metallurgical modelling of welding 2nd edition (1997)

MetallurgicalModellingof Welding

SECOND EDITION

0YSTEIN GRONG

Norwegian University ofScience and Technology,

Department of Metallurgy,N-7034 Trondheim, Norway

MATERIALS MODELLING SERIES

Editor: H. K. D. H. BhadeshiaThe University of Cambridge

Department of Materials Scienceand Metallurgy

T H E INSTITUTE OF MATERIALS

Originally typeset byPicA Publishing Services

Additional typesetting and corrections byFakenham Photosetting Ltd

Printed and bound in the UK atThe University Press, Cambridge

Book 677First published in 1997 byThe Institute of Materials1 Carlton House Terrace

London SWlY 5DB

First edition (Book 557)Published in 1994

The Institute of Materials 1997All rights reserved

ISBNl 86125 036 3

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 in-cluded a collection of different exercise problems which have been used in the training of stu-dents at NTNU. They illustrate how the models described in the previous chapters can be usedto solve practical problems of more interdisciplinary nature. Each of them contains a 'prob-lem description' and some background information on materials and welding conditions. Theexercises are designed to illuminate the microstructural connections throughout the weldthermal cycle and show how the properties achieved depend on the operating conditions ap-plied. Solutions to the problems are also presented. These are not complete or exhaustive, butare 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 weldingmetallurgy to graduate students, investigators and engineers who already have a good back-ground in physical metallurgy and materials science. However, in contrast to previous text-books covering the same field, the present book takes a more direct theoretical approach towelding metallurgy based on a synthesis of knowledge from diverse disciplines. The motiva-tion for this work has largely been provided by the need for improved physical models forprocess optimalisation and microstructure control in the light of the recent advances that havetaken place within the field of materials processing and alloy design.

The present textbook describes a novel approach to the modelling of dynamic processes inwelding metallurgy, not previously dealt with. In particular, attempts have been made to ra-tionalise chemical, structural and mechanical changes in weldments in terms of models basedon well established concepts from ladle refining, casting, rolling and heat treatment of steelsand aluminium alloys. The judicious construction of the constitutive equations makes full useof both dimensionless parameters and calibration techniques to eliminate poorly known ki-netic constants. Many of the models presented are thus generic in the sense that they can begeneralised to a wide range of materials and processing. To help the reader understand andapply the subjects and models treated, numerous example problems, exercise problems andcase studies have been worked out and integrated in the text. These are meant to illustrate thebasic physical principles that underline the experimental observations and to provide a way ofdeveloping the ideas further.

Over the years, I have benefited from interaction and collaboration with numerous peoplewithin the scientific community. In particular, I would like to acknowledge the contributionfrom my father Professor Tor Grong who is partly responsible for my professional upbringingand development as a metallurgist through his positive influence on and interest in my re-search work. Secondly, I am very grateful to the late Professor Nils Christensen who firstintroduced me to the fascinating field of welding metallurgy and later taught me the basicprinciples of scientific work and reasoning. I will also take this opportunity to thank all myfriends and colleagues at the Norwegian Institute of Technology (Norway), The Colorado Schoolof Mines (USA), the University of Cambridge (England), and the Universitat der BundeswehrHamburg (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. Reidun0stbye 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 contributionsare gratefully acknowledged.

Trondheim, 1 December, 1993

0ystein Grong

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

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 ................................................... 26

1.10.2.1 Transient Heating Period ............................. 28 1.10.2.2 Pseudo-steady State Temperature

Distribution ................................................... 31 1.10.2.3 Simplified Solution for a Fast-moving High

Power Source .............................................. 41 1.10.3 Thin Plate Solutions ..................................................... 45

1.10.3.1 Transient Heating Period ............................. 48 1.10.3.2 Pseudo-steady State Temperature

Distribution ................................................... 49

Contents vii

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

1.10.3.3 Simplified Solution for a Fast Moving High Power Source .............................................. 56

1.10.4 Medium Thick Plate Solution ....................................... 59 1.10.4.1 Dimensionless Maps for Heat Flow

Analyses ...................................................... 61 1.10.4.2 Experimental Verification of the Medium

Thick Plate Solution ..................................... 72 1.10.4.3 Practical Implications ................................... 75

1.10.5 Distributed Heat Sources ............................................. 77 1.10.5.1 General Solution .......................................... 77 1.10.5.2 Simplified Solution ....................................... 80

1.10.6 Thermal Conditions during Interrupted Welding .......... 91 1.10.7 Thermal Conditions during Root Pass Welding ........... 95 1.10.8 Semi-empirical Methods for Assessment of Bead

Morphology .................................................................. 96 1.10.8.1 Amounts of Deposit and Fused Parent

Metal ............................................................ 96 1.10.8.2 Bead Penetration ......................................... 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

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

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

2.7 Overall Kinetic Model for Mass Transfer during Cooling in the Weld Pool ............................................................................ 124

2.8 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 ...................................................... 131 2.8.4.1 Gas-shielded Welding .................................. 131 2.8.4.2 Covered Electrodes ..................................... 134 2.8.4.3 Submerged Arc Welding .............................. 138 2.8.4.4 Implications of Sievert’s Law ....................... 140 2.8.4.5 Hydrogen in Multi-run Weldments ............... 140 2.8.4.6 Hydrogen in Non-ferrous Weldments .......... 141

2.9 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 ................................................ 148

2.10.1.1 Sampling of Metal Concentrations at Elevated Temperatures ............................... 149

2.10.1.2 Oxidation of Carbon ..................................... 149 2.10.1.3 Oxidation of Silicon ...................................... 152 2.10.1.4 Evaporation of Manganese .......................... 156 2.10.1.5 Transient Concentrations of Oxygen ........... 160

Contents ix


2.10.1.6 Classification of Shielding Gases ................ 166 2.10.1.7 Overall Oxygen Balance .............................. 166 2.10.1.8 Effects of Welding Parameters .................... 169

2.10.2 Submerged Arc Welding .............................................. 170 2.10.2.1 Flux Basicity Index ....................................... 171 2.10.2.2 Transient Oxygen Concentrations ............... 172

2.10.3 Covered Electrodes ..................................................... 173 2.10.3.1 Reaction Model ............................................ 174 2.10.3.2 Absorption of Carbon and Oxygen .............. 176 2.10.3.3 Losses of Silicon and Manganese ............... 177 2.10.3.4 The Product [%C] [%O] ............................... 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 ................. 184

2.11.2.1 Buoyancy (Stokes Flotation) ........................ 185 2.11.2.2 Fluid Flow Pattern ........................................ 186 2.11.2.3 Separation Model ......................................... 188

2.11.3 Predictions of Retained Oxygen in the Weld Metal ...... 190 2.11.3.1 Thermodynamic Model ................................ 190 2.11.3.2 Implications of Model ................................... 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 ...................................... 195

2.12.2.1 Effect of Heat Input ...................................... 196 2.12.2.2 Coarsening Mechanism ............................... 196 2.12.2.3 Proposed Deoxidation Model ....................... 201

2.12.3 Constituent Elements and Phases in Inclusions .......... 202 2.12.3.1 Aluminium, Silicon and Manganese

Contents ...................................................... 202 2.12.3.2 Copper and Sulphur Contents ..................... 202 2.12.3.3 Titanium and Nitrogen Contents .................. 203 2.12.3.4 Constituent Phases ...................................... 204

x Contents


2.12.4 Prediction of Inclusion Composition ............................. 204 2.12.4.1 C-Mn Steel Weld Metals .............................. 204 2.12.4.2 Low-alloy Steel Weld Metals ........................ 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

3.4 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 ................................. 230

3.4.3.1 Nominal Crystal Growth Rate ...................... 230 3.4.3.2 Local Crystal Growth Rate ........................... 234

3.4.4 Reorientation of Columnar Grains ............................... 239 3.4.4.1 Bowing of Crystals ....................................... 240 3.4.4.2 Renucleation of Crystals .............................. 242

3.5 Solidification Microstructures .................................................... 251 3.5.1 Substructure Characteristics ........................................ 251 3.5.2 Stability of the Solidification Front ................................ 254

3.5.2.1 Interface Stability Criterion ........................... 254 3.5.2.2 Factors Affecting the Interface Stability ....... 256

3.5.3 Dendrite Morphology ................................................... 260 3.5.3.1 Dendrite Tip Radius ..................................... 260 3.5.3.2 Primary Dendrite Arm Spacing .................... 261 3.5.3.3 Secondary Dendrite Arm Spacing ............... 264

Contents xi


3.6 Equiaxed Dendritic Growth ....................................................... 268 3.6.1 Columnar to Equiaxed Transition ................................. 268 3.6.2 Nucleation Mechanisms ............................................... 272

3.7 Solute Redistribution ................................................................. 272 3.7.1 Microsegregation ......................................................... 272 3.7.2 Macrosegregation ........................................................ 278 3.7.3 Gas Porosity ................................................................ 279

3.7.3.1 Nucleation of Gas Bubbles .......................... 279 3.7.3.2 Growth and Detachment of Gas Bubbles .... 281 3.7.3.3 Separation of Gas Bubbles .......................... 284

3.7.4 Removal of Microsegregations during Cooling ............ 286 3.7.4.1 Diffusion Model ............................................ 286 3.7.4.2 Application to Continuous Cooling ............... 286

3.8 Peritectic Solidification .............................................................. 290 3.8.1 Primary Precipitation of the γp-phase ........................... 290 3.8.2 Transformation Behaviour of Low-alloy Steel Weld

Metals .......................................................................... 290 3.8.2.1 Primary Precipitation of Delta Ferrite ........... 290 3.8.2.2 Primary Precipitation of Austenite ................ 292 3.8.2.3 Primary Precipitation of Both Delta

Ferrite and Austenite ................................... 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 .................. 304

4.2.3.1 Equilibrium Precipitates ............................... 304 4.2.3.2 Metastable Precipitates ............................... 308

xii Contents


4.3 Particle Coarsening ................................................................... 314 4.3.1 Coarsening Kinetics ..................................................... 314 4.3.2 Application to Continuous Heating and Cooling ........... 314

4.3.2.1 Kinetic Strength of Thermal Cycle ............... 315 4.3.2.2 Model Limitations ......................................... 315

4.4 Particle Dissolution .................................................................... 316 4.4.1 Analytical Solutions ...................................................... 316

4.4.1.1 The Invariant Size Approximation ................ 319 4.4.1.2 Application to Continuous Heating and

Cooling ........................................................ 322 4.4.2 Numerical Solution ....................................................... 325

4.4.2.1 Two-dimensional Diffusion Model ................ 326 4.4.2.2 Generic Model ............................................. 328 4.4.2.3 Application to Continuous Heating and

Cooling ........................................................ 329 4.4.2.4 Process Diagrams for Single Pass 6082-

T6 Butt Welds .............................................. 332 References ......................................................................................... 334 Appendix 4.1: Nomenclature ............................................................ 334

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

5.3 Analytical Modelling of Normal Grain Growth ........................... 343 5.3.1 Limiting Grain Size ....................................................... 343 5.3.2 Grain Boundary Mobility ............................................... 345

Contents xiii


5.3.3 Grain Growth Mechanisms .......................................... 345 5.3.3.1 Generic Grain Growth Model ....................... 345 5.3.3.2 Grain Growth in the Absence of Pinning

Precipitates .................................................. 347 5.3.3.3 Grain Growth in the Presence of Stable

Precipitates .................................................. 348 5.3.3.4 Grain Growth in the Presence of Growing

Precipitates .................................................. 351 5.3.3.5 Grain Growth in the Presence of

Dissolving Precipitates ................................. 356 5.4 Grain Growth Diagrams for Steel Welding ................................ 360

5.4.1 Construction of Diagrams ............................................ 360 5.4.1.1 Heat Flow Models ........................................ 360 5.4.1.2 Grain Growth Model ..................................... 361 5.4.1.3 Calibration Procedure .................................. 361 5.4.1.4 Axes and Features of Diagrams .................. 363

5.4.2 Case Studies ............................................................... 364 5.4.2.1 Titanium-microalloyed Steels ....................... 364 5.4.2.2 Niobium-microalloyed Steels ....................... 367 5.4.2.3 C-Mn Steel Weld Metals .............................. 370 5.4.2.4 Cr-Mo Low-alloy Steels ................................ 372 5.4.2.5 Type 316 Austenitic Stainless Steels ........... 375

5.5 Computer Simulation of Grain Growth ...................................... 380 5.5.1 Grain Growth in the Presence of a Temperature

Gradient ....................................................................... 380 5.5.2 Free Surface Effects .................................................... 382

References ......................................................................................... 382 Appendix 5.1: Nomenclature ............................................................ 384

6. Solid State Transformations in Welds ................................... 387 6.1 Introduction ............................................................................... 387 6.2 Transformation Kinetics ............................................................ 387

6.2.1 Driving Force for Transformation Reactions ................ 387

xiv Contents


6.2.2 Heterogeneous Nucleation in Solids ............................ 389 6.2.2.1 Rate of Heterogeneous Nucleation .............. 389 6.2.2.2 Determination of ∆Ghet.* and Qd ................... 390 6.2.2.3 Mathematical Description of the C-curve ..... 392

6.2.3 Growth of Precipitates .................................................. 396 6.2.3.1 Interface-controlled Growth ......................... 396 6.2.3.2 Diffusion-controlled Growth ......................... 397

6.2.4 Overall Transformation Kinetics ................................... 400 6.2.4.1 Constant Nucleation and Growth Rates ...... 400 6.2.4.2 Site Saturation ............................................. 402

6.2.5 Non-isothermal Transformations .................................. 402 6.2.5.1 The Principles of Additivity ........................... 403 6.2.5.2 Isokinetic Reactions ..................................... 404 6.2.5.3 Additivity in Relation to the Avrami

Equation ...................................................... 404 6.2.5.4 Non-additive Reactions ................................ 405

6.3 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 ................................................ 408

6.3.3.1 Crystallography of Grain Boundary Ferrite .......................................................... 408

6.3.3.2 Nucleation of Grain Boundary Ferrite .......... 408 6.3.3.3 Growth of Grain Boundary Ferrite ................ 422

6.3.4 Widmanstätten Ferrite .................................................. 427 6.3.5 Acicular Ferrite in Steel Weld Deposits ........................ 428

6.3.5.1 Crystallography of Acicular Ferrite ............... 428 6.3.5.2 Texture Components of Acicular Ferrite ...... 429 6.3.5.3 Nature of Acicular Ferrite ............................. 430 6.3.5.4 Nucleation and Growth of Acicular

Ferrite .......................................................... 432 6.3.6 Acicular Ferrite in Wrought Steels ............................... 444

Contents xv


6.3.7 Bainite .......................................................................... 444 6.3.7.1 Upper Bainite ............................................... 444 6.3.7.2 Lower Bainite ............................................... 447

6.3.8 Martensite .................................................................... 448 6.3.8.1 Lath Martensite ............................................ 448 6.3.8.2 Plate (Twinned) Martensite .......................... 448

6.4 Austenitic Stainless Steels ........................................................ 453 6.4.1 Kinetics of Chromium Carbide Formation .................... 456 6.4.2 Area of Weld Decay ..................................................... 456

6.5 Al-Mg-Si Alloys .......................................................................... 458 6.5.1 Quench-sensitivity in Relation to Welding .................... 459

6.5.1.1 Conditions for β’(Mg2Si) Precipitation during Cooling .............................................. 459

6.5.1.2 Strength Recovery during Natural Ageing ......................................................... 461

6.5.2 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 Weld Metal Mechanical Properties .............................. 477 7.2.1.1 Weld Metal Strength Level ........................... 478 7.2.1.2 Weld Metal Resistance to Ductile

Fracture ....................................................... 480 7.2.1.3 Weld Metal Resistance to Cleavage

Fracture ....................................................... 485 7.2.1.4 The Weld Metal Ductile to Brittle

Transition ..................................................... 486

xvi Contents


7.2.1.5 Effects of Reheating on Weld Metal Toughness ................................................... 491

7.2.2 HAZ Mechanical Properties ......................................... 494 7.2.2.1 HAZ Hardness and Strength Level .............. 495 7.2.2.2 Tempering of the Heat Affected Zone .......... 500 7.2.2.3 HAZ Toughness ........................................... 502

7.2.3 Hydrogen Cracking ...................................................... 509 7.2.3.1 Mechanisms of Hydrogen Cracking ............. 509 7.2.3.2 Solubility of Hydrogen in Steel ..................... 513 7.2.3.3 Diffusivity of Hydrogen in Steel .................... 514 7.2.3.4 Diffusion of Hydrogen in Welds ................... 514 7.2.3.5 Factors Affecting the HAZ Cracking

Resistance ................................................... 518 7.2.4 H2S Stress Corrosion Cracking .................................... 524

7.2.4.1 Threshold Stress for Cracking ..................... 524 7.2.4.2 Prediction of HAZ Cracking Resistance ....... 525

7.3 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

7.4 Aluminium Weldments .............................................................. 536 7.4.1 Solidification Cracking .................................................. 536 7.4.2 Hot Cracking ................................................................ 540

7.4.2.1 Constitutional Liquation in Binary Al-Si Alloys ........................................................... 541

7.4.2.2 Constitutional Liquation in Ternary Al-Mg-Si Alloys ....................................................... 542

7.4.2.3 Factors Affecting the Hot Cracking Susceptibility ................................................ 544

7.4.3 HAZ Microstructure and Strength Evolution during Fusion Welding ............................................................ 547

Contents xvii


7.4.3.1 Effects of Reheating on Weld Properties ..... 547 7.4.3.2 Strengthening Mechanisms in Al-Mg-Si

Alloys ........................................................... 548 7.4.3.3 Constitutive Equations ................................. 548 7.4.3.4 Predictions of HAZ Hardness and

Strength Distribution .................................... 550 7.4.4 HAZ Microstructure and Strength Evolution during

Friction Welding ........................................................... 556 7.4.4.1 Heat Generation in Friction Welding ............ 556 7.4.4.2 Response of Al-Mg-Si Alloys and Al-SiC

MMCs to Friction Welding ............................ 557 7.4.4.3 Constitutive Equations ................................. 558 7.4.4.4 Coupling of Models ...................................... 558 7.4.4.5 Prediction of the HAZ Hardness

Distribution ................................................... 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

1Heat Flow and Temperature Distribution in

Welding

1.1 Introduction

Welding metallurgy is concerned with the application of well-known metallurgical principlesfor assessment of chemical and physical reactions occurring during welding. On purely prac-tical grounds it is nevertheless convenient to consider welding metallurgy as a profession of itsown because of the characteristic non-isothermal nature of the process. In welding the reac-tions are forced to take place within seconds in a small volume of metal where the thermalconditions are highly different from those prevailing in production, refining and fabrication ofmetals and alloys. For example, steel welding is characterised by:

High peak temperatures, up to several thousand 0C.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 detailedinformation about the weld thermal history. From a practical point of view the analyticalapproach to the solution of heat flow problems in welding is preferable, since this makes itpossible to derive relatively simple equations which provide the required background for anunderstanding of the temperature-time pattern. However, because of the complexity of theheat flow phenomena, it is always necessary to check the validity of such predictions againstmore reliable data obtained from numerical calculations and in situ thermocouple measure-ments. Although the analytical models suffer from a number of simplifying assumptions, it isobvious that these solutions in many cases are sufficiently accurate to provide at least a quali-tative description of the weld thermal programme.

An important aspect of the present treatment is the use of different dimensionless groupsfor a general outline of the temperature distribution in welding. Although this practice in-volves several problems, it is a convenient way to reduce the total number of variables to anacceptable level and hence, condense general information about the weld thermal programmeinto two-dimensional (2-D) maps or diagrams. Consequently, readers who are unfamiliar withthe concept should accept the challenge and try to overcome the barrier associated with the useof 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.

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 equa-tions is that the thermal properties of the base material are constant and independent of tem-perature. 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, thethermal properties are also dependent upon the chemical composition and the thermal historyof 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 theapplication of the analytical solutions. Nevertheless, experience has shown that these prob-lems to some extent can be overcome by the choice of reasonable average values for X, a andpc within a specific temperature range. Table 1.1 contains a summary of relevant thermalproperties for different metals and alloys, based on a critical review of literature data. It shouldbe noted that the thermal data in Table 1.1 do not include a correction for heat consumed inmelting of the parent materials. Although the latent heat of melting is temporarily removedduring fusion welding, experience has shown this effect can be accounted for by calibratingthe equations against a known isotherm (e.g. the fusion boundary). In practice, such correc-tions are done by adjusting the arc efficiency factor Tq until a good correlation is achievedbetween theory and experiments.

Since heat losses from free surfaces by radiation and convection are usually negligible inwelding, the temperature distribution can generally be obtained from the fundamental differ-ential equations for heat conduction in solids. For uniaxial heat conduction, the governingequation can be written as:1

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

For biaxial and triaxial heat conduction we may write by analogy:1

and

(i-D

(1-2)

d-3)

(1-4)

Hx-

H0 =

PC

(T-T

0 ),

J/m

m3

Carbon steel

Temperature, 0C

Fig. 1.1. Enthalpy increment H7-H0 referred to an initial temperature T0 = 200C. Data from Refs.2-4.

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

Material (WrTIm-10C-1) (mm2 s"1) (Jmnr3 0C"1) (0C) (J mnr3) (J mnr3)

Carbon 0.040 8 0.005 1520 7.50 2.0Steels

Low Alloy 0.025 5 0.005 1520 7.50 2.0Steels

High Alloy 0.020 4 0.005 1500 7.40 2.0Steels

Titanium 0.030 10 0.003 1650 4.89 1.4Alloys

Aluminium 0.230 85 0.0027 660 1.73 0.8(> 99% Al)

Al-Mg-Si 0.167 62 0.0027 652 1.71 0.8Alloys

Al-Mg 0.149 55 0.0027 650 1.70 0.8Alloys

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

X 9 W

/mm

0C

X,

W/m

m 0

C

(a)

Temperature, 0C

(b)High alloy steel

Temperature, 0C

Fig. 1.2. Factors affecting the thermal conductivity X of steels; (a) Temperature level and chemicalcomposition, (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 Itis seen from Fig. 1.3 that these solutions are based on the assumption that the heat is releasedinstantaneously at time t - 0 in an infinite medium of initial temperature T0, either across aplane (uniaxial conduction), along a line (biaxial conduction), or in a point (triaxial conduc-tion). The material outside the heat source is assumed to extend to x = + °° for a plane sourcein a long rod, to r = °° for a line source in a wide plate, or to R = °° for a point source in a heavyslab. 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-J0 = O for t = O and x * O (alternatively r > O or 7? > O)7-T0 = 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 flowequations (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):

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

(ii) Line source in a wide plate (Fig. 1.3b):

d-5)

(1-6)

(1-7)

where d is the plate thickness.

(iii) Point source in a heavy slab (Fig. 1.3c):

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

(a)

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

T

(b)

(C)

T

yX

R

T

Fig. 1.3.Schematic representation of instantaneous heat source models (continued); (b) Line source in awide 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 ofequation (1-7).

ModelThe model considers a point source on a heavy slab as illustrated in Fig. 1.4. The heat isassumed to be released instantaneously at time t = 0 on the surface of the slab. This causes atemperature 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 writeequation (1-8) in a dimensionless form. The following parameters are defined for this pur-pose:

— Dimensionless temperature:

(1-9)

d-10)

(1-11)

where Tc is the chosen reference temperature.

— Dimensionless time:

where tt is the arc ignition time.

— Dimensionless operating parameter:

where qo is the net arc power (equal to Qlt(), and (Hc-Ho) is the heat content per unit volume atthe reference temperature.

— Dimensionless radius vector:

(1-12)

(1-13)

By substituting these parameters into equation (1-8), we obtain:

0Zn 1

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 of CT1 and T1. The resultsare presented graphically in Fig. 1.5. Due to the inherent assumption of instantaneous releaseof heat in a point, it is not possible to use equation (1-13) down to very small values OfCT1 andT1. However, at some distance from the heat source and after a time not much shorter than thereal (assumed) time of heating, the calculated temperature-time pattern will be reasonablycorrect. Note that the heavy broken line in Fig. 1.5 represents the locus of the peak tempera-tures. This locus is obtained by setting 3In(OAi1VdT1 = 0:

Fig. 1.4. Instantaneous point source model for assessment of temperatures in arc strikes.

Heat source

3-D heat flow

Isotherms

from which

Substituting this into equation (1-13) gives:

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. Calcu-late the cooling time from 800 to 5000C (Af875), and the total width of the fully transformedregion adjacent to the fusion boundary. The operational conditions are as follows:

(1-14)

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

SolutionIn the present case it is convenient to use the melting point of the steel as a reference tempera-ture (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 0C, Af875will be independent of Cr1 and similar to that calculated for the centre-line ((J1 = 0). By rear-ranging equation (1-13) we get:

and

Total width of fully transformed regionZone widths can generally be calculated from equation (1-14), as illustrated in Fig. 1.6. Tak-ing 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 isdifficult to check the accuracy of these predictions, the calculated values for Ats/5 and ARlm areconsidered reasonably correct. Thus, because the cooling rate is very large, in arc strikes ahard martensitic microstructure would be expected to form within the transformed parts of theHAZ, 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 weldingof plates.

ModelThe model considers a line source which penetrates two overlapping plates of similar thermalproperties, 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).

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 givenby equation (1-6).

This equation can be written in a dimensionless form by introducing the following group ofparameters:

— Dimensionless time:

where th is the heating time (i.e. the duration of the pulse).

— Dimensionless operating parameter:

where dt is the total thickness of the joint.

— Dimensionless radius vector:

By substituting these parameters into equation (1-6), we get:

where 6 denotes the dimensionless temperature (previously defined in equation (1-9)).

(1-15)

(1-16)

(1-17)

(1-18)

Electrode

Heat source d

6/n 2

e/n 2

Linear time scale

T2

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 a2 andT2. A closer inspection of the graph reveals that the temperature-time pattern in spot weldingis similar to that observed during arc ignition (see Fig. 1.5). The locus of the peak tempera-tures 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 con-ditions:

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

SolutionIf we use the melting point of the steel as a reference temperature, the parameters n2 and 6 (at800 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 0CThe cooling rate at a specific temperature is obtained by differentiation of equation (1-18) withrespect 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 theweld 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:

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'= -L1 and x'- +L1. Thisgives (after some manipulation):

(1-22)

(1-21)

At time t this source produces a small rise of temperature at position JC, given by equation (1 -5):

(1-20)

It should be emphasised that the present heat flow model represents a crude oversimplifica-tion of the spot welding process. In a real welding situation, most of the heat is generated at theinterface between the two plates because of the large contact resistance. This gives rise to thedevelopment of an elliptical weld nugget inside the joint as shown in Fig. 1.9. Moreover, sincethe model neglects transfer of heat into the electrodes, the mode of heat flow will be mixed andnot truly two-dimensional as assumed above. Consequently, equation (1-18) cannot be ap-plied for reliable predictions of isothermal contours and zone widths. Nevertheless, the modelmay provide useful information about the cooling conditions during spot welding if the effi-ciency factor if] and the voltage drop between the electrodes can be estimated with a reasonabledegree 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 producecoalescence 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 prod-uct provides the energy source required to form the weld.

ModelIn thermit welding the time interval between the ignition of the powder mixture and the com-pletion 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 aninitial temperature Tt (see Fig. 1.10). The metal temperature outside the fusion zone is T0. Ifheat losses to the surroundings are neglected, the problem can be treated as uniaxial conduc-tion where the heat source (extending from -L1 to +L1) is represented by a series of elementarysources, each with a heat content of:

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

Isl'srau*'*'=]

F u s i o n z o n e

F u s i o n z o n e

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 theFortran subroutine given in Appendix 1.3.

Dimensionless temperature:

Dimensionless time:

Dimensionless jc-coordinate:

Substituting these parameters into equation (1-22) gives:

(1-23)

(1-24)

(1-25)

(1-26)

Equation (1-26) has been solved numerically for different values of Q and T3. The resultsare 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 temperaturesin 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 com-binations 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 thefollowing operational conditions:

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

91

Definition of parameters:

T3

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

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

Cooling time At8/5

From the above relation it is possible to calculate the cooling time from Tt = 22000C to 800 and5000C, 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, sincethe cooling curves at such low temperatures are reasonably parallel within the fusion zone.

Total width of fully transformed regionThe 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 theisotherm:

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 instantaneousrelease of heat immediately after powder ignition and the neglect of heat losses to the sur-roundings. Nevertheless, the present example is a good illustration of the versatility of theconcept of instantaneous heat sources, since these solutions can easily be added in space asshown 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 compressiveforce contact of one rotating and one stationary workpiece. The heat is generated at the weldinterface because of the continuous rubbing of the contact surfaces, which, in turn, causes atemperature rise and subsequent softening of the material. Eventually, the material at theinterface starts to flow plastically and forms an up-set collar. When a certain amount of up-setting has occurred, the rotation is stopped and the compressive force is maintained or slightlyincreased to consolidate the weld.

Model (after Rykalin et al.5jThe 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 wesubdivide 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)

(b)

Continuous heat source

t

q

Fig. 1.12. Idealised heat flow model for friction welding of rods; (a) Sketch of model, (b) Subdivision oftime into a series of infinitesimal elements dt'.

At time / this heat will cause a small rise of temperature in the material, in correspondancewith equation (1-5):

(1-29)

If we substitute t"=t-1'into equation (1 -29), the total temperature rise at time t is obtainedby 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 transfor-mation:

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):

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:

(1-31)

(1-32)

where t'h denotes the duration of the heating period (t < t'h). Measured contact section tem-peratures 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 followinggroups of parameters:

(1-33)

(1-34)

Dimensionless temperature:

Dimensionless time:

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 Measuring Temperature Level PartialCombination Method [0C] Melting

Steel Thermocouples 1080-1340 No

Steel-Nickel Direct readings1 1260-1400 No/Yes

Steel-Titanium Direct readings1 1080 No

Copper-Al Direct readings1 548 Yes

Copper-Nickel Direct readings1 1083 Yes

Al-Cu-2Mg Thermocouples 506 Yes

Al-4.3Cu Thermocouples 562 Yes

Al-12Si Thermocouples 575 Yes

Al-5Mg Thermocouples 582 Yes

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

— Dimensionless .^-coordinate:

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

(1-35)

(1-36)

Equation (1-36) describes the temperature in different positions from the weld contact sec-tion during the heating period. However, when the rotation stops, the weld will be subjected tofree cooling, since there is no generation of heat at the interface. As shown in Fig. 1.13(a) thiscan be accounted for by introducing an imaginary heat source of power +qo at time t = t'hwhich acts simultaneously with an imaginary heat sink of negative power -q o. It follows fromthe principles of superposition (see Fig. 1.13b) that the temperature during the cooling periodis given by:9

where 6"(x4) and 6"(T4- 1) are the temperatures calculated for the heat source and the heatsink, 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), thetemperature increases monotonically with time during the heating period, in correspondancewith the relationship:

(1-37)

(1-38)

(a)

q

t

Imaginary heat source

Imaginary heat sink

Real heatsource

(b)

e"

Heatingperiod

$ f f l 9

\

Fig. 1.13. Method for calculation of transient temperatures during friction welding; (a) Sketch ofimaginary 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 coolingrate lower than that calculated from equations (1-38) and (1-39).

e"

Heating 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 con-ditions:

Calculate the peak temperature distribution across the joint. Assume in these calculationsthat the thermal diffusivity of the Al-Cu-2Mg alloy is 70mm2 s"1.

SolutionReadings from Fig. 1.14 give:

In this particular case, it is possible to check the accuracy of the calculations against in situthermocouple measurements carried out on friction welded components made under similarconditions. A comparison with the data in Fig. 1.15 shows that the model is quite successful inpredicting the HAZ peak temperature distribution. In contrast, the weld heating and coolingcycles cannot be reproduced with the same degree of precision. This has to do with the factthat the present analytical solution omits a consideration of the plastic straining occurringduring friction welding, which displaces the coordinates and alters the heat balance for thesystem.

1.9 Moving Heat Sources and Pseudo-Steady State

In most fusion welding processes the heat source does not remain stationary. In the followingwe shall assume that the source moves at a constant speed along a straight line, and that the netpower supply from the source is constant. Experience shows that such conditions lead to afused zone of constant width. This is easily verified by moving a tungsten arc across a sheet ofsteel 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 bythe 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 withtime when observed from a point located in the heat source. Under such conditions the tem-perature field around the source can be described as a temperature 'mountain' moving in thedirection of welding (e.g. see Fig. 15 in Ref. 11). For points along the weld centre-line, thetemperature at different positions away from the heat source (which for a constant weldingspeed 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 steelwelding from the base plate ahead of the arc to well into the solidified weld metal trailing thearc. If we consider a fixed point on the weld centre-line, the temperature will increase veryrapidly during the initial period, reaching a maximum of about 2000-22000C for positionsimmediately beneath the root of the arc.11 When the arc has passed, the temperature will startto fall, and eventually (after long times) approach that of the base plate. In contrast, an ob-server 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 themathematical treatment of heat flow during fusion welding, although it imposes certain re-strictions 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

Next Page

2Chemical Reactions in Arc Welding

2.1 Introduction

The weld metal composition is controlled by chemical reactions occurring in the weld pool atelevated 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 theoperational conditions applied. In contrast to ladle refining of metals and alloys where thereactions occur under approximately isothermal conditions, a characteristic feature of the arcwelding 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 tempera-ture gradients are of the order of 1000°C mm"1 with corresponding cooling rates up to1000°C s"1. The complex thermal cycle experienced by the liquid metal during transfer fromthe 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 thereaction sequences during all stages of the process. Consequently, a complete understandingof the major controlling factors is still missing, which implies that fundamentally based pre-dictions of the final weld metal chemical composition are limited. Additional problems resultfrom the lack of adequate thermodynamic data for the complex slag-metal reaction systemsinvolved. However, within these restrictions, the development of weld metal compositionscan be treated with the basic principles of thermodynamics and kinetic theory considered inthe 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). Exam-ples of such kinetically controlled processes are separation of non-metallic inclusions from adeoxidised steel melt or removal of hydrogen from liquid aluminium. In welding, the reactionpattern is more difficult to assess because of the characteristic non-isothermal behaviour of theprocess (see Fig. 2.1). Nevertheless, experience shows that it is possible to analyse masstransfer in welding analogous to that in ladle refining by considering a simple two-stage reac-tion model, which assumes:1

(i) A high temperature stage, where the reactions approach a state of localpseudo-equilibrium.

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

Fig. 2.1. Schematic diagram showing the main process stages in GMA welding. Characteristic averagetemperature 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/metalinteractions 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 thesubsequent stage of cooling following the passage of the arc, a supersaturation rapidly in-creases because of the decrease in the element solubility with decreasing temperatures. Thesystem 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 lattercase the extent of mass transfer is determined by the separation rate of the reaction products inthe weld pool. It should be noted that the boundary between the two stages is not sharp, whichmeans that phase separation may proceed simultaneously with absorption in the hot part of theweld pool.

In the following sections, the chemistry of arc welding will be discussed in the light of thistwo-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 bewidely dissociated in the arc column because of the high temperatures involved (the arc plasmatemperature is typically of the order of 10 0000C or higher). From a thermodynamic stand-point, dissociation can be treated as gaseous chemical reactions, where the concentrations ofthe reactants are equal to their respective partial pressures. Hence, for dissociation of diatomicgases, we may write:

where X denotes any gaseous species.

(2-1)

Gas nozzleShielding gasFiller wire

Electrode tip droplet(1600-20000C)

Falling droplet (24000C)

Hot part of weld pool(1900-22000C)

Contact tube

Arc plasmatemperature~10000°C

Cold part ofweld pool (< 19000C)

Base plateWeld poolretention

time 2-1Os

Tem

pera

ture

Solid

wel

d m

etal

Solid

wel

d m

etal

Solid

wel

d m

etal

Conc

entra

tion

Solid

wel

d m

etal

'Hot1 part ofweld pool 'Cold' part of weld pool

Peak temperature

Grey jzonei

Rejection ofdissolved elements

Absorptionof elements

Peak concentration

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

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 tounity, the partial pressure of species X in the gas phase px is equal to:

Gas Dissociation Temperature (K)

CO2 3800

H2 4575

O2 5100

N2 8300

where H1 and nx are the total number of moles of components / (inert gas) and X, respectivelyin 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 dissoci-ates. Hence, equation (2-2) can be rewritten as:

(2-2)

(2-3)

where nXl is the total number of moles of component X2 which originally was present in theshielding gas.

If nXl and H1 are proportional to the volume concentrations of the respective gas compo-nents in the shielding gas, equation (2-3) becomes:

(2-4)

Similarly, if X2 is replaced by another gas component of the type YX2, we get:

(2-5)

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

Px-

(2-6)

(2-7)

and

It is evident from the graphical representations of equations (2-5) and (2-7) in Fig. 2.3 thatthe partial pressure of the dissociated component X increases monotonically with increasingconcentrations 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 gasphase due to the dissociation reaction. Moreover, it is interesting to note that the partial pres-sure px is also dependent on the nature of the active gas component in the arc column (i.e. thestoichiometry of the reaction). This means that the oxidation capacity of for instance CO2 isonly half that of O2 when comparison is made on the basis of equal concentrations in theshielding 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 gasphase (step one), it is a reasonable approximation to assume that all resistance to mass transferis confined to a stagnant layer of thickness 8 (in mm) adjacent to the metal surface, as shown inFig. 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.

Par

tial

pres

sure

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 bewritten as:

(2-9)

where A is the contact area (in mm2), 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 thebulk 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 Xin 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 theelement (in g mol"1), we obtain the following relation when /? x » p°x:

(2-10)

It follows from equation (2-10) that the transient concentration of element X in the hot partof the weld pool is proportional to the partial pressure of the dissociated component X in theplasma gas. Since this partial pressure is related to the initial content of the molecular speciesX2 or YX2 in the shielding gas through equations (2-5) and (2-7), we may write:

Arc columnBulk gasphase

Stagnant gaseousboundary layer

Gas/metal interface

Metal phase

Hot part ofweld pool

Fig. 2.5. Idealised kinetic model for gas absorption in arc welding (schematic).

(2-11)

(2-12)

and

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

2.5 The Concept of Pseudo-Equilibrium

Although the above analysis presupposes that the element absorption is controlled by atransport mechanism in the gas phase, the transient concentration of the active component X inthe hot part of the weld pool can alternatively be calculated from chemical thermodynamics byconsidering the following reaction:

(2-13)X(gas) X (dissolved)

By introducing the equilibrium constant K{ for the reaction and setting the activity coeffi-cient 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 partialpressure px at the gas/metal interface is directly proportional to the partial pressure of thedissociated component in the bulk phase. Unfortunately, the proportionality constant is diffi-cult to establish in practice.

2.6 Kinetics of Gas Desorption

During the subsequent stage of cooling following the passage of the arc, the concentrationsestablished at elevated temperatures will tend to readjust by rejection of dissolved elementsfrom the liquid. When it comes to gases such as hydrogen and nitrogen, this occurs through adesorption mechanism, where the driving force for the reaction is provided by the decrease inthe 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 pres-sure px at a high temperature T1, and then is rapidly cooled to a lower temperature T2 andimmediately brought in contact with diatomic X2 of partial pressure pXl (see Fig. 2.6). Undersuch 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 pres-

sure of component X2 at the gas/metal interface (in atm).

Bulk gasphase

Stagnant gaseousboundary layer

Gas/metal interface

Metal phase

Cold part ofweld 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 theliquid metal (in weight percent). Note that the activity coefficient has been set to unity in thederivation of equation (2-17).

The equilibrium constant K2 may be expressed in terms of the solubility of element X in theliquid metal at 1 atm total pressure Sx. Hence, equation (2-17) transforms to:

(2-18)

(2-19)

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

Data for the solubility of hydrogen and nitrogen in some metals up to about 22000C aregiven in Figs. 2.7 and 2.8, respectively. It is evident that the element solubility decreasessteadily with decreasing metal temperatures down to the melting point. This implies that thedesorption reaction is thermodynamically favoured by the thermal conditions existing in thecold part of the weld pool.

2.6.2. Sievert's law

It follows from equation (2-19) that desorption becomes kinetically unfeasible whenPx2 ~ Px2' corresponding to:

(2-20)

Equation (2-20) is known as the Sievert's law. This relation provides a basis for calculatingthe final weld metal composition in cases where the resistance to mass transfer is sufficientlysmall 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 toderive a complete kinetic model for mass transfer in arc welding from first principles. How-

ml H

2/100

g fu

sed

met

al

ml H

2/100

g fu

sed

met

al

ml H

2/100

g fu

sed

met

al

ml H

2/100

g fu

sed

met

al

(a) (b)

Aluminium

Temperature, 0C

Copper

Solid Cu

Temperature, 0C

(C) (d)

Iron Nickel

Temperature, 0CTemperature, 0C

Fig. 2.7. Solubility of hydrogen in some metals; (a) Aluminium, (b) Copper, (c) Iron, (d) Nickel. Datacompiled by Christensen.4

ever, for the idealised system considered in Fig. 2.9, it is possible to develop a simple math-ematical relation which provides quantitative information about the extent of element transferoccurring during cooling in the weld pool. Let [%X]eq denote the equilibrium concentration ofelement X in the melt. If we assume that the net flux of element X passing through the phaseboundary A per unit time is proportional to the difference ([%X] - [%X]eqX the followingbalance is obtained:3

where V is the volume of the melt (in mm3), kd is the overall mass transfer coefficient (inmm s"1), and A is the contact area between the two phases (in mm2).

(2-21)

log (w

t% N

)

Net f

lux

of X

Dist

ance

Temperature, 0C

Iron

104AT1 K

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

Phase I i

Contact area (A)

Phase i 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).

(X-X

^)Z(

X1-X

eq)

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

t , s

Under such conditions the final weld metal composition can be calculated from simplechemical thermodynamics.

Because of this flexibility, equation (2-23) is applicable to a wide range of metallurgicalproblems at the same time as it provides a simple physical picture of the resistance to masstransfer during cooling in the weld pool.

(2-24)

It follows that the final concentration of element X in the weld metal depends both on thecooling 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 thecase during deoxidation of steel weld metals where separation of oxide inclusions from theweld pool is the rate controlling step. Moreover, when t/t0 » 1 (small resistance to masstransfer), equation (2-23) reduces to:

(2-23)

It is evident from the graphical representation of equation (2-22) in Fig. 2.10 that the rate ofmass transfer depends on the ratio Vl kji, i.e. the time required to reduce the concentration ofelement X to a certain level is inversely proportional to the mass transfer coefficient kd. Thistype of response is typical of a first order kinetic reaction.

Although the above model refers to mass transfer under isothermal conditions, it is alsoapplicable to welding if we assume that the weld cooling cycle can be replaced by an equiva-lent isothermal hold-up at a chosen reference temperature. Thus, by rearranging equation (2-22), we get:

2.8 Absorption of Hydrogen

Some of the well-known harmful effects of hydrogen discussed in Chapters 3 and 7 (i.e. weldporosity and HAZ cold cracking) are closely related to the local concentration of hydrogenestablished in the weld pool at elevated temperatures due to chemical interactions betweenthe 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 inthe flux used in submerged arc (SA) or flux-cored arc (FCA) welding. Occasionally, moisturemay 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 theform of hydrated oxides (e.g. rust on the surface of electrode wires and iron powder), hydro-carbons (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 thesurface layers of welding wires and electrode cored wires.

It is evident from Fig. 2.11 that the weld metal hydrogen content may vary strongly fromone process to another. The lowest hydrogen levels are usually obtained with the use of low-moisture basic electrodes or GMA welding with solid wires. Submerged arc welding and flux-cored arc welding, on the other hand, may give high or low concentrations of hydrogen in theweld metal, depending on the flux quality and the operational conditions applied (note that theformer process is not included in Fig. 2.11). The highest hydrogen levels are normally associ-ated with cellulosic, acid, and rutile type electrodes. This is due to the presence of largeamounts 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 compositionsin GMA and SMA welding. Included are also typical ranges for the weld metal hydrogencontent.

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 roomtemperatures, and hence, some of it may be lost before an analysis can be made. This, coupledwith 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 resultsmay be compared between different laboratories and can be used to develop hydrogen controlprocedures, some international standardisation of these sampling and analysis methods is nec-essary.

Three methods are currently being used, as defined in the following standards:

Pote

ntia

l hyd

roge

n le

vel

FCAW

Verylow Low Medium High

Weld hydrogen level

Fig. 2.11. Ranking of different welding processes in terms of hydrogen level (schematic). The diagram isbased on the ideas of Coe.6

(i) The Japanese method (JIS Z 313-1975), which has been adopted with important ad-justments from the former ASTM designation A316-48T. This method involves collection ofreleased hydrogen from a single pass weld above glycerine for 48h at 45 0C. The total volumeof hydrogen is reported in ml per 10Og deposit. Only 5 s of delay are allowed from extinctionof the arc to quenching.

(ii) The French method (N.F.A. 81-305-1975) where two beads are deposited onto corewires 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 singlebead is deposited on previously degassed and weighed mild steel blocks clamped in a quick-release copper fixture. The weldment is quenched and refrigerated according to a rigorouslyspecified time schedule. Hydrogen released from the specimens is collected above mercuryfor 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 termsof deposited metal (ml per 10Og deposit), and HFM for the content referred to fused metal (mlper 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 agiven electrode. Approximate correlations have been established between the HW criteriaHDM and HFM and the numbers obtained by the Japanese and the French methods (designatedHJIS and HFR, respectively). For covered electrodes tested at various hydrogen levels, wehave:7

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 ra-tional criterion of concentration. Moreover, HDM values would be grossly unfair, if applied tohigh penetration processes like submerged arc welding. In GTA welds made without fillerwire 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 thecontent of 'residual hydrogen' determined on the same samples by vacuum or carrier gasextraction at 6500C. A very small additional amount may be observed on vacuum fusion of thesample, tentatively labelled 'fixed hydrogen'. There is no clear line of demarcation betweenthese categories of hydrogen. As will be discussed later, the extent of hydrogen trappingdepends both on the weld metal constitution and the thermal history of the metal. In single-bead 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 solidi-fied beads. Due to the rapid migration of hydrogen at elevated temperatures, such data do notrepresent the conditions in the hot part of the weld pool. Quenched end crater samples wouldbe better in this respect, but they are not representative of normal welding. Further complica-tions arise from the presence of hydrogen in different states (e.g. diffusible or residual hydro-gen) and the lack of consistent sampling methods.

Nevertheless, experience has shown that pick-up of hydrogen in arc welding can be inter-preted on the basis of the simple model outlined in Fig. 2.13. According to this model, twozones are considered:

(i) An inner zone of very high temperatures which is characterised by absorption of atomichydrogen from the surrounding arc atmosphere.

(2-25)

(2-26)

Fig. 2.12. The relation between HDM and HFM (0.9 is the conversion factor from ml per 10Og to g per ton).

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 issufficiently small to maintain full chemical equilibrium between the liquid weld metal and theambient (bulk) gas phase.

Under such conditions, the final weld metal hydrogen content should be proportional to thesquare root of the initial partial pressure of diatomic hydrogen in the shielding gas, in agree-ment 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 steelweld metals are quite wide, and therefore not suitable for a direct comparison of predictionwith measurement. For such purposes, the welding conditions and consumables must be moreprecisely defined.

2.8.4.1 Gas-shielded weldingIn GTA and GMA welds the hydrogen content is usually too low to make a direct comparisonbetween theory and experiments. An exception is welding under controlled laboratory condi-tions where the hydrogen content in the shielding gas can be varied within relatively widelimits. The results from such experiments are summarised in Fig. 2.14, from which it is seenthat Sievert's law indeed is valid. A closer inspection of the data reveals that the weld metalhydrogen 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 temperatureis sensitive to variations in the operational conditions.

An interesting effect of oxygen on the weld metal hydrogen content has been reported byMatsuda et al.9 Their data are reproduced in Fig. 2.15. It is evident that the hydrogen level issignificantly 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 ofhydrogen during cooling.

Hot part of weld poolAbsorption of atomic hydrogen

(controlled by pH in the arc column)

Electrode

Cold part of weld poolDesorption of hydrogen

(controlled by pH2 in ambient gas phase)

Hydrogentrapped inweld metal

Weld pool

ml H

2/10

0 g

fuse

d m

etal

, H

pM

Table 2.2 Measured arc atmosphere compositions in steel welding. Also included are typical ranges forthe weld metal hydrogen content. Data compiled by Christensen.4

Method

GMAW*(CO2)

SMAW(acid)

SMAW(rutile)

SMAW(basic)

FCAW(rutile)

FCAW(basic)

SAW(basic)

Primary Sourceof Hydrogen

Moisture introducedthrough the shielding gas

Firmly bound water inthe electrode coating

Firmly bound water inthe electrode coating

Loosely bound water inthe electrode coating

Firmly bound waterinflux

Loosely bound waterinflux

Loosely bound waterinflux

Arc Atmosphere Composition(vol%)

CO2

98-80

-4

~4

-19

CO

2-20

-34

-42

-77

H2+H2O

<0.02

-62

-54

-4

Weld MetalHydrogen

Content (ppm)

Range

1-5

10-30

10-30

2-10

10-20

2-5

2-10

Average

3

25

25

3-5

GTAW (low-alloy steel)

*The arc atmosphere composition can vary within wide limits, depending on the operational conditions applied.

ml H

2 /1

00 g

fuse

d m

etal

, HJ|

SGTAW (low-alloy steel)Welding conditions: 300A-18V-2.5 mm/s

Weld metal oxygen content, wt%

Fig. 2.15. Hydrogen pick-up in GTA welding at different levels of oxygen in the weld metal. Data fromMatsuda et al.9

Example (2.1)

Consider GTA welding (Ar-shielding) on a thick plate of low-alloy steel under the followingconditions:

/ = 200A, U = 15V, v = 3 mm s"1, TI = 0.5, T0 = 20°C

The shielding gas contains 0.1 vol% moisture (H2O) and is supplied at a rate of 15Nl mhr1.Calculate the 'potential' hydrogen level, assuming that all hydrogen introduced through theshielding gas is absorbed in the weld metal.

SolutionFirst we calculate the total mass of hydrogen per mm:

The resulting bead cross section and total mass of weld metal per mm can be estimatedfrom the Rosenthal equation by considering the dimensionless operating parameter at the meltingpoint (equation (1-50)):

Reading from Fig. 1.21 gives:

Taking the density of the steel equal to 7.85 X 10 3 g mm 3, we obtain:

The 'potential' hydrogen level is thus:

It is evident from the above calculations that the 'potential' hydrogen level is at least oneorder of magnitude higher than the expected weld metal hydrogen content (1 to 3 ppm). Thisshows that the hydrogen pick-up in GTA welding is not determined by the total amount ofhydrogen which is introduced through the shielding gas, but is mainly controlled by the result-ing partial pressure of hydrogen in the ambient (bulk) gas phase.

2.8.4.2 Covered electrodesIn SMA welding the partial pressure of hydrogen is more difficult to assess due to the presenceof trapped moisture and hydrogen-containing compounds in the electrode coating. Such com-pounds will loose their identity at the stage of introduction into the arc atmosphere. Since verylittle information is available on the species present in the arc column, we shall base our esti-mate on a simple thermodynamic approach, including only the molecular species H2 and H2Owhich can be determined by analysis (see data in Table 2.2). It follows that the combinedpartial pressure of H2 and H2O in the gas phase is given by:

The parameter pw can be estimated on the basis of combustion measurements of the elec-trode coating, assuming that no carbon is picked up or lost from the system in excess of theamount calculated from an analysis of the base plate and the electrode wire. For a recordedcontent of mw g H2O and mc g CO2 per 100 g of electrode coating, we obtain:

From a thermodynamic standpoint, replacement of pHl by /^ in the expression for Sievert'slaw requires the use of a modified solubility of hydrogen, defined as:

(2-27)

(2-28)

(2-29)

where K3 is the equilibrium constant for the H2O-H reaction, and [%O] is the weld metaloxygen content. In practice, the correction term ^ K3/(K3+[%0]) does not depart signifi-cantly from unity, which means that Sw ~ SH.

ml H

2/100

g fu

sed

met

al, H

pM •

During welding with basic covered electrodes considerable amounts of CO2 may form as aresult of decomposition of calcium carbonate, according to the reaction:

(2-30)

Modern basic electrodes contain between 20 to 40 weight percent CaCO3, which is equiva-lent with a CO2 content of 9 to 18 percent. Taking as an average mc equal to 15 g CO2 per 100 gelectrode coating, we obtain:

(2-31)

In Fig. 2.16 the validity of equation (2-31) has been checked against relevant literature data(compiled by Chew10). A closer inspection of the data reveals that the weld metal hydrogencontent falls within the range calculated for chemical equilibrium at 1520 to 2000°C, taking Sw

equal to the solubility of hydrogen in pure iron at the indicated temperatures (i.e. 27 and 40 mlH2 per 100 g fused metal, respectively). Although the observed scatter in the effective reactiontemperature is admittedly large, equation (2-31) points out a very interesting effect, namelythat the hydrogen content of SMA steel weld metals is controlled by the combined partialpressure of H2 and H2O in the ambient gas phase. For this reason it is frequently recom-mended that calcium carbonate is added to the electrode coating, which on decompositionproduces considerable amounts of shielding gas in the form of CO2. Hydrogen shielding canalso be achieved by additions of volatile alkali-fluorides, which on heating will evaporate anddilute the atmosphere with respect to hydrogen.

SMAW (low-alloy steel)

Fig. 2.16. Hydrogen pick-up in SMA welding at different water contents in the electrode coating. Datacompiled by Chew.10

Water content in electrode coating, wt%

Example (2.2)

Consider SMA welding on mild steel with basic covered electrodes. The electrode coatingcontains 35 wt% CaCO3 and 0.5 wt% H2O in the as-received condition. After drying at 3500Cfor 1 h the water content is reduced to 0.2 wt% H2O. Estimate the weld metal hydrogencontent (in ppm) both before and after drying of the electrode. Assume in these calculations aneffective reaction temperature of 18000C.

SolutionFirst we calculate the CO2 content per 100 g of electrode coating. Taking the atomic weight ofCaCO3 and CO2 equal to 100.1 and 40.0, respectively, we obtain:

The combined partial pressure pw can now be estimated from equation (2-28). Beforedrying we have:

After drying of the electrode, the partial pressure pw becomes:

From Fig. 2.7(c) it is evident that the solubility of hydrogen in liquid iron at 18000C isabout 37 ml H2 per 100 g fused metal. This corresponds to a modified solubility Sw (in ppm)of:

Substituting this value into the expression for Sievert's law gives:

(before drying)(after drying)

It follows from the above calculations that a low weld metal hydrogen level requires the useof 'dry' basic electrodes. In practice, this can be achieved by protecting the electrodes againstmoisture pick-up during storage (see Fig. 2.17). However, in certain cases it is necessary todifferentiate between strongly bound and loosely adsorbed moisture in the coating of basicelectrodes. This point is more clearly illustrated in Fig. 2.18, which shows the HDM content ofhydrogen in basic electrode deposits at various levels of coating moisture. It is seen that waterremaining from an insufficient baking treatment is more dangerous than moisture picked up byexposure of a properly dried coating. This has to do with the fact that loosely adsorbed mois-

ml

H2 /

100 d

eposi

t, H

DM

Wat

er c

onte

nt in

ele

ctro

de c

oatin

g, w

t%

very

low

low

med

ium

high

Fig. 2.18. Hydrogen pick-up in SMA welding at different levels (states) of adsorbed water in the elec-trode coating. Data from Evans and Bach.12

Water content, wt%

SMAW (low-alloy steel)

Fig. 2.17. Moisture content in basic electrode coating as a function of exposure time and relative humid-ity (R.H.) in ambient gas phase. Data from Evans.11

Exposure time, days

ml H

2/10

0 de

posi

t, H

DM

Hyd

roge

n co

nten

t, H

FM (p

pm)

ture will tend to evaporate during the welding operation (before it enters the arc column)because of resistance heating of the electrode, a process which is not feasible when the water isbound in rust on the surface of the electrode wire or the iron powder.

2.8.4.3 Submerged arc weldingThis method is usually classified as a pure slag-shielded process, because carbonates or othergas-producing compounds are not present in large quantities. A closed arc cavity does exist,however, as indicated by the falling volt-ampere curve characteristic of open arcs, and byobservations made by probes inserted through the flux cover.

It is reasonable to assume that the gas contained within this enclosure consists of metalvapour, volatile constituents originating from the flux, and relatively small fractions of carbonmonoxide and water vapour. Acid fluxes of the calcium silicate type will probably generatesilicon monoxide, while agglomerated fluxes bonded with alkali silicate will produce volatilealkali fluorides. In addition, carbon monoxide may be present as a result of oxidation of car-bon, or decomposition of carbonates.

A small but important contribution to the cavity atmosphere is the trace of moisture remain-ing in the flux even after careful drying. No direct measurements of partial pressures are avail-able, and the gas composition must therefore be inferred from observations of hydrogen ab-sorption in the weld metal. Hydrogen pick-up during SA welding has been examined by Evansand Bach.12 Their data are replotted in Fig. 2.19. The shape of the observed curve of hydrogenvs residual water content would seem to indicate a relationship similar to that predicted bySievert's law. In fact, a very close fit can be obtained through empirical calibration of thedilution term in equation (2-28). This, however, implies unreasonable amounts of CaCO3.Carbon monoxide in addition to that delivered by carbonates could be formed by oxidation ofcarbon. Again, an unreasonable amount of carbon loss would be required. Therefore, it mustbe concluded that further research is needed for a proper interpretation of the factors control-ling hydrogen pick-up in SA welding.

SAW (low-alloy steel)

Water content, wt%

Fig. 2.19. Hydrogen pick-up in SA welding at different water contents in the flux. Data from Evans andBach.12

Example (2.3)

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

The flux contains 0.04 wt% H2O and is consumed at a rate of 0.6 g per g weld deposit.Estimate both 'potential' and 'equilibrium' hydrogen levels when the total oxidation loss ofcarbon in the weld pool is 0.03 wt%.

SolutionFirst we calculate the total amount of fused parent metal and weld deposit formed on welding.From equations (1-75) and (1-120), we have:

and

When the dilution ratio DI(B + D) is known, it is possible to calculate the total flux con-sumption per gram fused weld metal:

The 'potential' hydrogen level is thus:

If we assume that all CO produced by reactions between dissolved carbon and oxygen isinfiltrated in the arc column, the following balance is obtained:

Total number of moles of CO per g fused weld metal:

Total number of moles of H2O per g fused weld metal:

This gives:

Since the effective reaction temperature of hydrogen absorption in SA welding is not known,the maximum solubility of hydrogen at 1 atm total pressure is taken equal to 33 ppm, similar tothat in the previous example. By inserting this value in the expression for Sievert's law, weobtain:

In practice, the 'potential' hydrogen level represents an upper limit for the hydrogen con-centration which cannot be exceeded. Thus, the contradictory results obtained in the presentexample clearly illustrate the difficulties involved in estimating the effective partial pressureof hydrogen in SA welding.

2.8.4.4 Implications of Sievert's lawAn important implication of Sievert's law is that the fraction of hydrogen picked up from thearc atmosphere is very high at low hydrogen pressures:

(2-32)

As seen from equation (2-32), the first traces of hydrogen added to the atmosphere arecompletely absorbed in the metal. At increasing partial pressures the fraction of hydrogenpicked up in the metal will gradually decrease, finally attaining a threshold of (SH/2) in thecase of pure H2. This shows that the concept of 'potential' hydrogen content frequently used tocharacterise filler materials (see Fig. 2.11) is a dangerous one, since the rates of absorption areso different in the high and low ranges of the hydrogen potential.

2.8.4.5 Hydrogen in multi-run weldmentsSo far, no standardised method is available for the determination of hydrogen in multi-layerwelds. Early measurements by Roux,13 using an arrangement similar to that subsequentlyadopted in French standards, indicate a constant ratio of extracted hydrogen to the mass offused metal, regardless of the number of passes. If hydrogen is reported on the basis of depos-ited metal, this ratio may vary by a factor of 2.5 when comparing a deposit made in five passesto a single bead.

Exploratory measurements of local hydrogen contents in large-size joints have been madeby Skjolberg,14 who butt welded a 40 mm plate with a self-shielding flux cored wire at aninterpass temperature of 2000C. Samples were cut from a refrigerated part of the weldment atmid-thickness, including positions in the weld metal close to the fusion line and samples in theHAZ. His results are summarised in Table 2.3.

Normal testing of the filler wire according to ISO 3690 gave fused metal hydrogen contentsof 3.3 ppm (diffusible) and 1.7 ppm (residual). A comparison with Table 2.3 shows that themulti-run content of diffusible hydrogen is much lower than the corresponding ISO value,probably as a result of a high interpass temperature which facilitates loss of hydrogen to thesurroundings through diffusion.

Table 2.3 Measured hydrogen contents in multi-run FCA steel weldment. Data from Skjolberg.14

Condition

As-welded

PWHT*(4h/150°C)

Weld Metal

0.6 ppm diffusible0.9 ppm residual

0.35 ppm diffusible2.25 ppm residual

HAZ

Distance from fusion line (mm)

Oto 5

0.25 ppmdiffusible

0.15 ppmdiffusible

5 to 10

0.15 ppmdiffusible

0.15 ppmdiffusible

10 to 15

0.10 ppmdiffusible

*Post weld heat treated.

2.8.4.6 Hydrogen in non-ferrous weldmentsThe solubility of hydrogen in metals and alloys of industrial importance increases with tem-perature, and passes through a maximum in the vicinity of the boiling point, where the oppos-ing trends of increasing solubility and increasing dilution by metal vapour balance. Solubilitycurves for hydrogen in aluminium, copper, and nickel up to about 22000C have previouslybeen presented in Fig. 2.7.

Since all these metals can dissolve considerable amounts of hydrogen, the risk of hydrogenabsorption during welding is imminent if moisture is present in the shielding gas. Resultsobtained from arc melting experiments with Cu, Al, Ni in Ar-H2 gas atmospheres indicate thathydrogen is absorbed at a high temperature zone under the arc and is transported by fluid flowto the outer, cooler regions of the pool.15 Rejection of the gas in the supersaturated outerregions is slower than the absorption in the hot zone, so the gas content throughout the poolapproximates to that in the absorption zone. Typical estimates of the effective reaction tem-perature of hydrogen desorption (based on the Sievert's law) gave the following result:15

Copper: 16500C

Aluminium: 19000C

Nickel: 19000C

At present, it is not known whether these reaction temperatures also apply to conventionalGTA or GMA welding of the same materials or are mainly restricted to the operational condi-tions employed in the arc melting experiments.

2.9 Absorption of Nitrogen

It is generally recognised that interstitial nitrogen embrittles steel (e.g. see discussion in Chap-ter 7). In steel weld metals the associated loss of toughness due to free nitrogen has beenattributed to solid solution hardening and dislocation locking effects. In addition, excessivenitrogen pick-up can cause porosity in steel weldments because of gas evolution during solidi-fication.

2.9.7 Sources of nitrogen

Since the total nitrogen level in most welding consumables and shielding gases is quite low,the main source of nitrogen contamination is air infiltrated in the arc column. For this reason,the weld metal nitrogen content is very sensitive to variations in the operational conditions(e.g. arc length, electrode stick-out, shielding gas flow rate etc.). The overall reaction of nitro-gen absorption is similar to that of hydrogen:

(dissolved) (2-33)

(2-34)

By introducing the equilibrium constant K4 for the reaction, we get:

where SN is the maximum solubility of nitrogen at 1 atm total pressure,/^ is the activity coef-ficient, and pNl is the resulting partial pressure of diatomic nitrogen in the gas phase.

The solubility of nitrogen in liquid iron is approximately given by:

(2-35)

where T is the temperature in K.At 1600 and 20000C, this equation gives equilibrium concentrations of 446 and 465 ppm,

respectively. In alloyed steel containing large amounts of nitride-forming elements (e.g.austenitic stainless steel), the activity coefficient of nitrogen fN is about 1/4 and hence, thesolubility will be about 4 times higher than that calculated from equation (2-35).

From a primitive model of pseudo-equilibrium between gaseous N2 and dissolved N a maxi-mum solubility of about 465 ppm would be expected in welding under 1 atm total pressure.Thus, the maximum pick-up of nitrogen in deposition of bare wire in air would be of the orderof 465A/OT8 ppm or 416 ppm. If a tentative estimate of air infiltration in the arc column ismade at 1 vol% N2, the expected pick-up of nitrogen would be 465 VoToT or about 47 ppm.

A comparison with the data in Table 2.4 shows that the measured weld metal nitrogencontents are much higher than predicted from Sievert's law. This implies that the mechanismof nitrogen desorption is different from that of hydrogen.

2.9.2 Gas-shielded welding

Information on the factors controlling nitrogen pick-up may be obtained from the work ofKobayashi et a/.,16 who examined the GMA welding process in a systematic manner. Some oftheir results are shown in Fig. 2.20.

Figure 2.20(a), for low-alloy steel, reveals that the square root relationship is a fair approxi-mation only for welding in mixtures of N2 and H2 (curve No. 5). Mixtures of N2 + Ar (curveNo. 3), N2 + CO2 (curve No. 2) and N2 + O2 (curve No. 1) show increasing deviation from thepredicted behaviour. Pure N2 under reduced pressure gives a curve (No. 4) of an entirely differ-ent shape including a maximum at pN ~ 0.05.

Table 2.4 Summary of measured weld metal nitrogen contents. Data compiled by Christensen.4

Similar features are seen from Fig. 2.20(b) for welding of stainless steel. Again, the devia-tion becomes more pronounced as the oxidation potential of the gas mixture is increased in thesequence H2-Ar-CO2-O2. Moreover, a comparison with Fig. 2.20(a) reveals that the displace-ment of the nitrogen concentrations in the presence of chromium is larger than expected fromthe calculated reduction of the nitrogen activity coefficient.

The trends observed in Fig. 2.20 have been confirmed by O'Brien and Jordan17 who studiednitrogen pick-up during CO2-shielded welding of low-alloy steel. As can be seen from Fig.2.21 (a) their curves are similar to those of Kobayashi et al.16 for short circuiting metal transfer,while a mixed spray/globular transfer gives a sharp rise of nitrogen absorption up to pNi = 0.3followed by a constant or slightly decreasing concentration (Fig. 2.21(b)). Both patterns areclearly not in accordance with predictions based on Sievert's law (equation (2-34)).

An interpretation of the observed trends should be made with a view to absorption of hy-drogen, where the concept of pseudo-equilibrium has proved useful for a semiquantitativeprediction. In both cases the molecular species H2 and N2 are known to dissociate in the arccolumn (see Table 2.1), and would therefore dissolve in the metal to an extent far beyond thesolubility controlled by pH or PN . The excess of dissolved hydrogen is probably released asgas at weld pool temperatures. This will also be the case with nitrogen in the absence of oxy-gen, as shown previously in Fig. 2.20(a) and (b). However, under oxidising conditions thedesorption of gaseous nitrogen becomes suppressed by the presence of oxygen at the gas/metalinterface and hence, nitrogen is retained at a level which by far exceeds the solubility limit at1 atm total pressure of N2. This has been confirmed experimentally by Uda and Ohno18 in theirclassic work on surface active elements (i.e. oxygen, sulphur and selenium) in liquid steel. Asimilar phenomenon was quoted in Section 2.8.4.1 from the work of Matsuda et al9 even inthe case of hydrogen, where increased entrapment of hydrogen was observed in the presenceof oxygen (see Fig. 2.15).

It appears thus that excessive absorption of nitrogen (and in some cases also hydrogen)should be interpreted as a state of incomplete release of solute, as described previously inSections 2.6 and 2.7. As a consequence, Sievert's law cannot be used for an estimate of nitro-gen pick-up in steel welding, unless the weld metal oxygen content is extremely low.

2.9.3 Covered electrodes

The nitrogen content of SMA weld deposits is known to be sensitive to variations in the arc

Welding Method Material Nitrogen Content (ppm)

SMAW (basic electrodes) Low-alloy steel 60-180

Stainless steel 550-650

SMAW (rutile electrodes) Low-alloy steel 200-350

Stainless steel 600-750

SAW Low-alloy steel 40-140

FCAW Low-alloy steel 125-275

GMAW Low-alloy steel 50-200

Nitr

ogen

con

tent

, wt%

Nitr

ogen

con

tent

, wt%

Fig. 2.20. Nitrogen pick-up in GMA welding at different concentrations of N2 in the shielding gas;(a) Low-alloy steel, (b) Stainless steel. Data from Kobayashi et al.16

Vol% N2 in shielding gas

GMAW (stainless steel)

(b)


GMAW (low-alloy steel)

(a)

Nitr

ogen c

onte

nt, w

t%

Nitr

ogen

con

tent

, wt%

(a)

Low-alloy steel

Experiment


Low-alloy steel

(b)

Experiment Fig. 2.21. Nitrogen pick-up in GMA weld-ing at different concentrations of N2 in theshielding gas; (a) Short circuting metaltransfer, (b) Mixed and free flight metaltransfer. Data from O'Brien and Jordan.17

Vol% N2in shielding gas

Nitr

ogen

con

tent

, ppm

length (voltage) because of the risk of air infiltration in the arc column. This point is moreclearly illustrated in Fig. 2.22, which shows that the resulting weld metal nitrogen level mayvary significantly from one weld to another, depending on the operational conditions applied.Consequently, the use of long arcs in SMAW should be avoided in order to prevent excessivepick-up of nitrogen from the surrounding atmosphere.

2.9.4 Submerged arc welding

In submerged arc welding the risk of air infiltration in the arc column is less imminent, sincewelding is performed under the shield of a flux. Hence, in multipass welds the filler wire itselfwill be the main source of nitrogen (see Fig. 2.23), while in single pass weldments the baseplate nitrogen content is more important because of the high dilution involved. The latter pointis illustrated by the following numerical example.

Example (2.4)

Consider SA (single pass) welding on a thick plate of low-alloy steel under the followingconditions:

Based on the 'rule of mixtures', calculate the weld metal nitrogen content. Assume in thesecalculations that the nitrogen content of the base plate and the filler wire is 0.005 and 0.012wt%, respectively.

SMAW (low-alloy steel)4 and 5 mm basic covered electrodes

Fig. 2.22. Natural fluctuations in nitrogen pick-up during SMA welding due to variations in the arclength. Data from Morigaki et al.19

Welder No.

A B C D

Wel

d m

etal

nitr

ogen

con

tent

, ppm

loss

gain

SAW (multipass steel weldments)

Nitrogen content in electrode wire, ppm

Fig. 2.23. Nitrogen pick-up in SA welding at different levels of nitrogen in the electrode wire. Data fromBhadeshia et a/.20

SolutionFirst we calculate the total amount of fused parent metal and weld deposit formed on welding.From equations (1-75) and (1-120), we have:

and

The 'rule of mixtures' gives us the nominal weld metal nitrogen content, which is definedas:

The above calculations show that the nitrogen content of single pass SA steel welds is closeto that of the base plate because of the high dilution involved. This is in agreement with gen-eral experience.

Next Page

3Solidification Behaviour of Fusion Welds

3.1 Introduction

Inherent to the welding process is the formation of a pool of molten metal directly below theheat source. The shape of this molten pool is influenced by the flow of both heat and metal,with melting occurring ahead of the heat source and solidification behind it. The heat inputdetermines the volume of molten metal and, hence, dilution and weld metal composition, aswell as the thermal conditions under which solidification takes place. Also important to solidi-fication is the crystal growth rate, which is geometrically related to weld travel speed and weldpool shape. Hence, weld pool shape, weld metal composition, cooling rate, and growth rateare all factors interrelated to heat input which will affect the solidification microstructure.Some important points regarding interpretation of weld metal microstructure in terms of thesefour factors will be discussed below.

Since the properties and integrity of the weld metal depend on the solidification microstruc-ture, a verified quantitative understanding of the weld pool solidification behaviour is essen-tial. At present, our knowledge of the chemical and physical reactions occurring during solidi-fication of fusion welds is limited. This situation arises mainly from a complex sequence ofreactions caused by the interplay between a number of variables which cannot readily be ac-counted for in a mathematical simulation of the process. Nevertheless, the present treatmentwill show that it is possible to rationalise the development of the weld metal solidificationmicrostructure with models based on well established concepts from casting and homogenisingtreatment of metals and alloys.

3.2 Structural Zones in Castings and Welds

The symbols and units used throughout this chapter are defined in Appendix 3.1.During ingot casting, three different structural zones can generally be observed, as shown

schematically in Fig. 3.1. The chill zone is produced by heterogeneous nucleation in the re-gion adjacent to the mould wall as a result of the pertinent thermal undercooling. These grainsrapidly become dendritic, and dendrites having their <100> direction (preferred easy growthdirection for cubic crystals) parallel to the maximum temperature gradient in the melt willsoon outgrow those grains that do not have this favourable orientation. Competitive growthoccurring during the initial stage of the solidification process leads to an alignment of thecrystals in the heat flow direction and eventually to the formation of a columnar zone.12 Fi-nally, an equiaxed zone may develop in the centre of the casting, mainly as a result of growthof detached dendrite arms within the remaining, slightly undercooled liquid.

A similar situation also exists in welding, as indicated in Fig. 3.2 However, in this case thechill zone is absent, since the partly melted base metal grains at the fusion boundary act as seedcrystals for the growing columnar grains.3 In addition, the growth direction of the columnar

Shrinkage pipe

Chill zone

Columnar zone

Equiaxed zone

Mould

Fig. 3.1. Transverse section of an ingot showing the chill zone, the columnar zone and the equiaxed zone(schematic).

grains will change continuously from the fusion line towards the centre of the weld due to acorresponding shift in the direction of the maximum temperature gradient in the weld pool.This change in orientation may result in a curvature of the columnar grains (Fig. 3.2(a)). Alter-natively, new grains can nucleate and grow in a columnar manner, producing a so-called 'stray'structure as shown schematically in Fig. 3.2(b). Finally, if the conditions for nucleation of newgrains are favourable, an equiaxed zone will form near the weld centreline similar to thatobserved in ingots or castings (see Fig. 3.2(b)).

Although the process of weld pool solidification is frequently compared with that of aningot in 'miniature', a number of basic differences, already mentioned, exist which stronglyinfluence the microstructure and properties of the weld metal. Of particular importance is alsothe disparity in cooling rate between a fusion weld and an ingot (see Fig. 3.3). For conven-tional processes such as shielded metal arc (SMA), gas metal arc (GMA), submerged arc (SA)or gas tungsten arc (GTA) welding the cooling rate may vary from 10 to 103 0C s"1, while formodern high energy beam processes such as electron beam (EB) and laser welding the coolingrate is typically of the order of 103 to 106 0C s"1.4 Consequently, to appreciate fully the impli-cations of these differences in general solidification behaviour between a weld pool and aningot, it is necessary to consider in detail the sequence of events taking place in the solidifyingweld metal beginning with the initiation of crystal growth at the fusion boundary.

3.3 Epitaxial Solidification

It is well established that initial solidification during welding takes place epitaxially, where thepartly melted base metal grains at the fusion boundary act as seed crystals for the columnargrains. This process is illustrated schematically in Fig. 3.4.

Welding direction

Welding direction

(a)

(b)

Columnar zone

Equiaxed zone

Columnar zone •

Fig. 3.2. Examples of structural zones in fusion welds (schematic); (a) Curved columnar grains,(b) Stray grain structure.

Coo

ling

rate

, °C

/s

SM

AW

, S

AW

,G

MA

W, G

TAW

Ele

ctro

n be

am w

eldi

ngLa

ser w

eldi

ng

Rap

id s

olid

ifica

tion

tech

nolo

gy

Fig. 3.3. Disparity in cooling conditions between casting, welding and rapid solidification.

Process

Fusio

nbo

unda

ry

Fig. 3.5. Schematic representation of heterogeneous nucleation.

Substrate (S)

Liquid (L)

Fig. 3.4. Schematic illustration showing epitaxial growth of columnar grains from partly melted basemetal grains at fusion boundary.

HAZ Weld metal

3.3.1 Energy barrier to nucleation

During epitaxial solidification, a solid embryo (nucleus) of the weld metal forms at the melted-back surface of the base metal grain. Assuming that the interfacial energy between the embryoand the liquid is isotropic, it can be shown, for a given volume of the embryo, that the interfa-cial energy of the whole system is minimised if the embryo has the shape of a spherical cap.Under such conditions, the following relationship exists between the interfacial energies (seeFig. 3.5):

where (3 is the wetting angle.The change in free energy, AGhet, accompanying the formation of a solid nucleus with this

configuration is given by:5

(3-1)

(3-2)

where VE is the volume of the solid embryo, AGV is the free energy change associated with theembryo formation, AEL and AES are the areas of the embryo-liquid and embryo-substrate inter-faces, respectively, and/(P) is the so-called shape factor, defined as:

(3-3)

The critical radius of the stable nucleus, r / , is found by differentiating equation (3-2) withrespect to rs and equating to zero:

(3-4)

By substituting equation (3-4) into equation (3-2), we obtain the following expression forthe energy barrier to heterogeneous nucleation (AG^r):

(3-5)

where AHm is the latent heat of melting, Tm is the melting point, and AJT is the undercooling.It is easy to verify that the first term in equation (3-5) is equal to the energy barrier to

homogeneous nucleation, AG^om. Hence, we may write:

(3-6)

Equation (3-6) shows that AG^ is a simple function of the wetting angle O). Since the

Under such conditions equation (3-1) predicts that the wetting angle 3 ~ 0 (cos(3 ~ 1),which implies that there is a negligible energy barrier to solidification of the weld metal (№}*het

~ 0), i.e. no undercooling of the melt is needed, and solidification occurs uniformly over thewhole grain of the base metal. This is in sharp contrast to conventional casting of metals andalloys where some undercooling of the melt is always required to overcome the inherent en-ergy barrier to solidification (see Fig. 3.6).

3.3.2 Implications of epitaxial solidification

Since the initial size of the weld metal columnar grains is inherited directly from the graingrowth zone adjacent to the fusion boundary, the solidification microstructure depends on thegrain coarsening behaviour of the base material. This is particularly a problem in high energyprocesses such as submerged arc and gas metal arc welding, where grain growth of the basemetal can be considerable. In such cases the size of the columnar grains at the fusion boundarywill be correspondingly coarse, as indicated by the data in Fig. 3.7.

Moreover, during multipass welding the columnar grains can renucleate at the boundarybetween for instance the first and the second weld pass and subsequently grow across theentire fusion zone, as illustrated in Fig. 3.8. This type of behaviour is usually observed inweldments which do not undergo transformations in the solid state (e.g. aluminium, certaintitanium alloys, stainless steel etc.). In practice, the problem can be eliminated by additions ofinoculants via the filler wire, which facilitates a refinement of the columnar grain structurethrough heterogeneous nucleation of new (equiaxed) grains ahead of the advancing interface(to be discussed later).

chemical composition and the crystal structure of the two solid phases are usually very similar,we have:6

AG

rs

CastingHomogeneous

nucleationWelding

Fig. 3.6. The free energy change associated with heterogeneous nucleation during casting and weldmetal solidification, respectively (schematic). The corresponding free energy change associated withhomogeneous nucleation is indicated by the broken curve in the graph.

Wel

d m

etal

prio

r aus

teni

te g

rain

siz

e (ji

m)

Fig. 3.8. Optical micrograph showing renucleation of columnar grains during multipass GMA weldingof a P-titanium alloy.

B a s e metal

2 . pass

1 . pass

H A Z

Fig. 3.7. Correlation between HAZ prior austenite grain size at the fusion boundary and the correspond-ing weld metal prior austenite grain size. Data from Grong et al?

HAZ prior austenite grain size (jim)

GMAW (low-alloy steel)

Fusionline

Weldmetal

HAZ

3.4 Weld Pool Shape and Columnar Grain Structures

Growth of the columnar grains always proceeds closely to the direction of the maximum ther-mal gradient in the weld pool, i.e. normal to the fusion boundary. This implies that the colum-nar grain morphology depends on the weld pool geometry.

3.4.1 Weld pool geometry

The weld pool geometry is a function of the welding speed and the balance between the heatinput and the cooling conditions, as influenced by the base plate thermal properties. At pseudo-steady state, these conditions establish a dynamic equilibrium between heat supply and heatextraction so that the shape of the weld pool remains constant for any given speed. Followingthe treatment in Chapter 1, the weld pool geometry depends on the dimensionless operatingparameter n3, defined as:

where qo is the net arc power, v is the welding speed, a is the thermal diffusivity of the baseplate, and Hm-Ho is the heat content per unit volume at the melting point.

As shown in Fig. 3.9(a), a tear-shaped weld pool is favoured by a high n3 value, which ischaracteristic of fast moving high power sources. In contrast, at a low arc power and a lowwelding speed the shape of the weld pool becomes more elliptical because of a shift in themode of heat flow (see Fig. 3.9(b)). Note, however, that the thermal properties of the basemetal is also of importance in this respect, since the n3 parameter is a function of both a andHm-Ho. Consequently, a tear-shaped weld pool is usually observed in weldments of a lowthermal diffusivity (e.g. austenitic stainless steel), whereas an elliptical or spherical weld poolis more likely to form during aluminium welding owing to the resulting higher thermal diffu-sivity of the base metal.

In addition to the factors mentioned above, the geometry of the weld pool is also affected byconvectional heat transfer due to the presence of buoyancy, electromagnetic or suface tensiongradient forces. Recently, attempts have been made to include such effects in heat flow mod-els for welding.8"11 Referring to Fig. 3.10(a) the buoyancy force will promote the formation ofa shallow, wide weld pool because of transport of 'hot' metal to the surface and 'cold' metal tothe bottom of the pool. In the presence of the electromagnetic force the flow pattern is re-versed, since the latter force will tend to push the liquid metal in the central part of the pooldownward to the root of the weld. This makes the weld pool deeper and more narrow, asshown in Fig. 3.10(b).

Moreover, it is generally accepted that surface tension gradients can promote circulation ofliquid metal within the weld pool from the region of low surface tension to the region of highersurface tension.9 In the absence of surface active elements such as oxygen and sulphur, thesurface tension decreases with increasing temperature as illustrated in Fig. 3.10(c), which forcesthe metal to flow outwards towards the fusion boundary. This results in the formation of arelatively wide and shallow weld pool. However, if oxygen or sulphur is present in sufficientquantities a positive temperature coefficient of the surface tension may develop, which facili-tates an inward fluid flow pattern and an increased weld penetration (see Fig. 3.10(d)). Theimportant influence of surface active elements on the resulting bead morphology is well docu-

(3-7)

HAZ isothermsFusion boundary

Weldpool

V

(a)

HAZ isotherms

Fusion boundary

VWeldpool

(b)

Fig. 3.9. Theoretical shape of fusion boundary and neighbouring isotherms under different operationalconditions; (a) High n3 values, (b) Low ^-values.

merited for ordinary GTA austenitic stainless steel welds.1213 The indications are that sucheffects become even more important under hyperbaric welding conditions.14

3.4.2 Columnar grain morphology

It is evident from the above discussion that a change in the weld pool geometry, caused byvariations in the operational conditions, may strongly alter the weld metal solidification micro-structure. In fact, more than nine different grain morphologies have been observed duringfusion welding.15 The two most important are shown in Fig. 3.11. Referring to Fig. 3.11(a) aspherical or elliptical weld pool will reveal curved and tapered columnar grains owing to ashift in the direction of the maximum thermal gradient in the liquid from the fusion boundarytowards the weld centre-line. In contrast, a tear-shaped weld pool yields straight and broad

Fig. 3.10. Schematic diagrams illustrating the major fluid flow mechanisms operating in a weld pool;(a) Buoyancy force (b) Electromagnetic force.

columnar grains as shown in Fig. 3.11(b), since the direction of the maximum temperaturegradient in the melt does not change significantly during the solidification process. The lat-ter condition is known to promote formation of centre-line cracking because of mechanicalentrapment of inclusions and enrichment of eutectic liquid at the trailing edge of the weldpool.

3.4.3 Growth rate of columnar grains

The growth rate of the columnar grains is geometrically related to the weld travel speed andthe weld pool shape.

3.4.3.1 Nominal crystal growth rateSince the shape of the weld pool remains constant during steady state welding, the growth rateof the columnar grains must vary with position along the fusion boundary. This point is moreclearly illustrated in Fig. 3.12 which shows a sketch of a single columnar grain growing paral-lel with the steepest temperature gradient in the weld pool. Taking the angle between the

(b)

Weld pool Arc

Electrode

(a)

Weld poolArc

Electrode

Sur

face

tens

ion

Sur

face

tens

ion

TemperatureElectrode

ArcWeld pool

(C)

TemperatureElectrode

ArcWeld pool

(d)

Fig. 3.10. Schematic diagrams illustrating the major fluid flow mechanisms operating in a weld pool(continued); (c) Surface tension gradient force (negative gradient); (d) Surface tension gradient force(positive gradient).

(a)

(b)

Heat source v

Heat source v

Fig. 3.11. Schematic comparison of columnar grain structures obtained under different welding condi-tions; (a) Elliptical weld pool (low n3 values), (b) Tear-shaped weld pool (high n3 values). Open arrowsindicate the direction of the maximum temperature gradient in the weld pool.

Fusion boundary

Heat source

Crystal

Fig. 3.12. Definition of the nominal crystal growth rate RN.

growth direction and the welding direction equal to a, the steady state growth rate, R N , be-comes:

(3-8)

where v is the welding speed.Considering spherical or elliptical weld pools, the nominal crystal growth rate is lowest at

the edge of the weld pool (a—>90°, cosa-^0) and highest at the weld centre-line where R N

approaches v (a->0, cosa^ l ) . In contrast, columnar grains trailing behind a tear-shaped weldpool will grow at an approximately constant rate which is significantly lower than the actualwelding speed (a » 0), since the direction of the maximum temperature gradient in the weldpool does not change during the solidification process. This is also in agreement with practicalexperience (see Fig. 3.13).

Nom

inal

gro

wth

rat

e (R

N),

mm

/sN

omin

al g

row

th r

ate

(RN),

mm

/s

Equ

iaxe

d zo

ne

Niobium (1 mm plate thickness)

Relative position from edge of weld pool (%)•

(b)

(a)

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) Stainlesssteel. Data from Senda et al.16

Example (3.1)

Consider electron beam (EB) welding of a lmm thin sheet of austenitic stainless steel underthe following conditions:

Estimate on the basis of the Rosenthal thin plate solution (equation 1-83) the steady stategrowth rate of the columnar grains trailing the weld pool.

SolutionThe contour of the fusion boundary can be calculated from the Rosenthal thin plate solutionaccording to the procedure shown in Example (1.10). If we include a correction for the latentheat of melting, the QbZn3 ratio at the melting point becomes:

Substitution of the above value into equation (1-83) gives the fusion boundary contourshown in Fig. 3.14. It is evident from Fig. 3.14 that the weld pool is very elongated under theprevailing circumstances due to a constrained heat flow in the -direction. This implies that theangle 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 rateEquation (3-8) does not take into account the inherent anisotropy of crystal growth. For fac-eted materials the dendrite growth directions are always those that are 'capped' by relativelyslow-growing (usually low-index) crystallographic planes.1 Figure 3.15 shows examples offaceted cubic crystals delimited by {100} and {111} planes, respectively. If the {111} planesare the slowest growing ones, the {100} planes will grow out, leaving the {111} facets and anew crystal growing in the <100> directions as shown schematically in Fig. 3.15(b).

Although most metals and alloys do not form faceted dendrites, the anisotropy of crystalgrowth is still maintained during solidification.2 In fact, experience has shown that the majordendrite growth direction is normally the axis of a pyramid whose sides are the most closelypacked planes with which a pyramid can be formed.1 These directions are thus <100> forbody- and face-centred cubic structures, < 1010 > for hexagonal close-packed structures, and<110> for body-centred tetragonal structures.

Because of the existence of preferred growth directions, the local growth rate of the crystalsRL will always be higher than the nominal growth rate R N defined in equation (3-8). Considernow a cubic crystal which grows along the steepest temperature gradient in the weld pool, asshown schematically in Fig. 3.16. If § denotes the angle between the interface normal and the<100> direction, the following relationship exists between RN and RL:

-y(m

m)

+yjm

m)

Columnar zone

Equiaxed zone

Columnar zone

Fusion boundary

Heat source

+x(mm)

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 delim-ited by {111} planes.

Tip

tem

pera

ture

, 0C

Fig. 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 thesolid curve in the graph. Data from Rappaz et alP

which gives:

Equation (3-10) shows that the local growth rate increases with increasing misalignment of

(3-9)

(3-10)

Tip velocity, mm/s-

Liquidus temperature

Fig. 3.16. Definition of the local crystal growth rate RL.

Welding direction (x)

Columnar grain

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 aheadof the solid/liquid interface (see Fig. 3.17), they will soon be outgrowed by other grains whichhave a more favourable orientation. Fusion welds of the fee and bcc type will therefore de-velop a sharp <100> solidification texture in the columnar grain region, similar to that docu-mented for ingots and castings. The weld metal columnar grains may nevertheless be sepa-rated by 'high-angle' boundaries, as shown in Fig. 3.1&, due to a possible rotation of the grainsin the plane perpendicular to their <100> length axes.

Example (3.2)

Consider electron beam welding of a 2mm thick single crystal disk of Fe-15Ni-15Cr underthe 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 ofthe dendrites trailing the weld pool under steady state welding conditions (assume 2-Dheat flow). Make also schematic drawings of the solidification microstructure in differentsections of the weld. Relevant thermal properties for the Fe-15Ni-15Cr single crystal aregiven below:

Solution

Since the base metal is a single crystal, separate columnar grains will not develop. Neverthe-less, under 2-D heat flow conditions growth of the dendrites can occur both in the [100] andthe [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 <100> direction (sche-matic).

Fig. 3.20. Schematic diagram showing the pertinent orientation relations between the fusion boundaryinterface 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 heatsource v. In contrast, the growth rate of the [010] dendrites depends both on v and a, and willtherefore vary with position along the fusion boundary. It follows from minimum velocitycriterion that the [100] dendrites will be selected when the interface normal angle a is less than45°, 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 platesolution (equation (1-83)) according to the procedure shown in Example (1.10). If we include

Welding direction

Fig. 3.19. Orientation of the single crystal Fe-15Ni-15Cr disk with respect to beam travel direction (Ex-ample (3.2)).

Heat source

Weld

Rh

k,/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 inFig. 3.22(a). Included in Fig. 3.22 are also schematic drawings of the predicted solidificationmicrostructure in different sections of the weld.

The results in Fig. 3.22 should be compared with the reconstructed 3-D image of the solidi-fication microstructure in Fig. 3.23, taken form Rappaz et al.17 Due to partial heat flow in thez-direction, [001] dendrite trunks will also develop. Nevertheless, these data confirm the gen-eral validity of equations (3-8) and (3-10) relating crystal growth rate to welding speed andweld pool shape.

3.4.4 Reorientation of columnar grains

In principle, there are two different ways a columnar grain can adjust its orientation duringsolidification in order to accommodate a shift in the direction of the maximum temperaturegradient in the weld pool, i.e.:

(i) Through bowing(ii) Through renucleation.

(a)

(b)

dendrites

dendrites

dendrites

-y (mm)

Heat source

+x (mm)

+y (mm)Fusion boundary

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 crystalsA continuous change in the crystal orientation due to bowing will result in curved columnargrains, as shown previously in Fig. 3.2(a). This type of grain morphology has been observedin for instance electron beam welded aluminium and iridium alloys.34 Normally, the adjust-ment of the crystal orientation is promoted by multiple branching of dendrites present withinthe grains. Alternatively, the reorientation can be accommodated by the presence of surfacedefects at the solid/liquid interface, e.g. screw dislocations, twin boundaries, rotation bounda-ries, etc. The latter process presumes, however, a faceted growth morphology, and is thereforeof minor interest in the present context.

Example (3.3)

Consider a curved columnar grain of iridium which grows from the fusion boundary towardsthe 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] dendritesin the [100] direction, calculate the maximum local growth rate of the crystal during solidifica-tion.

2

y

X

Fig. 3.23. Reconstructed 3-D image of solidification microstructure in an electron beam welded Fe-15Ni-15Cr single crystal. The letters (a), (b) and (c) refer to [100], [010] and [001] type of dendrites, respec-tively. After Rappaz et al.17

Weld centre-line

Fusion line

Fig. 3.24. Sketch of curved columnar grain in Example (3.3).

SolutionIn principle, the solution to this problem is identical to that presented in Example (3.2). Refer-ring 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 longas the interface normal angle a is larger than 45°, while the [100] direction is selected atsmaller angles. This means that the local growth rate of the dendrites, in practice, never willexceed the welding speed v.

3.4.4.2 Renucleation of crystalsIn ingots and castings, three different mechanisms for nucleation of new grains ahead of theadvancing interface are operative:12

(i) Heterogeneous nucleation(ii) Dendrite fragmentation(iii) Grain detachment.

The former mechanism is of particular importance in welding, since the weld metal oftencontains a high number of second phase particles which form in the liquid state. These parti-cles can either be primary products of the weld metal deoxidation or stem from reactionsbetween specific alloying elements which are deliberately introduced into the weld pool throughthe filler wire. The latter process is also known as inoculation.

Nucleation potency of second phase particlesIn general, the effectiveness of individual particles to act as heterogeneous nucleation sites canbe evaluated from a balance of interfacial energies, analogous to that described in Section3.3.1 for epitaxial nucleation. It follows from the definition of the wetting angle (3 in Fig. 3.5that the energy barrier to heterogeneous nucleation is a function of both the substrate/liquidinterfacial energy ySL, the substrate/embryo interfacial energy yES, and the embryo/liquid in-terfacial energy yEL. Complete wetting is achieved when:

(3-11)

Under such conditions, the nucleus will readily grow from the liquid on the substrate. Un-fortunately, data for interfacial energies are scarce and unreliable, which makes predictionsbased on equation (3-11) rather fortuitous.18

In pure metals, experience has shown that the solid/liquid interfacial energies are roughlyproportional to the melting point, as shown by the data in Fig. 3.25. On this basis, it can beexpected that the higher melting point phases will reveal the highest ySL values, and thus benucleants for lower melting phases. A similar situation also exists in the case of non-metallicinclusions in liquid steel, where the high-melting point phases are seen to exhibit the highestsolid/liquid interfacial energies (see Fig. 3.26).

In contrast, very little information is available on the substrate/embryo interfacial energyyES. 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 thenucleus, which results in a low lattice disregistry between the two phases. In general, assess-ment of the degree of atomic misfit between the nucleus n and the substrate s can be done on

lnte

rfaci

al e

nerg

y, J

/m2

Mel

ting

poin

t, K

Fig. 3.26. Values of interfacial energy 75L for different types of non-metallic inclusions in liquid steel at16000C as function of their melting points. Data compiled from miscellaneous sources.

Melting point, 0C

Fig. 3.25. Values of solid/liquid interfacial energy ySL of various metals as function of their melting points.Data from Mondolfo.18

Interfacial energy, J /m2

Und

erco

olin

g, 0C

Fig. 3.27. Relationship between planar lattice disregistry and undercooling for different nucleants insteel. Data compiled from miscellaneous sources.

« „ « >

In practice, the undercooling Ar (which is a measure of the energy barrier to heterogeneousnucleation) increases monotonically with increasing values of the planar lattice disregistry, asshown by the data in Fig. 3.27. This means that the most potent catalyst particles are thosewhich also provide a good epitaxial fit between the substrate and the embryo. Examples ofsuch catalyst particles are TiAl3 in aluminium 18 and TiN in steel.19 Nucleation of delta ferriteat titanium nitride will be considered below.

a low-index plane of the substrate;a low-index direction in (hkl)s

a low-index plane in the nucleated solid;a low-index direction in (hkl)n;

the interatomic spacing along [wvw]n;

the interatomic spacing along [WVH>]5; andthe angle between the [wvw] and the [wvw]w.

where

the basis of the Bramfitt's planar lattice disregistry model :19

(3-12)

Example (3.4)

In low-alloy steel weld metals, titanium nitride can form in the melt due to interactions be-tween dissolved titanium and nitrogen. Assume that the TiN particles are faceted and delim-ited by {100} planes. Calculate on the basis of equation (3-12) the minimum planar latticedisregistry between TiN and the nucleating delta-ferrite phase under the prevailing circum-stances. Indicate also the plausible orientation relationship between the two phases. Thelattice parameters of delta ferrite and TiN at 15200C may be taken equal to 0.293 and 0.43 lnm,respectively.

SolutionTitanium nitride has the NaCl crystal structure, while delta ferrite is body-centred cubic, asshown in Fig. 3.28(a) and (b). It is evident from Fig. 3.29(a) that a straight cube-to-cube ori-entation 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 toeach other (see Fig. 3.29(b)), conforming to the following orientation relationship:

A comparison with the data in Fig. 3.27 shows that the calculated lattice disregistry con-forms to an undercooling of about 1 to 2°C. This value is sufficiently small to facilitate hetero-geneous nucleation of new grains ahead of the advancing interface during solidification.

Considering other inclusions with more complex crystal structures, the chances of obtain-ing a small planar lattice disregistry between the substrate and the delta ferrite nucleus are

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:

Fe- atoms

N-atoms

Ti- atoms

Fig. 3.28. Crystal structures of phases considered in Example (3.4); (a) Titanium nitride, (b) Delta ferrite.

(b)(a)

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 arrange-ment along coherent TiN/d-Fe interface.

rather poor (see Fig. 3.27). Nevertheless, such particles can act as favourable sites for hetero-geneous nucleation if 7 ^ is sufficiently large compared with yEL and 7^ . This is illustrated bythe following example:

Example (3.5)

In low-alloy steel weld metals 7-Al2O3 inclusions can form during the primary deoxidationstage as discussed in Section 2.12.4.2 (Chapter 2). Based on the classic theory of heteroge-neous nucleation, evaluate the nucleation potency of such inclusions with respect delta ferrite.

Ti atoms N atoms 8-Fe atoms

(b)(C)

(a)

TiN

TiN

AG

*he/

AGho

m

No

wet

ting

Com

plet

e w

ettin

g

SolutionIt is readily seen from Fig. 3.27 that the planar lattice disregistry between delta ferrite andAl2O3 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 fer-rite/liquid and the inclusion/liquid interfacial energies:

and

According to equation (3-11) complete wetting is achieved when ySL > yES + yEL. Thisrequirement is clearly met under the prevailing circumstances.

Similar calculations can also be performed for other types of non-metallic inclusions insteel weld metals. The results are presented graphically in Fig. 3.30. It is evident that thenucleation potency of the inclusions increases in the order SiO2-MnO, Al2O3-Ti2O3-SiO2-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 decreasewith increasing Al2O3-contents in the inclusions. This observation is not surprising, consider-ing 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 solidificationmicrostructure is well documented in the literature.320"22

Rate of heterogeneous nucleationIt can be inferred from the classic theory of heterogeneous nucleation that the nucleation rate

p (degrees)

Embryo'

Inclusion

(YsfYES)/7EL

Fig. 3.30. Nucleation potency of different weld metal oxide inclusions with respect to delta ferrite.

Aver

age

wid

th o

f gra

ins,

i m

Aver

age

leng

th o

f gra

ins,

^m

Fig. 3.31.Effect of deoxidation practice on the columnar grain structure in low-alloy steel weld metals;(a) Average width of columnar grains, (b) Average length of columnar grains. Data from Kluken et al.22

Nhet(i.e. number of nuclei which form per unit time and unit volume of the melt) is interre-lated to the energy barrier AG^ through the following equation:5

< A % A I W[ % 0 W

(3-13)

whereZ1 is a frequency factor, Nv is the density of nucleation sites per unit volume of the melt,

95% confidence limit

Pure AI2O3

AI2O3 content (wt%)(b)

(A%AI)weld/[%O]anaL

Pure AI2O3

95% confidence limit

AI2O3 content (wt%)(a)

Aver

age

width

of g

rains

, (x m

AGD is the activation energy for diffusion of atoms across the interface, and k is the Boltzmannconstant.

Since AGD is often negligible compared with AG^et in liquids, equation (3-13) reduces to:

(3-14)

Equation (3-14) shows that the nucleation rate Nhet depends both on Nv and &Ghe{. Hence,under full wetting conditions (AGhet ~ 0), the number of nuclei which form per second and mm3

ahead of the advancing interface is directly proportional to the instantaneous concentration ofcatalyst particles in the melt. Examples of such particles are TiAl3 in aluminium and TiN/Al2O3

in steel. The important effect of controlled titanium additions and subsequent TiAl3 precipi-tation on the columnar grain structure in 1100 aluminium welds is illustrated in Fig. 3.32.

Critical cell/dendrite alignment angleIt follows from the minimum growth rate criterion and the definition of the local crystal growthrate in equation (3-10) that reorientation of the columnar grains will occur when the cell/dendrite alignment angle $ reaches a critical value <\>*. The value of 4>* will, in turn, depend onthe nucleation potency of the catalyst particles and can be estimated for different types ofwelds. If growth of the columnar grains is assumed to occur along a circle segment of lengthL (see Fig. 3.33), the critical cell/dendrite alignment angle is given by:

(3-15)

where co is the total grain rotation angle, and / is the average length of the columnar grains (inmm).

Titanium content, wt%

Fig. 3.32. Effect of titanium on the columnar grain structure in 1100 aluminium welds. The value Y isthe 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 low-alloy steel,22 we obtain:

(3-16)

Calculated values for 4>* in steel weld metals are presented in Fig. 3.34, using data fromKluken et al.22 An expected, the critical cell/dendrite alignment angle in fully aluminiumdeoxidised steel welds is seen to be very small (of the order of 2°), reflecting the fact thatnucleation of delta ferrite occurs readily at Al2O3 inclusions. The value of 4>* increases gradu-ally with decreasing Al2O3 contents in the inclusions and reaches a maximum of about 4° forSi-Mn deoxidised steel weld metals. This situation can be attributed to less favourable nucle-ating opportunities for delta ferrite at silica-containing inclusions, which reduces the possibili-ties of obtaining a change in the crystal orientation during solidification through a nucleationand growth process.

Dendrite fragmentationIn principle, nucleation of new grains ahead of the advancing interface can also occur fromrandom solid dendrite fragments contained in the weld pool. Although the source of thesesolid fragments has yet to be investigated, it is reasonable to assume that they are generated bysome process of interface fragmentation due to thermal fluctuations in the melt or mechanicaldisturbances at the solid/liquid interface.3 At present, it cannot be stated with certainty whethergrain refinement by dendrite fragmentation is a significant process in fusion welding.26

Grain detachmentSince the partially melted base metal grains at the fusion boundary are loosely held together byliquid films between them, there is also a possibility that some of these grains may detachthemselves from the base metal and be trapped in the solidification front.26 Like dendritefragments, such partially melted grains can act as seed crystals for the formation of new grainsin the weld metal during solidification if they are able to survive sufficiently long in the melt.

R L /

v co

s a

Calculated fromequation (3-10)

Critical cell/dendrite alignment angle ($*)

Fig. 3.34. Critical cell/dendrite alignment angle ()>* for reorientation of delta ferrite columnar grains dur-ing 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 weldmetal solidification microstructure. In general, each individual grain will exhibit a substruc-ture consisting of a parallel array of dendrites or cells. This substructure can readily be re-vealed by etching, also in cases where it is masked by subsequent solid state transformationreactions (as in ferrous alloys).2224

3.5.1 Substructure characteristics

A cellular substructure within a single grain consists of an array of parallel (hexagonal) cellswhich are separated from each other by 'low-angle' grain boundaries, as shown schematicallyin Fig. 3.35. In the presence of solute, these boundaries respond to etching even in the absenceof segregation. When the cellular to dendritic transition occurs, the cells become more dis-torted and will finally take the form of irregular cubes, as indicated by the optical micrographin Fig. 3.36. This is actually a dendritic type of substructure, where the formation of secondaryand tertiary dendrite arms is suppressed because of a relatively small temperature gradient inthe transverse direction compared with the longitudinal (growth) direction. Fully branceddendrites may, however, develop in the centre of the weld if the thermal conditions are favour-able. Branching will then occur in specific crystallographic directions, e.g. along the three<100> 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 pri-marily in their sensitivity to crystalline alignment. Cells do not necessarily have the <100>axis orientation, while dendrites do.2 Hence, cells can grow with their axes parallel to the heatflow direction, regardless of the crystal orientation. This important point is often overlookedwhen discussing competitive grain growth in fusion welding.

Next Page

4Precipitate Stability in Welds

4.1 Introduction

Precipitate stability is an important aspect of welding metallurgy. Normally, modern structuralsteels and aluminium alloys derive their balanced package of high strength, ductility and tough-ness via optimised thermomechanical processing to produce a fine-grained, precipitationstrengthened matrix. This delicate balance of microalloy precipitation and microstructure,however, is significantly disturbed by the heat of welding processes, which, in turn, affects themechanical integrity of the weldment.

When a commercial alloy is subjected to welding or heat treatment several competitiveprocesses are operative which may contribute to a change in the volume fraction and sizedistribution of the base metal precipitates. The two most important are:1

(i) Particle coarsening (Ostwald ripening)(ii) Particle dissolution (reversion)

Referring to Fig. 4.1, particle coarsening occurs typically at temperatures well below theequilibrium solvus Te of the precipitates, while particle dissolution is the dominating mecha-nism at higher temperatures. On the other hand, there exists no clear line of demarcationbetween these two processes, which means that particle coarsening can take place simultane-ously with reversion in certain regions of the weld where the peak temperature of the thermalcycle falls within the 'gray zone' in Fig. 4.1. Nevertheless, it is important to regard them asseparate processes, since the reaction kinetics are so different (coarsening is driven by thesurface energy alone, whereas dissolution, which involves a change in the total volume frac-tion, 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 productis widely used for an evaluation of the response of grain size-controlled and dispersion-hard-ened 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:

Tem

pera

ture

Incr

easin

g he

atin

g ra

te

Particle dissolution

'Grey zone1

Particle coarsening |

%B

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

At equilibrium, we have:

(4-1)

(4-2)

where AH° and AS° are the standard enthalpy and entropy of reaction, respectively. The othersymbols 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 equalto 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, thesolubility 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 isequal 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 precipi-tates in low-alloy steels and aluminium alloys.

In addition to the compounds listed in Table 4.1, different types of mixed precipitates mayform within systems which contain more than two alloying elements.3"6 However, since thepresence of such multiphase particles largely increases the complexity of the analysis, onlypure 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 ofthe 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 increas-ing concentrations of solute in the matrix. This is in agreement with the Le Chatelier's princi-ple.

Table 4.1 Equilibrium solubility products for different types of precipitates in low-alloy steels andaluminium alloys. Data compiled from miscellaneous sources.

Material/ phase Type of log [%A]n [%B]m

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

Al-Zn-Mgij: Zn2Mg 7.72 4255

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 disso-lution temperature of each of the following three nitride precipitates, i.e. NbN, AlN, and TiN.

SolutionThe equilibrium dissolution temperature of the precipitates can be computed from equation (4-4) 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 willdissolve readily at temperatures above 1050 to 11000C, while TiN is thermodynamically sta-ble up to about 14500C. In practice, however, a certain degree of superheating is alwaysrequired to overcome the inherent kinetic barrier against dissolution, particularly if the heatingrate is high. Consequently, in a real welding situation the actual dissolution temperature of theprecipitates may be considerably higher than that inferred from simple thermodynamic calcu-lations 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, thermo-dynamic calculations based on the solubility product represent in many cases the only practi-cal means of estimating the solid solubility of alloying elements in commercial low-alloy steelsand aluminium alloys.

4.2.3.1 Equilibrium precipitatesIn 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 beinferred directly from equation (4-3). If we replace / ^ by R (i.e. switch from common tonatural logarithms), this equation yields:

(4-5)

[%B

]

Fig. 4.2. Concentration displacements during dissolution of binary intermetallics (equilibrium condi-tions).

[%A]

Excess B

[%B]o

[%A]0

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 corre-

sponding change in the matrix concentrations during dissolution of pure AnBm for a given setof starting conditions.

Alternatively, we can express T as function of the product [%A]n [%B]m by utilising equa-tions (4-3) and (4-6). The combination of these equations provides a mathematical descriptionof the 'solvus boundary' of an equilibrium precipitate in a multi-component alloy system. It isevident from the graphical representation in Fig. 4.3 that the solid solubility will always in-

or

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

(4-6)

Tem

pera

ture

Red

uced

solid

solu

bili

tyof

ele

men

t A

Nom

inal

allo

y co

mposi

tion

Incr

ease

d a

dditi

ons

_o

f el

emen

t B

I Increased dissolution temperature

Concentration of element A

Fig. 4.3. Factors affecting the solid solubility of a binary intermetallic compound in a multi-componentalloy system (schematic).

crease with increasing temperature when AH° is positive. This type of behaviour is character-istic of intermetallics in metals and alloys, since the dissolution process in such systems isendothermic.7 As a result, increased additions of a second alloying element B will also reducethe solubility of the first alloying element A by shifting the 'solvus boundary' towards highertemperatures 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 theprecipitates/^ 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 concentra-tion of element B is sufficiently high to tie-up all A in the form of precipitates. Similarly, if Ais 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 tempera-ture annealing. Consider a pure ternary alloy which contains 0.75 wt% (0.83 at.%) Mg and 1.0wt% (0.96 at.%) Si. Estimate on the basis of the solubility product the equilibrium volumefraction of Mg2Si at 4000C. Make also a sketch of the Mg2Si solvus in a vertical sectionthrough the ternary Al-Mg-Si phase diagram. Relevant physical data for the Al-Mg-Si sys-tem are given below:

SolutionThe maximum possible volume fraction of Mg2Si precipitated at absolute zero (fmax) can beestimated 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 obtainedfrom 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 beexpressed solely in terms of the Mg-concentration. Substituting

into the above equation gives [at.% Mg] ~ 0.20. The equilibrium volume fraction OfMg2Si at4000C is thus:

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

Tem

pera

ture

, 0C

Nom

inal

allo

y co

mpo

sitio

n

Fig. 4.4. Solubility of Mg2Si in aluminium (Example (4.2)).

at% Mg

at%Mg Si

Dissolution temperature: 5600C

It is seen from the graphical representation of the above equation in Fig. 4.4 that the Mg2Sicompound is thermodynamically stable up to about 3000C. At higher temperatures the phasewill start to dissolve until the process is completed at 5600C.

It is obvious from these calculations that the microstructure of overaged Al-Mg-Si alloysshould be very persistent to the heat of welding processes. In practice, only a narrow solutionisedzone forms adjacent to the fusion boundary. However, within this zone significant strengthrecovery may occur after welding due to reprecipitation of hardening phases from thesupersaturated solid solution. Consequently, in such weldments the ultimate HAZ strengthlevel is usually higher than that of the base metal, as illustrated in Fig. 4.5.

4.2.3.2 Metastable precipitatesIn practice, the solid solubility is also affected by the size of the particles. If, for instance, a

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

Str

engt

h le

vel

After artificial ageing

After natural ageing

Immediately after welding

Unaffected base metalHAZ

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 isalso subjected to an extra pressure AP due to the curvature of the particle/matrix interface, justas a soap bubble exerts an extra pressure on its content (see Fig. 4.6(a)). The pressure AP isgiven 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 importantinfluence of particle curvature on the solid solubility has been extensively investigated andreported in the literature.18 Usually, the phenomenon is referred to as the capillary or theGibbs-Thompson effect.

In the following we shall assume that the thermodynamic and crystallographic propertiesof the metastable precipitates are similar to those of the equilibrium phase and that the re-duced thermal stability is only associated with capillary effects. For single phase precipitatesin binary alloy systems, it is fairly simple to show that the concentration of solute acrossa curved interface, [%A]r, is interrelated to the equilibrium concentration of solute across aplanar interface, [%A], through the following equation:8

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

(4-10)

Atm

osph

eric

pres

sure

Gib

bs e

nerg

y

where

(4-11)

(4-12)

Fig. 4.6. Effect of interfacial energy on the solubility of small particles; (a) Schematic representation ofspherical particles embedded in a metal matrix, (b) Integral molar Gibbs energy of matrix and precipi-tates at a constant temperature.

Assuming that this relationship also holds in the case of binary intermetallics, a combina-tion of equations (4-5) and (4-10) gives:

Concentration

[%A]r[%A]

Large precipitate

Matrix

Small precipitate

(b)

(a)Matrix

Tem

pera

ture

or

Alternatively, we can express T as a function of the product [%A]rn [%B]r

m. This gives thefollowing 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 solidsolubility at a given temperature is significantly increased at small particle radii. Taking as anexample 7 = 0.5 J nr 2 , Vm = 10~5 m3 moH, R = 8.314 J Kr1 moH, T = 500 K, we obtain fromequation (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.

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 artificialageing in the temperature range from 160-2000C. Consider a T6 heat treated ternary alloywhich contains 0.75 wt% (0.83 at.%) Mg and 1.0 wt% (0.96 at.%) Si. Based on equation (4-13) make a sketch of the metastable P "(Mg2Si) solvus in a vertical section through the ternaryAl-Mg-Si phase diagram. In these calculations we shall assume that the thermodynamicproperties 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. Relevantphysical data for the Al-Mg-Si system are given below:

SolutionFirst 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 bysubstituting

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 theparticle curvature has a dramatic effect on the solid solubility. A comparison with Fig. 4.4shows that the dissolution temperature drops from about 5600C in the case of the equilibriumMg2Si phase to approximately 225°C for the metastable |3"(Mg2Si)-phase. On this basis it isnot surprising to find that artificially aged (T6 heat treated) Al-Mg-Si alloys suffer from se-vere softening in the HAZ after welding, as shown schematically in Fig. 4.9. Moreover, it is

Tem

pera

ture

, 0C

Nom

inal

allo

yco

mpo

sitio

n A

Str

engt

h le

vel


Fig. 4.9. Response of artificially aged Al-Mg-Si alloys to welding and subsequent heat treatment (sche-matic).

HAZ

After artificial ageing

After natural ageing

Immediately after welding

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

at% Mg2Si

at% Mg

Metastable solvusboundary

Dissolution temperature: 225 0C

evident that the characteristic low dissolution temperature of the precipitates also gives rise tothe formation of a heat affected zone which is significantly wider than that observed duringwelding of overaged Al-Mg-Si alloys.9 This shows that the response of age-hardenable alu-minium alloys to welding and thermal processing depends strongly on the initial base metaltemper condition.

With the aid of equation (4-11) it is also possible to calculate an average (apparent) metastablesolvus boundary enthalpy for hardening |3"(Mg2Si)-precipitates in Al-Mg-Si alloys. A closerevaluation 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, thereis a tendency for the smaller particles to dissolve and for the material in them to precipitate onlarger particles. The driving force is provided by the consequent reduction in the total interfa-cial 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 andSlyovoz11 and by Wagner.12 The kinetics are generally controlled by volume diffusion throughthe matrix. At steady state, the time dependence of the mean particle radius r is found tobe:11'12

(4-14)

where ro is the initial particle radius, 7 is the particle-matrix interfacial energy, Dm is the ele-ment diffusivity, Cm is the concentration of solute in the matrix, Vm is the molar volume of theprecipitate per mole of the diffusate, and t is the retention time.

Although the classic Lifshitz-Wagner theory suffers from a number of simplifying assump-tions, experimental observations usually reveal a cubic growth law of the form given by equa-tion (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 continuousheating 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 (forbinary intermetallics Qs may be taken equal to the activation energy for diffusion of the lessmobile constituent atom of the precipitates in the matrix).

4.3.2.1 Kinetic strength of thermal cycleIt follows that the extent of particle coarsening occurring during a weld thermal cycle can becalculated 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 thethermal cycle with respect to particle coarsening, and can be determined by means of numer-ical methods when the weld thermal (T-t) programme is known. The resulting radius of theprecipitates may then be evaluated from equation (4-16) by inserting representative valuesfor the constants ro and C1 (e.g. obtained from quantitative particle measurements).

4.3.2.2 Model limitationsA salient assumption in the classic Lifshitz-Wagner theory is that the particles coarsen atalmost constant volume fraction, i.e. no solute is lost to the surrounding matrix during thecoarsening process. Consequently, equation (4-16) should only be applied in cases where thepeak 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 underthe following conditions:

Assume that the base metal contains a fine dispersion of TiN precipitates in the as-receivedcondition. 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 heataffected zone during welding. Relevant physical data for titanium-microalloyed steels aregiven below:

(activation energy for diffusion of Ti in austenite)

SolutionIn 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 thermalprogramme, as shown in Fig. 4.10(a). By substituting the appropriate values for qo, X, a and vinto the Rosenthal thick plate solution, the governing heat flow equation becomes:

where /?* refers to the three-dimensional radius vector in the moving coordinate system (desig-nated R in equation (1-45)), while x is the welding direction (equal to vt at pseudo-steadystate).

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 thetransformed 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 shownin 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 theHAZ during welding, particularly in regions close to the fusion boundary where the peaktemperature of the thermal cycle is high. A comparison with the experimental data of Ion etal.l4 (reproduced in Fig. 4.12) shows that the theory gives a fairly good prediction of particlesize as a function of the peak temperature, provided that the kinetic constant C1 in equation (4-16) can be estimated with a reasonable degree of accuracy. In practice, however, the numericalvalue of C1 will vary significantly with the chemical composition and thermal history of thebase metal (see Fig. 4.13). This means that empirical calibration of equation (4-16) to experi-mental 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 fusionboundary can result in complete dissolution of the base metal precipitates. Since this may giverise to subsequent strength loss and grain growth, it is important to understand how variationsin 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 ofparticle dissolution in metals and alloys at elevated temperatures.16 None of these solutions areexact, since they represent different approximations to the diffusion field around the dissolv-

(i/r)

exp(

-Qs/

RT

)Te

mpe

ratu

re

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).

Time

(b)

Time

Y~ regime

(a)

Weld metal

HAZ

Parti

cle ra

dius

, nm

Partl

y tra

nsfo

rmed

HAZ

Wel

d m

etal

Freq

uenc

y, %

•

Fig. 4.12. Measured size distribution of TiN before (broken lines) and after (full lines) weld thermalsimulation. 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 suffi-ciently accurate to capture the essential physics of the problem and to give valuable quantita-tive information on the extent of particle dissolution occurring during the weld thermal cycle.

Particle radius, nm

Rosenthal thick plate heat cycle:

Fig. 4.11. Coarsening of TiN during steel welding (Example (4.4)).

Peak temperature, 0C

Fully transformed HAZ •

Partic

le ra

dius,

nm

Annealing temperature: 1350 0C

Steel ASteel BSteel 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 approximationThe model described here is due to Whelan.17 Consider a spherical particle embedded in aninfinite matrix, as shown schematically in Fig. 4.14. The corresponding matrix concentrationprofile is plotted in the lower part of the figure. In this case the concentration of the constituentelement A is higher close to the particle/matrix interface than in the bulk. Hence, there is atendency 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 arrivedat the following expression for the dissolution rate of a spherical precipitate at a constanttemperature:

(4-17)

where r is the particle radius, a is the dimensionless supersaturation (defined in Fig. 4.14), andDm is the element bulk diffusivity.

The term Hr on the right-hand side of equation (4-17) stems from the steady-state part ofthe diffusion field, while the (1 A/7) term arises from the transient part. Because of the com-plex form of equation (4-17) it cannot be integrated analytically and hence, numericalmethods must be applied. However, if the transient part of equation (4-17) is neglected (con-forming to the solution after long times), it is possible to obtain a simple expression for theparticle 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-

Con

cent

ratio

n

Distance

Fig. 4J4. Schematic representation of the concentration profile around a dissolving spherical particle inan infinite matrix.

ently by Aaron et al.16 and is valid after a certain period of time, provided that there is noimpingement of diffusion fields from neighbouring precipitates. As shown in Fig. 4.15, thissimplified solution gives a reasonable description of the dissolution kinetics of small sphericalprecipitates in steel during reheating above the AC1 -temperature.

Following the treatment of Agren,18 the time required for complete dissolution of a spher-ical precipitate td can be obtained from equation (4-18) by setting r = 0:

Moreover, the volume fraction of the precipitates/as a function of time is given by:

(4-19)

(4-20)

where fo is the initial particle volume fraction.The former equation shows that the dissolution time td depends strongly on the initial parti-

cle size rQ.

Example (4.5)

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

Partic

le ra

dius,

jam

Numerical solution (Agren)

Simplified analyticalsolution (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 at13500C are given below:

Steel chemical composition:

Diffusivity of Nb in austenite at 13500C:

Atomic weight of Nb:Atomic weight of C :

SolutionIn the present example it is reasonable to assume that the dissolution rate of the precipitate iscontrolled by diffusion of Nb in austenite. For a single NbC precipitate embedded in a Nb-depleted 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 carbonconcentration at the interface is constant and equal to the nominal value of 0.12 wt% (i.e. thestoichiometry 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 appro-priate 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 4compared with that obtained from more sophisticated numerical calculations. This degree ofaccuracy is acceptable and justifies the use of equation (4-18) for prediction of the dissolutionrate of spherical precipitates under different thermal conditions provided that the model iscalibrated against experimental data points.

4.4.1.2 Application to continuous heating and coolingApplication of the model to continuous heating and cooling requires numerical integration ofequation (4-18) over the weld thermal cycle:

(4-21)

(4-22)

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

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

Dis

solu

tion

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 (0.10wt% C - 0.03 wt% Nb) under the following conditions:

Assume that the base metal contains a fine dispersion of NbC precipitates in the as-receivedcondition. 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 HAZduring welding. Relevant physical data for Nb-microalloyed steels are given below:

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

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

As shown in example (4.5), the equilibrium concentration of niobium at the particle/matrixinterface (in wt%) can be estimated from the solubility product by utilising data from Table4.1. If we assume that the carbon concentration at the interface is constant and equal to thenominal 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 ob-tain:

f/fo

Fig. 4.17. Dissolution of NbC during steel welding (Example (4.6)).


Complete dissolution

No dissolution-

Here the lower and upper integration limits refer to the total time spent in the thermal cyclefrom Ac3 to T and down again to Ac3.

The extent of particle dissolution occurring within the HAZ during welding can now becalculated in an iterative manner by numerical integration of the above equation over the weldthermal 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 thethermal cycle T exceeds the equilibrium dissolution temperature Td of the precipitate. Theprocess is completed when T approaches 13300C, conforming to a temperature interval of1900C. This shows that considerable superheating is required in order to overcome the inher-ent 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 fromneighbouring precipitates or the position of the particle/matrix interface during the dissolutionprocess. In certain cases, however, such phenomena will have a marked effect on the dissolu-tion kinetics.18"22 A good example is Al-Mg-Si alloys where the hardening P"(Mg2Si)-phaseforms a very fine distribution of needle-shaped precipitates along <100> directions in thealuminium matrix. These precipitates are closely spaced and will therefore interact stronglywith each other during dissolution (coupled reversion).

Con

cent

ratio

n

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

(b)

(a)

where ro is the initial cylinder (particle) radius.

(4-23)

4.4.2.1 Two-dimensional diffusion modelFor rod or needle-shaped precipitates in a finite, depleted matrix, the rate of dissolution can becalculated by numerical methods from a simplified two-dimensional diffusion model. Assum-ing that the precipitates are mainly aligned in one crystallographic direction, it is reasonable toapproximate their distribution by that of a face-centered cubic (close-packed) space lattice, asshown 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 ofsolute through the cell boundaries is zero, the dissolution zone is approximately defined by aninscribed cylinder whose volume is equivalent to that of the hexagonal cell. The modellingprinciples outlined in Fig. 4.18(a) and (b) have previously been used by a number of otherinvestigators to describe particle dissolution during isothermal heat treatment.18"22 Conse-quently, readers who are unfamiliar with the concept should consult the original papers forfurther details.

It follows from Fig. 4.18(b) that the rate of reversion can be reported as:

log

<1

- f/f

o)

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

Dimensionless time

Dimensionless supersaturation

(4-24)

(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)

where c2 is a kinetic constant, and n{ is a time exponent (assumed constant and equal to 0.5under the prevailing circumstances).

The rate of particle dissolution will gradually decline with increasing values of T as a resultof impingement of diffusion fields from neighbouring precipitates which reduces a. In prac-tice, this is seen as a continuous decrease in the slope of the flfo-x curves in Fig. 4.19 (nx < 0.5).In such cases equation (4-26) will only be valid within small increments of X.

Fig. 4.19. Dissolution kinetics of rod-shaped particles in a finite, depleted matrix. Data from Myhr andGrong.9

log T

4.4.2.2 Generic modelMyhr and Grong9 have shown how this model can be applied to specific alloy systems.

From equation (4-26) we have:

where n{ < 0.5.This equation can further be simplified if we assume that and

(4-27)

(4-28)

For isothermal heat treatment at a chosen reference temperature (Tn), the rate of particledissolution is determined by the retention time tr{. Let f* denote the maximum hold timerequired for complete dissolution of the precipitates. It follows that equation (4-28) can bewritten in a general form by normalising tn with respect to t*x. The parameter t*n is obtainedby setting flfo = 0:

(4-29)

where C3 is a new kinetic constant.If heat treatment is carried out at a different temperature (T * Tn) , the maximum hold time

t* is simply given by:

(4-30)

By inserting the approximate expressions for C1 and Dm into equation (4-30) (see previousexamples), and rearranging equation (4-28), we obtain:

(4-31)

(4-32)

and

where Q'apP. is the apparent (metastable) solvus boundary enthalpy (defined in Section 4.2.3.2),and Qs is the activation energy for diffusion of the less mobile constitutive atom of the precipi-tates.

log(

i-f/

f 0)

Fig. 4.20. 'Master-curve' for dissolution of hardening p"(Mg2Si)-precipitates in 6082-T6 aluminiumalloys. Data from Myhr and Grong.9

log (t/t*)

Equations (4-31) and (4-32) exploit some good modelling techniques. For example, the useof a dimensionless time eliminates an unknown kinetic constant which premultiplies t and 1*in the derivation of equation (4-32). Moreover, by raising the dimensionless time to a powerH1 means that the premultiplying constant, here unity, is independent of the value of nv and isitself also dimensionless. Finally, the form of equation (4-31) eliminates further unknownkinetic constants, and may readily be calibrated using an experimental time r* at a referencetemperature.

Figure 4.20 shows the variation inflfo with time (on log axes), from a range of isothermalexperiments carried out on 6082-T6 aluminium alloys, using hardness (or electrical conduc-tivity) measurements to evaluate/7/\ The curve (equation (4-32)) extrapolates back to a slopeof 0.5 (the exponent n{) for the case of the early stages of dissolution before impingement ofthe diffusion fields. The exponent nx is seen to fall to lower values when the proportion dis-solved is higher, in agreement with the theoretical curves in Fig. 4.19.

4.4.2.3 Application to continuous heating and coolingMyhr and Grong9 have also shown how this model can be applied to situations where thetemperature varies with time (as in welding).

In order to obtain a general description of particle dissolution under non-isothermal condi-tions, it is convenient to introduce the related concepts of an isokinetic reaction and the kineticstrength of a thermal cycle.23 A reaction is said to be isokinetic if the increments of transfor-mation in infinitesimal isothermal time steps are additive. Christian24 defines this mathemati-cally by stating that a reaction is isokinetic if the evolution equation for some state variable Xmay be written in the form:

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 con-

tains separable variables of X and T. The same criterion may also be applied to the modelsderived above. In the case of coupled reversion, we may write:

(4-33)

and

(4-34)

(4-35)

Since dfldlx and t\ are unique functions of/and T, respectively, the additivity condition issatisfied. Consequently, when the temperature varies with time, we replace the term 11 t*x inequation (4-34) by dt I t*x and integrate over the thermal cycle, giving:

(4-36)

This integral is called the kinetic strength of the thermal cycle with respect to reversion.The resulting volume fraction of the precipitates following a heating cycle is then found byevaluating the integral Z1 numerically (e.g. by utilising input data from Table 4.2) and replac-ing 111* with Z1 in equation (4-32), yielding a value for flfQ from the master curve of Fig. 4.20.

Case Study (4.1)

By utilising equation (4-36) and the general heat flow model for welding on medium thickplates (i.e. equation (1-104)), it is possible to calculate the variation in the f/fo ratio (i.e. thesolute distribution) across the HAZ of single pass 6082-T6 aluminium weldments for a widerange of operational conditions (see Table 4.3). The results from such computations are pre-sented graphically in Fig. 4.21 -4.23.

When stringer bead deposition is carried out on a plate of medium thickness, the solutedistribution in the transverse y direction is expected to vary with distance from the plate sur-face due to a continuous change in the heat flow conditions. A closer inspection of Figs. 4.21and 4.22 shows that this is correctly accounted for in the present model. In contrast, a fullpenetration butt weld will always reveal a similar solute distribution in the transverse directionof the weld, as shown in Fig. 4.23. This situation arises from the lack of a temperature gradientin the through-thickness z direction of the plate.

Table 4.2 Basic input data in dissolution model for hardening p" (Mg2Si)- precipitates in 6082-T6aluminium alloys. Data from Myhr and Grong.9

Parameter Q'app Qs nx t\(starting value) (375°C)

Value 3OkJm0I-1 13OkJm0I-1 0.5 600 s

Wo

Pea

k te

mpe

ratu

re, 0

C

f/fo

Pea

k te

mpe

ratu

re, 0

C

(a)

Comolete dissolution

Aym ,mm

(b)


ym,mm

Fig. 4.21. Dissolution of p"(Mg2Si)-precipitates during aluminium welding (Weld 1); (a) Upper platesurface, (b) Lower plate surface. Operational conditions as in Table 4.3.

Table 4.3 Operational conditions used in aluminium welding experiments (Case study 4.1).

Weld Material Plate thickness Net arc power Welding speed

No.* (mm) (kW) (mms"1)

1 AA6082 15 9.1 4.2

2 AA6082 15 5.7 9.1

3 AA6082 13 14.0 5.8

* Calibration of heat flow model is done by including an empirical correction for heat consumed in melting of theparent material (thermal data for the AA6082 alloy are given in Table 1.1, Chapter 1).

f/fo

Pea

k te

mpe

ratu

re, 0

CP

eak

tem

pera

ture

, 0C

Mo

(a)

(b)


Aym,mm


Fig. 4.22. Dissolution of (3"(Mg2Si)-PrCCiPiIaIeS during aluminium welding (Weld 2); (a) Upper platesurface, (b) Centre of plate. Operational conditions as in Table 4.3.

4.4.2.4 Process diagrams for single pass 6082-T6 butt weldsFor single pass butt welding of plates, the heat flow model (equation 1-104)) can largely besimplified if the net arc power is kept sufficiently high compared with the plate thickness (i.e.q /d>0.5 kW mm"1). Under such conditions the mode of heat flow becomes essentially one-dimensional, and the temperature distribution is determined by the ratio qo/vd, kJ ram"2 (seeSections 1.10.3.3 and 1.10.4.1 in Chapter 1).

ym,mm

Wo

Peak

tem

pera

ture

, 0C

f/fo


Ay ,mmm

Fig. 4.23. Dissolution of p"(Mg2Si)-precipitates during aluminium welding (Weld 3). Operational con-ditions as in Table 4.3.

Figure 4.24 shows plots of the variation in the flfo ratio across the HAZ of 6082-T6 alu-minium weldments for different values of qo Ivd. It follows that a narrow width of the dissolu-tion zone requires the use of a low energy per mm2 of the weld. In practice, this can beachieved by the use of an efficient welding process (e.g. electron beam or laser welding) whichfacilitates deposition off a full penetration butt weld without employing a groove preparation(i.e. eliminates the need for filler metals).

Scale:


Fig. 4.24. Process diagram showing the solute distribution within the HAZ of single-pass 6082-T6 alu-minium butt welds for different values of qo Ivd.

References

1. R.D. Doherty: Physical Metallurgy, 3rd Edn (Eds R.W. Chan and R Haasen), 1983, Amster-dam, North-Holland Physics Publ., 934-1030.

2. K.E. Easterling: Introduction to the Physical Metallurgy of Welding, 1983, London, Butterworths& Co., Ltd.

3. H. Adrian and RB. Pickering: Mater. ScL TechnoL, 1991, 7, 176-182.4. B. Loberg, A. Nordgren, J. Strid and K.E. Easterling: MetalL Trans., 1984,15A, 33-41.5. J. Strid and K.E. Easterling: Acta MetalL, 1985, 33, 2057-2074.6. S. Suzuki, G.C. Weatherly and D.C. Houghton: Acta. MetalL, 1987, 35, 341-352.7. J.L. Petty-Galis and R.D. Goolsby: J. Mater. ScL, 1989, 24, 1439-1446.8. D. A. Porter and K.E. Easterling: Phase Transformations in Metals and Alloys, 1981, Wokingham

(England), Van Nostrand Reinhold Co. Ltd.9. O.R. Myhr and 0. Grong: Acta MetalL Mater., 1991, 39, 2693-2702; ibid., 2703-2708.10. H.R. Shercliff and M.F. Ashby: Acta MetalL Mater., 1990, 38, 1789-1802; ibid., 1803-1812.11. J.M. Lifshitz and V.V. Slyozov: /. Phys. Chem. Solids, 1961,19, 35-50.12. C. Wagner: Z. Electrochem., 1961, 65, 581-591.13. L.C. Brown: Acta MetalL Mater., 1992, 40, 1293-1303.14. J.C. Ion, K.E. Easterling and M.F. Ashby: Acta MetalL, 1984, 32, 1949-1962.15. S. Matsuda and N. Okumura: Trans. ISIJ, 1978,18, 198-205.16. H.B. Aaron, D. Fainstein and G.R. Kotler: J. Appl. Phys., 1970, 41, 4404-4410.17. MJ. Whelan: Metal ScL J., 1969, 3, 95-97.18. J. Agren: Scand. J. MetalL, 1990,19, 2-8.19. R.A. Tanzilli and R.W. Heckel: Trans. Met. Soc. AIME, 1968, 242, 2313-2321.20. H.B. Aaron and R. Kotler: MetalL Trans., 1971, 2, 393-408.21. R. Asthana and S.K. Pabi: Mat. ScL Eng., 1990, A128, 253-258.22. U.H. Tundal and N. Ryum: MetalL Trans., 1992, 23A, 433-444; ibid., 445-449.23. H.R. Shercliff, 0 . Grong, O.R. Myhr and M.F. Ashby: Proc. 3rd Int. Conf. on Aluminium

Alloys — Their Physical and Mechanical Properties, Trondheim, Norway, June 1992, Vol. Ill,pp. 357-369, The University of Trondheim, The Norwegian Inst. of Technol.

24. J.W. Christian: Phase Transformations in Metals and Alloys, 1975, Oxford, Pergamon Press.

thermal diffusivity (mm2 s l)

activity of element A in alloy

activity of precipitate An Bm

in alloy

activity of element B in alloy

arbitrary alloying element

start temperature of f errite toaustenite transformation (0C)

end temperature of ferrite toaustenite transformation (0C)

equilibrium concentration ofelement A in matrix (wt% orat.%)

analytical content of elementA in alloy (wt% or at.%)

equilibrium concentration ofelement A across a curvedparticle/matrix interface(wt% or at.%)

Appendix 4.1Nomenclature

arbitrary alloying element

equilibrium concentration ofelement B in matrix (wt% orat.%)

analytical content of elementB in alloy (wt% or at.%)

equilibrium concentration ofelement B across a curvedparticle/matrix interface(wt% or at.%)

various kinetic constants andtemperature-dependent pa-rameters

normalised (dimensionless)entropy of reaction

concentration of solute atparticle/matrix interface(wt% or at.%)

nominal alloy composition(wt% or at.%)

concentration of solute inmatrix (mol irr3, wt% orat.%)

concentration of solute insidethe precipitates (wt% orat.%)

plate thickness (mm)

normalised enthalpy of reac-tion (K)

element diffusivity (mm2 s"1

or m2 s"1)

particle volume fraction

initial particle volume frac-tion

equilibrium particle volumefraction

maximum particle volumefraction at absolute zero

arbitrary function of X

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

gas metal arc welding

arbitrary function of T

standard enthalpy of reac-tion (J mol"1 or kJ mol"1)

amperage (A)

kinetic strength of thermalcycle with respect to rever-sion

equilibrium constant

mean interparticle spacing indissolution model (m, Jim ornm)

integer

atomic weight of element A(g mol"1)

atomic weight of binary pre-

cipitate (g mol"1)

atomic weight of element B(g mol-1)

integer

time exponent in dissolutionmodel

pressure caused by curvatureeffects (J nr3)

net arc power (W)

apparent (metastable) solvusboundary enthalpy (kJ mor1)

activation energy for diffu-sion (kJ moH)

particle radius (m, Jim or nm)

initial particle radius (m, (imor nm)

GMAW

H(T)

universal gas constant(8.314JK-1InOl-1)

universal gas constant multi-plied by InIO (19.14J Kr1

mol"1)

three-dimensional radiusvector in Rosenthal equation(mm)

standard entropy of reaction(J K mol"1)

submerged arc welding

time (s)

time necessary for completedissolution of precipitate(s)

integration limits (s)

time necessary for completereversion at T(s)

retention time at T1. (s)

time necessary for completereversion at Trl(s)

temperature (0C or K)

ambient temperature (0C orK)

equilibrium dissolution tem-perature of precipitate (0C orK)

melting point (0C or K)

peak temperature of thermalcycle (0C or K)

chosen reference temperaturein dissolution model (0C orK)

equilibrium solvus tempera-ture (0C or K)

solvus temperature ofmetastable precipitates (0C orK)

artificially aged condition

voltage (V)

welding speed (mm s"1)

welding direction (mm)

state variable

transverse direction (mm)width of HAZ referred to fu-sion boundary (mm)

through-thickness direction(mm)

molar volume of precipitate(m3 mol1)

molar volume of precipitateper mole of the diffusate (m3

mol-1)

density of precipitate An Bm

(g cm"3 or kg rrr3)

thermal conductivity (Wmm-1 0C-1)

dimensionless supersaturat-ion in dissolution model

density (g cm"3 or kg nr3)

arc efficiency factor

particle/matrix interfacialenergy (J m~2)

dimensionless time in disso-lution model

contribution of particle cur-vature to reaction enthalpy (Jmol"1 or kJ mol"1)

equilibrium phase in Al-Mg-Si alloys

hardening precipitate in Al-Mg-Si alloys

SAW

5Grain Growth in Welds

5.1 Introduction

Grain growth is an important aspect of welding metallurgy. Normal grain growth in metalsand alloys is a thermally activated process driven by the reduction in the grain boundary en-ergy. Physically, it occurs by growth of the larger grains at the expense of the smaller oneswhich tend to shrink.

Under isothermal heat treatment conditions, normal grain growth is well described by thefollowing empirical equation:1

(5-1)

where D is the mean grain size (diameter), D0 is the initial grain size, n is the time exponent,/ is the isothermal annealing time, Qapp. is the apparent activation energy for grain growth, andC1 is a kinetic constant. The other symbols have their usual meaning.

For most metals and alloys the time exponent n in equation (5-1) varies typically in therange from 0.1 to 0.4, as shown in Fig. 5.1. Only in the case of ultrapure metals annealed atvery high temperatures the time exponent may approach a constant value of 0.5. This corre-sponds to the limiting case where the grain boundary migration rate is directly proportional tothe driving pressure 7 /D (7 denotes the grain boundary interfacial energy per unit area, whileD is the grain size).

It is well recognised that alloying and impurity elements both in the dissolved state and inthe form of inclusions or second phase particles will retard grain growth.2"* Consequently, acomprehensive theoretical treatment of grain growth in welds must include a consideration ofsuch effects. The present analysis will therefore start with a closer examination of factorsaffecting the grain boundary mobility in metals and alloys under conditions applicable to weld-ing.

5.2 Factors Affecting the Grain Boundary Mobility

The symbols and units used throughout this chapter are defined in Appendix 5.1.

5.2.7 Characterisation of grain structures

A critical aspect of modelling grain growth is the quantitative description of grain structures,which is essential in making a comparison between theoretical predictions and experimental

(U) JU8U0CJX9 91U|1

•BrassZ.R.AI

Fig. 5.1. Temperature-dependence of the time exponent in isothermal grain growth (Z.R.: zone refined,H.R: high purity). Data compiled by Hu and Rath.1

measurements. Different parameters are used to describe the size and the shape of individualgrains. In three dimensions, individual grain volumes cannot be determined directly frommeasurements made in single cross sections through the structure. Therefore, certain geomet-ric assumptions must be employed to obtain these quantities.

Since most grain size measurements seek to correlate the interaction of grain boundarieswith specific properties (e.g. the transformation behaviour), an estimate of the grain boundaryarea per unit volume Sv is often required. This parameter can be calculated without assump-tions concerning grain shape and size distribution from measurements of the mean linear grainintercept D*.5

If the mean grain diameter D is required from 5V, this may be obtained by assuming aspherical grain shape. Noting that each boundary is shared by two adjacent grains, we obtain:

Homologous temperature (T/Tm)

(5-2)

from which

(5-3)

(5-4)

It follows that the mean linear grain intercept D* is always smaller than the actual grain sizeD.

A common observation in metals and alloys is that the size distributions of grain aggregates

F (

arbi

trary

uni

ts)

Fig. 5.2. Comparison of measured grain size data in iron with the Rayleigh and log-normal distributionfunctions F. The similarity of the size distributions at different annealing times illustrates the self-similarscaling behaviour of normal grain growth. After Pande.6

D/D

Log-normaldistribution

Rayleigh distribution

Zone refined iron

where y is the grain boundary interfacial energy, and p* is the radius of curvature.It is conventional practice to replace p* in equation (5-5) with some measure of the average

grain size, such as the mean linear grain intercept D*, or with the diameter of the equivalentspherical volume of some geometrically modelled average grain size. Experimental measure-ments performed on high purity aluminium indicate that p* ~ 3.23 D*.7 This observation isconsistent with the model of Hellman and Hillert,8 which predicts that the curvature of themost critical element of grain boundary that must be stabilised is p* = 3D. Under such condi-tions, the driving pressure becomes:

(5-6)

(5-5)

at different annealing times become equivalent when the measured grain size parameter, D, isnormalised (scaled) by the time-dependent average of this metric, D (see Fig. 5.2). Thismeans that grain structures can be completely characterised, in a statistical sense, by simpleprobability functions of the standard deviation of the distribution together with the time de-pendence of the average size scale D.

5.2.2 Driving pressure for grain growth

The thermodynamic driving pressure for motion of a spherically curved element of grain bound-ary is given by:7

In practice, the numerical constant in equation (5-6) can vary by, at least, a factor of three,depending on the assumptions of the models. Consequently, in the general case the averagedriving pressure is given by:

(5-7)

where c2 is a constant which is characteristic of the system under consideration.

5.2.3 Drag from impurity elements in solid solution

In the dissolved state impurity and alloying elements will retard grain growth through elasticattraction of the atoms towards the open structure of the grain boundary. The boundary mustthen either drag the impurity atoms along (so that its speed is limited by the diffusion rate ofthese atoms) or break away if the impurity concentration is sufficiently small or the drivingpressure or temperature is high enough.

An analysis of such effects can be done on the basis of the classic impurity drag theories ofChan2 and Lucke and Stiiwe,3 which deal with the following two extreme cases:

(i) A low velocity limit, where the rate of grain boundary migration is controlled by diffu-sion of impurity atoms perpendicular to the boundary.

(ii) A high velocity limit, where the grain boundary migration process is mainly governedby the diffusion of solvent atoms across the boundary (i.e. controlled by the rate of boundaryself diffusion).

The low velocity limit is associated with either a low driving pressure PG or a high impuritylevel C0, and is characterised by a linear type of relationship between the grain boundarymigration rate Va and PG:2

(5-8)

Here e denotes the intrinsic drag coefficient, while 1F is a parameter depending on thediffusivity and the interaction energy between the grain boundary and the impurity atoms.

For the other extreme (i.e. the high velocity limit), the grain boundary migration rate Vb isdescribed by the relationship:2

(5-9)

where 4Vp2 denotes another complex function of the impurity diffusivity and the interactionenergy between the grain boundary and the impurity atoms.

In the case of spherical grains, the classic grain growth equation predicts that the grainboundary migration rate V is a power function of the driving pressure (y /D). This is readilyseen by differentiating equation (5-1) and inserting 7 (the grain boundary interfacial energy)into the resulting expression:

log

V(5-10)

where c3 is a new kinetic constant.Note that at very high driving pressures or low impurity levels, equation (5-9) approaches

the limiting case where the migration rate Vb becomes directly proportional to PG, correspond-ing to a time exponent n = 0.5 in the grain growth equation. At this point the grain boundarywill break away from its surrounding impurity atmosphere and migrate at a rate close to therate of boundary self diffusion. In most cases, however, the relationship between V and PG

derived from equation (5-10) will be different from the theoretical one due to the empiricalnature of the grain growth equation.

For high driving pressures and intermediate impurity concentrations, the classic impuritydrag theories predict a discontinuous transition from the high to the low velocity limit. It has,however, been argued by Vandermeer9 that the observed transition may be considered as con-tinuous. Thus, in a log V vs log PG plot it would appear as a steep curve connecting the linesfor the high and low velocity extremes together, as illustrated schematically in Fig. 5.3.

5.2.4 Drag from a random particle distribution

The retardation of grain growth by second phase particles was first theoretically investigatedby Zener.10 There seems to be general agreement that the maximum pinnig force Fp exerted bya single particle of radius r on a grain boundary is given by:410

(5-11)

High velocity limit

Transition region

Low velocity limit

log PG

Fig. 5.3. Schematic variation of grain boundary migration rate V with driving pressure PQ according tothe classic impurity drag theories of Cahn2 and Liicke and Stiiwe.3 The diagram is based on the ideas ofVandermeer.9

If the number of interacting particles per unit area of the grain boundary is taken equal to na,the resulting retardation pressure becomes:

(5-12)

Assuming that only one half of the particles which touches the grain boundary will interactwith a maximum force, na is related to Nv (the number of particles per unit volume) through thefollowing equation:410

(5-13)

Given that the particles are spherical and of uniform size, Nv can be expressed as:

(5-14)

where/is the particle volume fraction.A combination of equations (5-12), (5-13), and (5-14) leads to the well-known expression

for the so-called Zener drag (or Zener retardation pressure):410

(5-15)

In practice, the numerical constant in equation (5-15) can vary by, at least, a factor of five,depending on the assumptions of the models.11 Consequently, in the general case the Zenerretardation pressure is given by:

(5-16)

where C4 is a constant which is characteristic of the system under consideration.

5.2.5 Combined effect of impurities and particles

As already stated in the introduction of this chapter, the time exponent n is a measure of theresistance to grain boundary motion in the presence of impurity and alloying elements in solidsolution. Based on equation (5-1) Hu and Rath112 have shown that the grain boundary migra-tion rate V is related to the effective driving pressure AP G and the time exponent n through thefollowing equation:

(5-17)

where M is the grain boundary mobility.In alloys containing grain boundary pinning precipitates, the effective driving pressure APG

is defined as the numerical difference between PG and Pz. By inserting the correct expressionsfor PG and Pz into equation (5-17), we obtain:

(5-18)

It follows from equation (5-18) that the grain boundary migration rate V becomes inverselyproportional to the average grain size D when n = 0.5 and/ = 0. This corresponds to thelimiting case where the grain boundary will break away from its surrounding impurity atmos-phere and migrate at a rate which is controlled by the diffusion of solvent atoms across theboundary. In most cases, however, the observed relationship between V and APG will bedifferent from the theoretical one due to drag from second phase particles (f> 0) or impurityelements 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 ispossible to obtain a simple differential equation which describes the variation in the averagegrain size D with time t and temperature T in the presence of impurities and grain boundarypinning 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 arerelated to the grain boundary mobility and the pinning efficiency of the precipitates, respec-tively.

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 asthe ratio between the numerical constants in equations (5-7) and (5-16), respectively. In theoriginal 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, depend-ing 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 Zenercoefficient.

Diim

.nm

Gladman

r/f, um

Fig. 5.4. Relation between limiting grain size Dum., particle radius r, and volume fraction/predicted bydifferent 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 limitingaustenite grain size Dlim in the transformed parts of the weld HAZ when the oxygen andsulphur 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 inclusionscan be calculated from equation (2-75):

Similarly, the average radius of the grain boundary pinning inclusions can be obtained fromequation (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 ofmagnitude, depending on the assumptions of the models. In practice, the Zener coefficient inlow-alloy steel weld metals falls within the range from 0.32 to 0.93, as shown in Fig. 5.5. Theaverage 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 Zenercoefficient varies typically between 0.75 and 0.25 during grain growth in the austenite re-gime.1617 This suggests that k ~ 0.50 is a reasonable estimate of the grain boundary pinningefficiency 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 nand the grain boundary mobility M. When n = 0.5 and/= 0, the classic impurity drag theoriespredict that the activation energy Qapp, should be close to the value for boundary self diffusionin the matrix material.2'3 This borderline case is approximately attained in steel welding, asshown in Fig. 5.6(a) and (b), since the driving pressure for austenite grain growth immediatelyfollowing the dissolution of the pinning precipitates is usually so large that the grain boundarymigration rate approaches the higher velocity limit defined in equation (5-9).18 On this basis itis not surprising to find that Qapp falls within the range reported for lattice self diffusion (284kJ mol"1) and boundary self diffusion (170 kJ mol~l) in pure 7-iron19 during welding.18 Inmost cases, however, the activation energy will be different from the theoretical one due tocomplex interactions between impurity atoms and grain boundaries (characterised by a timeexponent 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 impurityelements and second phase particles under different thermal conditions. This also includessituations where the grain boundary pinning precipitates either coarsen or dissolve during theheat treatment process.

5.3.3.1 Generic grain growth modelEquation (5-20) can readily be integrated to give the average grain size D as a function oftime. In the general case we may write:

(5-22)

Aus

teni

te g

rain

siz

e, J

imD|

|m. H

m

Fig. 5.5. Evaluation of the Zener coefficient in steel weld metals containing stable oxide and sulphideinclusions; (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 whenthe temperature-time programme is known. In practice, however, it is not necessary to solve thisintegral to evaluate the grain growth mechanisms. Consequently, the left-hand side of equation

r/f, urn

GMA and SA steelweld metals

(b)

Annealing temperature, 0C

SA steel weld metal

(a)

Log

(DxZ

D 1)

LogD

7

(a)

(b)

Steel A

Slope: n = 0.4

Log [number of cycles]

Steel ASteel B

Fig. 5.6. Evaluation of the time exponent n and the activation energy Q for austenite grain growth insteel 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 bepresented in the form of novel diagrams which show the competition between the variousprocesses 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 applicabilityto welding is given in Section 5.4.

5.3.3.2 Grain growth in the absence of pinning precipitatesIn the absence of grain boundary pinning precipitates, we have:/= 0, Dlim —> ~, and (1/ DlitrL) = 0.Under such conditions, equation (5-22) reduces to:

D, ^

m

Fig. 5.7. Predicted variation in average grain size D with /, and n for /= 0 and D0 = 0 ('free' graingrowth).

I1W"

(5-25)

Referring to Fig. 5.7, the average grain size D becomes a simple cube root function of Z1

when n = 0.5 and D0 = 0. In other situations (n < 0.5), the grains will coarsen at a slower ratedue to drag from alloying and impurity elements in solid solution. This is seen as a generalreduction in the slope of the D-Ix curves in Fig. 5.7.

The important austenite grain growth inhibiting effect of phosphorus and free nitrogen insteel following particle dissolution is shown in Fig. 5.8.

5.3.3.3 Grain growth in the presence of stable precipitatesIf grain growth occurs in the presence of stable precipitates, the limiting grain size {Dlim) inequation (5-22) becomes constant and independent of the thermal cycle. In the specific casewhen n = 0.5 the integral on the left-hand side of equation (5-22) has the following analyticalsolution:

(5-23)

(5-24)

After integration this equation yields:

DY,f

imD

y,um

(a)

(b)

Steel A

Number of cycles

Steel B

Number of cycles -

Fig. 5.8. Illustration of the austenite grain growth inhibiting effect of phosphorus and free nitrogen inlow-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 methodsmust be employed to evaluate D.

It is evident from the graphical representation of equation (5-25) in Fig. 5.9 that the graingrowth inhibiting effect of the precipitates is very small during the initial stage of the processwhen D « D lim. Under such conditions the grains will coarsen at a rate which is comparablewith that observed for free grain growth (n = 0.5,/= 0). The grain coarsening process becomesgradually retarded as the average grain size increases because of the associated reduction inthe effective driving pressure APG until it comes to a complete stop when AP0 = 0 (i.e. D =

D Hm)-

D, ji

mD,

(im

I1^m2

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

I1 , [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 impurityelements in solid solution, the situation becomes more complex. As shown in Fig. 5.10, adecrease in the time exponent from say 0.5 to 0.2 gives rise to a marked reduction in the slopeof the D-I1 curves, similar to that observed in Fig. 5.7 for particle-free systems (/= 0). How-ever, the predicted grain coarsening rate is lower than that evaluated from equation (5-24) dueto the extra drag exerted by the grain boundary pinning precipitates. This leads ultimately to astabilisation of the microstructure when D = DUm.

5.3.3.4 Grain growth in the presence of growing precipitatesVery little information is available in the literature on the matrix grain growth behaviour ofmetals and alloys in the presence of growing second phase particles. So far, virtually allmodelling work has been carried out on two phase a-(3 titanium alloys.14 Unfortunately, noneof these models can be extended to more complex alloy systems such as steels or aluminiumalloys.

When grain growth occurs in the presence of growing second phase particles, Dum. will nolonger be constant due to the associated increase in the particle rlf ratio with time. As shown inChapter 4 of this textbook, the Lifshitz-Wagner theory2021 provides a basis for modellingparticle growth during welding and heat treatment of metals and alloys in cases where the peaktemperature 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), inaccordance with equation (4-16):

(5-26)

where Qs is the activation energy for the coarsening process, C5 is a kinetic constant, and I2 isthe kinetic strength of the thermal cycle with respect to particle coarsening. The other symbolshave their usual meaning.

If the base metal contains particles of an initial radius ro and volume fraction/^, the limitinggrain size at I2 = 0 (D° lim) can be defined as:

from which

Similarly, when I2 > 0, we may write:

(5-27)

(5-28)

(5-29)

By combining equations (5-26), (5-28), and (5-29), we arrive at the following relationshipbetween (DUm) and I2:

(5-30)

It is seen from equation (5-30) that the limiting grain size in the presence of growingparticles depends on the product (k/fo)

3I1. In practice, the grain boundary pinning effect of theprecipitates is determined by the relative rates of particle coarsening and grain growth in thematerial, i.e. whether the grain boundary mobility is sufficiently high to keep pace with theincrease 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 Dcan readily be evaluated from equations (5-22), (5-30), and (5-31) by utilising an appropriateintegration procedure. However, since Qs normally differs from Qapp^ the (klfo)

3I1I Ix ratiowill depend on the thermal path during continuous heating and cooling. Consequently, solu-tion of these coupled equations generally requires stepwise integration in temperature-timespace 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. Undersuch 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 berewritten as:

(5-32)

From this we see that the two coupled equations (5-22) and (5-32) can be solved explicitlyfor different values of D°nm., n, m, and Z1. Hence, it is possible to present the results in the formof novel 'mechanism maps' which show the competition between particle coarsening andgrain 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 heattreatment is very sensitive to variations in the proportionality constant m. For large values ofm, the matrix grains will coarsen at a rate which is comparable with that observed in Fig. 5.7for particle-free systems (f = 0). This corresponds to a situation where the grain boundarypinning precipitates will completely outgrow the matrix grains. It is interesting to note thatparticle 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 ofimpurity elements in solid solution. In other systems, where the proportionality constant m iscloser to unity, the reduced coarsening rate of the precipitates gives rise to a higher Zenerretardation pressure and ultimately to a stagnation in the matrix grain growth. In the limitingcase, when m = 0, the grain growth behaviour becomes idential to that observed in Figs. 5.9and 5.10 for stable precipitates.

D.ji

mD,

fxm

Time exponent n = 0.5

I1,^m2

Fig. 5.11. Predicted variation in average grain size D with Ix and m for D°um. = 50jLim, n = 0.5, andD0 =0 (growing precipitates).


I1^m1'"

Fig. 5.12. Predicted variation in average grain size D with I1 and m for D°um. - 50|im, n = 0.3, andD0 = 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 as-received condition, conforming to a limiting austenite grain size T>°um. of 50 |iim. Provided thatboundary drag from impurity elements in solid solution can be neglected (i.e. n ~ 0.5), esti-mate on the basis of Fig. 5.11 the average austenite grain size D1 in the material after 25 s ofisothermal annealing at 13000C. Relevant physical data for titanium-microalloyed steels aregiven below:

(activation energy for diffusion of Ti in austenite)

SolutionThe initial volume fraction of TiN in the material can be estimated from simple stoichiometriccalculations by considering the difference between total and soluble titanium. Taking theatomic 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 canbe obtained directly from equations (5-31) and (5-22) without performing a numerical integra-tion:

D,ji

mSimilarly, in the case of Z1 we get:

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

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


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, andDo = 0 (growing precipitates).

It is seen from equation (5-36) that the limiting grain size increases from D°um. at I3 = 0 toinfinite when I3 = (fo Ik)2 (D°um. )2 • Since the magnitude of the Zener drag, in practice, dependson the relative rates of grain growth and particle dissolution in the material, the pinning condi-tions are defined by the (klfo)

2131 Ix ratio:

(5-36)

(5-37)

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 limitinggrain size with I3 during particle dissolution. After some manipulation, we obtain:

(5-35)

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):

(5-34)

where a is the dimensionless supersaturation (defined in Fig. 4.14), and Dm is the elementdiffusivity.

Application of the model to continuous heating and cooling requires numerical integrationof equation (5-33) over the weld thermal cycle:

(5-33)

5.3.3.5 Grain growth in the presence of dissolving precipitatesLittle information is available in the literature on the matrix grain growth behaviour of metalsand alloys in the presence of dissolving precipitates. As shown in Chapter 4, the model ofWhelan23 provides a basis for calculating the dissolution rate of single precipitates embeddedin an infinite matrix. If the transient part of the diffusion field is neglected, the variation in theparticle radius r with time t at a constant temperature is given by equation (4-18):

D,ji

mEquation (5-37) shows that the (k/fo)

2I3111 ratio is contingent upon the thermal path duringcontinuous heating and cooling. Consequently, application of the model to welding generallyrequires numerical integration of the coupled equations (5-22), (5-36), and (5-37) over theweld thermal cycle.

However, the integration procedure is largely simplified if heat treatment is carried outisothermally. In such cases the product (k/fo)

213 will only differ from Ix by a proportionalityconstant m*, which is characteristic of the system under consideration. By substituting m*Ix

into equation (5-36), we obtain:

From this we see thaUhe two coupled equations (5-22) and (5-38) can be solved explicitlyfor different values of Dun., n,m*, and I1. Hence, it is possible to present the results in theform of novel 'mechanism maps' which show the competition between particle dissolutionand 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 theproportionality constant m*. Normally, the precipitates will exert a drag on the grain bounda-ries as long as they are present in the metal matrix. However, when the dissolution process iscompleted, the matrix grains are free to grow without any interference from precipitates. This

(5-38)


Complete particledissolution

Stable particles

I1 ,nm2

Fig. 5.14. Predicted variation in average grain size D with Z1 and ra* for D°um. = 50 um, n = 0.5, andD0 =0 (dissolving precipitates).

D,j

im

Time exponent n = 0.3Complete particle dissolution

I1^m1'0

Fig. 5.15. Predicted variation in average grain size D with I1 and m* for D°um. - 50 Jim, n - 0.3, andDo =0 (dissolving precipitates).

means that the grains, after prolonged high temperature annealing, will coarsen at a rate whichis 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 5.10for 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-receivedcondition, conforming to a limiting austenite grain size Dnm. of 50 jim. Provided that theboundary drag from impurity elements in solid solution can be neglected (i.e. n ~ 0.5), esti-mate on the basis of Fig. 5.14 the average austenite grain size D7 in the material after 25 s ofisothermal annealing at 13000C. Relevant physical data for niobium-microalloyed steels aregiven below:

SolutionThe initial volume fraction of NbC in the material can be estimated from simple stoichiometriccalculations by considering the difference between total and soluble niobium. Taking theatomic 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 betweenthe 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-freesystem, it means that the presence of a fine dispersion of NbC in the base metal has no signifi-cant effect on the resulting austenite grain size under the prevailing circumstances. Other

types of niobium microalloyed steels may reveal a different grain coarsening behaviour, de-pending on the chemical composition, size distribution, and initial volume fraction of the basemetal precipitates. However, the pattern remains essentially the same, i.e. the growth inhibi-tion 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 ofthe HAZ grain coarsening behaviour rather complicated. The method adopted from Ashby et^ 24,25 j s baseci o n m e jdea of integrating the elementary kinetic models over the weld thermalcycle where the unknown kinetic constants are determined by fitting the integrals at certainfixed points to data from real or simulated welds. Although the introduction of the Zener dragin the grain growth equation largely increases the complexity of the problem, the methodologyand calibration procedure remain essentially the same. This means that the results from suchcomplex computations can be presented in the form of simple grain growth diagrams whichshow 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 astructural (kinetic) model.

5.4.1.1 Heat flow modelsAs a first simplification, the general Rosenthal equations26 are considered for the limiting caseof a high net power qo and a high welding speed v, maintaining the ratio qo/v within a rangeapplicable to arc welding. It has been shown in Chapter 1 that under such conditions, where noexchange 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)

Next Page

6Solid State Transformations in Welds

6.1 Introduction

The majority of phase transformations occurring in the solid state take place by thermallyactivated atomic movements. In welding we are particularly interested in transformations thatare induced by a change in temperature of an alloy with a fixed bulk composition. Suchtransformations include precipitation reactions, eutectoid transformations, and massive trans-formations both in the weld metal and in the heat affected zone.

Since welding metallurgy is concerned with a number of different alloy systems (includinglow and high alloy steels, aluminium alloys, titanium alloys etc.), it is not possible to cover allaspects of transformation behaviour. Consequently, the aim of the present chapter is to pro-vide the background material necessary for a verified quantitative understanding of phasetransformations in weldments in terms of models based on thermodynamics, kinetics, andsimple diffusion theory. These models will then be applied to specific alloy systems to illumi-nate the basic physical principles that underline the experimental observations and to predictbehaviour 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 toknow how far the reaction can go and how fast it will proceed. To answer the first question weneed to consider the thermodynamics, whereas kinetic theory provides information about thereaction 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, thisminimum molar free energy of transformation, AG, can be written as a balance between thefollowing four contributions:

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 nega-tive, since they assist the transformation, while AGS (increase in surface energy between thetwo phases) and AGE (increase in strain energy resulting from lattice distortion) are both posi-tive because they represent a barrier against nucleation. It follows that the transformation

(6-1)

Mol

ar fr

ee e

nerg

yTe

mpe

ratu

reStable (B) Stable (a)

Temperature

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

reaction can proceed when the driving force AG becomes greater than the right-hand side ofequation (6-1).

For an allotropic transformation, in which there is no compositional change, AG will be asimple function of temperature, as illustrated in Fig.6.1. For alloys the situation is slightlymore complex, since there is an additional variable, i.e. the composition. In such cases thetemperature at which the a-phase becomes thermodynamically unstable (Teq) corresponds to afixed point on the a-(3 solvus boundary in the equilibrium phase diagram, as shownschematically in Fig. 6.2. Since phase diagrams are available for many of the important indus-trial alloy systems, it means that the driving force for a transformation reaction can readily beobtained from such diagrams in the form of a characteristic undercooling (AT).

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

%B

AG

* /A

G*

het.

horn

.

Free

surfa

ces

Gra

inco

rner

s

Gra

inbo

unda

ries

Incl

usio

ns

Dis

loca

tions

/sta

ckin

g fa

ults

Vac

ancy

clu

ster

s

Fig. 6.3 Schematic diagram showing the most potent sites for heterogeneous nucleation in metals andalloys.

Nucleation site

Freesurface Inclusion

Grain boundary

where v is a vibration frequency factor, Nv is the total number of heterogeneous nucleationsites per unit volume, AG^, is the energy barrier against nucleation, and Qd is the activationenergy for atomic migration across the nucleus/matrix interface.

6.2.2 Heterogeneous nucleation in solids

In general, solid state transformations in metals and alloys occur heterogeneously by nuclea-tion at high energy sites such as grain corners, grain boundaries, inclusions, dislocations andvacancy clusters. The potency of a nucleation site, in turn, depends on the energy barrieragainst 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 isalways energetically more favourable than homogeneous nucleation (AG*het < tsG*hom ) butless favourable than nucleation at grain boundaries or free surfaces. As a result, the transfor-mation behaviour is strongly influenced by the type and density of lattice defects and secondphase particles present within the parent material.

6.2.2.1 Rate of heterogeneous nucleationWhereas every atom is a potential nucleation site during homogeneous nucleation, only thoseassociated with lattice defects or second phase particles can take part in heterogeneous nuclea-tion. In the latter case the rate of nucleation (Nhet) is given by:1'2

(6-2)

It follows from the graphical representation of equation (6-2) in Fig. 6.4 that the nucleationrate Nhet is highest at an intermediate temperature due to the competitive influence ofundercooling (driving force) and diffusivity on the reaction kinetics. This change in Nhet withtemperature gives rise to corresponding fluctuations in the transformation rate, as shownschematically 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 nucleationonly.

6.2.2.2 Determination of AGhet and Qd

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

(6-3)

(6-4)

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

If the complete C-curve is known for a specific transformation reaction, it is possible toevaluate 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, asshown in Fig. 6.6. At high undercoolings, when &G*het is negligible, the slope of the curvebecomes constant and equal to QdIR. The mathematical expression for this asymptote is:

Low undercoolingHigh diffusivity

High undercoolingLow diffusivity

TT

Nhe t.%B

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

Frac

tion

trans

form

ed

T

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 andthe extension of the lower asymptote amounts to (see Fig. 6.6):

(6-6)

(6-7)

from which

It follows that equations (6-5) and (6-7) provide a systematic basis for obtaining quantita-tive information about Qd and AGhet from experimental microstructure data through a simplegraphical analysis of the shape and position of the C-curve in temperature-time space.

1/r

T

lnt

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

6.2.2.3 Mathematical description of the C-curveIn order to obtain a full mathematical description of the C-curve, we need to know the varia-tion in the energy barrier AG*het with undercooling AT. For heterogeneous nucleation of pre-cipitates 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 nu-cleus and the matrix, AGV is the driving force for the precipitation reaction (i.e. the volume freeenergy change associated with the transformation), and 5(0) is the so-called shape factor whichtakes 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 alloysystems and the mathematical expression for the solvus boundary in the binary phase dia-gram.

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 theheterogeneous nucleation sites in the material. The value of A0 is, in turn, given by equations(6-7) and (6-10):

(6-11)

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

logt

C-cun/e(Nv=N^)

T

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

(6-13)

(6-14)

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

Equation (6-12) can further be modified to allow for compositional and structural varia-tions 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 temperatureT= Tr in an alloy containing Nv nucleation sites per unit volume. If we take the correspondingsolvus temperature of the (3-phase equal to T*q , the expression for t* becomes:

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

(6-12)

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

Example (6.1)

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

SolutionThe parameters A0 and Qd can be evaluated from the C-curve according to the procedureshown in Fig. 6.6. Referring to Fig. 6.11, the value of AG^ at the chosen reference tempera-ture 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).

Tem

pera

ture

, 0C

T T T

%B \e, logt

Fig. 6.9. Effect of solute content on the shape and position of C-curve in temperature-time space (sche-matic).

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 magne-sium in aluminium.6

Time, s

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

AA 6351 - T6

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 whichinvolves diffusion of solute atoms from the bulk phase to the matrix/nucleus interface.

6.2.3.1 Interface-controlled growthWhen transfer of atoms across the a/(3-interface becomes the rate-controlling step, the reac-tion is said to be interface-controlled. This growth mode is therefore observed during theinitial stage of a precipitation reaction before a large, solute-depleted zone has formed aroundthe particles. In the case of incoherent precipitates, the variation in the particle radius r withtime is given by:7

(6-15)

where M1 is a mobility term, C0 is the concentration of solute in matrix, Ca is the concentrationof solute at the particle/matrix interface, and Cp is the concentration of solute inside the pre-cipitate.

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 schematicallyin Fig. 6.12(a). In contrast, a coherent interface is essentially inmobile because transfer in thiscase 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 alonga low energy interface in a direction where the matrix is incoherent with respect to the particlelattice (see Fig. 6.13). In such cases the thickening rate of the precipitates U*aj^ is given by:3'7

Ua/

p

Incoherent Interface Coherent interface

(a)

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

Lateral move-ment of incoherenf

interface

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

where M1* is a new mobility term, and / is the interledge spacing.

6.2.3.2 Diffusion-controlled growthFor growth of incoherent precipitates above the metastable solvus, the rate-controlling stepwill be diffusion of solute in the matrix. If precipitation of the P-phase occurs from a

(6-16)

Tem

pera

ture

Con

cent

ratio

n

supersaturated a, the reaction proceeds by diffusion of solute to the growing p-particle, asshown schematically in Fig. 6.14. On the other hand, when the (3-phase is formed by rejectionof solute from the a-phase, the transformation occurs by diffusion of atoms away from the P-particle, as indicated in Fig. 6.15.

Aron et al.s have presented general solutions for diffusion-controlled growth of both flatplates and spheres under such conditions. In the former case the half thickness AZ of the plateis given by:

(6-17)

The parameter E1 in equation (6-17) is frequently referred to as the one-dimensional para-bolic thickening constant, and is defined as:

Liquid

%B

Diffusion of solute

Distance

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

Con

cent

ratio

nTe

mpe

ratu

re

%B

Diffusion of solute

Distance

Fig. 6.15. Schematic representation of concentration profile ahead of advancing interface during growthof 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 errorfunction (defined previously in Appendix 1.3, Chapter 1).

Similarly, for growth of spherical precipitates, the variation in the radius r with time can bewritten as:8

(6-19)

where e2 *s t n e corresponding parabolic thickening constant for a spherical geometry, definedas:

The parabolic relations in equations (6-17) and (6-19) imply that the growth rate slowsdown as the (3-phase grows. This is due to the fact that the total amount of solute partitionedduring growth decreases with time when the diffusion distance increases. Moreover, the formof equations (6-18) and (6-20) suggests that the maximum in the growth rate is achieved at anintermediate 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 willreveal a pattern similar to that shown in Fig. 6.4 for the nucleation rate, although the thicken-ing constants generally are less temperature-sensitive.

In addition to the models presented above for plates and spheres, approximate solutionsalso exist in the literature for thickening of needle-shaped precipitates, based on the Triveditheory for diffusion-controlled growth of parabolic cylinders.9 However, because of space limi-tations, 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 IT-diagram of the type shown in Fig. 6.5. Among the factors that determine the shape and posi-tion of the C-curve are the nucleation rate, the growth rate, the density and the distribution ofthe 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 shallassume that the overall microstructural evolution with time can be described by an Avrami-type of equation:10

(6-20)

(6-21)

where X is the fraction transformed, n is a time exponent, and k is a kinetic constant whichdepends on the nucleation and growth rates.

The exponential growth law summarised in the Avrami equation is valid for linear growthunder most circumstances, and approximately valid for the early stages of diffusion-controlledgrowth.10 Table 6.1 gives information about the value of the time exponent for different ex-perimental conditions.

In general, the value of n will not be constant, but change due to transient effects until thesteady-state nucleation rate is reached and n attains its maximum value. Subsequently, thenucleation rate starts to decrease as the sites become filled with nuclei and eventually ap-proach zero when complete saturation occurs. This is because the heterogeneous nucleationsites are not randomly distributed in the volume, but are concentrated near other nucleationsites leading to an overall reduction in n. From then on, the transformation rate is solelycontrolled by the growth rate.

6.2.4.1 Constant nucleation and growth ratesFor 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, interfacecontrolled 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 previoussections. In practice, however, this is a rather cumbersome method, particularly if the basemetal is of a heterogeneous chemical nature. Alternatively, we can calibrate the Avrami equa-tion against experimental microstructure data, e.g. obtained from generic IT-diagrams. A con-venient 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 beregarded as a time constant, which is characteristic of the system under consideration. Notethat this form of the Avrami equation is mathematically more appropriate, as the dimensions ofthe 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 thenucleation rate. Let f denote the time taken to precipitate a certain fraction of P (X = Xc) atan 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)

(6-24)

A combination of equations (6-22) and (6-23) then gives:

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 transforma-tion. 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 saturationIf the nucleation rate is considered to be zero by assuming early site saturation, the subsequentphase transformation simply involves the reconstructive thickening of the p-layer. In the one-dimensional case, the process can be modelled in terms of the normal migration of a planara/p interface, as shown schematically in Fig. 6.16. Let Aa/^ denote the interfacial area be-tween a and (3 per unit volume and Ua/^ the growth rate of the incoherent a/p-interface. FromFig. 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 trans-formation volumes, we may write in the general case:

which after integration yields:

(6-27)

(6-28)

This specific form of the Avrami equation is valid under conditions of early site saturationwhere 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 continu-ously 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 modellingof microstructural changes under predominantly isothermal conditions.1"411 In contrast, onlya limited number of investigations has been directed towards non-isothermal transforma-tions.51012"18 However, these studies have clearly demonstrated the advantage of using ana-lytical modelling techniques to describe the microstructural evolution during continuous cool-ing, instead of relying solely on empirical CCT-diagrams.

6.2.5.1 The principles of additivityFrom the literature reviewed it appears that there is considerable confusion regarding the ap-plication of isothermal transformation theory for prediction of non-isothermal transformationbehaviour. These difficulties are mainly due to the independent variations of the nucleationand growth rate with temperature. In fact, it can be shown on theoretical grounds that theproblem is only tractable when the instantaneous transformation rate is a unique function ofthe fraction transformed and the temperature.10 This leads to the additivity criterion describedbelow.

The principles of additivity are based on the theory advanced by Scheil.12 He proposed thatthe start of a transformation under non-isothermal conditions could be predicted by calculatingthe consumption of fractional incubation time at each isothermal temperature, with the trans-formation starting when the sum is equal to unity. The Scheil theory has later been extended tophase transformations to predict continuous cooling transformation kinetics from isothermalmicrostructure data.10'17'18

Let t* again denote the time taken to precipitate a certain fraction of P (X - Xc) at an arbi-trary temperature T. If the reaction is additive, the total time to reach Xc under continuouscooling conditions is obtained by adding the fractions of time to reach this stage isothermallyuntil the sum is equal to unity. Noting that t* varies with temperature, we may write in thegeneral case:

(6-29)

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

Cooling curve

Subdivision of time intoinfinitesimal steps of iso-thermal heat treatments.

T

logtFig. 6.17. Schematic illustration of the Scheil theory.

6.2.5.2 Isokinetic reactionsThe concept of an isokinetic reaction has previously been introduced in Section 4.4.2.3 (Chap-ter 4). A reaction is said to be isokinetic if the increments of transformation in infinitesimalisothermal time steps are additive, according to equation (6-29). Christian10 defines this math-ematically by stating that a reaction is isokinetic if the evolution equation for some state vari-able 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 con-

tains separable variables of X and T.

6.2.5.3 Additivity in relation to the Avrami equationThe concept of an isokinetic reaction can readily be applied to the Avrami equation. Differen-tiation of equation (6-22) with respect to time leads to the following expression for the rate oftransformation:

(6-31)

In a typical diffusion-controlled nucleation and growth process, the fraction transformed Xwill not be independent of temperature, since the equilibrium volume fraction of the precipi-tates decreases with temperature (e.g. see equation (4-7) in Chapter 4). However, for dilutealloys it is a fair approximation to neglect this variation as the solvus boundary becomes in-creasingly steeper and in the limiting case approaches that of a straight (vertical) line. Thus, ifn is constant and k* depends only on the transformation temperature, the reaction will be iso-kinetic 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 consideringthe form of the constitutive equations, it is obvious that the change in the nucleation rate withtemperature 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 ofthe nucleation and growth rates of grain boundary ferrite in a C-Mn steel. It is evident fromthese data that the change in the parabolic thickening constant £, is negligible compared withthe fluctuations in the nucleation rate. Consequently, in transformations that involve continu-ous cooling it is sufficient to allow for the variation of Nhet with temperature, provided thatsite saturation has not been reached. Thus, if n is constant we can apply the Scheil theorydirectly 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 P-precipitation. This parameter is generally defined by the integral:

-2 -

1N

ucle

atio

n ra

te (

N* h

et),

cm

s

Thick

enin

g co

nsta

nt C

e 1),|

ims"

Temperature, 0C

Fig. 6.18. Predicted variation in N*het and E1 with temperature during the austenite to ferrite transfor-mation 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 shownin Appendix 6.2

The principles of additivity are also applicable under conditions of early site saturation. Ifonly 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-timeprogramme is known.

6.2.5.4 Non-additive reactionsIf the additivity condition is not satisfied, it means that the fraction transformed is dependenton the thermal path, and the differential equation has no general solution. This, in turn, impliesthat the C-curve concept breaks down and cannot be applied to non-isothermal transforma-

tions. Solution of the differential equation then requires stepwise integration in tempera-ture-time space, using an appropriate numerical integration procedure. As already pointedout, this will generally be the case for diffusion-controlled precipitation reactions, since theevolution parameter X is a true function of temperature. Under such conditions, experimen-tally 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 therange 300-500 MPa, depending on the plate thickness.2021 During welding microstructuralchanges take place both within the heat affected zone (HAZ) and the fusion region, which, inturn, affect the mechanical integrity of the weldment.2122 In the HAZ, for instance, nitridesand carbides coarsen and dissolve, and grain growth occurs to an extent that depends on thedistance 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 bydisplacing the CCT curve to longer times, thereby producing more Widmanstatten ferrite, orincreasing the possibility of bainite and martensitic transformation products on cooling. Theformation of such microstructures may reduce the toughness of the weld and increase the riskof hydrogen cracking.2122

6.3.1 Classification of microstructures

It is appropriate to start this section with a detailed classification of the various microstructuralconstituents commonly found in low-alloy steel weldments.

During the austenite to ferrite transformation, a large variety of microstructures can de-velop, depending on the cooling rate and the steel chemical composition. Normally, the micro-structure formed within each single austenite grain after transformation will be a complexmixture of two or more of the following constituents, arranged in approximately decreasingorder of transformation temperature:

(i) grain boundary (or allotriomorphic) ferrite (GF)(ii) polygonal (or equiaxed) ferrite (PF)(iii) Widmanstatten ferrite (WF)(iv) acicular ferrite (AF)(v) upper bainite (UB)(vi) lower bainite (LB)(vii) martensite (M).

The microstructural constituents listed above are indicated in Fig. 6.19, which showsphotomicrographs 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 opticalmicroscopy. Several systems have been introduced throughout the years for the classificationof the various constituents, with each system reflecting different investigator's views and

Next Page

7Properties of Weldments

7.1 Introduction

Weldments are prime examples of components where the properties obtained depend upon thecharacteristics of the microstmcture. Since failure of welds often can have dramatic conse-quences, a wealth of information is available in the literature on structure-property relation-ships. However, in order to fit some of the apparently conflicting results into a more consistentpicture, a theoretical approach is adopted here rather than a review of the literature. Thisprocedure also involves the use of phenomenological models for the quantitative descriptionof 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 steelcarbon contents have been progressively lowered to below 0.10 wt% C. The desired strengthis largely achieved through a refinement of the ferrite grain size, produced by the additions ofmicroalloying elements such as aluminium, vanadium, niobium, and titanium in combinationwith various forms for thermomechanical processing.1 This procedure has made it possible toimprove 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 sacrificingbase metal strength, ductility, or low-temperature toughness.2 Controlled rolled HSLA steelsare currently produced with a minimum yield strength in the range from 350-550 MPa. Abovethis 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 devel-opments in welding consumables to produce weld metal deposits with mechanical propertiesessentially equivalent to the base metal.3 From the large volume of literature dealing withHSLA steel filler metals, it appears that the bulk of weld metal research over the past decadehas been concentrated on the achievement of a maximum toughness and ductility for a givenstrength level by control of the weld metal microstructure.34 There seems to be general agree-ment that microstructures primarily consisting of acicular ferrite provide optimum weld metalmechanical 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 detrimentalto toughness, since these structures provide preferential crack propagation paths, especiallywhen continuous films of carbides are present between the ferrite laths or plates. Attempts tocontrol the weld metal acicular ferrite content have led to the introduction of weldingconsumables containing complex deoxidisers (Si, Mn, Al, Ti) and balanced additions of vari-ous alloying elements (Nb, V, Cu, Ni, Cr, Mo, B).

The final weld metal microstructure will depend on complex interactions between severalimportant variables such as:3"5

(i) The total alloy content.(ii) 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 throughthe critical transformation temperature range in principle are the same as those occurring dur-ing rolling and heat treatment of steel, the conditions existing in welding are significantlydifferent from those employed in steel production because of the characteristic strong non-isothermal behaviour of the arc welding process. For example, in steel weld deposits thevolume fraction of non-metallic inclusions is considerably higher than that in normal cast steelproducts because of the limited time available for growth and separation of the particles. Oxy-gen is of particular interest in this respect, since a high number of oxide inclusions is known toinfluence strongly the austenite to ferrite transformation both by restricting the growth of theaustenite grains as well as by providing favourable nucleation sites for various types ofmicrostructural constituents (e.g. acicular ferrite). Moreover, during solidification of the weldmetal, alloying and impurity elements tend to segregate extensively to the centre parts of theinterdendritic or intercellular spaces under the conditions of rapid cooling.67 The existence ofextensive segregations further alters the kinetics of the subsequent solid state transformationreactions. Accordingly, the weld metal transformation behaviour is seen to be quite differentfrom that of the base metal, even when the nominal chemical composition has not been signifi-cantly changed by the welding process.3"5 This, in turn, will affect the mechanical integrity ofthe weldment.

7.2.1.1 Weld metal strength levelIn low-alloy steel weld metals there are at least four different strengthening mechanisms whichmay contribute to the final strength achieved. These are:

(i) Solid solution strengthening,(ii) Dislocation strengthening,(iii) Grain boundary strengthening,(iv) Precipitation strengthening.

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

Yie

ld s

treng

th,

MP

a

the weld thermal history. Because of the number of variables involved, a full physical treat-ment of the problem is not possible. Consequently, the simplified treatment of Gladman andPickering8 has been adopted here.

Figure 7.1 shows the individual strength contributions in low-carbon bainite, which is thedominating microconstituent in as-deposited steel weld metals (includes both upper and lowerbainite as well as acicular ferrite). Firstly, there are the solid solution strengthening incrementsfrom 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, thegrain size contribution to the yield stress is shown as a very substantial component, the magni-tude of which is determined by the bainite lath size. Finally, a typical increment for dispersionstrengthening is indicated. This contribution is negligible at large lath sizes typical of upperbainite, but becomes significant at small grain sizes because of a finer intralath carbide disper-sion.8 Hence, in steel weld deposits containing high proportions of acicular ferrite or lowerbainite carbides will make a direct contribution to strength, even at relatively low carbon lev-els.

The results in Fig. 7.1 are of significant practical importance, since they show the inherentlimitations of the system with regard to the maximum strength that can be achieved throughcontrol 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 goodagreement with the observed threshold strength of acicular ferrite containing steel weld depos-its.9 If higher strength levels are required, it is necessary to decrease the grain (lath) sizethrough a refinement of the microstructure, i.e. by replacing acicular ferrite with either lower

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

Dispersion

Grain size

Matrix strength

-1/2Bainitic 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 newgeneration of high strength steel weld metals with a yield strength in the range from 650 to 900MPa.10'11

7.2.1.2 Weld metal resistance to ductile fractureIt is well established that the weld metal resistance to ductile fracture is strongly influenced bythe volume fraction, shape, and size distribution of non-metallic inclusions.12"15 Although averified quantitative understanding of the fracture process is still lacking, there seems to begeneral agreement that it involves the following three basic steps:16

(i) Nucleation of internal cavities during plastic flow, preferentially at non-metallicinclusions.

(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 ofstress existing during deformation. Similarly, the fractographic appearance of the final frac-ture surface is also influenced by the same factors.

Effect of inclusion volume fractionThe primary variables affecting the true strain at fracture 8/ are the inclusion diameter dv, andthe inclusion volume fraction Vv. The relation between Ef and Vv has been determined experi-mentally 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 V-notch (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 withincreasing oxygen concentrations when testing is performed in the upper shelf region. FromFig. 7.4 we see that the CVN upper shelf energy is a linear function of the weld metal oxygencontent. This observation is not surprising, considering the fact that the inclusion volumefraction is directly proportional to the oxygen level (see equation (2-75) in Chapter 2).

Effect of inclusion size distributionVoid nucleation may occur both by cracking of the inclusions and by interface decohesion. Inthe 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 thestress concentration factor at the particle, and dv is the particle diameter.

CVN

upp

er s

helf

ener

gy, J

True

frac

ture

stra

in

GMAW(E=1.6kJ/mm)

Inclusion volume fraction

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

True fracture strain

Fig. 7.3. Correlation of CVN upper shelf energy with true fracture strain in tensile testing. Data fromAkselsen and Grong.20

Equation (7-2) predicts that large inclusions will tend to form voids first as the stress re-quired for initiation is proportional to (l/dv )1/2. This result is also in agreement with experi-mental observations. As shown in Fig. 7.5, the size distribution of inclusions located in thecentre of voids at the fracture surface is significantly coarser than the corresponding particlesize distribution in the material. In particular, large, angular shaped aluminium oxide (AI2O3)

SAW and FCAW

CV

N u

pper

she

lf en

ergy

, J

SAW

Oxygen content, wt%

Fig. 7.4. Correlation of CVN upper shelf energy with analytical weld metal oxygen content. Data fromDevillers et aL 13

inclusions appear to be preferential nucleation sites for microvoids in low-alloy steel weldmetals (see Fig. 7.5(b)). Although the combined effect of particle size and local stress concen-tration on the ductile fracture behaviour cannot readily be accounted for in a mathematicalsimulation 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 highresistance against dimpled rupture. In practice, this requires careful control of the weld metalaluminium-oxygen balance and the heat input applied during welding (see Section 2.12 inChapter 2).

Effect of strength levelThe toughness of a material reflects its ability to absorb energy in the plastic range. One way oflooking at toughness is to assume that it scales with the total area Uj under the stress-straincurve. Several mathematical expressions for this area have been suggested. For ductile mate-rials 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

Freq

uenc

y, %

Freq

uenc

y, %

Freq

uenc

y, %

Freq

uenc

y, %

Total inclusionpopulation SAW

Inclusions associatedwith dimples

(a) Inclusion diameter, jum

SAWTotal inclusionpopulation

Inclusions associatedwith dimples

Inclusion diameter, jum(b)

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

CV

N u

pper

she

lf en

ergy

, J

Tru

e f

ract

ure

str

ain

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.

Ultimate tensile strength, MPa

SAW and FCAW

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

Nv (dv>1.5 um)-105

SAW

High Ti levels

Medium Ti levels

Low Ti levels

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

(b)

(a)

It is evident from the tensile test data in Fig. 7.7 that the fracture strain is a true function ofRm, although the relationship appears to be linear rather than non-linear, as predicted by equa-tion (7-4). These results are of considerable practical importance, since they imply that theupper shelf energy absorption, and hence, the shape of the CVN transition curve is stronglyaffected by the weld metal strength level. Accordingly, control of the weld metal microstruc-ture becomes particularly urgent at high strength levels to avoid problems with the cleavagefracture resistance (to be discussed below).

7.2.1.3 Weld metal resistance to cleavage fractureCleavage fracture is characterised by very little plastic deformation prior to the crack propaga-tion, and occurs in a crystallographic fashion along planes of low indicies, i.e. of high atomicdensity.1 Body-centred cubic (bcc) iron cleaves typically along {100} planes, which impliesthat the cracks must be deflected at high angle grain (or packet) boundaries, as shownschematically in Fig. 7.8. Consequently, in steel weld metals the ferrite grain size and thebainite packet width are the main microstructural features controlling the resistance to cleav-age crack propagation.

Since the microstructure which forms within each single austenite grain will not be uniformbut a complex mixture of two or more constituent phases, it is difficult, in practice, to definea meaningful grain size or packet width. For this reason, most investigators have attempted tocorrelate toughness with the presence of specific microconstituents in the weld metal.3"5 Forexample, an increase in the volume fraction of acicular ferrite will result in a correspondingincrease in toughness (i.e. decrease in the CVN transition temperature), as shown in Fig. 7.9.

Tran

sitio

n te

mpe

ratu

re, 0

CSAW (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 ferritecontent. Data from Grong and Kluken.15

This observation is not surprising, considering the extremely fine lath size of the acicularferrite microstructure (typically less than 5jim).

Moreover, results obtained from fractographic examinations of SMA and FCA steel weldmetals have demonstrated that large non-metallic inclusions (> l|im) can strongly influencethe cleavage fracture resistance, either by acting as cleavage cracks themselves of by provid-ing internal sites of stress concentration which facilitate carbide-initiated cleavage in the adja-cent matrix.21'22 In the former case, the critical stress required for crack propagation in thematrix, 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 tothe 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 con-taining large inclusions should be more prone to cleavage cracking than others. This result isalso in agreement with general observations. For example, in self-shielded FCA steel weldmetals it has been demonstrated that cleavage crack initiation is usually associated with largealuminium-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 anadequate low-temperature toughness.

7.2.1.4 The weld metal ductile to brittle transitionIn addition to the parameters mentioned above, there are several other factors, some interre-lated, 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-containinginclusion; (a) Initiation site short distance ahead of the notch, (b) Detail of initiation site showing crackedinclusion, (c) Detail of cracked inclusion (remnants of particle are left in the hole).

(ii) Dislocation locking effects caused by interstitials or alloying elements in solidsolution (e.g. nitrogen and silicon),

(iii) Nucleation of cracks at twins,(iv) Nucleation of cracks at carbides.

In general, this picture is too complicated to establish a physical framework within whichthe various theoretical models for the ductile to brittle transition in steel can be embedded. Weare therefore forced to base our judgement and understanding of how key parameters affect theposition and shape of the CVN transition curve solely on scattered phenomenological observa-tions 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 tough-ness to the weld metal acicular ferrite content and the ultimate tensile strength (UTS). Figures7.11 and 7.12 show how each of these parameters influences the CVN transition curve. It isevident from the diagrams that control of the weld metal acicular ferrite content becomesparticularly important at high strength levels to avoid problems with the fracture toughness. Incases where undermatch is aimed at (i.e. a weld metal to base plate strength ratio less thanunity), the weld metal tensile strength is typically of the order of 450 to 550 MPa. Within thisrange a volume fraction of acicular ferrite beyond 25 vol% will generally be sufficient to meetcurrent toughness requirements (35 J at -400C). If overmatch is desired, the volume fractionof acicular ferrite becomes more critical, partly because of a higher weld metal strength leveland partly because of more stringent toughness requirements (e.g. 45 J rather than 35 J at-400C). 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 CVNtransition curve. Based on the experimental data in Fig. 7.13 it can be argued that suchcompositional variations can be equally detrimental to toughness as a decrease in the acicularferrite content. Consequently, further refinements of the models are required if a verifiedquantitative understanding of the ductile to brittle transition in low-alloy steel weld metals isto be obtained.

Example (7.1)

Consider multipass FCA steel welding with two different electrode wires, one with titaniumadditions and one without. Table 7.1 contains a summary of weld metal chemical composi-tions. Provided that the microstructure and the inclusion size distribution are similar in bothcases, use this information to evaluate the low-temperature toughness of the welds, as revealedby CVN testing.

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

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

Abso

rbed

energy, J

Absorbed

energy, J

(a)Tensile strength: 600 MPa

Vol% acicular ferrite

35 Joules

Test temperature, 0C

(b)Tensile strength: 800 MPa

Vol% acicular ferrite

35Joules.


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

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

Abso

rbed

energy, J

Absorbed

energy, J

Fig. 7.12. Predicted effect of weld metal ultimate tensile strength (UTS) on the CVN transition curve attwo different volume fractions of acicular ferrite; (a) 25 vol% AF, (b) 75 vol% AF. Data from Akselsenand 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


75 vo l% acicular ferrite

-..35J.Q.ute$-

UTS

(b)


35 Joules

25 vol% acicular ferrite

UTS

(a)

Abs

orbe

d en

ergy

, JAb

sorb

ed e

nerg

y, J

(a)

SMAW (basic electrodes) 95% confidence interval

Testing temperature: -400C

Nitrogen content, ppm

(b)

Low content of coarse inclusions

High content of coarseinclusions ( > 1}im )

Self-shielded FCA steelweld metals


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 toughnessIn principle, improvement of weld properties can be achieved through a post-weld heat treat-ment (PWHT). This may have the benefits of:3

(i) Enhancing the fatigue strength through a general reduction of welding residualstresses.

Abs

orbe

d en

ergy

WeIdB WeIdA


35 J

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) Quasi-cleavage (as-welded condition), (b) Intergranular fracture (after PWHT).

AC

VN

, J

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

For these reasons local PWHTs are commonly required for all structural parts above aspecified 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 com-position, and in some cases deterioration rather than improvement of the impact properties isobserved after PWHT. In such cases the reduction in toughness can be ascribed to:3'4

(i) Precipitation hardening reactions. Present experience indicates that elements suchas vanadium, niobium, and presumably titanium can produce a marked deteriora-tion in toughness because of precipitation of carbonitrides in the ferrite, providedthat these elements are present in the weld metal in sufficiently high concentra-tions.

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

Experience shows that Ti-B containing steel weld metals often fail by intergranular frac-ture 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 phosphorussegregations and borocarbide precipitation along the prior columnar austenite grain bounda-

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

SAW

Base line

Titanium content, wt%

Fig. 7.16. Observed displacement in the CVN toughness after PWHT (ACVN) as a function of the weldmetal boron and titanium contents. Negative values indicate loss of toughness. Data from Kluken andGrong.23

Fig. 7.17. TEM micrograph showing precipitation of borocarbides, Fe23(B,C)6, along prior austenitegrain boundaries in a Ti-B containing steel weld metal after PWHT (6000C-Ih).

ries (Fig. 7.17). Since borocarbides are brittle and partly incoherent with the matrix, they canbe regarded as microcracks (of length dp) ready to propagate. In such cases there is virtuallyno plastic deformation occurring before crack propagation, which implies that the intergranularfracture 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 energyand the plastic work), and dp is the particle diameter.

Although the value of yeg_ would be expected to be low in the presence of solidification-induced phosporus segregations,24 this alone is not sufficient to initiate intergranular fracturein the weld metal. However, during PWHT the borocarbides will start to grow from an ini-tially small value to a maximum size of about 0.1 to 0.2jim (Fig. 7.17), following the classicgrowth law for grain boundary precipitates dpatl/4?5 This implies that the intergranular frac-ture 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 frompredominantly quasi-cleavage in the as-welded condition (Fig. 7.15(a)) to intergranular rup-ture 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 oldsteels relied on the use of carbon for strength, the trend today is to rely more on grain refine-ment in combination with microalloy precipitation to meet the current demand for an im-proved weldability. This includes both the sensitivity to weld cracking and the HAZ mechani-cal properties required by service conditions and test temperatures. The latter aspect is ofparticular interest in the present context and will be discussed later.

Stre

ss

Mar

tens

ite c

onte

nt, v

ol%

HV

5,kp

/mm

2

Rp

0.2

>Rn

vMP

a

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 hard-ness, A%5.* cooling time from 800 to 5000C). Data from Akselsen et al.26

Cooling time, At8 / 5 , s

Fig. 7.18. Schematic illustration of the mechanisms of temper embrittlement in Ti-B containing steelweld metals (Gf(M): matrix fracture strength, (*/(/): intergranular fracture strength).

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

[Annealing time]174

Particle diameter

Intergranularfracture mode

Quasi-cleavagefracture mode

A number of different empirical models exist in the literature for prediction of HAZ peakhardness and strength.26"31 However, the aptness of some of these models is surprisinglygood, which justifies construction of iso-hardness and iso-strength diagrams for specific gradesof steels.32 Examples of such diagrams are given in Fig. 7.20. It is evident from Fig. 7.20 thatthe HAZ peak strength is controlled by two main variables, i.e. the steel chemical compositionand the weld cooling programme. The compositional effect is allowed for by the use of anempirical carbon equivalent, which ranks the influence of the various alloying elements on thesteel 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, andcan be read from nomograms of the type shown in Fig. 1.49 (Chapter 1). The axes of Fig. 1.49are dimensionless, but they can readily be converted into real numbers through the use of thefollowing conversion factors:33

Ordinate:

Abscissa:

(7-8)

(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 platethickness 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 thesteel 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 composi-tion 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%. Usethis information together with the diagrams in Figs. 1.49 and 7.20 to estimate the peak HAZstrength level when the plate thickness is 10 and 30 mm, respectively.

CE

||f w

t%C

En,

wt%

Fig. 7.20. HAZ iso-property diagrams for HSLA steels; (a) Iso-hardness contours, (b) Iso-yield strengthcontours. Data from Kluken et al.32

Cooling time, At8 7 5 , s

(b)

Cooling time, A t 8 / 5 , s

(a)

SolutionFirst 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 andyield 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 varia-tions in the welding conditions. Normally, the HAZ hardenability is high enough to facilitate

Rp

02 a

nd R

m,

BM JfL Gf[R

.GC

R

GCR

GRR

IR"

BM"

Rp0.2 a

nd

Rm>MP

a

GCR

"GRR

TR"

SR"

BM"

,BM

[SR JfL,

^GRR

.QQ

R.

Medium strengthsteels

High strengthsteels.

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

(a)

(b) Medium strengthsteels

High strengthsteels

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 coars-ened region); (a) Low heat input, (b) High heat input. Data from Akselsen and R0rvik.34

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

Vic

kers

har

dnes

s, V

PN

Filled symbols:t = 10 seconds

7.2.2.2 Tempering of the heat affected zoneCertain regulations for offshore structures require that no part of the welded joint shall beharder than a specified limit, e.g. 280, 300 or 325 VPN, to reduce the risk of hydrogen crack-ing. Such requirements cannot always be met by a suitable choice of preheating and weldingconditions.

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 theHollomon-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 theconstant B* in equation (7-10) is equal to 16.5 (with t in seconds). It is evident from Fig. 7.22that tempering at, say, 6000C for 1 h is more than sufficient to reduce the HAZ peak hardnessto values below 280 VPN. This implies that PWHT is an effective (but expensive) way ofreducing the HAZ strength level.

Deposition of temper weld beads has been suggested as an alternative means of reducingthe hardness of the HAZ.36"38 This procedure is indicated schematically in Fig. 7.23, showingtwo temper beads (black) in the lower sketch. If the beads are properly positioned with respectto the fusion line, the outer Ac\ contour of the HAZ produced by the temper bead should justtouch the fusion line of the last filler pass, as indicated in the upper sketch of Fig. 7.23. Thematerial reaustenitised by the temper bead would then be weld metal, while the HAZ remain-ing from the last filler pass would be tempered below the transformation range.

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

Lastfiller pass

Fusion line

Ac3 lineAc1 line

Fig. 7.23. Schematic illustration of weld bead tempering.

Since the Hollomon-Jaffe parameter is an empirical criterion developed for isothermal tem-pering of medium and high carbon steels, it cannot readily be applied to pulsed tempering. Abetter approach would be to use the so-called Dorn parameter,39 which in an integral form canbe 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 bydiffusion of carbon in ferrite. Qualitatively, the aptness of equation (7-11) can be illustrated ina plot of measured hardness against the diffusional parameter P^ ( s e e Fig- 7.24). It is evidentfrom Fig. 7.24 that the isothermal data points can be represented by a smooth curve whichcoincides with the upper boundary of the scatter band obtained in pulsed tempering. Theslightly higher hardness observed after isothermal tempering arises probably from a brief pe-riod 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 thelast filler pass and the temper bead, the latter one being positioned so as to give a peak tem-perature of 7200C at the fusion line of the former one. The temperature field around the two

Har

dnes

s ra

tio H

V/H

Vm

ax,

%

Vick

ers

hard

ness

. VP

N

Isothermal 10 sSeries 1

" 2" 3" 4

Double pulse

^ s 1 ' 2

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

beads is clearly the same. In Fig. 7.25 an estimate has been based on the simplified Rykalinthick 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 isobtained 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 differ-ent positions in the HAZ, i.e. y = 0 (former fusion line), y = 1 mm, and y = 2 mm (z = 0). Thecorresponding plots of dP2 ldt vs t are shown to the right. Taking the area P2 under each curveand reading the hardness ratio at TJP^ from Fig. 7.24, an expected hardness profile is ob-tained, as shown in the upper diagram of Fig. 7.25. The expected effect of tempering is seen torange 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 displacementhad been different from the chosen optimum of 2.1 mm (e.g. say 3 mm), the predicted hardnesscurve 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, anarrow zone of the original HAZ would be re-austenitised and therefore about as hard asbefore deposition of the temper bead.

The results from the above modelling exercise show that the HAZ hardness of weld toesand 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 positionedvery precisely for a successful result. Consequently, the use of temper beads for improvementof the HAZ properties has not found a wide application in the industry.3641

7.2.2.3 HAZ toughnessIn spite of the recent developments in steel plate manufacturing technology, there is still con-cern about the HAZ toughness of low-carbon microalloyed steels because of their tendency to

tem

per b

ead

last

filte

r pas

s

HV

/HVm

ax

106ex

p(-1

0000

/T)

y, mm

Parent plateHA2

We d metal

T, 0

C

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, im-provement of the HAZ toughness through PWHT is sometimes found to be difficult in contrastto experience with more traditional C-Mn steels.41'43 Consequently, the increasing use of low-carbon microalloyed steels in various welded structures has introduced new problems relatedto the HAZ brittle fracture resistance which formerly did not appear to be of particular con-cern.44

Fully transformed regionSpecific effects of peak temperature on HAZ toughness, as assessed on the basis of thermallycycled CVN specimens, are shown in Fig. 7.26. It is apparent from the graph that embrittlementin the fully transformed part of the HAZ is often located in the grain coarsened region adjacent

- 3

(D

cO

I

SR IR GRR GCR

Single cycle

Peak temperature, 0CFig. 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 eta/.45

to the fusion boundary where the peak temperature of the thermal cycle has been above about12000C. The problem can mainly be ascribed to the presence of low-toughness microstruc-tures such as upper bainite and Widmanstatten ferrite which form typically at intermediate andslow cooling rates (see Fig. 6.55 in Chapter 6). In contrast, the grain refined region will almostalways exhibit a satisfactory low-temperature toughness owing to the characteristic fine po-lygonal ferrite microstructure.41 An exception is low heat input welds produced from steelswith a heavily banded pearlite/ferrite microstructure, where the risk of a toughness deteriora-tion 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 charac-terised 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 ofindigenous titanium oxide inclusions (presumably Ti2O3). Although the mechanisms involvedare not yet fully understood, it is reasonable to assume that the improved toughness at highheat inputs arises from a refinement of the HAZ microstructure, as discussed previously inSection 6.3.6 (Chapter 6). It is interesting to note that the major effect of the titanium oxideinclusions in this case appears not to be control of the austenite grain size (which in some casescan exceed 500 |im at the fusion boundary), but is rather to act as favourable nucleation sitesfor acicular ferrite intragranularly.4748 Similar phenomena are well known from transforma-tion kinetics of low-alloy steel weld deposits, where non-metallic inclusions play an importantrole in the development of the acicular ferrite microstructure.3"5

Intercritical regionThe microstructural evolution in the intercritical HAZ of low-carbon steels has previouslybeen discussed in Section 6.3.8.2 (Chapter 6).

In order to understand the origin of embrittlement in the intercritical region, considerationmust be given to the stress fields and the transformation strains developed in the ferrite matrix

Tran

sitio

n te

mpe

ratu

re, 0

C

Ti-O steelTi-N steel


Fig. 7.27. Response of modern Ti-O steels and traditional Ti-N steels to CVN testing following weldthermal simulation. Data from Homma et al.41

as a result of the martensite formation.49 It follows from Fig. 7.28 that the hard martensite-austenite (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 thetwo phases. At the same time, the volume expansion associated with the austenite to martensitetransformation leads to significant elastic and plastic straining of the ferrite.50 At moderatelyhigh 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 ex-posed to cracking and debonding. With increasing strain, the cracks can grow into voids andfurther develop into deep holes, until final rupture occurs by hole/void coalescence due tointernal necking.49 However, when mechanical testing is performed at subzero temperaturesunder high strain rate conditions (> 102 s"1 for CVN testing), the flow strength of the ferriteincreases 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 furtherenhances the stress concentrations at the M-A/ferrite interface.52 Accordingly, the local stresslevel at the interface will eventually exceed the cleavage strength of the ferrite, with conse-quent initiation of brittle fracture. This conclusion is consistent with observations made fromtensile testing of dual-phase steels, showing that failure of dual-phase microstructures often iscaused by fracture in the ferrite region.52"54

Because the intercritical HAZ toughness is closely related to the volume fraction of theM-A constituent in the matrix, 4 5 5 1 5 5 embrittlement can normally be avoided by decreasingthe cooling rate through the critical transformation temperature range to facilitate pearlite for-mation (see Fig. 7.29). An exception is boron-containing steels, where the HAZ hardenabilityis high enough to stabilise the M-A constituent, even at slow cooling rates (see CVN data forsteel B in Fig. 7.29).

Abs

orbe

d en

ergy

, J

Nor

mal

ized

stre

ss

Stiffparticle

Normalized distance

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)

Steel B(L-T)

(T-L)

Cooling time, At6/4, s

Fig. 7.29. Effect of cooling time Ar674 on the intercritical HAZ toughness at -200C (thermally cycledspecimens). Steel A: 11 ppm B, Steel B: 26 ppm B. Data from Ramberg et al.55

Effect of PWHTConsidering the intercritical HAZ, a significant improvement of the CVN toughness can beachieved by applying a PWHT, as shown by the data of Akselsen et al51 This effect arisespartly from a reduction of the stress concentrations at the M-A/ferrite interface as a result ofmartensite tempering and partly from relaxation of transformation strains within the ferritematrix.51 Such recovery reactions will start to occur when the temperature is raised aboveabout1000C.

CTO

D a

t -1

O0C

, m

m

(a)

(b)

P content, wt%

Fig. 7.30. Effects of PWHT on the grain coarsened HAZ toughness; (a) Example of intergranular frac-ture along prior austenite grain boundaries after PWHT (6000C - 1 h), (b) Measured CTOD vs baseplate phosphorus content for post weld heat treated specimens (6000C - 4 h). Data quoted by Grong andAkselsen.41

In contrast to the behaviour described above for the intercritical HAZ, the reported effect ofPWHT on the grain coarsened HAZ toughness is much more complicated and rather confus-ing. However, experience has shown that particularly niobium-vanadium containing steelsare sensitive to PWHT due to the strong precipitation hardening potential of Nb(C,N) andV(C,N).43'56 In addition, a toughness deterioration may occur as a result of segregation ofimpurity 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 detrimentaleffect of phosphorus on the HAZ toughness of low carbon microalloyed steels after PWHT isshown in Fig. 7.30(b).

Example (7.3)

Consider procedure test SA welding on a thick plate of a Nb-microalloyed steel under thefollowing 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 tempera-

tures (i.e. 13500C, 10000C, and 7800C) under cooling conditions similar to those employed inthe SA welding trial. Based on the data in Table 7.2 and the simplified Rykalin thick platesolution (equation (1-73) in Chapter 1), estimate the locations of the brittle zones (referred tothe fusion boundary) within the HAZ of the SA procedure test weld considered above.

SolutionIt is evident from the CVN data in Table 7.2 that the HAZ toughness would be expected to below 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 simpli-fied Rykalin thick plate solution, the following expression can be derived for an arbitraryisothermal zone width, Ar*m, referred to the fusion boundary (see equation (5-47) in Chapter5):

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 testweld (Example (7.3))

Test results

Base metal

Thermally cycledspecimens

Weld HAZ*

Absorbed energy at -400C (J)

320, 310, 305; average: 312

Tp = 7800CT = 10000C7;= 13500C

40, 36, 34; average: 37225, 220, 219; average: 22150, 46, 40; average: 46

GCR: 63, GRR: 225, IR: 53

1GCR: grain coarsened region; GRR: grain refined region; IR: intercritical region.

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 bound-ary, respectively. A comparison with the procedure test results in Table 7.2 shows that themeasured CVN toughness after welding at these locations is slightly higher than that inferredfrom the weld thermal simulation experiments. This observation is not surprising, consideringthe fact the CVN specimens extracted from the procedure test weld, in practice, include awide spectrum of thermal regions which have undergone highly different temperature-timeprogrammes, whereas the microstructure within the thermally cycled CVN specimens is morehomogeneous due to a similar temperature-time pattern across the whole gauge length (seeFig. 7.31). Hence, weld thermal simulation cannot replace procedure testing carried out onreal welds. Nevertheless, it is a useful method of evaluating the microstructural stability andmechanical 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 ofcrack 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 ofhydrogen-induced cracking is that the process is time-dependent, i.e. the crack may first ap-pear after several minutes or hours from the time of arc extinction. Consequently, the phenom-enon is also referred to delayed cracking or cold cracking in the scientific literature.

7.2.3.1 Mechanisms of hydrogen crackingHydrogen embrittlement in steels in characterised by:59'60

(i) The crystal structure dependenceHydrogen embrittlement is mainly associated with materials which exhibit a bccor a bet crystal structure, i.e. ferritic and martensitic steels. Austenitic stainlesssteels and aluminium alloys with a fee crystal structure are usually not sensitive tohydrogen.

(ii) The microstructure dependenceA martensitic steel is generally more prone to hydrogen cracking than a ferriticsteel, but a martensitic microstructure is not a requirement for crack initiation.

Next Page

8Exercise Problems with Solutions

8.1 Introduction

This chapter contains a collection of different exercise problems which the author hasadopted in his welding metallurgy course for graduate (mature) students. They illustrate howthe models described in the previous chapters can be used to solve practical problems of moreinterdisciplinary nature. Each of them contains a 'problem description' and some backgroundinformation on materials and welding conditions. The exercises are designed to illuminate themicrostructural connections throughout the weld thermal cycle and show how the propertiesachieved depend on the operating conditions applied. Solutions to the problems are also pre-sented. These are not complete or exhaustive, but are just meant as an aid to the reader to de-velop 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) Tack welding of a T-joint (Fig. 8.1)(ii) Root pass deposition in a single V-groove (Fig. 8.2)(iii) Root pass deposition in a X-groove (Fig. 8.3)(iv) 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 withchemical compositions and properties as listed in Tables 8.1 and 8.2. Details of welding par-ameters 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 Si Mn P S Nb Al

C-Mn1 0.20 0.35 1.46 0.003 0.002 - 0.037

LC-Nb1 0.08 0.26 1.44 0.003 0.003 0.020 0.025

1Ti: -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 -40(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

fThe 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

fData compiled from dedicated filler wire 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 com-bination of base material and welding conditions (e.g. deposition of a cap layer on the top ofa thick multipass C-Mn steel weld). The problem here is to evaluate the response of the basematerial to heat released by the welding arc. The analysis should be quantitative in nature andbased 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 locatedin the heat source).

(c) Estimate the value of the deposition coefficient kx (in gA "1S"1), the weld cross sectionareas 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 contentin 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 follow-ing 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 mor-phology. Indicate also the type of substructure which form at different positions from theweld centre line.

(h) Evaluate the thermal stability of the base metal grain boundary pinning precipitates. Atwhich temperature will these precipitates dissolve?

(i) Calculate the austenite grain size profile across the HAZ. Estimate also the size of thecolumnar austenite grains in the weld metal.

(j) Estimate the primary reaction products which form in the weld metal and the HAZ afterthe austenite to ferrite transformation.

(k) Estimate the maximum hardness in the HAZ after welding. Use this information to eval-uate 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 steelshas been gradually lowered to values below 0.1 wt% in step with the progress in steelmanufacturing technology.

Solution:

In all cases we can use stringer bead deposition on thick plates as a model system. It followsfrom the analysis in Section 1.10.7 (Chapter 1) that the pertinent difference in the effectiveheat diffusion area between a bead-on-plate weld and a groove weld may conveniently be ac-counted 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 bewritten 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 con-ditions 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 movinghigh power source (equation (1-73)). Fig 1.24 provides a basis for such an evaluation. Themost 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 contributionfrom heat flow in the welding direction is sufficiently small that it can be disregarded in thecalculations of the HAZ thermal programme. This means that equation (1-73) can be used inreplacement 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 toapply the pseudo-steady state solution down to a peak temperature of, say, 7000C, the corre-sponding nJQ ratio at that temperature becomes:

From Fig. 1.21 we see that this ratio corresponds to a dimensionless radius vector a3m ofabout 5. The duration of the transient heating period may now be read from Fig. 1.18. A crudeextrapolation 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 1S \ which is in excellentagreement with the data quoted in Table 1.7. The area D of deposited metal thus becomes (seeequation (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 inputwelding is close to 0.67.

(d) The composition data in Table 8.4 refer to all weld metal deposit. Since the dilution withrespect to the base material in this case is small, the weld metal composition would be ex-pected 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 byconsidering the difference in chemical composition between the filler wire and the weldmetal. In the present case we get:

Loss of siliconAs shown in Section 2.10.1.3 (Chapter 2), the silicon loss can partly be ascribed to SiO(g) for-mation in the arc column (with consequent fume formation), and partly to reactions with oxy-gen 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. Takingthe fume formation rate (FFF) of silicon equal to 63 mg min"1, the total loss of silicon in thearc column amounts to:

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

Loss of manganeseAs shown in Section 2.10.1.4 (Chapter 2), manganese is partly lost in the arc column due evap-oration and partly in the weld pool due to deoxidation reactions. Taking the fume formationrate of manganese equal to 14 mg min"1 (from Table 2.6), the total loss of Mn in the arc col-umn amounts to:

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

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

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

Rejected oxygen from the weld poolThe amount of rejected oxygen is equal to the difference between the total and the residualoxygen level:

From this we see that most of the oxygen which is picked up at elevated temperatures isrejected again during cooling in the weld pool due to deoxidation reactions and subsequentphase separation.

Manganese silicate slag formationThe weld pool deoxidation reactions give rise to the formation of a top bead slag, as shownin Section 2.10.1.5 (Chapter 2). In the present example the amount of slag per 10Og weldmetal is equal to:

A comparison with Fig. 2.35 shows that the calculated weight of slag is in reasonable agree-ment with experimental observations.

(e) The oxygen balance is carried out in accordance with the procedure outlined in Section2.10.1.7 (Chapter 2). First we need to estimate the total mass of weld metal produced per unittime:

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 con-tent 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 inclu-sion composition. From Fig. 2.68 we see that the inclusions are essentially pure manganese sil-icates with an overall composition close to MnSiO3.

When the inclusion composition is known, it is possible to convert the residual weld metaloxygen content into an equivalent inclusion volume fraction according to the procedure out-lined in Section 2.12.1.Taking the stoichiometric conversion factor equal to 5.0 X 10~2 formanganese silicate slags, we obtain:

Moreover, we can use equation (2-79) in Section 2.12.2.2 to calculate the mean diameterof 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 inreasonable agreement with those reported for C-Mn steel weld metals.

(g) The characteristic growth pattern of columnar grains in bead-on-plate welds is shownschematically in Fig. 3.33. The first phase to form will be delta ferrite which subsequently de-composes to austenite via a peritectic transformation (see Fig. 3.72). The important question iswhether re-nucleation of the grains will occur during solidification. In practice, this depends onthe interplay between a number of variables which cannot readily be accounted for in a sim-plified analysis, including the weld pool geometry, the cooling rate and the nucleation potencyof the non-metallic inclusions. Broadly speaking, the energy barrier associated with nucleationof delta ferrite at manganese silicates is rather high (e.g. see Fig. 3.30), which suggests that for-mation of new grains ahead of the advancing solid/liquid interface is not very likely under theprevailing circumstances. Hence, the columnar grain zone would be expected to extend entirelyfrom 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 metalcolumnar grains. Close to weld centre-line the local crystal growth rate will approach thewelding speed (i.e. RL ~ 4 mm s"1). At the same time a simple analytical solution exists for thethermal gradient in the weld pool (equation (3-28)):

From this we see that a cellular-dendritic type of substructure is likely to form within thecentral 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-microalloyedsteel, the important grain boundary pinning precipitates within the HAZ are either NbC, NbNor a mixture of these. In the former case the equilibrium dissolution temperature may be es-timated from the solubility product of the pure binary compounds. From equation (4-4) andTable 4.1, we have:

and

This shows that NbC is thermodynamically more stable than NbN. In practice, the real dis-solution temperature may be significantly higher than that predicted from equation (4-4) be-cause of the kinetic superheating (see discussion in Section 4.4, Chapter 4). The grain growthdiagram 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, weobtain:

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 effectivegrain boundary pinning precipitates. These will be thermodynamically stable up to the melt-ing 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 sizeat the fusion boundary will exceed 100 /mm because of dissolution of the base metal grainboundary 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 muchlarger extent.The limiting austenite grain size may be calculated from equation (5-21).Takingthe 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 in-itial size of the weld metal delta ferrite/austenite columnar grains would be expected to becomparable to the size of the HAZ austenite grains adjacent to the fusion boundary. Since thelatter varies along the periphery of the fusion boundary at the same time as competitive graingrowth leads to a general coarsening of the solidification microstructure with increasing dis-tance from the fusion boundary, an average columnar austenite grain size of about 50 /mmseems reasonable under the prevailing circumstances.

(j) As an illustration of principles, we shall assume that the CCT diagram in Fig. 6.27(a) pro-vides an adequate description of the base plate transformation behaviour during welding. Thecooling 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 coarsenedand grain refined region of the HAZ, respectively:

Grain coarsened region (T ~ 13500C):Microstructure : 100% lath martensiteTransformation start temperature: ~ 470 0C

Grain refined region (Tp «10000C):Microstructure : ferrite + pearliteTransformation start temperature: ~ 600 0C

It follows that the observed difference in the HAZ transformation behaviour can mainlybe attributed to a corresponding difference in the prior austenite grain size, which accordingto 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 trans-formed) HAZ, where the peak temperature of the thermal cycle has been between Ac1 andAc3 (see discussion in Section 6.3.8.2, Chapter 6). Just above the Ac1 temperature the volumefraction of the M-A (martensite-austenite) constituent is approximately equal to the baseplate pearlite content (Fig. 6.66), which in the present case is about 8 vol%, as judged from thesteel carbon content.

Considering the weld metal, the situation is different. Here the oxide inclusions willstrongly affect the microstructure evolution by promoting intragranular nucleation of acicu-lar ferrite (see discussion in Section 6.3.5, Chapter 6). In practice, the role of inclusions in weldmetal 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 fornucleation 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 formationare particularly favourable within the as-deposited weld metal (Sx(I) > SJGB)), and some-what 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 tem-perature region of the HAZ, since nucleation of ferrite at austenite grain boundaries in thiscase will completely override nucleation at inclusions (SJGB) » SJI)).This is also in agree-ment 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 canbe estimated from the diagrams presented in Section 7.2.2 (Chapter 7) if the steel compositionand 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 therisk of hydrogen cracking and H2S stress corrosion cracking during service. In the former casean upper limit of about 300 to 325 VPN is incorporated in many welding specifications to avoidproblems with hydrogen cracking, but this restriction can be relaxed if specific precautionaryactions are taken during the welding operation to reduce the supply of hydrogen as shown inSection 7.2.3 (Chapter 7). Considering the H2S stress corrosion cracking resistance a maximumhardness level of 248 VPN is strictly enforced in many welding specifications, as discussed pre-viously in Section 7.2.4 (Chapter 7). Hence, significant tempering of the martensite would berequired 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 offshorestructures a minimum CVN toughness of 35J at — 400C is frequently specified. From the CVNdata in Tables 8.2 and 8.4 it apparent that both the base plate and the weld metal meet this re-quirement. Moreover, auto-tempered low carbon martensite and polygonal ferrite, whichform within the grain coarsened and grain refined region of the HAZ, respectively are knownto have an adequate cleavage resistance.This means that the intercritical HAZ is the mostcritical region of the joint when it comes to toughness due to the presence of high carbon platemartensite within the ferrite matrix (see Figs. 6.61 through 6.65 and discussion in Section7.2.2.3, Chapter 7). In practice, the problem may be solved by applying an appropriate postweld heat treatment (PWHT).

(m) Since the properties of martensite depend on the carbon content, C-Mn steel weldmentswill generally be more prone to hydrogen cracking, H2S stress corrosion cracking and brittlefraction 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 chemi-cal composition as listed in Table 8.5. The base plate has an average grain size of 18 /xm in thefully annealed condition, which conforms to a tensile yield strength of about 300 MPa. Thesheets shall be butt welded in one pass, using a simple I-groove with 3 mm root gap. In thiscase the addition of filler wire is adjusted so that the area of the weld reinforcement amountsto 50% of the groove cross section. Details of welding parameters and operational conditionsare 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 / (A) U (V) v (mm s"1)

Value 200 15 5

+The arc efficiency factor may be taken equal to 0.4. No preheating is applied (T0 = 20 0C).

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

Shielding gas:

Wire composition:

Weld metal*properties:

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 con-ditions described above. The analysis should be quantitative in nature and based on soundphysical principles. The following input data are recommended:

Argon

Specific questions:


(b) Estimate the minimum bead length which is required to achieve pseudo-steady statedown to a peak temperature of 1000 0C.

(c) Estimate the deposition rate (in gA^s"1), the weld cross section areas D and B (inmm2), and the dilution ratio B/(B + D) during welding.

(d) Estimate the weld metal chemical composition for the given combination of baseplate, filler wire and dilution ratio.

(e) Sketch the contour of the weld pool and the resulting columnar grain morphology inthe 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 thecolumnar 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 ofthe joint during service.

Solution:

(a) The problem of interest is whether we must use the general (but complex) Rosenthal thinplate solution (equation (1-81)) or can adopt the simplified solution for a fast moving highpower source (equation (1-100)). Fig 1.43 provides a basis for such an evaluation. The mostcritical position will be the fusion line. If we neglect the latent heat of melting, the BJn^ ratioat 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-Dmodel close to the fusion line, but that this solution is a good approximation within the lowpeak temperature region of the HAZ. Here equation (1-100) may be used in replacement ofequation (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 sol-ution 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 ofabout 5. The duration of the transient heating period may now be read from Fig. 1.28. A crudeextrapolation 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 n3/0p8ratio 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) inorder 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 meltingpoint equal to 0.5, it is easy to verify that the geometry of the weld pool in this case is tear-shaped. 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. 7.53by 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 avoidproblems 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 readfrom 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 fusionboundary, 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 fromFig. 6.69 that the risk of chromium carbide formation in this case is negligible because of thelow base plate carbon content. Hence, the corrosion resistance will not be significantly affec-ted 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 GMA welding of 5 mm A A 6082 extrusions with chemical composition as listed inTable 8.8. The base material has a Vickers hardness and tensile yield strength of 110 VPN and280 MPa, respectively in the T6 temper condition. The extrusions shall be butt welded in onepass, using a simple I-groove with no root gap. Two different filler wires are available, one Al-Siwire and one Al-Mg wire (in the following designated wire I and II, respectively). Details ofwelding 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 Si Mg Mn Fe

AA 6082 0.98 0.64 0.52 0.19

Table 8.9 Exercise problem III: Welding parameters1.

Parameter /(A) (/(V) v (mm s"1)

Value 200 28 10

|The arc efficiency factor may be taken equal to 0.8. No preheating is applied (T = 200C).

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

Shielding gas: Argon

Gas flow rate: 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* Wire I:properties: 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 con-ditions described above. The analysis should be quantitative in nature and based on soundphysical principles. The following input data are recommended:

Specific questions:

Tem

pera

ture

, 0C

Tem

pera

ture

, 0C

Atomic percent silicon

Weight percent silicon

Fig. 8.5. The binary Al-Si phase diagram.

Atomic percent magnesium

Weight percent magnesium

Fig. 8.6. The binary Al-Mg phase diagram.


(b) Estimate the minimum bead length which is required to achieve pseudo-steady state downto a peak temperature of 200 0C.

(c) Estimate the value of the deposition coefficient k' (in gA^s"1), the weld cross sectionareas 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 sol-idification. Indicate also the type of substructure which forms at different positions alongthe 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 estimatethe 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 re-duction 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, re-spectively. To what extent will the temper condition affect the microstructure and strengthevolution during welding?

Solution:

(a) The problem of interest is whether we must use the general (but complex) Rosenthal thinplate solution (equation (1-81)) or can adopt the simplified solution for a fast moving highpower source equation (1-100)). Fig 1.43 provides a basis for such an evaluation. The mostcritical position will be the fusion line. If we neglect the latent heat of melting, the 6 In3 ratioat 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-Dsolution close to the fusion line, but that equation (1-100) may be used (with some reserva-tions) 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 sol-ution 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 <r5m ofabout 5. The duration of the transient heating period may now be read from Fig. 1.28. A crudeextrapolation gives:

from which

It follows that the minimum bead length required to achieve pseudo-steady state duringaluminium welding is much longer than in steel welding due to the pertinent differences in theheat flow conditions (e.g. see Example 1.5, Chapter 1).

(c) The value of the deposition coefficient may be estimated from the data in Table 8.10:

This value corresponds to a A: Vp ratio of about 0.92 mm3A 1S \ which is in excellent agree-ment with the data quoted in Table 1.7. The area D of deposited metal thus becomes (seeequation (1-120)):

The total area of fused metal can be read from Fig. 1.31. At the melting point the nJ0p8ratio is close to 0.93, which gives:

and

This gives:

Note that in these calculations we have assumed that A2 is equal to the sum of (B + D) inorder to achieve realistic numbers.

(d) The weld metal composition can be calulated from a simple 'rule of mixtures':

By using input data from Tables 8.8 and 8.10, we get:

Wire I:

Wire II:

(e) The bead morphology can be read from Fig. 1.29. Taking the 68In3 ratio at the meltingpoint equal to 1, it is easy to verify that the shape of weld pool in this case is elliptical. Thecolumnar grain structure is therefore similar to that shown in Fig. 3.11 (a).

Moreover, Fig. 3.43 provides a basis for estimating the substructure of the weld metalcolumnar grains. Close to weld centre-line the local crystal growth rate will approach thewelding speed (i.e. RL ~ 10 mm s"1). At the same time a simple analytical solution exists forthe thermal gradient in the weld pool (equation (3-29)):

From this we see that a cellular-dendritic type of substructure is likely to form within thecentral parts of the fusion zone, in agreement with general experience.

If we only consider the contribution from the major alloying element in each case, the Scheilequation (equation (3-46)) may be used for an analysis of the segregation pattern during sol-idification. By using input data from the binary phase diagrams in Figs. 8.5 and 8.6, we get:

Wire I:

Wire II:

From this we see that the amount of eutectic liquid which forms during solidification is sen-sitive to variations in the filler wire chemical composition (i.e. the Si or Mg content).

(f) Fig. 7-54 provides a basis for evaluation of the hot cracking susceptibility.

Wire IIn this case the fraction of eutectic liquid is so abundant that it backfills and 'heals' all incipi-ent cracks. Hence, the hot cracking susceptibility is low.

Wire IIWhen the Al-Mg filler wire is used the fraction of eutectic liquid is just large enough to formcontinuous films at the columnar grain boundaries. Hence, the hot cracking susceptibility ishigh.

(g) Liquation cracking arises from melting of specific phases present within the base material(e.g. Mg2Si and Si), as discussed in Section 7. 4.2.1 (Chapter 7). Fig. 7.61 provides a basis forevaluating the HAZ cracking susceptibility:

Wire IIn this case the risk of liquation cracking is small because the solidus temperature of the weldmetal is lower than the actual melting temperatures of the base metal constituent phases.

Wire IIDue to the high Bi(B + D) ratio involved, the solidus temperature of the weld metal will ex-ceed the actual melting temperatures of the base metal constituent phases. This may lead toliquation cracking in parts of the HAZ where the peak temperature is greater than, say, 555to 559 0C.

(h) The sequence of reactions occurring within the HAZ during welding of AA 6082-T6 alu-minium alloys is shown in Fig. 7.62. In the present case we can use Fig. 4.24 for a quantitative

analysis of the /3" dissolution kinetics. Taking the net heat input per mm2 qjvd equal to 0.08kJmm~2, we obtain:

Total width of HAZ

Temperature for incipient dissolution of /3"

First we need to estimate the corresponding if/m -coordinate in the HAZ from Fig. 1.31:

Reading then gives:

from which

Total width of fully reverted HAZ:

Temperature for complete dissolution of /3"

First we need to estimate the corresponding if/m -coordinate in the HAZ from Fig. 1.31:

Reading then gives:

from which

A comparison with the phase diagram in Fig. 4.8 shows that the calculated temperature forincipient dissolution of /3" is in good agreement with that obtained from the solubility prod-uct.

(i) The yield strength in HAZ and the weld metal can be obtained from Fig. 7.67 and Table8.10, respectively:

Wire I:HAZ: Rp02 (min) « 130 MPa, Weld metal: Rp02 « 55 MPa , Base metal: Rp02 « 280 MPa

Strength reduction factor (weld metal control):

Wire II:HAZ: Rp02 (min) - 130 MPa7WeId metal: Rp02 > 130 MPa , Base metal: Rp02 « 280 MPa

Strength reduction factor (HAZ control):

From this we see that the Al-Mg filler wire (wire II) yields the best weld metal mechanicalproperties and should therefore be used, unless the cracking resistance is of particular con-cern.

(j) When the material is present in the O-temper condition, it will contain an appreciableamount of the equilibrium /3-Mg2Si phase. This will tend to accelerate the problem with li-quation cracking within the HAZ during welding.

In addition, it is evident from Figs. 4.4 and 4.8 that the equilibrium /3-Mg2Si phase is ther-modynamically much more stable than the metastable /3" phase. In practice, this means thatonly a narrow solutionised zone will form adjacent to the fusion boundary. However, withinthis zone significant strength recovery may occur after welding due to natural ageing effects(see Fig. 4.5), which may result in a HAZ hardness and tensile yield strength level of about 80VPN and 190 MPa, respectively. Hence, for the O-tempered material, we get:

Wire I

HAZ: Rp02 (max) - 190 MPa, Weld metal: Rp02^ 55 MPa, Base metal: Rp02 « 100 MPa

Strength reduction factor (weld metal control):

/=55/100 = 0.55

Wire II

HAZ: Rp()2 (max) - 190 MPa, Weld metal: Rp02 > 130 MPa, Base metal: Rp02 - 100 MPa

Strength reduction factor (base metal control):

/ = 100/100 = 1

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

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 246 272 293 effect on weld properties 481 486 solubility product of precipitates 303

aluminium weldments 458 536 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 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

596 Index terms Links


aluminium weldments (Continued) constitutive equations 548 558 during friction welding 555 during fusion welding 547

hot cracking 540 factors affecting 544

solidification cracking 536 strength evolution during welding 547

constitutive equations 548 558 during friction welding 555 hardness and strength distribution 550 560 strengthening mechanisms in alloys 547

amplitude of weaving – definition 80

arc atmosphere composition 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 449 conditions for 450

austenitic stainless steels 453 see also stainless steel weldments characteristics of 527 chromium carbide formation 456 grain growth diagrams for steel welding 375 weld decay area 456



Avrami equation in solid state transformations see also solid state transformation and transportation kinetics additivity in 404 475 exponents in 401

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 49

boron in steel effect on transformation behaviour 413 segregation of 294 weld properties 493 505

bowing of crystal 240

Bramfitt’s planar lattice disregistry model 244 see also solidification of welds

C carbon equivalents 496 521

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



cell/dendrite alignment angle 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 290 292

dendrite arm spacing 261 primary 261 secondary 264

dendrite fragmentation 250 see also solidification of welds



dendrite substructure 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 182 219 overall deoxidation model 201

deposit – amount of weld metal 96

deposition rate 96

dissociation of gases in arc column 117

distributed heat sources 77 112 general solution 77 simplified solution (Gaussian heat distribution) 112 simplified solution (planar heat distribution) 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 501



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 186 228

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



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 337 computer simulation 380 diagrams

construction of 360



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 340 342 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 486 494

gross heat input – definition 37

growth rate of crystals 230 local 234 nominal 230 see also solidification of welds



H Hall-Petch relation 529

heat flow models distributed heat sources 77 112 grain growth diagrams 360 instantaneous heat sources 5 local preheating 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



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 201 volume fraction 193

stoichiometric conversion factors 194

instantaneous heat sources 5 line source 5 plane source 5 point source 5

interface stability 254



interfacial energies 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 408 427 429

444 448

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



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



low-alloy steel weldments (Continued) transformation behaviour 290 406

solidification primary precipitation of austenite 292 primary precipitation of delta ferrite 290 292

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



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 403 and Avrami equation 404



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 248 272

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



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 166

gas arc metal welding 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 162 173 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



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



precipitate stability (Continued) stable and metastable solvus boundaries 304 thermodynamic background 301

preheating, local 100 heat flow model 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 122

pseudo-steady state temperature distribution, definition 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



Sievert’s law 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 404 475 high strength low-alloy steels 406 kinetics see transformation kinetics nomenclature 471

solid state transformation kinetics 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 256

example (3.7) – substructure characteristics of Al-Mg welds 258 primary dendrite arm spacing 261



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 263 secondary dendrite arm spacing 264

example (3.10) – secondary dendrite arm spacing in thick plate GTA Al-Si welds 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



solidification of welds (Continued) nucleation potency of second phase particles 242

rate of heterogeneous nucleation 247 reorientation of columnar grains 239

bowing of crystal 240 example (3.3) – bowing by dendritic branching 240

structural zones 221

solubility of gases in liquids and solids 125 hydrogen in Al 125 hydrogen in Cu 125 hydrogen in Fe 125 513 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



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 185 187 284

substructure of welds 251 see also solidification of welds

T texture in welds

solidification 221 290 solid state 429



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



thick plate solutions (Continued) 2-D heat flow model 41

volume of isothermal enclosures 35 transient heating period 29

thin plate solutions 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



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 36

volume fraction of inclusions 193

volume heat capacity 3

W Wagner-Lifshitz equation 196 314 351

water content 137 in electrode coating 137 in welding flux 138 see also hydrogen absorption



weld pool shape and geometry 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 341

in grain growth 341

Zener equation 342 344

Zener-Hollomon parameter 465

zinc in aluminium solubility product of precipitates 303

Author Index

AAaron, H.B. 320, 326, 398-9Aaronson, H.I. 408, 429Abson, DJ. 407, 428, 440, 477-8,

485,493, 504Adams, CM. 26Adrian, H. 301,303Agren, J. 320-1,326Akselsen, O.M. 97, 345, 347, 349,

367,406,414-15,419,444,446,448-54, 481, 484, 488-90, 495-6, 499, 502-7, 525

Alberry, RJ. 374, 500, 502Alcock, CB. 159AIi, A. 427-8American Society for Testing Mate-

rials (ASTM) 364Andersen, I. 483Anderson, M.P. 380Anderson, RD. 3Ankem, S. 343,351Apold,A. 174-5Araki, T. 505-6Ardeil, AJ. 494Ashby, M.F. 26, 201, 314, 318, 329,

360, 363-4, 375, 377-8, 459,461,464

Asthana, R. 326Atlas of isothermal transformation

and cooling transformation dia-grams 403

Avrami, M. 403, 422

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

Berge, J.O. 229Bernstein, LM. 512Betzold,J. 413Bhadeshia, H.K.D.H. 147, 206, 292,

408-9, 413, 422-9, 431, 4 3 3 ^ ,436,441,443-4

Bhatti,A.R. 208-10Biloni, H. 229Bjornbakk, B. 486,491Blander, M. 171,173Boiling, G.F. 290Bonnet, C 435, 440Bradstreet, BJ. 186Bramfitt, B.L. 244Bratland, D.H. 459-62, 556-8, 562British Iron and Steels Research As-

sociation 3Brody, H.D. 272, 276Brooks, J.A. 277-8, 533Brown, A.M. 345Brown, LT. 509, 511Brown, L.C. 314Burck, R 289Burgardt, R 229

CCahn, J.W. 337, 340-1, 345Cai, X.-L. 450Cameron, T.B. 413Camping, M. 556-8, 562Capes, J.F. 251,292-3,412Carslaw, H.S. 2, 4Chai,CS. 171Challenger, K.D. 434, 480Chan, J.W. 403Charpentier, F.R 435, 440Chen, J.H. 505-6Chew, B. 132, 135Chipman, J. 414Choi, H.S. 450Christensen, 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. 290Claes, J. 180

Cochrane, R.C. 292-3, 407, 428Coe,F.R. 128-9,509-10,515Coleman, M.C 259, 263-4Collins, F.R. 537Corbett, J.M. 203, 428Corderoy, DJ.H. 151, 155, 160-1Cotton, H J.U. 496Cottrell, CL.M. 496Crafts, W. 190Craig, I. 171Cross, CE. 251,259,292-3,412,538Crossland, B. 556

DDallam, CM. 441D'annessa, A.T. 280Das. G. 452Dauby, P. 180David, 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. 162DeArdo, AJ. 290Deb, P. 434, 480DebRoy,T.210Delong,WT.533Demarest, V. A. 449-50Devillers, L. 435,440,480, 482Devletian,J.H.279,285,413Dieter, G.E. 482,486, 524-5, 529Distin, PA. 157Doherty,R.D.301,309,396Dolby, R.E. 407,444Dons, A.L. 438,459, 541Dorn, XE. 501-2Dowling, J.M. 203,428Dube, CA. 408Dudas, J.H. 537Dumolt, S.D. 547

EEagar, T.W. 26, 96, 99, 105, 171-2,

174,228Easterling, 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. 201Edmonds, D.V. 409Edwards, G.R. 227,259,422-3,425,

428,441Eickhorn,F. 187-8Elliott, J.F. 151, 162, 174-5, 179,

182, 184, 191Engel,A. 187-8Enjo, T. 547Es-Souni, M. 440European Recommendations for Alu-

minium Alloy Structures 552Evans, G.M. 137-8, 192-3, 203,

420-1,435,440

FFainstein, D. 320, 398-9Farrar, R.A. 435, 441, 443,480Fast, J.D. 513Ferrar, R.A. 428,435,444,478,485,

504Fine, M.E. 389, 403Fischer, W. A. 162Fisher, DJ. 221, 234, 242, 251, 259,

261,265-6,270,274Fleck, N.A. 422-3, 428, 441Flemings, M.C. 221, 234, 242, 265,

272,275-6Fortes, M.A. 374-5, 380-1Fountain, R.W. 414Fradkov, V.E. 380Franklin, A.G. 195,208Fredriksson, H. 290Frost, HJ. 380Fruehan, RJ. 156Fujibayashi, K. 146

GGarcia, C.I. 290Garland, J. 505Garland, J.G. 221,240,247,250,278,

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

Grewal, G. 343,351Griffiths, E. 3,4Grong, 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. 503Guo, Z.H. 405,420-1

HHabrekke, T. 229Halmoy,E. 151Hannertz, N.E. 507Harris, D.R. 414Harrison, P.L. 428, 435, 444, 478,

485, 504Hatch, J.E. 3, 458, 547Hawkins, D.N. 208-10, 435, 440Hazzledine, P.M. 342-3Heckel, R.W. 326Hehemann, R.F. 429,452Heile, R.F. 154, 156-7, 169Heintze, G.N. 244, 247Heiple, CR. 229Hellman, P. 339, 343-5Hemmer,H. 371-2Hilbert, M. 339, 343-5Hill,D.C. 154, 156-7, 169Hillert, M. 290Hilty, D.C. 190Hjelen, J. 195, 292, 430-3, 438Hocking, L.M. 196Hollomon, J.H. 465, 500H6llrigl-Rosta,F.413Homma, H. 203, 444-5, 504-5Hondros,E.D. 414Honeycombe, R.W.K. 406,408,420,

429, 431, 444, 447-8, 453, 486Horii,Y. 187-8Houghton, D.C. 303, 323Howden, D.G. 141Howell, PR. 434-6, 441Hu, H. 337-8, 342-3, 345,430Hultgren, R. 3Hunderi, O. 337, 341-2, 380

IIbarra, S. 497Indacochea, J.E. 171,173International Institute of Welding

129, 152Ion, J.C. 314, 318, 360, 3 6 3 ^ , 368Ivanchev, I. 204-5

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

KKaplan, D. 435, 440, 480, 482Kasuya, T. 496Kato, M. 233Kawasaki, K. 380Keene, BJ. 96, 99, 105,228Kelly, A. 548Kelly, K.K. 3Kern, A. 380Kerr, H.W. 203, 247, 273, 290, 428Kiessling, R. 202^4Kihara,H. 131, 133, 134Kikuchi, T. 142^Kikuta, Y. 505-6Kim, B.C. 444Kim, LS. 450Kim, NJ. 444,451,505Kim, YG. 451Kinsman, K.R. 429, 452Kirkwood, RR. 292-3Kluken, A.O. 182, 186, 194-204,

206,209-11,247-8,250-4,256,290, 292-4, 371-2, 430-3, 435-6,438,440,446-7,479-80,484,486,491,493,497

Knacke, O. 154Knagenhjem, H.O. 229Knott, J.F. 486Kobayashi, T. 142^Kotler, G.R. 320, 326, 398-9Kou, S. 27, 75-6, 96, 99, 105, 228,

250, 264-5, 272, 377, 453, 455,458

Krauklis, P. 435-6, 441-4Kraus, H.G. 228

Krauss, G. 418Kubaschewski, O. 159Kuroda, T. 547Kurz, W. 221, 234, 242, 251, 259,

260-1,265-6,270,274Kuwabara, M. 146Kuwana, T. 142-4Kvaale, FE. 414-15, 419, 504

LLancaster, J.F. 118, 120, 162, 187Lanzillotto, C.A.N. 452, 505Le, Y. 27, 75-6, 265Lee, D.Y. 444Lee, J.-L. 504Lei, T.C. 505Li, W.B. 345, 367Lifshitz, J.M. 314, 351Lindborg,U. 170, 182-3, 185Liu, J.Z. 505Liu, S. 251, 292-3,412,422-3,428,

435-6,441,497Liu, Y. 339Loberg, B. 303Lohne, O. 380,459,541Long, CJ. 533, 535Lucke,K. 337, 340-1,345Lutony, MJ. 380

MMaitrepierre, Ph. 414Marandet, B. 435, 440, 480, 482Marder,A.R.451Marthinsen, K. 380Martins, G.P. 182, 185-6, 192-3Martukanitz, R.P. 459Matlock, 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, 271Matsuda, S. 203, 208, 319, 444-5,

504-5Matsuda, Y. 505-6Matsunawa, A. 96, 99, 105Mazzolani, F.M. 458McKnowlson, P 15McMahon, CJ. 418McPherson, R. 244, 247McQueen, HJ. 464McRobie, D.E. 486Mehl, R.F. 408, 436-7Metals Handbook 3, 545Midling, O.T. 465-6, 556-8, 560-3Miller, R.L. 449-50Mills, A.R. 435, 440

Mills, K.C. 96, 99,105,228Milner, D.R. 141Miranda, R.M. 374-5Mitra, U. 171-2Mizuno, M. 284Moisio, T. 290Mondolfo, L.F. 2A2-AMori, N. 187-8Morigaki, 0.146Morral, J.E. 413Mossinger, R. 554Mundra, K. 210Munitz, A. 267Murray, J.L. 203Muzzolani, F.M. 547,550,552Myers, RS. 26Myhr, O.R. 26, 61, 73-5, 77, 314,

327-30, 360, 458-62, 464, 496,547-9,550-5

NNaess, OJ. 503Nagai, T. 380Nakagawa,H. 131, 133, 134Nakata, K. 271Nes,E. 337, 341-2, 380Nicholson, R.B. 548Niles, R.W. 89Nilles,P. 180Nordgren, A. 303North, T.H. 171Nowicki,A. 171Nylund, H.K. 438

OO'Brien, J.E. 143, 145Odland, PT. 480Ohkita, S. 203, 444-5, 504-5Ohno, S. 143Ohshita, S. 103, 104,496,515Ohta, S. 380Okumura, M. 103, 104Okumura, N. 208, 319Olsen, K. 500, 502Olson, D.L. 171,173-4,176-9,181-

2, 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, 228Oriani, R.A. 514Orr, R.L. 3Ostrom, G. 5330verlie, H.G. 541Owen, W.S. 450Ozturk,B. 156

PPaauw, AJ. 446, 503Pabi, S.K. 326Pakrasi, S. 413Pan, Y-T. 504Pande, CS. 339Pardo, E. 247, 273Pargeter, RJ. 428, 440, 477-8, 485,

493, 504Patterson, B.R. 339Pepe,JJ. 541Petch,NJ. 512Petty-Galis, J.L. 306Phillip, R.H. 444Phillips, H.W.L. 543Pickering, RB. 301, 303, 452, 479,

505Pitsch, W. 436-7Plockinger, E. 186Porter, D.A. 247,309,389,392,403,

408,413,427,429,435,448Pottore,N.S.290Priestner, R. 451Pugin, A.I. 556-7

RRamachandran, S. 190-1, 204Ramakrishna, V. 151, 162, 174-5,

179, 191Ramberg, M. 450-1, 505-6Ramsay, CW. 480Rappaz, M. 236, 239, 241, 260Rath, B.B. 337-8, 342-3, 345Ravi Vishnu, P. 500, 502Reif, W. 380Reiso, O. 541-3Reti,T. 501-2Ribes, A. 435, 440, 480, 482Riboud, PV. 480, 482Ribound, PV. (Riboud ?) 435, 440Ricks, R.A. 434-5, 436, 441Ringer, S.P. 345, 367Rollett, A.D. 380Roper, J.R. 229Rorvik, G. 247-8, 250-4, 256, 292-

4, 430, 446-9, 495-6, 499,503,507, 525

Rose, R. 516Rosenthal, D. 26, 28, 31, 33, 38, 41,

48, 51, 56, 59-61, 76, 98, 133,360

Roux, R. 140Rykalin, N.N. 18, 21, 26, 41, 45, 56,

93,95, 556-7Ryum, N. 326,337,341-2,345,347,

349,367,380,382,390,396,403,541-3

SSaetre, T.O. 380, 382Saggese, ME. 208-10, 435,440Sagmo, G. 97Saito, S. 103, 104Sakaguchi, A. 284Savage, W.F. 541Schaeffler, A.L. 533Scheil, E. 403Schriever, U. 380Schumacher, J.E 162Schwan,M.21,25Scott, MH. 544-5Seah,MR414Seay, E.B. 96, 99, 105Senda, T. 233Shackleton, D.N. 166-7Shaller,F.W.509,512Shen, H.P. 505Shen,X.P.451Sherby, O.D. 501-2Shercliff, H.R. 314,329,459-62,464Shinozaki, K. 131, 133, 134Siewert, T.A. 182, 185-6, 192-3,

227,425,428Sigworth, G.K. 162Simonsen, T. 520-2Sims, CE. 512Skaland, T. 346Skjolberg, E.M. 140-1Slyozov,V.V. 314,351Smith, A. A. 166-7, 169, 170Soares, A. 380-1Solberg, J.K. 446, 450-4, 504-6Sommerville, LD. 204-5Speich, G.R. 449-50Srolovitz, DJ. 380Staley, J.T. 394-5, 459Steidl, G. 554Steigerwald,E.A.509,512Stjerndahl, J. 290Stoneham, A.M. 414Strangwood, M. 428-9, 431, 444Strid, J. 303, 542-3Stuwe,H. 337, 340-1,345Sugden, A.A.B. 292,431Suutala, N. 290Suzuki, H. 406, 444, 477, 496, 509,

515,520Suzuki, S. 303, 323Svensson, L.E. 147, 206, 413, 422-

8, 431, 4 3 3 ^ , 441, 444, 536Szekely, J. 96,99,105,120,162,183,

187,228,281,284Szewezyk, A.F. 505Szumachowski, E. 533

TTakalo,T.290Tamehiro, H. 496Tamura, 1.405,420-1Tanigaki, T. 146Tanzilli, R.A. 326Tardy, P. 501-2Tensi, H.M. 21,25Thaulow, C. 503Themelis, NJ. 120,162,183,187,281,

284Therrien,A.E.434,480Thewlis, G. 203,435,440-1Thivellier, D. 414Thomas, G. 505Thompson, A.W. 480,512Thompson, CV. 380Tichelaar, G.W. 156Tjotta, S. 459,460Tomii,Y.284Torsell, K. 182-3,185Tricot, R. 414Trivedi, R. 260, 400,427Troiano,A.R.509,512Tsai,N.S.26Tsukamoto, K. 271Tundal, UH. 326Turkdogan, E.T. 126, 182, 184-6,

191-2,195-6,207,214Turpin, M.L. 182,184

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

VVan Den Heuvel, G J P M . 156Van Stone, R.H. 480Vander Voort, G.F. 394, 403Vandermeer, R.A. 341Vasil'eva, VA. 556-7Verhoeven, J.D. 286, 429, 431, 433,

448-9Villafuerte, XC 247,273Vitek, J.M. 96,99,105,210,222,228,

240,250,272,278,478

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

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

520

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

metallurgical modelling of welding 2nd edition (1997)

Documents