappaz, M. 236, 239, 241, 260 Rath, B.B. 337-8, 342-3, 345 Ravi Vishnu, P. 500, 502 Reif, W. 380 Reiso, O. 541-3 Reti,T. 501-2 Ribes, A. 435, 440, 480, 482 Riboud, PV. 480, 482 Ribound, PV. (Riboud ?) 435, 440 Ricks, R.A. 434-5, 436, 441 Ringer, S.P. 345, 367 Rollett, A.D. 380 Roper, J.R. 229 Rorvik, G. 247-8, 250-4, 256, 2924, 430, 446-9, 495-6, 499,503, 507, 525 Rose, R. 516 Rosenthal, D. 26, 28, 31, 33, 38, 41, 48, 51, 56, 59-61, 76, 98, 133, 360 Roux, R. 140 Rykalin, N.N. 18, 21, 26, 41, 45, 56, 93,95, 556-7 Ryum, N. 326,337,341-2,345,347, 349,367,380,382,390,396,403, 541-3

S Saetre, T.O. 380, 382 Saggese, ME. 208-10, 435,440 Sagmo, G. 97 Saito, S. 103, 104 Sakaguchi, A. 284 Savage, W.F. 541 Schaeffler, A.L. 533 Scheil, E. 403 Schriever, U. 380 Schumacher, J.E 162 Schwan,M.21,25 Scott, MH. 544-5 Seah,MR414 Seay, E.B. 96, 99, 105 Senda, T. 233 Shackleton, D.N. 166-7 Shaller,F.W.509,512 Shen, H.P. 505 Shen,X.P.451 Sherby, O.D. 501-2 Shercliff, H.R. 314,329,459-62,464 Shinozaki, K. 131, 133, 134 Siewert, T.A. 182, 185-6, 192-3, 227,425,428 Sigworth, G.K. 162 Simonsen, T. 520-2 Sims, CE. 512 Skaland, T. 346 Skjolberg, E.M. 140-1 Slyozov,V.V. 314,351 Smith, A. A. 166-7, 169, 170 Soares, A. 380-1 Solberg, J.K. 446, 450-4, 504-6 Sommerville, LD. 204-5 Speich, G.R. 449-50 Srolovitz, DJ. 380 Staley, J.T. 394-5, 459 Steidl, G. 554 Steigerwald,E.A.509,512 Stjerndahl, J. 290 Stoneham, A.M. 414 Strangwood, M. 428-9, 431, 444 Strid, J. 303, 542-3 Stuwe,H. 337, 340-1,345 Sugden, A.A.B. 292,431 Suutala, N. 290 Suzuki, H. 406, 444, 477, 496, 509, 515,520 Suzuki, S. 303, 323 Svensson, L.E. 147, 206, 413, 4228, 431, 4 3 3 ^ , 441, 444, 536 Szekely, J. 96,99,105,120,162,183, 187,228,281,284 Szewezyk, A.F. 505 Szumachowski, E. 533

T Takalo,T.290 Tamehiro, H. 496 Tamura, 1.405,420-1 Tanigaki, T. 146 Tanzilli, R.A. 326 Tardy, P. 501-2 Tensi, H.M. 21,25 Thaulow, C. 503 Themelis, NJ. 120,162,183,187,281, 284 Therrien,A.E.434,480 Thewlis, G. 203,435,440-1 Thivellier, D. 414 Thomas, G. 505 Thompson, A.W. 480,512 Thompson, CV. 380 Tichelaar, G.W. 156 Tjotta, S. 459,460 Tomii,Y.284 Torsell, K. 182-3,185 Tricot, R. 414 Trivedi, R. 260, 400,427 Troiano,A.R.509,512 Tsai,N.S.26 Tsukamoto, K. 271 Tundal, UH. 326 Turkdogan, E.T. 126, 182, 184-6, 191-2,195-6,207,214 Turpin, M.L. 182,184

U Uda, M. 143 Udler, D.G. 380 UIe, R.L. 96, 99, 105 Umemoto, M. 405, 420-1 Underwood, E.E. 201, 338 Unstinovshchikov, J.I. 494

V Van Den Heuvel, G J P M . 156 Van Stone, R.H. 480 Vander Voort, G.F. 394, 403 Vandermeer, R.A. 341 Vasil'eva, VA. 556-7 Verhoeven, J.D. 286, 429, 431, 433, 448-9 Villafuerte, XC 247,273 Vitek, J.M. 96,99,105,210,222,228, 240,250,272,278,478

W Wagner, C 201, 314, 351 Wahlster, M. 186 Walsh, R. A. 190-1,204 Walton, D.T. 380 Wang, YH. 96, 99, 105, 228 Weatherly, G.C. 303, 323 Welding Handbook 24 Welz, W. 21,25 Whelan,MJ. 319, 356 Whiteman, J.A. 208-10, 435, 440 Widgery, DJ. 480-1 Willgoss, R.A. 132 Williams, J.C 533 Williams, TM. 414 Wolstenholme, D.A. 174 Woods, WE. 279, 285 Worner, CH. 342-3 Wriedt, H.A. 203

Y Yamamoto, K. 203, 444-5, 504-5 Yang, J.R. 428-9 Yi, JJ. 450 Yoneda, M. 505-6 Yurioka, N. 103, 104,496, 509,515, 520

Z Zacharia, T. 96, 99, 105, 228 Zapffe,CA.512 Zener, C 341-2,344,465 Zhang, C 515 Zhang, Z. 441,443