Metallurgical Modelling of Welding SECOND EDITION 0YSTEIN GRONG Norwegian University of Science and Technology, Department of Metallurgy, N-7034 Trondheim, Norway
MATERIALS MODELLING SERIES
Editor: H. K. D. H. Bhadeshia The University of Cambridge Department of Materials Science and Metallurgy
T H E INSTITUTE OF MATERIALS
Book 677 First published in 1997 by The Institute of Materials 1 Carlton House Terrace London SWlY 5DB First edition (Book 557) Published in 1994 The Institute of Materials 1997 All rights reserved ISBNl 86125 036 3
Originally typeset by PicA Publishing Services Additional typesetting and corrections by Fakenham Photosetting Ltd Printed and bound in the UK at The University Press, Cambridge
TO TORHILD, TORBJ0RN AND HAVARD without your support, this book would never have been finished.
Preface to the second edition
Besides correcting some minor linguistic and print errors, I have in the second edition included a collection of different exercise problems which have been used in the training of students at NTNU. They illustrate how the models described in the previous chapters can be used to solve practical problems of more interdisciplinary nature. Each of them contains a 'problem description' and some background information on materials and welding conditions. The exercises are designed to illuminate the microstructural connections throughout the weld thermal cycle and show how the properties achieved depend on the operating conditions applied. Solutions to the problems are also presented. These are not complete or exhaustive, but are just meant as an aid to the reader to develop the ideas further. Trondheim, 28 October, 1996 0ystein Grong
Preface to the first edition
The purpose of this textbook is to present a broad overview on the fundamentals of welding metallurgy to graduate students, investigators and engineers who already have a good background in physical metallurgy and materials science. However, in contrast to previous textbooks covering the same field, the present book takes a more direct theoretical approach to welding metallurgy based on a synthesis of knowledge from diverse disciplines. The motivation for this work has largely been provided by the need for improved physical models for process optimalisation and microstructure control in the light of the recent advances that have taken place within the field of materials processing and alloy design. The present textbook describes a novel approach to the modelling of dynamic processes in welding metallurgy, not previously dealt with. In particular, attempts have been made to rationalise chemical, structural and mechanical changes in weldments in terms of models based on well established concepts from ladle refining, casting, rolling and heat treatment of steels and aluminium alloys. The judicious construction of the constitutive equations makes full use of both dimensionless parameters and calibration techniques to eliminate poorly known kinetic constants. Many of the models presented are thus generic in the sense that they can be generalised to a wide range of materials and processing. To help the reader understand and apply the subjects and models treated, numerous example problems, exercise problems and case studies have been worked out and integrated in the text. These are meant to illustrate the basic physical principles that underline the experimental observations and to provide a way of developing the ideas further. Over the years, I have benefited from interaction and collaboration with numerous people within the scientific community. In particular, I would like to acknowledge the contribution from my father Professor Tor Grong who is partly responsible for my professional upbringing and development as a metallurgist through his positive influence on and interest in my research work. Secondly, I am very grateful to the late Professor Nils Christensen who first introduced me to the fascinating field of welding metallurgy and later taught me the basic principles of scientific work and reasoning. I will also take this opportunity to thank all my friends and colleagues at the Norwegian Institute of Technology (Norway), The Colorado School of Mines (USA), the University of Cambridge (England), and the Universitat der Bundeswehr Hamburg (Germany) whom I have worked with over the past decade. Of this group of people, I would particularly like to mention two names, i.e. our department secretary Mrs. Reidun 0stbye who has helped me to convert my original manuscript into a readable text and Mr. Roald Skjaerv0 who is responsible for all line-drawings in this textbook. Their contributions are gratefully acknowledged. Trondheim, 1 December, 1993 0ystein Grong
Contents
Preface to the Second Edition ........................................................
xiii
Preface to the First Edition .............................................................
xiv
1. Heat Flow and Temperature Distribution in Welding ...........
1
1.1
Introduction ...............................................................................
1
1.2
Non-steady Heat Conduction ....................................................
1
1.3
Thermal Properties of Some Metals and Alloys ........................
2
1.4
Instantaneous Heat Sources .....................................................
4
1.5
Local Fusion in Arc Strikes ........................................................
7
1.6
Spot Welding .............................................................................
10
1.7
Thermit Welding ........................................................................
14
1.8
Friction Welding ........................................................................
18
1.9
Moving Heat Sources and Pseudo-steady State ......................
24
1.10 Arc Welding ...............................................................................
24
1.10.1 Arc Efficiency Factors ..................................................
26
1.10.2 Thick Plate Solutions ................................................... 1.10.2.1 Transient Heating Period ............................. 1.10.2.2 Pseudo-steady State Temperature Distribution ................................................... 1.10.2.3 Simplified Solution for a Fast-moving High Power Source ..............................................
26 28
1.10.3 Thin Plate Solutions ..................................................... 1.10.3.1 Transient Heating Period ............................. 1.10.3.2 Pseudo-steady State Temperature Distribution ................................................... This page has been reformatted by Knovel to provide easier navigation.
31 41 45 48 49
vi
Contents
vii
1.10.3.3 Simplified Solution for a Fast Moving High Power Source ..............................................
56
1.10.4 Medium Thick Plate Solution ....................................... 1.10.4.1 Dimensionless Maps for Heat Flow Analyses ...................................................... 1.10.4.2 Experimental Verification of the Medium Thick Plate Solution ..................................... 1.10.4.3 Practical Implications ...................................
59
1.10.5 Distributed Heat Sources ............................................. 1.10.5.1 General Solution .......................................... 1.10.5.2 Simplified Solution .......................................
77 77 80
1.10.6 Thermal Conditions during Interrupted Welding ..........
91
1.10.7 Thermal Conditions during Root Pass Welding ...........
95
61 72 75
1.10.8 Semi-empirical Methods for Assessment of Bead Morphology .................................................................. 1.10.8.1 Amounts of Deposit and Fused Parent Metal ............................................................ 1.10.8.2 Bead Penetration .........................................
96 99
1.10.9 Local Preheating ..........................................................
100
References .........................................................................................
103
Appendix 1.1: Nomenclature ............................................................
105
Appendix 1.2: Refined Heat Flow Model for Spot Welding ..............
110
Appendix 1.3: The Gaussian Error Function ....................................
111
Appendix 1.4: Gaussian Heat Distribution .......................................
112
96
2. Chemical Reactions in Arc Welding ...................................... 116 2.1
Introduction ...............................................................................
116
2.2
Overall Reaction Model .............................................................
116
2.3
Dissociation of Gases in the Arc Column ..................................
117
2.4
Kinetics of Gas Absorption ........................................................
120
2.4.1
Thin Film Model ...........................................................
120
2.4.2
Rate of Element Absorption .........................................
121
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viii
Contents 2.5
The Concept of Pseudo-equilibrium ..........................................
122
2.6
Kinetics of Gas Desorption ........................................................
123
2.6.1
Rate of Element Desorption .........................................
123
2.6.2
Sievert’s Law ...............................................................
124
Overall Kinetic Model for Mass Transfer during Cooling in the Weld Pool ............................................................................
124
Absorption of Hydrogen ............................................................
128
2.8.1
Sources of Hydrogen ...................................................
128
2.8.2
Methods of Hydrogen Determination in Steel Welds ...........................................................................
128
2.8.3
Reaction Model ............................................................
130
2.8.4
Comparison between Measured and Predicted Hydrogen Contents ...................................................... 2.8.4.1 Gas-shielded Welding .................................. 2.8.4.2 Covered Electrodes ..................................... 2.8.4.3 Submerged Arc Welding .............................. 2.8.4.4 Implications of Sievert’s Law ....................... 2.8.4.5 Hydrogen in Multi-run Weldments ............... 2.8.4.6 Hydrogen in Non-ferrous Weldments ..........
131 131 134 138 140 140 141
Absorption of Nitrogen ..............................................................
141
2.9.1
Sources of Nitrogen .....................................................
142
2.9.2
Gas-shielded Welding ..................................................
142
2.9.3
Covered Electrodes .....................................................
143
2.9.4
Submerged Arc Welding ..............................................
146
2.10 Absorption of Oxygen ................................................................
148
2.10.1 Gas Metal Arc Welding ................................................ 2.10.1.1 Sampling of Metal Concentrations at Elevated Temperatures ............................... 2.10.1.2 Oxidation of Carbon ..................................... 2.10.1.3 Oxidation of Silicon ...................................... 2.10.1.4 Evaporation of Manganese .......................... 2.10.1.5 Transient Concentrations of Oxygen ...........
148
2.7 2.8
2.9
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149 149 152 156 160
Contents
ix
2.10.1.6 Classification of Shielding Gases ................ 2.10.1.7 Overall Oxygen Balance .............................. 2.10.1.8 Effects of Welding Parameters ....................
166 166 169
2.10.2 Submerged Arc Welding .............................................. 2.10.2.1 Flux Basicity Index ....................................... 2.10.2.2 Transient Oxygen Concentrations ...............
170 171 172
2.10.3 Covered Electrodes ..................................................... 2.10.3.1 Reaction Model ............................................ 2.10.3.2 Absorption of Carbon and Oxygen .............. 2.10.3.3 Losses of Silicon and Manganese ............... 2.10.3.4 The Product [%C] [%O] ...............................
173 174 176 177 179
2.11 Weld Pool Deoxidation Reactions .............................................
180
2.11.1 Nucleation of Oxide Inclusions .....................................
182
2.11.2 Growth and Separation of Oxide Inclusions ................. 2.11.2.1 Buoyancy (Stokes Flotation) ........................ 2.11.2.2 Fluid Flow Pattern ........................................ 2.11.2.3 Separation Model .........................................
184 185 186 188
2.11.3 Predictions of Retained Oxygen in the Weld Metal ...... 2.11.3.1 Thermodynamic Model ................................ 2.11.3.2 Implications of Model ...................................
190 190 192
2.12 Non-metallic Inclusions in Steel Weld Metals ...........................
192
2.12.1 Volume Fraction of Inclusions ......................................
193
2.12.2 Size Distribution of Inclusions ...................................... 2.12.2.1 Effect of Heat Input ...................................... 2.12.2.2 Coarsening Mechanism ............................... 2.12.2.3 Proposed Deoxidation Model .......................
195 196 196 201
2.12.3 Constituent Elements and Phases in Inclusions .......... 2.12.3.1 Aluminium, Silicon and Manganese Contents ...................................................... 2.12.3.2 Copper and Sulphur Contents ..................... 2.12.3.3 Titanium and Nitrogen Contents .................. 2.12.3.4 Constituent Phases ......................................
202
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202 202 203 204
x
Contents 2.12.4 Prediction of Inclusion Composition ............................. 2.12.4.1 C-Mn Steel Weld Metals .............................. 2.12.4.2 Low-alloy Steel Weld Metals ........................
204 204 206
References .........................................................................................
212
Appendix 2.1: Nomenclature ............................................................
215
Appendix 2.2: Derivation of Equation (2-60) ....................................
219
3. Solidification Behaviour of Fusion Welds ............................ 221 3.1
Introduction ...............................................................................
221
3.2
Structural Zones in Castings and Welds ...................................
221
3.3
Epitaxial Solidification ...............................................................
222
3.3.1
Energy Barrier to Nucleation ........................................
225
3.3.2
Implications of Epitaxial Solidification ..........................
226
Weld Pool Shape and Columnar Grain Structures ....................
228
3.4.1
Weld Pool Geometry ....................................................
228
3.4.2
Columnar Grain Morphology ........................................
229
3.4.3
Growth Rate of Columnar Grains ................................. 3.4.3.1 Nominal Crystal Growth Rate ...................... 3.4.3.2 Local Crystal Growth Rate ...........................
230 230 234
3.4.4
Reorientation of Columnar Grains ............................... 3.4.4.1 Bowing of Crystals ....................................... 3.4.4.2 Renucleation of Crystals ..............................
239 240 242
Solidification Microstructures ....................................................
251
3.5.1
Substructure Characteristics ........................................
251
3.5.2
Stability of the Solidification Front ................................ 3.5.2.1 Interface Stability Criterion ........................... 3.5.2.2 Factors Affecting the Interface Stability .......
254 254 256
3.5.3
Dendrite Morphology ................................................... 3.5.3.1 Dendrite Tip Radius ..................................... 3.5.3.2 Primary Dendrite Arm Spacing .................... 3.5.3.3 Secondary Dendrite Arm Spacing ...............
260 260 261 264
3.4
3.5
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Contents 3.6
3.7
3.8
xi
Equiaxed Dendritic Growth .......................................................
268
3.6.1
Columnar to Equiaxed Transition .................................
268
3.6.2
Nucleation Mechanisms ...............................................
272
Solute Redistribution .................................................................
272
3.7.1
Microsegregation .........................................................
272
3.7.2
Macrosegregation ........................................................
278
3.7.3
Gas Porosity ................................................................ 3.7.3.1 Nucleation of Gas Bubbles .......................... 3.7.3.2 Growth and Detachment of Gas Bubbles .... 3.7.3.3 Separation of Gas Bubbles ..........................
279 279 281 284
3.7.4
Removal of Microsegregations during Cooling ............ 3.7.4.1 Diffusion Model ............................................ 3.7.4.2 Application to Continuous Cooling ...............
286 286 286
Peritectic Solidification ..............................................................
290
3.8.1
Primary Precipitation of the γp-phase ...........................
290
3.8.2
Transformation Behaviour of Low-alloy Steel Weld Metals .......................................................................... 3.8.2.1 Primary Precipitation of Delta Ferrite ........... 3.8.2.2 Primary Precipitation of Austenite ................ 3.8.2.3 Primary Precipitation of Both Delta Ferrite and Austenite ...................................
290 290 292 292
References .........................................................................................
293
Appendix 3.1: Nomenclature ............................................................
296
4. Precipitate Stability in Welds ................................................. 301 4.1
Introduction ...............................................................................
301
4.2
The Solubility Product ...............................................................
301
4.2.1
Thermodynamic Background .......................................
301
4.2.2
Equilibrium Dissolution Temperature ...........................
303
4.2.3
Stable and Metastable Solvus Boundaries .................. 4.2.3.1 Equilibrium Precipitates ............................... 4.2.3.2 Metastable Precipitates ...............................
304 304 308
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xii
Contents 4.3
Particle Coarsening ...................................................................
314
4.3.1
Coarsening Kinetics .....................................................
314
4.3.2
Application to Continuous Heating and Cooling ........... 4.3.2.1 Kinetic Strength of Thermal Cycle ............... 4.3.2.2 Model Limitations .........................................
314 315 315
Particle Dissolution ....................................................................
316
4.4.1
Analytical Solutions ...................................................... 4.4.1.1 The Invariant Size Approximation ................ 4.4.1.2 Application to Continuous Heating and Cooling ........................................................
316 319
Numerical Solution ....................................................... 4.4.2.1 Two-dimensional Diffusion Model ................ 4.4.2.2 Generic Model ............................................. 4.4.2.3 Application to Continuous Heating and Cooling ........................................................ 4.4.2.4 Process Diagrams for Single Pass 6082T6 Butt Welds ..............................................
325 326 328
References .........................................................................................
334
Appendix 4.1: Nomenclature ............................................................
334
4.4
4.4.2
322
329 332
5. Grain Growth in Welds ........................................................... 337 5.1
Introduction ...............................................................................
337
5.2
Factors Affecting the Grain Boundary Mobility ..........................
337
5.2.1
Characterisation of Grain Structures ............................
337
5.2.2
Driving Pressure for Grain Growth ...............................
339
5.2.3
Drag from Impurity Elements in Solid Solution ............
340
5.2.4
Drag from a Random Particle Distribution ...................
341
5.2.5
Combined Effect of Impurities and Particles ................
342
Analytical Modelling of Normal Grain Growth ...........................
343
5.3.1
Limiting Grain Size .......................................................
343
5.3.2
Grain Boundary Mobility ...............................................
345
5.3
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Contents
xiii
Grain Growth Mechanisms .......................................... 5.3.3.1 Generic Grain Growth Model ....................... 5.3.3.2 Grain Growth in the Absence of Pinning Precipitates .................................................. 5.3.3.3 Grain Growth in the Presence of Stable Precipitates .................................................. 5.3.3.4 Grain Growth in the Presence of Growing Precipitates .................................................. 5.3.3.5 Grain Growth in the Presence of Dissolving Precipitates .................................
345 345
Grain Growth Diagrams for Steel Welding ................................
360
5.4.1
Construction of Diagrams ............................................ 5.4.1.1 Heat Flow Models ........................................ 5.4.1.2 Grain Growth Model ..................................... 5.4.1.3 Calibration Procedure .................................. 5.4.1.4 Axes and Features of Diagrams ..................
360 360 361 361 363
5.4.2
Case Studies ............................................................... 5.4.2.1 Titanium-microalloyed Steels ....................... 5.4.2.2 Niobium-microalloyed Steels ....................... 5.4.2.3 C-Mn Steel Weld Metals .............................. 5.4.2.4 Cr-Mo Low-alloy Steels ................................ 5.4.2.5 Type 316 Austenitic Stainless Steels ...........
364 364 367 370 372 375
Computer Simulation of Grain Growth ......................................
380
5.3.3
5.4
5.5
5.5.1
347 348 351 356
Grain Growth in the Presence of a Temperature Gradient .......................................................................
380
Free Surface Effects ....................................................
382
References .........................................................................................
382
Appendix 5.1: Nomenclature ............................................................
384
5.5.2
6. Solid State Transformations in Welds ................................... 387 6.1
Introduction ...............................................................................
387
6.2
Transformation Kinetics ............................................................
387
6.2.1
387
Driving Force for Transformation Reactions ................
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xiv
Contents
6.3
6.2.2
Heterogeneous Nucleation in Solids ............................ 6.2.2.1 Rate of Heterogeneous Nucleation .............. 6.2.2.2 Determination of ∆Ghet.* and Qd ................... 6.2.2.3 Mathematical Description of the C-curve .....
389 389 390 392
6.2.3
Growth of Precipitates .................................................. 6.2.3.1 Interface-controlled Growth ......................... 6.2.3.2 Diffusion-controlled Growth .........................
396 396 397
6.2.4
Overall Transformation Kinetics ................................... 6.2.4.1 Constant Nucleation and Growth Rates ...... 6.2.4.2 Site Saturation .............................................
400 400 402
6.2.5
Non-isothermal Transformations .................................. 6.2.5.1 The Principles of Additivity ........................... 6.2.5.2 Isokinetic Reactions ..................................... 6.2.5.3 Additivity in Relation to the Avrami Equation ...................................................... 6.2.5.4 Non-additive Reactions ................................
402 403 404
High Strength Low-alloy Steels .................................................
406
6.3.1
Classification of Microstructures ..................................
406
6.3.2
Currently Used Nomenclature ......................................
406
6.3.3
Grain Boundary Ferrite ................................................ 6.3.3.1 Crystallography of Grain Boundary Ferrite .......................................................... 6.3.3.2 Nucleation of Grain Boundary Ferrite .......... 6.3.3.3 Growth of Grain Boundary Ferrite ................
408 408 408 422
6.3.4
Widmanstätten Ferrite ..................................................
427
6.3.5
Acicular Ferrite in Steel Weld Deposits ........................ 6.3.5.1 Crystallography of Acicular Ferrite ............... 6.3.5.2 Texture Components of Acicular Ferrite ...... 6.3.5.3 Nature of Acicular Ferrite ............................. 6.3.5.4 Nucleation and Growth of Acicular Ferrite ..........................................................
428 428 429 430
Acicular Ferrite in Wrought Steels ...............................
444
6.3.6
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404 405
432
6.4
6.5
Contents
xv
6.3.7
Bainite .......................................................................... 6.3.7.1 Upper Bainite ............................................... 6.3.7.2 Lower Bainite ...............................................
444 444 447
6.3.8
Martensite .................................................................... 6.3.8.1 Lath Martensite ............................................ 6.3.8.2 Plate (Twinned) Martensite ..........................
448 448 448
Austenitic Stainless Steels ........................................................
453
6.4.1
Kinetics of Chromium Carbide Formation ....................
456
6.4.2
Area of Weld Decay .....................................................
456
Al-Mg-Si Alloys ..........................................................................
458
6.5.1
459
6.5.2
Quench-sensitivity in Relation to Welding .................... 6.5.1.1 Conditions for β’(Mg2Si) Precipitation during Cooling .............................................. 6.5.1.2 Strength Recovery during Natural Ageing .........................................................
459 461
Subgrain Evolution during Continuous Drive Friction Welding ...........................................................
464
References .........................................................................................
467
Appendix 6.1: Nomenclature ............................................................
471
Appendix 6.2: Additivity in Relation to the Avrami Equation ............
475
7. Properties of Weldments ........................................................ 477 7.1
Introduction ...............................................................................
477
7.2
Low-alloy Steel Weldments .......................................................
477
7.2.1
477 478
Weld Metal Mechanical Properties .............................. 7.2.1.1 Weld Metal Strength Level ........................... 7.2.1.2 Weld Metal Resistance to Ductile Fracture ....................................................... 7.2.1.3 Weld Metal Resistance to Cleavage Fracture ....................................................... 7.2.1.4 The Weld Metal Ductile to Brittle Transition .....................................................
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480 485 486
xvi
Contents 7.2.1.5
Effects of Reheating on Weld Metal Toughness ...................................................
491
7.2.2
HAZ Mechanical Properties ......................................... 7.2.2.1 HAZ Hardness and Strength Level .............. 7.2.2.2 Tempering of the Heat Affected Zone .......... 7.2.2.3 HAZ Toughness ...........................................
494 495 500 502
7.2.3
Hydrogen Cracking ...................................................... 7.2.3.1 Mechanisms of Hydrogen Cracking ............. 7.2.3.2 Solubility of Hydrogen in Steel ..................... 7.2.3.3 Diffusivity of Hydrogen in Steel .................... 7.2.3.4 Diffusion of Hydrogen in Welds ................... 7.2.3.5 Factors Affecting the HAZ Cracking Resistance ...................................................
509 509 513 514 514
H2S Stress Corrosion Cracking .................................... 7.2.4.1 Threshold Stress for Cracking ..................... 7.2.4.2 Prediction of HAZ Cracking Resistance .......
524 524 525
Stainless Steel Weldments .......................................................
527
7.3.1
HAZ Corrosion Resistance ..........................................
527
7.3.2
HAZ Strength Level .....................................................
529
7.3.3
HAZ Toughness ...........................................................
530
7.3.4
Solidification Cracking ..................................................
532
Aluminium Weldments ..............................................................
536
7.4.1
Solidification Cracking ..................................................
536
7.4.2
Hot Cracking ................................................................ 7.4.2.1 Constitutional Liquation in Binary Al-Si Alloys ........................................................... 7.4.2.2 Constitutional Liquation in Ternary Al-MgSi Alloys ....................................................... 7.4.2.3 Factors Affecting the Hot Cracking Susceptibility ................................................
540
7.2.4
7.3
7.4
7.4.3
HAZ Microstructure and Strength Evolution during Fusion Welding ............................................................
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518
541 542 544 547
Contents 7.4.3.1 7.4.3.2 7.4.3.3 7.4.3.4 7.4.4
Effects of Reheating on Weld Properties ..... Strengthening Mechanisms in Al-Mg-Si Alloys ........................................................... Constitutive Equations ................................. Predictions of HAZ Hardness and Strength Distribution ....................................
HAZ Microstructure and Strength Evolution during Friction Welding ........................................................... 7.4.4.1 Heat Generation in Friction Welding ............ 7.4.4.2 Response of Al-Mg-Si Alloys and Al-SiC MMCs to Friction Welding ............................ 7.4.4.3 Constitutive Equations ................................. 7.4.4.4 Coupling of Models ...................................... 7.4.4.5 Prediction of the HAZ Hardness Distribution ...................................................
xvii 547 548 548 550 556 556 557 558 558 560
References .........................................................................................
564
Appendix 7.1: Nomenclature ............................................................
567
8. Exercise Problems with Solutions ......................................... 571 8.1
Introduction ...............................................................................
571
8.2
Exercise Problem I: Welding of Low Alloy Steels ......................
571
8.3
Exercise Problem II: Welding of Austenitic Stainless Steels .....
583
8.4
Exercise Problem III: Welding of Al-Mg-Si Alloys ......................
587
Index .............................................................................................. 595 Author Index ................................................................................. 602
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1 Heat Flow and Temperature Distribution in Welding
1.1 Introduction Welding metallurgy is concerned with the application of well-known metallurgical principles for assessment of chemical and physical reactions occurring during welding. On purely practical grounds it is nevertheless convenient to consider welding metallurgy as a profession of its own because of the characteristic non-isothermal nature of the process. In welding the reactions are forced to take place within seconds in a small volume of metal where the thermal conditions are highly different from those prevailing in production, refining and fabrication of metals and alloys. For example, steel welding is characterised by: High peak temperatures, up to several thousand 0 C. High temperature gradients, locally of the order of 103 0C mm"1. Rapid temperature fluctuations, locally of the order of 103 0C s 1 . It follows that a quantitative analysis of metallurgical reactions in welding requires detailed information about the weld thermal history. From a practical point of view the analytical approach to the solution of heat flow problems in welding is preferable, since this makes it possible to derive relatively simple equations which provide the required background for an understanding of the temperature-time pattern. However, because of the complexity of the heat flow phenomena, it is always necessary to check the validity of such predictions against more reliable data obtained from numerical calculations and in situ thermocouple measurements. Although the analytical models suffer from a number of simplifying assumptions, it is obvious that these solutions in many cases are sufficiently accurate to provide at least a qualitative description of the weld thermal programme. An important aspect of the present treatment is the use of different dimensionless groups for a general outline of the temperature distribution in welding. Although this practice involves several problems, it is a convenient way to reduce the total number of variables to an acceptable level and hence, condense general information about the weld thermal programme into two-dimensional (2-D) maps or diagrams. Consequently, readers who are unfamiliar with the concept should accept the challenge and try to overcome the barrier associated with the use of such dimensionless groups in heat flow analyses.
1.2 Non-Steady Heat Conduction The symbols and units used throughout this chapter are defined in Appendix 1.1.
Since heat losses from free surfaces by radiation and convection are usually negligible in welding, the temperature distribution can generally be obtained from the fundamental differential equations for heat conduction in solids. For uniaxial heat conduction, the governing equation can be written as:1
(i-D where T is the temperature, t is the time, x is the heat flow direction, and a is the thermal diffusivity. The thermal diffusivity is related to the thermal conductivity X and the volume heat capacity pc through the following equation:
(1-2) For biaxial and triaxial heat conduction we may write by analogy:1
d-3) and
(1-4) The above equations must clearly be satisfied by all solutions of heat conduction problems, but for a given set of initial and boundary conditions there will be one and only one solution.
1.3 Thermal Properties of Some Metals and Alloys A pre-condition for obtaining simple analytical solutions to the differential heat flow equations is that the thermal properties of the base material are constant and independent of temperature. For most metals and alloys this is a rather unrealistic assumption, since both X, a, and pc may vary significantly with temperature as illustrated in Fig. 1.1. In addition, the thermal properties are also dependent upon the chemical composition and the thermal history of the base material (see Fig. 1.2), which further complicates the situation. By neglecting such effects in the heat flow models, we impose several limitations on the application of the analytical solutions. Nevertheless, experience has shown that these problems to some extent can be overcome by the choice of reasonable average values for X, a and pc within a specific temperature range. Table 1.1 contains a summary of relevant thermal properties for different metals and alloys, based on a critical review of literature data. It should be noted that the thermal data in Table 1.1 do not include a correction for heat consumed in melting of the parent materials. Although the latent heat of melting is temporarily removed during fusion welding, experience has shown this effect can be accounted for by calibrating the equations against a known isotherm (e.g. the fusion boundary). In practice, such corrections are done by adjusting the arc efficiency factor Tq until a good correlation is achieved between theory and experiments.
Hx-H0 = PC(T-T0 ),J/mm3
Carbon steel
Temperature, 0C Fig. 1.1. Enthalpy increment H7-H0 2-4.
referred to an initial temperature T0 = 200C. Data from Refs.
Table 1.1 Physical properties for some metals and alloys. Data from Refs 2 - 6 .
Material
(WrTIm-10C-1)
(mm2 s"1)
(Jmnr 3 0C"1)
(0C)
(J mnr 3 )
(J mnr 3 )
Carbon Steels
0.040
8
0.005
1520
7.50
2.0
Low Alloy Steels
0.025
5
0.005
1520
7.50
2.0
High Alloy Steels
0.020
4
0.005
1500
7.40
2.0
Titanium Alloys
0.030
10
0.003
1650
4.89
1.4
Aluminium (> 99% Al)
0.230
85
0.0027
660
1.73
0.8
Al-Mg-Si Alloys
0.167
62
0.0027
652
1.71
0.8
Al-Mg Alloys
0.149
55
0.0027
650
1.70
0.8
Does not include the latent heat of melting (AH1n).
X9 W/mm 0C
(a)
Temperature, 0C
(b)
X, W/mm 0C
High alloy steel
Temperature, 0C Fig. 1.2. Factors affecting the thermal conductivity X of steels; (a) Temperature level and chemical composition, (b) Heat treatment procedure. Data from Refs. 2-4.
1.4 Instantaneous Heat Sources The concept of instantaneous heat sources is widely used in the theory of heat conduction.1 It is seen from Fig. 1.3 that these solutions are based on the assumption that the heat is released instantaneously at time t - 0 in an infinite medium of initial temperature T0, either across a plane (uniaxial conduction), along a line (biaxial conduction), or in a point (triaxial conduction). The material outside the heat source is assumed to extend to x = + °° for a plane source in a long rod, to r = °° for a line source in a wide plate, or to R = °° for a point source in a heavy slab. The initial and boundary conditions can be summarised as follows:
T-T0 = oo for t = O and x = O (alternatively r = O or R = O) T-J 0 = O for t = O and x * O (alternatively r > O or 7? > O) 7-T 0 = O for O < t < oo when x = ± oo (alternatively r = oo or R = oo). It is easy to verify that the following solutions satisfy both the basic differential heat flow equations (1-1), (1-3) and (1-4) and the initial and boundary conditions listed above: (i)
Plane source in a long rod (Fig. 1.3a): d-5)
where Q is the net heat input (energy) released at time t = O, and A is the cross section of the rod. (ii)
Line source in a wide plate (Fig. 1.3b): (1-6)
where d is the plate thickness. (iii)
Point source in a heavy slab (Fig. 1.3c): (1-7)
Equations (1-5), (1-6) and (1-7) provide the required basis for a comprehensive theoretical treatment of heat flow phenomena in welding. These solutions can either be applied directly or be used in an integral or differential form. In the next sections a few examples will be given to illustrate the direct application of the instantaneous heat source concept to problems related to welding.
(a)
T
Fig. 1.3. Schematic representation of instantaneous heat source models; (a) Plane source in a long rod.
T
(b)
X
y
T
R (C)
Fig. 1.3.Schematic representation of instantaneous heat source models (continued); (b) Line source in a wide plate, (c) Point source in a heavy slab.
1.5 Local Fusion in Arc Strikes The series of fused metal spots formed on arc ignition make a good case for application of equation (1-7). Model
The model considers a point source on a heavy slab as illustrated in Fig. 1.4. The heat is assumed to be released instantaneously at time t = 0 on the surface of the slab. This causes a temperature rise in the material which is exactly twice as large as that calculated from equation (1-7): (1-8) In order to obtain a general survey of the thermal programme, it is convenient to write equation (1-8) in a dimensionless form. The following parameters are defined for this purpose: — Dimensionless temperature: (1-9) where Tc is the chosen reference temperature. — Dimensionless time: d-10) where tt is the arc ignition time. — Dimensionless operating parameter:
(1-11) where qo is the net arc power (equal to Qlt(), and (Hc-Ho) is the heat content per unit volume at the reference temperature. — Dimensionless radius vector: (1-12) By substituting these parameters into equation (1-8), we obtain:
(1-13)
Heat source
Isotherms
3-D heat flow Fig. 1.4. Instantaneous point source model for assessment of temperatures in arc strikes.
0Zn1
e/n
Linear time scale
T1
^i Fig. 1.5. Calculated temperatures in arc strikes. Equation (1-13) has been solved numerically for different values ofCT1and T1. The results are presented graphically in Fig. 1.5. Due to the inherent assumption of instantaneous release of heat in a point, it is not possible to use equation (1-13) down to very small values OfCT1 and T1. However, at some distance from the heat source and after a time not much shorter than the real (assumed) time of heating, the calculated temperature-time pattern will be reasonably correct. Note that the heavy broken line in Fig. 1.5 represents the locus of the peak temperatures. This locus is obtained by setting 3In(OAi1VdT1 = 0:
from which
Substituting this into equation (1-13) gives:
(1-14) where Qp is the peak temperature, and e is the natural logarithm base number. Example (1.1)
Consider a small weld crater formed in an arc strike on a thick plate of low alloy steel. Calculate the cooling time from 800 to 5000C (Af875), and the total width of the fully transformed region adjacent to the fusion boundary. The operational conditions are as follows:
where r| is the arc efficiency factor. Relevant thermal data for low alloy steel are given in Table 1.1. Solution
In the present case it is convenient to use the melting point of the steel as a reference temperature (i.e. 0 = 0m = 1 when Tc = TJ. The corresponding values OfZi1 and 9 (at 800 and 5000C, respectively) are:
Cooling time At8/5
Since the cooling curves in Fig. 1.5 are virtually parallel at temperatures below 800 0 C, Af875 will be independent of Cr1 and similar to that calculated for the centre-line ((J1 = 0). By rearranging equation (1-13) we get:
and
Total width offully transformed region Zone widths can generally be calculated from equation (1-14), as illustrated in Fig. 1.6. Taking the Ac3-temperature equal to 8900C for this particular steel, we obtain:
and
Alternatively, the same information could have been read from Fig. 1.5. Although it is difficult to check the accuracy of these predictions, the calculated values for Ats/5 and ARlm are considered reasonably correct. Thus, because the cooling rate is very large, in arc strikes a hard martensitic microstructure would be expected to form within the transformed parts of the HAZ, in agreement with general experience.
1.6 Spot Welding Equation (1-6) can be used for an assessment of the temperature-time pattern in spot welding of plates. Model
The model considers a line source which penetrates two overlapping plates of similar thermal properties, as illustrated in Fig. 1.7. The heat is assumed to be released instantaneously at time Heat source
Fig. 1.6. Definition of isothermal zone width in Example (1.1).
Electrode
Heat source
d
Fig. 1.7. Idealised heat flow model for spot welding of plates.
t = 0. If transfer of heat into the electrodes is neglected, the temperature distribution is given by equation (1-6). This equation can be written in a dimensionless form by introducing the following group of parameters: — Dimensionless time: (1-15) where th is the heating time (i.e. the duration of the pulse). — Dimensionless operating parameter: (1-16) where dt is the total thickness of the joint. — Dimensionless radius vector: (1-17) By substituting these parameters into equation (1-6), we get: (1-18) where 6 denotes the dimensionless temperature (previously defined in equation (1-9)).
6/n2
e/n2
Linear time scale
T
2
T2 Fig. 1.8. Calculated temperature-time pattern in spot welding. Figure 1.8 shows a graphical representation of equation (1-18) for a limited range of a 2 and T2. A closer inspection of the graph reveals that the temperature-time pattern in spot welding is similar to that observed during arc ignition (see Fig. 1.5). The locus of the peak temperatures in Fig. 1.8 is obtained by setting d\n{^ln7}ldx2 - 0.
which gives and (1-19)
Example (1.2)
Consider spot welding of 2 mm plates of low alloy steel under the following operational conditions:
Calculate the cooling time from 800 to 5000C (Af8/5) in the centre of the weld, and the cooling rate (CR.) at the onset of the austenite to ferrite transformation. Assume in these calculations that the total voltage drop between the electrodes is 1.6 V. The M^-temperature of the steel is taken equal to 475°C. Solution
If we use the melting point of the steel as a reference temperature, the parameters n2 and 6 (at 800 and 5000C, respectively) become:
Cooling time Atg/5
The parameter A%5 can be calculated from equation (1-18). For the weld centre-line (CT2 = 0), we get:
and
Cooling rate at 475 0C
The cooling rate at a specific temperature is obtained by differentiation of equation (1-18) with respect to time. When (J2 = 0 the cooling rate at 9 = 0.3 (475°C) becomes:
and
Since the cooling curves in Fig. 1.8 are virtually parallel at temperatures below 8000C (i.e. for QZn2 < 0.15), the computed values of Ar8/5 and CR. are also valid for positions outside the weld centre-line. In the present example the centre-line solutions can be applied down to (°"2m)2 ~ 2. According to equation (1-19), this corresponds to a lower peak temperature of:
which is equivalent with:
It should be emphasised that the present heat flow model represents a crude oversimplification of the spot welding process. In a real welding situation, most of the heat is generated at the interface between the two plates because of the large contact resistance. This gives rise to the development of an elliptical weld nugget inside the joint as shown in Fig. 1.9. Moreover, since the model neglects transfer of heat into the electrodes, the mode of heat flow will be mixed and not truly two-dimensional as assumed above. Consequently, equation (1-18) cannot be applied for reliable predictions of isothermal contours and zone widths. Nevertheless, the model may provide useful information about the cooling conditions during spot welding if the efficiency factor if] and the voltage drop between the electrodes can be estimated with a reasonable degree of accuracy. A more refined heat flow model for spot welding is presented in Appendix 1.2.
1.7 Thermit Welding Thermit welding is a process that uses heat from exothermic chemical reactions to produce coalescence between metals and alloys. The thermit mixture consists of two components, i.e. a metal oxide and a strong reducing agent. The excess heat of formation of the reaction product provides the energy source required to form the weld. Model
In thermit welding the time interval between the ignition of the powder mixture and the completion of the reduction process will be short because of the high reaction rates involved. Assume that a groove of width 2L1 is filled instantaneously at time t = 0 by liquid metal of an initial temperature Tt (see Fig. 1.10). The metal temperature outside the fusion zone is T0. If heat losses to the surroundings are neglected, the problem can be treated as uniaxial conduction where the heat source (extending from -L 1 to +L1) is represented by a series of elementary sources, each with a heat content of: (1-20) At time t this source produces a small rise of temperature at position JC, given by equation (1 -5):
(1-21)
The final temperature distribution is obtained by substituting u = (x-xy(4at)m (i.e. dx'- du(4at)m) into equation (1-21) and integrating between the limits JC'= -L 1 and x'- +L1. This gives (after some manipulation): (1-22)
Isl'srau*'*'=]
Fusion
zone
Fig. 1.9. Calculated peak temperature contours in spot welding of steel plates (numerical solution). Operational conditions: / = 23kA, 64 cycles. Data from Bently et al1
Fusion
zone
Fig. 1.10. Idealised heat flow model for thermit welding of rails. where erf(u) is the Gaussian error function. The error function is defined in Appendix 1.3*. Because of the complex nature of equation (1-22), it is convenient to present the different solutions in a dimensionless form by introducing the following groups of parameters: *The error function is available in tables. However, in numerical calculations it is more convenient to use the Fortran subroutine given in Appendix 1.3.
Dimensionless temperature: (1-23) Dimensionless time: (1-24) Dimensionless jc-coordinate: (1-25) Substituting these parameters into equation (1-22) gives: (1-26) Equation (1-26) has been solved numerically for different values of Q and T3. The results are presented graphically in Fig. 1.11. As would be expected, the fusion zone itself (Q < 1) cools in a monotonic manner, while the temperature in positions outside the fusion boundary (Q > 1) will pass through a maximum before cooling. The locus of the HAZ peak temperatures in Fig. 1.11 is defined by 3673T3 = 0. Referring to Appendix 1.3, we may write:
which gives (1-27) The peak temperature distribution is obtained by solving equation (1-27) for different combinations of Qm and T3m and inserting the roots into equation (1-26).
Example (1.3)
Consider thermit welding of steel rails (i.e. reduction of Fe2O3 with Al powder) under the following operational conditions:
Calculate the cooling time from 800 to 5000C in the centre of the weld, and the total width of the fully transformed region adjacent to the fusion boundary. The Ac3-temperature of the steel is taken equal to 8900C.
91
Definition of parameters:
T
3
Fig. 1.11. Calculated temperature-time pattern in thermit welding. Solution
For positions along the weld centre-line (Q. = 0) equation (1-26) reduces to:
Cooling time At 8/5
From the above relation it is possible to calculate the cooling time from Tt = 22000C to 800 and 5000C, respectively:
and
By rearranging equation (1-24), we obtain the following expression for Ar875:
The computed value for A/8/5 is also valid for positions outside the weld centre-line, since the cooling curves at such low temperatures are reasonably parallel within the fusion zone. Total width of fully transformed region The fusion boundary is defined by:
The locus of the 8900C isotherm in temperature-time space can be read from Fig. 1.11. Taking the ordinate equal to 0.40, we get:
By inserting this value into equation (1-27), we obtain the corresponding coordinate of the isotherm:
The total width of the fully transformed HAZ is thus:
Unfortunately, measurements are not available to check the accuracy of these predictions. Systematic errors would be expected, however, because of the assumption of instantaneous release of heat immediately after powder ignition and the neglect of heat losses to the surroundings. Nevertheless, the present example is a good illustration of the versatility of the concept of instantaneous heat sources, since these solutions can easily be added in space as shown here or in time for continuous heat sources (to be discussed below).
1.8 Friction Welding Friction welding is a solid state joining process that produces a weld under the compressive force contact of one rotating and one stationary workpiece. The heat is generated at the weld interface because of the continuous rubbing of the contact surfaces, which, in turn, causes a temperature rise and subsequent softening of the material. Eventually, the material at the interface starts to flow plastically and forms an up-set collar. When a certain amount of upsetting has occurred, the rotation is stopped and the compressive force is maintained or slightly increased to consolidate the weld. Model (after Rykalin et al.5j
The model considers a continuous (plane) heat source in a long rod as shown in Fig. 1.12(a). The heat is liberated at a constant rate q'o in the plane x = 0 starting at time / = 0. If we subdivide the time t during which the source operates into a series of infinitesimal elements dt/ (Fig. 1.12b), each element will have a heat content of: (1-28)
(a) Continuous heat source
(b) q
t Fig. 1.12. Idealised heatflowmodel for friction welding of rods; (a) Sketch of model, (b) Subdivision of time into a series of infinitesimal elements dt'. At time / this heat will cause a small rise of temperature in the material, in correspondance with equation (1-5): (1-29)
If we substitute t"=t-1'into equation (1 -29), the total temperature rise at time t is obtained by integrating from t"= t (t'= 0) to /"= 0 (t'= t):
(1-30) In order to evaluate this integral, we will make use of the following mathematical transformation:
where
and
Hence, we may write:
The latter integral can be expressed in terms of the complementary error function* erfc{u) by substituting:
and integrating between the limits u = x I (4at)l/2 and w = <*>. This gives (after some manipulation):
(1-31) If the temperature of the contact section at the end of the heating period is taken equal to Th, equation (1-31) can be rewritten as: (1-32)
where t'h denotes the duration of the heating period (t < t'h). Measured contact section temperatures for different metal/alloy combinations are given in Table 1.2. Equation (1-32) may be presented in a dimensionless form by the use of the following groups of parameters: Dimensionless temperature: (1-33) Dimensionless time: (1-34) The complementary error function is defined in Appendix 1.3.
Table 1.2 Measured contact section temperatures during friction welding of some metals and alloys. Data from Tensi et al.10 Metal/Alloy Combination
Measuring Method
Temperature Level [0C]
Partial Melting
Steel
Thermocouples
1080-1340
No
1260-1400
No/Yes
1080
No
Direct readings
1
548
Yes
Copper-Nickel
Direct readings
1
1083
Yes
Al-Cu-2Mg
Thermocouples
506
Yes
Al-4.3Cu
Thermocouples
562
Yes
Al-12Si
Thermocouples
575
Yes
Al-5Mg
Thermocouples
582
Yes
1
Steel-Nickel
Direct readings
Steel-Titanium
Direct readings1
Copper-Al
Based on direct readings of the voltage drop between the two work-pieces.
— Dimensionless .^-coordinate: (1-35)
By substituting these parameters into equation (1-32), we obtain: (1-36)
Equation (1-36) describes the temperature in different positions from the weld contact section during the heating period. However, when the rotation stops, the weld will be subjected to free cooling, since there is no generation of heat at the interface. As shown in Fig. 1.13(a) this can be accounted for by introducing an imaginary heat source of power +qo at time t = t'h which acts simultaneously with an imaginary heat sink of negative power -q o. It follows from the principles of superposition (see Fig. 1.13b) that the temperature during the cooling period is given by:9 (1-37) where 6"(x4) and 6"(T 4 - 1) are the temperatures calculated for the heat source and the heat sink, respectively, using equation (1-36). Equations (1-36) and (1-37) have been solved numerically for different values of Q'and T4. The results are presented graphically in Fig. 1.14. Considering the contact section (Q'= 0), the temperature increases monotonically with time during the heating period, in correspondance with the relationship: (1-38)
q (a) Imaginary heat source Real heat source t Imaginary heat sink
e" (b)
Heating period
$ffl9 \
Fig. 1.13. Method for calculation of transient temperatures during friction welding; (a) Sketch of imaginary heat source/heat sink model, (b) Principles of superposition.
Similarly, for the cooling period we get: (1-39) Outside the contact section (Q / > 0), the temperature rise will be smaller and the cooling rate lower than that calculated from equations (1-38) and (1-39).
Heating
e"
Cooling
\ Fig. 1.14. Calculated temperature-time pattern in friction welding.
Example (1.4)
Consider friction welding of 026mm aluminium rods (Al-Cu-2Mg) under the following conditions:
Calculate the peak temperature distribution across the joint. Assume in these calculations that the thermal diffusivity of the Al-Cu-2Mg alloy is 70mm2 s"1. Solution Readings from Fig. 1.14 give:
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In this particular case, it is possible to check the accuracy of the calculations against in situ thermocouple measurements carried out on friction welded components made under similar conditions. A comparison with the data in Fig. 1.15 shows that the model is quite successful in predicting the HAZ peak temperature distribution. In contrast, the weld heating and cooling cycles cannot be reproduced with the same degree of precision. This has to do with the fact that the present analytical solution omits a consideration of the plastic straining occurring during friction welding, which displaces the coordinates and alters the heat balance for the system.
1.9 Moving Heat Sources and Pseudo-Steady State In most fusion welding processes the heat source does not remain stationary. In the following we shall assume that the source moves at a constant speed along a straight line, and that the net power supply from the source is constant. Experience shows that such conditions lead to a fused zone of constant width. This is easily verified by moving a tungsten arc across a sheet of steel or aluminium, or by moving a soldering iron across a piece of lead or tin. Moreover, zones of temperatures below the melting point also remain at constant width, as indicated by the pattern of temper colours developed on welding ground or polished sheet. It follows from the definition of pseudo-steady state that the temperature will not vary with time when observed from a point located in the heat source. Under such conditions the temperature field around the source can be described as a temperature 'mountain' moving in the direction of welding (e.g. see Fig. 15 in Ref. 11). For points along the weld centre-line, the temperature at different positions away from the heat source (which for a constant welding speed becomes a time axis) may be presented in a two-dimensional plot as indicated in Fig. 1.16. Specifically, this figure shows a schematic representation of the temperature in steel welding from the base plate ahead of the arc to well into the solidified weld metal trailing the arc. If we consider a fixed point on the weld centre-line, the temperature will increase very rapidly during the initial period, reaching a maximum of about 2000-22000C for positions immediately beneath the root of the arc.11 When the arc has passed, the temperature will start to fall, and eventually (after long times) approach that of the base plate. In contrast, an observer moving along with the heat source will always see the same temperature landscape, since this will not change with time according to the presuppositions. It will be shown below that the assumption of pseudo-steady state largely simplifies the mathematical treatment of heat flow during fusion welding, although it imposes certain restrictions on the options of the models.
1.10 Arc Welding Arc welding is a collective term which includes the following processes*: - Shielded metal arc (SMA) welding. - Gas tungsten arc (GTA) welding. - Gas metal arc (GMA) welding. *The terminology used here is in accordance with the American Welding Society's recommendations. 12
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In this particular case, it is possible to check the accuracy of the calculations against in situ thermocouple measurements carried out on friction welded components made under similar conditions. A comparison with the data in Fig. 1.15 shows that the model is quite successful in predicting the HAZ peak temperature distribution. In contrast, the weld heating and cooling cycles cannot be reproduced with the same degree of precision. This has to do with the fact that the present analytical solution omits a consideration of the plastic straining occurring during friction welding, which displaces the coordinates and alters the heat balance for the system.
1.9 Moving Heat Sources and Pseudo-Steady State In most fusion welding processes the heat source does not remain stationary. In the following we shall assume that the source moves at a constant speed along a straight line, and that the net power supply from the source is constant. Experience shows that such conditions lead to a fused zone of constant width. This is easily verified by moving a tungsten arc across a sheet of steel or aluminium, or by moving a soldering iron across a piece of lead or tin. Moreover, zones of temperatures below the melting point also remain at constant width, as indicated by the pattern of temper colours developed on welding ground or polished sheet. It follows from the definition of pseudo-steady state that the temperature will not vary with time when observed from a point located in the heat source. Under such conditions the temperature field around the source can be described as a temperature 'mountain' moving in the direction of welding (e.g. see Fig. 15 in Ref. 11). For points along the weld centre-line, the temperature at different positions away from the heat source (which for a constant welding speed becomes a time axis) may be presented in a two-dimensional plot as indicated in Fig. 1.16. Specifically, this figure shows a schematic representation of the temperature in steel welding from the base plate ahead of the arc to well into the solidified weld metal trailing the arc. If we consider a fixed point on the weld centre-line, the temperature will increase very rapidly during the initial period, reaching a maximum of about 2000-22000C for positions immediately beneath the root of the arc.11 When the arc has passed, the temperature will start to fall, and eventually (after long times) approach that of the base plate. In contrast, an observer moving along with the heat source will always see the same temperature landscape, since this will not change with time according to the presuppositions. It will be shown below that the assumption of pseudo-steady state largely simplifies the mathematical treatment of heat flow during fusion welding, although it imposes certain restrictions on the options of the models.
1.10 Arc Welding Arc welding is a collective term which includes the following processes*: - Shielded metal arc (SMA) welding. - Gas tungsten arc (GTA) welding. - Gas metal arc (GMA) welding. *The terminology used here is in accordance with the American Welding Society's recommendations. 12
- Flux cored arc (FCA) welding. - Submerged arc (SA) welding. The main purpose of this section is to review the classical models for the pseudo-steady state temperature distribution around moving heat sources. The analytical solutions to the differential heat flow equations under conditions applicable to arc welding were first presented (a) Cooling period
Temperature, 0C
Heating period
Predicted heating and cooling cycles for the contact section (x=0)
Time, s
Peak temperature, 0C
(b)
Observed relationship
Predicted relationship
Distance from contact section, mm Fig. 1.15. Comparison between measured and predicted temperatures in friction welding of Al-Cu-2Mg alloys; (a) Temperature-time pattern, (b) Peak temperature distribution. Data from Tensi et al.10
by Rosenthal,1314 but the theory has later been extended and refined by a number of other inve stigators .9'n*15"20 1.10.1 Arc efficiency factors In arc welding heat losses by convection and radiation are taken into account by the efficiency factor r\, defined as: (1-40) where qo is the net power received by the weldment (e.g. measured by calorimetry), / is the welding current (amperage), and U is the arc voltage. For submerged arc (SA) welding the efficiency factor (r\) has been reported in the range from 90 to 98%, for SMA and GMA welding from 65 to 85%, and for GTA welding from 22 to 75%, depending on polarity and materials.11 A summary of ranges is given in Table 1.3. 7.70.2 Thick plate solutions Model (after Rykalin9) According to Fig. 1.17, the general thick plate model consists of an isotropic semi-infinite body at initial temperature T0 limited in one direction by a plane that is impermeable to heat. At time t = 0 a. point source of constant power qo starts on the surface at position O moving in the positive x-direction at a constant speed U The rise of temperature T- T0 in point P at time t is sought. During a very short time interval from ^'to t'+ dt'the amount of heat released at the surface is dQ = qodt'. According to equation (1-7) this will produce an infinitesimal rise of temperature in P at time t:
(1-41)
where
is the time available for conduction of heat over the distance
to point P. For a convenient presentation of the pseudo-steady state solution, the position P should be referred to that of the moving heat source. This is achieved by changing the coordinate system from O to O'(see Fig. 1.17):
and
Hence, we may write:
T
Solidified weld metal
Root of arc
Weld pool
X=Vt Relative position along weld centre-line Fig. 1.16. Schematic diagram showing weld centre-line temperature in different positions from the heat source during steel welding at pseudo-steady state.
Table 1.3 Recommended arc efficiency factors for different welding processes. Data from Refs 11,21. Arc efficiency factor j] Welding Process
Range
Mean
SA welding (steel)
0.91-O.99
0.95
SMA welding (steel)
0.66-0.85
0.80
GMA welding (CO2-steel)
0.75-0.93
0.85
GMA welding (Ar-steel)
0.66-0.70
0.70
GTA welding (Ar-steel)
0.25-0.75
0.40
GTA welding (He-Al)
0.55-0.80
0.60
GTA welding (Ar-Al)
0.22-0.46
0.40
(1-42)
where The total rise of temperature at P is obtained by substituting:
and
into equation (1-42), and integrating between the limits u = (R2l4af)m and u = o°.This gives (after some manipulation): (1-43) It is well-known that:
Hence, the general thick plate solution can be written as:
(1-44)
If u is sufficiently small (i.e. when welding has been performed over a sufficient period), we obtain the pseudo-steady state temperature distribution:
(1-45) This equation is often referred to as the Rosenthal thick plate solution,1314 in honour of D. Rosenthal who first derived the relation by solving the differential heat flow equation directly for the appropriate boundary conditions. 1.10.2.1 Transient heating period It follows from the above analysis that the pseudo-steady state temperature distribution is
Fig. 1.17. Moving point source on a semi-infinite slab. attained after a transient heating period. The duration of this heating period is determined by the integral in equation (1-44). Taking the ratio between the real and the pseudo-steady state temperature equal to K1, we have: (1-46) Equation (1-46) can be expressed in terms of the following parameters: Dimensionless radius vector: (1-47) Dimensionless time: (1-48) Substituting these into equation (1-46) gives: (1-49)
where
and
Equation (1-49) has been solved numerically for a limited range of cr3 and x. The results are presented graphically in Fig. 1.18. A closer inspection of Fig. 1.18 reveals that the duration of the transient heating period depends on the dimensionless radius vector a 3 . In practice this means that the Rosenthal equation is not valid during the initial period of welding unless the distance from the heat source to the observation point is very small. It should be noted, however, that a dimensionless distance o~3 may be 'short' for one combination of welding speed and thermal diffusivity, while the same position may represent a 'long' distance for another combination of V and a. Similarly, the dimensionless time T may be 'short' or 'long' at a chosen number of seconds, depending on the ratio v/2a. Example (1.5)
Consider stringer bead deposition on a thick plate of aluminium at a constant welding speed of 5 mm s"1. Calculate the duration of the heating period when the distance from the heat source to the point of observation is 17 mm. Solution
Ki = (T-T0)/(T-T0)p.s.
Taking a = 85 mm2 s"1, the dimensionless radius vector becomes:
T = v2t/2a Fig. 1.18. Ratio between real and pseudo-steady state temperature in thick plate welding for different combinations ofCT3and T.
It is seen from Fig. 1.18 that the pseudo-steady state temperature distribution is approached when T ~ 3, which gives:
This corresponds to a total bead length of:
The above calculations show that the Rosenthal equation is not valid if the ratio between R and L2 exceeds a certain critical value (typically 0.15 to 0.30 for aluminium welds and 0.4 to 0.6 for steel welds). This important point is often overlooked when discussing the relevance of the thick plate solution in arc welding. 1.10.2.2 Pseudo-steady state temperature distribution The Rosenthal equation gives, with the limitations inherent in the assumptions, full information on the thermal conditions for point sources on heavy slabs. Accordingly, in order to obtain a general survey of the pseudo-steady state temperature distribution, it is convenient to present the different solutions in a dimensionless form. The following parameters are defined for this purpose:11 — Dimensionless operating parameter: (1-50) Dimensionless jc-coordinate: (1-51) Dimensionless ^-coordinate: (1-52) Dimensionless z-coordinate: (1-53) By substituting these parameters into equation (1-45), we obtain: (1-54) where 6 and a 3 are the dimensionless temperature and radius vector, respectively (previously defined in equations (1-9) and (1-47)). Equation (1-54) has been solved numerically for chosen values of a 3 and £. A graphical presentation of the different solutions is shown in Fig. 1.19. These maps provide a good
e/n3
(a)
% Fig, /./P.Dimensionless temperature maps for point sources on heavy slabs; (a) Vertical sections parallel to the ^-axis. overall indication of the thermal conditions during thick plate welding, but are not suitable for precise readings. Consequently, for quantitative analyses, the following set of equations can be used:11 Isothermal zone widths The maximum width of an isothermal enclosure is obtained by setting 3ln(0M3)/9a3 = 0:
From the definition of a 3 we have:
(b)
%
V
%
V Fig. /.iP.Dimensionless temperature maps for point sources on heavy slabs (continued): (b) Isothermal contours in the £-\}/-plane for different ranges of 0/n3. Partial differentiation of the Rosenthal equation gives:
and (1-55) Equation (1-55) can be used for calculations of isothermal zone widths V|/w and cross sectional areas A1. From Fig. 1.20 we have: (1-56) and (1-57) A graphical presentation of equations (1-55), (1-56), and (1-57) is shown in Fig. 1.21. Length of isothermal enclosures Referring to Fig. 1.20, the total length of an isothermal enclosure £r is given by: (1-58) where £' and £"are the distance from the heat source to the front and the rear of the enclosure, respectively.
x,S Heat source
y.v
z, C
Fig. 1.20.Three-dimensional graphical representation of Rosenthal thick plate solution (schematic).
Vm,O3m,Al
1
V9P
Fig. 1.21. Dimensionless distance a3m, half width \|/m and cross sectional area A1 vs n3 /Qp. The coordinates £' and £" are found by setting a 3 = ± ^ in equation (1-54). This gives: (1-59)
and (1-60)
Volume of isothermal enclosures Since the assumption of a point heat source involves semi-circular isotherms in the \|/-£ plane, the volume of an isothermal enclosure is obtained by integration over the total length from £" tor: (1-61) The former integral is readily evaluated by substituting:
which follows from a differentiation of equation (1-54). Hence, we may write:
(1-62)
Noting that
d-65) Equation (1-65) provides a basis for calculating the cooling time within a specific temperature interval (e.g. from O1 to B2): (1-66) For welding of low alloy steel the cooling time from 800 to 5000C is widely accepted as an adequate index for the thermal conditions under which the austenite to ferrite transformation takes place. From equation (1-66), we have:
(1-67)
(1-69) Similarly, the cooling rate at a specific temperature is obtained by differentiating equation (1-65) with respect to time: (1-70) By multiplying equation (1-70) with the appropriate conversion factor, we get:
(1-71)
Example (1.6)
Consider stringer bead deposition (GMAW) on a thick plate of low alloy steel under the following conditions:
Sketch the contours of the fusion boundary and the Ac3-isotherm (9100C) in the £-\|/ (x-y) plane at pseudo-steady state. Solution
As shown in Fig. 1.22(a) it is sufficient to calculate the coordinates in four different (characteristic) positions to draw a sketch of the isothermal contours. If we neglect the latent heat of melting, the d/n3 ratio at the melting point becomes, according to equations (1-9) and (1-50):
End-points The end-points are readily obtained from equations (1-59) and (1-60):
and Maximum width The maximum width of an isothermal enclosure can generally be calculated from equations (1-55) and (1-56), or read from Fig. 1.21. Taking O^ /n3 = QIn3 = 0.088, we obtain:
V
(a)
Pos. (3) Pos. (2) Pos. (4)
Pos.(1) %
(b)
¥
\ x(mm)
y(mm)
Fig. 1.22. Calculation of isothermal contours from Rosenthal thick plate solution; (a) Calculation procedure, (b) Sketch of fusion boundary and Acj-isotherm in position £ = 0 (Example 1.6).
and
Intersection point with y/ (y)-axis In this case £ = £ = O, and cr3 = \|/. Hence, equation (1-54) reduces to:
which gives
Similarly, the contour of the Ac3-isotherm can be determined by inserting BZn3= 0.052 into the same set of equations. Figure 1.22(b) shows a graphical representation of the computed isothermal contours. Example (1.7)
Consider GTA welding on a thick plate of low alloy steel under the following conditions:
Calculate the weld pool volume, the weld bead cross section, the width of the fully transformed HAZ, the cooling time from 800 to 5000C, and the cooling rate at the onset of the austenite to ferrite transformation (e.g. at 6500C). The arc efficiency factor is taken equal to 0.5. Solution
If we neglect the latent heat of melting, the GM3 ratio at the melting point becomes:
Weld pool volume The coordinate £' may be calculated from equation (1-59):
We can now use equations (1-63) and (1-64) to calculate the weld pool volume. This gives:
and
Weld bead cross section The weld bead cross section can be read from Fig. 1.21. Taking n3 /6 p = 1/0.445 = 2.196, we obtain:
and
Width of fully transformed HAZ When Tp = 9100C, the n3 /Qp ratio becomes:
From Fig. 1.21 we have:
which gives
Cooling time from 800 to 5000C The cooling time, Af8/5, can be obtained from equation (1-68):
This value is also valid for positions outside the weld centre-line, since the cooling curves at such low temperatures are reasonably parallel down to Tp ~ 9100C (see Fig. 1.19(a)). Cooling rate at 6500C The cooling rate at a specific temperature is given by equation (1-71). Taking the transformation start temperature equal to 6500C, we get:
1. 10.2.3 Simplified solution for a fast-moving high power source Model (after Rykalin9) It follows from Fig. 1.19(b) that the isotherms behind the heat source become increasingly elongated as the arc power q0 and the welding speed v increase. In the limiting case, when qo —> oo? v —» oo and qo A) remains finite, the isotherms will degenerate into surfaces which are parallel to the welding x direction as shown in Fig. 1.23(a). Conduction of heat will then occur exclusively in directions normal to the jc-axis. In a short time interval dt, the amount of heat released per unit length of the weld is equal to:
(1-72) According to the assumptions this amount of heat will remain in a slice of thickness dx due to the lack of a temperature gradient in the welding direction. Since symmetry demands that the isotherms in the y-z plane are semi-circles*, the situation becomes identical to the temperature field around a linear instantaneous heat source in a thin plate, provided that the space above the slab is replaced by solid material and the strength of the source is doubled (see Fig. 1.23(b)). The solution is then given by equation (1-6) if we replace QId by Iq0 Iv: d-73) where r* is the two-dimensional radius vector in the y-z plane. Equation (1-73) represents the simplified solution for a fast moving high power source on a semi-infinite slab, and is valid within a limited range of the more general Rosenthal equation for three-dimensional heat flow (equation (1-45)). By introducing the dimensionless radius vector Cr4 = Dr*12a, equation (1-73) transforms to:
(1-74)
A graphical presentation of equation (1-74) gives a family of curves which resembles the thermal cycles shown in Fig. 1.19(a). Although the cooling conditions close to the weld centre-line are similar to those calculated from the Rosenthal equation, the predicted width/depth of the isotherms will always be greater than that inferred from the general thick plate solution as illustrated in Fig. 1.24 due to the assumption of 2-D heat flow. The parameter o~4m in Fig. 1.24 is obtained by differentiating equation (1-74) with respect to time:
*The isotherms must meet the plate surface at right angles in the absence of a temperature gradient across the boundary.
(a)
(b)
Symmetry plane
Fig. 1.23. Fast moving high power source on a semi-infinite slab; (a) Sketch of model, (b) Analogy between a fast moving high power source and an instantaneous line source.
4m m
Asymptote
0 /n P 3 Fig. 1.24. Theoretical width of isotherms under 2-D and 3-D heat flow conditions, respectively at pseudosteady state (thick plate welding).
which gives
Substituting this into equation (1-74) gives:
(1-75) It is interesting to note that the dimensionless width a4m will approach \j/ m when the dp /n3 ratio becomes sufficiently small (i.e. less than about 0.1). Under such conditions the isotherms will be strongly elongated in the welding direction (see Fig. 1.19(b)), which forces the heat to flow primarily in directions normal to the x-axis. A general graphical representation of the weld thermal programme can be obtained by combining equations (1-74) and (1-75):
(1-76) Equation (1-76) has been plotted in Fig. 1.25. This graph provides a basis for calculating the retention time within specific temperature intervals under various welding conditions.
e/ep
W ° J Fig. 1.25. Temperature-time pattern in thick plate welding at high arc power and high welding speed. Example (1.8)
Consider SA welding on a thick plate of low alloy steel under the following conditions:
Calculate the retention time within the austenite regime (T > 9100C) for points located lmm outside the fusion boundary. Solution
If we use the melting point of the steel as a reference temperature, the parameter n3 becomes:
A comparison with Fig. 1.24 shows that the assumption of 2-D heat flow is justified when dp < 1. Hence, the width of the fusion zone (8p = 1) can be calculated from equation (1-75):
which gives
The peak temperature lmm outside the fusion boundary is thus:
The total time spent in the thermal cycle from 0 = 0.59 (T= 9100C) to G^ = 0.78 and down again to 0 = 0.59 can now be read from Fig. 1.25. Taking the ordinate 0/0^ equal to 0.76, we obtain:
which gives
and
1.10.3 Thin plate solutions Model (after Rykalin9) As shown in Fig. 1.26, the general thin plate model considers a line source in a wide sheet of thickness d and initial temperature T0. At time t = 0 the source starts to move at a constant speed D in the positive x-direction. The rise of temperature T-T0 in point P at time t is sought. According to equation (1-6) the elementary source dQ = qo df released at position Vt' will cause a small rise of temperature dT in point P at time t:
(1-77)
where
is the time available for conduction of heat over the distance to point P.
If we refer the position P to that of the heat source at time t, we shall expect a solution independent of time at pseudo-steady state. This is achieved by changing the coordinate system from O to O' (see Fig. 1.26):
K0(U)1K1(U)
Fig. 1.26. Moving line source in a thin sheet.
U Fig. 1.27. Graphical representation of the Bessel functions Ko(u) and Kx{u).
Hence, we may write:
d-78) where
For integration of all contributions from
to
, we introduce:
from which
Substituting these parameters into equation (1-78) give:
d-79) It is well-known that:
where K0(G5) is the modified Bessel function of the second kind and zero order. A graphical representation of A^(W) is shown in Fig. 1.27. Hence, the general thin plate solution can be written as:
(1-80)
When w is sufficiently large (i.e. when welding has been performed over a sufficient period), we obtain the pseudo-steady state temperature distribution:
(1-81) Equation (1-81) is often referred to as the Rosenthal thin plate solution, in memory of its originator D. Rosenthal.1314 It follows that this model is applicable to all types of welding processes (including electron beam, plasma arc and laser welding), provided that a full throughthickness penetration is achieved in one pass. 1.10.3.1 Transient heating period In thin plate welding the duration of the transient heating period is determined by the integral in equation (1-80). Taking the ratio between the real and pseudo-steady state temperature equal to K2, we obtain:
(1-82)
where w = x/2, and dw = dill. Equation (1-82) has been solved numerically for a limited range of cr5 and x. The results are presented graphically in Fig. 1.28. Example (1.9)
Consider butt welding of a thin aluminium plate at a constant travel speed of 5mm s"1. Calculate the duration of the transient heating period when the distance from the heat source to the point of observation is 17mm. Solution
Taking a = 85 mm2 s"1, the dimensionless radius vector becomes:
It follows from Fig. 1.28 that the pseudo-steady state temperature distribution is approached when T ~ 5, which gives:
and
This minimum bead length is nearly twice as large as that calculated for 3-D heat flow for the same combination of welding speed, thermal diffusivity and radius vector (see Example
K2=(T-To)/(T-To)p.s.
t = v2t/2a Fig. 1.28. Ratio between real and pseudo-steady state temperature in thin plate welding for different combinations of a 5 and T.
(1.5)). Consequently, the duration of the transient heating period is significantly longer in thin plate welding than in thick plate welding due the pertinent differences in the heat flow conditions. 1.10.3.2 Pseudo-steady state temperature distribution A graphical presentation of the pseudo-steady state temperature distribution similar to that shown in Fig. 1.19 for three-dimensional heat flow may be obtained by introducing the dimensionless plate thickness 8 = vdlla, which is a measure of the relative speeds of the arc and the heat flow in the material. By rearranging equation (1-81), we get: (1-83) Plots of this equation are shown in Fig. 1.29. It follows that the pseudo-steady state temperature distribution in thin plate welding depends on the parameter 68//?3. In practice, this means that the shape of the isotherms is not influenced by the welding speed, since both 8 and n3 are proportional to v. Isothermal zone widths The maximum width of an isothermal enclosure is obtained by setting 3(68 /n3) /die, = 0. Noting that (d/du)Ko(u) - -Kx(u), where K1 (u) is the modified Bessel function of the second kind and first order (shown in Fig. 1.27), we get:
(1-84)
\
\
% \
V
V Fig. 1.29. Dimensionless temperature maps for line sources in thin plates for different ranges of 98/n3.
Heat source
Fig. 1.30. Graphical representation of Rosenthal thin plate solution (schematic) This gives: (1-85) and (1-86)
Equation (1-86) can be used for calculations of isothermal zone widths (v|/m) and cross sectional areas (A2) in thin plate welding. Referring to Fig. 1.30, we have:
d-87) and (1-88) Figure 1.31 shows a graphical presentation of equations (1-86), (1-87), and (1-88). Length of isothermal enclosures The distance from the heat source to the front (£') and the rear (^') of an isothermal enclosure is obtained by substituting o~5 = ± £ into equation (1-83). This gives: (1-89) and (1-90)
^5m.Vm-A 2 /8
n3/6p5
s\-?.*t
Fig. l.Ji.Dimensionless distance a5m, half width \|/m and cross sectional area A2/S vs n3/Qph.
n 3 /98 Fig. 1.32. Dimensionless distance from heat source to front (£') and rear (£") of isothermal enclosure vs «3/68 (thin plate welding).
A graphical presentation of equations (1-89) and (1-90) is shown in Fig. 1.32. Included is also a plot of the total length of the enclosure £t vs the parameter n3 /08. Cooling conditions close to weld centre-line For points located on the weld centre-line behind the heat source a 5 = -£ = X. When x is larger than about 1, (i.e. t > IaIv1), it is a fair approximation to set K0 (x)« exp(-x)Vrc/2x (see Fig. 1.27). Hence, equation (1-83) reduces to: (1-91) Equation (1-91) provides a basis for calculating the cooling time within a specific temperature interval (e.g. from O1 to 02):
(1-92)
The dimensionless cooling time from 800 to 5000C is thus given by:
(1-93) from which the real cooling time is obtained: (1-94) Taking as average values X = 0.025 W mm"1 0C"1, pc = 0.005 J mm"3 0C"1, and T0 = 200C for welding of low alloy steels, we have:
d-95) Similarly, the cooling rate at a specific temperature is obtained by differentiating equation (1-91) with respect to time: (1-96)
By multiplying equation (1-96) with the appropriate conversion factor, we get:
(1-97)
For welding of low alloy steels, the cooling rate becomes:
(1-98)
Example (LlO)
Consider GTA butt welding of a 2mm thick sheet of cold-rolled aluminium (Al-Mg alloy) under the following conditions:
Sketch the contours of the fusion boundary and the Ar-isotherm in the £-\|/ (x-y) plane at pseudo-steady state. The recrystallisation temperature Ar of the base material is taken equal to 2750 C. Calculate also the cross sectional area of the fully recrystallised HAZ and the cooling rate at 2750C for points located within this region. Solution Referring to Fig. 1.22(a) (Example (1.6)) it is sufficient to calculate the coordinates in four different (characteristic) positions to sketch the contour of the fusion boundary. If we neglect the latent heat of melting, the n3/68 ratio at the melting point becomes:
End-points The end-points can be read from Fig. 1.32:
and
Maximum widths The maximum width of an isothermal enclosure can generally be calculated from equations (1-86) and (1-87) or read from Fig. 1.31. When n3/QpS = 0.84, we obtain:
and
Intersection point with y/(y)-axis In this case £ = 0 and cr5 = \j/. Hence, equation (1-83) reduces to:
which gives
Similarly, the contour of the Ar-isotherm can be determined by inserting n3/db = 2.08 into the same set of equations. Figure 1.33 shows a graphical representation of the calculated isothermal contours.
V
§ x(mm)
y(mm) Fig. 1.33. Calculated contours of fusion boundary and Ar-isotherm in GTA butt welding of a 2mm thick aluminium plate (Example 1.10).
Cross sectional area of fully recrystallised HAZ In general, cross sectional areas can be read from Fig. 1.31. Taking the n3/OpS ratio equal to 0.84 (Qp= 1) and 2.08 (8 p = 0.48), respectively, we have:
which gives
Cooling rate at 275 0C The cooling rate at a specific temperature can be calculated from equation (1-97). In the present case, we obtain:
1.10.3.3 Simplified solution for a fast moving high power source Model (after Rykalin9) It follows from Fig. 1.29 that the isotherms behind the heat source become increasingly elongated as the 08M3 ratio decreases. In the limiting case the isotherms will degenerate into surfaces which are parallel to the welding x direction, as shown in Fig. 1.34. In a short time interval dt the amount of heat released per unit length of the weld is equal to:
(1-99) According to the assumptions this amount of heat will remain in a rod of constant cross sectional area due to the lack of a temperature gradient in the welding direction. Under such conditions the mode of heat flow becomes essentially one-dimensional, and the temperature distribution is given by equation (1-5): (1-100) Equation (1-100) represents the simplified solution for a fast moving high power source* in a thin sheet, and is valid within a limited range of the more general Rosenthal equation for twodimensional heat flow (equation (1-81)). By substituting the appropriate dimensionless parameters into equation (1-100), we obtain:
* Since the shape of a given isotherm in the x-y plane is determined by the qjd ratio, the minimum welding speed which is required to maintain 1-D heat flow increases with decreasing qjVd ratios. Hence, the term 'fast moving high power source' is also appropriate in the case of the thin plate welding.
Fig. 1.34. Fast moving high power source in a thin plate.
(1-101) The locus of the peak temperatures is readily evaluated from equation (1-101) by setting 3ln(e8M3)/3T = 0:
which gives
and (1-102) It is evident from the plot in Fig. 1.35 that the predicted width of the isotherms is always greater than that inferred from the general thin plate solution (equation (1-83)) due to the assumption of one-dimensional heat flow. However, such deviations become negligible at very small Qpb/n3 ratios because of a small temperature gradient in the welding x direction compared to the transverse y direction of the plate. A general graphical representation of the weld thermal programme (similar to that shown in Fig. 1.25 for a fast moving high power source on a heavy slab) can be obtained by combining equations (1-101) and (1-102):
¥m(1-D)/¥m(a-D)
Asymptote
0 p 8/n 3
e/ep
Fig. 1.35. Theoretical width of isotherms under 1-D and 2-D heat flow conditions, respectively at pseudosteady state (thin plate welding).
2t/(vm)2 Fig. 1.36. Temperature-time pattern in thin plate welding at high arc power and high welding speed.
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(1-103) Equation (1-103) has been plotted in Fig. 1.36. Example (LU) Consider butt welding of a 2mm thin plate of austenitic stainless steel with covered electrodes (SMAW) under the following conditions:
Calculate the retention time within the critical temperature range for chromium carbide precipitation (i.e. from 650 to 8500C) for points located at the 8500C isotherm. Solution
If we use the melting point of the steel as a reference temperature, the parameter n3/5 becomes:
A comparison with Fig. 1.35 shows that the assumption of 1-D heat flow is justified when Qp< 1. Hence, the total time spent in the thermal cycle from 6 = 0.43 (T = 6500C) to 0p = 0.56 (Tp = 8500C) and down again to 0 = 0.43 can be read from Fig. 1.36. Taking the ordinate 0/0p equal to 0.76, we obtain:
which gives
and
1.10.4 Medium thick plate solution In a real welding situation the assumption of three-dimensional or two-dimensional heat flow inherent in the Rosenthal equations is not always met because of variable temperature gradients in the through thickness z direction of the plate. Model (after Rosenthal14)
The general medium thick plate model considers a point heat source moving at constant speed across a wide plate of finite thickness d. With the exception of certain special cases (e.g. watercooling of the back side of the plate), it is a reasonable approximation to assume that the
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(1-103) Equation (1-103) has been plotted in Fig. 1.36. Example (LU) Consider butt welding of a 2mm thin plate of austenitic stainless steel with covered electrodes (SMAW) under the following conditions:
Calculate the retention time within the critical temperature range for chromium carbide precipitation (i.e. from 650 to 8500C) for points located at the 8500C isotherm. Solution
If we use the melting point of the steel as a reference temperature, the parameter n3/5 becomes:
A comparison with Fig. 1.35 shows that the assumption of 1-D heat flow is justified when Qp< 1. Hence, the total time spent in the thermal cycle from 6 = 0.43 (T = 6500C) to 0p = 0.56 (Tp = 8500C) and down again to 0 = 0.43 can be read from Fig. 1.36. Taking the ordinate 0/0p equal to 0.76, we obtain:
which gives
and
1.10.4 Medium thick plate solution In a real welding situation the assumption of three-dimensional or two-dimensional heat flow inherent in the Rosenthal equations is not always met because of variable temperature gradients in the through thickness z direction of the plate. Model (after Rosenthal14)
The general medium thick plate model considers a point heat source moving at constant speed across a wide plate of finite thickness d. With the exception of certain special cases (e.g. watercooling of the back side of the plate), it is a reasonable approximation to assume that the
plate surfaces are impermeable to heat. Thus, in order to maintain the net flux of heat through both boundaries equal to zero, it is necessary to account for mirror reflections of the source with respect to the planes of z = 0 and z = d. This can be done on the basis of the 'method of images' as illustrated in Fig. 1.37. By including all contributions from the imaginary sources ...2q__2 , 2g_i , 2q\ , 2q2 ,...located symmetrically at distances ± 2id below and above the upper surface of the plate, the pseudo-steady state temperature distribution is obtained in the form of a convergent series*:
(1-104)
where Note that equation (1-104) is simply the general Rosenthal thick plate solution (equation (1-45)) summed for each source.
Fig. 1.37. Real and imaginary point sources on a medium thick plate. *The number of imaginary heat sources necessary to achieve the required accuracy depends on the chosen values of R0 and vd/2a.
By substituting the dimensionless parameters defined above into equation (1-104), we obtain: (1-105) where
It follows from equation (1-104) that the thermal conditions will be similar to those in a thick plate close to the centre of the weld. Moreover, Rosenthal1314has shown on the basis of a Fourier series expansion that equation (1-104) converges to the general thin plate solution (equation (1-81) for points located sufficiently far away from the source. However, at intermediate distances from the heat source, the pseudo-steady state temperature distribution will deviate significantly from that observed in thick plate or thin plate welding because of variable temperature gradients in the through-thickness direction of the plate. Within this 'transition region', the thermal programme is only defined by the medium thick plate solution (equation (1-104)). 1.10.4.1 Dimensionless maps for heat flow analyses Based on the models described in the previous sections, it is possible to construct a series of dimensionless maps which provide a general outline of the pseudo-steady state temperature distribution during arc welding.20 Construction of the maps The construction of the maps is done on the basis of the medium thick plate solution (equation (1-105)). This model is generally applicable and allows for the plate thickness effect in a quantitative manner. Since the other solutions are only valid within specific ranges of this equation, they will have their own characteristic fields in the temperature-distance or the temperature-time space. The extension of the different fields can be determined from numerical calculations of the temperature distribution by comparing each of these models with the medium thick plate solution, using a conformity of 95% as a criterion. Similarly, when the 95% conformity is not met between the respective solutions, the fields are marked 'transition region'. Since any combination of dimensionless temperature, operating parameter, and plate thickness locates a point in a field, it means that the dominating heat flow mechanism can readily be read off from the maps. Peak temperature distribution The variation of peak temperature with distance in the \j/(^j-direction has been numerically evaluated from equation (1-105) for different values of the dimensionless plate thickness (8 = vdlla). The results are shown graphically in Fig. 1.38(a) and (b) for the two extreme cases of £ = 0 (z = 0) and £ = 8 (z = d), respectively. An inspection of the maps reveals that the temperature-time pattern in stringer bead weldments can be classified into three main categories:
(a)
VV
Thin plate solution (2-D heat flow) (1-D heat flow)
¥
%
Y
m
(b) Thin plate solution 1-D heat flow
V"3
(2-D heat flow)
Y
m
Fig. 1.38. Peak temperature distribution in transverse direction (\|/ = \\fm) of plate; (a) Upper plate surface (^ = 0), (b) Lower plate surface (J = 8).
1. Close to the heat source, the thermal programme will be similar to that in a thick plate (Fig. 1.38(a)), which means that the temperature distribution is determined by equation (154). For large values of the dimensionless plate thickness, the mode of heat flow may become essentially two-dimensional. This corresponds to the limiting case of a fast moving high power source in a thick plate (equation (1-74)). Under such conditions the slope of the Qp/n3-\ym curves in Fig. 1.38(a) attains a constant value of-2. 2. With increasing distance from the heat source, a transition from three-dimensional to two-dimensional heat flow may occur, depending on the dimensionless plate thickness and the operational conditions applied. Considering the upper surface of the plate (Fig. 1.38(a)), the extension of the transition region is seen to decrease with increasing values of 8 as the conditions for thick plate welding are approached. The opposite trend is observed for the bottom plate surface (Fig. 1.38(b)), since a small dimensionless plate thickness generally results in a more rapid equalisation of the temperature gradients in the t,(z) direction. When the curves in Fig. 1.38(b) become parallel with the jc-axis, the temperature at the bottom of the plate reaches its maximum value. Note that within the transition region, reliable predictions of the pseudo-steady temperature distribution can only be made from the medium thick plate solution (equation (1-105)). 3. For points located sufficiently far away from the heat source, the temperature gradients in the through-thickness direction of the plate become negligible. This implies that the temperature distribution at the upper and lower surface of the plate is similar, and can be computed from the thin plate solution (equation (1-83)). When the conditions for onedimensional heat flow are approached (equation (1-101)), the slope of the dp/n3-\\fm curves in Fig. 1.38(a) and (b) attains a constant value o f - 1 . Cooling conditions close to weld centre-line Figure 1.39 contains a plot of the cooling programme for points located on the weld centre-line (\j/ = £ = 0), as calculated from equation (1-105). A closer inspection of Fig. 1.39 reveals that the slope of the cooling curves increases gradually from -1 to -0.5 with increasing distance from the heat source. This corresponds to a change from three-dimensional to one-dimensional heat flow. From Fig. 1.39 it is possible to read-off the cooling time within specific temperature intervals for a wide range of operational conditions. These results are also valid for positions outside the weld centre-line, since the cooling curves are virtually parallel in the transverse \|/ direction of the plate. A requirement is, however, that the peak temperature of the thermal cycle is significantly higher than the actual temperature interval under consideration. Retention times at elevated temperatures The retention time, Axn is defined as the total time spent in a thermal cycle from a chosen reference temperature 0 to the peak temperature dp and down again to 9. This parameter can readily be computed from equation (1-105) by means of numerical methods. The results of such calculations (carried out in position £ = 0) are shown graphically in Fig. 1.40 for 9 = 0.5 An inspection of Fig. 1.40 reveals a complex temperature-time pattern. In this case it is not possible to determine the exact field boundaries between the respective solutions, since the
e/n3
e/n3
Thin plate solution (2-D heat flow) (1-D heat flow)
T= ^
e/n 3
X Fig. 1.39. Cooling programme for points located on the weld centre-line (\\f = £ =0).
6
T
AXf
Fig. 1.40. Total time spent in a thermal cycle from 9 through 9p to 9 for a chosen reference temperature of 9 = 0.59p.
mode of heat flow may vary within a single thermal cycle. Hence, the extension of the different fields is not indicated in the graph. The results in Fig. 1.40 provide a systematic basis for calculating the retention time within specific temperature intervals under various welding conditions. Isothermal contours Because of the number of variables involved, it is not possible to present a two-dimensional plot of the isotherms without first specifying the dimensionless plate thickness. Examples of calculated isotherms in different planes are shown in Figs. 1.41 and 1.42 for 8 equal to 0.5 and 5, respectively. It is evident that an increase in the dimensionless plate thickness from 0.5 to 5 has a dramatic effect on the shape and position of the isothermal contours. However, in order to explain these observations in an adequate manner, it is necessary to condense the results into a two-dimensional diagram. As shown in Fig. 1.43, this can be done by plotting the calculated field boundaries in Fig. 1.38(a) at maximum width of the isotherms vs the parameters Qp/n3
and vdlla. It is seen from Fig. 1.43 that a large plate thickness generally will favour three-dimensional heat flow. With decreasing values of Qp/n3, the conditions for a fast moving high power source are approached before the transition from the thick plate to the thin plate solution occurs. In such cases the isotherms at the bottom of the plate will be strongly elongated in the welding £ direction and shifted to positions far behind the heat source. The opposite trend is observed at small values of vdlla, since a rapid equalisation of the temperature gradients in the throughthickness direction of the plate will result in elliptical isotherms at both plate surfaces, located in an approximately equal distance from the heat source. In either case the temperature at which the cross-sectional isotherms approach a semi-circle or become parallel with the XXz)axis can be obtained from Fig. 1.43 by reading-off the intercept between the line for the dimensionless plate thickness and the respective field boundaries. Limitations of the maps Since the maps have been constructed on the basis of the analytical heat flow equations, it is obvious that they will apply only under conditions for which these equations are valid. The simplifying assumptions inherent in the models can be summarised as follows: (a)
The parent material is isotropic and homogeneous at all temperatures, and no phase changes occur on heating.
(b)
The thermal conductivity, density, and specific heat are constant and independent of temperature.
(c)
The plate is completely insulated from its surroundings, i.e. there are no heat losses by convection or radiation from the boundaries.
(d)
The plate is infinite except in the directions specifically noted.
(e)
The electrode is not consumed during welding, and all heat is concentrated in a zero-volume point or line.
(a)
¥
C
(b)
%
C
(C)
V
C Fig. 1.41. Computed isothermal contours in different sections for 8 = 0.5; (a) Front view (\j/ = \|/m), (b) Side view (\|/ = 0), (c) Top view (£ = 0) and bottom view (£ = 8).
(a)
¥
C
(b)
%
C
(C)
v
V
\Fig. 1.42.Computed isothermal contours in different sections for 8 = 5; (a) Front view (\|/ = \|/m); (b) Side view (\|/ = 0); (c) Top view (£ = 0) and bottom view (£ = 8).
ep/n3
Thick plate solution (3-D heat flow)
Thin plate solution
1-D heat flow Thick plate solution (2-D heat flow)
5 = vd/2a Fig. 1.43. Heat flow mechanism map showing calculated field boundaries in transverse direction (i|/ = i|/m) of plate vs Qp/n3 and 8 = vdlla.
(f)
Pseudo-steady state, i.e. the temperature does not vary with time when observed from a point located in the heat source.
In general, the justification of these assumptions relies on a good correlation between theory and experiments. However, since the analytical solutions ignore the important role of arc energy distribution and directed metal currents in the weld pool, predictions of the weld thermal programme should be restricted to positions well outside the fusion zone where such effects are of less importance (to be discussed below). Example (1.12)
Consider stringer bead welding (GMAW) on a 12mm thick plate of aluminium (> 99% Al) under the following conditions:
Based on Fig. 1.43, sketch the peak temperature contours in the transverse section of the weld at pseudo-steady state.
Solution If we neglect the latent heat of melting, the parameter n3 at the chosen reference temperature (Tc = Tm) becomes:
Similarly, when v = 3mm s l and a = 85mm2 s"1 we obtain the following value for the dimensionless plate thickness:
Readings from Fig. 1.43 give: ep
^, (0C)
Model System
Comments
0.50 —• 1.0
340 —• 660
Medium thick plate solution
Heat flow in x and y directions, partial heat flow in z direction
0.17 -> 0.50
130 -> 340
Thin plate solution (2-D heat flow)
Heat flow in x and y directions, negligible heat flow in z direction
< 0.17
< 130
Thin plate solution (1 -D heat flow)
Heat flow in y direction, negligible heat flow in x and z directions
A sketch of the HAZ peak temperature contours in the transverse section of the weld is shown in Fig. 1.44. Case Study (Ll) Consider stringer bead GMA welding on 12.5mm thick plates of low alloy steel and aluminium (i.e. a Al-Mg-Si alloy), respectively under the conditions E = 1.5 kJ mm"1 and r\ = 0.8. Details of welding parameters for the four series involved are given in Table 1.4. Computed peak temperature contours in the transverse section of the welds are given in Figs. 1.45 and 1.46.
Arrows indicate heat flow directions
Fusion zone
Fig. 1.44. Schematic diagram showing specific peak temperature contours within the HAZ of an aluminium weld at pseudo-steady state (Example 1.12).
WELD A1 y(mm)
(b)
WELD A2
z(mm)
(a)
z(mm)
y(mm)
Fig. 1.45. Computed peak temperature contours in aluminium welding at pseudo-steady state (Case study 1.1); (a) Weld Al, (b) Weld A2. Black regions indicate fusion zone.
Aluminium welding In general, the maximum width of the isotherms at the upper and lower surface of the plate can be obtained from Fig. 1.38(a) and (b), although these maps are not suitable for precise readings. A comparison with the computed peak temperature contours in Fig. 1.45(a) and (b) reveals a strong influence of the welding speed on the shape and position of the cross-sectional isotherms at a constant gross heat input of 1.5 kJ mm"1. It is evident that the extension of the fusion zone and the neighbouring isotherms becomes considerably larger when the welding speed is increased from 2.5 to 5 mm s"1. This effect can be attributed to an associated shift from elliptical to more elongated isotherms at the plate surfaces (e.g. see Fig. 1.43), which reduces heat conduction in the welding direction. It follows from Fig. 1.43 that the upper left corner of the map represents the typical operating region for aluminium welding. Because of the pertinent differences in the heat flow conditions, the temperature-time pattern will also vary significantly between the respective series as indicated by the maps in Figs. 1.39 and 1.40. Hence, in the case of aluminium welding the usual procedure of reporting arc power and travel speed in terms of an equivalent heat input per unit length of the bead is highly questionable, since this parameter does not define the weld thermal programme. In general, the correct course would be to specify both qo, v and d, and compare the weld thermal history on the basis of the dimensionless parameters n3 and 8. Steel welding If welding is performed on a steel plate of similar thickness, the operating region will be shifted to the lower right corner of Fig. 1.43. Under such conditions, the isotherms adjacent to the fusion boundary will be strongly elongated in the x-direction even at very low welding speeds (see Fig. 1.42). This implies that the thermal programme approaches a state where the temperature distribution is uniquely defined by the net heat input r\E, corresponding to the
(a)
W E L D S1
z(mm)
y(mm)
(b)
WELD S2
z(mm)
y(mm)
Fig. 7.46.Computed peak temperature contours in steel welding at pseudo-steady state (Case study 1.1); (a) Weld Sl, (b) Weld S2. Black regions indicate fusion zone.
Table 1.4 Operational conditions assumed in Case study (1.1). qo
V
d
E
Series
(W)
(mras"1)
(mm)
(kJmrrr 1 )
Al-Mg-Si alloy
Al A2
6000 3000
5 2.5
12.5 12.5
Low alloy steel
Sl S2
9600 4800
8 4
12.5 12.5
Material
n3
8
1.5 1.5
0.36 0.09
0.50 0.25
1.5 1.5
32.6 8.2
10 5
limiting case of a fast moving high power source. As a result, the calculated shape and width of the fusion boundary and neighbouring isotherms are seen to be virtually independent of choice of qo and v as illustrated in Fig. 1.46(a) and (b). 1.10.4.2 Experimental verification of the medium thick plate solution It is clear from the above discussion that the medium thick plate solution provides a systematic basis for calculating the temperature distribution within the HAZ of stringer bead weldments under various welding conditions. In the following, the accuracy of the model will be checked against extensive experimental data, as obtained from in situ thermocouple measurements and numerical analyses of a large number of bead-on-plate welds. Weld thermal cycles Examples of measured and predicted weld thermal cycles in aluminium welding are presented in Fig. 1.47. It is evident that the medium thick plate solution predicts adequately the HAZ temperature-time pattern under different heat flow conditions for fixed values of the peak temperature. This, in turn, implies that the model is also capable of predicting the total time spent in a thermal cycle within a specific temperature interval as shown in Fig. 1.48. Weld cooling programme At temperatures representative of the austenite to ferrite transformation in mild and low alloy steel weldments, the conditions for a fast moving high power source are normally approached before the transition from thick plate to thin plate welding occurs (see Fig. 1.39). In such cases, it is possible to present the different solutions for Ax875 (at \|/ = £ = 0) in a single graph by introducing the following groups of variables*:
Ordinate:
Abscissa: Relevant literature data for the cooling time between 800 and 5000C are given in Fig. 1.49. A closer inspection of the figure reveals a reasonable agreement between observed and predicted values in all cases. For welding of thick plates, the ordinate attains a constant value of 1. Similarly, in thin sheet welding, the slope of the curve becomes equal to 1. In aluminium welding, the thermal conditions will be much more complex because of the resulting higher base plate thermal diffusivity (see Fig. 1.39). Hence, it is not possible to describe the weld cooling programme in terms of equations (1-74) and (1-101), which apply to fast moving high power sources. The plot in Fig. 1.50 confirms, however, that the medium thick plate solution is also capable of predicting the cooling time within specific temperature intervals (e.g. from 300 to 1000C) in aluminium weldments.
These groups of variables can be obtained from equations (1-74) and (1-101).
Measured Predicted
Temperature (0C)
GMAW: q 0 = 3872 W, v = 8.8 mm/s, d =8 mm
Time (sec)
A tr(s), observed
Fig. 1.47. Comparison between measured and predicted weld thermal cycles in aluminium welding for fixed values of Tp. Data from Myhr and Grong.20
T
P t
A tr(s), predicted Fig. /.4#. Comparison between measured and predicted retention times in aluminium welding for fixed values of Tp. Data from Myhr and Grong.20
8/5 AT
n 3 [-i--4-
1
SMAW SMAW SAW SAW THICK PLATE SOLUTION
THIN PLATE SOLUTION
-2Hr + Ir 1 5 6SOO 6SOO Fig. 1.49. Comparison between observed and predicted cooling times from 800 to 5000C in steel welding (solid lines represent theoretical calculations). Data from Myhr and Grong.20
At
(sec), observed
GMAW (Al+2.5 wt% Mg)
T(0C)
t(sec)
At
(sec), predicted
Fig. 1.50. Comparison between observed and predicted cooling times from 300 to 1000C in aluminium welding. Data from Myhr and Grong.20
Peak temperatures and isothermal contours Figure 1.51 shows a comparison between measured and predicted HAZ peak temperatures in aluminium welding. It is evident that the relative positions of the HAZ isotherms can be calculated with a reasonable degree of accuracy from the medium thick plate solution, provided that the equation is precalibrated against a known isotherm (i.e. the fusion boundary). Additional information on the HAZ peak temperature distribution in aluminium welding can be obtained from the data of Koe and Lee21 reproduced in Fig. 1.52. These numerical calculations* showed a good correlation with experimental measurements. A comparison with the medium thick plate solution in Fig. 1.52 reveals a fair agreement between numerically and analytically computed isothermal contours. It is interesting to note that even though the plate thickness is small (i.e. 3.2mm), the mode of heat flow becomes essentially three-dimensional close to the fusion boundary. This important point is often overlooked when discussing the relevance of the analytical heat flow models in thin sheet welding. LlOAJ Practical implications The following important conclusions can be drawn from the results presented in Figs. 1.381.52:
Tp, 0C , observed
GMAW (Al +2.5 wt% Mg)
Tp, 0C , predicted Fig. 1.51. Comparison between observed and predicted HAZ peak temperatures in aluminium welding. Data from Myhr and Grong.20 Based on the finite difference method (FDM).
Z (mm)
y (mm)
Fig. 1.52. Comparison between numerically and analytically computed peak temperature contours in GTA welding of a 3.2mm thin aluminium sheet. (Broken lines: numerical model; solid lines: analytical model.) Data for welding parameters and material properties are given in Ref. 21.
1. Considering heat flow and temperature distribution in fusion welding, there exists no defined plate thickness which can be regarded as 'thick' or 'thin'. Accordingly, in a real welding situation, the mode of heat flow will vary continuously with increasing distance from the heat source. 2. Close to the centre of the weld, the thermal conditions will be similar to those in a heavy slab. This means that the temperature distribution is approximately described by the Rosenthal thick plate solution. 3. At intermediate distances from the heat source, the temperature distribution will deviate significantly from that observed in thick plate welding because of variable temperature gradients in the through-thickness direction of the plate. Within this transition region, reliable predictions of the pseudo-steady state temperature distribution can only be made from the medium thick plate solution. 4. For points located sufficiently far away from the heat source, the temperature gradients in the through-thickness direction of the plate become negligible. Under such conditions, the weld thermal programme is approximately defined by the Rosenthal thin plate solution. 5. In general, a full description of the weld thermal history requires that both the arc power qo, the travel speed V, and the plate thickness d are explicitly specified. Hence, the usual procedure of reporting welding variables in terms of an equivalent heat input per unit length of the bead, £(kJ mm"1), is highly questionable, since this parameter does not define the weld thermal programme. An exception is welding of thick steel plates, where the temperature distribution approaches that of a fast moving high power source because of a low thermal diffusivity of the base metal. 6. A comparison between theory and experiments shows that the medium thick plate solution predicts adequately both the peak temperature distribution and the temperaturetime pattern within the HAZ of stringer bead weldments for a wide range of operational conditions (including aluminium and steel welding). A requirement is, however, that the equation is calibrated against a known isotherm (e.g. the fusion boundary) due to the simplifying assumptions inherent in the model.
1.10.5 Distributed heat sources In some cases it is also necessary to consider the important influence of filler metal additions, arc energy distribution, and convectional heat flow in the weld pool on the resulting bead morphology to obtain a good agreement between theory and experiments. Of particular interest in this respect is the formation of the so-called weld crater/weld finger, frequently observed in GMA and SA stringer bead weldments (see Fig. 1.53). Although the nature of these phenomena is very complex, they can readily be accounted for by applying an empirical correction for the effective heat distribution in the weld pool. 1.10.5.1 General solution Model (after Myhr and Grong22) The heat distribution used to simulate the weld crater/weld finger formation is shown schematically in Fig. 1.54(a). Here we consider two discreate distributions of elementary point sources, which extend in the y- and z-direction of the plate, respectively. The contribution from each source to the temperature rise in an arbitrary point P located within the plate is calculated on the basis of the "method of images", as shown in Fig. 1.54(b) and (c). For a heat source displaced in the y-direction (Fig. 1.54(b)), the temperature field is given by equation (1 104):
(1-106) where
y Crater
HAZ"
Finger Fusion line
Z Fig. 1.53. Schematic diagram showing the weld crater/weld finger formation during stringer bead welding.
(a)
y
X
Z
(b)
y
Z Fig. 1.54. General heat flow model for welding on medium thick plates; (a) Physical representation of the heat distribution by elementary point sources, (b) Method for calculating the temperature field around an elementary point source displaced along the y-axis.
(C)
y
Z Fig. 1.54. General heat flow model for welding on medium thick plates(continued): (c) Method for calculating the temperature field around an elementary (submerged) point source displaced along the z-axis. Similarly, for a submerged point source located along the z-axis (Fig. 1.54(c))> we obtain:
(1-107)
where and
Note that equation (1-107) correctly reduces to equation (1-106) when A approaches zero. The total temperature rise in point P is then obtained by superposition of the temperature fields from the different elementary heat sources, i.e.: (1-108) where
In practice, we can subdivide the heat distributions into a relatively small number of elementary point sources, and usually a total number of 8 to 10 sources is sufficient to obtain good results (i.e. smooth curves). However, the relative strength of each heat source and their distribution along the y- and z-axes must be determined individually by trial and error by comparing the calculated shape of the fusion boundary with the real (measured) one. Figure 1.55 shows the results from such calculations, carried out for a single pass (bead-ingroove) GMA steel weld. It is evident that the important effect of the weld crater/weld finger formation on the HAZ peak temperature distribution is adequately accounted for by the present model. A weakness of the model is, of course, that the shape and location of the fusion boundary must be determined experimentally before a prediction can be made. 1.10.5.2 Simplified solution Similar to the situation described above, the point heat source will clearly not be a good model when the heat is supplied over a large area. Welding with a weaving technique and surfacing with strip electrodes are prime examples of this kind. Model (after Grong and Christensen19)
As a first simplification, the Rosenthal thick plate solution is considered for the limiting case of a high arc power qo and a high welding speed D, maintaining the ratio qo Iv within a range applicable to arc welding. Consider next a distributed heat source of net power density qo I2L extending from -L to +L on either side of the weld centre-line in the y-direction*, as shown schematically in Fig. 1.56. It follows from equation (1-73) that an infinitesimal source dqy located between y and y + dy will cause a small rise of temperature in point P at time f, as: (1-109) where
and
Alternatively, we can use a Gaussian heat distribution, as shown in Appendix 1.4.
z (mm)
Shaded region indicates fusion zone
y (mm) Fig. 1.55. Calculated peak temperature contours in the transverse section of a GMA steel weldment (Operational conditions: / = 450A, U - 30V, v = 2.6mm s"1, d = 50mm).
2-D heat flow
Fig. 1.56. Distributed heat source of net power density qJ2L on a semi-infinite body (2-D heat flow).
(1-110)
where erf(u) is the Gaussian error function (previously defined in Appendix 1.3). Peak temperature distribution Because of the complex nature of equation (1-110), the variation of peak temperature with distance in the y-z plane can only be obtained by numerical or graphical methods. Accordingly, it is convenient to present the different solutions in a dimensionless form. The following parameters are defined for this purpose: — Dimensionless operating parameter:
(1-111)
Dimensionless time: (1-112) Dimensionless y-coordinate: (1-113) Dimensionless z-coordinate: (1-114) By substituting these parameters into equation (1-110), we obtain:
(1-115)
where 0 is the dimensionless temperature (previously defined in equation (1-9)).
The variation of peak temperature Qp with distance in the y-z plane has been numerically evaluated from equation (1-115) for chosen values of P and 7 (i.e. P = 0, (3 = 3/4, P = I , and 7 = 0). The results are presented graphically in Figs. 1.57 and 1.58 for the through thickness (z = zm) and the transverse (y = ym) directions, respectively. These figures provide a systematic basis for calculating the shape of the weld pool and neighbouring isotherms under various welding conditions. In Fig. 1.59 the weld width to depth ratio has been computed and plotted for different combinations of nw and 9p. It is evident that the predicted width of the isotherms generally is much greater, and the depth correspondingly smaller than that inferred from the point source model. Such deviations tend to become less pronounced with decreasing peak temperatures (i.e. increasing distance from the heat source). At very large value of nw, the theoretical shape of the isotherms approaches that of a semi-circle, which is characteristic of a point heat source. Example (1.13)
Consider GMA welding with a weaving technique on a thick plate of low alloy steel under the following conditions:
Sketch the contours of the fusion boundary and the Ac r isotherm (71O0C) in the y-z plane. Compare the shape of these isotherms with that obtained from the point heat source model. Solution If we neglect the latent heat of melting, the operating parameter at the chosen reference temperature (Tc = Tm) becomes:
Fusion boundary Here we have:
Readings from Figs. 1.57 and 1.58 give:
Ac j-temperature In this case the peak temperature should be referred to 7200C, i.e.:
ep/nw
V -
ep/nw
Fig. /.57. Calculated peak temperature distribution in the through-thickness direction of the plate at different positions along the weld surface.
y m /L Fig. 1.58. Calculated peak temperature distribution in the transverse direction of the plate at position y (Z) = 0.
y m /z m
nw Fig. 1.59. Effects of nw and dp on the weld width to depth ratio.
from which
Readings from Figs. 1.57 and 1.58 give:
Similarly, equation (1-75) provides a basis for calculating the width of the isotherms in the limiting case where all heat is concentrated in a zero-volume point. By rearranging this equation, we obtain:
which gives 6.3 mm when Bp = 1(Tp = 15200C)
and when Figure 1.60 shows a graphical presentation of the calculated peak temperature contours. Implications of model
It is evident from Fig. 1.60 that the predicted shape of the isotherms, as evaluated from equation (1-110), departs quite strongly from the semi-circular contours required by a point heat source. Moreover, a closer inspection of the figure shows that inclusion of the heat distribution also gives rise to systematic variations in the weld thermal programme along a specific isotherm, as evidenced by the steeper temperature gradient in the v-direction compared with the z-direction of the plate. This point is more clearly illustrated in Fig. 1.61, which compares the HAZ temperature-time programme for the two extreme cases of z = 0 and y = 0, respectively. It is obvious from Fig. 1.61 that the retention time within the austenite regime is considerably longer in the latter case, although the cooling time from 800 to 5000C, Af8/5, is reasonably similar. These results clearly underline the important difference between a point heat source and a distributed heat source as far as the weld thermal programme is concerned. Model limitations
In the present model, we have used the simplified solution for a fast moving high power source (equation 1-73)) as a starting point for predicting the temperature-time pattern. Since the equations derived later are obtained by integrating equation (1-73), they will, of course, apply only under conditions for which this solution is valid. Moreover, a salient assumption in the model is that the heat distribution during weaving can be represented by a linear heat source orientated perpendicular to the welding direction. Although this is a rather crude approximation, experience shows that the assumed heat dis-
z, mm Fig. /.60. Predicted shape of fusion boundary and Acpisotherm during GMA welding of steel with an oscillating electrode (Example 1.13). Solid lines: Distributed heat source; Broken lines: Point heat source.
Temperature, 0C
Time, s Fig. L61. Calculated HAZ thermal cycles in positions y = 0 and z = 0 (Example 1.13). tribution is not critical unless the rate of weaving is kept close to the travel speed. However, for most practical applications weaving at such low rates would be undesirable owing to an unfavourable bead morphology. Case Study (1.2)
Surfacing with strip electrodes makes a good case for application of equation (1-110). Specifically, we shall consider SA welding of low alloy steel with 60mm X 0.5mm stainless steel electrodes. The operational conditions employed are listed in Table 1.5. It is evident from the metallographic data presented in Fig. 1.62 that neither the bead penetration nor the HAZ depth (referred to the plate surface) can be predicted readily on the basis of the present heat flow model when welding is carried out with a consumable electrode, owing to the formation of a reinforcement. This situation arises from the simplifications made in deriving equation (1-110). The problem, however, may be eliminated by calculating the depth of the Ac3 and Ac1 regions relative to the fusion boundary, i.e. Azm = zm(Qp) - zm (Qp = 1), or Aym = ym (8p) - ym (6p = 1), for specific positions along the weld fusion line, as shown by the solid curves in Fig. 1.62 for Qp = 0.54 and 0.45, respectively. An inspection of the graphs reveals satisfactory agreement between theory and experiments in all three cases, which implies that the model is quite adequate for predicting the HAZ thermal programme as far as strip electrode welding is concerned. This result is to be expected, since the assumption of twodimensional heat flow is a realistic one under the prevailing circumstances. Case Study (1.3)
As a second example we shall consider GTA welding (without filler wire additions) at various heat inputs and amplitudes of weaving within the range from 1 to 2.5 kJ mm"1 and 0 to 15mm, respectively. Data for welding parameters are given in Table 1.6.
Stainless steel! y, mm
Weld S3
Fusion line
z, mm
Stainless steel y, mm
Weld S4
z, mm Stainless steel! y, mm Weld S5
z, mm Fig. 1.62. Comparison between observed and predicted Ac3 and Ac1 contours during strip electrode welding (Case study 1.2). Data from Grong and Christensen.19 Table 1.5 Operational conditions used in strip electrode welding experiments (Case study 1.2). Base metal/ filler metal combination
Weld No.
S3 Low alloy steel/ stainless steel
/ (A)
730
S4
73
S5
730
°
U (V)
27 27
27
v (mms"1)
2L (mm)
nw Cn = 0.7)
1.8
60
0.34
2 2
-
2.5
60 60
0.28 0.24
Table 1,6 Operational conditions used in GTA welding experiments (Case study 1.3). I
U
v
2L 1
nw "V=O-
12
WeIdNo.
(A)
(V)
(mms" )
(mm)
T] = 0.23
Bl
200
13.5
2.6
9.5
0.20
0.40
B2
200
14.0
1.1
15.0
0.20
0.40
B3
200
13.5
2.5
-
B4
200
12.5
1.0
Calibration procedure In general, a comparison between theory and experiments requires that the arc efficiency factor can be established with a reasonable degree of accuracy. Unfortunately, the arc efficiency factor for GTA welding has not yet been firmly settled, where values from 0.25 up to 0.75 have been reported in the literature (see Table 1.3). Additional problems result from the fact that only a certain fraction of the total amount of heat transferred from the arc to the base plate is sufficiently intense to cause melting. This has led to the introduction of the melting efficiency factor T]m, which normally is found to be 30-70% lower than the total arc efficiency of the process, depending on the latent heat of melting, the applied amperage, voltage, shielding gas composition, or electrode vertex angle.23 Consequently, since these parameters cannot readily be obtained from the literature, the following reasonable values for r\m and r\ have been assumed to calculate nw in Table 1.6, based on a pre-evaluation of the experimental data: j \ m = 0.12 (fusion zone), TI = 0.23 (HAZ). It should be noted that the above values also include a correction for three-dimensional heat flow, since the assumption of a fast moving high power source during low heat input GTA welding is not valid. Hence, both the arc efficiency factor and the melting efficiency factor used in the present case study are seen to be lower than those commonly employed in the literature. Full weaving (welds Bl and B2) The results from the metallographic examination of the two GTA welds deposited under full weaving conditions are presented graphically in Fig. 1.63. Note that the shape of the fusion boundary as well as the Ac3 and the Ac1 isotherms can be predicted adequately from the present model for both combinations of E and L (an exception is the HAZ end points in position z = 0), provided that proper adjustments of i\m and Tj are made. The good correlation obtained in Fig. 1.63 between the observed and the calculated peak temperature contours justifies the adaptation of the model to low heat input processes such as GTA welding, despite the fact that the assumption of two-dimensional heat flow is not valid under the prevailing circumstances. No weaving (welds B3 and B4) For the limiting case of no weaving (Fig. 1.64), the concept of an equivalent amplitude of weaving has been used in order to calculate the peak temperature contours from the model. This parameter (designated Leq) takes into account the effects of convectional heat flow in the weld pool on the resulting bead geometry, and is evaluated empirically from measurements of the actual weld samples. At low heat inputs (Fig. 1.64(a)), the agreement between theory and
y, mm
Weld B1
z, mm Fusion line
y, mm
Weld B2
z, mm
Fig. 1.63. Comparison between observed and predicted fusion line, Ac3 and Ac1 contours during GTA welding under full weaving conditions (Case study 1.3). Data from Grong and Christensen.19 experiments is largely improved by inserting 2Leq = 7.5mm into equation (1-110), when comparison is made on the basis of the point source model. In contrast, at a heat input of 2.5 kJ mm"1 (Fig. 1.64(b)), the measured shape of the HAZ isotherms is seen to approach that of a semi-circle, and hence the deviation between the present model and the simplified solution for a fast moving high power point source is less apparent. Intermediate weaving At intermediate amplitudes of weaving (2L = 5 and 7.5mm, respectively), convectional heat flow in the weld pool will also tend to increase the bead width to depth ratio beyond the theoretical value predicted from the present model, as shown in Fig. 1.65. The plot in Fig. 1.65
Weld B3 y, mm
z, mm
Fusion line
y, mm
Weld B4
z, mm Fig. 1.64. Comparison between observed and predicted fusion line, Ac3 and Ac1 contours during GTA welding with a stationary arc (Case study 1.3). Solid lines: Distributed heat source, Broken lines: Point heat source. Data from Grong and Christensen.19 includes all data obtained in the GTA welding experiments with an oscillating arc, as reported by Grong and Christensen.19 These results suggest that the applied amplitude of weaving must be quite large before such effects become negligible. Consequently, adaptation of the model to the weld series considered above would require an empirical calibration of the weaving amplitude similar to that performed in Fig. 1.64 for stringer bead weldments to ensure satisfactory agreement between theory and experiments. 1.10.6 Thermal conditions during interrupted welding Rapid variations of temperatures as a result of interruption of the welding operation can have an adversely effect on the microstructure and consequently the mechanical properties of the weldment.
Width
Width to depth ratio
Depth
Theoretical curve
n
w
Fig. 1.65.Comparison between observed and predicted weld width to depth ratios during GTA welding with an oscillating arc (Case study 1.3). Data from Grong and Christensen.19
T,e
t,t
Fig. 1.66. Idealised heat flow model for prediction of transient temperatures during interrupted welding.
Model (after Rykalin9)
The situation existing after arc extinction may be described as shown in Fig. 1.66. From time t = t* there is no net heat supply to the weldment. This condition is satisfied if the real source q0 is considered maintained by adding an imaginary source +qo and sink -qo of the same strength at t*. The temperature at some later time t** in a given position R0 (measured from the origin 0") is then equal to the difference of temperatures due to the positive heat sources qo and +qo and the negative heat sink -qo. Each of these temperature contributions will be a product of a pseudo-steady state temperature Tps, and a correction factor K1 or K2 (given by equations (1-49) and (1-82), respectively). Hence, for 3-D heat flow, we have: (1-116) where and Similarly, for 2-D heat flow, we get: (1-117) where
(ro is the position of the weld with respect to the imaginary heat source at time f* in the x —y plane). Example (1.14)
Consider repair welding of a heavy steel casting with covered electrodes under the following conditions:
Suppose that a 50mm long bead is deposited on the top of the casting. Calculate the temperature in the centre of the weld 5 s after arc extinction. Solution
The pseudo-steady state temperature for points located on the weld centre-line (i|/ = £= 0) can be obtained from equation (1-65). When t** - t* = 5 s, we get:
Referring to Fig. 1.67, the position of the weld with respect to the imaginary heat source at time f* is 10mm, which gives:
Fig. 1.67. Sketch of weld bead in Example 1.14.
(a) 3-D heat flow
(b) 3-D heat flow
(C) 3-D heat flow
Fig. /.6#. Recommended correction factor/for some joint configurations; (a) Single V-groove, (b) Double V-groove, (c) T-joint.
Moreover, the dimensionless times T** and T** - x* are:
and At these coordinates, the correction factor K1 is seen to be 1 and 0.62, respectively (Fig. 1.18). The temperature in the centre of the weld 5 s after arc extinction is thus: which is equivalent to
LlOJ
Thermal conditions during root pass welding
During conventional bead-on-plate welding the angle of heat conduction is equal to 180° due to symmetry effects (e.g. see Fig. 1.23). In order to apply the same heat flow equations during root pass welding, it is necessary to introduce a correction factor,/, which takes into account variations in the effective heat diffusion area due to differences in the joint geometry. Taking /equal to 1 for ordinary bead-on-plate welding (b.o.p.), we can define the net heat input of a groove weld as:9 (1-118) Recommended values of the correction factor/for some joint configurations are given in Fig. 1.68. Example (Ll5)
Consider deposition of a root pass steel weld in a double-V-groove with covered electrodes (SMAW) under the following conditions:
Calculate the cooling time from 800 to 5000C (Ar875), and the cooling rate (CR.) at 6500C in the centre of the weld when the groove angle is 60°. Solution
The cooling time, Ar875, and the cooling rate, CR., can be obtained from equation (1-68) and (1-71), respectively: Cooling time, Atm
Cooling rate at 6500C
The above calculations show that the thermal conditions existing in root pass welding may deviate significantly from those prevailing during ordinary stringer bead deposition due to differences in the effective heat diffusion area. These results are in agreement with general experience (see Fig. 1.69). 1.10.8 Semi-empirical methods for assessment of bead morphology In fusion welding fluid flow phenomena will have a strong effect on the shape of the weld pool. Since flow in the weld pool is generally driven by a combination of buoyancy, electromagnetic, and surface tension forces (e.g. see Fig. 3.10 in Chapter 3), prediction of bead morphology from first principles would require detailed consideration of the current and heat flux distribution in the arc, the interaction of the arc with the weld pool free surface, convective heat transfer due to fluid flow in the liquid pool, heat of fusion, convective and radiative losses from the surface, as well as heat and mass loss due to evaporation. Over the years, a number of successful studies have been directed towards numerical weld pool modelling, based on the finite difference, the finite element, or the control volume approach.24"31 Although these studies provide valuable insight into the mechanisms of weld pool development, the solutions are far too complex to give a good overall indication of the heatand fluid-flow pattern. The present treatment is therefore confined to a discussion of factors affecting the nominal composition of single-bead fusion welds. This composition can be obtained from an analysis of the amount of deposit D and the fused part of the base material B, from which we can calculate the mixing ratio BI(B + D) or DI(B + D). Methods have been outlined in the preceding sections for handling such problems by means of point or line source models. The following section gives a brief description of procedures which can be used for predictions of the desired quantities in cases where the classic models break down, or where the calculation will be too tedious. 1.10.8.1 Amounts of deposit and fused parent metal The heat conduction theory does not allow for the presence of deposited metal. The rate of deposition, dMwldt, is roughly proportional to the welding current /, and is often reported as a coefficient of deposition, defined as: (1-119) Since the area of deposited metal D is frequently wanted, we may write: (1-120) where p is the density, and v is the welding speed.
Groove angle: <> | = 60°
Cooling time, AtQ/5(s)
Plate thickness:
Heat input, E (kJ/mm) Fig. 1.69. Comparison between observed and predicted cooling times from 800 to 5000C in root pass welding of steel plates (groove preparation as in Fig. 1.68(b)). Data from Akselsen and Sagmo.34 Recommended values of k'/p for some arc welding processes are given in Table 1.7. In practice, the deposition coefficient k'/p will also vary with current density and electrode stickout due to resistance heating of the electrode. Consequently, the numbers contained in Table 1.7 are estimated averages, and should therefore be used with care. Example (1.16)
Consider stringer bead deposition (S AW) on a thick plate of low alloy steel under the following conditions:
Table 1.7 Average rates of volume deposition in arc welding. Data from Christensen.32 Welding Process
k'/p (mm3 A"1 s l)
SMAW
0.3-0.5
GMAW, steel
0.6-0.7
GMAW, aluminium
-0.9
SAW, steel
-0.7
Calculate the mixing ratio Bf(B + D) at pseudo-steady state. Solution
The amount of fused parent material can be obtained from equation (1-75). If we include an empirical correction for the latent heat of melting, the dimensionless radius vector a4m becomes:
This gives:
Similarly, the amount of deposited metal can be calculated from equation (1-120). Taking ifc'/p equal to 0.7mm3 A"1 s"1 for SAW (Table 1.7), we get:
The mixing ratio is thus:
Example (L 17)
Consider stringer bead deposition with covered electrodes (SMAW) on a thick plate of low alloy steel under the following conditions:
Calculate the mixing ratio BI(B + D) at pseudo-steady state. Solution
In this particular case the conditions for a fast moving high power source are not met. Thus, in order to eliminate the risk of systematic errors, the amount of fused parent metal should be calculated from the general Rosenthal thick plate solution (equation (1-45)) or read from Fig. 1.21. When Tc = Tm (i.e. 8^ = 1), we obtain:
Reading from Fig. 1.21 gives:
and
Moreover, the amount of deposited metal can be calculated from equation (1-120). Taking k'/p equal to 0.4mm3 A"1 s~l for SMAW (Table 1.7), we get:
and
The above calculations indicate a small difference in the mixing ratio between SA and SMA welding, but the data are not conclusive. In practice, a value of BI(B + D) between 1/3 and 1/2 is frequently observed for SMAW, while the mixing ratio for SAW is typically 2/3 or higher. The observed discrepancy between theory and experiments arises probably from difficulties in estimating the amount of fused parent metal from the point heat source model. 1.10.8.2 Bead penetration It is a general experience in arc welding that the shape of the fusion boundary will depart quite strongly from that of a semi-circle due to the existence of high-velocity fluid flow fields in the weld pool.24"31 For combinations of operational parameters within the normal range of arc welding, a fair prediction of bead penetration h can be made from the empirical equation derived by Jackson et al.:33 (1-121) A summary of Jackson's data is shown in Table 1.8. It is seen that the constant C in equation (1-121) has a value close to 0.024 for SAW and SMAW with E6015 type electrodes, and about 0.050 for GMAW with CO2 -shielding gas. Penetration measurements of GMA/Ar + O2, GMA/Ar, and GMA/He welds, on the other hand, show a strong dependence of polarity, and shielding gas composition, to an extent which makes the equation useless for a general prediction. Such data have therefore not been included in Table 1.8. Example (1.18)
Based on the Jackson equation (equation (1-121)), calculate the bead penetration for the two specific welds considered in Examples (1.16) and (1.17). Use these results to evaluate the applicability of the point heat source model under the prevailing circumstances. Solution
From equation (1-121) and Table 1.8, we have:
Table 1.8 Recommended bead penetration coefficients for some arc welding processes. Data from Jackson.33 Welding Process
C
Comments
SAW, steel
-0.024
Various types of fluxes (Zz from 3 to 15 mm)
SMAW, steel (E6015)
-0.024
Wide range of /, U, and v (h from 0.7 to 5mm)
GMAW, steel (CO2 - shielding)
-0.050
Electrode positive (h from 6.5 to 8mm)
and
The corresponding values predicted from the point heat source model are:
and
Provided that the Jackson equation gives the correct numbers, it is obvious from the above calculations that the point heat source model is not suitable for reliable predictions of the bead penetration during arc welding. This observation is not surprising. 1.10.9 Local preheating So far, we have assumed that the ambient temperature T0 remains constant during the welding operation (i.e. is independent of time). The use of a constant value of T0 is a reasonable approximation if the work-piece as a whole is subjected to preheating. In many cases, however, the dimensions of the weldment allow only preheating of a narrow zone close to the weld. This, in turn, will have a significant influence on the predicted weld cooling programme, particularly in the low temperature regime where the classic models eventually break down when T approaches T0. Model (after Christensen n)
The idealised preheating model is shown in Fig. 1.70. Here it is assumed that the weld centreline temperature is equal to the sum of the contributions from the arc and from the field of preheating. The former contribution is given by equation (1-45) for R = -x = Vt, provided that the plate thickness is sufficiently large to maintain 3-D heat flow. Similarly, the temperature field due to preheating can be calculated as shown in Section 1.7 for uniaxial heat conduction from extended sources (thermit welding). By combining equations (1-45) and (1-22), we obtain the following relation for the weld centre-line: (1-122)
T
Temperature profile att = 0
Weld Preheated zone
z Fig. 1.70. Sketch of preheating model. where T* is the local preheating temperature, and L* is the half width of the preheated zone. Equation (1-122) can be written in a general form by introducing the following groups of parameters: — Dimensionless temperature: (1-123)
Time constant: (1-124)
Dimensionless time: (1-125)
Dimensionless half width of preheated zone: (1-126) By inserting these parameters into equation (1-122), we obtain: (1-127)
It is evident from the graphical representation of equation (1-127) in Fig. 1.71 that the predicted weld cooling programme falls within the limits calculated for Q"-^ 0 (no preheating) and Q /7 -> oo (global preheating). The controlling parameter is seen to be the dimensionless half width of the preheated zone Q", which depends both on the actual width L*, the base plate thermal properties a, X, and the net heat input qo Iv. Example (1.19)
Consider stringer bead deposition with covered electrodes (SMAW) on a thick plate of low alloy steel under the following conditions:
Calculate the cooling time from 800 to 50O0C (A%5), and the cooling time £1Oo measured from the moment of arc passage to the temperature in the centre of the weld reaches 10O0C. Solution First we calculate the time constant to from equation (1-124):
e*-
from which we obtain
^6
Fig. 1.71. Graphical representation of equation (1-127).
Next Page Cooling time, At8/5
The dimensionless temperatures conforming to 800 and 5000C are:
Reading from Fig. 1.71 gives:
from which
This cooling time is only slightly longer than that calculated from equation (1-68) for T0 = 200C (6.9s), showing that moderate preheating up to 1000C is not an effective method of controlling Ar875. Cooling time, t]00
When T=T0* = 1000C, the dimensionless temperature 9* = 1. Reading from Fig. 1.71 gives T 6 - 10, from which:
The above value should be compared with that evaluated from the numerical data of Yurioka et al.,35 replotted in Fig. 1.72 (see p.104). It follows from Fig. 1.72 that the weld cooling programme in practice is also a function of the plate thickness d, an effect which cannot readily be accounted for in a simple analytical treatment of the heat diffusion process. For the specific case considered above the parameter ^100 varies typically from 500 to 900s, depending on the chosen value of d. This cooling time is significantly shorter than that calculated from equation (1-127), indicating that the analytical model is only suitable for qualitative predictions.
References 1. 2. 3. 4. 5. 6.
H.S. Carslaw and J.C. Jaeger: Conduction of Heat in Solids; 1959, Oxford, Oxford University Press. British Iron and Steels Research Association: Physical Constants of some Commercial Steels at Selected Temperatures; 1953, London, Butterworths. R. Hultgren, R.L. Orr, RD. Anderson and K.K. Kelly: Selected Values of Thermodynamic Properties of Metals and Alloys; 1963, New York, J. Wiley & Sons. E. Griffiths (ed.): J. Iron and Steel Inst., 1946,154, 83-121. J.E. Hatch (ed.): Aluminium — Properties and Physical Metallurgy; 1984, Metals Park (Ohio), American Society for Metals. Metals Handbook, 9th edn., Vol. 2, 1979, Metals Park (Ohio), American Society for Metals.
Previous Page Cooling time, At8/5
The dimensionless temperatures conforming to 800 and 5000C are:
Reading from Fig. 1.71 gives:
from which
This cooling time is only slightly longer than that calculated from equation (1-68) for T0 = 200C (6.9s), showing that moderate preheating up to 1000C is not an effective method of controlling Ar875. Cooling time, t]00
When T=T0* = 1000C, the dimensionless temperature 9* = 1. Reading from Fig. 1.71 gives T 6 - 10, from which:
The above value should be compared with that evaluated from the numerical data of Yurioka et al.,35 replotted in Fig. 1.72 (see p.104). It follows from Fig. 1.72 that the weld cooling programme in practice is also a function of the plate thickness d, an effect which cannot readily be accounted for in a simple analytical treatment of the heat diffusion process. For the specific case considered above the parameter ^100 varies typically from 500 to 900s, depending on the chosen value of d. This cooling time is significantly shorter than that calculated from equation (1-127), indicating that the analytical model is only suitable for qualitative predictions.
References 1. 2. 3. 4. 5. 6.
H.S. Carslaw and J.C. Jaeger: Conduction of Heat in Solids; 1959, Oxford, Oxford University Press. British Iron and Steels Research Association: Physical Constants of some Commercial Steels at Selected Temperatures; 1953, London, Butterworths. R. Hultgren, R.L. Orr, RD. Anderson and K.K. Kelly: Selected Values of Thermodynamic Properties of Metals and Alloys; 1963, New York, J. Wiley & Sons. E. Griffiths (ed.): J. Iron and Steel Inst., 1946,154, 83-121. J.E. Hatch (ed.): Aluminium — Properties and Physical Metallurgy; 1984, Metals Park (Ohio), American Society for Metals. Metals Handbook, 9th edn., Vol. 2, 1979, Metals Park (Ohio), American Society for Metals.
Cooling time, t100(s)
Heat input: E=1.7 kJ/mm
Preheating temperature, T^ (0C) Fig. 1.72. Cooling time to 1000C, tm, in steel welding for different combinations of T0*, L*, d and E. Data from Yurioka et a/.35
7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.
K.P. Bentley, J.A. Greenwood, R McKnowlson and R.G. Bakes: Brit. Weld. J., 1963,10, 613619. N.N. Rykalin, A.I. Pugin and V.A. Vasil'eva: Weld. Prod., 1959, 6, 42-52. N.N. Rykalin: Berechnung der Warmevorgdnge beim Schweissen; 1953, Berlin, VEB Verlag Technik. H.M. Tensi, W. Welz and M. Schwalm: Aluminium, 1981, 58, 515-518. N. Christensen, V. de L. Davis and K. Gjermundsen: Brit. Weld. J., 1965,12, 54-75. Welding Handbook, 8th edn., Vol. 2, 1991, Miami (Florida), American Welding Society. D. Rosenthal: Weld. / , 1 9 4 1 , 20, 220s-234s. D. Rosenthal: Trans. ASME, 1946, 68, 849-866. CM. Adams: Weld. J., 1958, 37, 210s-215s. RS. Myers, O.A. Uyehara and G.L. Borman: Weld. Res. Bull., 1967, 123, 1-46. T.W Eagar and N.S. Tsai: Weld. J., 1983, 62, 346s-355s. M.F. Ashby and K.E. Easterling: Ada Metall, 1984, 32, 1935-1948. 0. Grong and N. Christensen: Mater. ScL Tech., 1986, 2, 967-973. O.R. Myhr and 0 . Grong: Acta Metall. Mater., 1990, 38, 449-460. S. Kou and Y. Le: Metall. Trans., 1983,14A, 2245-2253.
22. 23. 24. 25. 26. 27. 28. 29. 30. 32. 33. 34. 35.
O.R. Myhr and 0. Grong: Unpublished work, 1990, University of Trondheim, The Norwegian Institute of Technology. R.W. Niles and CE. Jackson: Weld. J., 1975, 54, 25s-32s. G.M. Oreper, T.W. Eagar and J. Szekely: Weld J., 1983, 62, 307s-312s. Y.H. Wang and S. Kou: Proc. Int. Conf. on Trends in Welding Research, Gatlinburg, TN, May, 1986, pp. 65-69, Publ. ASM International. S.A. David and J.M Vitek: Int. Mater. Rev., 1989, 34, 213-245. K.C. Mills and BJ. Keene: Int. Mater. Rev., 1990, 35, 185-216. R.L. UIe, Y. Joshi and E.B. Sedy: Metall. Trans., 1990, 21B, 1033-1047. T. Zacharia, S.A. David, J.M. Vitek and H.G. Kraus: Metall. Trans., 1991, 22B, 243-257. A. Matsunawa: Proc. 3rd Int. Conf. on Trends in Welding Research, Gatlinburg, TN, 1992, pp.3-16, Publ. ASM International. N. Christensen: Welding Metallurgy Compendium, 1985, University of Trondheim, The Norwegian Institute of Technology. CE. Jackson: Weld. J., 1960, 39, 226s-230s. O.M. Akselsen and G. Sagmo: Technical Report STF34 A89147, 1989, Trondheim (Norway), Sintef-Division of Metallurgy. N. Yurioka, M. Okumura, S. Ohshita and S. Saito: HW Doc. XII-E-10-81, 1981.
Appendix 1.1 Nomenclature General symbols thermal diffusivity (mm2 s"1)
finite difference method heat content per unit volume at Tc (J mm"3)
cross section (mm2) start temperature of ferrite to austenite transformation (0C) end temperature of ferrite to austenite transformation (0C) recrystallisation temperature (0C)
enthalpy increment referred to an initial temperature T0 (J mm' 3 ) latent heat of melting (J mm"3) amperage (A) modified Bessel function of second kind and zero order
cooling rate (0C s"1) plate thickness (mm)
modified Bessel function of second kind and first order
natural logarithm base number
integration parameter
Gaussian error function
integration parameter
complementary Gaussian error function
start temperature of austenite to martensite transformation (0C)
integration parameter
y-axis/transverse direction (mm)
net power (W)
z-axis/through thickness direction (mm)
net heat input (J) efficiency factor two-dimensional radius vector (mm)
dimensionless temperature
locus of peak temperature in T-r space (mm)
dimensionless temperature conforming to 8000C
three-dimensional radius vector (mm)
dimensionless temperature conforming to 5000C
locus of peak temperature in T-R space (mm)
dimensionless temperature conforming to the melting point
isothermal zone width (mm)
dimensionless peak temperature
temperature (0C)
volume heat capacity (J mm-3 0C-1)
reference temperature (0C) ambient temperature (0C)
thermal conductivity (W mm"1 0C-1)
melting point (0C)
dimensionless time
peak temperature (0C)
dimensionless cooling time
time (s)
dimensionless cooling time from 800 to 5000C
time variable (s) dimensionless cooling time from 300 to 1000C
time variable (s) cooling time (s)
Specific symbols 0
cooling time from 800 to 500 C (s)
Local Fusion in Arc Strikes
0
cooling time from 300 to 100 C (s) integration parameter voltage (V) integration parameter x-axis/welding direction (mm)
dimensionless operating parameter arc ignition time (s) isothermal zone width (mm) dimensionless R-vector locus of peak temperature in G-CT1 space
dimensionless isothermal zone width
locus of peak temperature in 0'-£2 space (star denotes a specific peak temperature)
dimensionless time dimensionless time locus of peak temperature in 0-T1 space
dimensionless cooling time from ^ to 5000C
dimensionless cooling time locus of peak temperature in (T-T3 space
Spot Welding thickness of overlapping plates (mm) dimensionless operating parameter
Friction Welding integral in equation (1-30)
heating time (s)
net power generation at weld interface (W)
dimensionless r-vector
duration of heating period (s)
locus of peak temperature in 0-cr2 space
contact section temperature at the end of heating period (0C)
dimensionless time
dimensionless temperature
locus of peak temperature in 0-T2 space
dimensionless peak temperature
dimensionless cooling time
Thermit Welding
dimensionless jc-coordinate locus of peak temperature in 6"Q.' space dimensionless time
half width of groove (mm) initial temperature of liquid metal (0C) distance from reference point to infinitesimal source (mm) dimensionless temperature dimensionless peak temperature dimensionless .^-coordinate
Arc Welding amount of fused parent metal (mm2) constant in Jackson equation amount of deposited metal (mm2) gross heat input per unit length of weld (kJ mm"1) correction factor for the net heat input during root pass welding
FCAW
flux cored arc welding
imaginary heat source of net arc power qo, qa, or qb (W)
GMAW gas metal arc welding GTAW
maximum intensity of distributed (Gaussian) heat source (W mm"1)
gas tungsten arc welding bead penetration (mm)
power density of distributed (Gaussian) heat source (W mm"1)
integer variables.... -1,0, L... infinitesimal heat source (W) constant in heat distribution function (mm"2)
two-dimensional radius vector in y-z plane (mm)
coefficient of weld metal deposition (g A"1 s"1)
locus of peak temperature in T-r* space (mm)
amplitude of weaving or half width of strip electrode (mm)
distance from infinitesimal heat source to point P in x-y or y-z plane (mm)
half width of preheated zone (mm)
position of weld end-crater with respect to imaginary heat source at time t** in x-y plane (mm)
equivalent amplitude of weaving (mm) half width of linear source in Gaussian heat distribution model (mm)
distance from infinitesimal heat source to point P in x-y-z space (mm)
length of weld bead (mm) k
mass of weld metal (g)
distances from real and imaginary heat sources to point P in x-y-z space (mm)
dimensionless operating parameter position of weld with respect to imaginary heat source at time f** in x-y-z space (mm)
dimensionless operating parameter in weaving model reference point in stationary coordinate system reference point in moving coordinate system
SAW
submerged arc welding
SMAW
shielded metal arc welding time at moment of arc extinction (s)
arbitrary reference point time constant in preheating model arbitrary point of observation strength of elementary heat sources (W)
(S)
cooling time to 1000C (s)
time constant in heat distribution function (s)
displacement of elementary heat source in z-direction (mm)
time referred to moment of arc ignition (s)
groove angle
retention time (s)
ratio between real and pseudo-steady state temperature (thick plate welding)
preheating temperature (0C) welding speed (mm s"1) volume of isothermal enclosure (mm3) welding direction in stationary coordinate system (mm) ^-coordinate at maximum width of isotherm (mm) transverse direction in stationary coordinate system (mm) distance from infinitesimal heat source to point P in j-direction (mm) ^-coordinate at maximum width of isotherm (mm)
ratio between real and pseudosteady state temperature (thin plate welding) dimensionless temperature in preheating model dimensionless cross sectional area of isothermal enclosure (thick plate welding) dimensionless cross sectional area of isothermal enclosure (thin plate welding) density of weld metal (g mm 3 ) dimensionless distance from real and imaginary heat sources to point P dimensionless /^-vector
isothermal zone width (mm) dimensionless R0-vector through-thickness direction in stationary coordinate system (mm) z-coordinate at maximum width of isotherms (mm) isothermal zone width (mm) dimensionless y-coordinate in weaving model dimensionless z-coordinate in weaving model dimensionless plate thickness
locus of peak temperature in 0-a3 space dimensionless r*-vector locus of peak temperature in 0-04 space dimensionless r-vector dimensionless r^-vector locus of peak temperature in 8-CT5 space
dimensionless jc-axis
dimensionless zo -axis
dimensionless xo -axis
dimensionless z-coordinate at maximum depth of isotherm
dimensionless jc-coordinate at maximum width of isotherm
melting efficiency factor
dimensionless length of isothermal enclosure
dimensionless volume of isothermal enclosure
dimensionless distance from heat source to front of isothermal enclosure
dimensionless half width of preheated zone
dimensionless distance from heat source to rear of isothermal enclosure
dimensionless time in weaving model dimensionless time in preheating model
dimensionless y-axis dimensionless yo -axis dimensionless ^-coordinate at maximum width of isotherm dimensionless isothermal zone width dimensionless z-axis
locus of peak temperature in 6-x space dimensionless retention time dimensionless time at moment of arc extinction dimensionless time referred to moment of arc ignition
Appendix 1.2 Refined Heat Flow Model for Spot Welding The refined model is based on the assumption that all heat is released instantaneously at time t = 0 in a point located at the interface between the two overlapping plates, which implies that equation (1-7) is valid. However, in order to maintain the net flux of heat through both plate surfaces equal to zero, it is necessary to account for mirror reflections of the source with respect to the planes z = dt/2 and z = - dt/2. This can be done on the basis of the method of images, as illustrated in Fig. A 1.1. By including all contributions from the imaginary sources "Q-2 >Q-i ,Q\,Qi >••• located symmetrically at distances ± idt below and above the centre-axis of the joint, the temperature distribution is obtained in the form of a convergent series:
(Al-I) where
y
Z Fig. Al.l.Refined heat flow model for spot welding of plates. and i is an integer variable (...-1, 0, 1...)A numerical solution of equation (Al.l) gives a peak temperature distribution similar to that shown in Fig. 1.9.
Appendix 1.3 The Gaussian Error Function The eiTor function erf(u) and the complementary error function erfc(u) are special cases of the incomplete gamma function. Their definitions are:
and
The functions have the following limiting values and symmetries:
and
The following Fortran subroutine can be used for calculations of the error functions with a fractional error less than 1.2 X 10~7: FUNCTION ERFC(U) Z=ABS(U) T=l./(l.+0.5*Z) ERFC=T*EXP(-Z*Z-1.26551223+T*(1.00002368+T*(.37409196+ *
T%09678418+T*(-.18628806+T%27886807+T*(-l.13520398+
*
T*(1.48851587+T*(-.82215223+T*.17O87277)))))))))
IF (U.LT.O.) ERFC=2.-ERFC RETURN END
Appendix 1.4 Gaussian Heat Distribution Following the treatment of Rykalin,9 the situation may be described as shown in Fig. Al.2. Here we consider a distributed heat source of net power density (in W mm"1): (Al-2) The total power of the source qo is obtained by integration of equation (Al-2). Substituting and integrating from u = -©© to u = +<*>, gives:
from which
(Al-3)
It follows from equation (1-73) that an infinitesimal source dqy> located between j ' a n d will cause a small rise of temperature dTy> in point P at time t, as:
(Al-4) where
and
Integration of equation (Al-4) between the limits y'= -°o and >>'= +00 gives:
(Al-5)
q(y)
P
2-D heat flow
z Fig, Al.2. Distributed heat source of net power density q(y) on a semi-infinite body.
where
is a time constant)and n = Aat.
The latter integral can be evaluated by substituting:
from which
and integrating between the limits w = -°° and This gives (after some manipulation):
(Al-6) If we replace the Gaussian heat distribution by a linear source of the same strength, which extends from -L0 to +L0 on either side of the weld centre-line in the y-direction (see Fig. A1.3), we may write:
By rearranging this equation, we obtain:
(Al-7) In practice, the parameter L0 has the same physical significance as the weaving amplitude L in equation (1-110). Consequently, these solutions are equivalent in the sense that they predict a similar temperature-time pattern.
q(y)
Fig. Al.3. Physical representation of a Gaussian heat distribution by a linear source of width 2LO.
2 Chemical Reactions in Arc Welding
2.1 Introduction The weld metal composition is controlled by chemical reactions occurring in the weld pool at elevated temperatures, and is therefore influenced by the choice of welding consumables (i.e. combination of filler metal, flux, and/or shielding gas), the base metal chemistry, as well as the operational conditions applied. In contrast to ladle refining of metals and alloys where the reactions occur under approximately isothermal conditions, a characteristic feature of the arc welding process is that the chemical interactions between the liquid metal and its surroundings (arc atmosphere, slag) take place within seconds in a small volume where the metal temperature gradients are of the order of 1000°C mm"1 with corresponding cooling rates up to 1000°C s"1. The complex thermal cycle experienced by the liquid metal during transfer from the electrode tip to the weld pool in GMA welding of steel is shown schematically in Fig. 2.1. As a result of this strong non-isothermal behaviour, it is very difficult to elucidate the reaction sequences during all stages of the process. Consequently, a complete understanding of the major controlling factors is still missing, which implies that fundamentally based predictions of the final weld metal chemical composition are limited. Additional problems result from the lack of adequate thermodynamic data for the complex slag-metal reaction systems involved. However, within these restrictions, the development of weld metal compositions can be treated with the basic principles of thermodynamics and kinetic theory considered in the following sections.
2.2 Overall Reaction Model The symbols and units used throughout this chapter are defined in Appendix 2.1. In ladle refining of metals and alloys, the reaction kinetics are usually controlled by mass transfer between the liquid metal and its surroundings (slag or ambient atmosphere). Examples of such kinetically controlled processes are separation of non-metallic inclusions from a deoxidised steel melt or removal of hydrogen from liquid aluminium. In welding, the reaction pattern is more difficult to assess because of the characteristic non-isothermal behaviour of the process (see Fig. 2.1). Nevertheless, experience shows that it is possible to analyse mass transfer in welding analogous to that in ladle refining by considering a simple two-stage reaction model, which assumes:1 (i)
A high temperature stage, where the reactions approach a state of local pseudo-equilibrium.
(ii)
A cooling stage, where the concentrations established during the initial stage tend to readjust by rejection of dissolved elements from the liquid.
Gas nozzle Shielding gas Filler wire
Contact tube
Arc plasma temperature~10000°C
Electrode tip droplet (1600-20000C) Falling droplet (24000C) Hot part of weld pool (1900-22000C)
Cold part of weld pool (< 19000C)
Weld pool retention time 2-1Os
Base plate
Fig. 2.1. Schematic diagram showing the main process stages in GMA welding. Characteristic average temperature ranges at each stage are indicated by values in parenthesis.
As indicated in Fig. 2.2 the high temperature stage comprises both gas/metal and slag/metal interactions occurring at the electrode tip, in the arc plasma, or in the hot part of the weld pool, and is characterised by extensive absorption of elements into the liquid metal. During the subsequent stage of cooling following the passage of the arc, a supersaturation rapidly increases because of the decrease in the element solubility with decreasing temperatures. The system will respond to this supersaturation by rejection of dissolved elements from the liquid, either through a gas/metal reaction (desorption) or by precipitation of new phases. In the latter case the extent of mass transfer is determined by the separation rate of the reaction products in the weld pool. It should be noted that the boundary between the two stages is not sharp, which means that phase separation may proceed simultaneously with absorption in the hot part of the weld pool. In the following sections, the chemistry of arc welding will be discussed in the light of this two-stage reaction model.
2.3 Dissociation of Gases in the Arc Column As shown in Table 2.1, gases such as hydrogen, nitrogen, oxygen, and carbon dioxide will be widely dissociated in the arc column because of the high temperatures involved (the arc plasma temperature is typically of the order of 10 0000C or higher). From a thermodynamic standpoint, dissociation can be treated as gaseous chemical reactions, where the concentrations of the reactants are equal to their respective partial pressures. Hence, for dissociation of diatomic gases, we may write: (2-1) where X denotes any gaseous species.
'Cold' part of weld pool
Solid weld metal
Solid weld metal
Peak temperature
Grey j zonei
Rejection of dissolved elements
Peak concentration
Solid weld metal
Concentration
Absorption of elements
Solid weld metal
Temperature
'Hot1 part of weld pool
Equilibrium concentration at melting point
Time Fig. 2.2. Idealised two-stage reaction model for arc welding (schematic). Table 2.1 Temperature for 90% dissociation of some gases in the arc column. Data from Lancaster.2 Gas
Dissociation Temperature (K)
CO 2
3800
H2
4575
O2
5100
N2
8300
Next, consider a shielding gas which consists of two components, i.e. one inert component (argon or helium) and one active component X2. When the fraction dissociated is close to unity, the partial pressure of species X in the gas phase px is equal to:
(2-2) where H1 and nx are the total number of moles of components / (inert gas) and X, respectively in the shielding gas, andptot is the total pressure (in atm). It follows from equation (2-1) that two moles of X form from each mole of X2 that dissociates. Hence, equation (2-2) can be rewritten as:
(2-3)
where nXl is the total number of moles of component X2 which originally was present in the shielding gas. If nXl and H1 are proportional to the volume concentrations of the respective gas components in the shielding gas, equation (2-3) becomes:
(2-4)
Taking vol% / = (100 - vol% X2) andp,ot = 1 atm, we obtain the following expression for Px(2-5)
Similarly, if X2 is replaced by another gas component of the type YX2, we get: (2-6) and (2-7)
It is evident from the graphical representations of equations (2-5) and (2-7) in Fig. 2.3 that the partial pressure of the dissociated component X increases monotonically with increasing concentrations of X2 and YX2 in the shielding gas. The observed non-linear variation of px arises from the associated change in the total number of moles of constituent species in the gas phase due to the dissociation reaction. Moreover, it is interesting to note that the partial pressure px is also dependent on the nature of the active gas component in the arc column (i.e. the stoichiometry of the reaction). This means that the oxidation capacity of for instance CO2 is only half that of O2 when comparison is made on the basis of equal concentrations in the shielding gas (to be discussed later).
Px
Vol%)^ f VoRGYX2 Fig. 2.3. Graphical representation of equations (2-5) and (2-7).
2.4 Kinetics of Gas Absorption In general, mass transfer between a gas phase and a melt involves:3 (i)
Transport of reactants from the bulk phase to the gas/metal interface.
(ii)
Chemical reaction at the interface.
(iii)
Transport of dissolved elements from the interface to the bulk of the metal.
2.4.1 Thin film model In cases where the rate of element absorption is controlled by a transport mechanism in the gas phase (step one), it is a reasonable approximation to assume that all resistance to mass transfer is confined to a stagnant layer of thickness 8 (in mm) adjacent to the metal surface, as shown in Fig. 2.4. Under such conditions, the overall mass transfer coefficient is given by:2
(2-8) where Dx is the diffusion coefficient of the transferring species X (in mm2 s~*). Although the validity of equation (2-8) may be questioned, the thin film model provides a simple physical picture of the resistance to mass transfer during gas absorption.
Partial pressure
Distance Fig. 2.4. Film model for mass transfer (schematic).
2.4.2 Rate of element absorption Referring to Fig. 2.5, the rate of mass transfer between the two phases (in mol s"1) can be written as: (2-9) where A is the contact area (in mm 2 ), R is the universal gas constant (in mm3 atm K"1 mol"1), T is the absolute temperature (in K), px is the partial pressure of the dissociated species X in the bulk phase (in atm), and px is the equilibrium partial pressure of the same species at the gas/ metal interface (in atm). Based on equation (2-9) it is possible to calculate the transient concentration of element X in the hot part of the weld pool. Let m denote the total mass of liquid weld metal entering/ leaving the reaction zone per unit time (in g s"1). If Mx represents the atomic weight of the element (in g mol"1), we obtain the following relation w h e n / ? x » p°x:
(2-10)
It follows from equation (2-10) that the transient concentration of element X in the hot part of the weld pool is proportional to the partial pressure of the dissociated component X in the plasma gas. Since this partial pressure is related to the initial content of the molecular species X2 or YX2 in the shielding gas through equations (2-5) and (2-7), we may write:
Arc column
Bulk gas phase
Stagnant gaseous boundary layer Gas/metal interface Metal phase Hot part of weld pool Fig. 2.5. Idealised kinetic model for gas absorption in arc welding (schematic). (2-11) and (2-12)
where C1 and C2 are kinetic constants which are characteristic of the reaction systems under consideration.
2.5 The Concept of Pseudo-Equilibrium Although the above analysis presupposes that the element absorption is controlled by a transport mechanism in the gas phase, the transient concentration of the active component X in the hot part of the weld pool can alternatively be calculated from chemical thermodynamics by considering the following reaction: X(gas)
X (dissolved)
(2-13)
By introducing the equilibrium constant K{ for the reaction and setting the activity coefficient to unity, we get: (2-14) This equation should be compared with equation (2-10) which predicts a linear relationship
between wt% X and px. If the above analysis is correct, one would expect that the partial pressure px at the gas/metal interface is directly proportional to the partial pressure of the dissociated component in the bulk phase. Unfortunately, the proportionality constant is difficult to establish in practice.
2.6 Kinetics of Gas Desorption During the subsequent stage of cooling following the passage of the arc, the concentrations established at elevated temperatures will tend to readjust by rejection of dissolved elements from the liquid. When it comes to gases such as hydrogen and nitrogen, this occurs through a desorption mechanism, where the driving force for the reaction is provided by the decrease in the element solubility with decreasing metal temperatures. 2.6.1 Rate of element desorption Consider a melt which first is brought in equilibrium with a monoatomic gas of partial pressure px at a high temperature T1, and then is rapidly cooled to a lower temperature T2 and immediately brought in contact with diatomic X2 of partial pressure pXl (see Fig. 2.6). Under such conditions, the rate of element desorption (in mol s"1) is given by:
(2-15)
where k'd is the mass transfer coefficient (in mm s 1X and p°x is the equilibrium partial pressure of component X2 at the gas/metal interface (in atm).
Bulk gas phase
Stagnant gaseous boundary layer Gas/metal interface Metal phase Cold part of weld pool Fig. 2.6. Idealised kinetic model for gas desorption in arc welding (schematic).
The partial pressure pX2 can be calculated from chemical thermodynamics by considering the following reaction: 2X(dissolved) = X2 (gas) (2-16) from which (2-17) where K2 is the equilibrium constant, and [wt% X] is the concentration of element X in the liquid metal (in weight percent). Note that the activity coefficient has been set to unity in the derivation of equation (2-17). The equilibrium constant K2 may be expressed in terms of the solubility of element X in the liquid metal at 1 atm total pressure Sx. Hence, equation (2-17) transforms to:
(2-18)
By combining equations (2-15) and (2-18), we get:
(2-19) Data for the solubility of hydrogen and nitrogen in some metals up to about 22000C are given in Figs. 2.7 and 2.8, respectively. It is evident that the element solubility decreases steadily with decreasing metal temperatures down to the melting point. This implies that the desorption reaction is thermodynamically favoured by the thermal conditions existing in the cold part of the weld pool. 2.6.2. Sievert's law It follows from equation (2-19) that desorption becomes kinetically unfeasible when Px2 ~ Px2' corresponding to: (2-20) Equation (2-20) is known as the Sievert's law. This relation provides a basis for calculating the final weld metal composition in cases where the resistance to mass transfer is sufficiently small to maintain full chemical equilibrium between the liquid metal and the ambient (bulk) gas phase.
2.7 Overall Kinetic Model for Mass Transfer during Cooling in the Weld Pool Because of the complexity of the rate phenomena involved, it would be a formidable task to derive a complete kinetic model for mass transfer in arc welding from first principles. How-
(b)
Aluminium
ml H2/100 g fused metal
ml H2/100 g fused metal
(a)
Temperature, 0C
Solid Cu
Temperature, 0C
Iron
Temperature, 0C
ml H2/100g fused metal
(d)
(C)
ml H2/100g fused metal
Copper
Nickel
Temperature, 0C
Fig. 2.7. Solubility of hydrogen in some metals; (a) Aluminium, (b) Copper, (c) Iron, (d) Nickel. Data compiled by Christensen.4 ever, for the idealised system considered in Fig. 2.9, it is possible to develop a simple mathematical relation which provides quantitative information about the extent of element transfer occurring during cooling in the weld pool. Let [%X]eq denote the equilibrium concentration of element X in the melt. If we assume that the net flux of element X passing through the phase boundary A per unit time is proportional to the difference ([%X] - [%X]eqX the following balance is obtained:3 (2-21) where V is the volume of the melt (in mm 3 ), kd is the overall mass transfer coefficient (in mm s"1), and A is the contact area between the two phases (in mm 2 ).
Temperature, 0C
log (wt% N)
Iron
104AT1 K Fig. 2.8. Solubility of nitrogen in iron. Data from Turkdogan.5
Phase I i
Phase i
Distance
Net flux of X
Contact area (A)
Volume (V)
Concentration Fig. 2.9. Idealised kinetic model for mass transfer in arc welding (schematic). By rearranging equation (2-21) and integrating between the limife [%X]( (att = O) and [%X] (at an arbitrary time t\ we get:
(2-22)
where to is a time constant (equal to VI kjA).
It is evident from the graphical representation of equation (2-22) in Fig. 2.10 that the rate of mass transfer depends on the ratio Vl kji, i.e. the time required to reduce the concentration of element X to a certain level is inversely proportional to the mass transfer coefficient kd. This type of response is typical of a first order kinetic reaction. Although the above model refers to mass transfer under isothermal conditions, it is also applicable to welding if we assume that the weld cooling cycle can be replaced by an equivalent isothermal hold-up at a chosen reference temperature. Thus, by rearranging equation (222), we get: (2-23) It follows that the final concentration of element X in the weld metal depends both on the cooling conditions and on the intrinsic resistance to mass transfer, combined in the ratio t/to. When [%X]eq is sufficiently small, equation (2-23) predicts a direct proportionality between [%X] and [%X\t (i.e. the initial concentration of element X in the weld pool). This will be the case during deoxidation of steel weld metals where separation of oxide inclusions from the weld pool is the rate controlling step. Moreover, when t/t0 » 1 (small resistance to mass transfer), equation (2-23) reduces to: (2-24)
(X-X^)Z(X1-Xeq)
Under such conditions the final weld metal composition can be calculated from simple chemical thermodynamics. Because of this flexibility, equation (2-23) is applicable to a wide range of metallurgical problems at the same time as it provides a simple physical picture of the resistance to mass transfer during cooling in the weld pool.
t,s Fig. 2.10. Graphical representation of equation (2-22).
2.8 Absorption of Hydrogen Some of the well-known harmful effects of hydrogen discussed in Chapters 3 and 7 (i.e. weld porosity and HAZ cold cracking) are closely related to the local concentration of hydrogen established in the weld pool at elevated temperatures due to chemical interactions between the liquid metal and its surroundings. 2.8.1 Sources of hydrogen Broadly speaking, the principal sources of hydrogen in welding consumables are:6 (i) Loosely bound moisture in the coating of shielded metal arc (SMA) electrodes and in the flux used in submerged arc (SA) or flux-cored arc (FCA) welding. Occasionally, moisture may also be introduced through the shielding gas in gas metal arc (GMA) and gas tungsten arc (GTA) welding. (ii) Firmly bound water in the electrode coating or the welding flux. This can be in the form of hydrated oxides (e.g. rust on the surface of electrode wires and iron powder), hydrocarbons (in cellulose), or crystal water (bound in clay, astbestos, binder etc.). (iii) Oil, dirt and grease, either on the surface of the work piece itself, or trapped in the surface layers of welding wires and electrode cored wires. It is evident from Fig. 2.11 that the weld metal hydrogen content may vary strongly from one process to another. The lowest hydrogen levels are usually obtained with the use of lowmoisture basic electrodes or GMA welding with solid wires. Submerged arc welding and fluxcored arc welding, on the other hand, may give high or low concentrations of hydrogen in the weld metal, depending on the flux quality and the operational conditions applied (note that the former process is not included in Fig. 2.11). The highest hydrogen levels are normally associated with cellulosic, acid, and rutile type electrodes. This is due to the presence of large amounts of asbestos, clay and other hydrogen-containing compounds in the electrode coating. Table 2.2 (shown on page 132) gives a summary of measured arc atmosphere compositions in GMA and SMA welding. Included are also typical ranges for the weld metal hydrogen content. 2.8.2 Methods of hydrogen determination in steel welds Hydrogen is unlike other elements in weld metal in that it diffuses rapidly at normal room temperatures, and hence, some of it may be lost before an analysis can be made. This, coupled with the fact that the concentrations to be measured are usually at the parts per million level, means that special sampling and analysis procedures are needed. In order that research results may be compared between different laboratories and can be used to develop hydrogen control procedures, some international standardisation of these sampling and analysis methods is necessary. Three methods are currently being used, as defined in the following standards:
Potential hydrogen level
FCAW
Very Low Medium low Weld hydrogen level
High
Fig. 2.11. Ranking of different welding processes in terms of hydrogen level (schematic). The diagram is based on the ideas of Coe.6 (i) The Japanese method (JIS Z 313-1975), which has been adopted with important adjustments from the former ASTM designation A316-48T. This method involves collection of released hydrogen from a single pass weld above glycerine for 48h at 45 0 C. The total volume of hydrogen is reported in ml per 10Og deposit. Only 5 s of delay are allowed from extinction of the arc to quenching. (ii) The French method (N.F.A. 81-305-1975) where two beads are deposited onto core wires placed in a copper mould. Hydrogen released from this bead is collected above mercury, and the volume is reported in ml per 10Og fused metal (including the fused core wire metal). (iii) The International Institute of Welding (HW) method (ISO 3690-1977), where a single bead is deposited on previously degassed and weighed mild steel blocks clamped in a quickrelease copper fixture. The weldment is quenched and refrigerated according to a rigorously specified time schedule. Hydrogen released from the specimens is collected above mercury for 72 h at 25°C, and the results are reported in ml per 10Og deposit, or in g per ton fused metal. To avoid confusion, it is recommended to use the symbol HDM for the content reported in terms of deposited metal (ml per 10Og deposit), and HFM for the content referred to fused metal (ml per 100 g or g per ton fused metal). The relationship between HDM and HFM is shown in Fig. 2.12. As would be expected, these three methods do not give identical results when applied to a given electrode. Approximate correlations have been established between the HW criteria HDM and HFM and the numbers obtained by the Japanese and the French methods (designated HJIS and HFR, respectively). For covered electrodes tested at various hydrogen levels, we have:7
Fig. 2.12. The relation between HDM and HFM (0.9 is the conversion factor from ml per 10Og to g per ton). (2-25) (2-26) The conversion factor from HFR to HFM applies to a ratio of deposited to fused metal, DI(B + D), equal to 0.6, which is a reasonable average for basic electrodes. The use of HFM in preference of HDM is normally recommended, because it is a more rational criterion of concentration. Moreover, HDM values would be grossly unfair, if applied to high penetration processes like submerged arc welding. In GTA welds made without filler wire HDM cannot be used at all, since there is no deposit. It should be noted that the present HW procedure gives the amount of 'diffusible hydrogen'. For certain purposes the total hydrogen content may be wanted. It is obtained by adding the content of 'residual hydrogen' determined on the same samples by vacuum or carrier gas extraction at 6500C. A very small additional amount may be observed on vacuum fusion of the sample, tentatively labelled 'fixed hydrogen'. There is no clear line of demarcation between these categories of hydrogen. As will be discussed later, the extent of hydrogen trapping depends both on the weld metal constitution and the thermal history of the metal. In singlebead basic electrode deposits the diffusible fraction is usually well above 90%. 2.8.3 Reaction model Normally, measurements of hydrogen in weld metals are carried out on samples from solidified beads. Due to the rapid migration of hydrogen at elevated temperatures, such data do not represent the conditions in the hot part of the weld pool. Quenched end crater samples would be better in this respect, but they are not representative of normal welding. Further complications arise from the presence of hydrogen in different states (e.g. diffusible or residual hydrogen) and the lack of consistent sampling methods. Nevertheless, experience has shown that pick-up of hydrogen in arc welding can be interpreted on the basis of the simple model outlined in Fig. 2.13. According to this model, two zones are considered: (i) An inner zone of very high temperatures which is characterised by absorption of atomic hydrogen from the surrounding arc atmosphere.
Electrode Hot part of weld pool Absorption of atomic hydrogen (controlled by pH in the arc column)
Cold part of weld pool Desorption of hydrogen (controlled by pH2 in ambient gas phase)
Hydrogen trapped in weld metal Weld pool
Fig. 2.13. Idealised reaction model for hydrogen pick-up in arc welding. (ii) An outer zone of lower temperatures where the resistance to hydrogen desorption is sufficiently small to maintain full chemical equilibrium between the liquid weld metal and the ambient (bulk) gas phase. Under such conditions, the final weld metal hydrogen content should be proportional to the square root of the initial partial pressure of diatomic hydrogen in the shielding gas, in agreement with Sievert's law (equation (2-20)). 2.8.4 Comparison between measured and predicted hydrogen contents It is evident from the data in Table 2.2 that the reported ranges for hydrogen contents in steel weld metals are quite wide, and therefore not suitable for a direct comparison of prediction with measurement. For such purposes, the welding conditions and consumables must be more precisely defined. 2.8.4.1 Gas-shielded welding In GTA and GMA welds the hydrogen content is usually too low to make a direct comparison between theory and experiments. An exception is welding under controlled laboratory conditions where the hydrogen content in the shielding gas can be varied within relatively wide limits. The results from such experiments are summarised in Fig. 2.14, from which it is seen that Sievert's law indeed is valid. A closer inspection of the data reveals that the weld metal hydrogen content falls within the range calculated for chemical equilibrium at 1550 and 20000C, depending on the applied welding current. This shows that the effective reaction temperature is sensitive to variations in the operational conditions. An interesting effect of oxygen on the weld metal hydrogen content has been reported by Matsuda et al.9 Their data are reproduced in Fig. 2.15. It is evident that the hydrogen level is significantly higher in the presence of oxygen. This is probably due to the formation of a thin (protective) layer of slag on the top of the bead, which kinetically suppresses the desorption of hydrogen during cooling.
Table 2.2 Measured arc atmosphere compositions in steel welding. Also included are typical ranges for the weld metal hydrogen content. Data compiled by Christensen.4 Arc Atmosphere Composition (vol%) Method
Primary Source of Hydrogen
Weld Metal Hydrogen Content (ppm)
CO2
CO
H 2 +H 2 O
Range
Average
98-80
2-20
<0.02
1-5
3
GMAW* (CO2)
Moisture introduced through the shielding gas
SMAW (acid)
Firmly bound water in the electrode coating
-4
-34
-62
10-30
25
SMAW (rutile)
Firmly bound water in the electrode coating
~4
-42
-54
10-30
25
SMAW (basic)
Loosely bound water in the electrode coating
-19
-77
-4
2-10
3-5
FCAW (rutile)
Firmly bound water influx
10-20
FCAW (basic)
Loosely bound water influx
2-5
SAW (basic)
Loosely bound water influx
2-10
*The arc atmosphere composition can vary within wide limits, depending on the operational conditions applied.
ml H2/100 g fused metal, HpM
GTAW (low-alloy steel)
ml H2 /100 g fused metal, HJ|S
GTAW (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 from Matsuda et al.9 Example (2.1)
Consider GTA welding (Ar-shielding) on a thick plate of low-alloy steel under the following conditions: / = 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 mhr 1 . Calculate the 'potential' hydrogen level, assuming that all hydrogen introduced through the shielding gas is absorbed in the weld metal. Solution
First we calculate the total mass of hydrogen per mm:
The resulting bead cross section and total mass of weld metal per mm can be estimated from the Rosenthal equation by considering the dimensionless operating parameter at the melting point (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 one order of magnitude higher than the expected weld metal hydrogen content (1 to 3 ppm). This shows that the hydrogen pick-up in GTA welding is not determined by the total amount of hydrogen which is introduced through the shielding gas, but is mainly controlled by the resulting partial pressure of hydrogen in the ambient (bulk) gas phase. 2.8.4.2 Covered electrodes In SMA welding the partial pressure of hydrogen is more difficult to assess due to the presence of trapped moisture and hydrogen-containing compounds in the electrode coating. Such compounds will loose their identity at the stage of introduction into the arc atmosphere. Since very little information is available on the species present in the arc column, we shall base our estimate on a simple thermodynamic approach, including only the molecular species H2 and H2O which can be determined by analysis (see data in Table 2.2). It follows that the combined partial pressure of H2 and H2O in the gas phase is given by: (2-27) The parameter pw can be estimated on the basis of combustion measurements of the electrode coating, assuming that no carbon is picked up or lost from the system in excess of the amount calculated from an analysis of the base plate and the electrode wire. For a recorded content of mw g H2O and mc g CO2 per 100 g of electrode coating, we obtain: (2-28) From a thermodynamic standpoint, replacement of pHl b y / ^ in the expression for Sievert's law requires the use of a modified solubility of hydrogen, defined as:
(2-29)
where K3 is the equilibrium constant for the H 2 O-H reaction, and [%O] is the weld metal oxygen content. In practice, the correction term ^ K3/(K3+[%0]) does not depart significantly from unity, which means that Sw ~ SH.
During welding with basic covered electrodes considerable amounts of CO2 may form as a result of decomposition of calcium carbonate, according to the reaction: (2-30) Modern basic electrodes contain between 20 to 40 weight percent CaCO3, which is equivalent with a CO2 content of 9 to 18 percent. Taking as an average mc equal to 15 g CO2 per 100 g electrode 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 hydrogen content 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 ml H2 per 100 g fused metal, respectively). Although the observed scatter in the effective reaction temperature is admittedly large, equation (2-31) points out a very interesting effect, namely that the hydrogen content of SMA steel weld metals is controlled by the combined partial pressure of H2 and H2O in the ambient gas phase. For this reason it is frequently recommended that calcium carbonate is added to the electrode coating, which on decomposition produces considerable amounts of shielding gas in the form of CO2. Hydrogen shielding can also be achieved by additions of volatile alkali-fluorides, which on heating will evaporate and dilute the atmosphere with respect to hydrogen.
ml H2/100 g fused metal, HpM •
SMAW (low-alloy steel)
Water content in electrode coating, wt% Fig. 2.16. Hydrogen pick-up in SMA welding at different water contents in the electrode coating. Data compiled by Chew.10
Example (2.2)
Consider SMA welding on mild steel with basic covered electrodes. The electrode coating contains 35 wt% CaCO3 and 0.5 wt% H2O in the as-received condition. After drying at 3500C for 1 h the water content is reduced to 0.2 wt% H2O. Estimate the weld metal hydrogen content (in ppm) both before and after drying of the electrode. Assume in these calculations an effective reaction temperature of 18000C. Solution
First we calculate the CO2 content per 100 g of electrode coating. Taking the atomic weight of CaCO3 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). Before drying 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 is about 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 use of 'dry' basic electrodes. In practice, this can be achieved by protecting the electrodes against moisture pick-up during storage (see Fig. 2.17). However, in certain cases it is necessary to differentiate between strongly bound and loosely adsorbed moisture in the coating of basic electrodes. This point is more clearly illustrated in Fig. 2.18, which shows the HDM content of hydrogen in basic electrode deposits at various levels of coating moisture. It is seen that water remaining from an insufficient baking treatment is more dangerous than moisture picked up by exposure of a properly dried coating. This has to do with the fact that loosely adsorbed mois-
Water content in electrode coating, wt%
Exposure time, days
very low
low
medium
ml H2 /100 deposit, HDM
SMAW (low-alloy steel)
high
Fig. 2.17. Moisture content in basic electrode coating as a function of exposure time and relative humidity (R.H.) in ambient gas phase. Data from Evans.11
Water content, wt% Fig. 2.18. Hydrogen pick-up in SMA welding at different levels (states) of adsorbed water in the electrode coating. Data from Evans and Bach.12
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 is bound in rust on the surface of the electrode wire or the iron powder. 2.8.4.3 Submerged arc welding This method is usually classified as a pure slag-shielded process, because carbonates or other gas-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 by observations made by probes inserted through the flux cover. It is reasonable to assume that the gas contained within this enclosure consists of metal vapour, volatile constituents originating from the flux, and relatively small fractions of carbon monoxide and water vapour. Acid fluxes of the calcium silicate type will probably generate silicon monoxide, while agglomerated fluxes bonded with alkali silicate will produce volatile alkali fluorides. In addition, carbon monoxide may be present as a result of oxidation of carbon, or decomposition of carbonates. A small but important contribution to the cavity atmosphere is the trace of moisture remaining in the flux even after careful drying. No direct measurements of partial pressures are available, and the gas composition must therefore be inferred from observations of hydrogen absorption in the weld metal. Hydrogen pick-up during SA welding has been examined by Evans and Bach.12 Their data are replotted in Fig. 2.19. The shape of the observed curve of hydrogen vs residual water content would seem to indicate a relationship similar to that predicted by Sievert's law. In fact, a very close fit can be obtained through empirical calibration of the dilution 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 of carbon. Again, an unreasonable amount of carbon loss would be required. Therefore, it must be concluded that further research is needed for a proper interpretation of the factors controlling hydrogen pick-up in SA welding.
ml H2/100 deposit, HDM
Hydrogen content, HFM (ppm)
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 and Bach.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 of carbon in the weld pool is 0.03 wt%. Solution
First 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 consumption 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 is infiltrated 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 to that in the previous example. By inserting this value in the expression for Sievert's law, we obtain:
In practice, the 'potential' hydrogen level represents an upper limit for the hydrogen concentration which cannot be exceeded. Thus, the contradictory results obtained in the present example clearly illustrate the difficulties involved in estimating the effective partial pressure of hydrogen in SA welding. 2.8.4.4 Implications of Sievert's law An important implication of Sievert's law is that the fraction of hydrogen picked up from the arc 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 are completely absorbed in the metal. At increasing partial pressures the fraction of hydrogen picked up in the metal will gradually decrease, finally attaining a threshold of (SH/2) in the case of pure H2. This shows that the concept of 'potential' hydrogen content frequently used to characterise filler materials (see Fig. 2.11) is a dangerous one, since the rates of absorption are so different in the high and low ranges of the hydrogen potential. 2.8.4.5 Hydrogen in multi-run weldments So far, no standardised method is available for the determination of hydrogen in multi-layer welds. Early measurements by Roux,13 using an arrangement similar to that subsequently adopted in French standards, indicate a constant ratio of extracted hydrogen to the mass of fused metal, regardless of the number of passes. If hydrogen is reported on the basis of deposited metal, this ratio may vary by a factor of 2.5 when comparing a deposit made in five passes to a single bead. Exploratory measurements of local hydrogen contents in large-size joints have been made by Skjolberg,14 who butt welded a 40 mm plate with a self-shielding flux cored wire at an interpass temperature of 2000C. Samples were cut from a refrigerated part of the weldment at mid-thickness, including positions in the weld metal close to the fusion line and samples in the HAZ. His results are summarised in Table 2.3. Normal testing of the filler wire according to ISO 3690 gave fused metal hydrogen contents of 3.3 ppm (diffusible) and 1.7 ppm (residual). A comparison with Table 2.3 shows that the multi-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 the surroundings through diffusion.
Table 2.3 Measured hydrogen contents in multi-run FCA steel weldment. Data from Skjolberg.14 HAZ Distance from fusion line (mm) Condition
Weld Metal
As-welded PWHT* (4h/150°C)
Oto 5
5 to 10
0.6 ppm diffusible 0.9 ppm residual
0.25 ppm diffusible
0.15 ppm diffusible
0.35 ppm diffusible 2.25 ppm residual
0.15 ppm diffusible
0.15 ppm diffusible
10 to 15
0.10 ppm diffusible
*Post weld heat treated.
2.8.4.6 Hydrogen in non-ferrous weldments The solubility of hydrogen in metals and alloys of industrial importance increases with temperature, and passes through a maximum in the vicinity of the boiling point, where the opposing trends of increasing solubility and increasing dilution by metal vapour balance. Solubility curves for hydrogen in aluminium, copper, and nickel up to about 22000C have previously been presented in Fig. 2.7. Since all these metals can dissolve considerable amounts of hydrogen, the risk of hydrogen absorption during welding is imminent if moisture is present in the shielding gas. Results obtained from arc melting experiments with Cu, Al, Ni in Ar-H 2 gas atmospheres indicate that hydrogen is absorbed at a high temperature zone under the arc and is transported by fluid flow to the outer, cooler regions of the pool.15 Rejection of the gas in the supersaturated outer regions is slower than the absorption in the hot zone, so the gas content throughout the pool approximates to that in the absorption zone. Typical estimates of the effective reaction temperature 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 conventional GTA or GMA welding of the same materials or are mainly restricted to the operational conditions 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 Chapter 7). In steel weld metals the associated loss of toughness due to free nitrogen has been attributed to solid solution hardening and dislocation locking effects. In addition, excessive nitrogen pick-up can cause porosity in steel weldments because of gas evolution during solidification.
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 nitrogen absorption is similar to that of hydrogen: (dissolved)
(2-33)
By introducing the equilibrium constant K4 for the reaction, we get:
(2-34)
where SN is the maximum solubility of nitrogen at 1 atm total pressure,/^ is the activity coefficient, 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, the solubility 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 maximum 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 order of 465A/OT8 ppm or 416 ppm. If a tentative estimate of air infiltration in the arc column is made 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 nitrogen contents are much higher than predicted from Sievert's law. This implies that the mechanism of 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 of Kobayashi et a/.,16 who examined the GMA welding process in a systematic manner. Some of their results are shown in Fig. 2.20. Figure 2.20(a), for low-alloy steel, reveals that the square root relationship is a fair approximation only for welding in mixtures of N 2 and H 2 (curve No. 5). Mixtures of N2 + Ar (curve No. 3), N 2 + CO2 (curve No. 2) and N2 + O 2 (curve No. 1) show increasing deviation from the predicted behaviour. Pure N2 under reduced pressure gives a curve (No. 4) of an entirely different shape including a maximum at pN ~ 0.05.
Table 2.4 Summary of measured weld metal nitrogen contents. Data compiled by Christensen.4 Welding Method
Material
SMAW (basic electrodes)
Low-alloy steel
60-180
Stainless steel
550-650
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
SMAW (rutile electrodes)
Nitrogen Content (ppm)
Similar features are seen from Fig. 2.20(b) for welding of stainless steel. Again, the deviation becomes more pronounced as the oxidation potential of the gas mixture is increased in the sequence H 2 -Ar-CO 2 -O 2 . Moreover, a comparison with Fig. 2.20(a) reveals that the displacement of the nitrogen concentrations in the presence of chromium is larger than expected from the calculated reduction of the nitrogen activity coefficient. The trends observed in Fig. 2.20 have been confirmed by O'Brien and Jordan17 who studied nitrogen 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 = 0.3 followed by a constant or slightly decreasing concentration (Fig. 2.21(b)). Both patterns are clearly 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 hydrogen, where the concept of pseudo-equilibrium has proved useful for a semiquantitative prediction. In both cases the molecular species H2 and N 2 are known to dissociate in the arc column (see Table 2.1), and would therefore dissolve in the metal to an extent far beyond the solubility controlled by pH or PN . The excess of dissolved hydrogen is probably released as gas at weld pool temperatures. This will also be the case with nitrogen in the absence of oxygen, as shown previously in Fig. 2.20(a) and (b). However, under oxidising conditions the desorption of gaseous nitrogen becomes suppressed by the presence of oxygen at the gas/metal interface and hence, nitrogen is retained at a level which by far exceeds the solubility limit at 1 atm total pressure of N2. This has been confirmed experimentally by Uda and Ohno18 in their classic work on surface active elements (i.e. oxygen, sulphur and selenium) in liquid steel. A similar phenomenon was quoted in Section 2.8.4.1 from the work of Matsuda et al9 even in the case of hydrogen, where increased entrapment of hydrogen was observed in the presence of 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 in Sections 2.6 and 2.7. As a consequence, Sievert's law cannot be used for an estimate of nitrogen 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
(a)
Nitrogen content, wt%
GMAW (low-alloy steel)
Vol% N 2 in shielding gas
(b)
Nitrogen content, wt%
GMAW (stainless steel)
Vol% N 2 in shielding gas 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
(a)
Nitrogen content, wt%
Low-alloy steel
Experiment
Vol% N 2 in shielding gas (b)
Nitrogen content, wt%
Low-alloy steel
Experiment
Vol% N2in shielding gas
Fig. 2.21. Nitrogen pick-up in GMA welding at different concentrations of N2 in the shielding gas; (a) Short circuting metal transfer, (b) Mixed and free flight metal transfer. Data from O'Brien and Jordan.17
length (voltage) because of the risk of air infiltration in the arc column. This point is more clearly illustrated in Fig. 2.22, which shows that the resulting weld metal nitrogen level may vary 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 excessive pick-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, since welding is performed under the shield of a flux. Hence, in multipass welds the filler wire itself will be the main source of nitrogen (see Fig. 2.23), while in single pass weldments the base plate nitrogen content is more important because of the high dilution involved. The latter point is illustrated by the following numerical example. Example (2.4)
Consider SA (single pass) welding on a thick plate of low-alloy steel under the following conditions:
Based on the 'rule of mixtures', calculate the weld metal nitrogen content. Assume in these calculations that the nitrogen content of the base plate and the filler wire is 0.005 and 0.012 wt%, respectively.
Nitrogen content, ppm
SMAW (low-alloy steel) 4 and 5 mm basic covered electrodes
A
B
C
D
Welder No. Fig. 2.22. Natural fluctuations in nitrogen pick-up during SMA welding due to variations in the arc length. Data from Morigaki et al.19
Next Page
gain
loss
Weld metal nitrogen content, ppm
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 from Bhadeshia et a/.20 Solution
First 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 defined as:
The above calculations show that the nitrogen content of single pass SA steel welds is close to that of the base plate because of the high dilution involved. This is in agreement with general experience.
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2.10 Absorption of Oxygen Partial oxidation almost invariably accompanies the welding of steel. It is well established that considerable interaction takes place between the liquid weld metal and its surroundings (arc atmosphere, slag) when welding is performed in the presence of oxygen. For slag-protected processes, the flux is the main source of oxygen because of its content of easily-reduced oxides, such as iron oxide, manganese oxide, silica, or rutile. In gas metal arc (GMA) welding, oxygen is often deliberately introduced through the shielding gas to improve the arc stability and bead morphology, but at the expense of an increased oxygen content in the weld metal and intensified losses of alloying elements. The oxidation reactions proceed very rapidly under the prevailing conditions owing to the high metal temperatures and the large interfacial contact area available for interactions. A general survey of oxygen contents in fusion welds is shown in Table 2.5. 2.10.1 Gas metal arc welding The GMA welding process offers a special advantage in the way that it allows the reactions to be studied through variations of the shielding gas composition without the complicating presence of a flux. Gas-shielded welding is also interesting form a practical point of view, since the process is readily mechanised and can be applied for welding of nearly all types of steel. Moreover, many of the reactions in the weld pool will be similar to those occurring during welding with covered electrodes or submerged arc fluxes. The amount of oxygen transferred to the metal during the high-temperature stage will clearly depend on the atmosphere. In GMA welding with active gases such as CO2, Ar + O2 or Ar + O2 + CO2 the extent of element absorption is controlled by the oxygen potential of the shielding gas. This type of gas/metal interaction will be discussed below. The analytical weld metal oxygen content is also affected by the presence of deoxidisers, because the transition from the high-temperature stage to the cooling stage is not sharp. As was Table 2.5 Summary of measured weld metal oxygen contents. Data compiled by Christensen.4 Welding Method
Material
SMAW (basic electrodes)
Low-alloy steel
250^40
SMAW (rutile electrodes)
Low-alloy steel
500-1300
SMAW (acid electrodes)
Low-alloy steel
700-1400
GTAW (pure Ar or He)
Low-alloy steel
50-100
GMAW (Ar-O 2 mixtures)
Low-alloy steel
200-1300*
GMAW (CO2)
Low-alloy steel
500-800
FCAW (self-shielded cored wire)
Low-alloy steel
130-200
SAW (calcium silicate fluxes)
Low-alloy steel
450-2600
SAW (manganese silicate fluxes)
Low-alloy steel
400-750
SAW (basic fluxes)
Low-alloy steel
180-350
Depends on the oxygen potential of the shielding gas.
Oxygen Content (ppm)
discussed briefly in the introduction to Chapter 2, a separation of non-metallic inclusions may occur towards the end of stage one and possibly at the beginning of stage two. A necessary condition for removal of oxygen introduced into the metal is, of course, the formation of oxygen-rich phases and compounds (e.g. microslag or carbon monoxide). These matters will be considered in a separate section on weld metal deoxidation reactions. 2.10.1.1 Sampling of metal concentrations at elevated temperatures In order to understand the extent and direction of the oxidation reactions, it is not sufficient to characterise the initial and final conditions (i.e. consumables/parent plate and the weld metal). Accordingly, especially designed experiments are required for assessment of the reactions taking place at the four main process stages: (1) Electrode tip (2) Arc column (3) Hot part of the weld pool (4) Cold part of the weld pool. Proper sampling techniques are needed for basic studies of this kind, which allow sampling of the falling droplets during their flight through the arc column. An additional requirement is that the speed of quenching is sufficiently high to freeze-in the metal composition established at elevated temperatures. If not, spontaneous reactions and subsequent losses of dissolved elements due to CO gas formation and manganese silicate slag precipitation may take place on cooling. To overcome these problems, a special 'melt spinning' technique has been developed by Grong and Christensen,1 utilising the same principles as those employed in production of amorphous alloy ribbons. By using a water-cooled, fast rotating copper wheel (spinner) as a cathode, rapid crystallisation of droplets released from the electrode tip can be obtained in the absence of a weld pool*. The reactions which normally occur in the pool during regular multirun deposition may then be assessed by comparison of analytical data for chilled metal (i.e. falling droplets) and normal multi-layer weldment, respectively. 2.10.1.2 Oxidation of carbon Filler wires intended for GMAW are usually overalloyed with respect to carbon, silicon, and manganese to compensate for heavy oxidation losses of these elements during the welding operation. It is evident from the data presented in Fig. 2.24(a) and (b) that virtually identical carbon contents are obtained for chilled and multilayer weld metal, except when welding is performed in extremely oxidising atmospheres (beyond 20 vol% O2 in Ar). This implies that oxidation of carbon does not normally take place in the weld pool, but is located to one or both of the preceding stages, i.e. electrode tip or arc column. However, since the carbon oxidation at the electrode tip is more than sufficient to account for the observed total loss1, it is likely that little, if any, carbon is lost in the latter stage. The fact that carbon is found to oxidise readily at the electrode tip but not in later stages, indicates that the supply of oxygen and/or the conditions of nucleation are more favourable in *The estimated cooling rate is of the order of 105 0C s"1 or higher.1 The measured electrode tip carbon content also includes oxidation after arc extinction. This accounts for the observed loss of carbon beyond that recorded in chilled metal or multi-layer weld deposit. f
(a)
Wt% C
Electrode tip Chilled metal (falling droplet) Multi-layer weld metal Electrode wire
Vol% O 2 in Ar
(b)
wt%c
Electrode tip Chilled metal (failing droplet) Multi-layer weld metal Electrode wire
V o l % C O 2 in Ar
Fig. 2.24. Measured carbon contents in electrode tip droplets, chilled metal and multi-layer weld deposit vs the oxygen potential of the shielding gas; (a) Ar-C>2 gas mixtures, (b) Ar-CC>2 gas mixtures. Data from Grong and Christensen.1
Carbon control
Silicon control
Pco>
atm
the former case. Normally, homogeneous nucleation of CO gas within the liquid metal is considered impossible, which means that the CO nucleation in practice must take place heterogeneously. However, the most probable site for CO evolution during droplet formation at the electrode tip will be the gas/metal interface itself, which allows carbon to be oxidised simultaneously with silicon and manganese. It is reasonable to assume that most of the observed carbon oxidation is located to the hot layers facing the arc, where the reaction is thermodynamically favoured. At other surface positions Si and Mn are expected to prevent carbon from reacting due to a rather low metal temperature, stated to be only slightly above the melting point at the time of detachment.21 It is evident from the data in Fig. 2.24(a) and (b) that the carbon losses increase with increasing O2 or CO2 contents in the shielding gas up to a certain critical level. Hence, supply of oxygen to the tip droplet surface is the rate controlling step for oxidation of carbon at low oxygen potentials. This conclusion is also consistent with calculations made by Corderoy et al.,22 who found that transport of atomic oxygen through a stagnant gaseous boundary layer close to the metal surface controls the oxidation rate of alloying elements at this stage of the process. The carbon oxidation will gradually decline with increasing oxygen concentrations in the shielding gas, probably as a result of build-up of carbon monoxide in the surrounding atmosphere. When the critical CO gas pressure is reached, the carbon reaction is blocked, silicon (and manganese) now exercising control of the oxygen level, as indicated in Fig. 2.25. For ArO 2 gas mixtures this critical pco pressure is attained at about 10 to 15 vol% O 2 in the shielding gas, corresponding roughly to 0.05 wt% C oxidised in chilled metal. When welding is performed in Ar-CO 2 mixtures the reaction is blocked at a much earlier stage of carbon oxidation (equal to about 0.02 wt% C lost in chilled metal), since dissociation of CO2 in this case will produce an additional amount of CO to concentrate in the surrounding gas phase.
Temperature, 0C Fig. 2.25. Break even equilibrium partial pressure of CO vs temperature for silicon control of oxygen level at 0.8 wt% Si and silica saturation. Data from Elliott et al. 23
The mechanism indicated above is supported by the data presented in Fig. 2.26, which show that a CO2-rich atmosphere even may act carburising if the initial carbon content of the electrode wire is sufficiently low. Moreover, it is interesting to note that the carbon-oxygen reaction is also influenced by the rate of droplet detachment. Since the highest carbon oxidation losses are normally associated with a coarse globular droplet transfer mode, this suggests that the reaction time is more important than the effective contact area available for interaction which depends on the droplet size. 2.10.1.3 Oxidation of silicon It is evident from the data in Fig. 2.27 that loss of silicon mainly take place in the weld pool, as indicated by the difference between the measured silicon content in chilled and multi-layer weld metal. In Ar-O 2 mixtures the Si loss increases steadily with increasing oxygen potential of the shielding gas. Thus, at 30 vol% O2 in Ar it amounts to 0.59 wt% Si (or 0.67 wt% O) removed from the weld pool as a result of deoxidation reactions. A similar situation exists in the case of CO2-shielded welding up to about 20 vol% CO2 in Ar. At higher CO2 contents, the Si loss tends to drop off, finally attaining an upper limit of approximately 0.30 wt% Si corresponding to 0.34 wt% O removed from the weld pool. In comparison, the amount of Si lost in the two preceding stages (i.e. electrode tip and arc column) is much smaller, as shown by the data for the chilled metal Si content. Since no slag is formed under the conditions of rapid cooling, silicon must escape in the form of a gaseous
Weld metal carbon content, wt%
GMAW (low-alloy steel)
(Gain)
(Loss)
Filler wire carbon content, wt% Fig. 2.26. Correlation between filler wire and weld metal carbon contents in CO2-shielded welding. Data from Ref.24.
(a) Chilled metal (falling droplet) Multi-layer weld metal
Wt% Si
Electrode wire
Vol% O 2 in Ar
(b) Chilled metal (falling droplet) Multi-layer weld metal
Wt% Si
Electrode wire
Vol% CO 2 in Ar
Fig. 2.27. Measured silicon contents in chilled and multi-layer weld metals vs the oxygen potential of the shielding gas; (a) Ar-02 gas mixtures, (b) Ar-CC>2 gas mixtures. Data from Grong and Christensen.1
product. Evaporation losses can in this case be excluded due to a very low vapour pressure of silicon at the prevailing temperatures. It is therefore reasonable to assume that SiO(g) forms as a result of chemical reactions occurring at the electrode tip. The observed decrease in chilled metal Si content with increasing O2 and CO2 contents in the shielding gas is probably caused by the presence of CO at the gas/metal interface, which facilitates SiO formation according to the reaction: (slag) (gas) (gas) (gas) (2-36)
PSiO,10-3atm
Figure 2.28 shows a plot of the equilibrium partial pressure of SiO vs temperature at silica saturation for three different CO levels. Note that stoichiometric amounts of CO2 have been assumed to form in order to calculate psi0. It is evident from the thermodynamical data presented in Fig. 2.28 that the formation of SiO is strongly dependent on the CO partial pressure at the slag/metal interface. Thus, from a thermodynamic standpoint the silicon loss at the electrode tip should be most pronounced during CO2-shielded welding due to the resulting higher CO pressure. The data shown in Fig. 2.27(a) and (b) support this assumption. It is seen that the silicon loss is increased by a factor of 3 to 5 in presence of CO2 when comparison is made on the basis of equal oxygen potential of the shielding gas (i.e. equal loss of deoxidants in the weld pool). Similar observations have also been made by Heile and Hill27 from determination of silicon in collected GMA welding fumes. The recorded chilled metal Si loss in Fig. 2.27(a) and (b) is in good agreement with the reported fume formation rates of silicon. Since all CO consumed in reaction (2.36) is expected to be regenerated immediately by decomposition of CO2 at the metal surface, the high CO partial pressure required for SiO formation at the electrode tip is maintained even in the case of extensive silicon losses. Consequently, the net reaction can be written as:
Temperature, 0C Fig. 2.28. Equilibrium partial pressure of SiO vs temperature at different CO levels. Data from Refs. 25 and 26.
(slag)
(dissolved)
(gas)
(2-37)
When welding is performed in Ar-O 2 gas mixtures, pSiO andpco may be taken proportional to the recorded loss of silicon and carbon in chilled metal (see data in Fig. 2.29). It is evident from this plot that the silicon loss is directly proportional to the corresponding loss of carbon up to a certain critical level. Thus, during the initial period of carbon oxidation at the electrode tip the SiO formation is probably controlled by the resulting partial pressure of CO at the slag/ metal interface, according to reaction (2-36). When the carbon reaction is blocked, the chilled metal silicon loss becomes independent of the CO partial pressure (see reaction (2-37)), since all CO consumed in the SiO formation will immediately be recirculated within the system. However, at the break even point for silicon control of the oxygen level at the electrode tip, the CO pressure in the surrounding gas phase will be the same for both Ar-O 2 and Ar-CO 2 gas mixtures. Hence, the recorded loss of silicon in chilled metal at 20 vol% CO2 in Ar is seen to be similar to that in Ar + 10 vol% O2, as indicated by the heavy broken line in Fig. 2.29. At the temperatures where liquid steel is normally deoxidised, silicon and manganese have a strong affinity to oxygen. Their ability to form stable oxides decreases rapidly with increasing temperature, and above approximately 180O0C silicon and manganese do no longer act as efficient deoxidation agents. Precipitation of manganese silicate slags is therefore favoured by the lower metal temperatures prevailing at the electrode tip and in the cold part of the weld pool. At higher temperatures, these oxides become unstable. Consequently, as a result of the metal superheating occurring during droplet transfer through the arc column, the macroscopic slag phase formed earlier at the electrode tip surface (as reported by Corderoy et ah12) will redissolve in the metal. This gives rise to a relatively high chilled metal oxygen content (to be discussed below).
Loss of silicon (%)
Ar+20 vol% CO2
Ar+10vol%O2
Loss of carbon (%) Fig. 2.29. Correlation between loss of carbon and silicon in chilled metal at different O 2 levels in the shielding gas. The corresponding loss of silicon at 20 vol% CO2 in Ar is indicated by the heavy broken line in the graph. Data from Grong and Christensen.1
Example (2.5)
Consider CO2-shielded welding on a thin sheet of low-alloy steel with a 0.8mm dia. electrode wire under the following conditions:
Based on the data presented in Fig. 2.27(b), calculate the fume formation rate (FFR) of silicon (in mg per min) due to SiO formation at the electrode tip. The wire feed rate is 125mm s"1. Solution
The total loss of silicon due to SiO formation may be taken equal to the observed difference between the filler wire and the chilled metal silicon contents. For welding in pure CO2, we get:
The corresponding fume formation rate of silicon (in mg min"1) can readily be calculated when the wire feed rate (WFR) is known. Taking the density of the steel equal to 7.85mg mm"3, we obtain:
A comparison with the measured FFR of silicon in Table 2.6 (at / = 13OA) shows that the calculated value is reasonable correct. Moreover, these data support our previous conclusion that the SiO formation is favoured by a high CO2 content in the shielding gas due to the dissociation reaction. In fact, more detailed studies of the reaction kinetics have confirmed that the rate of SiO formation is proportional to the resulting partial pressure of CO at the gas/metal interface,28 in agreement with equation (2-36). 2.10.1.4 Evaporation of manganese It is seen from the data in Fig. 2.30(a) and (b) that the amount of manganese lost in chilled metal is virtually independent of the oxygen potential of the shielding gas, as indicated by the constant difference of about 0.35 wt% between the filler wire and the chilled metal Mn contents in both graphs. This implies that significant amounts of manganese are lost during droplet transfer through the arc column as a result of evaporation. At the prevailing temperatures, the vapour pressure of iron is also high due to the almost unity activity of Fe. If the average arc metal temperature is taken equal to about 24000C,29 the data in Fig. 2.31 indicate that the vapour pressures of iron and manganese (at 1.27 wt% Mn) are nearly identical and close to 0.05 atm. In the hot surface layers of liquid metal facing the arc the temperature will be even higher, which means that iron vapour will dominate. Measurements of collected GMA welding fume reported by Heile and Hill27 (see data in Table 2.6) show a substantial higher loss of iron than that derived from simple thermodynamical calculations taking the rate of element loss proportional to the vapour pressure. From their results a reasonable value of the average mass ratio Fe to Mn in dust is about 5. Consequently, as a preliminary estimate the loss of iron may be taken 5 times the amount of manganese lost
Table 2.6 Measured fume formation rates in GMA welding of ferrous materials. Data from Heile and Hill.27
Shielding Gas
Argon
Ar+ 2 % O 2
Ar+ 5% O 2
Ar + 25% CO2
Pure CO2
Current
Voltage
(A)
(V)
Fume Formation Rate (mg min"1) Mn
Si
Fe
250
29
1
1
22
300 350
31 35
1 5
0 4
12 51
150 200 300 400
28 28 29 34
15 12 5 18
8 10 4 16
134 75 35 86
100 200 300
28 28 28
29 16 10
33 22 23
273 129 76
100
23
11
20
75
150 300
27 35
13 29
35 62
105 191
130 150 200 250 300
27 30 30 30 30
13 14 19 31 36
59 63 73 112 125
86 120 126 216 214
in chilled metal, corresponding to a total loss of 1.7 wt% (Fe + Mn) or 500mg (Fe + Mn) per min. The reported fume formation rate of Fe and Mn under nearly similar conditions is only one half of that stated above, which indicates that the calculated flux of metal vapour may be somewhat overestimated. However, if these two values are considered to represent borderline cases, the volume of metal vapour is in the range from 300 to 500 times that of the droplets and will therefore be more than sufficient to protect the metal from arc atmosphere oxidation at this stage of the process. This conclusion is consistent with statements made by Distin et al?1 who claim that iron vapour acts as an effective oxygen getter already at about 19000C. Very large amounts of manganese are also lost in the weld pool stage, as shown by the difference between the measured Mn contents in chilled and multi-layer weld metals. This situation appears to be quite similar to that of silicon. For Ar-O 2 mixtures the manganese loss increases steadily with increasing oxygen contents in the shielding gas, and reaches a value of about 1.08 wt% Mn (or 0.31 wt% O) removed from the weld pool at 30 vol% O2 in Ar. In the case OfAr-CO2 shielded welding the Mn oxidation loss starts to drop off at a CO2 content of about 20 vol%, finally attaining an upper limit of about 0.50 wt% Mn corresponding to 0.15 wt% O removed from the weld pool. A more detailed discussion of oxidation reactions in GMA welding is given in Section 2.10.1.5. Example (2.6)
Consider GMA welding low-alloy of steel under conditions similar to those in Example 2.5.
(a)
Wt% Mn
Chilled metal (falling droplet)
Multi-layer weld metal Electrode wire
Vol% O 2 in Ar
Wt% Mn
(b)
Chilled metal (falling droplet) Multi-layer weld metal Electrode wire
Vol%CO 2 inAr Fig. 2.30. Measured manganese contents in chilled and multi-layer weld metals vs the oxygen potential of the shielding gas; (a) Ar-02 gas mixtures, (b) Ar-CO2 gas mixtures. Data from Grong and Christensen.1 Based on the data presented in Fig. 2.30(b), calculate the fume formation rate (FFR) of manganese due to evaporation losses occurring during droplet transfer through the arc column. Estimate also the effective mass transfer coefficient for manganese evaporation under the prevailing circumstances by utilising the vapour pressure data in Fig. 2.31. The surface temperature of the falling droplets is assumed constant and equal to 26000C.
PMr/PFe
LogpMn,atm
Temperature, 0C Fig. 2.31. Equilibrium manganese vapour pressure and corresponding vapour pressure ratio pMn to PFe vs temperature at 1.27 wt% Mn in iron. Data from Kubaschewski and Alcock. 30 Solution
The total loss of manganese due to evaporation may be taken equal to the observed difference between the filler wire and the chilled metal manganese contents. For welding in pure CO2, we have:
The corresponding fume formation rate of manganese (in mg min"1) can readily be calculated when the wire feed rate (WFR) is known. Taking the density of the steel equal to 7.85mg mm~3, we obtain:
A comparison with the data in Table 2.6 reveals that the reported fume formation rate of manganese (at / = 13OA) is much lower than computed in the present example. This discrepancy can probably be attributed to differences in the filler wire manganese content. Assuming that the evaporation loss of manganese is controlled by a transport mechanism in the gas phase, we can estimate the effective mass transfer coefficient from equation (2-15) by inserting a reasonable average value for the manganese vapour pressure at the gas/metal interface (pMn in the bulk phase is taken equal to zero). Reading from Fig. 2.31 (at T= 26000C) gives:
If the diameter of the falling droplets is taken equal to the diameter of the filler wire, it is possible to calculate the total loss of manganese associated with one droplet (in mol):
Since the average flight time of large, globular droplets through the arc column is of the order of one second, the corresponding flux of manganese vapour per unit time is close to 9.97 X 10~8 mol s"1. Thus, by rearranging equation (2-15), we obtain the following value for the effective mass transfer coefficient:
Although the above value is rather uncertain, the calculated mass transfer coefficient is of the expected order of magnitude. This supports our previous conclusion that the evaporation kinetics are controlled by a transport mechanism in the gas phase. 2.10.1.5 Transient concentrations of oxygen It is evident from the data summarised in Fig. 2.32 that the oxygen content in both chilled and multi-layer weld metal increases with increasing oxygen potential of the shielding gas. The chilled metal analysis is representative of the oxygen absorption occurring at the electrode tip due to the lack of gas/metal interaction in the arc column. Measurements of manganese oxidation losses during droplet formation have been performed by Corderoy et al.22 From the curve presented for 20ms tip melting cycles, a reasonable estimate for the manganese oxidation loss in Ar-O 2 shielding gas mixtures may be: (2-38) Taking the Si to Mn mass ratio in precipitated slag equal to 0.66,22 the corresponding loss of silicon is equal to: (2-39) Based on equations (2-38) and (2-39) it is possible to calculate the oxygen absorption at the electrode tip which is associated with the MnO and the SiO2 slag formation. If corrections also are made for the amount of oxygen simultaneously removed as iron oxide*, we obtain: (2-40)
*An approximate correction can be made from an analysis of the Fe to Mn mass ratio in precipitated slag, which under the prevailing circumstances is close to 0.16.22
(a)
Wt% O
Chilled metal (falling droplet) Multi-layer weld metal Electrode wire
Vol%O2inAr (b)
Wt% O
Chilled metal (falling droplet) Multi-layer weld metal Electrode wire
Vol% CO2 in Ar Fig. 2.32. Measured oxygen contents in chilled and multi-layer weld metals vs the oxygen potential of the shielding gas; (a) Ar-C>2 gas mixtures, (b) Ar-CO2 gas mixtures. Data from Grong and Christensen.1 At 30 vol% O2 in Ar the absorption of oxygen is roughly 0.27 wt% O, which is reasonably close to that recorded in the chilled metal analysis (about 0.23 wt% O). The rate controlling step for metal oxidation at this stage of the process is believed to be transport of atomic oxygen through a stagnant gaseous boundary layer of Ar and/or CO adjacent to the metal surface.22 On the other hand, the measured chilled metal oxygen contents are much too low to account for the heavy oxidation losses of deoxidants observed in multi-layer welds. This indicates that
considerable amounts of oxygen are introduced in the hot part of the weld pool immediately beneath the root of the arc. Although the gas/metal interfacial contact area available for reaction is much smaller than that of the electrode tip (or falling) droplets, the strong turbulence existing in the hot part of the pool will provide an effective circulation of the liquid metal through the reaction zone.32 Moreover, absorption of oxygen at this stage of the process will be favoured by the increased time available for gas/metal interaction. If the diameter of the reaction zone is taken equal to about 3mm, the time available for oxygen absorption in the weld pool is of the order of one second for a typical welding speed of 3mm s"1. In comparison, the corresponding reaction time during droplet formation at the electrode tip is only 20 to 50 ms. Calculations of the total oxygen absorption can be done on the basis of the measured difference between silicon and manganese contents in chilled and multi-layer weld metals, designated A[%S7] and A[%Mn], respectively*. Moreover, corrections should be made for the amount of oxygen simultaneously removed as iron oxide from the weld pool. For deoxidation with silicon and manganese the mass ratio wt% Fe to wt% Mn in precipitated slag is equal to about O.I.1 This leads to the following balance: (2-41) At 30 vol% O2 in Ar the total oxygen absorption amounts to:
It is seen from the graphical representation of equation (2-41) in Fig. 2.33(a) and (b) that most of the oxygen pick-up takes place in the weld pool. However, at present it is not clear whether the calculated values represent a real transient concentration in the hot part of the weld pool or a number in concentration units representing precipitation of manganese silicate slags. According to Fischer and Schumacher33 the solubility of oxygen in liquid iron is 0.94 wt% at 19000C and 1.48 wt% at 20000C This temperature range is probably relevant with respect to the hot part of the weld pool, although the surface metal temperature will be even higher.34 However, in steel weld metals the oxygen concentrations should be well below this solubility limit in the presence of silicon and manganese. Taking the average weld pool silicon content equal to 0.50 wt%, the corresponding oxygen content in equilibrium with a silicasaturated slag is roughly 0.10 and 0.20 wt% at 1900 and 20000C, respectively.23 On the other hand, under the prevailing circumstances there will be no solid/liquid interface available for nucleation of oxide particles, and hence homogeneous nucleation is the only possibility. According to Sigworth and Elliott35 this requires a relatively high degree of supersaturation, which means that the oxygen concentration most likely will exceed the Si-Mn-O equilibrium value before slag precipitation occurs. The data in Fig. 2.33(a) and (b) indicate that the weld pool oxygen absorption is controlled by a complex transport mechanism in the gas phase. However, since mass transfer in gas-jet/ liquid systems is not fully understood,3 we shall only consider the limiting case where the resistance to mass transfer is confined to a stagnant gaseous boundary layer adjacent to the metal surface. Under such conditions equation (2-10) predicts that the transient oxygen concentration is determined by the partial pressure of atomic oxygen in the plasma gas, as shown *Oxygen consumed in CO and SiO formation is not included.
(a)
Wt% O
Calculated total oxygen absorption Analytical weld metal oxygen content
Vol% O2 in Ar
(b)
Wt% O
Calculated total oxygen absorption Analytical weld metal oxygen content
Vol% CO2 in Ar Fig. 2.33. Calculated total oxygen absorption in GMA welding at different oxygen potentials of the shielding gas; (a) Ar-O 2 gas mixtures, (b) Ar-CO 2 gas mixtures. The analytical weld metal oxygen content is indicated by the broken lines in the graphs. Data from Grong and Christensen.1
by the plots in Fig. 2.34. If we as a borderline case assume that all oxygen present in the plasma gas is immediately absorbed in the liquid metal, the slope of the curve in Fig. 2.34 for Ar-O 2 gas mixtures (equal to about 2.67 wt% dissolved oxygen at one atmosphere total pressure of atomic oxygen) is representative of the total amount of gas passing through the arc column. Taking the mass of liquid metal leaving/entering the reaction zone equal to 3Og min"1 under the prevailing circumstances,1 the following gas flow rate is obtained (in Nl min"1).
This value corresponds to about 6 per cent of the total shielding gas flow rate. In contrast to the situation described in Fig. 2.34 for Ar-O 2 gas mixtures, a large deviation from the expected relationship is observed for welding in CO2-rich atmospheres. At present, the reason for this shift in the reaction kinetics is not known. However, it is evident from the data presented in Fig. 2.34 that the effective mass transfer coefficient decreases by a factor of about 2.5 when the CO2 content in the shielding gas increases from 10 to 100 vol%. This implies that the oxidation capacity of pure CO2 is comparable with that of Ar + 13 vol% O2, although the partial pressure of atomic oxygen in the plasma gas is equivalent with an oxygen content of about 33 vol%. Example (2.7)
[%O]t0t,wt%
Consider GMA welding of low-alloy steel in Ar + 20 vol% CO2 and pure CO2, respectively. Based on the results in Figs. 2.27(b) and 2.30(b), calculate the total weight of top bead slag (in gram per 100 gram weld deposit) which forms as a result of deoxidation reactions. Assume in these calculations that the iron to manganese mass ratio in precipitated slag is equal to 0.1.
Pure CO2
P0, atm Fig. 2.34. Calculated total oxygen absorption in GMA welding at different partial pressures of atomic oxygen in the plasma gas. Data from Grong and Christensen.1
Solution
The amount of silicon and manganese lost as a result of deoxidation reactions is equal to the observed difference in the chilled and multi-layer weld metal Si and Mn contents. Assuming that these elements are removed from the weld pool as SiO2 and MnO, respectively, the following balance is obtained:
Thus, for welding in Ar + 20 vol% CO2, the total weight of slag amounts to:
Similarly, for CO2-shielded welding, we get:
A comparison with the experimental data in Fig. 2.35 shows that there is a fair agreement between the amount of slag recorded by weighing and that calculated from a simple mass balance of silicon, manganese and iron.
g slag/10Og deposit
Calculated weight of slag Measured weight of slag
Vol% CO2 in Ar Fig. 2.35. Comparison between measured and calculated weight of top bead slag in CO2-shielded welding. Data from Grong and Christensen.1
2.10.1.6 Classification of shielding gases The data in Fig. 2.34 provide a basis for evaluating the oxidation capacity of various shielding gases. For welding in Ar + O2 and Ar+CO2 gas mixtures up to 10 vol% CO2 in argon, the total oxygen absorption is approximately given by the following equation:
(2-42) Similarly, for welding with CO2-rich shielding gases (i.e. between 10 and 100 vol% CO2), we obtain: (2-43) Equal oxidation capacity means that the total weld metal oxygen absorption is the same for both shielding gas mixtures. Hence, we may write:
(2-44) when the CO2 content in the shielding gas is less than 10 vol%, and
(2-45)
when welding is performed with CO2-rich shielding gases (more than 10 vol% CO2 in Ar). Based on equations (2-44) and (2-45) it is possible to compare the oxidation capacity of various shielding gases (see Table 2.7). Included in Table 2.7 is also a slightly modified version of the International Institute of Welding (HW) classification system,36 which is based on an evaluation of retained (analytical) oxygen in the weld deposit. It is evident from these data that both systems are applicable and mutual consistent, although the former one utilises a more rational criterion for the shielding gas oxidation capacity. 2.10.1.7 Overall oxygen balance In GMA welding with solid wires, the CO content in the exhaust gas provides a direct measure of the extent of gas/metal interaction. This CO content should be compatible with that calculated from an overall oxygen balance for the reaction system.37 Example (2.8)
Consider GMA welding of low-alloy steel under the following conditions:
Table 2.7 Proposed shielding gas classification scheme for GMA welding of low-alloy steel according to equations (2-44) and (2-45). Included is also a modified version of the corresponding IIW's classification system.36 Shielding Gas Composition
[%O] tot
Vol%CO2
Vol%O 2
Vol%Ar
(wt%)
IIW's Terminology*
0-4 0-2
0-2 0-1
balance balance balance
<0.10
Lightly oxidising (<0.02)
4-10 2-5
2-5 1-2V2
balance balance balance
0.1-0.25
Oxidising (0.025-0.035)
10-25 25-100
5-8 -
balance balance
0.25-0.40
Oxidising (0.035-0.045)
8-13 -
balance balance
0.40-0.60
Strongly oxidising (0.045-0.07)
> 13
balance
>0.60
Extremely oxidising (> 0.07)
The analytical weld metal oxygen content (in wt%) is given by the values in brackets. The shielding gas is pure CO2 and is supplied at a constant rate of 15Nl min *. Based on the composition data in Table 2.8 calculate the resulting CO content in the welding exhaust gas. Solution First we calculate the nominal weld metal chemical composition by neglecting oxidation loss of alloying elements due to chemical reactions:
The dilution ratios BI(B + D) and DI(B + D) can be estimated from the classic heat flow theory presented in Chapter 1. From equations (1-75) and (1-120), we have:
Table 2.8 Chemical composition of filler wire, base plate and weld metal used in Example 2.8. C (wt%)
O (wt%)
Si (wt%)
Mn (wt%)
Filler wire
0.10
0.01
0.93
1.52
Baseplate
0.14
0.007
0.40
1.30
Weld metal
0.09
0.065
0.35
0.81
Element
and
This gives:
The extent of gas/metal interaction can then be evaluated from the observed concentration displacements:
Calculated values for the concentration displacements of carbon, oxygen, silicon and manganese utilising the composition data in Table 2.8 are given below. Element \-%X\nom.
[A%X]
C 0
-
1 2
-0.03
O 0
-
0 0 8
0.057
0
'
Si
Mn
6 3
L 3 9
-0.28
-0.58
The total CO evolution (in mol min l) can now be computed from an overall oxygen balance for the reaction system. In these calculations we shall assume that Si and Mn lost as SiO(g) and Mn(vap.) immediately react with CO2 to form SiO2 and MnO, respectively*. Taking the density of steel equal to 7.85 X 10~3 g mm"3, the total mass of weld metal produced per unit time amounts to:
Overall oxygen balance (i.e. consumption of CO2) Oxidation of carbon:
Oxidation of silicon:
:
CO 2 consumed in oxidation of iron vapour is disregarded.
Oxidation of manganese:
Increase in oxygen content:
Total CO evolution (sum):(13.4 + 53.5 + 28.3 + 9.6) X 10~3 mol CO min - 1 = 104.8 X 10~3 mol CO min' 1 Based on this information it is possible to calculate the resulting CO content in the welding exhaust gas:
A comparison with the data in Table 2.2 shows that a CO content of about 15 vol% is reasonably close to that determined by analysis. 2.10.1.8 Effects of welding parameters So far, gas/metal interactions in GMA welding has mainly been discussed in terms of the oxygen potential of the shielding gas. In the following, some consideration will be given to the effects of welding parameters on the weld metal chemistry. Amperage
When the welding current is raised, the time available for interaction decreases due to the more rapid detachment of the electrode tip droplets. At the same time the interfacial contact area increases as the average droplet size becomes smaller. From measurements of fume formation rates in GMA welding,27 it has been shown that these two counteracting effects will almost cancel, i.e. the total amount of emitted dust (in mg per g deposit) is found to be constant and nearly independent of the applied amperage. On the other hand, the total fume formation rate is probably not a reliable index for the burn-off of Si and Mn, since the evolution of iron vapour during droplet transfer will tend to conceal the corresponding loss of alloying elements. The effect of amperage (or more correct the droplet detachment frequency) on the burn-off of carbon, silicon, and manganese in CO2-shielded welding has been investigated by Smith et al.38 They found that the recovery of alloying elements in the weld deposit increased with increasing welding current (i.e. droplet detachment frequency). In view of the previous discussion, it is reasonable to assume that the higher weld metal carbon and silicon contents reported by Smith et al3S are a result of a reduced CO and SiO gas evolution at the electrode tip due to the shorter time available for chemical interaction. In the case of manganese reduced evaporation losses because of a more rapid transfer of the droplets through the arc column offers a
reasonable explanation to the increased element recovery. This shows that the weld metal chemistry is sensitive to variations in the welding current. Arc voltage
Since the arc voltage neither affects the melting rate nor the droplet size to any great extent,39 variations in the arc voltage should only have a minor effect on the weld metal chemistry. This conclusion is apparently in conflict with observations made by Lindborg,40 who found that the oxidation reactions in GMA welding were strongly voltage dependent and at the same time independent of the welding current, the droplet detachment frequency, and the mode of metal transfer (spray or short-circuiting). Consequently, further investigations are required to explain these discrepancies. Welding speed
It can be inferred from the data of Grong and Christensen1 that the analytical weld metal carbon and oxygen contents are virtually independent of the welding speed v within the normal range of GMAW (i.e. from 0.4 to 6 mm s"1). However, the intensified losses of silicon and manganese observed at low welding speeds indicate that more oxygen is absorbed in the weld pool under such conditions. This point is more clearly illustrated in Fig. 2.36 which shows a plot of [%O]tot vs v for a series of multi-pass GMA welds deposited under the shield of Ar + 10 vol% O2. It is evident that the total oxygen absorption increases nearly by a factor of two when the welding speed decreases from 6 to 0.4mm s"1. This shows that the welding speed has a marked effect on the transient oxygen pick-up in the hot part of the weld pool during GMA welding, since it controls the time available for element absorption. 2.10.2 Submerged arc welding In flux-shielded processes the reaction pattern is much more difficult to assess because of the
[%O]tot,wt%
Calculated total oxygen absorption
Travel speed, mm/s Fig. 2.36. Calculated total oxygen absorption in GMA welding at different travel speeds. Data from Grong and Christensen.1
complicating presence of the slag. For this reason most investigators have chosen to analyse empirically slag/metal reactions in SA welding. Nevertheless, some authors have been able to interpret their results on more theoretical grounds in spite of the complex reaction systems involved.41"*5 Unfortunately, these thermodynamic approaches give, at best, only a qualitative description of the compositional changes occurring during the welding operation. Recently, a kinetic model has been developed by Mitra and Eagar46 to account for variations in the element recovery in both single-pass and multi-pass SA steel weldments. From their work it is evident that the transfer of alloying elements between the slag phase and the weld metal cannot be adequately described by means of a primitive model of pseudo-equilibrium without including a more detailed analysis of the reaction kinetics. This shows that the conditions existing in SA welding are quite similar to those prevailing during GMA welding, although the experimental and theoretical challenges are much greater in the former case due to the complicating presence of a macroscopic slag phase. 2.10.2.1 Flux basicity index During SA welding of steel, oxygen may be transferred from the slag to the weld metal due to decomposition of easily reduced oxides at elevated temperatures according to the overall reaction: MxOy = xM (dissolved) + y O (dissolved)
(2-46)
where MxOy denotes any oxide component in the slag phase (e.g. SiO2, MnO or FeO). The basicity index (B.I.), originally adopted from steel ladle refining practice, is most frequently employed for assessment of oxygen pick-up in SA welding, since it gives an approximate measure of the flux oxidation capacity. A number of different expressions exists in the literature, but for the purpose of convenience the basicity index defined by Eagar47 has been adopted here: basic oxides" non- basic oxides
(2-47) where the concentration of each flux component is given in weight percent. It is evident from Fig. 2.37, which shows a typical correlation between the weld metal oxygen content and B.L, that the oxygen level of welds produced under acid fluxes (i.e. low B.I.) is strongly dependent on the basicity index. In contrast, the oxygen concentrations of welds deposited under basic fluxes are seen to be essentially independent of B.I., as indicated by the horizontal part of the curve in Fig. 2.37. It should be noted that this analysis gives no information about the extent of slag/metal interaction, since it is based on data for retained oxygen in the weld deposit. Consequently, because of the empirical nature and limited applicability of the basicity index, its role in the choice of welding fluxes for SA welding is a keenly debated question.
Oxygen content, wt%
Basic fluxes
Acid fluxes
Flux basicity index Fig. 2.37. Correlation between retained oxygen and flux basicity in SA welding. Data from Eagar.47
2.10.2.2 Transient oxygen concentrations In SA welding of C-Mn steels, the transient flux of oxygen passing through the weld pool can be estimated from the observed concentration displacements of silicon and manganese, which may be taken equal to the difference between absorbed and rejected Si and Mn, respectively: (2-48) and (2-49) If we assume that rejection of Si and Mn in the weld pool occurs as a result of MnSiO3 microslag precipitation and subsequent phase separation, [%Mn]rej^ is bound to [%Si]rej. through the following stoichiometric relationship: (2-50) Taking the ratio between absorbed Mn and Si in the weld metal equal to k, a combination of equations (2-48), (2-49) and (2-50) gives:
(2-51) The value of k is difficult to evaluate in practice, but in view of the reported mass transfer coefficients for Mn and Si a reasonable estimate would be about 0.5 in the case of manganese silicate fluxes.46 Under such conditions the total oxygen absorption, [%O]abs is given by:
(2-52) where [A%O] is the observed concentration displacement of oxygen in the weld metal, and [%O]rej. is the amount of oxygen rejected from the weld pool as a result of deoxidation reactions. Based on equation (2-52) it is possible to estimate the total oxygen absorption during SA welding of C-Mn steels from an analysis of measured concentration displacements of oxygen, silicon, and manganese in the weld metal. The results of such calculations are shown graphically in Fig. 2.38, using data from Indacochea et a/.44 It is evident from this plot that the total oxygen absorption during SA welding is much larger than that inferred from an analysis of retained oxygen in the weld deposit. The situation is thus quite similar to that observed experimentally in GMA welding (see Fig. 2.33). It should be noted that the calculated values for [%O]abs. in Fig. 2.38 may be encumbered by systematic errors due to the number of simplifying assumptions inherent in equation (2-52). However, this does not affect our main conclusion regarding the significance of the oxygen absorption, since more refined calculations give a pattern similar to that observed above (see Fig. 2.39). 2.10.3 Covered electrodes Chemical reactions during SMA welding have been studied by several investigators in the
Oxygen content, wt%
Experimental MnO-FeO-SiO2 fluxes
Retained oxygen
[A% Si]0.5 - [A%Mn] Fig. 2.38. Calculated total oxygen absorption in SA welding with experimental MnO-FeO-SiO2 fluxes. Data from Indacochea et al.AA
Oxygen content, wt%
Flux Type CS: Bead on Plate » — : Two Wires Filled Symbols: Flux FB
Absorbed oxygen Retained oxygen
Silicon content, wt% Fig. 2.39. Calculated total oxygen absorption in SA welding with commercial calcium silicate (CS) and fluoride-basic (FB) fluxes. Data from Christensen and Grong.45 past.47"51 Most of these investigators have interpreted their results as a high-temperature equilibrium between the slag and the weld metal, but a verified quantitative understanding of the transfer of elements during welding is lacking. This situation arises mainly from the lack of adequate thermodynamic data for the complex slag/metal systems involved. 2.10.3.1 Reaction model The reaction model presented here is restricted to welding with basic covered electrodes. During SMA welding gases are generated by decomposition of compounds present in the electrode coating. In the case of basic covered electrodes, the decomposition of limestone results in an atmosphere consisting predominantly of carbon monoxide and carbon dioxide, containing only small amounts OfH2 and H2O (see data in Table 2.2). The characteristic high concentrations of CO and CO2 in the arc atmosphere would be expected to lead to extensive absorption of carbon and oxygen in the weld metal. Under the prevailing circumstances, it is reasonable to assume that these reactions approach a state of local pseudo-equilibrium during droplet transfer through the arc column. During the subsequent stage of cooling in the weld pool, a supersaturation with respect to the various deoxidation reactions is initially increasing, which is released when the conditions for nucleation of the respective reaction products are reached. Since carbon is a much stronger deoxidant than silicon and manganese at temperatures above about 17000C,23 it is reasonable to assume that carbon will be in control of the oxygen level during the initial stage of cooling*, in accordance with the reaction: C (dissolved) + O (dissolved) = CO(gas)
(2-53)
* Although gases such as CO and CO2 are widely dissociated and ionised in the arc column, from a thermodynamic standpoint, there is no objection to the choice of molecular species as components for the system, provided that equilibrium is maintained down to temperatures where such species are stable.
Oxygen content, wt%
Carbon boil in the weld pool has been detected experimentally during welding with covered electrodes,49 which implies that heterogeneous nucleation of CO is kinetically feasible under the prevailing circumstances. Possible nucleation sites for CO are gas bubbles present in the macroscopic slag layer covering the metal, created by the vigorous stirring action of the arc plasma jet. It should be noted that this behaviour is in sharp contrast to experience with GMA welding, where little or no oxidation of carbon takes place in the weld pool, as shown previously in Section 2.10.1.2. It is tentatively suggested that the apparent difference between SMA and GMA welding regarding the possibilities for CO nucleation in the weld pool arises from the lack of a macroscopic slag layer in the latter case. Unlike carbon, the deoxidation capacity of silicon (and manganese) increases rapidly with decreasing metal temperatures (se Fig. 2.40), which means that carbon oxidation becomes gradually suppressed during cooling in the weld pool. Upon reaching the critical temperature indicated in Fig. 2.40, the carbon reaction is blocked, silicon and manganese now control the oxygen level. An unknown but significant fraction of the manganese silicate inclusions precipitated in the hot part of the weld pool beneath the root of the arc are brought by convection currents to the interface between the macroslag and the metal, where they are readily absorbed. The remaining fraction formed in the cold and unstirred part of the weld pool is trapped in the metal solidification front in the form of finely dispersed oxide particles. This results in a high and rather unpredictable weld metal oxygen content. The above reaction model has been tested experimentally against data obtained from a series of hyperbaric welding experiments carried out in a remotely controlled pressure chamber with basic covered electrodes containing various levels of ferrosilicon in the electrode coating (see Table 2.9). Welding under hyperbaric conditions offer the special advantage of assessing the reactions through variations in the ambient pressure without changing the composition of the electrode coating or the core wire. Consequently, if the proposed reaction model
0.1 wt%Cat10bar.
0.1 wt% C at 1 bar
Temperature,°C Fig. 2.40. The break even equilibrium temperature for silicon control of oxygen level at 0.1 wt% C and 0.3 wt% Si. Data from Elliott et al.23
Table 2.9 Contents of ferrosilicon and iron powder in the electrode coating of experimental consumables used in the hyperbaric welding experiments. Electrode
FeSi (76 wt% Si)
Iron Powder
R*
4.5 wt%
31wt%
A
5.5 wt%
30 wt%
B
6.5 wt%
29 wt%
C
7.5 wt%
28 wt%
Carbon content, wt%
^Reference electrode (E8018-C1 type electrode).
Electrode R A B C
Low FeSi levels
Total pressure, bar
Fig. 2.41. Carbon absorption in hyperbaric SMA welding. Data from Grong et al.51 is at least qualitatively correct would expect a correlation between the weld metal carbon content and the concentrations of oxygen, silicon and manganese, both under atmospheric and hyperbaric welding conditions. The main effect of pressure on weld metal chemistry is thus to suppress the carbon-oxygen reaction in the weld pool at the expense of intensified oxidation losses of silicon and manganese, as indicated by the thermodynamic data in Fig. 2.40. 2.103.2 Absorption of carbon and oxygen It is evident from the data presented Fig. 2.41 that the weld metal carbon content increases monotonically with pressure from 1 to 31 bar for all four electrodes involved. This indicates that the carbon oxidation in the weld pool is systematically suppressed under hyperbaric welding conditions. Moreover, Fig. 2.41 reveals a small but important effect of electrode deoxidation capacity on the weld metal carbon content. Since ferrosilicon itself is an insignificant source of carbon, the observed increase in the carbon concentrations with increasing additions of ferrosilicon to the electrode coating is an indication that carbon oxidation in the weld pool is blocked at an earlier stage of the process at high silicon levels, according to the reaction:
Si (dissolved) + 2CO(gas) = 2 C (dissolved) + SiO2 (slag)
(2-54)
This interpretation is further supported by the results from the oxygen determination contained in Fig. 2.42. Although there is considerable scatter in the data in this figure, it is evident that the recorded enhancement of the weld metal carbon content at high ferrosilicon levels in the electrode coating is accompanied by a corresponding reduction in the oxygen concentrations. 2.10.3.3 Losses of silicon and manganese Suppression of carbon oxidation in the weld pool at elevated pressures gives rise to intensified oxidation losses of silicon and manganese, as shown in Figs. 2.43 and 2.44. Moreover, it is apparent that increased additions of ferrosilicon to the electrode coating result in a corresponding increase in both the silicon and the manganese concentrations. This finding suggests that the final weld metal content of the deoxidants is controlled by the reaction: Si (dissolved) + 2MnO (slag) = 2 Mn (dissolved) + SiO2 (slag)
(2-55)
Assuming the activity ratio (tf Mn0 ) / (aSio2 )in precipitated slag to be constant and independent of pressure, equation (2-55) may be rewritten as: (2-56)
Oxygen content, ppm
In Fig. 2.45 the weld metal manganese content has been plotted versus the square root of the silicon content by inserting data from Figs. 2.43 and 2.44. As it appears from Fig. 2.45, the
Electrode R
A B C
Total pressure, bar Fig. 2.42. Oxygen absorption in hyperbaric SMA welding. Data from Grong et al.51
Silicon content, wt%
Electrode R A B C
Total pressure, bar
Manganese content, wt%
Fig. 2.43. Silicon oxidation in hyperbaric SMA welding. Data from Grong et al.51
Electrode R A B C
High FeSi levels
Low FeSi levels
Total pressure, bar Fig. 2.44. Manganese oxidation in hyperbaric SMA welding. Data from Grong et al.51 experimental data cluster around a straight line passing through the origin, which confirms that the silicon and manganese concentrations are balanced by a reaction according to equation (2-55).
Manganese content, wt%
Electrode R A B C
1/2 [Silicon content, wt%] Fig. 2.45. Correlation between weld metal manganese and silicon contents. Data from Grong et a/.51
2.103.4 The product [%C] [%O] From steelmaking practice, the product [%C] [%O] is generally accepted as an adequate index of the interaction between carbon and oxygen during the refining stage. This product is related to the equilibrium content of dissolved carbon and oxygen in contact with carbon monoxide of a partial pressure pco: (2-57) Here K5 is the equilibrium constant for reaction (2-53) (equal to about 2.0 X 10"3 at 16000C and 2.6 X 10~3 at 20000C),23 Nco is the mole fraction of CO in the reaction product (equal to the partial pressure of CO at 1 bar), andptotis the total ambient pressure. During the initial stage of cooling in the weld pool, the oxygen content in an assumed equilibrium with carbon would be expected to be higher than the analytical values. This situation applies in particular to welds made under hyperbaric conditions, where significant quantities of oxygen clearly are removed from the weld pool in the form of oxide inclusions after the completion of the carbon oxidation. The concentration of dissolved oxygen at the break even temperature for silicon control of the oxygen level can be estimated from the measured concentration displacements of oxygen, silicon and manganese in the weld deposit with increasing pressures, relative to 1 bar (designated A[%(9], A[%Si] and A[%Mrc], respectively). If the total amount of oxygen which reacts with silicon and manganese at 1 bar, as a first approximation, is taken equal to the analytical weld metal oxygen content, the following balance is obtained:
(2-58)
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Here [%0]eq. is the oxygen concentration in an assumed equilibrium with carbon at a given pressure, and [%O]anaL is the analytical weld metal oxygen content. For this correlation, minor vaporisation losses of manganese as well as possible reactions between oxygen and liquid iron have been neglected. In Fig. 2.46 the product m = [%C] [%O] is plotted vs the total ambient pressure. Calculations of m have been done both on the basis of [%O]anaL and [%O]eq. It can be seen from Fig. 2.46 that the former set of data (i.e. open symbols in the graph) cannot be represented by a straight line passing through the origin, which should apply to a true equilibrium reaction. However, when proper corrections are made for the amount of oxygen removed from the weld pool after the completion of the carbon oxidation, such a correlation may be obtained as shown by the solid line in Fig. 2.46. No clear effect of the electrode deoxidation capacity (i.e. ferrosilicon content) on the product m = [%C] [%O] can be observed within the precision of measurements. This result is to be expected if the weld metal carbon content is controlled by a local equilibrium with oxygen established at elevated temperatures in the weld pool. Also, inspection of the slope of the curve (i.e. heavy solid line in Fig. 2.46) indicates that the product K5Nco is about 1.14 X 10~3 under the prevailing circumstances. If a reasonable average value for the equilibrium constant K5 of 2.3 X 10~3 is assumed within the specific temperature range of the reaction, we get: Nco~0.5 (2-59) The above calculations suggest that the controlling partial pressure of CO in the reaction product is significantly lower than the ambient pressure under hyperbaric welding conditions. This probably arises from an extensive infiltration of helium in the nucleating bubbles at the slag/metal interface which, thermodynamically, will enhance the deoxidation capacity of carbon according to Le Chatelier's Principle. The conditions existing in hyperbaric SMA welding thus appear to be similar to OBM/Q-BOP steelmaking, where simultaneous injection of oxygen and inert gas from the bottom of the convenor during the decarburisation stage results in a steel carbon content which is typically below the value calculated for equilibrium between oxygen and carbon at 1 atm partial pressure of CO.52
2.11 Weld Pool Deoxidation Reactions During cooling, the metal concentrations established at high temperatures due to dissolution of oxygen tend to readjust by precipitation of new phases. Accordingly, a supersaturation with respect to the various deoxidation reactants initially increases and thus provides the driving force for nucleation of oxides. Subsequently, the deoxidation reactions will proceed rapidly through growth of nuclei above a critical size. Equilibrium conditions will finally establish the limits for the degree of deoxidation that can be achieved. In spite of the fact that large amounts of oxygen are removed from the weld pool during the deoxidation stage, the analytical weld metal oxygen content exceeds by far the value predicted from chemical thermodynamics, assuming that equilibrium conditions are maintained down to the solidification temperature (see data in Table 2.5). This situation cannot be ascribed to a large deviation from chemical equilibrium, but is mainly a result of an incomplete phase separation. Consequently, due consideration must be given to the kinetics. The three basic consecutive steps in steel deoxidation are shown in Fig. 2.47.
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Here [%0]eq. is the oxygen concentration in an assumed equilibrium with carbon at a given pressure, and [%O]anaL is the analytical weld metal oxygen content. For this correlation, minor vaporisation losses of manganese as well as possible reactions between oxygen and liquid iron have been neglected. In Fig. 2.46 the product m = [%C] [%O] is plotted vs the total ambient pressure. Calculations of m have been done both on the basis of [%O]anaL and [%O]eq. It can be seen from Fig. 2.46 that the former set of data (i.e. open symbols in the graph) cannot be represented by a straight line passing through the origin, which should apply to a true equilibrium reaction. However, when proper corrections are made for the amount of oxygen removed from the weld pool after the completion of the carbon oxidation, such a correlation may be obtained as shown by the solid line in Fig. 2.46. No clear effect of the electrode deoxidation capacity (i.e. ferrosilicon content) on the product m = [%C] [%O] can be observed within the precision of measurements. This result is to be expected if the weld metal carbon content is controlled by a local equilibrium with oxygen established at elevated temperatures in the weld pool. Also, inspection of the slope of the curve (i.e. heavy solid line in Fig. 2.46) indicates that the product K5Nco is about 1.14 X 10~3 under the prevailing circumstances. If a reasonable average value for the equilibrium constant K5 of 2.3 X 10~3 is assumed within the specific temperature range of the reaction, we get: Nco~0.5 (2-59) The above calculations suggest that the controlling partial pressure of CO in the reaction product is significantly lower than the ambient pressure under hyperbaric welding conditions. This probably arises from an extensive infiltration of helium in the nucleating bubbles at the slag/metal interface which, thermodynamically, will enhance the deoxidation capacity of carbon according to Le Chatelier's Principle. The conditions existing in hyperbaric SMA welding thus appear to be similar to OBM/Q-BOP steelmaking, where simultaneous injection of oxygen and inert gas from the bottom of the convenor during the decarburisation stage results in a steel carbon content which is typically below the value calculated for equilibrium between oxygen and carbon at 1 atm partial pressure of CO.52
2.11 Weld Pool Deoxidation Reactions During cooling, the metal concentrations established at high temperatures due to dissolution of oxygen tend to readjust by precipitation of new phases. Accordingly, a supersaturation with respect to the various deoxidation reactants initially increases and thus provides the driving force for nucleation of oxides. Subsequently, the deoxidation reactions will proceed rapidly through growth of nuclei above a critical size. Equilibrium conditions will finally establish the limits for the degree of deoxidation that can be achieved. In spite of the fact that large amounts of oxygen are removed from the weld pool during the deoxidation stage, the analytical weld metal oxygen content exceeds by far the value predicted from chemical thermodynamics, assuming that equilibrium conditions are maintained down to the solidification temperature (see data in Table 2.5). This situation cannot be ascribed to a large deviation from chemical equilibrium, but is mainly a result of an incomplete phase separation. Consequently, due consideration must be given to the kinetics. The three basic consecutive steps in steel deoxidation are shown in Fig. 2.47.
[%C][%O]x102
Electrode R A B C
Total pressure, bar
Separation Stage Buoyancy Surface tension Stirring
Growth Stage Diffusion of reactants in the melt to the oxide nuclei Particle coalescence
Nucleation Stage Homogeneous nucleation Heterogeneous nucleation
Average particle size
Fig. 2.46. The product [%C][%0] in hyperbaric SMA welding. Solid symbols: calculations based on [%O]eq.. Open symbols: calculations based on [%O]anai.- Data from Grong et al. 51
Reaction time
Fig. 2.47. The three major consecutive steps in steel deoxidation (schematic).
Although rate phenomena in ladle refining of liquid steel are extensively investigated and reported in the literature,53"55 only recently attempts have been made to include such effects in an analysis of deoxidation reactions in arc welding. 1 ' 56 ' 57 2.11.1 Nucleation of oxide inclusions During ladle-refining of liquid steel, it is well established that homogeneous nucleation of oxide inclusions may occur in certain regions of the melt where the supersaturation is sufficiently high.55'58 Over the composition range normally applicable to deoxidation of steel, the number of nuclei formed at the time of addition of deoxidisers is approximately 105 mirr 3 . 55 However, in steel weld metals, the number of oxide nuclei formed during the initial stage of deoxidation must be considerably higher to account for the observed inclusion number density of about 107 mm~3 to 108 mm"3.56'57 This implies that the supersaturation established in the weld pool on cooling as a result of rapid temperature fluctuations (~103 0C s"1) exceeds by far that obtained by additions of deoxidisers to a liquid steel melt under approximately isothermal conditions. There are several theories available for treating nucleation phenomena, but for the purpose of convenience, a simplified version of the model of Turpin and Elliott58 has been adopted here. Consider a steel melt which is brought to a state of supersaturation by first equilibrating it with pure MxOy at a high temperature T\ and then rapidly cooling it to a lower temperature T2, as shown schematically in Fig. 2.48. It follows from the classical theory of homogeneous nucleation that the required temperature difference T1-T2 necessary to achieve spontaneous precipitation of MxOy is approximately given by the following relationship:
(2-60) where AH° is the standard enthalpy of reaction, G is the oxide-steel interfacial energy (assumed to be constant and independent of temperature), and Vm is the molar volume of the nucleus. The derivation of equation (2-60) is shown in Appendix 2.2. Example (2.9)
Assume that precipitation of manganese silicates in the weld pool occurs according to the following reaction: Si (dissolved) + Mn (dissolved) + 3 O (dissolved) = MnSiO3 (slag)
(2-61)
where AG°(J) = 858620 + 3457. Based on equation (2-60), calculate the critical temperature interval of subcooling for homogeneous nucleation OfMnSiO3. Typical physical data for liquid steel and manganese silicate slags are given in Table 2.10.
£
Time
Fig. 2.48. Idealised model for homogeneous nucleation of oxide inclusions in steel weld metals (schematic). Table 2.10 Physical data for liquid steel and manganese silicate slags at 16000C. Data from Refs. 3 and 53.
Property
Density (kgnr 3 )
Viscosity (kgm^s- 1 )
Steel
6900
4.3 X 10~3
Silicate slag
2300
-
Interfacial Energyt (Jm" 2 )
0.8
1
In contact with liquid steel.
Solution
First we estimate the molar volume of the nucleus:
By inserting the appropriate values for Vm, AH°, and a in equation (2-60), we obtain:
from which
If we assume that the supersaturation is released at T2 = 16000C (1873K), the initial temperature of the liquid T1 becomes:
The critical temperature interval of subcooling is thus:
Critical temperature interval, AT (0C)
Similar calculations can also be carried out for other types of oxide inclusions, e.g. FeO(I), SiO2(s), and Al2O3(S). The results of such computations are presented graphically in Fig. 2.49, using data from Refs 55 and 58. It is evident from these plots that the critical temperature interval of subcooling depends on the interfacial energy, G. Although data for oxide-steel interfacial energies are scarce, the following average values are frequently used in the literature, 5558 i.e. a(FeO-Fe) = 0.3 J m"2; G(SiO2-Fe) = 0.9 J m~2; and G(Al2O3-Fe) - 1.5 J mr2. If these values are accepted, the results in Fig. 2.49 indicate that the critical temperature interval of subcooling for homogeneous nucleation of FeO (1), SiO2(s), and Al2O3(S) is of the order of 200 to 30O0C. Considering the fact that the liquid weld metal spans a temperature range of about 2200 to 15000C,34 it is not surprising to find that nucleation of oxide inclusions occurs readily in the weld pool during cooling. It should be noted that the quoted data for G are representative of ladle-refined steel deoxidised at 16000C. At higher metal temperatures, in the presence of large amounts of dissolved oxygen, the oxide-steel interfacial energies would be expected to be significantly lower.59 Hence, it is reasonable to assume that the actual temperature interval of subcooling required for spontaneous oxide precipitation in a weld pool is well below 2000C.
Interfacial energy,o(J/m2) Fig. 2.49. Critical temperature interval of subcooling for homogeneous nucleation of oxide inclusions in steel weld metals at 16000C as a function of the interfacial energy a.
2.11.2 Growth and separation of oxide inclusions In practice, there are three major growth processes in steel deoxidation:55
(i) Collision (ii) Diffusion (iii) Ostwald ripening. From deoxidation and ladle refining of liquid steel it is well established that the flotation rate of the oxides generally depends on their growth rates, since large inclusions separate much more rapidly than small ones, in agreement with Stokes law.55 Growth of the oxides can proceed either through diffusion of reactants in the melt to the oxide nuclei or by collision and coalescence of ascending inclusions, and is therefore influenced by factors such as the number density of the nuclei, interfacial tensions, and the extent of melt stirring.53"55 The last factor is of particular importance in welding, because the stirring action will increase the possibilities for collision and coalescence of inclusions and, depending on the direction of flow, can give rise to circulation of inclusion-laden metal to the surface. As a result, the separation of small oxide particles, i.e. microslag, is strongly favoured by the turbulent conditions existing in the hot part of the weld pool immediately beneath the root of the arc. 2.11.2.1 Buoyancy (Stokes flotation) Assessment of the role of buoyancy (Stokes flotation) in the separation of deoxidation products from the weld pool can be done on the basis of the experimental data of Grong et ai56 reproduced in Fig. 2.50. It is evident that a change in the welding position (i.e. from flat to overhead position) has no significant effect on the weld metal oxygen content. This shows that the buoyancy effect does not play an important role in the separation process of oxide inclusions during welding.
Oxygen content, wt%
Upward welding Downward welding
Horizontal
Welding orientation, degrees Fig. 2.50. Effect of welding position on retained oxygen in GMA steel weld deposits. Data from Grong et a/. 56
The above conclusion is also in agreement with predictions based on the Stokes law, which gives the terminal velocity of the ascending particles (u) relative to the liquid:55 (2-62) where g is the gravity constant, dv is the particle diameter, Ap is the difference in densities between the liquid steel and the inclusions, and |x is the steel viscosity. Taking the Stokes parameter, gAp/18|ji, equal to 0.6 jjinr1 s"1 for manganese silicate slags in steel (Table 2.10), equation (2-62) becomes: (2-63) Generally, the majority of non-metallic inclusions in steel weld metals are of a diameter below 2 jxm.56'57 According to equation (2-63), such particles have a relative velocity less than 2.4 |xm s"1. This implies that the buoyancy effect alone is far too insignificant to promote flotation of the inclusions out of the weld pool before solidification, when it is recognised that the average fluid flow velocity in the weld pool is four to five orders of magnitude higher (to be discussed later). Stokes law is based on the assumption that the inclusions are completely wetted by the liquid steel, i.e. there is no slip at the oxide/metal interface.55 Normally, interfacial tension effects promote slip at the particle/metal interface, which, in turn, enhances the flotation rate of the ascending oxides (often referred to as the Plockinger effect).60 The concept of a wetting angle has been used in this context. But, the slip phenomenon is probably perceived better in terms of a secondary flow in the interfacial region between the liquid metal and the solid precipitate, which is produced by gradients in interfacial tension. In the rare case of no wetting (0 = 180°), it has been shown that the average terminal velocity of the inclusions is approximately 50% higher than that given by equation (2-62).55 For silica slags, the wetting angle (in the presence of air) is close to 115°,54 indicating that the correction in the particle terminal velocity due to the slip at the oxide/metal interface in less than about 30%. Consequently, interfacial tension effects between the slag and the steel do not significantly affect the flotation rate of the particles, and, therefore, can be ignored. 2.11.2.2 Fluid flow pattern It is evident from the above discussion that the separation of deoxidation products during arc welding is controlled by the fluid flow fields set up within the weld pool. The typical flow pattern in a submerged arc weld pool is shown in Fig. 2.51. It can be seen from the figure that a depression is formed at the forward edge of the pool, which forces the melted metal to flow underneath and on either side of the depression, following the arrows in Fig. 2.51. At the rear of the weld pool the flow direction is reversed, and the metal streams back along the pool surface. A similar flow pattern has also been observed in GMA weld pools.61 As a result, the inclusions precipitated in the turbulent part of the weld pool are rapidly brought to the upper surface behind the arc due to the high-velocity flow field created within the liquid metal, and disengaged by the surface tension effects in the pool. The drag force exerted on the particles because of the liquid flow-field velocity can be estimated from published data for weld pool flow velocities following electromagnetic fluid mechanics theory. Normally, for weld pools the Peclet number for heat transfer lies within the
range from 10 to 5000, which indicates that the heat flow is predominately convectional.62 The limits quoted above for the Peclet number correspond to a range in the average weld pool fluid velocity from about 0.025 to 0.4 m s"1 in the case of SA welding.6364 Unfortunately, specific information about the fluid flow velocity gradients in the weld pool are lacking, which prevents a more complete analysis of variations in the flow pattern with increasing distance from the root of the arc. Generally, the drag force, Fd, acting on a spherical particle in relative motion to a fluid can be expressed as:3 (2-64) where Cd is the drag coefficient, p is the fluid density, u is the bulk velocity of the fluid relative to the particle, and dv is the particle diameter. The drag coefficient is, in turn, a function of the particle Reynolds number, A^,:3 (2-65) where |x is the fluid viscosity. Typical physical-property data for liquid steel are given in Table 2.10. By inserting the values for p and JJL from Table 2.10, then using the relative velocity calculated in equation (2-63) (2.4 |xm s"1) as one extreme and the fluid flow velocity (0.4 m s"1) as the other (i.e. assuming a stationary particle), one can demonstrate that the particle Reynolds numbers obtained never exceed 1.3 for most weld metal inclusions. The limit calculated above for the Reynolds number is within the so-called creeping flow region where Stokes law is indeed valid. Under such conditions, the ratio between the particle drag force Fd and the corresponding gravity force Fg is given by the expression:3 (2-66) Note that equation (2-66) is the basis for obtaining Stokes law (equation (2-62)). For steady motion of the particle, Fd and Fg are, of course, equal. However, the significance of Fd can also be interpreted in a transient sense, by considering the limiting case where the particle is stationary and its instantaneous motion is governed by the forces acting on it. In this case, the ratio of Fd (max) acting on the particle relative to the net gravity force (given by Electrode
Pulsating cavity
Base plate
Fig. 2.51. Typical flow pattern in SA weld pools. For clarity, the arc, slag and flux have been omitted. The sketch is based on the ideas of Lancaster.32
equation (2-66)) can determine the dominant force responsible for the particle's trajectory. In Fig. 2.52 the above ratio has been calculated and plotted against the particle diameter, dv, for values of u' equal to 0.025 and 0.4 m s"1, which represent the typical velocities reported for SA steel weld pools. 63 ' 64 It can be seen from the figure that the drag force is always several orders of magnitude greater than the gravity force for particles within the typical size range of weld metal inclusions (i.e. less than 2 |xm in diameter). This result is to be expected, since the relative velocity, based on Stokes law and calculated in equation (2-63), is negligible compared with the liquid velocities in the weld pool (2.4 \xm s"1 vs 0.02 to 0.4 m s"1). This calculation thus supports our previous conclusion that the separation of the oxide inclusions is controlled solely by the fluid flow behaviour in the weld pool. The fact that the phase separation proceeds under strongly turbulent conditions is also evidenced by the large number of iron droplets being mechanically dispersed in the top bead slag of GMA steel welds, as shown by the optical micrographs in Fig. 2.53. In the case of GMA welding, the non-metallic inclusions that are brought to the upper surface behind the arc coalesce rapidly to form large slag clusters that float on the top of the bead. Generally, re-entrapment of the slag does not occur owing to the decrease in the total surface free energy of the system, which is caused by the emergence of the inclusions from the weld metal.54 Consequently, the slag will remain floating on the top of the bead even when welding is performed in the overhead position, as shown previously in Fig. 2.50.
*ci(max/Fg
2.11.2.3 Separation model Based mainly on experience with the GMA welding process, a simple model for the assessment of the sequence of deoxidation reactions in arc welding has been proposed,1 and is shown schematically in Fig. 2.54. The model is based on the assumption that equilibrium between the reacting elements and precipitated slag is maintained down to low metal temperatures, and divides the weld pool into the following two main reaction zones:
Inclusion diameter, |i.m Fig. 2.52. The ratio between maximum particle drag force, Fornax) and the corresponding gravity force, F8, vs the inclusion diameter at two different flow velocities in the weld pool. Calculations are based on equation (2-66).
(a)
(b)
Fig. 2.53. Optical micrographs showing characteristic "comet's tails" of trapped iron droplets (light areas) in collected top bead slags of GMA steel welds; (a) Ar + 5vol%O2, (b) Ar + 5vol%CO2.
Electrode (a)
Cold part of weld pooN
Arc
Hot part of weld pool Base plate
S e c t i o n A-A
Cold part of weld pool: Hot part of weld pool: Deoxidation/phase Deoxidation/incomplete separation phase separation
Temperature
(b)
Final weld metal, oxygen concentration
Oxygen content Fig. 2.54. Schematic diagrams showing the sequence of reactions occurring during weld metal deoxidation; (a) Longitudinal section of weld pool, (b) Cross section of weld pool along A-A. The diagrams are based on the ideas of Grong and Christensen.1
(i) The hot part of the weld pool, characterised by simultaneous oxidation and deoxidation of the metal, where the separation of microslag takes place continuously as a result of highly turbulent flow conditions. (ii) The cold part of the weld pool, where precipitated slag will largely remain in the metal as finely dispersed particles as a result of inadequate melt stirring. Under such conditions equation (2-23) predicts a direct correlation between absorbed and retained (analytical) oxygen in the weld metal, i.e.:
(2-67) in agreement with experimental observations (see plots in Figs. 2.33, 2.38, and 2.39). Typically, the proportionality constant C4 varies between 0.1 to 0.2, which corresponds to a range in the t/to ratio from 2.3 to 1.6. This shows that the boundary between 'hot' and 'cold' parts of the weld pool is not well defined, but depends on the welding system under consideration as well as on the operational conditions applied. 2.11.3 Predictions of retained oxygen in the weld metal Although the weld metal oxygen content is controlled by a transport mechanism in the weld pool, the concept of pseudo-equilibrium can still be used for an assessment of slag/metal reactions in arc welding. 2.11.3.1 Thermodynamic model In the case of silicon deoxidation of steel weld metals, we may write: Si (dissolved) + 2 O (dissolved) = SiO2 (slag)
(2-68)
On introduction of the equilibrium constant for the reaction, we obtain: (2-69) To allow for the decrease in the silica activity with increasing manganese-to-silicon ratios, it is essential to establish a correlation that links the activity of silica to the concentrations of the deoxidation elements in the weld metal. A semi-empirical corr61ation of this kind has been presented by Walsh and Ramachandran,65 derived from a re-analysis of activity data for silica in the Fe-Mn-Si-O system previously published by Hilty and Crafts.66 Within the temperature range from 1550 to 16500C, they showed that the silica activity in the deoxidation product can be approximately expressed as: (2-70) where K1 represents the manganese-to-silicon ratio at which the activity of silica becomes
unity for a given temperature. A check of this equation against more recent data for silica activities in MnO-SiO2 slags reported by Turkdogan67 supports the findings of Walsh and Ramachandran65 that the activity of silica is approximately given by equation (2-70) for a wide range in the steel manganese-to-silicon ratio (i.e. from 0.1 to 50). By combining equations (269) and (2-70), it is possible to obtain an expression for the equilibrium oxygen content, solely in terms of the silicon and manganese concentrations: (2-71) where K^ is a temperature-dependent parameter equal to (K1I K6)05. The temperature dependence of the Si-O reaction (equation (2-68)) is well established and is approximately given by the relationship:23 (2-72) when pure SiO2 is used as the standard state for the silica activity. For a rough estimate of the temperature dependence of equation (2-70), the results of Turkdogan55 can be used. It should be noted that Walsh and Ramachandran65 did calculate the temperature dependence of K1 within the range from 1550 to 16500C. However, because equation (2-70) is empirical, the function cannot be extrapolated beyond these temperature limits. The data quoted in Ref. 55 are derived directly from the Si-Mn reaction (equation (2-55)) and activity data for MnO at silica saturation. On introduction of the equilibrium constant for equation (2-55), we obtain: (2-73) By using data from Ref.55, the initial [%Mn]2/[%Si] ratio for precipitation of silica saturated slags (equal to K9(aMnO)2) at 1500,1550,1600 and 16500C has been recorded and replotted against temperature, as shown in Fig. 2.55. The figure shows that the critical [%Mn]2/[%Si] ratio for precipitation of silica saturated slags is temperature dependent and decreases from about 5 at 15000C to below 1.5 at 16500C. On the basis of a crude extrapolation of the data to higher metal temperatures, it can, however, be argued that the ratio would approach a constant value of approximately 0.75 at temperatures beyond about 17500C (indicated by the broken horizontal line in Fig. 2.55). The above observation reflects the fact that the Si-Mn-O reaction equilibrium (equation (2-55)) is not very sensitive to a change in temperature (i.e. the enthalpy for the reaction is small). Over the composition range normally applicable to Si-Mn deoxidation of steel weld metals the observed threshold for the critical [%Mn]2/[%Si] ratio for precipitation of silica-saturated slags in Fig. 2.55 corresponds to a manganese-to-silicon ratio closely equal to unity. Consequently, at temperatures higher than about 17500C, K1 can, as a first approximation, be taken constant and independent of temperature (i.e. K1- Y). The temperature dependence of equation (2-71) is thus simply (1/^ 6 ) 05 or: (2-74)
for temperatures higher than about 17500C (2023K).
[%Mn]2/[%Si]
Temperature, 0C Fig. 2.55. The critical [%Mn]2/ [%Si] ratio for precipitation of silica-saturated slags as a function of temperature. Data from Turkdogan.55
2.11.3.2 Implications of model Figure 2.56 shows plots of retained (analytical) oxygen in GMA and SMA steel weld metals vs the theoretical deoxidation parameter ([%Si][%Mn])~°25, using relevant literature data. 5668 This parameter allows for the inherent decrease in the silica activity with increasing weld metal Mn to Si ratios. A closer inspection of the slopes of the curves reveals that the effective reaction temperature falls within the range calculated for chemical equilibrium between silicon, manganese, and oxygen at 1800 to 19000C. Although the boundary between 'hot' and 'cold' parts of the weld pool for possible inclusion removal in practice is not sharp, the results in Fig. 2.56 literally suggest that all oxides precipitated above 1800 to 19000C are simultaneously removed from the weld pool under the prevailing turbulent flow conditions. At lower temperatures, the degree of melt stirring is too low to promote separation of the deoxidation products out of the pool before solidification and hence, they are trapped in the metal solidification front in the form of finely dispersed inclusions. Moreover, the observed difference in the effective reaction temperature between GMA and SMA welding supports our previous conclusion that any change in welding parameters, flux or shielding gas composition, which alters the fluid flow pattern in the weld pool, will often have a stronger influence on the weld metal oxygen content than variations in the deoxidation practice. This implies that control of the weld metal oxygen level through additions of deoxidants, in practice, is difficult to achieve.
2.12 Non-Metallic Inclusions in Steel Weld Metals Inclusions commonly found in steel weldments will either be exogenous or indigenous, dependent on their origin. The first type arises from entrapment of welding slags and surface scale, while indigenous inclusions are formed within the system as a result of deoxidation reactions (oxides) or precipitation reactions (nitrides, sulphides). The latter group is almost always seen to be heterogeneous in nature both with respect to chemistry (multiphase parti-
Oxygen content, wt%
GMA Welding SMA Welding
([%SI] [%Mn]f°"25 Fig. 2.56. Examples of pseudo-equilibrium in GMA and SMA welding of C-Mn steels. The solid lines in the graph represent thermodynamical calculations at indicated temperatures. Data from Refs. 56 and 68. cles), shape (angular or spherical particles), and crystallographic properties as a result of the complex alloying systems involved69 (see Fig. 2.57). An exception may be C-Mn steel welds, where the oxide inclusions will be predominately glassy, spherical, manganese silicates.1 A survey of important weld metal inclusion characteristics is given in Table 2.11. 2.12.1 Volume fraction of inclusions It is evident from Table 2.11 that the volume fraction of non-metallic inclusions in steel weld metals normally falls within the range from 2 X 10~3 to 8 X 10~3, depending on the type of weld under consideration. Based on simple stoichiometric calculations it is possible to convert the analytical weld metal oxygen and sulphur contents to an equivalent inclusion volume fraction when the chemical composition of the reaction products is known. This is shown below. Table 2.11 Summary of weld metal inclusion characteristics. The data are compiled from miscellaneous sources. Size Distribution*
Chemical Composition
Type of Weld
C-Mn steel weld metals Low-alloy steel weld metals
Constituent elements
Reported phases
10-50
Si, Mn, O, S (traces of Al, Ti, and Cu)
SiO2, MnOSiO2, MnS, (CuxS)
10-40
Al, Ti, Si, Mn, O, S, N (Cu)
MnOAl2O3, 7-Al2O35TiN, MnOSiO2, SiO2, a-MnS, (3-MnS, (Cu^S)
Vv X 10"3
dv
NvX 107
Sv
3-8
0.3-0.6
1-10
2-6
0.3-0.7
0.5-5
*Vy: volume fraction; dv: arithmetic mean (3-D) particle diameter (jxm); Nv: number of particles per unit volume (mm"3); Sv\ total particle surface area per unit volume (mm2 per mm3).
Fig. 2.57. Digital STEM brightfield image and Si, Al, S, Mn and Ti X-ray images of a multiphase weld metal inclusion. After Kluken and Grong.57
Solution
First we calculate the total weight of retained MnOSiO2 per 100 g weld metal:
This corresponds to an equivalent volume fraction of:
Similarly, we can calculate the weight and volume fraction of MnS in the weld metal:
and
The total volume fraction of MnOSiO2 and MnS is thus:
In practice, the stoichiometric conversion factors for oxygen and sulphur are virtually constant for a wide spectrum of inclusions70 and hence, they can be regarded as independent of composition. Taking the solubility of sulphur in solid steel equal to 0.003 wt%, the following relationship is obtained for steel weld metals:57'70 (2-75) The validity of equation (2-75) has been confirmed experimentally by comparison with microscopic assessment methods.5771 In steel weld metals the majority of the inclusions will be in the submicroscopic range owing to the limited time available for growth of the oxides. From the histogram in Fig. 2.58 it is seen that particles with diameters between 0.3 to 0.8 |xm contribute to nearly 50 percent of the total inclusion volume fraction. This trend is not significantly changed by additions of strong deoxidisers, such as aluminium and titanium, or by a moderate increase/decrease in the heat input.57 2.12.2 Size distribution of inclusions As shown in Fig. 2.59 the majority of the three-dimensional (3-D) inclusion diameters fall within the range of 0.05 to 1.5 |xm, with a characteristic peak in the particle frequency at about 0.4 to 0.5 |jim. These data obey the log-normal law, since a plot of the frequencies against the logarithms of the diameters approximately gives a symmetrical curve. Considering specific inclusion size classes, deoxidation with aluminium generally results in a higher fraction of coarse particles (> 1 |xm) due to incipient clustering of Al2O3.57' 69 However, the observed particle clustering has no significant influence on the arithmetic mean 3-D inclusion diameter, as shown by the data in Fig. 2.59.
Relative volume fraction (%)
Particle diameter (jim) Fig. 2.58. Percental contribution of different size classes to the total volume fraction of non-metallic inclusions in a low-alloy steel weld metal. Data from Kluken and Grong.57
2.12.2.1 Effect of heat input In contrast to the situation described above, the 3-D inclusion size distribution is strongly affected an increase in the heat input (see Fig. 2.60). At 1 kJ mm"1, the measured 3-D inclusion diameters fall within the range from 0.05 to 1 |xm, with a well-defined peak in the particle frequency at about 0.3 |xm. When the heat input is increased to 8 kJ mm"1, the content of coarse inclusions will dominate (>0.5 |xm), which results in a broader distribution curve and a shift in the peak frequency towards larger particle diameters. A comparison with Fig. 2.61 reveals that the arithmetic mean 3-D inclusion diameter is approximately a cube-root function of the heat input. This result is to be expected if Ostwald ripening is the dominating coarsening mechanism in the cold part of the weld pool (to be discussed below). 2.12.2.2 Coarsening mechanism As already mentioned in Section 2.11.2 there are three major growth processes in steel deoxidation, i.e. (i) collision, (ii) diffusion, and (iii) Ostwald ripening. In the cold part of the weld pool, particle growth by collision can be excluded in the absence of adequate melt stirring because of a low collision probability of inclusions while ascending in the molten steel within the regime of Stokes law.72 In addition, the diffusion-controlled part of the deoxidation reaction (which involves diffusion of reactants in the melt to the oxide nuclei) would be expected to be essentially complete within a fraction of a second when the number of nuclei is greater than 107 mm"3.55 This implies that the observed increase in the inclusion diameter with increasing heat inputs (Fig. 2.61) can be attributed solely to Ostwald ripening effects. Before discussing details of the inclusion growth kinetics, it is essential to clarify the temperature level in the 'cold' part of the weld pool. As shown by the results in Fig. 2.62, the liquid metal temperature in the trailing edge of the weld pool is fairly constant and slightly above the melting point of the steel. Accordingly, inclusion growth in welding (at a fixed volume fraction) can be treated as an isothermal process, where the time dependence of the mean particle diameter dv is approximately given by the Wagner equation:
(a)
Frequency (%)
Low Al (0.018 wt%) Low Ti (0.005 wt%)
Particle diameter (fxm)
(b) High Al (0.053 wt%) Frequency (%)
High Ti (0.053 wt%)
Particle diameter, p,m Fig. 2.59. Three-dimensional (3-D) size distribution of non-metallic inclusions in two different lowalloy steel weld metals; (a) Low weld metal aluminium and titanium levels, (b) High weld metal aluminium and titanium levels. Data from Kluken and Grong.57
(2-76)
Here do is the initial particle diameter, a is the oxide-steel interfacial energy, Dm is the element diffusivity, Cm is the element bulk concentration, V'm is the molar volume of the oxide per mole of the diffusate, and t is the retention time.
Frequency (%)
Particle diameter, p,m
Particle diameter, u,m
Fig. 2.60. Effect of heat input on the 3-D inclusion size distribution in low-alloy steel weld metals. Data from Kluken and Grong.57
Heat input, kJ/mm
Fig. 2.61. Variation of arithmetic mean 3-D inclusion diameter with heat input during SA welding. Data from Kluken and Grong.57 For welding of thick plates, the time available for growth of particles in the 'cold' part of the weld pool can be estimated from the Rosenthal equation, i.e. equation (1-45) in Section 1.10.2 (Chapter 1). If the characteristic length of the cooling zone is taken equal to the weld ripple lag (defined in Fig. 2.63), the retention time t is approximately given by the following relationship:
Temperature, C°
"Tpeak = 1538°C (about 8 mm from edge of weld pool)
Time, seconds Fig. 2.62. Measured temperature level in the trailing edge of the weld pool during GMA welding. Data from Kluken and Grong.57
Top view of weld crater (z = 0)
Max. width
Retention time Weld ripple lag Welding speed Heat source
Fusion boundary
Fig. 2.63. Definition of weld ripple lag xm, and retention time t.
(2-77) where J\ is the arc efficiency (equal to about 0.95 for SAW and 0.80 for GMAW /SMAW), and E is the gross heat input (kJ mm"1). Note that equation (2-77) assumes constant values for the steel thermal diffusivity and volume heat capacity (5 mm2 s"1 and 0.0063 J mm"3 0C"1, respectively), and no preheating (T0* = 200C). In Fig. 2.64 the Ostwald ripening theory has been tested against relevant literature data, which may be considered representative of the 3-D particle size distribution. Although there is some scatter in the data, the observed inclusion growth rates fall within the range calculated for oxygen diffusion-controlled coarsening of SiO2 and Al2O3 at 15500C, using the Wagner equation. In these calculations, a reasonable average value for the bulk diffusivity of oxygen has been assumed (i.e. 10~2 mm2 s"1).55 If the effective inclusion growth rate constant for lowalloy steel weld metals is taken equal to the slope of the curve in Fig. 2.64, the following relationship is achieved:
GMAW SAW
dv,jLim
SMAW
•1/3 i i sJ/3 Fig. 2.64. Relation between arithmetic mean (3-D) inclusion diameter dv and retention time t for different arc welding processes. Data compiled by Kluken and Grong.57 CoId1 part of weld pool
Deoxidation Phase separation Deoxidation Incomplete phase; separation Homogeneous nucleation
Growth of inclusions
Oxidation
Solid weld metal
Temperature
Gas/metalslag/metal reactions
Solid weld metal
1
'Hot' part of weld pool
Ostwald ripening
Time Fig. 2.65. Proposed deoxidation model for steel weld metals (schematic). The diagram is based on the ideas of Kluken and Grong.57
(2-78) By substituting equation (2-77) into equation (2-78), we obtain a direct correlation between the arithmetic mean 3-D inclusion diameter dv and the net heat input T\E: (2-79)
Equation (2-79) predicts that dv is a simple cube root function of E, in agreement with the experimental data in Fig. 2.61. It should be noted that the measured shape of the particle distributions (see Figs. 2.59 and 2.60) deviates somewhat from that required by the Wagner equation, which assumes a quasistationary distribution curve, and that the maximum stable particle diameter is about 1.5 times the mean diameter of the system.73 Although the origin of this discrepancy remains to be resolved, this suggests that particle clustering is also a significant process in steel weld metals as it is in other metallurgical systems. In fact, such effects would be expected to be most pronounced at high aluminium levels because of a large interfacial energy between Al2O3 and liquid steel, in agreement with experimental observations.57'69 2.12.2.3 Proposed deoxidation model Referring to Fig. 2.65, the sequence of reactions occurring during weld metal deoxidation can be summarised as follows. In general, nucleation of oxide inclusions occurs homogeneously as a result of the supersaturation established during cooling in the weld pool. The diffusioncontrolled deoxidation reactions (i.e. diffusion of reactants to the oxide nuclei) will be essentially complete when the liquid metal temperature attains a constant level of about 15500C at some distance behind the root of the arc. Growth of the particles may then proceed under approximately isothermal conditions at a rate controlled by the Wagner equation until the temperature reaches the melting point of the steel. Since retention times in welding generally depend on the heat input, it follows that choice of operating parameters will finally determine the degree of particle coarsening to be achieved. Example (2.11)
Consider SA welding with a basic flux on a thick plate of low-alloy steel under the following conditions:
Previous experience has shown that this steel/flux combination gives a weld metal oxygen and sulphur content of 0.035 and 0.008 weight percent, respectively. Based on the stereometric relationships given below, calculate the total number of particles per unit volume Nv, the total number of particles per unit area Na, the total particle surface area per unit volume Sv, and the mean particle centre to centre volume spacing Xv in the weld deposit:74'75
(2-80) (2-81)
(2-82)
(2-83)
Solution
First we calculate the total volume fraction of oxide and sulphide inclusions from equation (2-75): Vv = 10-2 [5.0(0.035) + 5.4(0.008 -0.003)] = 2.0 X 10~3 The arithmetic mean (3-D) inclusion diameter can then be evaluated from equation (2-79):
This gives: particles per mm3
particles per mm 2 mm 2 per mm3
particles per mm3
particles per mm 2 mm 2 per mm3
2.123 Constituent elements and phases in inclusions It is evident from Table 2.11 that non-metallic inclusions commonly found in low-alloy steel weld metals may contain a considerable number of constituent elements and phases. 2.12.3.1 Aluminium, silicon and manganese contents Figure 2.66 shows examples of measured X-ray intensity histograms for silicon, manganese, and aluminium in inclusions extracted from a low-alloy steel weld metal. These results have been converted into arbitrary elemental weight concentrations by normalising the collected Xray data for all preselected elements (i.e. Al, Si, Mn, Ti, Cu, and S) to 100%. The characteristic normal distribution curves recorded for silicon, manganese, and aluminium show that the content of each oxide phase may vary significantly from one particle to another. This observation is not surprising, considering the complex chemical nature of the weld metal inclusions (see Fig. 2.57). 2.12.3.2 Copper and sulphur contents In addition, the inclusions may contain significant levels of both copper and sulphur in addition to aluminium, silicon, manganese and titanium. Sulphide shells around extracted inclusions have frequently been observed in SA and SMA steel welds, often in combination with copper. This has been taken as an indication of copper sulphide formation. However, based on the wavelength dispersive X-ray (WDX) data reported by Kluken and Grong,57 it can be argued that copper sulphide is a rather unlikely reaction product in steel weld metals as it is in ordinary ladle-refined steel.76 From their data it is evident that the total
Silicon
Manganese
Aluminium
Frequency (%)
26 wt%
20 wt%
28 wt%
Arbitrary elemental weight concentrations, wt% Fig. 2.66. Measured X-ray intensity histograms for silicon, manganese and aluminium in inclusions extracted from a low-alloy steel weld metal. Arrows indicate average composition. Data from Kluken and Grong.57 number of counts recorded for copper in discrete particles is not significantly higher than the corresponding matrix value, which shows that the copper content of the inclusions is low. Since these measurements were carried out on mechanically polished specimens and not on carbon extraction replicas, as done in the EDX analysis, the indications are that the higher inclusion copper level observed in the latter case mainly results from surface copper contamination inherent from the extraction process. In contrast, the WDX analysis of sulphur revealed evidence of sulphur enrichment in most of the particles. Considering the fact that these particles also contained significant amounts of manganese, it is reasonable to assume that most of the sulphur is present in the form of MnS (possibly with some copper in solid solution).76 2.12.3.3 Titanium and nitrogen contents From the literature reviewed, it is apparent that conflicting views are held about the role of titanium in weld metal deoxidation. From a thermodynamic standpoint, Ti2O3 is the stable reaction product in titanium deoxidation,76 but this phase has not yet been detected experimentally in steel weldments (only in continuous cast steel).77 However several authors have reported the presence of crystalline patches containing titanium toward the edges of inclusions.78"80 This constituent has a cubic crystal structure with a lattice parameter close to 0.42 nm, conforming to either 7-TiO, TiN, or TiC (note that the 7-T1O phase is the hightemperature modification of the titanium monoxide).81 In general, formation of titanium monoxide requires strongly reducing conditions, which
implies that the 7-TiO constituent is not an equilibrium reaction product in steel deoxidation.55'76 Hence, it is reasonable to assume that the titanium-rich crystalline patches observed toward the edges of weld metal inclusions are titanium nitride. This conclusion has later been confirmed experimentally by Kluken and Grong.57 2.12.3.4 Constituent phases Based on the above discussion, it is possible to rationalise the formation of primary and secondary reaction products (i.e. oxides, sulphides and nitrides) during cooling in the weld pool, as shown in Fig. 2.67. In general, the inclusions will consist of an oxide core which is formed during the primary deoxidation stage. The chemical composition of the deoxidation product can vary within wide limits, depending on the activities of Al, Ti, Si, Mn, and O in the weld metal. The surface of the oxides will partly be covered by MnS and TiN (see also STEM micrograph in Fig. 2.57). Precipitation of these phases occurs after the completion of the weld metal deoxidation, probably during solidification, where the reactions are favoured by solute enrichment in the interdendritic liquid. Additional precipitation of TiN may occur in the solid state as a result of diffusion of titanium and nitrogen to the surface of the inclusions. 2.12.4 Prediction of inclusion composition Since the diffusion-controlled deoxidation reactions are completed within a fraction of a second when the number of nuclei is of the order of 107 mm"3 or higher,55 the average chemical composition of the inclusions should be compatible with that calculated for chemical equilibrium at temperatures close to the melting point (e.g. 15500C). 2.12.4.1 C-Mn steel weld metals Over the composition range normally applicable to silicon-manganese deoxidation of steel weld metals (i.e. between 0.4 to 0.7 wt% Si and 0.8 to 1.5 wt% Mn) the equilibrium reaction product at 15500C should be silica-saturated slags with a mole fraction of SiO2 close to 0.55. 5565 Since the two other slag components are MnO and FeO, we may write: (2-84) The activity coefficients for MnO and FeO in the ternary system SiO 2 -MnO-FeO can be computed from the equations presented by Sommerville et al.:S2 (2-85) and (2-86) For the specific case of silica-saturated slags, we obtain: (2-87) and (2-88)
TiN (secondary reaction product) Oxide Core (primary reaction product] MnS (secondary reaction product) Fig. 2.67. Schematic diagram showing the presence of primary and secondary phases in weld metal inclusions. Under such conditions the activity ratio aMnO/aFeO in the slag is given by:
(2-89)
The activity ratio aMnO/aFeO can also be estimated from the equilibrium constant for the FeMn reaction at 15500C,23 i.e.: (2-90)
The corresponding mole fractions of MnO and FeO in the slag phase are then obtained by combining equations (2-89) and (2-90): (2-91) and (2-92)
Equations (2-91) and (2-92) provide a basis for calculating the chemical composition of the inclusions under different deoxidation conditions. A requirement is, however, that the weld metal Si to Mn ratio is sufficiently high to promote precipitation of silica-saturated slags at 15500C.
and
This gives the following chemical composition of the inclusions (in wt%):
The above calculations should be compared with the composition data presented in Fig. 2.68. It is evident from this plot that the agreement between predictions and experiments is reasonably good both at high and low weld metal manganese levels. This justifies the simplifications made in deriving equations (2-91) and (2-92). 2.12.4.2 Low-alloy steel weld metals In principle, a procedure similar to that described above could also be used to establish a theoretical basis for predicting the chemical composition of the inclusions in the case lowalloy steel weld metals. Unfortunately, adequate activity data for the Fe-Al-Ti-Si-Mn-O system are not available in the literature. An alternative approach would be to calculate the average inclusion composition from simple mass balances, assuming that all oxygen combines stoichiometrically with the various deoxidation elements to form stable oxides in the order Al2O3, Ti2O3, SiO2, and MnO, according to their oxygen affinity in liquid steel (see Fig. 2.69). If reasonable average values for the inclusion and steel densities are used (i.e. 4.2 and 7.8 g cm"3, respectively), the following set of equations* can be derived from a balance of O, Al, Ti, S, Si, and Mn and data for acid soluble aluminium and titanium in the weld metal:57 Aluminium
The average aluminium content of the inclusions, [%Al]inch can be estimated from the measured difference between total and acid soluble aluminium in the weld metal, (k%Al)we[d. This difference is, in turn, equal to the total mass of aluminium in the inclusions: (2-93) where mind and Vv (cal) are the total mass and volume fraction of non-metallic inclusions in the weld deposit, respectively. *The numerical constants in the constitutive equations given below could alternatively be expressed in terms of atomic weights etc. to bring out more clearly their physical significance (e.g. see the treatment of Bhadeshia and Svensson83).
Mole fraction
Ar - O2 gas mixtures Ar - CO2 gas mixtures
Manganese content, wt% Fig. 2.68. Comparison between measured and predicted microslag composition in GMA welding of C-Mn steels. Solid lines represent theoretical calculations based on equations (2-91) and (2-92). Data from Grong and Christensen.1
Oxygen in solution, wt%
Iron oxide in solution at 16000C Mn
Si Ti
Al
Deoxidizer in solution, wt% Fig. 2.69.Deoxidation equilibria in liquid steel at 1600°C.Data from Turkdogan.55
By rearranging equation (2-93), we get:
(2-94)
However, since data for acid soluble aluminium (and titanium), in practice, may contain large inherent errors, the following restriction applies: (2-95) where [%O]anaL is the analytical weld metal oxygen content. Titanium
Similarly, the average titanium content of the inclusions, [%Ti]incl, can be estimated from the measured difference between total and acid soluble titanium, (A%Ti)weld. However, since TiN dissolves readily in strong acid, it is necessary to include an empirical correction for the amount of titanium nitride which simultaneously forms at the surface of the inclusions during solidification. This can be done on the basis of published data for the solubility product of TiN in liquid steel.84 If we assume that the nitrogen content of the inclusions is proportional to the calculated difference between total and dissolved nitrogen at the melting point (15200C), the following relationship is obtained:
(2-96)
where [%N]anai is the analytical weld metal nitrogen content, and [%Ti]soL is acid soluble titanium. Note that the correction term for TiN, in practice, neither can be negative nor exceed [%Ti]soh
In this case, the maximum amount of titanium which can be bound as Ti2O3 is determined by the overall oxygen balance: (2-97) Sulphur
If the solubility of sulphur in solid steel is taken equal to 0.003 wt%,70 the average sulphur content of the inclusions, [%S]ind is given by:
(2-98) where [%S]anai is the analytical weld metal sulphur content. Silicon and manganese
From the experimental data of Saggese et al.S5 reproduced in Fig. 2.70, it is evident that the mass ratio between SiO2 and MnO in the oxide phase may be considered constant and virtually independent of composition (i.e. equal to about 0.94). This implies that the average silicon content of the inclusions, [%Si]ind, can be calculated from a balance of oxygen:
SiO2
Al2O3
MnO wt% AI2O3
Fig. 2.70. Measured inclusion compositions in low-alloy steel weld metals. Data from Saggese et alP
(2-99) Considering manganese, proper adjustments should also be made for the amount of MnS formed at the surface of the inclusions during solidification. Hence, the average manganese content of the inclusions, [%Mn]inci, is given by the sum of the oxygen and the sulphur contributions:
(2-100)
Experimental verification of model
In Fig. 2.71, the accuracy of the model has been tested against the experimental SA/GMA inclusion data reported by Kluken and Grong,57 taking the sum (%A1 + %Ti + %S + %Si + %Mn) equal to 100%. A closer inspection of the graphs reveals a reasonable agreement between calculated and measured average inclusion compositions in all cases, which confirms that the model is sound. Included in Fig. 2.71 is also a collection of data for SMA low-alloy steel weld metals (3 kJ mm"1 — basic electrodes). Since these results follow the same pattern, it implies that the model is generally applicable and, therefore, can be adopted to all relevant arc welding processes.
Measured composition, wt%
Aluminium Sulphur
Marked symbols: SMAW
Measured composition, wt%
Calculated composition, wt%
Titanium Manganese Silicon
Marked symbols: SMAW
Calculated composition, wt% Fig. 2.71. Comparison between measured and predicted inclusion compositions; (a) Aluminium and sulphur, (b) Titanium, manganese and silicon. Data from Kluken and Grong57'86 Implications of model
It can be inferred from equations (2-94) and (2-95) that the chemical composition of the inclusion oxide core is directly related to the aluminium to oxygen ratio in the weld metal. Referring to Fig. 2.72, the fraction of MnOAl2O3 and 7-Al2O3 in the inclusions is seen to increase steadily with increasing (A%Al)wdJ[%O]anal ratios until the stoichiometric composition for precipitation of aluminium oxide is reached at 1.13. At higher ratios, the deoxidation product will be pure Al2O3, since aluminium is present in an over-stoichiometric amount with respect to oxygen. When titanium is added to the weld metal, titanium oxide (in the form of Ti2O3) may also enter the reaction product. At the same time both TiN and a-MnS form epitaxially on the surface of the inclusions during solidification. Consequently, in Al-Ti-Si-Mn deoxidised steel weld metals the total number of constituent phases within the inclusions may approach six. The kinetics of inclusion formation are further discussed in Ref. 87.
SiO2
MnO
Fig. 2.72. Coexisting phases in inclusions at different weld metal aluminium-to-oxygen ratios. Shaded region indicates the approximate composition range for the oxide phase. The diagram is constructed on the basis of the model of Kluken and Grong57 and relevant literature data.
Example (2.13)
Consider SA welding of low-alloy steel with two different basic fluxes. Data for the weld metal chemical compositions are given in Table 2.12. Based on Fig. 2.72, estimate the total number of constituent phases in the inclusions in each case. Solution
It follows from Fig. 2.72 that the chemical composition of the deoxidation product is determined by the aluminium to oxygen ratio in the weld metal. For weld A, we have:
Since this ratio is higher than the stoichiometric factor of 1.13, all oxygen is probably tied up as aluminium oxide. In addition, weld A contains small amounts of titanium and sulphur, which may give rise to precipitation of TiN and MnS at the surface of the inclusions during solidification. Hence, the three major constituent phases in the weld metal inclusions are 7-Al2O3, TiN, and ot-MnS.
Table 2.12 Chemical composition of SA steel weld metals considered in Example 2.13. Weld No.
C (wt%)
O (wt%)
Si (wt%)
Mn (wt%)
S (wt%)
N (wt%)
Al* (wt%)
Ti* (wt%)
A
0.09
0.021
0.45
1.52
0.01
0.006
0.028 (0.003)
0.010 (0.009)
B
0.09
0.045
0.45
1.52
0.01
0.006
0.028 (0.003)
0.028 (0.010)
*Data for acid soluble Al and Ti are given by the values in brackets.
In the case of weld B the situation is much more complex due to a higher content of oxygen and titanium. From Table 2.12, we have:
and
These calculations show that Al and Ti are not present in sufficient amounts to tie-up all oxygen. Under such conditions Fig. 2.72 predicts that the total number of constituent phases in the inclusions is six, i.e.: SiO2, MnOAl2O3, 7-Al2O3, Ti2O3, a-MnS and TiN. References 1 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
0 . Grong and N. Christensen: Scand. J. Metall, 1983,12, 155-165. J.F. Lancaster: Metallurgy of Welding, 3rd Edn, 1980, London, George Allen & Unwin Ltd. J. Szekely and NJ. Themelis: Rate Phenomena in Process Metallurgy, 1971, New York, John Wiley & Sons, Inc. N. Christensen: Welding Metallurgy Compendium, 1985, University of Trondheim, The Norwegian Institute of Technology, Trondheim, Norway. E.T. Turkdogan: Physical Chemistry of Oxygen Steelmaking, Thermochemistry and Thermodynamics, 1970, United States Steel Corporation. F.R. Coe: Welding Steels without Hydrogen Cracking, 1973, Abington (Cambridge), The Welding Institute. Doc. IIS/IIW-532-77: Weld. World, 1977,15, 69-72. B. Chew and R. A. Willgoss: Proc. Int. Conf Weld Pool Chemistry and Metallurgy, London, April 1980, Paper 25,155-165. Publ. The Welding Institute (England). F. Matsuda, H. Nakagawa, K. Shinozaki and H. Kihara: Trans. JWRI, 1978, 7, 135-137. B. Chew: Weld. J., 1973, 52, 386s-391s. GM. Evans: Schweissmitteilungen (Oerlikon), 1977, No. 79, 4-8. GM. Evans and H. Bach: HW Doc. IIA-363-74, 1974.
13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51.
R. Roux: Rev. Met. 1954,192-209. E.M. Skjolberg: M.Sc. thesis, 1980, University of Trondheim, The Norwegian Institute of Technology, Trondheim, Norway. D.G. Howden and D.R. Milner: Brit. Weld. J., 1963,10, 304-316. T. Kobayashi, T. Kuwana and T. Kikuchi: HW Doc. XII-265-65, 1965. J.E. O'Brien and M.F. Jordan: Met. Constr. Brit. Weld. J., 1971,3, 299-303. M. Uda and S. Ohno: Trans. Nat. Res. Inst. for Metals, 1973,15, 20-28. O. Morigaki, T. Tanigaki, M. Kuwabara and K. Fujibayashi: HW Doc. 11-746-75, 1975. H.K.D.H. Bhadeshia, L.E. Svensson and B. Gretoft: J. Mater. ScL Lett, 1988, 7, 610-612. E. Halm0y: Proc. Int. Conf. on Arc Physics and Weld Pool Behaviour, London, May, 1979,4957. Publ. The Welding Institute (England). D.J.H. Corderoy, B. Wills and G.R. Wallwork: Proc. Int. Conf. on Weld Pool Chemistry and Metallurgy, London, April 1980, 147-153. Publ. The Welding Institute (England). J.F. Elliott, M.Gleiser and V. Ramakrishna: Thermochemistry for Steelmaking (Vol. II), 1963, London, Addison-Wesley Publ. Company (Pergamon Press). Doc. IIS/IIW-343-70: Weld. World, 1970, 8, 28-35. I. Barin and O. Knacke: The Thermochemical Properties of Inorganic Substances, 1973, Berlin, Springer Verlag. Janaf, Thermochemical Tables - 2nd Edn (NSRDS); 1971, New York, National Bureau of Standards. R.F. Heile and D.C. Hill: Weld. J., 1975, 54, 201s-210s. B. Ozturk and RJ. Fruehan: Metall Trans. B, 1985,16B, 801-806. G. Jelmorini, G.W. Tichelaar and GJ.P.M. Van den Heuvel: HW Doc. 212-411-77, 1977. O. Kubaschewski and C B . Alcock: Metallurgical Thermochemistry, 5th Edn, 1979, Oxford, Pergamon Press. PA. Distin, S.G. Whiteway and CR. Masson: Can. Metall. Quart., 1971,10, 13-18. J.F. Lancaster: The Physics of Welding, 1984, Oxford, HW-Pergamon Press, 204-267. WA. Fischer and J.F. Schumacher: Arch. Eisenhiittenwesen, 1978, 49, 431-435. N. Christensen, V. de L. Davis and K. Gjermundsen: Brit. Weld. J., 1965,12, 54-75. G.K. Sigworth and J.F. Elliott: Metall. Trans., 1973, 4,105-113. D.N. Shackleton and A.A. Smith: HW Doc. XII-832-84, 1984. 0. Grong, N.H. Rora and N. Christensen: Scand. J. Metall., 1984,13,154-156. A.A. Smith et al: Weld. World., 1970, 8, 28-35. A.A. Smith: CO2-Shielded Consumable Electrode Arc Welding, 2nd Edn, 1965, Brit. Weld. Res. Assoc. U. Lindborg: Met. Constr. and Brit. Weld. J., 1972, 4, 52-55. T.H. North, H.B. Bell, A. Nowicki and I. Craig: Weld. J., 1978, 57, 63s-71s. CS. Chai and T. W. Eagar: Metall. Trans., 1981,12B, 539-547. U. Mitra and T.W. Eagar: Metall. Trans., 1984,15A, 217-227. J.E. Indacochea, M. Blander, N. Christensen and D.L. Olson: Metall. Trans., 1985, 16B, 237245. N. Christensen and 0 . Grong: Scand. J. Metall, 1986,15, 30-40. U. Mitra and T.W. Eagar: Metall Trans., 1991, 22B, 65-100. T.W. Eagar: Weld. J., 1978, 57, 76s-80s. N. Christensen and J. Chipman: Weld. Res. Coun. Bull. Series, 1953, No. 15, New York, Welding Research Council (USA). A. Apold: Carbon Oxidation in the Weld Pool, 1962, Oxford, Pergamon Press. D.A. Wolstenholme: Proc. Int. Conf on Trends in Steel and Consumables for Welding, London, 1978,123-134. Publ. The Welding Institute (England). 0 . Grong, D.L. Olson and N. Christensen: Metal Constr., 1985,17, 810R-814R.
52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85.
86. 87.
P. Nilles, P. Dauby and J. Claes: Proc. Int. Conf. Basic Oxygen Steelmaking —A New Technology Emerges, London, 1978, 60-72, The Metals Society (England). U. Lindborg and K. Torsell: Trans. TMS-AIME, 1968, 242, 94-102. N.F. Grevillius: Jernkont. Ann., 1969,153, 547-572. E.T. Turkdogan: Proc. Int. Conf. on Chem. Metall. of Iron and Steel, Sheffield, July 1971,153170, Publ. The Iron and Steel Institute (England). 0 . Grong. T.A. Siewert, G.P. Martins and D.L. Olson: Metall. Trans. A, 1986,17A, 1797-1807. A.O. Kluken and 0 . Grong: Metall. Trans. A, 1989, 2OA, 1335-1349. M.L. Turpin and J.F. Elliott: J. Iron Steel Inst., 1966, 204, 217-225. E.T. Turkdogan: Physicochemical Properties of Molten Slags and Glasses, 1983, London, The Metals Society. E. Plockinger and M. Wahlster: Stahl und Eisen, 1960, 80, 659-669. BJ. Bradstreet: HW Doc. 212-138-68, 1968. J.F. Lancaster: Phys. Technol, 1984,15, 73-79 F. Eickhorn and A. Engel: HW Doc. 212-201-70, 1970. N. Mori and Y. Horii: HW Doc. 212-188-70, 1970. R.A. Walsh and S. Ramachandran: Trans. TMS-AIME, 1963, 227, 560-562. D.C. Hilty and W. Crafts: Trans.-AIME, 1950,188, 425-436. E.T. Turkdogan: Trans. TMS-AIME, 1965, 233, 2100-2112. G.M. Evans: HW Doc. IIA-630-84, 1984. 0 . Grong and D.K Matlock: Int. Met. Rev., 1986, 31, 27-48. A.G. Franklin: J. Iron Steel Inst., 1969, 207, 181-186. A.O. Kluken, 0. Grong and J. Hjelen: Mat. ScL Technol., 1988, 4, 649-654. L.M. Hocking: Quart. J. Royal Meterol. Soc, 1959, 85, 44-50. C. Wagner: Z Electrochemie, 1961, 65, 581-591. E.E. Underwood: Quantitative Stereology, 1970, London, Addison-Wesley Publ. Co. M.F. Ashby and R. Ebeling: Trans. TMS-AIME, 1966, 236, 1396-1404. R. Kiessling: Non-Metallic Inclusions in Steel, 1978, London, The Metals Society (TMS). H. Homma, S. Ohkita, S. Matsuda and K. Yamamoto: Weld. J., 1987, 66, 301s-309s. G. Thewlis: HW Doc. IIA-736-88, 1988. J.M. Dowling, J.M. Corbett and H.W. Kerr: Metall. Trans. A, 1986,17A, 1611-1623. G.M. Evans: Metal Constr., 1986,18, 631R-636R. J.L. Murray and H.A. Wriedt: Bull. Alloy Phase Diagr., 1987, 8, 148-165. LD. Sommerville, I. Ivanchev and H.B. Bell: Proc. Int. Conf Chem. Metall of Iron and Steel, Sheffield, July 1971, 23-25, Publ. The Iron and Steel Inst. (1973). H.K.D.H. Bhadeshia and L.E. Svensson: Mathematical Modelling of Weld Phenomena (Eds H. Cerjak and K.E. Easterling), 1993, London, The Institute of Materials, 109-180. S. Matsuda and N. Okumura: Trans. ISIJ, 1978,18, 198-205. M.E. Saggese, A.R. Bhatti, D.N. Hawkins and J.A. Whiteman: Proc. Int. Conf on the Effect of Residual, Impurity and Micro-Alloy ing Elements on Weldability and Weld Properties, London, Nov. 1983, Paper 15, Publ. The Welding Institute (England). A.O. Kluken and 0 . Grong: Report No. STF34 F87125, 1987, Sintef, Trondheim, Norway. S.S. Babu, S.A. David, J.M. Vitek, K. Mundra and T. DebRoy: Mater. ScL Technol., 1995,11,186199.
Appendix 2.1 Nomenclature contact area (mm2)
activity coefficient of element X
difference between total and acid soluble Al in weld metal (wt%)
gravity constant (9.81ms- 2 )
thermal diffusivity (mm2 s 1 )
standard free energy of reaction (J mol"1 or kJ mol-1)
activity of arbitrary slag component
energy barrier for homogeneous nucleation (kJ mol-1)
cross section of fused parent metal (mm2)
driving force for precipitation of oxide inclusions (J nr 3 )
flux basicity index kinetic constants GMAW
gas metal arc welding
GTAW
gas tungsten arc welding
drag coefficient molar concentration of element X in the liquid (mol m~3) cross section of deposited metal (mm2) element diffusivity in liquid phase (m2 s"1 or mm2 s"1) diffusivity of element X in gas phase (mm2 s"1) gross heat input (kJ mm"1) FCAW
standard enthalpy of reaction (J mol-1 or kJ mol-1) hydrogen content related to deposited metal (ml per 10Og deposit) hydrogen content related to fused metal (ml per 10Og or g per ton)
flux cored arc welding
hydrogen content related to French practice (g per ton)
drag force acting on spherical particle in relative motion to a fluid (N)
heat content per unit volume at the melting point (J mm"3)
gravity force acting on a spherical particle in relative motion to a fluid (N)
hydrogen content related to Japanese practice (ml per 10Og deposit)
fume formation rate (mg miir 1 )
amperage (A)
nucleation rate of oxide inclusions in the weld pool (nuclei nr 3 s"1) constant in equation (A2-1) (nuclei rrrV 1 ) ratio between absorbed Si and Mn in the weld metal coefficient of weld metal deposition (g A-1S"1) mass transfer coefficient for gas absorption (mm s"1) mass transfer coefficient for gas desorption (mm s"1) overall mass transfer coefficient (mm s"1) equilibrium constants
total mass of liquid metal leaving/entering the reaction zone per unit time (g s-1) arbitrary flux or slag component concentration displacement of manganese referred to different standard states (wt%) total manganese absorption in the weld metal due to slag/metal interactions (wt%) rejected manganese during cooling in the weld pool (wt%) oxidation loss of manganese at electrode tip (wt%)
the product [%C][%O] atomic weight of element X mass of CO2 per 100 g of electrode coating (g or wt%)
dimensionless operating parameter
total mass of inclusions per 100 g weld deposit (g)
total number of moles of component /
mass of H2O per 100 g of electrode coating (g or wt%)
absorption/desorption rate of element X in the weld pool (mol s"1)
total weight of retained MnOSiO2 (g per 100 g weld deposit)
total number of moles of component X
total weight of precipitated microslag (in g per 100 g weld deposit) total weight of precipitated MnS (g per 100 g weld deposit)
total number of moles of component X2 number of particles per unit area (mm"2) Avogadro constant (6.022 X 1023 mor 1 )
mole fraction of arbitrary slag component
combined partial pressure of H2 and H2O (atm)
analytical weld metal nitrogen content (wt%)
post weld heat treatment parts per million (g per ton)
mole fraction of CO in gas phase Reynolds number number of particles per unit volume (No. per mm"3) calculated oxygen absorption in electrode tip or falling droplets (wt%) analytical weld metal oxygen content (wt%)
net arc energy (W) universal gas constant (J K-1 mol-1) relative humidity (%) analytical weld metal sulphur content (wt%) standard entropy of reaction (J K -1 mol"1)
equilibrium weld metal oxygen content (wt%)
concentration displacement of silicon referred to different standard states (wt%)
rejected oxygen during cooling in the weld pool (wt%)
total silicon absorption in the weld metal due to slag/ metal interactions (wt%)
total oxygen absorption in hot part of weld pool (wt%)
rejected silicon during cooling in the weld pool (wt%)
total pressure (atm or bar) partial pressure of component X in bulk gas phase (atm) equilibrium partial pressure of component X at gas/ metal interface (atm) partial pressure of component X2 in bulk gas phase (atm) equilibrium partial pressure of component X2 at gas/ metal interface (atm)
oxidation loss of silicon at electrode tip (wt%) solubility of element X at 1 atm total pressure (ml per 10Og, ppm or wt%) total particle surface area per unit volume (mm2 per mm3) modified solubility of hydrogen at 1 atm total pressure (ml per 100 g, ppm or wt%)
SAW
submerged arc welding
SMAW
shielded metal arc welding
STEM
scanning transmission electron microscope
volume fraction of inclusions concentration of component / (vol%) concentration of component X2 (vol%)
time (s) time constant (s) acid soluble titanium in weld metal (wt%) difference between total and acid soluble Ti in weld metal (wt%) temperature (0C or K)
concentration of component YX2 (vol%) WDX
wavelength dispersive Xray analysis
WFR
wire feed rate (mm s -1 or m min"1) arbitrary element or gaseous species
ambient temperature (0C or K)
weld ripple lag (mm)
preheating temperature (0C or K)
concentration of element X in the weld metal (wt%)
reference temperatures (0C or K)
concentration displacement of element X referred to nominal weld metal composition (wt%)
rising velocity of ascending particles relative to the liquid (|jLms-1) bulk velocity of the fluid relative to the particles (ms- 1 )
equilibrium concentration of element X in the weld pool (wt%)
voltage (V)
initial concentration of element X in the weld pool (wt%)
welding (travel) speed (mm s"1)
average content of element X in inclusions (wt%)
volume of melt (mm3)
nominal concentration of element X in weld metal (wt%)
molar volume of nucleus (m3 mol-1) molar volume of oxide per mole of the diffusate (m3 mol-1)
concentration of element X in base plate (wt%)
concentration of element X in filler wire (wt%) arbitrary element or gaseous species density (kg irr 3 or g mm"3)
thickness of stagnant gaseous boundary layer (mm) wetting angle mean particle centre to centre volume spacing (jxm)
difference in density between liquid steel and inclusion (kg irr 3 or g mm"3)
dimensionless y-coordinate at maximum width of isotherm
slag/metal interfacial energy (J nr 2 )
activity coefficient for MnO in slag phase
arc efficiency factor
activity coefficient for SiO2 in slag phase
viscosity (kg nr 1 s"1)
Appendix 2.2 Derivation of equation (2-60) The nucleation rate / as a function of temperature can be expressed as: (A2-1) where J0 is a constant (with the unit nuclei per m3 and s) and AG* is the energy barrier for nucleation. By rearranging equation (A2-1) and inserting reasonable values for J and J0 for the specific case of homogeneous nucleation of oxide inclusions in liquid steel,55 we obtain:
(A2-2)
From the classic theory of homogeneous nucleation AG* is given by:
(A2-3) where NA is the Avogadro constant, o is the interfacial energy between the nucleus and the liquid (in J nr 2 ) and AGV is the driving force for the precipitation reaction (in J nr 3 ).
The parameter AGV can be expressed as:
(A2-4) where AH° and AS° are the standard entalpy and entropy of the precipitation reaction, respectively and Vm is the molar volume of the nucleus (in m3 mol"1). It is evident from Fig. 2.48 that AGV = 0 when T=Tu which gives \S° = A//7 T\. Hence, equation (A2-4) may be rewritten as: (A2-5)
By combining equations (A2-2), (A2-3) and (A2-5), we obtain the following relationship between T\ and T^-
(A2- 6)
3 Solidification Behaviour of Fusion Welds
3.1 Introduction Inherent to the welding process is the formation of a pool of molten metal directly below the heat source. The shape of this molten pool is influenced by the flow of both heat and metal, with melting occurring ahead of the heat source and solidification behind it. The heat input determines the volume of molten metal and, hence, dilution and weld metal composition, as well as the thermal conditions under which solidification takes place. Also important to solidification is the crystal growth rate, which is geometrically related to weld travel speed and weld pool shape. Hence, weld pool shape, weld metal composition, cooling rate, and growth rate are all factors interrelated to heat input which will affect the solidification microstructure. Some important points regarding interpretation of weld metal microstructure in terms of these four factors will be discussed below. Since the properties and integrity of the weld metal depend on the solidification microstructure, a verified quantitative understanding of the weld pool solidification behaviour is essential. At present, our knowledge of the chemical and physical reactions occurring during solidification of fusion welds is limited. This situation arises mainly from a complex sequence of reactions caused by the interplay between a number of variables which cannot readily be accounted for in a mathematical simulation of the process. Nevertheless, the present treatment will show that it is possible to rationalise the development of the weld metal solidification microstructure with models based on well established concepts from casting and homogenising treatment of metals and alloys.
3.2 Structural Zones in Castings and Welds The symbols and units used throughout this chapter are defined in Appendix 3.1. During ingot casting, three different structural zones can generally be observed, as shown schematically in Fig. 3.1. The chill zone is produced by heterogeneous nucleation in the region adjacent to the mould wall as a result of the pertinent thermal undercooling. These grains rapidly become dendritic, and dendrites having their <100> direction (preferred easy growth direction for cubic crystals) parallel to the maximum temperature gradient in the melt will soon outgrow those grains that do not have this favourable orientation. Competitive growth occurring during the initial stage of the solidification process leads to an alignment of the crystals in the heat flow direction and eventually to the formation of a columnar zone. 12 Finally, an equiaxed zone may develop in the centre of the casting, mainly as a result of growth of detached dendrite arms within the remaining, slightly undercooled liquid. A similar situation also exists in welding, as indicated in Fig. 3.2 However, in this case the chill zone is absent, since the partly melted base metal grains at the fusion boundary act as seed crystals for the growing columnar grains.3 In addition, the growth direction of the columnar
Shrinkage pipe
Chill zone Columnar zone Equiaxed zone Mould
Fig. 3.1. Transverse section of an ingot showing the chill zone, the columnar zone and the equiaxed zone (schematic). grains will change continuously from the fusion line towards the centre of the weld due to a corresponding shift in the direction of the maximum temperature gradient in the weld pool. This change in orientation may result in a curvature of the columnar grains (Fig. 3.2(a)). Alternatively, new grains can nucleate and grow in a columnar manner, producing a so-called 'stray' structure as shown schematically in Fig. 3.2(b). Finally, if the conditions for nucleation of new grains are favourable, an equiaxed zone will form near the weld centreline similar to that observed in ingots or castings (see Fig. 3.2(b)). Although the process of weld pool solidification is frequently compared with that of an ingot in 'miniature', a number of basic differences, already mentioned, exist which strongly influence the microstructure and properties of the weld metal. Of particular importance is also the disparity in cooling rate between a fusion weld and an ingot (see Fig. 3.3). For conventional processes such as shielded metal arc (SMA), gas metal arc (GMA), submerged arc (SA) or gas tungsten arc (GTA) welding the cooling rate may vary from 10 to 103 0 C s"1, while for modern high energy beam processes such as electron beam (EB) and laser welding the cooling rate is typically of the order of 103 to 106 0 C s"1.4 Consequently, to appreciate fully the implications of these differences in general solidification behaviour between a weld pool and an ingot, it is necessary to consider in detail the sequence of events taking place in the solidifying weld metal beginning with the initiation of crystal growth at the fusion boundary.
3.3 Epitaxial Solidification It is well established that initial solidification during welding takes place epitaxially, where the partly melted base metal grains at the fusion boundary act as seed crystals for the columnar grains. This process is illustrated schematically in Fig. 3.4.
(a) Welding direction
(b) Columnar zone Welding direction
Equiaxed zone Columnar zone •
Rapid solidification technology
SMAW, SAW, GMAW, GTAW
Electron beam welding Laser welding
Cooling rate, °C/s
Fig. 3.2. Examples of structural zones in fusion welds (schematic); (a) Curved columnar grains, (b) Stray grain structure.
Process Fig. 3.3. Disparity in cooling conditions between casting, welding and rapid solidification.
Fusion boundary HAZ
Weld metal
Fig. 3.4. Schematic illustration showing epitaxial growth of columnar grains from partly melted base metal grains at fusion boundary. Liquid (L)
Substrate (S)
Fig. 3.5. Schematic representation of heterogeneous nucleation.
3.3.1 Energy barrier to nucleation During epitaxial solidification, a solid embryo (nucleus) of the weld metal forms at the meltedback surface of the base metal grain. Assuming that the interfacial energy between the embryo and the liquid is isotropic, it can be shown, for a given volume of the embryo, that the interfacial energy of the whole system is minimised if the embryo has the shape of a spherical cap. Under such conditions, the following relationship exists between the interfacial energies (see Fig. 3.5): (3-1) where (3 is the wetting angle. The change in free energy, AGhet, accompanying the formation of a solid nucleus with this configuration is given by:5 (3-2)
where VE is the volume of the solid embryo, AGV is the free energy change associated with the embryo formation, AEL and AES are the areas of the embryo-liquid and embryo-substrate interfaces, respectively, and/(P) is the so-called shape factor, defined as:
(3-3)
The critical radius of the stable nucleus, r / , is found by differentiating equation (3-2) with respect to rs and equating to zero: (3-4)
By substituting equation (3-4) into equation (3-2), we obtain the following expression for the energy barrier to heterogeneous nucleation (AG^ r ):
(3-5)
where AHm is the latent heat of melting, Tm is the melting point, and AJT is the undercooling. It is easy to verify that the first term in equation (3-5) is equal to the energy barrier to homogeneous nucleation, 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
chemical composition and the crystal structure of the two solid phases are usually very similar, we have:6
Under such conditions equation (3-1) predicts that the wetting angle 3 ~ 0 (cos(3 ~ 1), which implies that there is a negligible energy barrier to solidification of the weld metal (№}*het ~ 0), i.e. no undercooling of the melt is needed, and solidification occurs uniformly over the whole grain of the base metal. This is in sharp contrast to conventional casting of metals and alloys where some undercooling of the melt is always required to overcome the inherent energy barrier to solidification (see Fig. 3.6). 3.3.2 Implications of epitaxial solidification Since the initial size of the weld metal columnar grains is inherited directly from the grain growth zone adjacent to the fusion boundary, the solidification microstructure depends on the grain coarsening behaviour of the base material. This is particularly a problem in high energy processes such as submerged arc and gas metal arc welding, where grain growth of the base metal can be considerable. In such cases the size of the columnar grains at the fusion boundary will be correspondingly coarse, as indicated by the data in Fig. 3.7. Moreover, during multipass welding the columnar grains can renucleate at the boundary between for instance the first and the second weld pass and subsequently grow across the entire fusion zone, as illustrated in Fig. 3.8. This type of behaviour is usually observed in weldments which do not undergo transformations in the solid state (e.g. aluminium, certain titanium alloys, stainless steel etc.). In practice, the problem can be eliminated by additions of inoculants via the filler wire, which facilitates a refinement of the columnar grain structure through heterogeneous nucleation of new (equiaxed) grains ahead of the advancing interface (to be discussed later).
AG
r
s
Welding
Casting Homogeneous nucleation
Fig. 3.6. The free energy change associated with heterogeneous nucleation during casting and weld metal solidification, respectively (schematic). The corresponding free energy change associated with homogeneous nucleation is indicated by the broken curve in the graph.
Weld metal prior austenite grain size (jim)
Fusion line
HAZ
Weld metal
GMAW (low-alloy steel)
HAZ prior austenite grain size (jim) Fig. 3.7. Correlation between HAZ prior austenite grain size at the fusion boundary and the corresponding weld metal prior austenite grain size. Data from Grong et al?
2. pass
1. pass HAZ
Base metal
Fig. 3.8. Optical micrograph showing renucleation of columnar grains during multipass GMA welding of a P-titanium alloy.
3.4 Weld Pool Shape and Columnar Grain Structures Growth of the columnar grains always proceeds closely to the direction of the maximum thermal gradient in the weld pool, i.e. normal to the fusion boundary. This implies that the columnar grain morphology depends on the weld pool geometry. 3.4.1 Weld pool geometry The weld pool geometry is a function of the welding speed and the balance between the heat input and the cooling conditions, as influenced by the base plate thermal properties. At pseudosteady state, these conditions establish a dynamic equilibrium between heat supply and heat extraction so that the shape of the weld pool remains constant for any given speed. Following the treatment in Chapter 1, the weld pool geometry depends on the dimensionless operating parameter n3, defined as: (3-7) where qo is the net arc power, v is the welding speed, a is the thermal diffusivity of the base plate, and Hm-Ho is the heat content per unit volume at the melting point. As shown in Fig. 3.9(a), a tear-shaped weld pool is favoured by a high n3 value, which is characteristic of fast moving high power sources. In contrast, at a low arc power and a low welding speed the shape of the weld pool becomes more elliptical because of a shift in the mode of heat flow (see Fig. 3.9(b)). Note, however, that the thermal properties of the base metal is also of importance in this respect, since the n3 parameter is a function of both a and Hm-Ho. Consequently, a tear-shaped weld pool is usually observed in weldments of a low thermal diffusivity (e.g. austenitic stainless steel), whereas an elliptical or spherical weld pool is more likely to form during aluminium welding owing to the resulting higher thermal diffusivity of the base metal. In addition to the factors mentioned above, the geometry of the weld pool is also affected by convectional heat transfer due to the presence of buoyancy, electromagnetic or suface tension gradient forces. Recently, attempts have been made to include such effects in heat flow models for welding.8"11 Referring to Fig. 3.10(a) the buoyancy force will promote the formation of a shallow, wide weld pool because of transport of 'hot' metal to the surface and 'cold' metal to the bottom of the pool. In the presence of the electromagnetic force the flow pattern is reversed, since the latter force will tend to push the liquid metal in the central part of the pool downward to the root of the weld. This makes the weld pool deeper and more narrow, as shown in Fig. 3.10(b). Moreover, it is generally accepted that surface tension gradients can promote circulation of liquid metal within the weld pool from the region of low surface tension to the region of higher surface tension.9 In the absence of surface active elements such as oxygen and sulphur, the surface tension decreases with increasing temperature as illustrated in Fig. 3.10(c), which forces the metal to flow outwards towards the fusion boundary. This results in the formation of a relatively wide and shallow weld pool. However, if oxygen or sulphur is present in sufficient quantities a positive temperature coefficient of the surface tension may develop, which facilitates an inward fluid flow pattern and an increased weld penetration (see Fig. 3.10(d)). The important influence of surface active elements on the resulting bead morphology is well docu-
HAZ isotherms Fusion boundary
V
Weld pool
(a) HAZ isotherms Fusion boundary
Weld pool
V
(b) Fig. 3.9. Theoretical shape of fusion boundary and neighbouring isotherms under different operational conditions; (a) High n3 values, (b) Low ^-values. merited for ordinary GTA austenitic stainless steel welds. 1 2 1 3 The indications are that such effects become even more important under hyperbaric welding conditions. 14
3.4.2 Columnar grain morphology It is evident from the above discussion that a change in the weld pool geometry, caused by variations in the operational conditions, may strongly alter the weld metal solidification microstructure. In fact, more than nine different grain morphologies have been observed during fusion welding.15 The two most important are shown in Fig. 3.11. Referring to Fig. 3.11(a) a spherical or elliptical weld pool will reveal curved and tapered columnar grains owing to a shift in the direction of the maximum thermal gradient in the liquid from the fusion boundary towards the weld centre-line. In contrast, a tear-shaped weld pool yields straight and broad
Electrode
Weld pool
Arc
(a)
Electrode
Weld pool
Arc
(b)
Fig. 3.10. Schematic diagrams illustrating the major fluid flow mechanisms operating in a weld pool; (a) Buoyancy force (b) Electromagnetic force. columnar grains as shown in Fig. 3.11(b), since the direction of the maximum temperature gradient in the melt does not change significantly during the solidification process. The latter condition is known to promote formation of centre-line cracking because of mechanical entrapment of inclusions and enrichment of eutectic liquid at the trailing edge of the weld pool. 3.4.3 Growth rate of columnar grains The growth rate of the columnar grains is geometrically related to the weld travel speed and the weld pool shape. 3.4.3.1 Nominal crystal growth rate Since the shape of the weld pool remains constant during steady state welding, the growth rate of the columnar grains must vary with position along the fusion boundary. This point is more clearly illustrated in Fig. 3.12 which shows a sketch of a single columnar grain growing parallel with the steepest temperature gradient in the weld pool. Taking the angle between the
Surface tension Temperature Electrode
Weld pool
Arc
Surface tension
(C)
Temperature
Electrode
Arc Weld pool
(d)
Fig. 3.10. Schematic diagrams illustrating the major fluid flow mechanisms operating in a weld pool (continued); (c) Surface tension gradient force (negative gradient); (d) Surface tension gradient force (positive gradient).
Heat source
v
Heat source
v
(a)
(b)
Fig. 3.11. Schematic comparison of columnar grain structures obtained under different welding conditions; (a) Elliptical weld pool (low n3 values), (b) Tear-shaped weld pool (high n3 values). Open arrows indicate the direction of the maximum temperature gradient in the weld pool.
Fusion boundary
Heat source Crystal Fig. 3.12. Definition of the nominal crystal growth rate RN. growth direction and the welding direction equal to a, the steady state growth rate, R N , becomes: (3-8) where v is the welding speed. Considering spherical or elliptical weld pools, the nominal crystal growth rate is lowest at the edge of the weld pool (a—>90°, cosa-^0) and highest at the weld centre-line where R N approaches v (a->0, c o s a ^ l ) . In contrast, columnar grains trailing behind a tear-shaped weld pool will grow at an approximately constant rate which is significantly lower than the actual welding speed (a » 0), since the direction of the maximum temperature gradient in the weld pool does not change during the solidification process. This is also in agreement with practical experience (see Fig. 3.13).
(a) Nominal growth rate (RN), mm/s
Niobium (1 mm plate thickness)
Relative position from edge of weld pool (%)•
(b)
Equiaxed zone
Nominal growth rate (RN), mm/s
Stainless steel (1 mm plate thickness)
Relative position from edge of weld pool (%) Fig. 3.13. Measured crystal growth rates in thin sheet electron beam welding; (a) Niobium, (b) Stainless steel. Data from Senda et al.16
Example (3.1)
Consider electron beam (EB) welding of a lmm thin sheet of austenitic stainless steel under the following conditions:
Estimate on the basis of the Rosenthal thin plate solution (equation 1-83) the steady state growth rate of the columnar grains trailing the weld pool. Solution
The contour of the fusion boundary can be calculated from the Rosenthal thin plate solution according to the procedure shown in Example (1.10). If we include a correction for the latent heat of melting, the QbZn3 ratio at the melting point becomes:
Substitution of the above value into equation (1-83) gives the fusion boundary contour shown in Fig. 3.14. It is evident from Fig. 3.14 that the weld pool is very elongated under the prevailing circumstances due to a constrained heat flow in the ^-direction. This implies that the angle a will not change significantly during the solidification process. Taking a as an average, equal to about 70°, the steady-state crystal growth rate R N becomes:
This value is in reasonable agreement with the measured crystal growth rates in Fig. 3.13(b). 3.4.3.2 Local crystal growth rate Equation (3-8) does not take into account the inherent anisotropy of crystal growth. For faceted materials the dendrite growth directions are always those that are 'capped' by relatively slow-growing (usually low-index) crystallographic planes.1 Figure 3.15 shows examples of faceted cubic crystals delimited by {100} and {111} planes, respectively. If the {111} planes are the slowest growing ones, the {100} planes will grow out, leaving the {111} facets and a new crystal growing in the <100> directions as shown schematically in Fig. 3.15(b). Although most metals and alloys do not form faceted dendrites, the anisotropy of crystal growth is still maintained during solidification.2 In fact, experience has shown that the major dendrite growth direction is normally the axis of a pyramid whose sides are the most closely packed planes with which a pyramid can be formed.1 These directions are thus <100> for body- 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 crystals RL will always be higher than the nominal growth rate R N defined in equation (3-8). Consider now a cubic crystal which grows along the steepest temperature gradient in the weld pool, as shown schematically in Fig. 3.16. If § denotes the angle between the interface normal and the <100> direction, the following relationship exists between RN and RL:
-y(mm) Columnar zone
Heat source
Equiaxed zone +x(mm)
Columnar zone
+yjmm)
Fusion boundary
Fig. 3.14. Predicted shape of fusion boundary during electron beam welding of austenitic stainless steel (Example (3.1)).
(a)
(b)
Fig. 3.25.Examples of faceted cubic crystals; (a) Crystal delimited by {100} planes, (b) Crystal delimited by {111} planes.
Columnar grain
Welding direction (x)
Tip temperature, 0C
Fig. 3.16. Definition of the local crystal growth rate RL.
Liquidus temperature
Tip velocity, mm/sFig. 3.17. Calculated dendrite tip temperature vs dendrite growth velocity for an Fe-15Ni-15Cr alloy. The undercooling of the dendrite tip is given by the difference between the liquidus temperature and the solid curve in the graph. Data from Rappaz et alP
(3-9) which gives:
(3-10) Equation (3-10) shows that the local growth rate increases with increasing misalignment of
the crystal with respect to the direction of the maximum temperature gradient in the weld pool. Since such crystals cannot advance without a corresponding increase in the undercooling ahead of the solid/liquid interface (see Fig. 3.17), they will soon be outgrowed by other grains which have a more favourable orientation. Fusion welds of the fee and bcc type will therefore develop a sharp <100> solidification texture in the columnar grain region, similar to that documented for ingots and castings. The weld metal columnar grains may nevertheless be separated by 'high-angle' boundaries, as shown in Fig. 3.1&, due to a possible rotation of the grains in the plane perpendicular to their <100> length axes. Example (3.2)
Consider electron beam welding of a 2mm thick single crystal disk of Fe-15Ni-15Cr under the following conditions:
The orientation of the disk with respect to the beam travel direction is shown in Fig. 3.19. Calculate on the basis of the minimum velocity (undercooling) criterion the growth rate of the dendrites trailing the weld pool under steady state welding conditions (assume 2-D heat flow). Make also schematic drawings of the solidification microstructure in different sections of the weld. Relevant thermal properties for the Fe-15Ni-15Cr single crystal are given below:
Solution
Since the base metal is a single crystal, separate columnar grains will not develop. Nevertheless, under 2-D heat flow conditions growth of the dendrites can occur both in the [100] and the [010] (alternatively the [010]) direction. Referring to Fig. 3.20 the growth rate of the [100] and the [010] deridrites is given by:
and
Fig. 3.18. Spatial misorientation between two columnar grains growing in the <100> direction (schematic).
Heat source
Weld
Fig. 3.19. Orientation of the single crystal Fe-15Ni-15Cr disk with respect to beam travel direction (Example (3.2)).
Welding direction
Fig. 3.20. Schematic diagram showing the pertinent orientation relations between the fusion boundary interface normal and the dendrite growth directions (Example (3.2)). From this it is seen that the velocity of the [100] dendrites is always equal to that of the heat source v. In contrast, the growth rate of the [010] dendrites depends both on v and a, and will therefore vary with position along the fusion boundary. It follows from minimum velocity criterion that the [100] dendrites will be selected when the interface normal angle a is less than 45°, while the [010] dendrites will develop at larger angles. This is shown graphically in Fig. 3.21. At pseudo-steady state the fusion boundary can be calculated from the Rosenthal thin plate solution (equation (1-83)) according to the procedure shown in Example (1.10). If we include
R
hk ,
/V
dendrites
a, degrees Fig. 3.21.Normalised minimum dendrite tip velocity vs interface normal angle a (Example 3.2)).
a correction for the latent heat of melting, the QbIn3 ratio at the melting point becomes:
Substitution of this value into equation (1-83) gives the fusion boundary contour shown in Fig. 3.22(a). Included in Fig. 3.22 are also schematic drawings of the predicted solidification microstructure in different sections of the weld. The results in Fig. 3.22 should be compared with the reconstructed 3-D image of the solidification microstructure in Fig. 3.23, taken form Rappaz et al.17 Due to partial heat flow in the z-direction, [001] dendrite trunks will also develop. Nevertheless, these data confirm the general validity of equations (3-8) and (3-10) relating crystal growth rate to welding speed and weld pool shape. 3.4.4 Reorientation of columnar grains In principle, there are two different ways a columnar grain can adjust its orientation during solidification in order to accommodate a shift in the direction of the maximum temperature gradient in the weld pool, i.e.: (i) (ii)
Through bowing Through renucleation.
-y (mm)
(a)
dendrites
Heat source
dendrites
+x (mm)
dendrites +y (mm) Fusion boundary (b)
Fusion zone (4.4 mm)
Base plate
dendrites
dendrites
dendrites
Fig. 3.22. Schematic representation of the weld metal solidification micro structure (Example 3.2)); (a) Top view of fusion zone, (b) Transverse section of fusion zone.
3.4.4.1 Bowing of crystals A continuous change in the crystal orientation due to bowing will result in curved columnar grains, as shown previously in Fig. 3.2(a). This type of grain morphology has been observed in for instance electron beam welded aluminium and iridium alloys.34 Normally, the adjustment of the crystal orientation is promoted by multiple branching of dendrites present within the grains. Alternatively, the reorientation can be accommodated by the presence of surface defects at the solid/liquid interface, e.g. screw dislocations, twin boundaries, rotation boundaries, etc. The latter process presumes, however, a faceted growth morphology, and is therefore of minor interest in the present context. Example (3.3)
Consider a curved columnar grain of iridium which grows from the fusion boundary towards the weld centre-line along a circle segment of length L, as shown schematically in Fig. 3.24. Based on the assumption that the bowing is accommodated solely by branching of [010] dendrites in the [100] direction, calculate the maximum local growth rate of the crystal during solidification.
y X
2 Fig. 3.23. Reconstructed 3-D image of solidification microstructure in an electron beam welded Fe-15Ni15Cr single crystal. The letters (a), (b) and (c) refer to [100], [010] and [001] type of dendrites, respectively. After Rappaz et al.17 Weld centre-line
Fusion line
Fig. 3.24. Sketch of curved columnar grain in Example (3.3). Solution In principle, the solution to this problem is identical to that presented in Example (3.2). Referring to Fig. 3.24 the growth rate of [100] and the [010] dendrite stems is given by:
and
It follows from Fig. 3.21 that growth will occur preferentially in the [010] direction as long as the interface normal angle a is larger than 45°, while the [100] direction is selected at smaller angles. This means that the local growth rate of the dendrites, in practice, never will exceed the welding speed v. 3.4.4.2 Renucleation of crystals In ingots and castings, three different mechanisms for nucleation of new grains ahead of the advancing interface are operative:12 (i) (ii) (iii)
Heterogeneous nucleation Dendrite fragmentation Grain detachment.
The former mechanism is of particular importance in welding, since the weld metal often contains a high number of second phase particles which form in the liquid state. These particles can either be primary products of the weld metal deoxidation or stem from reactions between specific alloying elements which are deliberately introduced into the weld pool through the filler wire. The latter process is also known as inoculation. Nucleation potency of second phase particles In general, the effectiveness of individual particles to act as heterogeneous nucleation sites can be evaluated from a balance of interfacial energies, analogous to that described in Section 3.3.1 for epitaxial nucleation. It follows from the definition of the wetting angle (3 in Fig. 3.5 that the energy barrier to heterogeneous nucleation is a function of both the substrate/liquid interfacial energy ySL, the substrate/embryo interfacial energy yES, and the embryo/liquid interfacial energy yEL. Complete wetting is achieved when: (3-11) Under such conditions, the nucleus will readily grow from the liquid on the substrate. Unfortunately, data for interfacial energies are scarce and unreliable, which makes predictions based on equation (3-11) rather fortuitous.18 In pure metals, experience has shown that the solid/liquid interfacial energies are roughly proportional to the melting point, as shown by the data in Fig. 3.25. On this basis, it can be expected that the higher melting point phases will reveal the highest ySL values, and thus be nucleants for lower melting phases. A similar situation also exists in the case of non-metallic inclusions in liquid steel, where the high-melting point phases are seen to exhibit the highest solid/liquid interfacial energies (see Fig. 3.26). In contrast, very little information is available on the substrate/embryo interfacial energy yES. For fully incoherent interfaces, yES would be expected to be of the order of 0.5 to 1 J m~2.5 However, this value will be greatly reduced if there is epitaxy between the inclusions and the nucleus, which results in a low lattice disregistry between the two phases. In general, assessment of the degree of atomic misfit between the nucleus n and the substrate s can be done on
Melting point, K
Interfacial energy, J / m 2
lnterfacial energy, J/m2
Fig. 3.25. Values of solid/liquid interfacial energy ySL of various metals as function of their melting points. Data from Mondolfo.18
Melting point, 0 C Fig. 3.26. Values of interfacial energy 7 5L for different types of non-metallic inclusions in liquid steel at 16000C as function of their melting points. Data compiled from miscellaneous sources.
the basis of the Bramfitt's planar lattice disregistry model :19
(3-12)
a low-index a low-index a low-index a low-index
where
plane of the substrate; direction in (hkl)s plane in the nucleated solid; direction in (hkl)n;
the interatomic spacing along [wvw]n; the interatomic spacing along [WVH>]5; and the angle between the [wvw]^ and the [wvw]w.
Undercooling, 0C
In practice, the undercooling Ar (which is a measure of the energy barrier to heterogeneous nucleation) increases monotonically with increasing values of the planar lattice disregistry, as shown by the data in Fig. 3.27. This means that the most potent catalyst particles are those which also provide a good epitaxial fit between the substrate and the embryo. Examples of such catalyst particles are TiAl3 in aluminium 18 and TiN in steel.19 Nucleation of delta ferrite at titanium nitride will be considered below.
« „ « > Fig. 3.27. Relationship between planar lattice disregistry and undercooling for different nucleants in steel. Data compiled from miscellaneous sources.
Example (3.4)
In low-alloy steel weld metals, titanium nitride can form in the melt due to interactions between dissolved titanium and nitrogen. Assume that the TiN particles are faceted and delimited by {100} planes. Calculate on the basis of equation (3-12) the minimum planar lattice disregistry between TiN and the nucleating delta-ferrite phase under the prevailing circumstances. Indicate also the plausible orientation relationship between the two phases. The lattice parameters of delta ferrite and TiN at 15200C may be taken equal to 0.293 and 0.43 lnm, respectively. Solution
Titanium nitride has the NaCl crystal structure, while delta ferrite is body-centred cubic, as shown in Fig. 3.28(a) and (b). It is evident from Fig. 3.29(a) that a straight cube-to-cube orientation relationship between TiN and 8-Fe will not result in a small lattice disregistry. However, the situation is largely improved if the two phases are rotated 45° with respect to each other (see Fig. 3.29(b)), conforming to the following orientation relationship:
The resulting crystallographic relationship at the interface is shown schematically in Fig. 3.29(c). Since the lattice arrangements are similar in this case, equation (3-12) reduces to:
A comparison with the data in Fig. 3.27 shows that the calculated lattice disregistry conforms to an undercooling of about 1 to 2°C. This value is sufficiently small to facilitate heterogeneous nucleation of new grains ahead of the advancing interface during solidification. Considering other inclusions with more complex crystal structures, the chances of obtaining a small planar lattice disregistry between the substrate and the delta ferrite nucleus are
Fe- atoms
N-atoms
Ti- atoms (a)
(b)
Fig. 3.28. Crystal structures of phases considered in Example (3.4); (a) Titanium nitride, (b) Delta ferrite.
TiN
(a)
TiN
(C) (b)
Ti atoms
N atoms
8-Fe atoms
Fig. 3.29. Possible crystallographic relationships between titanium nitride and delta ferrite (Example (3.4)); (a) Straight cube-to-cube orientation, (b) Twisted cube-to-cube orientation, (c) Details of lattice arrangement along coherent TiN/d-Fe interface.
rather poor (see Fig. 3.27). Nevertheless, such particles can act as favourable sites for heterogeneous nucleation if 7 ^ is sufficiently large compared with yEL and 7 ^ . This is illustrated by the following example: Example (3.5)
In low-alloy steel weld metals 7-Al2O3 inclusions can form during the primary deoxidation stage as discussed in Section 2.12.4.2 (Chapter 2). Based on the classic theory of heterogeneous nucleation, evaluate the nucleation potency of such inclusions with respect delta ferrite.
Solution
It is readily seen from Fig. 3.27 that the planar lattice disregistry between delta ferrite and Al2O3 is very large, which indicates of a fully incoherent interface (i.e. yES « 0.75 J m" 2 ). Moreover, readings from Figs. 3.25 and 3.26 give the following average values for the delta ferrite/liquid and the inclusion/liquid interfacial energies:
and
According to equation (3-11) complete wetting is achieved when ySL > yES + yEL. This requirement is clearly met under the prevailing circumstances. Similar calculations can also be performed for other types of non-metallic inclusions in steel weld metals. The results are presented graphically in Fig. 3.30. It is evident that the nucleation potency of the inclusions increases in the order SiO2-MnO, Al 2 O 3 -Ti 2 O 3 -SiO 2 MnO, Al2O3, reflecting a corresponding increase in the inclusion/liquid interfacial energy ySL. The resulting change in the weld metal solidification microstructure is shown in Fig. 3.31, from which it is seen that both the average width and length of the columnar grains decrease with increasing Al2O3-contents in the inclusions. This observation is not surprising, considering the characteristic high solid/liquid interfacial energy between aluminium oxide and steel (see Fig. 3.26). The important effect of deoxidation practice on the weld metal solidification microstructure is well documented in the literature.320"22 Rate of heterogeneous nucleation It can be inferred from the classic theory of heterogeneous nucleation that the nucleation rate
Complete wetting
No wetting
Embryo'
A
G*he/AGhom
p (degrees)
Inclusion
(Y sf Y ES )/7 EL Fig. 3.30. Nucleation potency of different weld metal oxide inclusions with respect to delta ferrite.
AI2O3 content (wt%)
(a)
Average width of grains, ^i m
95% confidence limit
Pure AI2O3
(A%AI)weld/[%O]anaL AI2O3 content (wt%)
(b)
Average length of grains, ^m
95% confidence limit Pure AI2O3
Nhet(i.e. number of nuclei which form per unit time and unit volume of the melt) is interrelated to the energy barrier AG^ through the following equation:5
(3-13) whereZ1 is a frequency factor, Nv is the density of nucleation sites per unit volume of the melt,
AGD is the activation energy for diffusion of atoms across the interface, and k is the Boltzmann constant. 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 of catalyst 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 precipitation on the columnar grain structure in 1100 aluminium welds is illustrated in Fig. 3.32.
Critical cell/dendrite alignment angle It follows from the minimum growth rate criterion and the definition of the local crystal growth rate 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 on the nucleation potency of the catalyst particles and can be estimated for different types of welds. If growth of the columnar grains is assumed to occur along a circle segment of length L (see Fig. 3.33), the critical cell/dendrite alignment angle is given by: (3-15)
Average width of grains, (x m
where co is the total grain rotation angle, and / is the average length of the columnar grains (in mm).
Titanium content, wt% Fig. 3.32. Effect of titanium on the columnar grain structure in 1100 aluminium welds. The value Y is the fractional distance from fusion line to top surface of weld metal. Data from Yunjia et alP
Weld metal
Fig. 3.33. Characteristic growth pattern of columnar grains in bead-on-plate welds (schematic). By introducing reasonable average values for co and / in the case of SA welding of lowalloy steel,22 we obtain: (3-16) Calculated values for 4>* in steel weld metals are presented in Fig. 3.34, using data from Kluken et al.22 An expected, the critical cell/dendrite alignment angle in fully aluminium deoxidised steel welds is seen to be very small (of the order of 2°), reflecting the fact that nucleation of delta ferrite occurs readily at Al2O3 inclusions. The value of 4>* increases gradually with decreasing Al2O3 contents in the inclusions and reaches a maximum of about 4° for Si-Mn deoxidised steel weld metals. This situation can be attributed to less favourable nucleating opportunities for delta ferrite at silica-containing inclusions, which reduces the possibilities of obtaining a change in the crystal orientation during solidification through a nucleation and growth process. Dendrite fragmentation In principle, nucleation of new grains ahead of the advancing interface can also occur from random solid dendrite fragments contained in the weld pool. Although the source of these solid fragments has yet to be investigated, it is reasonable to assume that they are generated by some process of interface fragmentation due to thermal fluctuations in the melt or mechanical disturbances at the solid/liquid interface.3 At present, it cannot be stated with certainty whether grain refinement by dendrite fragmentation is a significant process in fusion welding.26 Grain detachment Since the partially melted base metal grains at the fusion boundary are loosely held together by liquid films between them, there is also a possibility that some of these grains may detach themselves from the base metal and be trapped in the solidification front.26 Like dendrite fragments, such partially melted grains can act as seed crystals for the formation of new grains in the weld metal during solidification if they are able to survive sufficiently long in the melt.
R L / v cos a
Next Page
Calculated from equation (3-10)
Critical cell/dendrite alignment angle ($*) Fig. 3.34. Critical cell/dendrite alignment angle ()>* for reorientation of delta ferrite columnar grains during solidification of steel weld metals. Data from Kluken et al.22
3.5 Solidification Microstructures So far, we have discussed growth of columnar grains without considering in detail the weld metal solidification microstructure. In general, each individual grain will exhibit a substructure consisting of a parallel array of dendrites or cells. This substructure can readily be revealed by etching, also in cases where it is masked by subsequent solid state transformation reactions (as in ferrous alloys).2224 3.5.1 Substructure characteristics A cellular substructure within a single grain consists of an array of parallel (hexagonal) cells which are separated from each other by 'low-angle' grain boundaries, as shown schematically in Fig. 3.35. In the presence of solute, these boundaries respond to etching even in the absence of segregation. When the cellular to dendritic transition occurs, the cells become more distorted and will finally take the form of irregular cubes, as indicated by the optical micrograph in Fig. 3.36. This is actually a dendritic type of substructure, where the formation of secondary and tertiary dendrite arms is suppressed because of a relatively small temperature gradient in the transverse direction compared with the longitudinal (growth) direction. Fully branced dendrites may, however, develop in the centre of the weld if the thermal conditions are favourable. Branching will then occur in specific crystallographic directions, e.g. along the three <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 primarily 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 heat flow direction, regardless of the crystal orientation. This important point is often overlooked when discussing competitive grain growth in fusion welding.
R L / v cos a
Previous Page
Calculated from equation (3-10)
Critical cell/dendrite alignment angle ($*) Fig. 3.34. Critical cell/dendrite alignment angle ()>* for reorientation of delta ferrite columnar grains during solidification of steel weld metals. Data from Kluken et al.22
3.5 Solidification Microstructures So far, we have discussed growth of columnar grains without considering in detail the weld metal solidification microstructure. In general, each individual grain will exhibit a substructure consisting of a parallel array of dendrites or cells. This substructure can readily be revealed by etching, also in cases where it is masked by subsequent solid state transformation reactions (as in ferrous alloys).2224 3.5.1 Substructure characteristics A cellular substructure within a single grain consists of an array of parallel (hexagonal) cells which are separated from each other by 'low-angle' grain boundaries, as shown schematically in Fig. 3.35. In the presence of solute, these boundaries respond to etching even in the absence of segregation. When the cellular to dendritic transition occurs, the cells become more distorted and will finally take the form of irregular cubes, as indicated by the optical micrograph in Fig. 3.36. This is actually a dendritic type of substructure, where the formation of secondary and tertiary dendrite arms is suppressed because of a relatively small temperature gradient in the transverse direction compared with the longitudinal (growth) direction. Fully branced dendrites may, however, develop in the centre of the weld if the thermal conditions are favourable. Branching will then occur in specific crystallographic directions, e.g. along the three <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 primarily 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 heat flow direction, regardless of the crystal orientation. This important point is often overlooked when discussing competitive grain growth in fusion welding.
Cell wall'
Fig. 3.35. Schematic representation of the cellular substructure.
Fig. 3.36. Optical micrograph showing the characteristic cellular-dendritic substructure in a low-alloy steel weld. The metallographic section is normal to the columnar grain growth direction. After Kluken etal.22
Fig. 3.37. Schematic representation of the development of primary, secondary and tertiary dendrite arms along <100> directions in cubic crystals.
A characteristic feature of cellular and cellular-dendritic growth is also that the boundary between two adjacent columnar grains will closely follow the contours of the original cell boundaries. An illustration of this point is contained in Fig. 3.38. Consequently, since all cell walls are preferential sites for segregation during solidification (see ion micrograph in Fig. 3.39), the presence of solute at the columnar grain boundaries can strongly alter the kinetics of subsequent solid state transformation reactions. The indications are that for instance phosphorus segregations at prior austenite grain boundaries will promote the formation of grain boundary ferrite in low-alloy steel weld metals during the 7 to a transformation because of the associated increase in the A
(a)
(b)
Fig. 3.39. Ion (SIMS) micrograph showing evidence of phosphorus segregations at primary solidification (cell) boundaries in a low-alloy steel weld. After Kluken et al22
3.5.2 Stability of the solidification front The stability of the solid/liquid interface is critical in determining the microstructural characteristics of the weld metal. 3.5.2.1 Interface stability criterion The simplified treatment given here is based on the constitutional undercooling criterion which ignores the important effect of capillarity on the interface stability. Consider a simple binary system, the phase diagram of which is given in Fig. 3.40(a). During solidification, a solute-rich layer will form in front of the growing interface, as shown schematically in Fig. 3.40(b). At steady state, the mass of solute transferred from the liquid to the interface, R1(C1Jp is equal to the mass of solute which accumulates in the solid, R1(C8)^ minus the amout which diffuses back into the liquid, D1(O1C1Za1X)1. Hence, we may write:
(3-17) Provided that equilibrium exists at the solid/liquid interface, i.e. (Cs)t = IcJC1J1, equation (3-17) can be rewritten as: (3-18) where DL is the diffusivity of the solute in the liquid, and ko is the equilibrium partition coefficient (Jco < 1).
Temperature
(a)
Concentration
Liquid composition
(b)
Distance (x)
Temperature
(C)
Liquidus temperature (TL)
Constitutionally undercooled region
Distance (x) Fig. 3.40. Constitutional undercooling in alloy solidification; (a) Schematic representation of binary phase diagram, (b) Build-up of solute-enriched layer in front of solid/liquid interface, (c) Undercooled region ahead of solid/liquid interface.
With the aid of the phase diagram in Fig. 3.40(a) it is easy to verify that the equilibrium liquidus temperature increases with distance from the interface because of the lower solute content. Referring to Fig. 3.40(c) the latent heat of melting AHm will diffuse away from the interface (thereby stabilising possible interface protuberances) if the actual temperature gradient in the liquid (dTA/dx)t is less than the equilibrium liquidus temperature gradient (3T1ZdX)1. The latter gradient can be expressed as: (3-19)
where (dTL/dCL)i denotes the slope of the liquidus curve in the phase diagram (designated mL). By combining equations (3-18) and (3-19), we obtain the following criterion for the interface stability: (3-20)
Taking (C1). = C0Ik0 and Rj = RL this equation can alternatively be written as:
(3-21)
3.5.2.2 Factors affecting the interface stability It follows from equation (3-21) that the stability of the weld metal solidification front is controlled by the extent of constitutional undercooling ahead of the advancing interface, and is therefore influenced by factors such as the total amount of alloying or impurity elements present, C0, the local crystal growth rate, RL, and the thermal gradient in the weld pool, GL. The combined effects of alloy content, growth rate, and thermal gradient are presented schematically in Fig. 3.41. It can be seen from the figure that a planar solidification front is favoured by a high GL/RL ratio, in agreement with predictions based on equation (3-21). At lower GLIRL ratios, the morphology of the interface changes to cellular, cellular-dendritic or dendritic, depending on the degree of constitutional undercooling ahead of the advancing interface. Normally, the GL/RL ratio close to the fusion line is large enough to facilitate cellular solidification. The temperature gradient in the weld pool decreases, however, with distance from the fusion boundary and hence, a cellular-dendritic type of substructure is often observed in the central areas of the columnar grain region.22 This substructure may change to dendritic close to the weld centre-line if the degree of constitutional undercooling in front of the advancing interface is sufficiently large. The various types of growth products that may develop during normal solidification of fusion welds are shown schematically in Fig. 3.42. Example (3.6)
In aluminium welding, binary Al-Si and Al-Mg alloys are frequently used as filler metals. Consider stringer bead deposition with an Al-4.5wt%Si filler wire at a constant welding speed of 1.5mm s"1. Based on equation (3-21) calculate the critical (minimum) temperature gradient
Alloying level (C )
Planar
GL/RL Fig. 3.41. Schematic representation of the combined effect of crystal growth rate RL and melt thermal gradient GL on the weld metal solidification microstructure.
Fusion zone v
Larger R L, Small RL, Small GL Large G1
Weld centre-line
Equiaxed-dendritic Cellular-dendritic Cellular
HAZ grains
Fig. 3.42. Schematic diagram illustrating structural variations in the weld metal solidification microstructure across the fusion zone. in the weld pool which gives a planar solidification front. Relevant physical data for the Al-Si system are given below:2
Solution
When mL, ko and D1 are known the critical temperature gradient (G1)cr can readily be calculated from equation (3-21). Taking RL ~ v, we obtain:
The above calculations show that the temperature gradient in the weld pool must be extremely large in order to promote a planar solidification front. The calculated value for (GL)cr corresponds to a cooling rate of about 92 4000C s"1 (CR. = G1R1). Besides low-heat input electron beam and laser welding, such high cooling rates are rarely observed in fusion welding (see Fig. 3.3). On this basis it is not surprising to find that the weld metal solidification microstructure is normally of the cellular or the dendritic type. For a rough evaluation of the weld metal solidification microstructure the diagram in Fig. 3.43 can be used. This diagram summarises the various microstructures which can be obtained (using a typical alloy with a melting range of 500C) when the imposed temperature gradient GL and crystal growth rate RL are varied. Moving from the lower left to the upper right along the lines at 45° leads to a refinement of the structure without changing the morphology (constant GL/RL ratio). Crossing these lines by passing from the upper left to the lower right leads to changes in the morphology from planar to cellular or dendritic growth, while the scale of the microstructure remains essentially the same. The gray bands define the regions over which one structure changes into another. An example of the application of this diagram is given below. Example (3.7)
Consider GTA butt welding of a 2mm thin sheet of aluminium (Al-Mg alloy) under the following conditions:
Based on the diagram in Fig. 3.43, estimate the weld metal solidification microstructure in different positions from the fusion boundary. In these calculations we shall assume that the actual thermal gradient in the weld pool is equal to the average thermal gradient within the temperature interval from 680 to 5500C, as evaluated from the Rosenthal thin plate solution (equation (1-83)). Relevant thermal data for the Al-Mg alloy are given in Table 1.1 (Chapter 1). Solution
The contours of the fusion boundary and the 680 and the 5500C isotherms can be calculated according to the procedure shown in Example (1.10). If we neglect the latent heat of melting, the corresponding 68//?3 ratios at these temperatures become:
GL,°C/mm
RL, mm/s Fig. 3.43. Variation of weld metal solidification microstructure with GL and RL. The diagram is based on the ideas of Kurz and Fisher.2
Substitution of the above values into equation (1-83) gives the isothermal contours shown in Fig. 3.44. It follows from Fig. 3.44 that the thermal gradient decreases from about 25°C mnr 1 at the fusion boundary to approximately 100C mm"1 close to the weld centre-line. This occurs parallel with an increase in the nominal crystal growth rate from 0.8 to 4mm s"1. According to Fig. 3.43 the calculated values of GL and RL conform to a cellular-dendritic solidification microstructure within the central regions of the weld and an equiaxed-dendritic microstructure close to the weld centre-line. Both types of substructures are commonly observed in aluminium weldments.2728 Weld pool (680 0C) Fusion boundary (650 0C) HAZ (550 0C)
+x (mm)
+Y (mm) Fig. 3.44. Predicted shape of fusion boundary and neighbouring isotherms during thin plate aluminium welding (Example (3.6)).
3.5.3 Dendrite morphology Within the fully dendritic region of the weld, the dendrite morphology remains largely unchanged over a wide range of cooling rates. Nevertheless, it will become finer as the heat is extracted at greater rates.
Tip radius,\irr\
3.5.3.1 Dendrite tip radius A combination of stability analysis with diffusion considerations and the specification of a dendrite tip shape and a radius selection criterion can lead to an unique solution for the morphology and solute distribution around a growing dendrite.2930 Based on such analyses it is possible to calculate the dendrite tip radius rd as function of the growth rate RL and the thermal gradient GL in the weld pool for a given alloy system.17 Referring to Fig. 3.45, the dendrite growth is seen to occur between two stability limits. At low speeds, the rd vs R1 curve reaches a threshold where the tip radius increases rapidly and finally approaches an infinite value corresponding to a planar solidification front. At high speeds, an absolute stability limit is also found. This corresponds to the limiting case where the transport of solute across the interface becomes too sluggish to keep pace with the advancing solidification front. However, within the central areas of the curve, the dendrite tip radius is seen to decrease steadily with increasing values of RD typically as l/(RL)m. Note that the thermal gradient in the weld pool GL will have a strong influence on the low growth rate stability limit. In contrast, the absolute stability limit is essentially independent of GL, as indicated in Fig. 3.45.
Growth rate, mm/s Fig. 3.45. Predicted relationship between dendrite tip radius rd, crystal growth rate RL and melt thermal gradient GL for a Fe-15Cr-15Ni alloy. Data from David and Vitek.4
3.5.3.2 Primary dendrite arm spacing The primary dendrite arm spacing (defined in Fig. 3.46) is an important characteristic of the solidification microstructure and has a marked effect on the weld metal mechanical properties. If it is assumed that the dendrite envelope, representing the mean cross-section of the trunk, can be described by an ellipse (see Fig. 3.47), the radius of curvature of the ellipse is given by:2 (3-22) In general, the half width b of the dendrite stem is proportional to the primary arm spacing X1. In cases where the arrangement of the dendrite trunks can be represented by a simple close-packed hexagonal array, the value of b is exactly equal to X1 IV3 -2 Similarly, the total length of the dendrite stem g can be calculated by considering the difference between the tip temperature Ttip and the root temperature Troot, as shown in Fig. 3.48. Taking the thermal gradient in the mushy zone equal to GL, we obtain:
(3-23)
This gives the following relationship between the primary dendrite arm spacing X1, the tip radius rd and the thermal gradient GL: (3-24)
rd
9
b Fig. 3.46. Definition of primary X1 and secondary X2 dendrite arm spacings.
tig. 3.47.Geometrical relationship between the radius of curvature rd and the width to length ratio of an elliptical dendrite.
Ttip
Troot 9 Heat flow
X
Cell/dendrite
Fig. 3.48. Definition of the dendrite tip Ttip and root Troot temperatures. If we also take into account that the dendrite tip radius rd is inversely proportional to the square root of the crystal growth rate RL within the central range of RL (see Fig. 3.45), equation (3-24)reduces to: (3-25)
where c{ is a kinetic constant which is characteristic of the alloy system under consideration. It is evident from the above analysis that the primary dendrite arm spacing cannot readily be characterised by one single parameter (e.g. the cooling rate), since its dependence on GL and R1 have different exponents.
Example (3.8)
Based on equation (3-25), show that the following relationships exist between the primary dendrite arm spacing X1, the net arc power qo, and the weld travel speed v during thick plate and thin plate welding, respectively: Thick plate welding: (3-26) Thin plate welding: (3-27) where c2 and c3 are proportionality constants.
Solution
Under 3-D heat flow conditions, the pseudo-steady state temperature distribution is given by the Rosenthal thick plate solution (equation (1 -45)). For points located on the weld centre-line behind the heat source y = z = 0, and R* = -x. Hence, equation (1-45) reduces to:
The thermal gradient GL in the mushy zone close to the weld centre-line can be obtained by differentiating of the above equation with respect to the x-coordinate:
(3-28)
By inserting the appropriate expressions for GLandRL into equation (3-25) (noting that RL=v at the weld centre-line), we arrive at an expression for X1 which is identical with the one presented in equation (3-26). Similarly, under 2-D heat flow conditions, the pseudo-steady state temperature distribution is given by the Rosenthal thin plate solution (equation 1-81). For points located on the weld centre-line behind the heat source y = 0 and r = -x = vt. If IxI is sufficiently large, it is a fair approximation to set Ko(u) ~ exp(-u)^n!2u . Hence, equation (1-81) reduces to:
The thermal gradient GL is then given as:
(3-29) From this we see that the primary dendrite arm spacmg X1 during thin plate welding is interrelated to qo and v through a relationship of the type shown in equation (3-27). In Fig. 3.49 the validity of equation (3-26) has been checked against the experimental data of Jordan and Coleman,27 who measured the primary dendrite arm spacing in different GMA Al-Mg-Mn welds. It is evident from this plot that their data-points can approximately be represented by straight lines passing through the origin, as required by the theory. Moreover, a closer inspection of the figure shows that the dendrite arm spacing close to the centre-line varies systematically from the bottom to the top of the weld. This observation is not surprising, considering the fact that the rate of solidification increases progressively from the toe to the surface of the plate. Example (3.9)
Consider GTA butt welding of a 2mm thin aluminium sheet (Al-Mg alloy) under conditions similar to those employed in Example (3.7). Based on equation (3-25) calculate the relative change in the primary dendrite arm spacing X1 from the fusion boundary to the weld centreline during solidification.
Primary dendrite arm spacing, p,m
GMAW (Al-Mg-Mn alloys) Just above toe of weld Level with surface of plate
Parallel to plate surface Just above toe. of weld
[(qo)1/2/(v)1/4],(WS1/2/mm1/2)1/2 Fig. 3.49. Experimental verification of equation (3-26). Data from Jordan and Coleman.27
Solution
As shown in Fig. 3.44, the thermal gradient, GL, decreases from about 25°C mm"1 at the fusion boundary to approximately 10°C mm"1 close to the weld centre-line. This occurs parallel with an increase in the nominal crystal growth rate from 0.8 to 4mm s"1. Taking the primary dendrite arm spacing at the fusion boundary equal to X1*, the ratio X1 /X1* in different positions of the weld becomes: Central region of columnar zone:
Weld centre-line:
In contrast to that predicted above, the smallest dendrite arm spacing is normally observed at the weld centre-line.26 This has to do with the fact that the constant C1 in equation (3-25), in practice, decreases with increasing distance from the fusion boundary due to solute segregation, which gradually reduces the coarsening rate of the dendrites. 3.5.3.3 Secondary dendrite arm spacing It follows from the above analysis that the primary dendrite arm spacing, once it has been
established, will remain constant during subsequent cooling of the weld. This is not true of the secondary arms (see definition in Fig. 3.46), which undergo a continuous ripening process. Hence, their size and morphology will change with time as the thicker branches grow larger at the expense of the smaller ones.2 The driving force for the ripening process is the disparity in chemical potential (interfacial energy) between branches with different curvature. Since this process is analogous to the Ostwald ripening of precipitates (see equation (2-76)), the spacing of the branches, X2, will be a simple cube root function of the local solidification time fo:1'2 (3-30) where M is a mobility term defined as:2 (3-31)
The parameter Q in equation (3-31) refers to the Gibbs-Thomson coefficient and is given as: (3-32) where a is the solid/liquid interfacial energy, and AS, is the entropy of fusion. In practice, the value of M can easily vary by an order of magnitude. Nevertheless, its effect on the secondary dendrite arm spacing is rather weak, since X2 is proportional to the cube root of M. Hence, a plot of the secondary dendrite arm spacing vs the local solidification time in a logarithmic diagram will normally reveal a straight-line relationship between X2 and to with a slope close to 0.33, as shown in Fig. 3.50.
X2^m
GTAW (Stainless steel)
Slopes 0.33
to'5 Fig. 3.50. Relation between secondary dendrite arm spacing X2 and local solidification time to in type AISI 310 stainless steel welds. Data from Kou and Lee.31
Example (3.10)
Based on equation (3-30), derive a relationship between the secondary dendrite arm spacing X2, the net arc power qo, and the weld travel speed v during thick plate welding. Calculate then the secondary dendrite arm spacing in the centre of a thick GTA Al-Si weld deposited under the following conditions:
Relevant physical data for the Al-Si system are given below:2
Solution
The local solidification time to is the time for the dendrite array to pass an arbitrary point in the weld and is therefore a measure of the solidification rate. Referring to Fig. 3.48, the local solidification time is defined as: (3-33)
By inserting the appropriate expressions for GL (equation (3-28)) and RL in position y = z = 0, we obtain the following relationship between to, qo and v during thick plate welding:
(3-34)
A combination of equations (3-30) and (3-34) gives:
(3-35)
In the present example, the numerical values of M and X2 are:
and
Although reliable experimental data are not available for a direct comparison, the calculated value for X2 is considered reasonably correct. In Al-Cu castings a secondary dendrite arm spacing of about 4(im corresponds to a cooling rate of the order of 103 °C s"1, as shown in Fig. 3.51. In the present example, the cooling rate at the solid/liquid interface is close to:
This value is compatible with a secondary dendrite arm spacing of 4|am. Example (3.11)
The operating parameters given in Example (3.10) are also applicable to single pass butt welding of thin aluminium plates. Based on equation (3-30), estimate the secondary dendrite arm spacing in the centre of a 2mm thick Al-Si butt weld deposited under such conditions. Solution
In thin plate welding the local solidification time to is obtained by combining equations (3-29) and (3-33). Noting that RL = v at the weld centre-line, we get:
(3-36)
X 2 ,nm
AI-4.5 wt% Cu
Cooling rate, °C/s Fig. 3.57.Relation between secondary dendrite arm spacing X2 and cooling rate CR. in Al-Cu castings. Data compiled by Munitz.32
The secondary dendrite arm spacing is thus given as:
(3-37)
Taking pc equal to 0.0027 J mm
3
C ] in the case of Al-Si alloys, we obtain:
It is evident from the above calculation that the secondary dendrite arm spacing is significantly coarser in thin plate welding compared with thick plate welding. This observation is not surprising, considering the pertinent difference in the heat transfer mode and thus the cooling rate between these two types of weldments. In the former case, we have:
A comparison with the data in Fig. 3.51 shows that a cooling rate of about 78°C s"1 is compatible with a secondary dendrite arm spacing of 13 jim.
3.6 Equiaxed Dendritic Growth As already stated in the introduction of the chapter, an equiaxed zone is often observed close to the weld centre-line. This zone can in certain cases be very dominating and completely override the columnar grain zone, as shown in Fig. 3.52. As long as growth occurs in a columnar manner the crystals are in contact with solid metal. The heat will therefore be conducted through the crystals in a direction which is parallel and opposite to their growth direction, as illustrated in Fig. 3.53(a). In equiaxed dendritic growth the situation is different. Here the melt will be slightly undercooled because of extensive segregation of solute to the weld centre-line where the solidification fronts growing from each side impinge. This makes the crystals hotter than the liquid and gives rise to a radial heat flow away from the crystals in the same direction as that of growth (see Fig. 3.53(b)). 3.6.1 Columnar to equiaxed transition In fusion welds, the GL/RL ratio decreases continuously from the fusion boundary to the weld centre-line during the crystallisation process. For a given alloy system containing a fixed number of heterogenous nucleation sites it is reasonable to assume that the columnar to equiaxed
CL
FL
FL
CL
Fig. 3.52.Example of grain refinement in an Al-Mg-Si plasma arc weld due to TiAl3-precipitation (FL: fusion line, CL: centre-line). Courtesy of M.I. Onsoien, SINTEF, Trondheim, Norway. transition occurs when the GJR1 ratio drops below a certain critical value fcn. Hence, we may write: (3-38) During thick plate welding (3-D heat flow) the temperature gradient at the weld centre-line is given by equation (3-28). Taking RL = v, a combination of equations (3-28) and (3-38) gives:
(3-39)
where c4 is a kinetic constant which is characteristic of the alloy system under consideration. Similarly, for welding of medium thick plates (mixed heat flow), we get: (3-40) where c5 is a new kinetic constant, and n is an exponent which varies between zero and unity depending on the mode of heat flow (i.e. thin, medium thick or thick plate welding).
(a)
(b)
Heat flow
Fig. 3.53. Schematic diagrams showing different dendrite growth morphologies in castings; (a) Columnar dendritic growth, (b) Equiaxed dendritic growth. The diagrams are based on the ideas of Kurz and Fisher.2
Equation (3-40) predicts that the columnar to equiaxed transition in fusion welds occurs at critical combinations of the net arc power qo and the welding speed v. Thus, a decrease in qo must always be compensated by a corresponding increase in v in order to maintain equiaxed dendritic growth at the weld centre-line. This is also in agreement with general experience (see Fig. 3.54). Example (3.12)
Based on the experimental data in Fig. 3.54, calculate the critical G1IR1 ratio which provides equiaxed dendritic growth during thick plate welding of Al-Mg alloys (5083 series). Relevant thermal data for the Al-Mg system are given in Table 1.1 (Chapter 1).
Net arc power, kW
Plate thickness: 10-12 mm
Welding speed, mm/s Fig. 3.54. Effect of net arc power qo and welding speed v on the columnar to equiaxed transition in different aluminium welds. Data from Matsuda et al.33
Solution
The critical G1IR1 ratio is obtained by rearranging equation (3-39):
By inserting data from Fig. 3.54 and Table 1.1, we get:
By multiplying fcr with the welding speed we see that the calculated value corresponds to a critical temperature gradient of about 928°C mm"1. This means that the thermal conditions existing in welding will favour growth of equiaxed dendrites close to the weld centre-line. A requirement is, of course, that the melt contains a sufficient number of seed crystals to facilitate heterogeneous nucleation of new grains ahead of the advancing solid/liquid interface.
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3.6.2 Nucleation mechanisms Several nucleation mechanisms have been proposed to explain the columnar to equiaxed transition during weld pool solidification, including:26 (i) (ii) (iii)
Heterogeneous nucleation Dendrite fragmentation Grain detachment.
The former mechanism is particularly relevant to welding, since the weld metal often contains a high number of second phase particles which form in the liquid state. As already mentioned in Section 3.4.4.2, these particles can either be primary products of the weld metal deoxidation or stem from reactions between specific alloying elements which are deliberately introduced into the weld pool through the filler wire. The important effect of deoxidation practice (inclusions) on the columnar to equiaxed transition in ferritic stainless steel GTA welds is shown in Figs. 3.55 and 3.56.
3.7 Solute Redistribution During solidification of fusion welds, alloying and impurity elements tend to segregate extensively to the centre parts of the intercellular or interdendritic spaces under the conditions of rapid cooling. This, in turn, alters the kinetics of the subsequent solid state transformation reactions. 3.7.1 Micro segregation In general, microsegregation in ingots and castings is caused by the interplay between a number of variables which cannot readily be accounted for in a mathematical simulation of the process 12 Nevertheless, several important deductions can be made from the well known nonequilibrium lever rule or Scheil equation which, in spite of its simple nature, gives a reasonable description of the segregation pattern during weld metal solidification.4'34 The Scheil equation applies to directional solidification of long bars and is based on the following assumptions: (i) (ii) (iii) (iv) (v)
Uniform liquid composition (i.e. complete mixing in the liquid state). A flat solid/liquid interface. Local equilibrium at the solid/liquid interface (ko is constant). Negligible solid-state diffusion. Equal solid and liquid densities.
Under such conditions it is fairly simple to derive an expression for the solute concentration in the metal as a function of the fraction solidified. Referring to Fig. 3.57, a mass balance gives: (3-41) Since dz « z and Cs = ko C1, equation (3-41) can be rewritten as:
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3.6.2 Nucleation mechanisms Several nucleation mechanisms have been proposed to explain the columnar to equiaxed transition during weld pool solidification, including:26 (i) (ii) (iii)
Heterogeneous nucleation Dendrite fragmentation Grain detachment.
The former mechanism is particularly relevant to welding, since the weld metal often contains a high number of second phase particles which form in the liquid state. As already mentioned in Section 3.4.4.2, these particles can either be primary products of the weld metal deoxidation or stem from reactions between specific alloying elements which are deliberately introduced into the weld pool through the filler wire. The important effect of deoxidation practice (inclusions) on the columnar to equiaxed transition in ferritic stainless steel GTA welds is shown in Figs. 3.55 and 3.56.
3.7 Solute Redistribution During solidification of fusion welds, alloying and impurity elements tend to segregate extensively to the centre parts of the intercellular or interdendritic spaces under the conditions of rapid cooling. This, in turn, alters the kinetics of the subsequent solid state transformation reactions. 3.7.1 Micro segregation In general, microsegregation in ingots and castings is caused by the interplay between a number of variables which cannot readily be accounted for in a mathematical simulation of the process 12 Nevertheless, several important deductions can be made from the well known nonequilibrium lever rule or Scheil equation which, in spite of its simple nature, gives a reasonable description of the segregation pattern during weld metal solidification.4'34 The Scheil equation applies to directional solidification of long bars and is based on the following assumptions: (i) (ii) (iii) (iv) (v)
Uniform liquid composition (i.e. complete mixing in the liquid state). A flat solid/liquid interface. Local equilibrium at the solid/liquid interface (ko is constant). Negligible solid-state diffusion. Equal solid and liquid densities.
Under such conditions it is fairly simple to derive an expression for the solute concentration in the metal as a function of the fraction solidified. Referring to Fig. 3.57, a mass balance gives: (3-41) Since dz « z and Cs = ko C1, equation (3-41) can be rewritten as:
Fraction equiaxed grains (%) (a)
Average grain size, Jim
Aluminium content, wt%
(b) Aluminium content, wt% Fig. 3.55. Effect of deoxidation practice (aluminium additions) on the columnar to equiaxed transition in ferritic stainless steel GTA welds; (a) Average fraction of equiaxed grains observed at the surface of the welds vs aluminium content, (b) Surface equiaxed grain size vs aluminium content. Data from Villafuerte etal21 (3-42) Integration of this equation gives:
(3-43)
Fraction equiaxecl grains (%)
(a)
Titanium content, wt%
Average grain size, JI m
(b)
Titanium content, wt% Fig. 3.56. Effect of deoxidation practice (titanium additions) on the equiaxed transition in ferritic stainless steel GTA welds; (a) Average fraction of equiaxed grains observed at the surface of the weld vs titanium content, (b) Surface equiaxed grain size vs titanium content. Data from Villafuerte et al.21 from which (3-44) and (3-45) where fs is the fraction solidified (equal to z/L*).
Liquid
Concentration, C
Solid
Distance, z Fig. 3.57. Solute redistribution during non-equilibrium freezing according to the Scheil equation. Equation (3-44) is valid up to CL = Ceut where the remaining melt solidifies in the form of intercellular or interdendritic eutectics. The eutectic fraction feut is, in turn, given as:
(3-46)
Figure 3.58 shows how the Scheil equation can be used for an evaluation of the microsegregation pattern in binary alloy systems by considering a small volume element of length L* which solidifies perpendicular to the cell/dendrite growth direction. Since the Scheil equation does not allow for solid state diffusion during solidification, a slightly refined version of this equation also exists in the literature:1
(3-47)
where a* is a dimensionless diffusion parameter, defined as:
(3-48)
Solid Liquid
Fig. 3.58.Idealised model for microsegregation in ingots and castings (schematic). Equation (3-47) has been used by Brody and Flemings34 to evaluate the effect of solid diffusion on the amount of eutectic in different cast structures. The extent of this diffusion depends on the dimensionless product a* ko and it becomes significant only for values of a* Jc0 greater than about O.I.1 Note that in cellular or cellular-dendritic growth the primary dendrite arm spacing X1 provides a measure of the diffusion length. Taking L* = X ,/2, equation (3-48) can be rewritten as: (3-49) In contrast, during equiaxed dendritic growth the secondary dendrite arm spacing X2 is a more appropriate dimension for the solidification microstructure, since the back diffusion process here occurs mainly between secondary arms and not between primary trunks.2 In such cases we may write: (3-50)
Example (3.13)
Consider GTA welding of an Al-2wt%Cu alloy under the following solidification conditions: Welding speed Cooling rate Primary dendrite arm spacing
Estimate on the basis of the Scheil equation the degree of microsegregation occurring during weld metal solidification. Relevant physical data for the Al-Cu system are given below:
Solution
The local solidification time can be calculated from equation (3-33). Taking RL = v, we get:
Since the solidification conditions in this case facilitate the formation of a cellular-dendritic type of substructure close to the weld centre-line (see Fig. 3.43), the characteristic diffusion length L* is determined by the primary dendrite arm spacing X1. The product a* ko is then given as:
Because the numerical value of a* ko is very small, the contribution from diffusion in the solid state can be neglected. Hence, the extent of microsegregation occurring during solidification can be evaluated from equation (3-45). Taking C0 = 2wt% and ko = 0.17, we obtain:
The results are presented graphically in Fig. 3.59. As expected, the copper concentration is seen to increase monotonically from the core to the periphery (surface) of the dendrite stem. When the eutectic composition is reached, the remaining fraction solidifies as Al(5.6wt%Cu) + CuAl2. According to equation (3-46) the eutectic fraction is equal to:
These results should be compared with the experimental data of Brooks and Baskes35 replotted in Fig. 3.60. It is evident that the measured copper concentration profile for the Al2wt%Cu GTA weld is similar to that inferred from the Scheil equation, although the observed dendrite core concentration lies significantly above the predicted one. Consequently, the Scheil equation gives a reasonable description of the segregation pattern during weld metal solidification, in spite of the simplifying assumptions inherent in the model.
Cu concentration, wt%
z.^m
Normalized distance (z/L*) Fig. 3.59.Predicted Cu concentration profile based on the Scheil equation (Example (3.13)).
Cu concentration, wt%
GTAW (Al-2wt% Cu)
Position, ]im Fig. 3.60. Electron microprobe analysis of Cu across primary solidification (cell) boundaries in an Al2wt% Cu GTA weld. Data from Brooks and Baskes.35
3.7.2 Macro segregation Macrosegregation in the form of solute banding is also frequently observed after weld metal solidification.34 This type of segregation arises from a periodic enrichment and/or depletion of solute elements, caused by a non-steady advancement of the solidification front (see Fig.
Fig. 3.6/. Example of solute banding (dark stripes) in a phosphorus-containing copper weld. After Garland and Davis.36 3.61). Although the origin of the phenomenon is not yet fully understood, it is reasonable to assume that the pertinent fluctuations in the solidification rate occurs as a result of frequent variations in the heat flux during welding. Direct experimental evidence for such a correlation can be obtained from the data of Garland and Davis.36 Moreover, there is a pronounced tendency for alloying and impurity elements to segregate to the weld centre-line where the columnar grains growing from each side impinge. This, in turn, may produce hot tearing as a result of the formation of low-melting eutectics between the dendrite arms. In general, the risk of hot tearing decreases with increasing width to depth ratio of the weld because of a more favourable crystal growth mode, as illustrated in Fig. 3.62. 3.7.3 Gas porosity Troublesome impurities in fusion welds are those which precipitate, alone or in combination with other elements, to form various gaseous reaction products.37 These reaction products may be simple diatomic gases such as H2 and N2 or more complex gaseous compounds like CO, or H2O. An illustration of gas porosity due to hydrogen evolution is contained in Fig. 3.63. Following the discussion in Chapter 2, absorption of gases occurs readily in the hot part of the weld pool during welding because of interactions with the surrounding arc atmosphere. During the subsequent stage of cooling a supersaturation rapidly increases due to the associated decrease in the element solubility with decreasing temperatures (see Figs. 2.7 and 2.8). The system will respond to this supersaturation by rejection of dissolved elements from the liquid, either through a gas/metal reaction (desorption) or by precipitation of new phases. The latter incident may result in porosity if the gas bubbles become trapped in the weld metal solidification front. 3.7.3.1 Nucleation of gas bubbles In liquid metals a bubble will be stable if the gas pressure inside the bubble is sufficiently high to balance the external forces. These external forces are the liquid/vapour interfacial energy
(b) Incorrect width to depth ratio
(a) Correct width to depth ratio
Width
Depth
Depth
Width
Fig. 3.62. Effect of weld width to depth ratio on the tendency to centre-line cracking; (a) Correct width to depth ratio, (b) Incorrect width to depth ratio.
Fig. 3.63. Example of gas porosity in a GTA 7106 aluminium weld. After D'annessa.39
Transport of dissolved gaseous species
Liquid Gas bubble
Solid Fig. 3.64. Growth of a gas bubble due to diffusion in the liquid phase (schematic).
a*, the metallostatic pressure head/?m, and the ambient pressure pa. Thus, for a stable bubble, we may write:1 (3-51) where pg is the total gas pressure inside the bubble, and rg is the radius of the gas bubble. For shallow welds, the contribution from the metallostatic pressure head pm can be ignored. Hence, equation (3-51) reduces to: (3-52) Since a* is typically of the order of 1 J m 2 (9.87 atm |im) for most gas-metal systems, we may write: (3-53) It is evident from equation (3-53) that the interfacial energy term is negligible at large values of r . However, if the radius of curvature becomes sufficiently small, extremely large pressures are required to maintain a stable bubble. Thus, there is a bubble nucleation problem, which is formally similar to that of nucleation of a solid from a liquid (discussed in Section 3.3.1). In fact, it can be shown on the basis of classic nucleation theory that the driving force normally associated with rejection of dissolved gases in liquid metals is by far too small to allow for homogeneous nucleation of gas bubbles in the weld pool during cooling. This, in turn, implies that solid particles (e.g. inclusions) entrained in the liquid metal will be the most probable sites for gas bubble formation in fusion welds. 3.7.3.2 Growth and detachment of gas bubbles As shown in Fig. 3.64, growth of gas bubbles in liquids is a diffusion-controlled process where the time dependence of the mean bubble radius is given by:38 (3-54) Here Q.* is the growth constant, defined as:
(3-55) where CL is the molar concentration of solute in the supersaturated liquid, C6 is the equilibrium molar concentration of the solute at the gas/liquid interface, and p^ is the gas density (in the same units as CL and C6). Equations (3-54) and (3-55) may be used to estimate the growth rate of a bubble while it is still attached to the solid/liquid interface. The bubble becomes detached when the buoyancy force, which is pushing it upwards, exceeds the surface tension force, which tends to keep it attached to the solid surface. The bubble radius at which detachment occurs is given by the socalled Fritz equation:38
(3-56)
where gc is the gravity constant, and P is the wetting angle (in degrees). Based on equations (3-54) and (3-56) it is possible to evaluate the conditions for growth and detachment of gas bubbles during weld metal solidification. This is a subject of considerable importance in welding, since the pore formation will inevitably affect the mechanical integrity of the weldment. Example (3.14)
Consider GTA butt welding of a 3mm thin Al-Mg sheet under the following conditions:
Suppose that gas bubbles form at the solid/liquid interface during solidification due to rejection of dissolved hydrogen from a supersaturated liquid. Based on equations (3-54) and (3-56) estimate the maximum theoretical radius of the gas bubbles and the critical radius at which the bubbles detach themselves from the solid/liquid interface during welding. Relevant physical data for the Al-Mg system are given below:
Solution
Since particles located at the solid/liquid interface are the most probable sites for hydrogen gas evolution, the local solidification time t0 provides a conservative estimate of the growth time t in equation (3-54). From equation (3-36), we have:
In order to calculate the growth constant from equation (3-55), it is necessary to convert the concentration driving force to molar units:
The molar density of the gas p is obtained from the ideal gas law:
The value of the growth constant is thus:
The maximum theoretical radius of the gas bubbles can now be evaluated from equation (3-54) by inserting the appropriate values for Q*, DH, and to:
Similarly, the critical radius at which the hydrogen bubbles become detached may be estimated from equation (3-56). Since PM > > PH 2 , we obtain:
By inserting this value into equation (3-54) it is also possible to estimate the average bubble detachment frequency under the prevailing circumstances:
Since r (crit.)« r (max), the maximum pore radius will probably be closer to 0.7mm than 30mm in a real welding situation. This is also in agreement with practical experience (see Fig. 3.65).
Cumulative probability (%)
GTAW (Aluminium)
Diameter of pores, mm Fig. 3.65. Measured distribution of pore diameters in some GTA aluminium welds deposited with different hydrogen-containing shielding gases. Data from Tomii et al.40
3.7.3.3 Separation of gas bubbles It follows that the gas bubbles will start to migrate towards the surface of the weld immediately after they become detached from the solid/liquid interface. Small, spherical bubbles (characterised by a bubble Reynold number less than 2) will rise at a terminal velocity determined by Stokes law:38 (3-57) where dg is the diameter of the gas bubbles, and jLl is the viscosity of the liquid. Larger gas bubbles (characterised by a bubble Reynold number between 2 and 400) will also rise in a rectilinear manner, but their terminal velocity may be as much as 50% greater than that predicted from Stokes law.38 Depending on their flotation rate, such ascending gas bubbles will either escape to the weld surface or be trapped in the weld metal solidification front in the form of macroscopic gas porosity (see Fig. 3.63). Example (3.15)
Based on Stokes law (equation (3-57)) calculate the rising velocity of a 0.2mm large hydrogen bubble ascending in liquid aluminium. Relevant physical data for liquid aluminium are given below:
Solution
Since p z » p , we may write:
It is evident from the above calculations that the flotation rate of such gas bubbles is quite high and of the same order of magnitude as the weld pool fluid flow velocity (discussed in Section 2.11.2). Hence, the buoyancy force would be expected to play a significant role in the separation process of detached gas bubbles in the weld pool. On this basis it is not surprising to find that a change in the welding position (e.g. from flat to overhead) results in a dramatic increase in the volume of porosity during GTAW of aluminium alloys (see Fig. 3.66). Although a great deal has been reported on the causes and effects of porosity in weld metals (see Ref. 37 for an excellent discussion), little is known about the mechanism of pore formation relative to solidification mechanics, nucleation, growth and transport of gas bubbles in the weld pool. Consequently, a more fundamental approach to the porosity problem in fusion welding (along the lines indicated above) is necessary in order to obtain a verified, quantitative understanding of the phenomenon.
GTAW
Volume of pores, ml/10Og
Overhead position
Flat position
Welding orientation, degrees Fig. 3.66. Porosity in GTA welds deposited on 2mm sheets of aluminium at various orientations from flat to overhead. Data compiled by Devletian and Woods.37
3.7.4 Removal of microsegregations during cooling As shown in Section 3.7.1, the characteristic growth pattern of cellular and dendritic solidification, in combination with the rapid cooling rates normally associated with fusion welding, lead to extensive segregation of alloying and impurity elements to the intercellular or interdendritic spaces. Segregation produced by this means is remarkably persistent, and can in certain cases only be eliminated by prolonged high-temperature heat treatment. A simplified analysis of homogenisation of microsegregations in fusion welds is given below. 3.7.4.1 Diffusion model It is a reasonable approximation to regard microsegregations in cast structures as periodic, where the concentration at any point and time along an arbitrary line, C(x,t), is given by:41
where C and Cmax are as indicated in Fig. 3.67, lavg is the average distance between adjacent maxima and minima, and Ds is the diffusivity of the solute in the solid. Equation (3-58) states that the concentration remains constant and equal to Cavg at positions JC = 0, JC = lavg, x = 2/ etc., while the peak of the sine wave is attained at distances x = lavg /2, x = 5lavg /2 etc. during the decay. If only the peak concentration is considered, the sine term becomes equal to unity and equation (3-58) reduces to: (3-59) from which the homogenisation time during isothermal heat treatment thom can be obtained:
(3-60)
Since the diffusion length I , in practice, is equal to the half dendrite arm spacing (X1 /2 or X2/2), equation (3-60) predicts that the homogenisation time is proportional to the square OfX1 or X2. The latter parameters are, in turn, determined by the thermal conditions existing within the mushy zone during weld metal solidification, and are therefore sensitive to variations in welding variables such as the net arc power qo and the travel speed v. 3.7.4.2 Application to continuous cooling During cooling of the weld in the solid state, some equalisation of microsegregations will occur through diffusion. The extent of this diffusion can be reported in terms of an equivalent isothermal homogenisation time at a chosen reference temperature Tr. If Qs denotes the activation energy for diffusion of the solute in the solid, the equivalent isothermal homogenisation time tr at Tr is given by:
(3-61)
Concentration
Dendrite arm spacing
x Fig. 3.67. Relaxation of sinusoidal distribution of solute during isothermal annealing.
The integral on the right-hand side of equation (3-61) represents the kinetic strength of the weld thermal cycle with respect to homogenisation (solid state diffusion), and can be determined by means of numerical methods when the cooling programme is known. The extent of solute diffusion may then be evaluated from equation (3-60) by inserting representative values for t and / : T
UY'g.
(3-62)
Example (3.16)
[n low-alloy steel, both carbon, phosphorus, and manganese are known to segregate to the interdendritic spaces during solidification. Consider SA welding on a thick plate of steel under the following conditions:
Based on equations (3-61) and (3-62) calculate the extent of homogenisation occurring within the solid weld metal during cooling in the austenite regime (i.e. from 1520 to 7000C). Relevant data for the diffusivity of carbon, phosphorus, and manganese in austenite are given below:
Solution
During thick plate welding, the cooling programme can be calculated from equation (1-45). For points located on the weld centre-line behind the heat source y = z = 0, and R* = -x = vt. Hence, equation (1-45) reduces to:
By inserting representative values for T0, qo, v and \ , we obtain:
From this it is seen that the actual transformation temperatures (i.e. 1520 and 7000C) are reached after 20.9 and 46.2s, respectively. If 13500C is used as a reference temperature, the kinetic strength of the cooling cycle with respect to solute diffusion can be expressed as:
Numerical integration of this equation over the weld cooling cycle gives:
At 13500C (1623 K) the diffusivities of C, P and Mn in austenite are:
The extent of homogenisation is thus:
It is evident from the above calculations that interdendritic segregations of carbon are readily removed during cooling of the weld from the solidification temperature due to a high diffusivity of C in austenite. In contrast, segregations of phosphorus and manganese are much more persistent, since the diffusion cannot keep pace with the falling temperature. In the latter case the initial concentration gradients will largely be maintained down to temperatures where the austenite to ferrite transformation occurs (see ion micrograph of phosphorus segregations in Fig. 3.39). This, in turn, can promote the formation of different types of transformation products (ranging from ferrite to martensite depending on the nature of the segregants) along the primary solidification boundaries due to local variations in the steel hardenability. An example of martensite banding in an AISI 4340 SA steel weld is shown in Fig. 3.68. It should be noted that the conditions for equalisation of interdendritic segregations (e.g. phosphorus) are not dramatically altered by a change in the heat input as long as the tr I l\vg ratio in equation (3-62) remains fairly constant. For instance, if the net arc power qQ in the above example is reduced by a factor of four (conforming to welding with covered electrodes), the corresponding change in / and J1350 (P) will be:
and from which
This value is reasonably close to that obtained during high-heat input SA welding (0.036 s jirrr2), as shown in the above example.
Fig. 3.68. Banding of martensite (M) along primary solidification boundaries in an AISI 4340 SA steel weld. After Burck.42
3.8 Peritectic Solidification Referring to the schematic phase diagram in Fig. 3.69, crystallisation within peritectic systems starts with primary precipitation of the 8p-phase from the liquid. At the peritectic temperature T a new solid phase 7 forms, according to the reaction: 5p+ liquid -> yp
<3"63)
Because of the nature of this reaction, there is a strong tendency for the secondary phase 7 to grow along the 8^/liquid interface and, thus, to isolate the primary phase from contact with the liquid.43 Depending on the growth mode, the decomposition of the primary 8^-phase is said to occur either through a peritectic reaction or by a peritectic transformation,44 as shown schematically in Fig. 3.70 and 3.71, respectively. 3.8.1 Primary precipitation of the y -phase Primary precipitation of the 7^-phase from the liquid is also possible if the temperature is gradually decreasing during solidification.43 As shown by Kerr et al.44^6 this type of precipitation is favoured by the presence of solid particles within the liquid metal which can act as seed crystals for the 7^-phase in a selective manner. Particularly at high cooling rates, the formation of the primary 8^-phase can be completely suppressed, thereby allowing the secondary 7 -phase to nucleate and grow directly from the supercooled liquid. 3.8.2 Transformation behaviour of low-alloy steel weld metals In general, low-alloy steels undergo multiple phase transformations during solidification and subsequent cooling. Depending on the cooling rate, carbon or the substitutional alloy content, the primary solidification product will either be delta ferrite 8 Fe , austenite 7 Fe or a mixture of both. 47 ^ 9 3.8.2.1 Primary precipitation of delta ferrite When a low-alloy steel is slowly cooled below the crystallisation temperature, delta ferrite will be the first phase to form.50 In fusion welds, the delta ferrite grains will reveal an anisotropic columnar morphology, with their major axes aligned in the direction of the steepest temperature gradient in the weld pool. On further cooling below the peritectic temperature, austenite nucleates epitaxially at the primary delta ferrite grain boundaries, as shown schematically in Fig. 3.72, since these sites provide the lowest energy barrier against heterogeneous nucleation (requires a Kurdjumow-Sachs or a Nishiyama-Wasserman type of orientation relationship between 8Fe and 7Fe).51 Subsequent growth of the austenite into the delta ferrite may then proceed by a peritectic transformation at a rate which is controlled by diffusion of carbon in the austenite. This reaction pattern is analogous to that documented for growth of 7 F e Widmanstatten sideplates in duplex stainless steel.5253 Since the austenite is bound by an orientation relationship with the delta ferrite,51 the austenite cannot grow across the primary delta ferrite solidification boundaries. Hence, after the peritectic transformation the columnar 7Fe grains will adopt the original 8Fe morphology, as shown in Fig. 3.72. Direct experimental evidence for such a correspondence can be obtained from the optical micrographs in Fig. 3.38 and the texture data presented in Section 6.3.5 (Chapter 6).
Temperature
Liquid (L)
Fig. 3.69.Peritectic phase diagram (schematic).
Growth direction Liquid
Diffusion of solute atoms
Fig. 3.70.Peritectic reaction by which the secondary 7p-phase grows along the surface of the primary 8p-phase (schematic).
Liquid
Fig. 3.7L Peritectic transformation involving long-range diffusion of solute atoms through the secondary 7^-phase (schematic).
Delta ferrite Liquid
Solute segregations
Austenite
Austenite grain boundary Fig. 3.72. Primary delta ferrite solidification with subsequent growth of austenite along the boundaries of the primary 8Fe-phase (schematic).
3.8.2.2 Primary precipitation of austenite Under certain welding conditions the weld metal can solidify directly as austenite without any primary precipitation of delta ferrite (see Fig. 3.73). This solidification mode has been observed during welding with covered electrodes on high-carbon steels.54 Because of competitive growth occurring during the initial stage of the solidification process, the columnar austenite grains will have one of their <100> axes aligned in the direction of the maximum temperature gradient in the weld pool. Consequently, the weld metal will develop a solidification texture which is similar to that observed during primary precipitation of delta ferrite.51 3.8.2.3 Primary precipitation of both delta ferrite and austenite In certain low-alloy steel weld metals the austenite grain boundaries will systematically cross the original delta ferrite solidification boundaries, as indicated in Fig. 3.74 because of a shift in the mechanism of the peritectic transformation.3'22'2454"56 This point is more clearly illustrated in Fig. 3.75, which shows ion (SIMS) micrographs of phosphorus and boron segregations
Austenite Columnar grain Liquid
Fig. 3.73. Primary austenite solidification (schematic).
Fig. 3.74. Optical micrograph showing austenite grain boundaries crossing primary delta ferrite solidification boundaries in a low-alloy SA steel weld (indicated by arrows). After Kluken et al.22 at prior solidification (cell) and austenite grain boundaries*, respectively in a SA steel weld metal deposited under the shield of a basic flux. It is obvious from Fig. 3.75 that there is no matching between the two types of boundaries in this particular case. It follows from the analysis of Kluken et al?2 that the observed shift in the mechanism of the peritectic transformation can probably be attributed to heterogeneous nucleation of austenite at inclusions (e.g. Al2O3), which is energetically more favourable than nucleation at 8Fe/8Fe grain boundaries. Under such conditions, the austenite is not bound by an orientation relationship with the delta ferrite and is thus free to grow across the original delta ferrite columnar grain boundaries, as shown schematically in Fig. 3.76. The austenite grains will therefore adopt a morphology which is different from the columnar one.245556
References 1. 2. 3. 4. 5. 6. 7. 8. 9.
M.C. Flemings: Solidification Processing, 1974, New York, McGraw-Hill Book Company. W. Kurz and DJ. Fisher: Fundamentals of Solidification, 3rd Edn, 1989, Aedermannsdorf (Switzerland), Trans. Tech. Publications. GJ. Davis and J.G. Garland: Int. MetalL Rev., 1975, 20, 83-106. S.A. David and J.M. Vitek: Int. Mater. Rev., 1989, 34, 213-245. D. A. Porter and K.E. Easterling: Phase Transformations in Metals and Alloys, 1981, Wokingham (England), Van Nostrand Reinhold Co. Ltd. K.E. Easterling: Introduction to the Physical Metallurgy of Welding, 1983, London, Butterworths & Co (Publisher) Ltd. 0. Grong, TA. Siewert and G.R. Edwards: Weld. J., 1986, 65, 279s-288s. G.M. Oreper, TW. Eagar and J. Szekely: Weld. J., 1983, 62, 307s-312s. Y.H. Wang and S. Kou: Proc. Int. Conf. on Advances in Welding Science, Gatlinburg, TN, May, 1986, 65-69, Publ. ASM International.
*Because of a similar atomic weight of BO2~ and AlO~, both types of ions will be sampled in the SIMS analysis. Consequently, the white spots observed within the interior of the grains are probably traces of aluminium oxide inclusions.
(a)
(b)
Fig. 3.75. Ion (SIMS) micrographs showing austenite grain boundaries crossing primary delta ferrite solidification boundaries in a low-alloy SA steel weld; (a) Phosphorus segregations at primary solidification (cell) boundaries, (b) Boron segregations at prior austenite grain boundaries (same area as in Fig. 3.75(a)). After Kluken et alP
Delta ferrite.
Solute segregations
Liquid
Inclusions (e.g. AI2O3)
Austenite
Austenite grain boundary
Fig. 3.76. Primary delta ferrite solidification with subsequent nucleation of austenite at inclusions (schematic). 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29.
K.C. Mills and BJ. Keene: Int. Mater. Rev., 1990, 35, 185-216. T. Zacharia, S.A. David, J.M. Vitek and H.G. Kraus: Metall. Trans., 1991, 22B, 243-257. CR. Heiple and J.R. Roper: Weld. J., 1982, 61, 97s-102s. CR. Heiple and P. Burgardt: Weld. J., 1985, 64, 159s-162s. T. Habrekke, H.O. Knagenhjem and J.O. Berge: Proc. 9th. Int. Conf. on Offshore Mech. and Arctic Engin., Houston, TX, Feb., 1990, 511-515, Publ. ASME. H. Biloni: Physical Metallurgy, 3rd Edn (Eds R.W. Chan and P. Haasen), 1983, Amsterdam, North-Holland Physics Publ., 478-579. T. Senda, F. Matsuda and M. Kato: Techn. Reports of the Osaka University (Japan), 1970,20, 527-558. M. Rappaz, S.A. David, J.M. Vitek and L.A. Boatner: Metall. Trans. A, 1989,2OA, 1125-1138. L.F. Mondolfo: Mat. ScL and TechnoL, 1989, 5, 118-122. B.L. Bramfitt: Metall. Trans., 1970, 1, 1987-1995. G.N. Heintze and R. McPherson: Weld. /., 1986, 65, 71s-81s. J.C. Villafuerte, E. Pardo and H.W. Kerr: Metall. Trans. A, 1990, 21A, 2009-2019. A.O. Kluken, 0. Grong and G. R0rvik: Metall. Trans. A, 1990, 21 A, 2047-2058. H. Yunjia, R.H. Frost, D.L. Olson and G.R. Edwards: Weld. J., 1989, 68, 280s-289s. CE. Cross, 0. Grong, S. Liu and J.F. Capes: Applied Metallography, (Ed. G.F. Vander Voort), 1986, New York, Van Nostrand Reinhold Inc., 197-210. A.O. Kluken and 0 . Grong: Proc. Int. Conf. on Recent Trends in Welding ScL and TechnoL (TWR 89), Gatlinburg, TN, May, 1989, 781-786, Publ. ASM International. S. Kou: Welding Metallurgy, 1987, New York, John Wiley & Sons. M.F. Jordan and M.C. Coleman: Brit. Weld. J., 1968,15, 553-558. CE. Cross and G.R. Edwards: Treatise on Mat. ScL TechnoL, 1989, 31, 171-187. W. Kurz, B. Giovanola and R. Trivedi: Acta Metall., 1986, 34, 823-830.
30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56.
R. Trivedi and W. Kurz: Acta MetalL, 1986, 34, 1663-1670. S. Kou and Y. Lee: MetalL Trans., 1982,13A, 1141-1152. A. Munitz: MetalL Trans., 1985,16B, 149-161. F. Matsuda, K. Nakata, K. Tsukamoto and K. Arai: Trans. JWRI, 1983,12, 81-87. H.D. Brody and M.C. Flemings: Trans. AIME, 1966, 236, 615-623. J.A. Brooks and M.I. Baskes: Proc. Int. Conf. on Trends in Welding Research (TWR 86), Gatlinburg, TN, May, 1986, 93-99, Publ. ASM International. J.G. Garland and GJ. Davis: Brit. Weld. J., 1970,17, 171-175. J.H. Devletian and W.E. Woods: Weld. Res. Council Bull., 1983, 290, 1-18. J. Szekely and NJ. Themelis: Rate Phenomena in Process Metallurgy, 1971, New York, John Wiley & Sons, Inc. A.T. D'annessa: Weld. J., 1967, 46, 491s-499s. Y. Tomii, A. Sakaguchi and M. Mizuno: Proc. 4th Int. Conf. on Aluminium Weldments, Tokyo (Japan), 1988, 46-60, Publ. Japan Light Metal Welding and Construction Association. J.D. Verhoeven: Fundamentals of Physical Metallurgy, 1975, New York, John Wiley & Sons, Inc. P. Burck: M.Sc. thesis, 1984, Colorado School of Mines, Golden, Colorado (USA). M. Hillert: Solidification and Casting of Metals, 1979, London, The Metals Society, 81-87. H. W. Kerr, J. Cisse and G.F. Boiling: Acta MetalL, 1974, 22, 677-686. J. Cisse, G.F. Boiling and H.W. Kerr: /. Cryst. Growth, 1972,13/14, 777-781. J. Cisse, H.W. Kerr and G.F. Boiling: MetalL Trans., 1974, 5, 633-641. H. Fredriksson: Met. ScL, 1976,10, 77-86. H. Fredriksson and J. Stjerndahl: MetalL Trans., 1977, 8A, 1107-1115. H. Fredriksson and J. Stjerndahl: Met. ScL, 1982,10, 575-585. N.S. Pottore, CL Garcia and AJ. DeArdo: MetalL Trans., 1991, 22A, 1871-1880. A.O. Kluken, 0. Grong and J. Hjelen: MetalL Trans., 1991, 22A, 657-663. N. Suutala, T. Takalo and T. Moisio: MetalL Trans., 1979,10A, 1183-1190. S.A. David: Weld. J., 1981, 60, 63s-71s. A.A.B. Sugden and H.K.D.H. Bhadeshia: MetalL Trans., 1987,19A, 669-674. J.G. Garland and RR. Kirkwood: Proc. Int. Symp. on Welding of Line Pipe Steels, St. Louis (USA), 1977, 176-227, Publ. Welding Research Council (New York). R.C. Cochrane: Weld, in the World, 1983, 21, 16-29.
Appendix 3.1 Nomenclature thermal diffusivity (mm2 s-1)
difference between total and acid soluble Al in weld metal (wt%)
lattice parameter (nm) b equilibrium 7/a solvus temperature (°C)
(|Lim)
bcc area of embryo-liquid interface (m2) area of embryo-substrate interface (m2)
half width of dendrite stem body-centred cubic structure various kinetic constants and temperature-dependent parameters
average solute concentration in solid phase (wt%)
eutectic fraction fraction solidified
initial alloy concentration (wt%)
shape factor face-centred cubic structure
equilibrium concentration of solute at gas/liquid interphase (wt% or mol cirr3)
length of dendrite stem (jam)
eutectic concentration (wt%)
gravity constant (m s"2)
concentration of alloying element in liquid phase (wt% or mol cm"3)
temperature gradient in weld pool (°C mm"1 or K irr 1 )
maximum solute concentration in solid phase (wt%) concentration of alloying element in solid phase (wt%) solute concentration at position x and time t (wt%) cooling rate (0C s~l or K s"1) plate thickness (mm) the interatomic spacing along [MVW] n
GMAW
gas metal arc welding
GTAW
gas tungsten arc welding activation energy for diffusion of atoms across the interface (J) energy barrier to heterogeneous nucleation (J) energy barrier to homogeneous nucleation (J) free energy change associated with the embryo formation (J irr 3 )
the interatomic spacing along
[uvw\
heat content per unit volume at the melting point (J mm"3)
diffusion coefficient in liquid (mirr s [)
latent heat of melting (J irr 3 )
diffusion coefficient in solid (mm2 s-1)
a low-index plane in the nucleated solid
diffusion coefficient of arbitrary element X (mm2 s~!)
a low-index plane of the substrate amperage (A)
EBW
electron beam welding frequency factor (s"1)
Boltzmann constant (1.381 X 10" 23 JK- 1 )
detachment frequency of gas bubbles (s"1)
equilibrium partition coefficient
critical GJR1 ratio which facilitates equiaxed dendritic growth(°Csmm" 2 )
modified Bessel function of second kind and zero order
length of columnar grain (mm)
radius of spherical nucleus (m)
average distance between adjacent maxima and minima concentrations (|im)
critical radius of stable nucleus (m)
total length of circle segment (mm)
universal gas constant (8.314 J K-1 mol-1)
total length of volume element (mm or Jim)
three-dimensional radius vector (mm)
slope of the liquidus curve (°C per wt%)
dendrite growth rate in hkl direction (mm s"1)
mobility term (mm3 s"1)
steady-state growth rate of solid/liquid interface (mm s"1)
exponent
local crystal growth rate (mm
dimensionless operating parameter
nominal crystal growth rate (mm s'1)
rate of heterogeneous nucleation (nuclei per s and mm3) density of nucleation sites per unit volume of melt (nuclei per mm3) analytical weld metal oxygen content (wt%) ambient pressure (atm) total gas pressure in bubbles (atm)
SAW
submerged arc welding
SIMS
secondary spectrometry
SMAW
shielded metal arc welding
ion
mass
entropy of fusion per unit volume (J nr 3 Kr1) time (s) integration limits (s)
metallostatic pressure head (atm)
homogenisation time (s)
net arc power (W)
local solidification time (s)
activation energy for diffusion of solute in solid (kJ mol-1)
equivalent isothermal homogenisation time (s)
two-dimensional radius vector (mm) dendrite tip radius (Jim) radius of gas bubble (mm)
temperature (°C or K) ambient temperature (°C or K) actual temperature in the liquid (°C or K)
liquidus temperature according to phase diagram (°C or K)
primary peritectic phase
melting point (°C or K)
interface normal angle (degrees)
peritectic temperature (°C or K) reference temperature (°C or K) dendrite root temperature (°C or K) dendrite tip temperature (°C or K)
efficiency factor
dimensionless diffusion parameter molar density of gas (mol cm"3) density of liquid (kg n r 3 or g cm"3) volume heat capacity (J mm~3 0C"1)
undercooling (°C or K) temperature difference between tip and root of dendrite stem (°C or K)
cell/dendrite alignment angle (degrees) critical cell/dendrite alignment angle (degrees)
a low-index direction in (UcQn
Gibbs-Thomson coefficient (mm °C or mK)
a low-index direction in
W),
dimensionless growth constant
voltage (V) dimensionless temperature rising velocity of gas bubbles (mm s"1)
dimensionless temperature at the melting point
volume of solid embryo (m3) wetting angle (degrees) welding speed (mm s"1) Jt-axis/welding direction (mm)
viscosity of liquid metal (kg nr 1 s-1) angle between [MVW]^ and
y-axis/transverse direction (mm)
[«vw]n (degrees) austenite
z-axis/through thickness direction (mm)
secondary peritectic phase
dimensionless plate thickness
total grain rotation angle (degrees)
delta ferrite
solid/liquid interfacial energy (J mr2)
lattice disregistry between a nucleus n and a substrate s
liquid/vapour interfacial energy (J nr 2 )
embryo/liquid interfacial energy (J rrr2)
primary dendrite arm spacing (Mm)
embryo/substrate interfacial energy (J nr 2 )
primary dendrite arm spacing close to fusion boundary (Mm)
substrate/liquid interfacial energy (J rrr2) thermal conductivity (W mm-10C"1)
secondary dendrite arm spacing (Mm)
4 Precipitate Stability in Welds
4.1 Introduction Precipitate stability is an important aspect of welding metallurgy. Normally, modern structural steels and aluminium alloys derive their balanced package of high strength, ductility and toughness via optimised thermomechanical processing to produce a fine-grained, precipitation strengthened matrix. This delicate balance of microalloy precipitation and microstructure, however, is significantly disturbed by the heat of welding processes, which, in turn, affects the mechanical integrity of the weldment. When a commercial alloy is subjected to welding or heat treatment several competitive processes are operative which may contribute to a change in the volume fraction and size distribution of the base metal precipitates. The two most important are:1 (i) (ii)
Particle coarsening (Ostwald ripening) Particle dissolution (reversion)
Referring to Fig. 4.1, particle coarsening occurs typically at temperatures well below the equilibrium solvus Te of the precipitates, while particle dissolution is the dominating mechanism at higher temperatures. On the other hand, there exists no clear line of demarcation between these two processes, which means that particle coarsening can take place simultaneously with reversion in certain regions of the weld where the peak temperature of the thermal cycle falls within the 'gray zone' in Fig. 4.1. Nevertheless, it is important to regard them as separate processes, since the reaction kinetics are so different (coarsening is driven by the surface energy alone, whereas dissolution, which involves a change in the total volume fraction, is driven by the free energy change of transformation).
4.2 The Solubility Product The symbols and units used throughout this chapter are defined in Appendix 4.1. The solubility product is a basic thermodynamic quantity which determines the stability of the particles under equilibrium conditions. Because of its simple nature, the solubility product is widely used for an evaluation of the response of grain size-controlled and dispersion-hardened materials to welding and thermal processing.23 4.2.1 Thermodynamic background In general, the solubility product can be derived from an analysis of the Gibbs free energy AG° of the following dissolution reaction:
'Grey zone1
Particle coarsening |
Increasing heating rate
Temperature
Particle dissolution
%B Fig. 4.1. Schematic diagram showing the characteristic temperature ranges where specific physical reactions occur during reheating of grain size-controlled and dispersion-hardened materials.
(4-1) At equilibrium, we have:
(4-2) where AH° and AS° are the standard enthalpy and entropy of reaction, respectively. The other symbols have their usual meaning (see Appendix 4.1). When pure An Bm is used as a standard state, the activity of the precipitate {aAn Bm) is equal to unity. In addition, for dilute solutions it is a fair approximation to set aA~[%A] and aB~[%B], where the matrix concentrations of elements A and B are either in wt% or at%*. Hence, the solubility product can be written as: (4-3)
*For the solute, the standard state is usually a hypothetical 1 % solution. This implies that the activity coefficient is equal to unity as long as Henry's law is obeyed.
Table 4.1 gives a summary of equilibrium solubility products for a wide range of precipitates in low-alloy steels and aluminium alloys. In addition to the compounds listed in Table 4.1, different types of mixed precipitates may form within systems which contain more than two alloying elements.3"6 However, since the presence of such multiphase particles largely increases the complexity of the analysis, only pure binary intermetallics will be considered below. 4.2.2 Equilibrium dissolution temperature Based on equation (4-3) it is possible to calculate the equilibrium dissolution temperature Td of the precipitates. By rearranging this equation, we get:
(4-4) where [%A]o and [%B]o refer to the analytical content of elements A and B in the base metal, respectively. Equation (4-4) shows that the equilibrium dissolution temperature increases with increasing concentrations of solute in the matrix. This is in agreement with the Le Chatelier's principle. Table 4.1 Equilibrium solubility products for different types of precipitates in low-alloy steels and aluminium alloys. Data compiled from miscellaneous sources. Material/ phase
log [%A]n [%B]m
Type of Precipitate
C* = AS°/R'
D* = Mi0IR'
TiN
0.32
8000
TiC
5.33
10475
NbN
4.04
10230
Low-alloy steel
NbC
2.26
6770
(austenite)t
VN
3.02
7840
VC
6.72
9500
AIN
1.79
7184
Mo2C
5.0
7375
Al-Mg-Si^
Mg2Si
5.85
5010
Al-Cu-Mg$
CuMg
6.64
4005
MgZn
5.33
2985
Zn2Mg
7.72
4255
Al-Zn-Mgij:
All concentrations in wt% All concentrations in at.%
Example (4.1)
Consider a low-alloy steel with the following chemical composition:
Calculate on the basis of the reported solubility products in Table 4.1 the equilibrium dissolution temperature of each of the following three nitride precipitates, i.e. NbN, AlN, and TiN.
Solution
The equilibrium dissolution temperature of the precipitates can be computed from equation (44) by inserting the correct values for C* and D* from Table 4.1:
It is evident from these calculations that precipitates of the NbN and the AlN type will dissolve readily at temperatures above 1050 to 11000C, while TiN is thermodynamically stable up to about 14500C. In practice, however, a certain degree of superheating is always required to overcome the inherent kinetic barrier against dissolution, particularly if the heating rate is high. Consequently, in a real welding situation the actual dissolution temperature of the precipitates may be considerably higher than that inferred from simple thermodynamic calculations based on the solubility product (to be discussed later). 4.2.3 Stable and metastable solvus boundaries Due to the lack of adequate phase diagrams for the complex alloy systems involved, thermodynamic calculations based on the solubility product represent in many cases the only practical means of estimating the solid solubility of alloying elements in commercial low-alloy steels and aluminium alloys. 4.2.3.1 Equilibrium precipitates In the case of large, incoherent precipitates (where the Gibbs-Thomson effect can be neglected), the concentration of element A in equilibrium with pure An Bm at different temperatures can be inferred directly from equation (4-3). If we replace / ^ by R (i.e. switch from common to natural logarithms), this equation yields: (4-5)
Equation (4-5) describes the solvus surface within the solvent-rich corner of the phase diagram. However, when a pure binary compound dissolves the concentration of elements A and B in solid solution is fixed by the stoichiometry of the reaction. The following relationship exists between [%B] and [%A]:
(4-6) or
where MA and MB are the atomic weight of elements A and B, respectively. Figure 4.2 shows a graphical representation of equations (4-5) and (4-6), and the corresponding change in the matrix concentrations during dissolution of pure AnBm for a given set of starting conditions. Alternatively, we can express T as function of the product [%A]n [%B]m by utilising equations (4-3) and (4-6). The combination of these equations provides a mathematical description of the 'solvus boundary' of an equilibrium precipitate in a multi-component alloy system. It is evident from the graphical representation in Fig. 4.3 that the solid solubility will always in-
[%B]
[%A]0
[%B]o
Excess B [%A] Fig. 4.2. Concentration displacements during dissolution of binary intermetallics (equilibrium conditions).
Increased additions _of element B
Nominal alloy composition
Reduced solid solubility of element A
Temperature
I Increased dissolution temperature
Concentration of element A Fig. 4.3. Factors affecting the solid solubility of a binary intermetallic compound in a multi-component alloy system (schematic).
crease with increasing temperature when AH° is positive. This type of behaviour is characteristic of intermetallics in metals and alloys, since the dissolution process in such systems is endothermic.7 As a result, increased additions of a second alloying element B will also reduce the solubility of the first alloying element A by shifting the 'solvus boundary' towards higher temperatures when an intermetallic compound between A and B is formed. With the aid of Fig. 4.3 it is easy to verify that the equilibrium volume fraction of the precipitates/^ at a fixed temperature is given by:
(4-7)
where fmax is the maximum possible volume fraction precipitated at absolute zero. Equation (4-7) provides a basis for estimating the equilibrium volume fraction of binary intermetallics in complex alloy systems at different temperatures in cases where the concentration of element B is sufficiently high to tie-up all A in the form of precipitates. Similarly, if A is present in an overstoichiometric amount with respect to B, we may write:
(4-8)
Example (4.2)
In Al-Mg-Si alloys the equilibrium Mg2Si phase may form during prolonged high temperature annealing. Consider a pure ternary alloy which contains 0.75 wt% (0.83 at.%) Mg and 1.0 wt% (0.96 at.%) Si. Estimate on the basis of the solubility product the equilibrium volume fraction of Mg2Si at 4000C. Make also a sketch of the Mg2Si solvus in a vertical section through the ternary Al-Mg-Si phase diagram. Relevant physical data for the Al-Mg-Si system are given below:
Solution
The maximum possible volume fraction of Mg2Si precipitated at absolute zero (fmax) can be estimated from a simple mass balance by considering the stoichiometry of the reaction:
Moreover, the solubility product [at.% Mg]2 [at.% Si] at 4000C (673K) can be obtained from equation (4-3) by utilising data from Table 4.1:
from which
If we also take into account the stoichiometry of the reaction, the solubility product can be expressed solely in terms of the Mg-concentration. Substituting
into the above equation gives [at.% Mg] ~ 0.20. The equilibrium volume fraction OfMg2Si at 4000C is thus:
Similarly, the equilibrium Mg2Si solvus can be calculated from the solubility product by substituting
into equation (4-3). By inserting data from Table 4.1 and rearranging this equation, we get:
It is seen from the graphical representation of the above equation in Fig. 4.4 that the Mg2Si compound is thermodynamically stable up to about 3000C. At higher temperatures the phase will start to dissolve until the process is completed at 5600C. It is obvious from these calculations that the microstructure of overaged Al-Mg-Si alloys should be very persistent to the heat of welding processes. In practice, only a narrow solutionised zone forms adjacent to the fusion boundary. However, within this zone significant strength recovery may occur after welding due to reprecipitation of hardening phases from the supersaturated solid solution. Consequently, in such weldments the ultimate HAZ strength level is usually higher than that of the base metal, as illustrated in Fig. 4.5. 4.2.3.2 Metastable precipitates In practice, the solid solubility is also affected by the size of the particles. If, for instance, a
Nominal alloy composition
Temperature, 0C
Dissolution temperature: 5600C
at% Mg at%Mg Si Fig. 4.4. Solubility of Mg2Si in aluminium (Example (4.2)).
Strength level
After artificial ageing After natural ageing Immediately after welding
HAZ
Unaffected base metal Distance from fusion line
Fig. 4.5. Response of overaged Al-Mg-Si alloys to welding and subsequent heat treatment (schematic). spherical precipitate is acted on by an external pressure of say 1 atm, the same precipitate is also subjected to an extra pressure AP due to the curvature of the particle/matrix interface, just as a soap bubble exerts an extra pressure on its content (see Fig. 4.6(a)). The pressure AP is given as:8 (4-9) where 7 is the particle/matrix interfacial energy, and r is the radius of the precipitate. Because of this extra pressure, the Gibbs energy of a small precipitate will be higher than that of a large one, which, in turn, increases its solubility (see Fig. 4.6(b)). The important influence of particle curvature on the solid solubility has been extensively investigated and reported in the literature.18 Usually, the phenomenon is referred to as the capillary or the Gibbs-Thompson effect. In the following we shall assume that the thermodynamic and crystallographic properties of the metastable precipitates are similar to those of the equilibrium phase and that the reduced thermal stability is only associated with capillary effects. For single phase precipitates in binary alloy systems, it is fairly simple to show that the concentration of solute across a curved interface, [%A]r, is interrelated to the equilibrium concentration of solute across a planar interface, [%A], through the following equation:8
(4-10) where Vn is the molar volume of the precipitate (in m3 mol"1), and Q is the contribution of the interface curvature to the reaction enthalpy (equal to IyVJr).
(a)
Atmospheric pressure
Matrix
(b)
Gibbs energy
Small precipitate
Matrix
Large precipitate
[%A]
[%A] r Concentration
Fig. 4.6. Effect of interfacial energy on the solubility of small particles; (a) Schematic representation of spherical particles embedded in a metal matrix, (b) Integral molar Gibbs energy of matrix and precipitates at a constant temperature. Assuming that this relationship also holds in the case of binary intermetallics, a combination of equations (4-5) and (4-10) gives:
(4-11)
where (4-12)
or
Alternatively, we can express T as a function of the product [%A]rn [%B]rm. This gives the following expression for the solvus temperature of metastable precipitates T'eq: (4-13) It is evident from the graphical representation of equation (4-13) in Fig. 4.7 that the solid solubility at a given temperature is significantly increased at small particle radii. Taking as an example 7 = 0.5 J n r 2 , Vm = 10~5 m3 moH, R = 8.314 J Kr1 moH, T = 500 K, we obtain from equation (4-10):
or
where r is the particle radius in nm. From this it is seen that quite large solubility differences can arise for particles in the range from r = 1 - 50nm.
Temperature
Large (equilibrium) precipitates
Small (metastable) precipitates
Concentration Fig. 4.7. Graphical representation of equation (4-13) (schematic).
Example (4.3)
In Al-Mg-Si alloys metastable (hardening) p"(Mg2Si)-precipitates m a y form during artificial ageing in the temperature range from 160-2000C. Consider a T6 heat treated ternary alloy which contains 0.75 wt% (0.83 at.%) Mg and 1.0 wt% (0.96 at.%) Si. Based on equation (413) make a sketch of the metastable P "(Mg2Si) solvus in a vertical section through the ternary Al-Mg-Si phase diagram. In these calculations we shall assume that the thermodynamic properties of the metastable (3"(Mg2Si) phase are similar to those of the equilibrium (3 (Mg2Si) phase, i.e. the reduced thermal stability is only related to the Gibbs-Thomson effect. Relevant physical data for the Al-Mg-Si system are given below:
Solution
First we estimate the molar volume of the precipitate:
The contribution of the particle curvature to the reaction enthalpy is thus:
The metastable [3"(Mg2Si) solvus can now be calculated from the solubility product by substituting
into equation (4-13). By inserting data from Table 4.1 and rearranging this equation, we get:
It is evident from the graphical representation of the above equation in Fig. 4.8 that the particle curvature has a dramatic effect on the solid solubility. A comparison with Fig. 4.4 shows that the dissolution temperature drops from about 5600C in the case of the equilibrium Mg2Si phase to approximately 225°C for the metastable |3"(Mg2Si)-phase. On this basis it is not surprising to find that artificially aged (T6 heat treated) Al-Mg-Si alloys suffer from severe softening in the HAZ after welding, as shown schematically in Fig. 4.9. Moreover, it is
Nominal alloy composition A
Temperature, 0C
Dissolution temperature: 225 0C
Metastable solvus boundary
at% Mg at% Mg 2 Si
Strength level
Fig. 4.8. Solubility of (3"(Mg2Si) in aluminium (Example (4.3)).
After artificial ageing After natural ageing Immediately after welding
HAZ Distance from fusion line Fig. 4.9. Response of artificially aged Al-Mg-Si alloys to welding and subsequent heat treatment (schematic).
evident that the characteristic low dissolution temperature of the precipitates also gives rise to the formation of a heat affected zone which is significantly wider than that observed during welding of overaged Al-Mg-Si alloys.9 This shows that the response of age-hardenable aluminium alloys to welding and thermal processing depends strongly on the initial base metal temper condition. With the aid of equation (4-11) it is also possible to calculate an average (apparent) metastable solvus boundary enthalpy for hardening |3"(Mg2Si)-precipitates in Al-Mg-Si alloys. A closer evaluation of the exponent gives:
This value is in close agreement with the reported solvus boundary enthalpy for (3"(Mg2Si)precipitates in 6082-T6 aluminium alloys. 910
4.3 Particle Coarsening When dispersed particles have some solubility in the matrix in which they are contained, there is a tendency for the smaller particles to dissolve and for the material in them to precipitate on larger particles. The driving force is provided by the consequent reduction in the total interfacial energy and ultimately, only a single large particle would exist within the system. 4.3.1 Coarsening kinetics The classical theory for particle coarsening was developed independently by Lifshitz and Slyovoz11 and by Wagner.12 The kinetics are generally controlled by volume diffusion through the matrix. At steady state, the time dependence of the mean particle radius r is found to be:11'12 (4-14) where ro is the initial particle radius, 7 is the particle-matrix interfacial energy, Dm is the element diffusivity, Cm is the concentration of solute in the matrix, Vm is the molar volume of the precipitate per mole of the diffusate, and t is the retention time. Although the classic Lifshitz-Wagner theory suffers from a number of simplifying assumptions, experimental observations usually reveal a cubic growth law of the form given by equation (4-14).13 4.3.2 Application to continuous heating and cooling Ion, Easterling and Ashby14 have shown how equation (4-14) can be applied to continuous heating and cooling. In their analysis equation (4-14) was used in a more general form: (4-15)
where c{ is a kinetic constant, and Qs is the activation energy for the coarsening process (for binary intermetallics Qs may be taken equal to the activation energy for diffusion of the less mobile constituent atom of the precipitates in the matrix). 4.3.2.1 Kinetic strength of thermal cycle It follows that the extent of particle coarsening occurring during a weld thermal cycle can be calculated by integration of equation (4-15) between the limits t = t{ and t = t2:
(4-16) The integral on the right-hand side of equation (4-16) represents the kinetic strength of the thermal cycle with respect to particle coarsening, and can be determined by means of numerical methods when the weld thermal (T-t) programme is known. The resulting radius of the precipitates may then be evaluated from equation (4-16) by inserting representative values for the constants ro and C1 (e.g. obtained from quantitative particle measurements). 4.3.2.2 Model limitations A salient assumption in the classic Lifshitz-Wagner theory is that the particles coarsen at almost constant volume fraction, i.e. no solute is lost to the surrounding matrix during the coarsening process. Consequently, equation (4-16) should only be applied in cases where the peak temperature of the thermal cycle is well below the equilibrium solvus of the precipitates. Example (4.4)
Consider stringer bead deposition (GMAW) on a thick plate of a Ti-microalloyed steel under the following conditions:
Assume that the base metal contains a fine dispersion of TiN precipitates in the as-received condition. Calculate on the basis of equation (4-16) and the Rosenthal thick plate solution (equation (1-45)) the extent of particle coarsening occurring within the fully transformed heat affected zone during welding. Relevant physical data for titanium-microalloyed steels are given below:
(activation energy for diffusion of Ti in austenite) Solution
In the present example the problem is to calculate the size of the TiN precipitates in different
positions from the fusion boundary. This requires detailed information about the weld thermal programme, as shown in Fig. 4.10(a). By substituting the appropriate values for qo, X, a and v into the Rosenthal thick plate solution, the governing heat flow equation becomes:
where /?* refers to the three-dimensional radius vector in the moving coordinate system (designated R in equation (1-45)), while x is the welding direction (equal to vt at pseudo-steady state). Since titanium nitride is thermodynamically stable up to the melting point of the steel, equation (4-16) can be used to calculate the extent of particle coarsening occurring within the transformed parts of the HAZ. In the present example, we may write:
where the times tx and t2 are defined in Fig. 4.10(a). The kinetic strength of the weld thermal cycle with respect to particle coarsening can now be evaluated from these two equations by utilising the numerical integration procedure shown in Fig. 4.10(b). The results from such computations are presented graphically in Fig. 4.11. It is evident from this figure that significant coarsening of the precipitates occurs within the HAZ during welding, particularly in regions close to the fusion boundary where the peak temperature of the thermal cycle is high. A comparison with the experimental data of Ion et al.l4 (reproduced in Fig. 4.12) shows that the theory gives a fairly good prediction of particle size as a function of the peak temperature, provided that the kinetic constant C1 in equation (416) can be estimated with a reasonable degree of accuracy. In practice, however, the numerical value of C1 will vary significantly with the chemical composition and thermal history of the base metal (see Fig. 4.13). This means that empirical calibration of equation (4-16) to experimental data is always required to avoid systematic deviations between theory and experiments.
4.4 Particle Dissolution During welding, the thermal pulse experienced by the heat affected zone adjacent to the fusion boundary can result in complete dissolution of the base metal precipitates. Since this may give rise to subsequent strength loss and grain growth, it is important to understand how variations in welding parameters and operational conditions affect the dissolution rate. In the following, the kinetics of particle dissolution will be discussed from a more fundamental point of view. 4.4.1 Analytical solutions Over the years, several analytical models have been developed which describe the kinetics of particle dissolution in metals and alloys at elevated temperatures.16 None of these solutions are exact, since they represent different approximations to the diffusion field around the dissolv-
(a) Weld metal
Temperature
HAZ
Y~ regime
Time
(i/r)exp(-Qs/RT)
(b)
Time
Fig. 4.10. Kinetic strength of weld thermal cycle with respect to particle coarsening (Example (4.4)); (a) HAZ temperature-time programme (schematic), (b) Numerical integration procedure (schematic).
Weld metal
Partly transformed HAZ
Particle radius, nm
Fully transformed HAZ •
Peak temperature, 0C Fig. 4.11. Coarsening of TiN during steel welding (Example (4.4)).
Frequency, %•
Rosenthal thick plate heat cycle:
Particle radius, nm
Fig. 4.12. Measured size distribution of TiN before (broken lines) and after (full lines) weld thermal simulation. Operational conditions as in Example (4.4). Data from Ion et al.14 ing precipitates. Nevertheless, it will be shown below that at least some of them are sufficiently accurate to capture the essential physics of the problem and to give valuable quantitative information on the extent of particle dissolution occurring during the weld thermal cycle.
Particle radius, nm
Annealing temperature: 1350 0C
Steel A Steel B Steel C
Annealing time, s Fig. 4.13. Effects of annealing time and steel chemical composition on the mean particle size of TiN. Data from Matsuda and Okumura.15
4.4. L1 The invariant size approximation The model described here is due to Whelan.17 Consider a spherical particle embedded in an infinite matrix, as shown schematically in Fig. 4.14. The corresponding matrix concentration profile is plotted in the lower part of the figure. In this case the concentration of the constituent element A is higher close to the particle/matrix interface than in the bulk. Hence, there is a tendency for the element to diffuse away from the particle and into the surrounding matrix (i.e. the particle dissolves). Based on the assumption that the particle/matrix interface is stationary (i.e. the diffusion field has no memory of the past position of the interface), Whelan17 arrived at the following expression for the dissolution rate of a spherical precipitate at a constant temperature: (4-17) where r is the particle radius, a is the dimensionless supersaturation (defined in Fig. 4.14), and Dm is the element bulk diffusivity. The term Hr on the right-hand side of equation (4-17) stems from the steady-state part of the diffusion field, while the (1 A/7) term arises from the transient part. Because of the complex form of equation (4-17) it cannot be integrated analytically and hence, numerical methods must be applied. However, if the transient part of equation (4-17) is neglected (conforming to the solution after long times), it is possible to obtain a simple expression for the particle radius as a function of time: (4-18) where ro is the initial particle radius. Equation (4-18) is identical with the so-called invariant-field solution developed independ-
Concentration
Distance Fig. 4J4. Schematic representation of the concentration profile around a dissolving spherical particle in an infinite matrix. ently by Aaron et al.16 and is valid after a certain period of time, provided that there is no impingement of diffusion fields from neighbouring precipitates. As shown in Fig. 4.15, this simplified solution gives a reasonable description of the dissolution kinetics of small spherical precipitates in steel during reheating above the AC1 -temperature. Following the treatment of Agren,18 the time required for complete dissolution of a spherical precipitate td can be obtained from equation (4-18) by setting r = 0:
(4-19) Moreover, the volume fraction of the precipitates/as a function of time is given by:
(4-20) where fo is the initial particle volume fraction. The former equation shows that the dissolution time td depends strongly on the initial particle size rQ. Example (4.5)
The following example illustrates the direct application of equations (4-18) and (4-19). Consider a niobium-microalloyed steel which contains a fine dispersion of NbC precipitates. Provided that impingement of diffusion fields from neighbouring particles can be neglected, calculate the total time required for complete dissolution of a 100 nm large NbC precipitate at
Particle radius, jam
Numerical solution (Agren)
Simplified analytical solution (Whelan)
Time, s Fig. 4.15. Dissolution kinetics of spherical cementite particles in austenite at 8500C. Data from Agren.18 135O°C. Data for the steel chemical composition and the diffusivity of Nb in austenite at 13500C are given below: Steel chemical composition:
Diffusivity of Nb in austenite at 13500C:
Atomic weight of Nb: Atomic weight of C : Solution
In the present example it is reasonable to assume that the dissolution rate of the precipitate is controlled by diffusion of Nb in austenite. For a single NbC precipitate embedded in a Nbdepleted matrix, the dimensionless supersaturation becomes:
The equilibrium concentration of niobium at the particle/matrix interface can be estimated
from the solubility product by utilising data from Table 4.1. If we assume that the carbon concentration at the interface is constant and equal to the nominal value of 0.12 wt% (i.e. the stoichiometry of the dissolution reaction is neglected), equation (4-5) reduces to:
Moreover, the concentration of Nb in the precipitate is equal to:
This gives:
The dissolution time td can now be calculated from equation (4-19) by inserting the appropriate values for ro, aNt)J and Dm\
A comparison with Fig. 4.16 shows that the predicted value is off by a factor of about 4 compared with that obtained from more sophisticated numerical calculations. This degree of accuracy is acceptable and justifies the use of equation (4-18) for prediction of the dissolution rate of spherical precipitates under different thermal conditions provided that the model is calibrated against experimental data points. 4.4.1.2 Application to continuous heating and cooling Application of the model to continuous heating and cooling requires numerical integration of equation (4-18) over the weld thermal cycle:
(4-21)
Under such conditions the volume fraction of the precipitates is given by:
(4-22)
Equations (4-21) and (4-22) provide a basis for predicting the extent of particle dissolution occurring within the HAZ during welding in the absence of impingement of diffusion fields from neighbouring precipitates.
Dissolution time, s
Particle diameter, nm Fig. 4.16. The dissolution time of NbC in austenite at 13500C as function of initial particle diameter lro for different Nb and C levels (numerical solution). Data from Suzuki et al.6 Example (4.6)
Consider stringer bead deposition (SAW) on a thick plate of a Nb-microalloyed steel (0.10 wt% C - 0.03 wt% Nb) under the following conditions:
Assume that the base metal contains a fine dispersion of NbC precipitates in the as-received condition. Calculate on the basis of equation (4-22) and the Rosenthal thick plate solution (equation (1-45)) the extent of particle dissolution occurring within the fully transformed HAZ during welding. Relevant physical data for Nb-microalloyed steels are given below:
Solution
In the present example the problem is to calculate the variation in the//fo ratio across the fully transformed HAZ. By substituting the appropriate values for qo, X, a, and v into the Rosenthal thick plate solution, the governing heat flow equation becomes:
Since it is reasonable to assume that the dissolution rate of the precipitates is controlled by diffusion of Nb in austenite, the dimensionless supersaturation reduces to:
As shown in example (4.5), the equilibrium concentration of niobium at the particle/matrix interface (in wt%) can be estimated from the solubility product by utilising data from Table 4.1. If we assume that the carbon concentration at the interface is constant and equal to the nominal value of 0.10 wt%, equation (4-5) becomes:
Moreover, the concentration of Nb in the precipitate is equal to:
This gives:
By substituting the appropriate expressions for aNb and DNb into equation (4-22), we obtain:
Here the lower and upper integration limits refer to the total time spent in the thermal cycle from Ac3 to T and down again to Ac3. The extent of particle dissolution occurring within the HAZ during welding can now be calculated in an iterative manner by numerical integration of the above equation over the weld thermal cycle. The results from such computations are presented graphically in Fig. 4.17. It is evident from these data that NbC starts to dissolve when the peak temperature of the thermal cycle T exceeds the equilibrium dissolution temperature Td of the precipitate. The process is completed when T approaches 13300C, conforming to a temperature interval of 1900C. This shows that considerable superheating is required in order to overcome the inherent kinetic barrier against particle dissolution under the prevailing circumstances. 4.4.2 Numerical solution In the previous treatment, no consideration is given to impingement of diffusion fields from neighbouring precipitates or the position of the particle/matrix interface during the dissolution process. In certain cases, however, such phenomena will have a marked effect on the dissolution kinetics.18"22 A good example is Al-Mg-Si alloys where the hardening P"(Mg2Si)-phase forms a very fine distribution of needle-shaped precipitates along <100> directions in the aluminium matrix. These precipitates are closely spaced and will therefore interact strongly with each other during dissolution (coupled reversion).
f/fo
No dissolution-
Complete dissolution Peak temperature, 0C Fig. 4.17. Dissolution of NbC during steel welding (Example (4.6)).
4.4.2.1 Two-dimensional diffusion model For rod or needle-shaped precipitates in a finite, depleted matrix, the rate of dissolution can be calculated by numerical methods from a simplified two-dimensional diffusion model. Assuming that the precipitates are mainly aligned in one crystallographic direction, it is reasonable to approximate their distribution by that of a face-centered cubic (close-packed) space lattice, as shown in Fig. 4.18(a). If planes are placed midway between the nearest-neighbour particles, they enclose each particle in a separate cell. Since symmetry demands that the net flux of solute through the cell boundaries is zero, the dissolution zone is approximately defined by an inscribed cylinder whose volume is equivalent to that of the hexagonal cell. The modelling principles outlined in Fig. 4.18(a) and (b) have previously been used by a number of other investigators to describe particle dissolution during isothermal heat treatment.18"22 Consequently, readers who are unfamiliar with the concept should consult the original papers for further details. It follows from Fig. 4.18(b) that the rate of reversion can be reported as: (4-23)
where ro is the initial cylinder (particle) radius. (a)
Concentration
(b)
Distance Fig. 4.18. Numerical model for dissolution of rod-shaped particles in a finite, depleted matrix; (a) Dissolution cell geometry, (b) Particle/matrix concentration profile (moving boundary).
For a specific alloy, the ratio between ro and L (the mean interparticle spacing) can be calculated from a simple mass balance, assuming that all solute is tied-up in precipitates. Taking this ratio equal to 0.06 for rod-shaped precipitates in diluted alloys,9 the kinetics of particle dissolution during isothermal heat treatment have been examined for a wide range of operational conditions. These results are presented in a general form in Fig. 4.19 by the use of the following groups of dimensionless parameters: Dimensionless time
(4-24)
Dimensionless supersaturation
(4-25)
(a is defined previously in Fig. 4.14). The data in Fig. 4.19 suggest that the reaction kinetics during the initial stage of the process are approximately described by the relation: (4-26)
log <1 - f/fo)
where c2 is a kinetic constant, and n{ is a time exponent (assumed constant and equal to 0.5 under the prevailing circumstances). The rate of particle dissolution will gradually decline with increasing values of T as a result of impingement of diffusion fields from neighbouring precipitates which reduces a. In practice, 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.
log T Fig. 4.19. Dissolution kinetics of rod-shaped particles in a finite, depleted matrix. Data from Myhr and Grong.9
4.4.2.2 Generic model Myhr and Grong9 have shown how this model can be applied to specific alloy systems. From equation (4-26) we have:
(4-27) where n{ < 0.5. This equation can further be simplified if we assume that
and
(4-28) For isothermal heat treatment at a chosen reference temperature (Tn), the rate of particle dissolution is determined by the retention time tr{. Let f* denote the maximum hold time required for complete dissolution of the precipitates. It follows that equation (4-28) can be written in a general form by normalising tn with respect to t*x. The parameter t*n is obtained by 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 previous examples), and rearranging equation (4-28), we obtain:
(4-31)
and (4-32) 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 precipitates.
Equations (4-31) and (4-32) exploit some good modelling techniques. For example, the use of 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 power H1 means that the premultiplying constant, here unity, is independent of the value of nv and is itself also dimensionless. Finally, the form of equation (4-31) eliminates further unknown kinetic constants, and may readily be calibrated using an experimental time r* at a reference temperature. Figure 4.20 shows the variation inflfo with time (on log axes), from a range of isothermal experiments carried out on 6082-T6 aluminium alloys, using hardness (or electrical conductivity) measurements to evaluate/7/\ The curve (equation (4-32)) extrapolates back to a slope of 0.5 (the exponent n{) for the case of the early stages of dissolution before impingement of the diffusion fields. The exponent nx is seen to fall to lower values when the proportion dissolved is higher, in agreement with the theoretical curves in Fig. 4.19.
log(i-f/f 0 )
4.4.2.3 Application to continuous heating and cooling Myhr and Grong9 have also shown how this model can be applied to situations where the temperature varies with time (as in welding). In order to obtain a general description of particle dissolution under non-isothermal conditions, it is convenient to introduce the related concepts of an isokinetic reaction and the kinetic strength of a thermal cycle.23 A reaction is said to be isokinetic if the increments of transformation in infinitesimal isothermal time steps are additive. Christian24 defines this mathematically by stating that a reaction is isokinetic if the evolution equation for some state variable X may be written in the form:
log (t/t*) Fig. 4.20. 'Master-curve' for dissolution of hardening p"(Mg2Si)-precipitates in 6082-T6 aluminium alloys. Data from Myhr and Grong.9
(4-33) where G(X) and H{T) are arbitrary functions of X and T, respectively. For a given thermal history T(t), this essentially means that the differential equation contains separable variables of X and T. The same criterion may also be applied to the models derived above. In the case of coupled reversion, we may write: (4-34) and (4-35) Since dfldlx and t\ are unique functions of/and T, respectively, the additivity condition is satisfied. Consequently, when the temperature varies with time, we replace the term 11 t*x in equation (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 by evaluating the integral Z1 numerically (e.g. by utilising input data from Table 4.2) and replacing 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 thick plates (i.e. equation (1-104)), it is possible to calculate the variation in the f/fo ratio (i.e. the solute distribution) across the HAZ of single pass 6082-T6 aluminium weldments for a wide range of operational conditions (see Table 4.3). The results from such computations are presented graphically in Fig. 4.21 -4.23. When stringer bead deposition is carried out on a plate of medium thickness, the solute distribution in the transverse y direction is expected to vary with distance from the plate surface due to a continuous change in the heat flow conditions. A closer inspection of Figs. 4.21 and 4.22 shows that this is correctly accounted for in the present model. In contrast, a full penetration butt weld will always reveal a similar solute distribution in the transverse direction of the weld, as shown in Fig. 4.23. This situation arises from the lack of a temperature gradient in the through-thickness z direction of the plate. Table 4.2 Basic input data in dissolution model for hardening p" (Mg2Si)- precipitates in 6082-T6 aluminium alloys. Data from Myhr and Grong.9 Parameter
Q'app
Qs
nx (starting value)
t\ (375°C)
Value
3OkJm0I-1
13OkJm 0 I- 1
0.5
600 s
Wo
Peak temperature, 0C
(a)
Comolete dissolution
Aym ,mm
f/fo
Peak temperature, 0C
(b)
Complete dissolution
ym,mm Fig. 4.21. Dissolution of p"(Mg2Si)-precipitates during aluminium welding (Weld 1); (a) Upper plate surface, (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
No.*
Plate thickness
Net arc power
Welding speed
(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 the parent material (thermal data for the AA6082 alloy are given in Table 1.1, Chapter 1).
Complete dissolution
Peak temperature, 0C
Mo
(a)
Aym,mm
Complete dissolution
Peak temperature, 0C
f/fo
(b)
ym,mm Fig. 4.22. Dissolution of (3"(Mg2Si)-PrCCiPiIaIeS during aluminium welding (Weld 2); (a) Upper plate surface, (b) Centre of plate. Operational conditions as in Table 4.3.
4.4.2.4 Process diagrams for single pass 6082-T6 butt welds For single pass butt welding of plates, the heat flow model (equation 1-104)) can largely be simplified 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 onedimensional, and the temperature distribution is determined by the ratio qo/vd, kJ ram"2 (see Sections 1.10.3.3 and 1.10.4.1 in Chapter 1).
Peak temperature, 0C
Wo
Complete dissolution
Ay ,mm m Fig. 4.23. Dissolution of p"(Mg2Si)-precipitates during aluminium welding (Weld 3). Operational conditions as in Table 4.3.
f/fo
Figure 4.24 shows plots of the variation in the flfo ratio across the HAZ of 6082-T6 aluminium weldments for different values of qo Ivd. It follows that a narrow width of the dissolution zone requires the use of a low energy per mm2 of the weld. In practice, this can be achieved by the use of an efficient welding process (e.g. electron beam or laser welding) which facilitates deposition off a full penetration butt weld without employing a groove preparation (i.e. eliminates the need for filler metals).
Scale:
Distance from fusion line Fig. 4.24. Process diagram showing the solute distribution within the HAZ of single-pass 6082-T6 aluminium butt welds for different values of qo Ivd.
References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23.
24.
R.D. Doherty: Physical Metallurgy, 3rd Edn (Eds R.W. Chan and R Haasen), 1983, Amsterdam, North-Holland Physics Publ., 934-1030. K.E. Easterling: Introduction to the Physical Metallurgy of Welding, 1983, London, Butterworths & Co., Ltd. H. Adrian and RB. Pickering: Mater. ScL TechnoL, 1991, 7, 176-182. B. Loberg, A. Nordgren, J. Strid and K.E. Easterling: MetalL Trans., 1984,15A, 33-41. J. Strid and K.E. Easterling: Acta MetalL, 1985, 33, 2057-2074. S. Suzuki, G.C. Weatherly and D.C. Houghton: Acta. MetalL, 1987, 35, 341-352. J.L. Petty-Galis and R.D. Goolsby: J. Mater. ScL, 1989, 24, 1439-1446. D. A. Porter and K.E. Easterling: Phase Transformations in Metals and Alloys, 1981, Wokingham (England), Van Nostrand Reinhold Co. Ltd. O.R. Myhr and 0. Grong: Acta MetalL Mater., 1991, 39, 2693-2702; ibid., 2703-2708. H.R. Shercliff and M.F. Ashby: Acta MetalL Mater., 1990, 38, 1789-1802; ibid., 1803-1812. J.M. Lifshitz and V.V. Slyozov: /. Phys. Chem. Solids, 1961,19, 35-50. C. Wagner: Z. Electrochem., 1961, 65, 581-591. L.C. Brown: Acta MetalL Mater., 1992, 40, 1293-1303. J.C. Ion, K.E. Easterling and M.F. Ashby: Acta MetalL, 1984, 32, 1949-1962. S. Matsuda and N. Okumura: Trans. ISIJ, 1978,18, 198-205. H.B. Aaron, D. Fainstein and G.R. Kotler: J. Appl. Phys., 1970, 41, 4404-4410. MJ. Whelan: Metal ScL J., 1969, 3, 95-97. J. Agren: Scand. J. MetalL, 1990,19, 2-8. R.A. Tanzilli and R.W. Heckel: Trans. Met. Soc. AIME, 1968, 242, 2313-2321. H.B. Aaron and R. Kotler: MetalL Trans., 1971, 2, 393-408. R. Asthana and S.K. Pabi: Mat. ScL Eng., 1990, A128, 253-258. U.H. Tundal and N. Ryum: MetalL Trans., 1992, 23A, 433-444; ibid., 445-449. 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. J.W. Christian: Phase Transformations in Metals and Alloys, 1975, Oxford, Pergamon Press.
Appendix 4.1 Nomenclature thermal diffusivity (mm2 s l)
end temperature of ferrite to austenite transformation (0C)
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 ferrite to austenite transformation (0C)
equilibrium concentration of element A in matrix (wt% or at.%) analytical content of element A in alloy (wt% or at.%) equilibrium concentration of element A across a curved particle/matrix interface (wt% or at.%)
standard free energy of reaction (J mol"1 or kJ mol"1)
arbitrary alloying element equilibrium concentration of element B in matrix (wt% or at.%) analytical content of element B in alloy (wt% or at.%) equilibrium concentration of element B across a curved particle/matrix interface (wt% or at.%) various kinetic constants and temperature-dependent parameters normalised (dimensionless) entropy of reaction concentration of solute at particle/matrix interface (wt% or at.%) nominal alloy composition (wt% or at.%) concentration of solute in matrix (mol irr 3 , wt% or at.%) concentration of solute inside the precipitates (wt% or at.%) plate thickness (mm) normalised enthalpy of reaction (K) element diffusivity (mm2 s"1 or m2 s"1) particle volume fraction initial particle volume fraction
GMAW
gas metal arc welding
H(T)
arbitrary function of T standard enthalpy of reaction (J mol"1 or kJ mol"1) amperage (A) kinetic strength of thermal cycle with respect to reversion equilibrium constant mean interparticle spacing in dissolution model (m, Jim or nm) integer atomic weight of element A (g mol"1) atomic weight of binary precipitate (g mol"1) atomic weight of element B (g mol-1) integer time exponent in dissolution model pressure caused by curvature effects (J nr 3 ) net arc power (W) apparent (metastable) solvus boundary enthalpy (kJ mor 1 ) activation energy for diffusion (kJ moH)
equilibrium particle volume fraction
particle radius (m, Jim or nm)
maximum particle volume fraction at absolute zero
initial particle radius (m, (im or nm)
arbitrary function of X
universal gas constant (8.314JK-1InOl-1)
artificially aged condition voltage (V)
universal gas constant multiplied by InIO (19.14J Kr1 mol"1)
welding speed (mm s"1)
three-dimensional radius vector in Rosenthal equation (mm)
state variable
standard entropy of reaction (J K mol"1) SAW
submerged arc welding
welding direction (mm)
transverse direction (mm) width of HAZ referred to fusion boundary (mm) through-thickness direction (mm)
time (s) time necessary for complete dissolution of precipitate(s) integration limits (s) time necessary for complete reversion at T(s)
molar volume of precipitate (m3 mol 1 ) molar volume of precipitate per mole of the diffusate (m3 mol-1)
retention time at T1. (s)
density of precipitate An Bm (g cm"3 or kg rrr3)
time necessary for complete reversion at Trl(s)
thermal conductivity (W mm-1 0C-1)
temperature (0C or K)
dimensionless supersaturation in dissolution model
ambient temperature (0C or K) equilibrium dissolution temperature of precipitate (0C or K)
density (g cm"3 or kg nr 3 ) arc efficiency factor particle/matrix interfacial energy (J m~2)
melting point (0C or K) peak temperature of thermal cycle (0C or K) chosen reference temperature in dissolution model (0C or K) equilibrium solvus temperature (0C or K) solvus temperature of metastable precipitates (0C or K)
dimensionless time in dissolution model contribution of particle curvature to reaction enthalpy (J mol"1 or kJ mol"1) equilibrium phase in Al-MgSi alloys hardening precipitate in AlMg-Si alloys
5 Grain Growth in Welds
5.1 Introduction Grain growth is an important aspect of welding metallurgy. Normal grain growth in metals and alloys is a thermally activated process driven by the reduction in the grain boundary energy. Physically, it occurs by growth of the larger grains at the expense of the smaller ones which tend to shrink. Under isothermal heat treatment conditions, normal grain growth is well described by the following 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, and C1 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 the range from 0.1 to 0.4, as shown in Fig. 5.1. Only in the case of ultrapure metals annealed at very high temperatures the time exponent may approach a constant value of 0.5. This corresponds to the limiting case where the grain boundary migration rate is directly proportional to the driving pressure 7 /D (7 denotes the grain boundary interfacial energy per unit area, while D is the grain size). It is well recognised that alloying and impurity elements both in the dissolved state and in the form of inclusions or second phase particles will retard grain growth.2"* Consequently, a comprehensive theoretical treatment of grain growth in welds must include a consideration of such effects. The present analysis will therefore start with a closer examination of factors affecting the grain boundary mobility in metals and alloys under conditions applicable to welding.
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
Z.R.AI
•Brass
Homologous temperature (T/Tm) 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 individual grains. In three dimensions, individual grain volumes cannot be determined directly from measurements made in single cross sections through the structure. Therefore, certain geometric assumptions must be employed to obtain these quantities. Since most grain size measurements seek to correlate the interaction of grain boundaries with specific properties (e.g. the transformation behaviour), an estimate of the grain boundary area per unit volume Sv is often required. This parameter can be calculated without assumptions concerning grain shape and size distribution from measurements of the mean linear grain intercept D*.5 (5-2) If the mean grain diameter D is required from 5V, this may be obtained by assuming a spherical grain shape. Noting that each boundary is shared by two adjacent grains, we obtain:
(5-3) from which (5-4) It follows that the mean linear grain intercept D* is always smaller than the actual grain size D. A common observation in metals and alloys is that the size distributions of grain aggregates
at different annealing times become equivalent when the measured grain size parameter, D, is normalised (scaled) by the time-dependent average of this metric, D (see Fig. 5.2). This means that grain structures can be completely characterised, in a statistical sense, by simple probability functions of the standard deviation of the distribution together with the time dependence 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 boundary is given by:7 (5-5) 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 equivalent spherical volume of some geometrically modelled average grain size. Experimental measurements performed on high purity aluminium indicate that p* ~ 3.23 D*.7 This observation is consistent with the model of Hellman and Hillert,8 which predicts that the curvature of the most critical element of grain boundary that must be stabilised is p* = 3 D . Under such conditions, the driving pressure becomes: (5-6)
F (arbitrary units)
Zone refined iron
Rayleigh distribution
Log-normal distribution
D/D Fig. 5.2. Comparison of measured grain size data in iron with the Rayleigh and log-normal distribution functions F. The similarity of the size distributions at different annealing times illustrates the self-similar scaling behaviour of normal grain growth. After Pande.6
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 average driving 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 elastic attraction of the atoms towards the open structure of the grain boundary. The boundary must then either drag the impurity atoms along (so that its speed is limited by the diffusion rate of these atoms) or break away if the impurity concentration is sufficiently small or the driving pressure or temperature is high enough. An analysis of such effects can be done on the basis of the classic impurity drag theories of Chan2 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 diffusion of impurity atoms perpendicular to the boundary. (ii) A high velocity limit, where the grain boundary migration process is mainly governed by the diffusion of solvent atoms across the boundary (i.e. controlled by the rate of boundary self diffusion). The low velocity limit is associated with either a low driving pressure PG or a high impurity level C0, and is characterised by a linear type of relationship between the grain boundary migration rate Va and PG:2 (5-8) Here e denotes the intrinsic drag coefficient, while 1F is a parameter depending on the diffusivity 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 is described by the relationship:2 (5-9) where 4Vp2 denotes another complex function of the impurity diffusivity and the interaction energy between the grain boundary and the impurity atoms. In the case of spherical grains, the classic grain growth equation predicts that the grain boundary migration rate V is a power function of the driving pressure (y /D). This is readily seen by differentiating equation (5-1) and inserting 7 (the grain boundary interfacial energy) into the resulting expression:
(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, corresponding to a time exponent n = 0.5 in the grain growth equation. At this point the grain boundary will break away from its surrounding impurity atmosphere and migrate at a rate close to the rate 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 empirical nature of the grain growth equation. For high driving pressures and intermediate impurity concentrations, the classic impurity drag 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 continuous. Thus, in a log V vs log PG plot it would appear as a steep curve connecting the lines for 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 investigated by Zener.10 There seems to be general agreement that the maximum pinnig force Fp exerted by a single particle of radius r on a grain boundary is given by: 410 (5-11)
log V
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 to the classic impurity drag theories of Cahn2 and Liicke and Stiiwe.3 The diagram is based on the ideas of Vandermeer.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 interact with a maximum force, na is related to Nv (the number of particles per unit volume) through the following 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 Zener retardation 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 the resistance to grain boundary motion in the presence of impurity and alloying elements in solid solution. Based on equation (5-1) Hu and Rath 112 have shown that the grain boundary migration rate V is related to the effective driving pressure APG and the time exponent n through the following 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 expressions for 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 inversely proportional to the average grain size D when n = 0.5 a n d / = 0. This corresponds to the limiting case where the grain boundary will break away from its surrounding impurity atmosphere and migrate at a rate which is controlled by the diffusion of solvent atoms across the boundary. In most cases, however, the observed relationship between V and APG will be different from the theoretical one due to drag from second phase particles (f> 0) or impurity elements in solid solution (n < 0.5).
5.3 Analytical Modelling of Normal Grain Growth By substituting V = V2 (dD/dt) and M = M0 exp (- QappIRT) into equation (5-18), it is possible to obtain a simple differential equation which describes the variation in the average grain size D with time t and temperature T in the presence of impurities and grain boundary pinning precipitates: (5-19) Equation (5-19) can be written in a more general form by setting
and (5-20)
From this it is seen that the parameters M0 and k are true physical constants which are related to the grain boundary mobility and the pinning efficiency of the precipitates, respectively. 5.3.1 Limiting grain size Equation (5-20) shows that the grain structure is stabilised when (d D ldi) - 0. The stable (limiting) grain size is given by: (5-21) The parameter k (which in the following is referred to as the Zener coefficient) is defined as the ratio between the numerical constants in equations (5-7) and (5-16), respectively. In the original Zener's model k = 4/3, while other investigators have arrived at different results.811"14 As shown in Fig. 5.4, the limiting grain size may vary by over one order of magnitude, depending upon the assumptions of the models. This makes it difficult to apply equations (5-20) and (5-21) for quantitative grain size analyses without further background information on the Zener coefficient.
Diim.nm
Gladman
r/f, um Fig. 5.4. Relation between limiting grain size Dum., particle radius r, and volume fraction/predicted by different models. Example (5. J)
Consider multipass GMA welding on a thick steel plate under the following conditions:
Based on the models of Zener,10 Hellman and Hillert,8 and Gladman13 estimate the limiting austenite grain size Dlim in the transformed parts of the weld HAZ when the oxygen and sulphur contents of the as-deposited weld metal are 0.04 and 0.01 wt%, respectively. Solution
As shown in Chapter 2 of this textbook the volume fraction of oxide and sulphide inclusions can be calculated from equation (2-75):
Similarly, the average radius of the grain boundary pinning inclusions can be obtained from equation (2-79):
This gives the following values for the limiting austenite grain size:
Zener:
Hellman and Hillert:
Gladman: and As expected, the limiting austenite grain size is seen to vary by more than one order of magnitude, depending on the assumptions of the models. In practice, the Zener coefficient in low-alloy steel weld metals falls within the range from 0.32 to 0.93, as shown in Fig. 5.5. The average value of A: is close to 0.52, which is the same as that inferred from the Gladman model (upper limit). When it comes to intermetallic compounds such as titanium nitride, the Zener coefficient varies typically between 0.75 and 0.25 during grain growth in the austenite regime. 1617 This suggests that k ~ 0.50 is a reasonable estimate of the grain boundary pinning efficiency of oxides and nitrides in steel. 5.3.2 Grain boundary mobility Direct application of equation (5-20) requires also reliable information on the time exponent n and the grain boundary mobility M. When n = 0.5 and/= 0, the classic impurity drag theories predict that the activation energy Qapp, should be close to the value for boundary self diffusion in the matrix material.2'3 This borderline case is approximately attained in steel welding, as shown in Fig. 5.6(a) and (b), since the driving pressure for austenite grain growth immediately following the dissolution of the pinning precipitates is usually so large that the grain boundary migration rate approaches the higher velocity limit defined in equation (5-9).18 On this basis it is not surprising to find that Qapp falls within the range reported for lattice self diffusion (284 kJ mol"1) and boundary self diffusion (170 kJ mol~l) in pure 7-iron19 during welding.18 In most cases, however, the activation energy will be different from the theoretical one due to complex interactions between impurity atoms and grain boundaries (characterised by a time exponent n < 0.5). Under such conditions, the value of Qapp has no physical meaning.1 5.3.3 Grain growth mechanisms Equation (5-20) provides a basis for evaluating the grain growth inhibiting effect of impurity elements and second phase particles under different thermal conditions. This also includes situations where the grain boundary pinning precipitates either coarsen or dissolve during the heat treatment process. 5.3.3.1 Generic grain growth model Equation (5-20) can readily be integrated to give the average grain size D as a function of time. In the general case we may write: (5-22)
(a) Austenite grain size, Jim
SA steel weld metal
Annealing temperature, 0 C
(b)
D||m. Hm
GMA and SA steel weld metals
r/f, urn
Fig. 5.5. Evaluation of the Zener coefficient in steel weld metals containing stable oxide and sulphide inclusions; (a) Determination of Dum. from isothermal grain growth data (holding time: 30 min), (b) Variation in Dum. with the inclusion rlf ratio. Data from Skaland and Grong.15 where D{im is the limiting grain size (defined in equation (5-21)). The integral I1 on the right-hand side of equation (5-22) represents the kinetic strength of the thermal cycle with respect to grain growth and can be determined by numerical methods when the temperature-time programme is known. In practice, however, it is not necessary to solve this integral to evaluate the grain growth mechanisms. Consequently, the left-hand side of equation
(a) Steel A Log (DxZD1)
Slope: n = 0.4
Log [number of cycles]
(b)
LogD7
Steel A Steel B
Fig. 5.6. Evaluation of the time exponent n and the activation energy Q for austenite grain growth in steel under thermal conditions applicable to welding; (a) Time exponent n, (b) Activation energy Qapp. Data from Akselsen et ah18
(5-22) can be solved explicitly for different values of DUm, n, and Z1. The results may then be presented in the form of novel diagrams which show the competition between the various processes that lead to grain growth during heat treatment of metals and alloys. A more thorough documentation of the predictive power of the model and its applicability to welding is given in Section 5.4. 5.3.3.2 Grain growth in the absence ofpinning precipitates In the absence of grain boundary pinning precipitates, we have:/= 0, Dlim —> ~ , and (1/ DlitrL) = 0. Under such conditions, equation (5-22) reduces to:
(5-23)
After integration this equation yields: (5-24) Referring to Fig. 5.7, the average grain size D becomes a simple cube root function of Z1 when n = 0.5 and D 0 = 0. In other situations (n < 0.5), the grains will coarsen at a slower rate due to drag from alloying and impurity elements in solid solution. This is seen as a general reduction in the slope of the D-Ix curves in Fig. 5.7. The important austenite grain growth inhibiting effect of phosphorus and free nitrogen in steel following particle dissolution is shown in Fig. 5.8. 5.3.3.3 Grain growth in the presence of stable precipitates
If grain growth occurs in the presence of stable precipitates, the limiting grain size {Dlim) in equation (5-22) becomes constant and independent of the thermal cycle. In the specific case when n = 0.5 the integral on the left-hand side of equation (5-22) has the following analytical solution:
D, ^m
(5-25)
I1W" Fig. 5.7. Predicted variation in average grain size D with /, and n f o r / = 0 and D0 = 0 ('free' grain growth).
(a)
D Y ,fim
Steel A
Number of cycles (b)
D y ,um
Steel B
Number of cycles Fig. 5.8. Illustration of the austenite grain growth inhibiting effect of phosphorus and free nitrogen in low-alloy steel during reheating above the Ac^ temperature (multi-cycle weld thermal simulation); (a) Steel A (50ppm P, 20ppm N), (b) Steel B (180ppm P, 80ppm N). Data from Akselsen et a/.18
from which the average grain size D is readily obtained. In other cases, numerical methods must be employed to evaluate D. It is evident from the graphical representation of equation (5-25) in Fig. 5.9 that the grain growth inhibiting effect of the precipitates is very small during the initial stage of the process when D « D lim. Under such conditions the grains will coarsen at a rate which is comparable with that observed for free grain growth (n = 0.5,/= 0). The grain coarsening process becomes gradually retarded as the average grain size increases because of the associated reduction in the effective driving pressure APG until it comes to a complete stop when AP0 = 0 (i.e. D = D Hm)-
D, jim
I 1 ^m 2
D, (im
Fig. 5.9. Predicted variation in average grain size D with Z1 and Dnm. for n = 0.5 and D0 = 0 (stable precipitates).
I 1 , [nm]1/n
Fig. 5.10. Predicted variation in average grain size D with Z1 and n for Dum. = 250|Jin and D0 = 0 (stable precipitates). Dotted curves correspond to grain growth in the absence of pinning precipitates.
If grain growth at the same time occurs under the action of a constant drag from impurity elements in solid solution, the situation becomes more complex. As shown in Fig. 5.10, a decrease in the time exponent from say 0.5 to 0.2 gives rise to a marked reduction in the slope of the D-I 1 curves, similar to that observed in Fig. 5.7 for particle-free systems (/= 0). However, the predicted grain coarsening rate is lower than that evaluated from equation (5-24) due to the extra drag exerted by the grain boundary pinning precipitates. This leads ultimately to a stabilisation of the microstructure when D = DUm. 5.3.3.4 Grain growth in the presence of growing precipitates Very little information is available in the literature on the matrix grain growth behaviour of metals and alloys in the presence of growing second phase particles. So far, virtually all modelling work has been carried out on two phase a-(3 titanium alloys.14 Unfortunately, none of these models can be extended to more complex alloy systems such as steels or aluminium alloys. When grain growth occurs in the presence of growing second phase particles, Dum. will no longer be constant due to the associated increase in the particle rlf ratio with time. As shown in Chapter 4 of this textbook, the Lifshitz-Wagner theory2021 provides a basis for modelling particle growth during welding and heat treatment of metals and alloys in cases where the peak temperature of the thermal cycle is kept well below the equilibrium solvus of the precipitates. Under such conditions, the particles will coarsen at almost constant volume fraction (f=fo), in accordance with equation (4-16): (5-26) where Qs is the activation energy for the coarsening process, C5 is a kinetic constant, and I2 is the kinetic strength of the thermal cycle with respect to particle coarsening. The other symbols have their usual meaning. If the base metal contains particles of an initial radius ro and volume fraction/^, the limiting grain size at I2 = 0 (D° lim) can be defined as:
(5-27) from which (5-28) Similarly, when I2 > 0, we may write: (5-29) By combining equations (5-26), (5-28), and (5-29), we arrive at the following relationship between (D Um ) and I2: (5-30)
It is seen from equation (5-30) that the limiting grain size in the presence of growing particles depends on the product (k/fo)3I1. In practice, the grain boundary pinning effect of the precipitates is determined by the relative rates of particle coarsening and grain growth in the material, i.e. whether the grain boundary mobility is sufficiently high to keep pace with the increase in DUm during heat treatment. Generally, the pinning conditions are defined by the (k/fo)3 I1IIx ratio, which after substitution and rearranging yields:
(5-31)
In cases where the parameters c5 ,Qs, M0*, and Qapp are known, the average grain size D can readily be evaluated from equations (5-22), (5-30), and (5-31) by utilising an appropriate integration procedure. However, since Qs normally differs from Qapp^ the (klfo)3I1I Ix ratio will depend on the thermal path during continuous heating and cooling. Consequently, solution of these coupled equations generally requires stepwise integration in temperature-time space via a fourth heat flow equation. This problem will be dealt with in Section 5.4. The situation becomes much simpler if heat treatment is carried out isothermally. Under such conditions the product (k/fo)311 will only differ from Ix by a proportionality constant m, which is characteristic of the system under consideration. Accordingly, equation (5-30) can be rewritten as: (5-32) From this we see that the two coupled equations (5-22) and (5-32) can be solved explicitly for different values of D°nm., n, m, and Z1. Hence, it is possible to present the results in the form of novel 'mechanism maps' which show the competition between particle coarsening and grain growth during isothermal heat treatment for a wide range of operational conditions. Examples of such diagrams are given in Figs. 5.11 and 5.12. It is evident from these figures that the grain coarsening behaviour during isothermal heat treatment is very sensitive to variations in the proportionality constant m. For large values of m, the matrix grains will coarsen at a rate which is comparable with that observed in Fig. 5.7 for particle-free systems (f = 0). This corresponds to a situation where the grain boundary pinning precipitates will completely outgrow the matrix grains. It is interesting to note that particle outgrowing is more likely to occur if the time exponent n is small, as shown in Fig. 5.12, because of the associated reduction in the grain boundary mobility in the presence of impurity elements in solid solution. In other systems, where the proportionality constant m is closer to unity, the reduced coarsening rate of the precipitates gives rise to a higher Zener retardation pressure and ultimately to a stagnation in the matrix grain growth. In the limiting case, when m = 0, the grain growth behaviour becomes idential to that observed in Figs. 5.9 and 5.10 for stable precipitates.
D.jim
Time exponent n = 0.5
I 1 ,^m 2 Fig. 5.11. Predicted variation in average grain size D with Ix and m for D°um. = 50jLim, n = 0.5, and D0 =0 (growing precipitates).
D,fxm
Time exponent n = 0.3
I1^m1'" Fig. 5.12. Predicted variation in average grain size D with I1 and m for D°um. - 50|im, n = 0.3, and D0 = 0 (growing precipitates).
Example (5.2)
Consider a titanium-microalloyed steel with the following chemical composition: Ti(total): 0.016 wt%, Ti(soluble): 0.009 wt%, N: 0.006 wt% Assume that the base metal contains an uniform dispersion of TiN precipitates in the asreceived condition, conforming to a limiting austenite grain size T>°um. of 50 |iim. Provided that boundary drag from impurity elements in solid solution can be neglected (i.e. n ~ 0.5), estimate on the basis of Fig. 5.11 the average austenite grain size D1 in the material after 25 s of isothermal annealing at 13000C. Relevant physical data for titanium-microalloyed steels are given below: (activation energy for diffusion of Ti in austenite)
Solution
The initial volume fraction of TiN in the material can be estimated from simple stoichiometric calculations by considering the difference between total and soluble titanium. Taking the atomic weight of Ti and N equal to 47.9 and 14.0 g mol"1, respectively, we obtain:
From this we see that the initial radius of the TiN precipitates in the base metal is close to:
Since heat treatment is carried out under isothermal conditions, the parameters m and Z1 can be obtained directly from equations (5-31) and (5-22) without performing a numerical integration:
Similarly, in the case of Z1 we get:
The average austenite grain size can now be read from Fig. 5.11 by linear interpolation between the curves for m = 10 and 100 Jim. This gives:
Although experimental data are not available for a direct comparison, the predicted grain size is of the expected order of magnitude. From this it is obvious that considerable austenite grain growth may occur in titanium-microalloyed steels because of particle coarsening, in spite of the fact that TiN, from a thermodynamic standpoint, is stable up to the melting point of the steel. The process can, to some extent, be counteracted by the use of a finer dispersion of TiN precipitates in the material. For example, if the initial particle radius is reduced by a factor of five (conforming to a change in I W from 50 to 10 Jim), the austenite grain size of the annealed material decreases from 75 to 65 jLim, as shown in Fig. 5.13. Nevertheless, since particle coarsening is a physical phenomenon occurring during high temperature heat treatment of metals and alloys, austenite grain growth cannot be avoided. This explains why, for instance, conventional titanium-microalloyed steels are not suitable for high heat input welding due to their tendency to form brittle zones of Widmanstatten ferrite and upper bainite in the coarse grained HAZ region adjacent to the fusion boundary.22
D,jim
Time exponent n = 0.5
Stable particles I1-Hm2 Fig. 5.13. Predicted variation in average grain size D with Z1 and m for D°Hm. = 10 um, n = 0.5, and Do = 0 (growing precipitates).
5.3.3.5 Grain growth in the presence of dissolving precipitates Little information is available in the literature on the matrix grain growth behaviour of metals and alloys in the presence of dissolving precipitates. As shown in Chapter 4, the model of Whelan23 provides a basis for calculating the dissolution rate of single precipitates embedded in an infinite matrix. If the transient part of the diffusion field is neglected, the variation in the particle radius r with time t at a constant temperature is given by equation (4-18): (5-33) where a is the dimensionless supersaturation (defined in Fig. 4.14), and Dm is the element diffusivity. Application of the model to continuous heating and cooling requires numerical integration of equation (5-33) over the weld thermal cycle: (5-34)
where I3 is the kinetic strength of the thermal cycle with respect to particle dissolution. From this relation the following expression for the particle volume fraction can be derived (see equation (4-22), Chapter 4):
(5-35) where fo is the initial particle volume fraction. By substituting Dlim - k(rlf) and D°nm. = Kr0If0) into equations (5-34) and (5-35), it is possible to obtain a simple mathematical relation which describes the variation in the limiting grain size with I3 during particle dissolution. After some manipulation, we obtain:
(5-36)
It is seen from equation (5-36) that the limiting grain size increases from D°um. at I3 = 0 to infinite when I3 = (fo Ik)2 (D°um. )2 • Since the magnitude of the Zener drag, in practice, depends on the relative rates of grain growth and particle dissolution in the material, the pinning conditions are defined by the (klfo)2131 Ix ratio:
(5-37)
Equation (5-37) shows that the (k/fo)2I3111 ratio is contingent upon the thermal path during continuous heating and cooling. Consequently, application of the model to welding generally requires numerical integration of the coupled equations (5-22), (5-36), and (5-37) over the weld thermal cycle. However, the integration procedure is largely simplified if heat treatment is carried out isothermally. In such cases the product (k/fo)213 will only differ from Ix by a proportionality constant m*, which is characteristic of the system under consideration. By substituting m*Ix into equation (5-36), we obtain:
(5-38) From this we see thaUhe two coupled equations (5-22) and (5-38) can be solved explicitly for different values of Dun., n,m*, and I1. Hence, it is possible to present the results in the form of novel 'mechanism maps' which show the competition between particle dissolution and grain growth during isothermal heat treatment for a wide range of operational conditions. Examples of such diagrams are given in Figs. 5.14 and 5.15. As expected, the stability of the second phase particles is sensitive to variations in the proportionality constant m*. Normally, the precipitates will exert a drag on the grain boundaries as long as they are present in the metal matrix. However, when the dissolution process is completed, the matrix grains are free to grow without any interference from precipitates. This
Time exponent n = 0.5
D,jim
Complete particle dissolution
Stable particles
I 1 ,nm 2 Fig. 5.14. Predicted variation in average grain size D with Z1 and ra* for D°um. = 50 um, n = 0.5, and D0 =0 (dissolving precipitates).
D,jim
Time exponent n = 0.3 Complete particle dissolution
I 1 ^m 1 ' 0 Fig. 5.15. Predicted variation in average grain size D with I1 and m* for D°um. - 50 Jim, n - 0.3, and Do =0 (dissolving precipitates). means that the grains, after prolonged high temperature annealing, will coarsen at a rate which is comparable with that observed in Fig. 5.7 for particle-free systems. In the limiting case, when m* = 0, the grain growth behaviour becomes identical to that shown in Figs. 5.9 and 5.10 for stable precipitates. Example (5.3)
Consider a niobium-microalloyed steel with the following composition: Nb(total): 0.025 wt%, Nb(soluble): 0.010 wt%, C: 0.10 wt% Assume that the base metal contains a fine dispersion of NbC precipitates in the as-received condition, conforming to a limiting austenite grain size Dnm. of 50 jim. Provided that the boundary drag from impurity elements in solid solution can be neglected (i.e. n ~ 0.5), estimate on the basis of Fig. 5.14 the average austenite grain size D 7 in the material after 25 s of isothermal annealing at 13000C. Relevant physical data for niobium-microalloyed steels are given below:
Solution
The initial volume fraction of NbC in the material can be estimated from simple stoichiometric calculations by considering the difference between total and soluble niobium. Taking the atomic weight of Nb and C equal to 92.9 and 12.0 g mol"1, respectively, we obtain:
From this we see that the radius of the NbC precipitates in the base metal is close to:
As shown in Example 4.6 (Chapter 4), the dimensionless supersaturation of niobium a ^ adjacent to the particle/matrix interface during dissolution can be written as:
By substituting this value into the expression for the proportionality constant m*, we obtain:
Moreover, at 1300°C the value OfZ1 becomes:
The average austenite grain size can now be read from Fig. 5.14 by interpolation between the curves for m* = 1 and/= 0 (free grain growth). This gives:
Since the calculated value of D1 is reasonably close to that observed for a particle-free system, it means that the presence of a fine dispersion of NbC in the base metal has no significant effect on the resulting austenite grain size under the prevailing circumstances. Other
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types of niobium microalloyed steels may reveal a different grain coarsening behaviour, depending on the chemical composition, size distribution, and initial volume fraction of the base metal precipitates. However, the pattern remains essentially the same, i.e. the growth inhibition is always succeeded by grain coarsening as long as the precipitates are thermally unstable.
5.4 Grain Growth Diagrams for Steel Welding In welding the temperature will change continuously with time, which makes predictions of the HAZ grain coarsening behaviour rather complicated. The method adopted from Ashby et ^ 24,25 j s b asec i o n m e jd e a o f integrating the elementary kinetic models over the weld thermal cycle where the unknown kinetic constants are determined by fitting the integrals at certain fixed points to data from real or simulated welds. Although the introduction of the Zener drag in the grain growth equation largely increases the complexity of the problem, the methodology and calibration procedure remain essentially the same. This means that the results from such complex computations can be presented in the form of simple grain growth diagrams which show contours of constant grain size in temperature-time space. 5.4.1 Construction of diagrams A grain growth model for welding consists of two components, i.e. a heat flow model, and a structural (kinetic) model. 5.4.1.1 Heat flow models As a first simplification, the general Rosenthal equations26 are considered for the limiting case of a high net power qo and a high welding speed v, maintaining the ratio qo/v within a range applicable to arc welding. It has been shown in Chapter 1 that under such conditions, where no exchange of heat occurs in the .^-direction, the following equations apply: Thick plate welding (2-D heat flow) (5-39) Thin plate welding (1-D heat flow)
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types of niobium microalloyed steels may reveal a different grain coarsening behaviour, depending on the chemical composition, size distribution, and initial volume fraction of the base metal precipitates. However, the pattern remains essentially the same, i.e. the growth inhibition is always succeeded by grain coarsening as long as the precipitates are thermally unstable.
5.4 Grain Growth Diagrams for Steel Welding In welding the temperature will change continuously with time, which makes predictions of the HAZ grain coarsening behaviour rather complicated. The method adopted from Ashby et ^ 24,25 j s b asec i o n m e jd e a o f integrating the elementary kinetic models over the weld thermal cycle where the unknown kinetic constants are determined by fitting the integrals at certain fixed points to data from real or simulated welds. Although the introduction of the Zener drag in the grain growth equation largely increases the complexity of the problem, the methodology and calibration procedure remain essentially the same. This means that the results from such complex computations can be presented in the form of simple grain growth diagrams which show contours of constant grain size in temperature-time space. 5.4.1 Construction of diagrams A grain growth model for welding consists of two components, i.e. a heat flow model, and a structural (kinetic) model. 5.4.1.1 Heat flow models As a first simplification, the general Rosenthal equations26 are considered for the limiting case of a high net power qo and a high welding speed v, maintaining the ratio qo/v within a range applicable to arc welding. It has been shown in Chapter 1 that under such conditions, where no exchange of heat occurs in the .^-direction, the following equations apply: Thick plate welding (2-D heat flow) (5-39) Thin plate welding (1-D heat flow)
5.4.1.2 Grain growth model The use of equation (5-22) for prediction of the HAZ grain structure requires quantitative information about the different kinetic constants entering the model. In the following we shall assume that data for the time exponent n, the activation energies Qam and Qs, the temperature dependence of the dimensionless supersaturation a and the element diffusivity Dm as well as the initial and limiting grain sizes D0 and Dum. are available in the literature. From knowledge of these parameters it is possible to calibrate the model against data from real or simulated welds by adjusting the remaining kinetic constants so that a good agreement is obtained between theory and experiments. 5.4.1.3 Calibration procedure The calibration procedure involves the following basic steps: Evaluation of experimental data Supposejhat the mean grain size at two different locations in the HAZ is known (designated D1 and Z)2, respectively). At each of these locations the peak temperature T and the cooling time within a specific temperature range (e.g. from 800 to 5000C), Af8/5, are given. The thermal cycles for the points can then be computed from either equation (5-39) or (5-40). Using these temperature profiles and an appropriate value for the activation energy Q , the I1IM* ratio is calculated from the integral:
(5-41) where the limits tx and t2 refer to the total time spent in the thermal cycle from the chosen reference temperature Tc to the peak temperature Tp and down again to Tc. Tuning of coarsening model When the parameters n, Qapp., Qs, D0, and D°lim are known, it is possible to evaluate the remaining (unknown) kinetic constants from equations (5-22) and (5-30) by an iterative procedure. The following parameter is defined for this purpose: (5-42) The next step is to calculate the integral (5-43)
for the same pairs of values of Tp and Ar875 as above. The differential grain growth equation can now be solved by selecting an appropriate starting value for M0* and evaluating the corresponding Q-value which conforms to a mean grain size of D\ and D2, respectively. The computations are repeated by adjusting M0* until a contour in Mo*-Q space is built up for each grain size. The accepted values of M* and Q are then found by considering the intersection point between the two curves, as shown schematically in Fig. 5.16(a).
(a)
MS.
Accepted, "" value Accepted^ " ~vaTue~
a (b)
MJ
Accepted. ~ value" " Acce|3ted_ value" "
Q* Fig. 5.16. Method for calibrating unknown kinetic constants to experimental grain growth data; (a) M*o-Q. (coarsening model), (b) M*o-Q* (dissolution model).
Tuning of dissolution model In this case the unknown kinetic constants are combined in a single calibration parameter £2*, defined as: (5-44) where a° and D°m include all constants entering the expressions for the dimensionless supersaturation a and the element diffusivity Dm, respectively.
Under such conditions equation (5-37) becomes: (5-45) where AH* is the standard enthalpy of the dissolution reaction per mole of the diffusate (defined by the solubility product in equation (4-5), Chapter 4), and Qd is the activation energy for diffusion of the less mobile constituent atom of the precipitates in the matrix. By calculating the integral in equation (5-45) for the same pairs of values of Tp and Af8/5 as above and selecting an appropriate starting value for Mo* in equation (5-41), it is possible to build up a contour in Mo*-£T space for each grain size that satisfies the differential grain growth equation. The accepted values of M* and Q* are then found by considering the intersection point between the curves representing D1 and D2 in Fig. 5.16(b). 5.4.1.4 Axes and features of diagrams The microstructural information calculated using the mathematical models described in the previous sections may be plotted on various kinds of welding diagrams. The graphical representation chosen here has been adopted from Ashby et al?^25 The process diagrams have axes of weld input energy and peak temperature, and display contours of constant grain size along with information about the thermal stability of the grain boundary pinning precipitates. The axes can, in turn, be converted into an equivalent cooling time, Atm, and isothermal zone width Ar* or Aym through equations (5-39) and (5-40): Thick plate welding (2-D heat flow)
(5-46)
(5-47)
where Tp < Tn, (Tn, is the melting point). Thin plate welding (1-D heat flow)
(5-48)
(5-49) where Tp < Tn,.
Welding diagrams of this kind are very useful, since they summarise the effect of the important process variables in a systematic and illustrative manner at the same time as they provide a good overall indication of the grain growth behaviour of materials during welding. In addition, the diagrams can be used for quantitative predictions of the austenite grain size across the HAZ of steel welds for a wide range of operational conditions. This will be illustrated below in various numerical examples. 5.4.2 Case studies The following section describes grain growth diagrams for different types of steels. The parameters used to construct the maps are either tabulated or included in the text. Some of these are taken from the literature, while others are arrived at by fitting the theory of the previous sections to data from real or simulated welds according to the procedure shown in Fig. 5.16. To obtain a consistent basis, all grain sizes reported here conform to the mean linear intercept.28 Conversion to three-dimensional grain sizes may then be done through equation (5-4) or by the use of other appropriate conversion factors (e.g. 1.776 as recommended by Ashby et a/.24'25). 5.4.2.1 Titanium-microalloyed steels Titanium-microalloyed steels are widely used in welded structures. From a thermodynamic standpoint, additions of small amounts of titanium to steel would be expected to impede austenite grain coarsening during welding by virtue of its ability to form stable nitrides even at high temperatures (see discussion in Chapter 4). However, certain restrictions must be adhered during casting and subsequent thermomechanical processing of the steel so that the number density of TiN particles is sufficiently high to retard grain growth.22 This currently limits the use of titanium for austenite grain size control to continuously cast and controlled rolled steels. Typical HAZ grain growth diagrams for Ti-microalloyed steels can be constructed on the basis the experimental data reported by Ion et al.25 Tables 5.1 and 5.2 contain information about the steel chemical composition and the parameters used in the computations, while Fig. 5.17 gives an overall indication of the accuracy of the predictions after calibration of the model against two experimental data points. Table 5.1 Chemical composition of Ti-microalloyed steel used by Ion et al.25 (in wt%). C
Si
Mn
P
S
Al
Ti
N
0.12
0.23
1.53
0.005
0.006
0.02
0.011
0.009
Table 5.2 Data used to construct welding maps for Ti-microalloyed steel (compiled from miscellaneous sources).
" 0.5
I ~PP I Q? I »°Hm.
I K I ^* I «
(kJmol-1)
(kJmol-1)
(|xm)
(jun)
(IJLm2S-1)
(1JLm3Ks-1)
224
240
20
9
7.7 X 109
9.9 X 1014
!Activation energy for diffusion of Ti in austenite.
Ti-microalioyed steel E =i s (a I Oi I i Calibration point
Predicted grain size,jim Fig. 5.17. Comparison between measured and predicted HAZ austenite grain sizes after calibration of model to data reported by Ion et al.25 for Ti-microalloyed steel (simulated thick plate welds). The response of the base material to welding under 2-D and 1-D heat flow conditions is shown in Fig. 5.18(a) and (b), respectively. As expected, the presence of TiN particles is seen to retard austenite grain growth within the heat affected zone during welding. However, since particle coarsening is a physical process occurring at temperatures well below the equilibrium solvus of the precipitates, the problem cannot be eliminated. This means that a coarse grained region will always form adjacent to the fusion boundary, even at very low heat inputs, as indicated by the nomograms in Fig. 5.18(a) and (b). Example (5.4)
Consider SA welding on a thick plate of a titanium-microalloyed steel under the following conditions:
Evaluate on the basis of the nomograms in Fig. 5.18(a) the variation in the austenite grain size across the fully transformed HAZ after welding. Estimate also the total width of the HAZ (referred to the fusion boundary) under the prevailing circumstances. Solution
First we calculate the net heat input per unit length of the weld:
Readings from Fig. 5.18(a) give the HAZ austenite grain size profile shown in Fig. 5.19.
Thick plate welding (2-D heat flow) Prior austenite grain size (^m) Relative size of pinning precipitates (r/ro)
Cooling time, At B/5 , s
Net heat input (qo/v), kJ/mm
(a)
Peak temperature, 0C Thin plate welding (1-D heat flow) Prior austenite grain size dim) Relative size of pinning precipitates (r/ro)
Net heat input (qo/vd), kJ/mm2
(b)
Peak temperature, 0C FZg. 5.18. HAZ grain growth diagrams for titanium-microalloyed steel; (a) Thick plate welding (2-D heat flow), (b) Thin plate welding (1-D heat flow). No preheating (T0 = 200C).
Austenite grain size, ^m
SAW (Ti-microalloyed steel)
Peak temperature, 0C Fig. 5.19. Predicted variation in austenite grain size across the fully transformed HAZ of a Ti-microalloyed steel weld (Example 5.4). The total width of the fully transformed HAZ can now be estimated from equation (5-47) by using data from Table 1.1 (Chapter 1). Taking the Ac3 -temperature equal to 9100C, we obtain:
Based on the quoted value of £2 in Table 5.2, it is also possible to estimate the initial volume fraction of TiN in the base metal. Taking C5 « 6.67 X 104 |im3 K s"1 and k « 0.5 for titaniummicroalloyed steels, we obtain from equation (5-42):
A comparison with the experimental data of Ringer et aill shows that a volume fraction of 2 X 10"4 is reasonably close to that measured by microscopic assessment methods.
5.4.2.2 Niobium-microalloyed steels This class of steel is used for a variety of applications, including ship building, pressure vessels, oil platforms and bridges. The steels contain small amounts of microalloying elements such as niobium, vanadium, and aluminium which during thermomechanical processing combine with carbon and nitrogen to form fine dispersions of grain boundary pinning precipitates. They are readily weldable, but suffer from severe HAZ grain coarsening due to dissolution of the carbo-nitrides at elevated temperatures.1822
Typical HAZ grain growth diagrams for Nb-microalloyed steels (with chemical composition as in Table 5.3) can be constructed on the basis of the experimental data of Ion et al. 25 The parameters used to compute the diagrams are listed in Table 5.4. Figure 5.20 shows a correlation between predicted and observed grain sizes after calibration of the model against two experimental data points. It is evident from the nomograms in Fig. 5.21 (a) and (b) that considerable austenite grain growth occurs during welding of niobium-microalloyed steels because of dissolution of the grain boundary pinning precipitates. On the average, the HAZ austenite grain size adjacent to the fusion boundary is four to six times larger than that observed for titanium-microalloyed steels. This gives rise to a high HAZ hardenability, which facilitates formation of low temperature transformation products such as martensite and bainite during welding ?2 Example (5.5)
In Table 5.4 the quoted value for the effective grain boundary pinning constant Q* is 5.0 X 1018 |im 2 s"1. Based on equations (5-27) and (5-44), estimate the initial volume fraction/, and radius ro of NbC in the parent material under the prevailing circumstances. Table 5.3 Chemical composition of Nb-microalloyed steel used by Ion et al.25 (in wt%). C
Si
Mn
P
S
Al
Nb
N
0.12
0.16
0.91
0.002
0.005
0.04
0.021
0.011
Measured grain size, urn
Nb-microalloyed steel SAW GMAW Laser welding Weld simulation Calibration point
Predicted grain size, jam Fig. 5.20. Comparison between measured and predicted HAZ austenite grain sizes after calibration of model to data reported by Ion et al.25 for Nb-microalloyed steel (real and simulated thick plate welds).
Thick plate welding (2-D heat flow) Prior austenite grain size (urn) Relative volume fraction of pinning precipitates (f/fo)
Cooling time, M8^, s
Net heat input (qo/v), kJ/mm
(a)
Peak temperature, 0C Thin plate welding (1-D heat flow) Prior austenite grain size (urn) Relative volume fraction of pinning precipitates (f/fo)
Net heat Input (qo/vd), kJ/mm2
(b)
Peak temperature, 0C Fig. 5.21. HAZ grain growth diagrams for niobium-microalloyed steel; (a) Thick plate welding (2-D heat flow), (b) Thin plate welding (1-D heat flow). No preheating (T0 = 200C).
Table 5.4 Data used to construct welding maps for Nb-microalloyed steel (compiled from miscellaneous sources).
n 0.5
I Qapp. I ^*f I 0} I D°lim. (kJmol-1)
(kJmol-1)
(kJ mol-1)
((Jim)
224
130
343
11
I ^
(|xm) 6
I K* I
"^
(1Xm2S-1)
(1Xm2S-1)
37 X 109
5.0 X 1018
fEstimated from the solubility product of NbC in austenite. ^Activation energy for diffusion of Nb in austenite.
Reasonable average values for a 0 , D°m, k, and D°nm. are given below: 20.5 (estimated from the solubility product of NbC in austenite, Example 4.6) 5.9 X 1010 Jim2 s"1 (diffusion constant for Nb in austenite) 0.5 (Zener coefficient) 11 |Lim (from Table 5.4) Solution
The initial volume fraction of NbC can be estimated from equation (5-44). After rearranging this equation, we obtain:
The corresponding radius of the precipitates can now be obtained from equation (5-27):
Although experimental data are not available for a direct comparison, the calculated values for/o and ro are reasonable and of the expected order of magnitude (see Example 5.3). 5.4.2.3 C-Mn steel weld metals In C-Mn steel weld metals the volume fraction of non-metallic inclusions is considerably higher than for normal cast steel products because of the limited time available for growth and separation of the deoxidation products (see discussion in Chapter T). For the same reason, the weld metal inclusions are also significantly smaller in dimension and more finely dispersed. Since oxides and sulphides will neither coarsen nor dissolve during the weld thermal cycle, they will ultimately lead to a stabilisation of the austenite grain structure within the reheated regions of multipass steel weld metals. This is illustrated schematically in Fig. 5.22. Grain growth diagrams for C-Mn steel weld metals (with chemical compostion as in Table 5.5) can be constructed on the basis of the theory described in the previous sections by selecting reasonable average values for the kinetic constants in equation (5-22). The combination of parameters listed in Table 5.6 gives a fair agreement between predictions and measurements, as shown in Fig. 5.23. The response of the material to reheating above the Ac3-temperature under 2-D and 1-D heat flow conditions is illustrated in Fig. 5.24(a) and (b). As expected, the presence of finely
Weld metal
Base plate
AustenJte grain size
Fully transformed HAZ
Peak temperature Fig. 5.22. Schematic diagram illustrating the effect of non-metallic inclusions on the weld metal grain coarsening behaviour. Table 5.5 Chemical composition of C-Mn steel weld metal used by Kluken et al.29 (in wt%). C
O
Si
Mn
P
S
N
Nb
V
Al
Ti
0.09
0.034
0.48
1.86
0.01
0.01
0.005
0.004
0.02
0.018
0.005
Table 5.6 Data used to construct welding maps for C-Mn steel weld metal (compiled from miscellaneous sources).
"
I 0.5
~pp. I K 1
I bHm. I K?
(kJmol" )
(|xm)
(|xm)
(JJLm2S-1)
224
10
95
20X109
dispersed inclusions within the weld metal gives rise to a strong austenite grain boundary pinning effect, similar to that documented for TiN in microalloyed steels. However, since no particle coarsening occurs in the present case, it means that a small austenite grain size (< 95jnm) is preserved at all relevant peak temperatures, irrespectively of the applied heat input. Accordingly, the weld metal grain growth behaviour is seen to be quite different from that of the base metal, even when the nominal chemical composition has not been significantly changed by the welding process.
Austenite grain size, jim
C-Mn steel weld metal Peak temperature: —1350° C
Cooling time, A t . . s 8/5
Fig. 5.23. Comparison between measured and predicted austenite grain sizes after calibration of model to data reported by Kluken et al.29 for C-Mn steel weld metal (simulated thick plate heat cycles). Example (5.6)
Consider deposition of a cap layer (GMAW) on the top of a thick multipass Nb-microalloyed steel weld under the following conditions:
Estimate on the basis of the nomograms in Figs. 5.21(a) and 5.24(a) the variation in the prior austenite grain size across the fully transformed HAZ at different locations along the periphery of the weld after arc extinction. The situation is illustrated in Fig. 5.25. Solution
First we calculate the net heat input per unit length of the weld:
Readings from Figs. 5.21(a) and 5.24(a) give the HAZ austenite grain size profiles shown in Fig. 5.26. From this we see that the prior austenite grain size adjacent to the fusion boundary of a cap layer will vary significantly with position along the periphery of the weld, depending on the type of material sampled (i.e. base plate or weld metal). 5.4.2.4 Cr-Mo low-alloy steels Chromium-molybdenum low-alloy steels are widely used in the petroleum industry and in high-power-generating equipment because of their good corrosion and oxidation resistance
Thick plate welding (2-D heat flow)
Cooling time, At 8/5 , s
Net heat input (qo/v), kJ/mm
(a)
Peak temperature, 0C Thin plate welding (1 -D heat flow)
Net heat input (qo/vd), kJ/mm2
(b)
Peak temperature, 0C Fig. 5.24. Grain growth diagrams for reheated C-Mn steel weld metal; (a) Thick plate welding (2-D heat flow), (b) Thin plate welding (1-D heat flow). No preheating (T0 = 200C).
HAZ
Base plate
Dissolution of NbC
Austenite grain size, ^m
Fig. 5.25. Sketch of multipass steel weld in Example 5.6.
Peak temperature, 0C Fig. 5.26. Predicted variation in austenite grain size across the fully transformed HAZ at different locations along the periphery of the weld (Example 5.6).
and their high creep strength. They are readily weldable, although reheat cracking and cold cracking in the HAZ and fusion zone may be a problem.30 In practice, these difficulties can be overcome by the choice of an appropriate welding procedure (e.g. preheating in combination with a low heat input), which reduces austenite grain growth and maximises the proportion of the HAZ refined by subsequent weld passes.3031 The grain growth data of Miranda and Fortes31 provide a basis of calibrating the kinetic constants in equations (5-22) and (5-45), as shown in Fig. 5.27. Information about steel chemical composition and parameters used to construct the maps are contained in Table 5.7 and 5.8, respectively. It is seen from the nomograms in Fig. 5.28(a) and (b) that considerable austenite grain growth occurs in Cr-Mo low-alloy steel weldments due to dissolution of molybdenum carbide (Mo2C) at elevated temperatures. However, the maximum HAZ austenite grain size is signifiTable 5.7 Chemical composition of Cr-Mo steel used by Miranda and Fortes31 (in wt%). C
Si
Mn
P
S
Cr
Mo
Ni
Cu
Al
V
0.10
0.24
0.46
0.01
0.01
2.19
0.94
0.23
0.1
0.01
0.01
Predicted grain size, jam
Calibration points
Symbol * w s >
Measured grain size, |im Fig. 5.27. Comparison between measured and predicted HAZ austenite grain sizes after calibration of model to data reported by Miranda and Fortes31 for Cr-Mo low-alloy steel (SAW-thick plates). Table 5.8 Data used to construct welding maps for Cr-Mo low-alloy steel (from Refs. 24 and 31).
n 0.32
I QapP. I A//*+ I QP I b°lm
T ~ F I MO* I QT~
(kJmol-1)
(kJmol-1)
(kJmor"1)
(^m)
(fim)
(IJLm1711S-1)
(IXm2S-1)
180
71
300
20
8
1.3 X 109
7.8 X 1017
f Estimated from the solubility product of Mo2C in austenite. f f Activation energy for diffusion of Mo in austenite.
cantly smaller than that observed during welding of Nb-microalloyed steels, in spite of the fact that Mo2C is less stable than NbC. This situation can probably be attributed to drag from alloying and impurity elements in solid solution, which retard grain growth through elastic attraction of the atoms towards the open structure of the grain boundary (indicated by a time exponent n = 0.32 in Table 5.8). 5.4.2.5 Type 316 austenitic stainless steels The 316 series of stainless steels have good general corrosion resistance, but are sensitive to stress corrosion cracking in the presence of chlorides. They are used extensively in the chemical industry and in power plants, particularly in advanced nuclear technology. During welding dissolution of the base metal chromium carbides (e.g. C^C 6 ) will occur in parts of the HAZ where the peak temperature of the thermal cycle has been above about 8500C. This gives rise to considerable austenite grain growth.24 HAZ grain growth diagrams for this type of steel (with chemical composition as in Table 5.9) can be constructed on the basis of the experimental data of Ashby and Easterling,24 using the parameters listed in Table 5.10. Figure 5.29 shows a correlation between predicted and observed grain sizes after calibration of the model against two experimental data points.
Thick plate welding (2-D heat flow) Prior austenite grain size (urn) Relative volume fraction of pinning precipitates (Vi0)
Cooling time, At 8751 s
Net heat input (qo/v), kJ/mm
(a)
Peak temperature, 0C Thin plate welding (1-D heat flow) Prior austenite grain size (urn) Relative volume fraction of pinning precipitates (f/y
Net heat input (qo/vd), kJ/mm2
(b)
Peak temperature, 0C Fig. 5.28. HAZ grain growth diagrams for Cr-Mo low-alloy steel; (a) Thick plate welding (2-D heat flow), (b) Thin plate welding (1-D heat flow). No preheating (T0 = 200C).
Table 5.9 Chemical composition of type 316 austenitic stainless steel used by Ashby and Easterling24 (in wt%). C
Mn
Si
Cr
Ni
Mo
P
S
0.05
2.0
1.0
19
11
2.3
0.045
0.030
Table 5.10 Data used to construct welding maps for type 316 austenitic stainless steel (compiled from miscellaneous sources).
n
I Qapp.
I Atf*+ I Q/ I D°lm. 1
1
I K
I
M
o*
(kJmol- )
(kJmol- )
(kJ mol" )
(|jim)
(fxm)
(1JLm2S-1)
224
60
240
18
18
3.4 X IQ9
0.5
1
I ^*
(1Xm2S-1)
2.1 X IQ14
Measured grain size, u.m
!Estimated from data quoted by Kou32 for Cr23C6 in 304 stainless steel. ^Activation energy for diffusion of Cr in austenite.
Calibration point
Predicted grain size, ^m
Fig. 5.29. Comparison between measured and predicted HAZ austenite grain sizes after calibration of model to data reported by Ashby and Easterling24 for type 316 stainless steel (simulated thick plate welds). It follows from the nomograms in Fig. 5.30(a) and (b) that the presence of Cr23C6 has little influence on the HAZ grain coarsening behaviour because it dissolves at a fairly low temperature. This results in a rather coarse austenite grain structure adjacent to the fusion boundary, which in certain cases may exceed 100 jim.
Cooling time, At8/5, s
Net heat input (qo/v), kJ/mm
Thick plate welding (2-D heat flow) Austenite grain size ^x m) Relative volume fraction of pinning precipitates (f/fo)
Peak temperature, 0C
Net heat input (qo/vd), kJ/mm2
Thin plate welding (1 -D heat flow) Austenite grain size (JLIITI) Relative volume fraction of pinning precipitates (f/fo)
Peak temperature, 0C Fig. 5.30. HAZ grain growth diagrams for type 316 austenitic stainless steel; (a) Thick plate welding (2-D heat flow), (b) Thin plate welding (1-D heat flow). No preheating (T0 = 200C).
Example (5.7)
Consider GTA butt welding of a 2mm thin sheet of type 316 austenitic stainless steel under the following conditions:
Provided that the conditions for one dimensional (1-D) heat flow are met, estimate on the basis of the nomograms in Fig. 5.30(b) the variation in the austenite grain size across the HAZ after welding. Estimate also the total width of the HAZ (referred to the fusion boundary) under the prevailing circumstances. Solution
First we calculate the net heat input per mm2 of the weld:
Austenite grain size, jim
Readings from Fig. 5.30(b) give the HAZ austenite grain size profile shown in Fig. 5.31. The total width of the grain growth zone can be estimated from equation (5-49) by using data from Table 1.1 (Chapter 1). Taking the peak temperature for incipient dissolution of Cr23C6 equal to 9000C, we obtain:
Peak temperature, 0C Fig. 5.31. Predicted variation in austenite grain size across the HAZ of a 316 austenitic stainless steel weld (Example 5.7).
5.5 Computer Simulation of Grain Growth The multivariable characteristics of grain growth impose several restrictions on the use of analytical modelling techniques for a mathematical description of the grain evolution during welding. However, many of these restrictions can be relaxed by employing novel computational techniques in mainframe facilities which enable the modelling of exact grain shapes in topological connected microstructures. Historically, the application of the computer simulation technique to poly cry stalline microstructures has evolved along two different paths. The first approach treats the grain boundaries as continuous interfaces, which are governed by determistic equations of motion.33"37 The other approach is a Monte Carlo-based technique that takes into account explicitly the interactions among individual grains by discretising the microstructure to construct an image of the grain aggregates in the computer.38"43 Both approaches have been applied to the modelling of grain growth phenomena in welding 374445 with the objective of incorporating important sideeffects which cannot readily be accounted for in a simple analytical treatment of the process. 5.5.1 Grain growth in the presence of a temperature gradient In comparing HAZ grain growth in thermally simulated and real welds it is sometimes found that the maximum grain size is larger in simulated specimens than in a weld HAZ when comparison is made on the basis of a similar temperature-time programme.16 A possible explanation to this observation is the phenomenon of 'thermal pinning' which can be attributed to the presence of steep temperature gradients in a weld HAZ. This effect has been disregarded in the previous analytical analysis, but can readily be incorporated in a numerical model. Following the treatment of Fortes and Soares37 the effect of 'thermal pinning' can be simulated by considering 1-D grain growth in a thin polycrystal with a Gaussian grain distribution. As an illustration of principles, a constant mobility gradient was assumed, the extreme mobilities being in the ratio of 5:1 and 10:1 in different simulations. Simulation with a uniform grain mobility (UNIF) was then carried out for comparison. The polycrystal was subsequently divided into three regions of the same size, i.e. cold (C), intermediate (IM), and hot (H) regions, respectively, and the grain size distributions were obtained for each of these regions and for the entire polycrystal (G: global region). The simulations were carried out until the total number of grains were reduced from initially 5000 to 1500 grains. The results of the computations are summarised in Fig. 5.32. It is evident from Fig. 5.32(a) that grain growth is slower in a mobility gradient than under isothermal heat treatment conditions (UNIF). This effect becomes more pronounced as the mobility gradient increases. Moreover, a closer inspection of Figs. 5.32(b) and (c) reveals that the grain growth rate of the entire crystal (global region: G) is slower than the corresponding coarsening rate of the intermediate region (IM), which again indicates that grain growth is slower in a mobility gradient. Although the simulation results in Fig. 5.32 are not directly applicable to welding (in welding the temperature, and hence the mobility, at a fixed point in the crystal will not be constant but vary with time), these findings provide a strong motivation for incorporating the 'thermal pinning' effect in future refinements of the HAZ grain growth models.
D x 10 (arbitrary units)
(a)
t1/2 (arbitrary units)
D x 10 (arbitrary units)
(b)
t1/2 (arbitrary units)
D x 10 (arbitrary units)
(C)
t1/2 (arbitrary units) Fig. 5.32. Effect of 'thermal pinning' on grain growth; (a) Plot of D vs t for different simulation conditions, (b) Coarsening kinetics of different thermal regions for a mobility gradient of 5:1, (c) Same as in (b) for a mobility gradient of 10:1. Data from Fortes and Soares.37
5.5.2 Free surface effects In a weld HAZ the fusion line represents a physical barrier against grain growth which cannot be exceeded. In principle, it can be regarded as a free surface, which means that the grain boundaries must meet the fusion line at right angles. The simulation results of Saetre and Ryum36 provide a basis for evaluating to what extent grain growth under isothermal conditions is affected by the presence of a free surface. Figure 5.33 shows the evolution of a 2-D Voronoi structure with time. In Fig. 5.33(a) all grain boundaries are straight lines, but the triple line junctions are not in equilibrium. However, adjustments of the triple line junctions into equilibrium positions lead to local curvatures of the grain boundaries near the junctions, and the grain growth process is thus initiated. Initially, the Voronoi structure contained 485 grains, but this number is gradually reduced during the coarsening process (Figs. 5.33(b), (c) and (d)). A qualitative inspection of the diagrams reveals, on the other hand, no clear difference in the grain size in the radial position, which indicates that the constrain provided by the free surface is only of minor importance in the present context. It should be noted that this does not exclude the possibility that the HAZ grain size is influenced by the presence of a fusion boundary, since other effects such as surface grooving and solute segregation (not studied here) can impose additional restrictions on the system by contributing to physical pinning of the grain boundaries. Consequently, further modelling work is required to explore these possibilities.
References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.
H. Hu and B.B. Rath: Metall Trans., 1970,1, 3181-3184. J.W. Cahn: Acta Metall, 1962,10, 789-798. K. Lucke and H. Stuwe: in Recovery and Recrystallization of Metals, 1963, New York, Interscience. E. Nes, N. Ryum and O. Hunderi: Acta Metall, 1985, 33, 11-22. E.E. Underwood: Quantitative Stereology, 1970, London, Addison-Wesley Publ. Co. C S . Pande: Acta Metall, 1987, 35, 2671-2678. B.R. Patterson and Y. Liu: Metall Trans., 1992, 23A, 2481-2482. P. Hellman and M. Hillert: Scand. J. Metall, 1975, 4, 211-219. R.A. Vandermeer: Acta Metall, 1967,15, 447-458. C. Zener (quoted by C S . Smith): Trans. AIME, 1948,175, 15-51. CH. Worner and P.M. Hazzledine: JOM, 1992, 44 (No. 9), 16-20. B.B. Rath and H. Hu: Trans. TMS-AIME, 1969, 245, 1243-1252, ibid., 1577-1585. T. Gladman: Proc. Roy. Soc, 1966, 294A, 298-309. G. Grewal and S. Ankem: Acta Metall Mater, 1990, 38, 1607-1617. T. Skaland and 0. Grong: University of Trondheim, The Norwegian Institute of Technology, Trondheim Norway (unpublished work). K.E. Easterling: Introduction to the Physical Metallurgy of Welding, 2nd Edn, 1992, Oxford, Butterworth-Heinemann Ltd. S.P. Ringer, W.B. Li and K.E. Easterling: Acta Metall, 1989, 37, 831-841. O.M. Akselsen, 0. Grong, N. Ryum and N. Christensen: Acta Metall, 1986, 34, 1807-1815. A.M. Brown and M.F. Ashby: Acta Metall, 1980, 28, 1085-1101. J.M. Lifshitz and V.V. Slyozov: J. Physics Chem. Solids, 1961,19, 35-50. C. Wagner: Z. Electrochem., 1961, 65, 581-591. 0. Grong and O.M. Akselsen: Metal Construction, 1986,18, 557-562.
(a)
(b)
(C)
(d)
Fig. 5.33. The evolution of 2-D grain structures during normal grain growth; (a) Initial Voronoi structure, 485 grains, (b) 456 grains, (c) 349 grains, (d) 251 grains. Data from Saetre and Ryum.36
23. 24. 25. 26. 27. 28. 29.
MJ. Whelan: Metal ScL J., 1969, 3, 95-97. M.F. Ashby and K.E. Easterling: Acta MetalL, 1982, 30, 1969-1978. J.C. Ion, K.E. Easterling and M.F. Ashby: Ada MetalL, 1984, 32,1949-1962. D. Rosenthal: Trans. ASME, 1946, 68, 849-866. O.R. Myhr and 0. Grong: Acta MetalL Mater., 1990, 38, 449-460. ASTM Standard, El 12-84 (1984). A.O. Kluken, 0. Grong and H. Hemmer: Technical Report STF34 F87093, 1987, Trondheim (Norway), Sintef-Division of Metallurgy.
30. RJ. Alberry and W.K.C. Jones: Metals Technology, 1977, 4, 45-51; ibid., 360-364; ibid., 557566. 31. R.M. Miranda and M.A. Fortes: Mater. ScL Eng., 1989, A108, 1-8. 32. S. Kou: Welding Metallurgy, 1987, Toronto, John Wiley & Sons. 33. V.E. Fradkov and D.G. Udler: in Simulation and Theory of Evolving Microstructures (Eds M.R Anderson and A.D. Rollett), 1990, TMS, Warrendale, Pa, pp. 15-29. 34. HJ. Frost, CV. Thompson and D.T. Walton: ibid., pp.31-39. 35. K. Kawasaki, T.Nagai and S. Ohta: ibid., pp.65-77. 36. T.O. Saetre and N. Ryum: in Modelling of Coarsening and Grain Growth (Eds C S . Pande and S.R Marsh), 1993, The Minerals, Metals & Materials Society, pp.281-294. 37. M.A. Fortes and A. Soares: ibid., pp. 257-270. 38. A.D. Rollett, DJ. Srolovitz and M.R Anderson: Acta Metall, 1989, 37, 1227-1240. 39. G.S. Grest, M.R Anderson, DJ. Srolovitz and A.D. Rollett: Scripta Metall Mater., 1990, 24, 661-665. 40. DJ. Srolovitz, G.S. Grest and M.R Anderson: Acta Metall, 1986, 34, 1833-1845; ibid, 1988, 36,2115-2128. 41. T.O. Sartre, O. Hunderi and E. Nes: Acta Metall, 1986, 34, 981- 987. 42. K. Marthinsen, O. Lohne and E. Nes: Acta Metall, 1989, 37, 135-145. 43. A.D. Rollett, MJ. Lutony and DJ. Srolovitz: Acta Metall. Mater., 1992, 40, 43-55. 44. A. Kern, W. Reif and U. Schriever: Proc. Int. Conf. on Grain Coarsening, 18-21 June, 1991, Rome, Mater. ScL Forum, 1992, vols 94-96, 709-714, Trans. Tech Publications. 45. B. Radhakrishnan and T. Zacharia: Proc. Int. Conf. on Modeling and Control of Joining Processes, 8-10 Dec, 1993, Orlando, FL, American Welding Society.
Appendix 5.1 Nomenclature thermal diffusivity (mm2 s"1)
limiting grain size at h - 0 (|im or m)
end temperature of ferrite to austenite transformation (0C or K)
element diffusivity (jum2 s"1, mm2 s"1 or m2 s"1)
nominal alloy composition (wt%, at.% or mol rrr3)
kinetic constant in expression for Dm (|Ltm2 s"1, mm2 s"1 or m2 s"1)
various kinetic constants and temperature-dependent parameters
particle volume fraction
plate thickness (mm)
initial particle volume fraction
grain size (jLirn or m)
maximum pinning force exerted by a single particle ( J m 1 )
mean grain size (\im or m) GMAW gas metal arc welding mean linear grain intercept (JJJTI or m) GTAW
gas tungsten arc welding
initial grain size (jim or m) limiting grain size (jim or m)
standard enthalpy of dissolution reaction per mole of the diffusate (J mol"1 or kJ mol"1)
amperage (A)
activation energy for particle coarsening (J mor 1 or kJ mor 1 )
kinetic strength of thermal cycle with respect to grain growth (jam1/n)
particle radius (nm, jam or m)
kinetic strength of thermal cycle with respect to particle coarsening (fxm3)
initial particle radius at t - 0 (nm, jam or m)
kinetic strength of thermal cycle with respect to particle dissolution (jim2)
two-dimensional radius vector in y-z plane (mm)
Zener coefficient
universial gas constant (8.314 J Kr1 mor 1 )
constant related to the relative rates of grain growth and particle coarsening in the material (jum3"1/n)
grain boundary area per unit volume (jam2 per jum3 or m2 per m3)
constant related to the relative rates of grain growth and particle dissolution in the material (jam2"I/n)
time (s or min)
grain boundary mobility (variable units)
integration limits (s)
kinetic constant in expression for M (variable units)
cooling time from 800 to 5000C (s)
submerged arc welding
temperature (0C or K)
modified kinetic constant in expression for M(J^m1711S-1)
reference temperature (0C or K)
time exponent in grain growth equation
ambient temperature (0C or K)
number of interacting particles per unit area of grain boundary (nr 2 )
melting point (0C or K)
number of particles per unit volume (nr 3 ) driving pressure for grain growth (J m-3) effective driving pressure for grain growth (J nr 3 ) retardation pressure due to second phase particles (J irr 3 ) net arc power (W) apparent activation energy for grain growth (J mor 1 or kJ mor 1 )
peak temperature (0C or K) voltage (V) welding speed (mm s"1) grain boundary migration rate (jam s~{ or m s"1) grain boundary migration rate conforming to the low velocity limit (|Lim s 1 or ms- 1 ) grain boundary migration rate conforming to the high velocity limit (jam s~l or ms" 1 ) x-axis/welding direction (mm)
activation energy for element diffusion in dissolution model (J moT 1 or kJ mor 1 )
y-axis/transverse direction (mm)
z-axis/through thickness direction (mm) dimensionless supersaturation in dissolution model
grain boundary interfacial energy (J m-2) calibration constant in coarsening model (|Lim3 K s"1)
kinetic constant in expression for a parameter depending on the diffusivity and the interaction energy between the grain boundary and the impurity atoms
calibration constant in dissolution model (|Lim2 s"1) density (g cm"3 or kg rrr3)
another complex function of the impurity diffusivity and the interaction energy between the grain boundary and the impurity atoms
radius of curvature of a spherical grain (jum or m)
intrinsic drag coefficient
thermal conductivity (W mm"1 0C"1)
arc efficiency
volume heat capacity (J mm"3 0C"1)
6 Solid State Transformations in Welds
6.1 Introduction The majority of phase transformations occurring in the solid state take place by thermally activated atomic movements. In welding we are particularly interested in transformations that are induced by a change in temperature of an alloy with a fixed bulk composition. Such transformations include precipitation reactions, eutectoid transformations, and massive transformations both in the weld metal and in the heat affected zone. Since welding metallurgy is concerned with a number of different alloy systems (including low and high alloy steels, aluminium alloys, titanium alloys etc.), it is not possible to cover all aspects of transformation behaviour. Consequently, the aim of the present chapter is to provide the background material necessary for a verified quantitative understanding of phase transformations in weldments in terms of models based on thermodynamics, kinetics, and simple diffusion theory. These models will then be applied to specific alloy systems to illuminate the basic physical principles that underline the experimental observations and to predict behaviour under conditions which have not yet been studied.
6.2 Transformation Kinetics In order to understand the extent and direction of a transformation reaction, it is essential to know how far the reaction can go and how fast it will proceed. To answer the first question we need to consider the thermodynamics, whereas kinetic theory provides information about the reaction rate. 6.2.1 Driving force for transformation reactions The symbols and units used throughout this chapter are defined in Appendix 6.1. In practice, solid state transformations require a certain degree of undercooling, which is essential to accommodate the surface and strain energies of the new phase.1 Generally, this minimum molar free energy of transformation, AG, can be written as a balance between the following four contributions: (6-1) Here AGy (the volume free energy change associated with the transformation) and AGD (free energy donated to the system when the nucleation takes place heterogeneously) are negative, since they assist the transformation, while AGS (increase in surface energy between the two phases) and AGE (increase in strain energy resulting from lattice distortion) are both positive because they represent a barrier against nucleation. It follows that the transformation
Molar free energy
Stable (B)
Stable (a)
Temperature Fig. 6.1. Schematic representation of the molar free energies of two solid a and P phases as a function of temperature (allotrophic transformation — no compositional change).
Temperature
reaction can proceed when the driving force AG becomes greater than the right-hand side of equation (6-1). For an allotropic transformation, in which there is no compositional change, AG will be a simple function of temperature, as illustrated in Fig.6.1. For alloys the situation is slightly more complex, since there is an additional variable, i.e. the composition. In such cases the temperature at which the a-phase becomes thermodynamically unstable (Teq) corresponds to a fixed point on the a-(3 solvus boundary in the equilibrium phase diagram, as shown schematically in Fig. 6.2. Since phase diagrams are available for many of the important industrial alloy systems, it means that the driving force for a transformation reaction can readily be obtained from such diagrams in the form of a characteristic undercooling (AT).
%B Fig. 6.2. Schematic representation of the a-(3 solvus boundary in a simple binary phase diagram.
6.2.2 Heterogeneous nucleation in solids In general, solid state transformations in metals and alloys occur heterogeneously by nucleation at high energy sites such as grain corners, grain boundaries, inclusions, dislocations and vacancy clusters. The potency of a nucleation site, in turn, depends on the energy barrier against nucleation (AG*^) which is a function of the 'wetting' conditions at the substrate/ nucleus interface.1 It can be seen from Fig. 6.3 that nucleation at for instance inclusions or dislocations is always energetically more favourable than homogeneous nucleation (AG*het < tsG*hom ) but less favourable than nucleation at grain boundaries or free surfaces. As a result, the transformation behaviour is strongly influenced by the type and density of lattice defects and second phase particles present within the parent material. 6.2.2.1 Rate of heterogeneous nucleation Whereas every atom is a potential nucleation site during homogeneous nucleation, only those associated with lattice defects or second phase particles can take part in heterogeneous nucleation. In the latter case the rate of nucleation (Nhet) is given by:1'2
(6-2) where v is a vibration frequency factor, Nv is the total number of heterogeneous nucleation sites per unit volume, AG^, is the energy barrier against nucleation, and Qd is the activation energy for atomic migration across the nucleus/matrix interface.
Grain boundary
Vacancy clusters
Dislocations/stacking faults
Inclusions
Grain boundaries
Inclusion
Grain corners
Free surfaces
AG* /AG* het. horn.
Free surface
Nucleation site Fig. 6.3 Schematic diagram showing the most potent sites for heterogeneous nucleation in metals and alloys.
It follows from the graphical representation of equation (6-2) in Fig. 6.4 that the nucleation rate Nhet is highest at an intermediate temperature due to the competitive influence of undercooling (driving force) and diffusivity on the reaction kinetics. This change in Nhet with temperature gives rise to corresponding fluctuations in the transformation rate, as shown schematically in Fig. 6.5. Note that the peak in transformation rate is due to two functions, growth and nucleation (which peak at different T) whereas peak in Nhet is due to nucleation only. 6.2.2.2 Determination
of AGhet and Qd
During the early stages of a precipitation reaction, the reaction rate may be controlled by the nucleation rate Nhet. Under such conditions, the time taken to precipitate a certain fraction of the new phase t* is inversely proportional to Nhet\
(6-3) where C1 and C2 are kinetic constants. By taking the natural logarithm on both sides of equation (6-3), we obtain:
(6-4) If the complete C-curve is known for a specific transformation reaction, it is possible to evaluate AG*het and Qd from equation (6-4) according to the procedure described by Ryum.3 In general, a plot of In t* vs HT will yield a distorted C-curve with well-defined asymptotes, as shown in Fig. 6.6. At high undercoolings, when &G*het is negligible, the slope of the curve becomes constant and equal to QdIR. The mathematical expression for this asymptote is: T
T
Low undercooling High diffusivity
High undercooling Low diffusivity %B
Nhet.
Fig. 6.4. Schematic diagram showing the competitive influence of undercooling (driving force) and diffusivity on the heterogeneous nucleation rate.
T
Fraction transformed
logt
logt Fig. 6.5. Fraction transformed as a function of time referred to the C-curve (schematic). (6-5) At the chosen reference temperature Tr the time difference between the real C-curve and the extension of the lower asymptote amounts to (see Fig. 6.6): (6-6) from which (6-7) It follows that equations (6-5) and (6-7) provide a systematic basis for obtaining quantitative information about Qd and AGhet from experimental microstructure data through a simple graphical analysis of the shape and position of the C-curve in temperature-time space.
T
1/r
lnt Fig. 6.6. Determination of AG*het and Qd from the C-curve (schematic).
6.2.2.3 Mathematical description of the C-curve In order to obtain a full mathematical description of the C-curve, we need to know the variation in the energy barrier AG*het with undercooling AT. For heterogeneous nucleation of precipitates above the metastable solvus, the strain energy term entering the expression for AG*het can usually be ignored. In such cases the energy barrier is simply given as:1 (6-8)
where TV4 is the Avogadro constant, ^ n is the interfacial energy per unit area between the nucleus and the matrix, AGV is the driving force for the precipitation reaction (i.e. the volume free energy change associated with the transformation), and 5(0) is the so-called shape factor which takes into account the wetting conditions at the nucleus/substrate interface. For a particular alloy, AGV is for small Ar proportional to the degree of undercooling:l (6-9) where C3 is a kinetic constant. This equation follows from the definition of AGv in diluted alloy systems and the mathematical expression for the solvus boundary in the binary phase diagram. By substituting equation (6-9) into equation (6-8), we get: (6-10) It follows that A0 is a characteristic material constant which is related to the potency of the heterogeneous nucleation sites in the material. The value of A0 is, in turn, given by equations (6-7) and (6-10): (6-11)
In cases where A0 is known, it is possible to obtain a more general expression for t* by substituting equation (6-10) into equation (6-3):
(6-12)
Equation (6-12) can further be modified to allow for compositional and structural variations in the parent material by using the calibration procedure outlined in Fig. 6.7. Let tr denote the time taken to precipitate a certain fraction of (3 at a chosen reference temperature T= Tr in an alloy containing Nv nucleation sites per unit volume. If we take the corresponding solvus temperature of the (3-phase equal to T*q , the expression for t* becomes:
(6-13)
A combination of equations (6-12) and (6-13) then yields:
(6-14)
Equation (6-14) provides a basis for predicting the displacement of the C-curve in temperature-time space due to compositional or structural variations in the parent material. In genT
C-cun/e(Nv=N^)
logt Fig. 6.7. Method for eliminating unknown kinetic constant in expression for t*.
eral, an increase in Nv will shift the nose of the C-curve to the left in the diagram (i.e. towards shorter times), as shown schematically in Fig. 6.8, because of the resulting increase in the nucleation rate. Moreover, in solute-depleted alloys the critical undercooling for nucleation will be reached at lower absolute temperatures where the diffusion is slower. This results in a marked drop in Nhet, which displaces the C-curve towards lower temperatures and longer times in the IT-diagram, as indicated in Fig. 6.9. Example (6.1)
Isothermal transformation (IT) or continuous cooling transformation (CCT) diagrams are available for many of the important alloy systems.4 In the case of aluminium, so-called temperature-property diagrams exist for different types of wrought alloys.45 Suppose that the C-curve in Fig. 6.10 conforms to incipient precipitation of [3'(Mg2Si) particles at manganese-containing dispersoids in 6351 extrusions. Use this information to estimate the values of A0 and Qd in equation (6-3) when the solvus temperature of (3'(Mg2Si) is 5200C. Solution
The parameters A0 and Qd can be evaluated from the C-curve according to the procedure shown in Fig. 6.6. Referring to Fig. 6.11, the value of AG^ at the chosen reference temperature Tr = 35O°C (623K) is equal to:
When AGhet is known, the parameter A0 can be obtained from equation (6-11): T
iogt Fig. 6.8. Effect of Nv on the shape and position of C-curve in temperature-time space (schematic).
T
T
T
logt \e, Fig. 6.9. Effect of solute content on the shape and position of C-curve in temperature-time space (schematic). %B
Similarly, Qd can be read from Fig. 6.11 by considering the slope of the lower asymptote:
This value is in good agreement with the reported activation energy for diffusion of magnesium in aluminium.6
Temperature, 0C
AA 6351 - T6
Time, s Fig. 6.10. C-curve for 99.5% maximum yield strength of an AA6351-T6 extrusion. After Staley.5
103/T, K"1
Solvus temperature: 520 0C
lnt Fig. 6.11. Determination of kG*heU and Qd from the C-curve in Fig. 6.10 (Example 6.1).
6.2.3 Growth of precipitates If the embryo is larger than some critical size, it will grow by a transport mechanism which involves diffusion of solute atoms from the bulk phase to the matrix/nucleus interface. 6.2.3.1 Interface-controlled growth When transfer of atoms across the a/(3-interface becomes the rate-controlling step, the reaction is said to be interface-controlled. This growth mode is therefore observed during the initial stage of a precipitation reaction before a large, solute-depleted zone has formed around the particles. In the case of incoherent precipitates, the variation in the particle radius r with time is given by:7 (6-15)
where M1 is a mobility term, C0 is the concentration of solute in matrix, Ca is the concentration of solute at the particle/matrix interface, and Cp is the concentration of solute inside the precipitate. In general, the mobility of incoherent interfaces is high, since the solute atoms can easily 'jump' across the interface and find a new position in the particle lattice, as shown schematically in Fig. 6.12(a). In contrast, a coherent interface is essentially inmobile because transfer in this case involves trapping of atoms in an intermediate lattice position, as indicated in Fig. 6.12(b). As a result, semi-coherent precipitates are forced to grow by lateral movement of ledges along a low energy interface in a direction where the matrix is incoherent with respect to the particle lattice (see Fig. 6.13). In such cases the thickening rate of the precipitates U*aj^ is given by:3'7
Incoherent Interface
Coherent interface
(a) (b)
U
a/p
Fig. 6J2. Schematic illustration of atom transfer across different kinds of interfaces; (a) Incoherent interface, (b) Coherent interface.
Lateral movement of incoherenf interface
Fig. 6.13. Thickening of plate-like precipitates by the ledge mechanism (schematic).
(6-16)
where M1* is a new mobility term, and / is the interledge spacing. 6.2.3.2 Diffusion-controlled growth For growth of incoherent precipitates above the metastable solvus, the rate-controlling step will be diffusion of solute in the matrix. If precipitation of the P-phase occurs from a
supersaturated a, the reaction proceeds by diffusion of solute to the growing p-particle, as shown schematically in Fig. 6.14. On the other hand, when the (3-phase is formed by rejection of solute from the a-phase, the transformation occurs by diffusion of atoms away from the Pparticle, as indicated in Fig. 6.15. Aron et al.s have presented general solutions for diffusion-controlled growth of both flat plates and spheres under such conditions. In the former case the half thickness AZ of the plate is given by: (6-17) The parameter E1 in equation (6-17) is frequently referred to as the one-dimensional parabolic thickening constant, and is defined as:
Temperature
Liquid
Concentration
%B
Diffusion of solute
Distance Fig. 6.14. Schematic representation of concentration profile ahead of advancing interface during precipitation of (B from a supersaturated a-phase.
Temperature Concentration
%B
Diffusion of solute
Distance Fig. 6.15. Schematic representation of concentration profile ahead of advancing interface during growth of solute-depleted P into a metastable a-phase.
(6-18)
where Dm is the diffusivity of the solute in the matrix, and erfc(u) is the complementary error function (defined previously in Appendix 1.3, Chapter 1). Similarly, for growth of spherical precipitates, the variation in the radius r with time can be written as:8 (6-19) where e 2 *s t n e corresponding parabolic thickening constant for a spherical geometry, defined as:
(6-20)
The parabolic relations in equations (6-17) and (6-19) imply that the growth rate slows down as the (3-phase grows. This is due to the fact that the total amount of solute partitioned during growth decreases with time when the diffusion distance increases. Moreover, the form of equations (6-18) and (6-20) suggests that the maximum in the growth rate is achieved at an intermediate temperature because of the competitive influence of undercooling (driving force) and diffusivity on the reaction kinetics. Consequently, a plot of E1 or £2 vs temperature will reveal a pattern similar to that shown in Fig. 6.4 for the nucleation rate, although the thickening constants generally are less temperature-sensitive. In addition to the models presented above for plates and spheres, approximate solutions also exist in the literature for thickening of needle-shaped precipitates, based on the Trivedi theory for diffusion-controlled growth of parabolic cylinders.9 However, because of space limitations, these solutions will not be considered here. 6.2.4 Overall transformation kinetics The progress of an isothermal phase transformation may be conveniently represented by an ITdiagram of the type shown in Fig. 6.5. Among the factors that determine the shape and position of the C-curve are the nucleation rate, the growth rate, the density and the distribution of the nucleation sites as well as the physical impingement of adjacent transformed volumes. Due to the lack of adequate kinetic models for diffusion-controlled precipitation, we shall assume that the overall microstructural evolution with time can be described by an Avramitype of equation:10 (6-21) where X is the fraction transformed, n is a time exponent, and k is a kinetic constant which depends on the nucleation and growth rates. The exponential growth law summarised in the Avrami equation is valid for linear growth under most circumstances, and approximately valid for the early stages of diffusion-controlled growth.10 Table 6.1 gives information about the value of the time exponent for different experimental conditions. In general, the value of n will not be constant, but change due to transient effects until the steady-state nucleation rate is reached and n attains its maximum value. Subsequently, the nucleation rate starts to decrease as the sites become filled with nuclei and eventually approach zero when complete saturation occurs. This is because the heterogeneous nucleation sites are not randomly distributed in the volume, but are concentrated near other nucleation sites leading to an overall reduction in n. From then on, the transformation rate is solely controlled by the growth rate. 6.2.4.1 Constant nucleation and growth rates For a specific transformation reaction, the value of k in equation (6-21) can be estimated from
Table 6.1 Values of the time exponent n in the Avrami equation. After Christian.10 Polymorphic changes, discontinuous precipitation, eutectoid reactions, interface controlled growth, etc. Increasing nucleation rate Constant nucleation rate Decreasing nucleation rate Zero nucleation rate (saturation of point sites) Grain edge nucleation after saturation Grain boundary nucleation after saturation Diffusion controlled growth All shapes growing from small dimensions, increasing nucleation rate All shapes growing from small dimensions, constant nucleation rate All shapes growing from small dimensions, decreasing nucleation rate All shapes growing from small dimensions, zero nucleation rate Growth of particles of appreciable initial volume Needles and plates of finite long dimensions, small in comparison with their separation Thickening of long cylinders (needles) (e.g. after complete end impingement) Thickening of very large plates (e.g. after complete edge impingement) Precipitation on dislocations (very early stages)
kinetic theory, using the classic models of nucleation and growth described in the previous sections. In practice, however, this is a rather cumbersome method, particularly if the base metal is of a heterogeneous chemical nature. Alternatively, we can calibrate the Avrami equation against experimental microstructure data, e.g. obtained from generic IT-diagrams. A convenient basis for such a calibration is to write equation (6-21) in a more general form: (6-22) where k* is a new kinetic constant (equal to kr1/n). In the latter equation the parameter k* can be regarded as a time constant, which is characteristic of the system under consideration. Note that this form of the Avrami equation is mathematically more appropriate, as the dimensions of the k* constant are not influenced by the value of the time exponent n. During the early stages of a transformation reaction, the reaction rate is controlled by the nucleation rate. Let f denote the time taken to precipitate a certain fraction of P (X = Xc) at an arbitrary temperature T (previously defined in equation (6-14)). It follows from equation (6-22) that the value of k* in this case is given as: (6-23) A combination of equations (6-22) and (6-23) then gives:
(6-24)
from which (6-25) Equation (6-25) represents an alternative mathematical description of the Avrami equation, and is valid as long as the nucleation and growth rates do not change during the transformation. It has therefore the following limiting values and characteristics: X=O when t = 0, X = Xc when t = t*, and X—>1 when r—> <*>. 6.2.4.2 Site saturation If the nucleation rate is considered to be zero by assuming early site saturation, the subsequent phase transformation simply involves the reconstructive thickening of the p-layer. In the onedimensional case, the process can be modelled in terms of the normal migration of a planar a/p interface, as shown schematically in Fig. 6.16. Let Aa/^ denote the interfacial area between a and (3 per unit volume and Ua/^ the growth rate of the incoherent a/p-interface. From Fig. 6.16 we see that the volume fraction of the transformed (3-phase is given as: (6-26) By using the standard Johnson-Mehl correction for physical impingement of adjacent transformation volumes, we may write in the general case: (6-27) which after integration yields: (6-28) This specific form of the Avrami equation is valid under conditions of early site saturation where the a/p-interface is completely covered by P nuclei at the onset of the transformation. 6.2.5 Non-isothermal transformations So far, we have assumed that the phase transformations occur isothermally. This is, of course, a rather unrealistic assumption in the case of welding where the temperature varies continuously with time. From the large volume of literature dealing with solid state transformations in
Fig. 6.16, Schematic illustration of the planar geometry assumed in the site saturation model.
metals and alloys, it appears that the bulk of the research has been concentrated on modelling of microstructural changes under predominantly isothermal conditions.1"411 In contrast, only a limited number of investigations has been directed towards non-isothermal transformations. 51012 " 18 However, these studies have clearly demonstrated the advantage of using analytical modelling techniques to describe the microstructural evolution during continuous cooling, instead of relying solely on empirical CCT-diagrams. 6.2.5.1 The principles of additivity From the literature reviewed it appears that there is considerable confusion regarding the application of isothermal transformation theory for prediction of non-isothermal transformation behaviour. These difficulties are mainly due to the independent variations of the nucleation and growth rate with temperature. In fact, it can be shown on theoretical grounds that the problem is only tractable when the instantaneous transformation rate is a unique function of the fraction transformed and the temperature.10 This leads to the additivity criterion described below. The principles of additivity are based on the theory advanced by Scheil.12 He proposed that the start of a transformation under non-isothermal conditions could be predicted by calculating the consumption of fractional incubation time at each isothermal temperature, with the transformation starting when the sum is equal to unity. The Scheil theory has later been extended to phase transformations to predict continuous cooling transformation kinetics from isothermal microstructure data.10'17'18 Let t* again denote the time taken to precipitate a certain fraction of P (X - Xc) at an arbitrary temperature T. If the reaction is additive, the total time to reach Xc under continuous cooling conditions is obtained by adding the fractions of time to reach this stage isothermally until the sum is equal to unity. Noting that t* varies with temperature, we may write in the general case: (6-29)
A schematic illustration of the Scheil theory is contained in Fig. 6.17. T
Cooling curve
Subdivision of time into infinitesimal steps of isothermal heat treatments.
logt Fig. 6.17. Schematic illustration of the Scheil theory.
6.2.5.2 Isokinetic reactions The concept of an isokinetic reaction has previously been introduced in Section 4.4.2.3 (Chapter 4). A reaction is said to be isokinetic if the increments of transformation in infinitesimal isothermal time steps are additive, according to equation (6-29). Christian10 defines this mathematically by stating that a reaction is isokinetic if the evolution equation for some state variable X may be written in the form: (6-30) where G(X) and H(T) are arbitrary functions of X and T, respectively. For a given thermal history, T(t), this essentially means that the differential equation contains separable variables of X and T. 6.2.5.3 Additivity in relation to the Avrami equation The concept of an isokinetic reaction can readily be applied to the Avrami equation. Differentiation of equation (6-22) with respect to time leads to the following expression for the rate of transformation: (6-31)
In a typical diffusion-controlled nucleation and growth process, the fraction transformed X will not be independent of temperature, since the equilibrium volume fraction of the precipitates decreases with temperature (e.g. see equation (4-7) in Chapter 4). However, for dilute alloys it is a fair approximation to neglect this variation as the solvus boundary becomes increasingly steeper and in the limiting case approaches that of a straight (vertical) line. Thus, if n is constant and k* depends only on the transformation temperature, the reaction will be isokinetic in the general sense defined by Christian.10 Because of the independent variations of the nucleation and growth rate with temperature, the transformation rate will not be a simple function of temperature. However, by considering the form of the constitutive equations, it is obvious that the change in the nucleation rate with temperature is far more significant than the corresponding fluctuations in the growth rate. This point is more clearly illustrated in Fig. 6.18, which shows the temperature-dependency of the nucleation and growth rates of grain boundary ferrite in a C-Mn steel. It is evident from these data that the change in the parabolic thickening constant £, is negligible compared with the fluctuations in the nucleation rate. Consequently, in transformations that involve continuous cooling it is sufficient to allow for the variation of Nhet with temperature, provided that site saturation has not been reached. Thus, if n is constant we can apply the Scheil theory directly and rewrite equation (6-25) in an integral form: (6-32) In equation (6-32) Z1 represents the kinetic strength of the thermal cycle with respect to Pprecipitation. This parameter is generally defined by the integral:
Thickening constant Ce1),|ims"
-2 -1 Nucleation rate (N*het), cm s
Temperature, 0C Fig. 6.18. Predicted variation in N*het and E1 with temperature during the austenite to ferrite transformation in a C-Mn steel (0.15 wt% C, 0.40 wt% Mn). Data from Umemoto et al.19
(6-33)
where dt is the time increment at T, and f is the corresponding hold time required to reach Xc at the same temperature (given by equation (6-14)). The derivation of equation (6-32) is shown in Appendix 6.2 The principles of additivity are also applicable under conditions of early site saturation. If only U^p varies with temperature, it is possible to rewrite equation (6-28) in an integral form:
(6-34)
This equation can readily be integrated by numerical methods when the temperature-time programme is known. 6.2.5.4 Non-additive reactions If the additivity condition is not satisfied, it means that the fraction transformed is dependent on the thermal path, and the differential equation has no general solution. This, in turn, implies that the C-curve concept breaks down and cannot be applied to non-isothermal transforma-
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tions. Solution of the differential equation then requires stepwise integration in temperature-time space, using an appropriate numerical integration procedure. As already pointed out, this will generally be the case for diffusion-controlled precipitation reactions, since the evolution parameter X is a true function of temperature. Under such conditions, experimentally based continuous cooling transformation (CCT) diagrams must be employed.
6.3 High Strength Low-Alloy Steels High-strength low-alloy steels are typically produced with a minimum yield strength in the range 300-500 MPa, depending on the plate thickness.2021 During welding microstructural changes take place both within the heat affected zone (HAZ) and the fusion region, which, in turn, affect the mechanical integrity of the weldment.2122 In the HAZ, for instance, nitrides and carbides coarsen and dissolve, and grain growth occurs to an extent that depends on the distance from the fusion boundary and the exposure time characteristic of the welding process. This can have a profound effect on the subsequent structure and properties of the weld by displacing the CCT curve to longer times, thereby producing more Widmanstatten ferrite, or increasing the possibility of bainite and martensitic transformation products on cooling. The formation of such microstructures may reduce the toughness of the weld and increase the risk of hydrogen cracking.2122 6.3.1 Classification of microstructures It is appropriate to start this section with a detailed classification of the various microstructural constituents commonly found in low-alloy steel weldments. During the austenite to ferrite transformation, a large variety of microstructures can develop, depending on the cooling rate and the steel chemical composition. Normally, the microstructure formed within each single austenite grain after transformation will be a complex mixture of two or more of the following constituents, arranged in approximately decreasing order of transformation temperature: (i) (ii) (iii) (iv) (v) (vi) (vii)
grain boundary (or allotriomorphic) ferrite (GF) polygonal (or equiaxed) ferrite (PF) Widmanstatten ferrite (WF) acicular ferrite (AF) upper bainite (UB) lower bainite (LB) martensite (M).
The microstructural constituents listed above are indicated in Fig. 6.19, which shows photomicrographs of typical regions within low-alloy steel weldments. 6.3.2 Currently used nomenclature Quantification of microstructures in steel welds is most commonly done by means of optical microscopy. Several systems have been introduced throughout the years for the classification of the various constituents, with each system reflecting different investigator's views and
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tions. Solution of the differential equation then requires stepwise integration in temperature-time space, using an appropriate numerical integration procedure. As already pointed out, this will generally be the case for diffusion-controlled precipitation reactions, since the evolution parameter X is a true function of temperature. Under such conditions, experimentally based continuous cooling transformation (CCT) diagrams must be employed.
6.3 High Strength Low-Alloy Steels High-strength low-alloy steels are typically produced with a minimum yield strength in the range 300-500 MPa, depending on the plate thickness.2021 During welding microstructural changes take place both within the heat affected zone (HAZ) and the fusion region, which, in turn, affect the mechanical integrity of the weldment.2122 In the HAZ, for instance, nitrides and carbides coarsen and dissolve, and grain growth occurs to an extent that depends on the distance from the fusion boundary and the exposure time characteristic of the welding process. This can have a profound effect on the subsequent structure and properties of the weld by displacing the CCT curve to longer times, thereby producing more Widmanstatten ferrite, or increasing the possibility of bainite and martensitic transformation products on cooling. The formation of such microstructures may reduce the toughness of the weld and increase the risk of hydrogen cracking.2122 6.3.1 Classification of microstructures It is appropriate to start this section with a detailed classification of the various microstructural constituents commonly found in low-alloy steel weldments. During the austenite to ferrite transformation, a large variety of microstructures can develop, depending on the cooling rate and the steel chemical composition. Normally, the microstructure formed within each single austenite grain after transformation will be a complex mixture of two or more of the following constituents, arranged in approximately decreasing order of transformation temperature: (i) (ii) (iii) (iv) (v) (vi) (vii)
grain boundary (or allotriomorphic) ferrite (GF) polygonal (or equiaxed) ferrite (PF) Widmanstatten ferrite (WF) acicular ferrite (AF) upper bainite (UB) lower bainite (LB) martensite (M).
The microstructural constituents listed above are indicated in Fig. 6.19, which shows photomicrographs of typical regions within low-alloy steel weldments. 6.3.2 Currently used nomenclature Quantification of microstructures in steel welds is most commonly done by means of optical microscopy. Several systems have been introduced throughout the years for the classification of the various constituents, with each system reflecting different investigator's views and
(a)
(b)
(C)
(d)
Fig. 6.19. Optical micrographs showing various microstructural constituents commonly found in lowalloy steel weldments; (a) Coarse grained HAZ (low heat input welding), (b) Coarse grained HAZ (high heat input welding), (c) As-deposited weld metal (low heat input welding), (d) Reheated weld metal (low heat input welding). Letters in micrographs are defined in the text.
discretions. This controversy in terminology has been a source of confusion, and the work by Sub-Commission IXJ of the International Institute of Welding (HW)23 for developing guidelines for quantification of microstructures is, therefore, an important step towards a standardised system of nomenclature. The IIW recommendations are based on the scheme originally proposed by Abson and Dolby.23 The IIW system involves a simplified classification procedure compared with the outline used in Fig. 6.19, since the distinction between acicular ferrite and the various sideplate structures is based on features such as aspect ratio, relative lath size, and number of parallel
laths. This has led to the introduction of the FS-constituent (ferrite with aligned second phase), which, in principle, comprises both Widmanstatten ferrite and upper bainite. In contrast to the HW approach to classifying microstructural elements based on their appearance in the optical microscope, other investigators rank the various constituents solely in terms of their transformation behaviour, according to the scheme originally proposed by Dube et ai26 From a scientific point of view, this classification system is more correct, since it does not violate common terminology based on thermodynamics and kinetics of transformation reactions. However, with the omission of the FS-constituent grouping utilised by the HW, the Dube system is more inconvenient to use in practice because the different transformation products often cannot readily be identified on the basis of their transformation characteristics. Consequently, both classification systems appear to have their weaknesses, which, in turn, limit their applicability. 6.3.3 Grain boundary ferrite Grain boundary (or allotriomorphic) ferrite is the first phase to form on cooling below the Ae3temperature. It nucleates preferentially at austenite grain corners and boundaries, since these sites generally provide the lowest energy barrier against nucleation (see Fig. 6.3). The fundamental aspects of grain boundary ferrite have been reviewed in detail by Bhadeshia,26 where many of the original references can also be found. 6.3.3.1 Crystallography of grain boundary ferrite The grain boundary ferrite allotriomorphs nucleate having a Kurdjumow-Sachs type orientation relationship with one of the austenite grains:20
This orientation relationship, which lies within the so-called Bain orientation region,27 is adopted in order to minimise the increase in the strain energy resulting from lattice distortion AGEby formation of a low-energy interface between the ferrite nucleus and the parent austenite phase.1 Subsequent growth of the ferrite may then occur into the adjacent austenite grain with which the ferrite has a random orientation relationship,28 since a disordered (incoherent) interface generally has a higher mobility than an ordered (coherent/semi-coherent) interface at low undercoolings. 6.3.3.2 Nucleation of grain boundary ferrite As shown in Fig. 6.20, allotriomorphic ferrite can nucleate both at grain corners, grain edges and grain faces, the former ones being the most potent sites for ferrite nucleation.1 If we assume that ferrite nucleation occurs preferentially at austenite grain faces, the A^_/ Nv term in equation (6-14) may be replaced by the inverse grain size ratio Dy /Dy, where Dy and Dy refer to the austenite grain size in the actual and the reference material, respectively. This leads to the following expression for t*: (6-35)
Edge
Corner
Fig. 6,20. Sketch of an austenite grain showing different sites for ferrite nucleation.
Based on equation (6-35) it is possible to predict the displacement of the C-curve in temperature-time space due to structural or compositional variations in the parent material. As an illustration, we shall assume that the parameters listed in Table 6.2 are representative of nucleation of grain boundary ferrite in a low-alloy steel with an initial austenite grain size of 10 jim. In addition, we need information about the Ae3-temperature in the equilibrium phase diagram. This temperature can readily be obtained from thermodynamic calculations, even for multicomponent systems.29 Alternatively, we can use the empirical relationship quoted by Leslie:30
(6-36)
where all compositions are given in weight %. By lowering the A
Parameter I T Value
(K)
I
(s)
T
I
T*eq I (K)
T0 (Jmol"1)
823
0.6
1108
700
f Activation energy for diffusion of carbon in austenite.
I
Q]
I Dy
(kJmol-1)
(jim)
135
10
Example (6.2)
Consider SA welding on a thick plate of a Nb-microalloyed steel under the following conditions:
Evaluate on the basis of the grain growth diagram in Fig. 5.21 (a) (Chapter 5) and equations (6-32), (6-33), and (6-35) the conditions for ferrite formation at two different positions within the HAZ corresponding to a peak temperature Tpof 13500C and 10000C, respectively. Assume in these calculations that the ferrite may form within the temperature range from 800 to 6000C, and that the equilibrium volume fraction of ferrite (f^qFe) in the fully transformed steel is 0.9. Solution
First we calculate the net heat input per unit length of the weld:
Readings from Fig. 5.21 (a) give the following HAZ grain sizes:
By substituting data from Table 6.2 into equation (6-35), we obtain: Grain refined region ( Dy - 1 OfJm):
Grain coarsened region ( Dy = 150 jlm):
As expected, the theoretical C-curves in Fig. 6.21 reveal a strong effect of the austenite grain size on the HAZ transformation kinetics. By considering the superimposed weld cooling curve, it is possible to estimate the volume fraction of ferrite/""7^ which forms in each case from equations (6-32) and (6-33). Taking the time exponent n in the Avrami equation equal to 5/2 for nucleation of ferrite at austenite grain boundaries10 and 1 — Xc = 0.98, we obtain: Grain refined region (Dy = 10 jlm):
Temperature, 0C
Time, s Fig. 6.21. Effect of austenite grain size on the HAZ transformation kinetics (Example 6.2). The superimposed cooling curve corresponds to a cooling time, A%5, of 21s. and
Grain coarsened region ( Dy = 150 jim):
and
From this we see that polygonal ferrite dominates the microstructure within the grain refined region, whereas ferrite hardly forms within the grain coarsened HAZ under the prevailing circumstances. Although experimental data are not available for a direct comparison, the predicted effect of the austenite grain size on the HAZ transformation kinetics is reasonable and consistent with general experience (e.g. see experimental CCT-diagrams in Fig. 6.22). Effect of austenite and ferrite stabilising elements In practice, the transformation behaviour of steel weldments is affected both by the prior austenite grain size and by alloying additions. In welding metallurgy, the combined effects are often discussed by considering their influence on hardenability. Broadly speaking, additions of hardenability elements may serve two purposes: (i)
To ensure the desired strength level by solid solution or precipitation strengthening;
(ii)
To control the microstructure through modification of the nucleation and growth rates of proeutectoid ferrite.
Temperature, 0C
Time, s Fig. 6.22. CCT-diagrams for a low-carbon Cu-Ni containing steel. Superimposed on the CCT-diagrams are two cooling curves corresponding to Af875 of 10 and 100 s, respectively. Austenitising conditions; Heavy solid lines: 9000C for 5 min, Heavy broken lines: 13000C for 5 s. Data from Cross et al?x
In the latter case the effect is related to a shift in the Ae3-temperature of the steel, which alters the undercooling and hence, the driving force for the austenite to ferrite transformation. This point is illustrated by the following example. Example (6.3)
Consider SA welding on a thick plate of a Nb-microalloyed steel under conditions similar to those employed in Example (6.2). Based on equations (6-32), (6-33), and (6-35) estimate the volume fraction of grain boundary ferrite in the grain coarsened HAZ (Tp = 13500C) after welding when the A^-temperature of the steel is 863°C (1136K). Solution
By substituting data from Table 6.2 into equation (6-35), we arrive at the following expression for r *50:
It is evident from the graphical representation of the above equation in Fig. 6.23 that an increase in the v4e3-temperature (e.g. from 1108 to 1136K) displaces the C-curve towards higher temperatures and shorter times in the IT-diagram. This, in turn, gives rise to improved conditions for ferrite nucleation. Taking the time exponent n in the Avrami equation equal to 5/2 and (1 — Xc) = 0.98 as in the previous example, we obtain after integration:
Temperature, 0C
Time, s Fig. 6.23.Effect of steel chemical composition (Ae3-temperature) on the HAZ transformation kinetics (Example 6.3). The superimposed cooling curve corresponds to a cooling time, Ar875, of 21s.
and
Although the calculated value offa'Fe is rather uncertain, the trends predicted in the present example are reasonable and consistent with general experience.
Effect of boron alloying The role of boron in steel transformation kinetics has been a subject of research for many years. A number of hardenability mechanisms have been proposed to explain the behaviour of boron in steels. Of these, only four have survived to the present.32 All assume that boron influences hardenability by increasing the energy barrier against ferrite nucleation at austenite grain boundaries* and that it does not influence the thermodynamic properties of the austenite and ferrite phases, i.e. reduces the A
During welding, quantitative information about the extent of boron segregation which occurs to the austenite grain boundaries under various thermal programmes can be obtained on the basis of a well established theoretical model for quench-induced segregation of boron in steel.3839 At peak temperatures above 1000 to 11000C, borocarbides and -nitrides present in the base plate will rapidly dissolve in the matrix,4041 leading to a significant increase in the amount of free diffusible boron. Generally, solute atoms in a crystal lattice will have an associated strain energy,38 which implies that it is energetically feasible to pair the solute boron atom with a vacancy. Since the formation of vacancies is a thermally activated process, it follows that the fraction of boron occupying such sites, [B]v, increases exponentially with temperature:39 (6-37)
Here m contains various geometric and entropy terms, Zy is the vacancy formation energy, Eb is the vacancy-boron binding energy, and [B] is the bulk concentration of free boron. By substituting reasonable average values for ra, Ep and Eb into equation (6-37), we arrive at the following expression for [B]V:39A2 (6-38)
During cooling, the vacancy concentration initially established at elevated temperatures tends to readjust by elimination of excess point defects at grain boundaries through diffusion. This, in turn, results in an associated flow of solute boron to the austenite grain boundaries (the extent of which is controlled by the peak temperature and the bulk boron concentration), provided that the diffusivity of the boron-vacancy complexes is higher than that of the vacancies and the boron atoms at all relevant temperatures. Consider now the limiting case where the boron-vacancy complex diffusion to the grain boundaries occurs sufficiently rapid to keep pace with the falling temperature; i.e. the equilibrium concentration, [B]v, is maintained from the peak temperature Tp down to the start temperature of the austenite to ferrite transformation Ae3. In view of the high diffusivity of boronvacancy complexes in austenite, this is not an unrealistic assumption when the cooling rate is of the order of 500C s"1 (representative of a weld HAZ).39 Under such conditions, the amount of boron which segregates to the austenite grain boundaries within the temperature interval from Tp to Ae3 on cooling, [B]gb, can approximately be written as:42
when Tp » Ae3. In addition to the diffusible boron content, the grain size is also an important variable in steel hardenability. A quantitative estimate of the combined effect of boron segregations and
austenite grain size on the HAZ transformation kinetics can be obtained by assuming that the ferrite nucleates primarily on grain faces. In such cases the total number of heterogeneous nucleation sites per unit volume Nvis given as: (6-40) where na is the number of nucleation sites per unit grain boundary area, and Sv is the grain boundary surface area per unit volume (equal to 2/Dy). If we, as a second approximation, assume that na is inversely proportional to the amount of boron which diffuses to the grain boundaries on cooling, the N* / Nv ratio in equation (6-14) can be written as: (6-41) Equation (6-41) predicts that the position of the ferrite C-curve in temperature-time space depends on the l[B]gb Z)7) I l[B]*gb Z>y J ratio, as shown schematically in Fig. 6.24. Consequently, this ratio can be regarded as a measure of the HAZ hardenability during welding of boroncontaining steels. In Fig. 6.25 the microstructure data of Akselsen et al.42 have been replotted vs the hardenability parameter [B]gbDy, taking the product [B]*gbDy in the reference steel equal to unity for a direct comparison between theory and experiments. It is evident from the graph that the HAZ martensite content of the two boron-containing steels can be represented by one single curve under the prevailing circumstances. This result is to be expected if the displacement of the ferrite C-curve in temperature-time space is determined by a relationship of the type shown in equation (6-41).
D
Temperature
High values of [B]
Low values of [Bl D gb Y
Cooling curve
log time Fig. 6.24. Effect of boron alloying on the shape and position of ferrite C-curve in temperature-time space according to the site blocking mechanism (schematic).
Martensite, vol%
Steel A (11 ppm B) Steel B (26 ppm B)
Hardenability parameter ([B] D ) Fig. 6.25. Relation between the volume fraction of martensite and the hardenability parameter [B]gb Dy for simulated weld HAZs ([B]gb in ppm, Dy in urn, [B]gbDy = 1). Data from Akselsene£#/.42 Example (6.4)
Consider GMA welding on a thick plate of a boron-containing steel under the following conditions: /=300A, U = 30V, v = 4mm s-1, TI = 0.8, T0 = 200C Suppose that the free (diffusible) boron content of the steel at elevated temperatures is 40 ppm. Estimate on the basis of the theory outlined in the previous sections the conditions for ferrite/martensite formation in the grain refined HAZ (Tp = 11000C) when the austenite grain size is 15|Lim. In these calculations we shall assume that the [B]*gb Dy product in the reference steel (with thermodynamic properties as in Table 6.2) is close to unity. Solution
First we estimate the amount of boron which segregates to the austenite grain boundaries during cooling from equation (6-39). When Tp = 11000C (1373K), we get:
This gives the following value of the Af* / Nv ratio (equation 6-41):
The resulting displacement of the ferrite C-curve can now be calculated from equation (614), using input data from Table 6.2:
As expected, the theoretical C-curves in Fig. 6.26 reveal a strong effect of boron alloying on the HAZ transformation kinetics. By considering the superimposed weld cooling curve, it is possible to estimate the volume fraction of ferrite f^~Fe which forms from equations (6-32) and (6-33). Taking the time exponent n in the Avrami equation equal to 5/2 for nucleation of ferrite at austenite grain boundaries and (1 - Xc) = 0.98 as in the previous examples, we obtain after integration within the temperature range from 800 to 600° C:
and
If the same calculations are performed for the reference steel in Table 6.2 (characterised by
[*]gb = iBfgb )> we get:
and From this we see that boron, even in small quantities, can have a dramatic effect on the HAZ transformation kinetics by promoting the formation of bainite and martensite at the expense of grain boundary ferrite. This is in good agreement with general experience (see experimental CCT-diagrams in Fig. 6.27). Effect of solidification-induced segregation As shown in Chapter 3 of this textbook, the characteristic solidification pattern of mild and low-alloy steel weld metals leads to extensive segregation of alloying and impurity elements to grain boundaries and interdendritic spaces. Of particular interest in this respect is phosphorus segregations at columnar austenite grain boundaries. Referring to Figs. 3.38 and 3.39 (Chapter 3), the phosphorus-rich zone is seen to extend about ±7jam on either side of the grain boundaries. Since phosphorus is among the strongest ferrite stabilising elements in steel (see equation (6-36)), the existence of such solidification-induced segregations would be expected
Temperature, 0C Time, s Fig. 6.26. Predicted displacement of ferrite C-curve in temperature-time space due to segregation of boron to prior austenite grain boundaries (Example 6.4). The superimposed cooling curve corresponds to a cooling time, Ats/5, of 9.2s. to enhance the nucleation rate of grain boundary ferrite at these sites due to the associated increase in the Ae3-temperature. The above phenomenon should not be confused with equilibrium segregation of phosphorus to austenite grain boundaries during heat treatment of steel, which stems form attraction of the atoms towards the open structure of the boundary. In the latter case phosphorus may act as a hardenability element by occupying favourable sites for ferrite nucleation at the austenite grain boundaries analogous to that documented for boron in steel.43'44 Example (6.5)
Suppose that the local phosphorus content adjacent to the columnar austenite grain boundaries in a low-alloy steel weld metal is 500 ppm, whereas the bulk concentration of phosphorus is 100 ppm. Estimate on the basis of the theory developed in the previous sections the resulting displacement of the ferrite C-curve in temperature-time space when the columnar austenite grain size is 80|jun. In these calculations we shall assume that the transformation characteristic of the bulk metal is similar to that of the reference steel in Table 6.2. Solution
First we estimate the actual Ae3-temperature within the phosphorus-rich region adjacent to the columnar austenite grain boundaries from equation (6-36). Taking the A
By substituting data from Table 6.2 into equation (6-35), we arrive at the following expression for ^ 0 :
(a)
Temperature, 0C
Steel A (11 ppmB)
Cooling time, At0,., s (b)
Temperature, 0C
Steel B (26 ppm B)
Cooling time, A t 8/5 , s Fig. 6.27. CCT-diagrams for boron-containing steels; (a) Steel A (llppm B), (b) Steel B (26ppm B). Data from Akselsen et al.42
It is evident from the graphical representation of the above equation in Fig. 6.28 that the observed increase in the yl^-temperature from 1108 to 1136K displaces the ferrite C-curve towards higher temperatures and shorter times in the IT-diagram. The resulting effect on the weld metal transformation kinetics is obvious, since an increase in the nucleation rate of ferrite will favour early site saturation at the austenite grain boundaries. On this basis it is not surprising to find that allotriomorphic ferrite in low-alloy steel weld metals tends to form continuous veins of blocky ferrite along the columnar austenite grain boundaries, as shown in Fig. 6.19(c). Outside the fusion zone the conditions for early site saturation are less favourable, since modern steelmaking practice implies that solidification-induced segregations are removed by prolonged high-temperature annealing prior to the welding operation. Hence, ferrite veining of the type shown in Fig. 6.19(c) is not commonly observed within the reheated regions of the base plate, unless the heat input is extremely large (see Fig. 6.19(a) and (b)).
Temperature, 0C
Time, s Fig. 6.28. Effect of solidification-induced phosphorus segregations on the austenite to ferrite transformation in low-alloy steel weld metals (Example 6.5).
Effect of cooling rate on ferrite grain size In steel metallurgy it is well accepted that accelerated cooling refines the ferrite grain size, and thus improves both strength and toughness of the parent material. 1920 If the austenite is allowed to recrystallise before it transforms, the final ferrite grain size Da in the base plate will be an unique function of the prior austenite grain size D1 and the cooling rate through the critical transformation temperature range for ferrite formation (CR.). The fundamental aspects of ferrite grain refinement by accelerated cooling have been considered by Umemoto et al.19 By allowing for the variation in the nucleation and growth rates of allotriomorphic ferrite with temperature (see Fig. 6.18), they arrived at the following theoretical expression for Da when austenite grain faces are the dominant nucleation site of ferrite: (6-42) where D1 is in |im and (CR.) is in 0C s"1. In practice, Umemoto et al.19 observed a discrepancy between theory and experiments due to competitive nucleation of ferrite at austenite grain edges and corners (characterised by a theoretical grain size dependence of D12/3 and D1, respectively). Consequently, the real ferrite grain size in the steel varied with austenite grain size and cooling rate as: (6-43) where C4 is a kinetic constant which is characteristic of the alloy system under consideration. An indication of the applicability of equation (6-43) to welding can be obtained from the micro structure data of Evans,45 reproduced in Fig. 6.29. In this plot, the reported heat inputs have been converted into an equivalent cooling rate at 7000C via equation (1-71) (Chapter 1). It is evident from the figure that the observed variation in the ferrite grain size with cooling rate is consistent with calculations based on equation (6-43). Hence, the model of Umemoto et
Ferrite grain size,jim
Equation (6-43)
Weld A (0.04 wt% C, 0.58 wt% Mn) Weld C (0.05 wt% C, 1.33 wt% Mn)
Cooling rate at 700 0C1 °C/s Fig. 6.29. Variation of ferrite grain size with cooling rate in reheated C-Mn steel weld metals. Data from Evans.45 al19 can readily be employed for prediction of the ferrite grain size within the grain refined region of both single pass and multipass steel welds, provided that the austenite grain size and the cooling rate can be estimated with a reasonable degree of accuracy. Example (6.6)
Consider multipass welding with covered electrodes (SMAW) on a thick plate of low-alloy steel under the following conditions:
Previous experience has shown that polygonal ferrite forms within the low-temperature reheated regions of the weld metal, typically 1.0 to 1.7 mm beneath the surface (fusion boundary) of subsequent weld passes. Estimate on the basis of the grain growth diagram in Fig. 5.24(a) (Chapter 5) and equation (6-43) the maximum variation in the ferrite grain size across the weld HAZ under the prevailing circumstances. Thermal data for low-alloy steels are given in Table 1.1 (Chapter 1). Solution
First we need to convert the depths at which polygonal ferrite appears beneath the fusion boundary to an equivalent (characteristic) peak temperature range. If we neglect the contribution from heat flow in the welding direction, this conversion can be done on the basis of equation (5-47) in Chapter 5:
Taking Ar*m equal to 1 and 1.7mm, respectively, we get:
and
The prior austenite grain size Dy at these two locations can now be read from Fig. 5.24(a) and Table 5.6, respectively:
Since the cooling rate (CR.) at a given temperature is essentially the same across the weld HAZ, the maximum variation in the ferrite grain size can be evaluated directly from equation (6-43) without further background information:
From this we see that the variation in the ferrite grain size is significantly smaller than the corresponding change in the prior austenite grain size. This result is in good agreement with general experience. 6.3.3.3 Growth of grain boundary ferrite If the austenite grain boundaries become rapidly decorated with a continuous layer of ferrite (so that the subsequent transformation involves the reconstructive thickening of these layers), the evolution of allotriomorphic ferrite is determined solely by its growth kinetics.37 As shown in Example 6.5, this is a realistic assumption in the case of as-deposited steel weld metals, where the presence of solidification-induced phosphorus segregations at the columnar austenite grain boundaries favours an early site saturation. Several investigators have modelled the evolution of allotriomorphic ferrite in low-alloy steel weld metals along the lines indicated above.46"48 The most thorough analysis is probably that of Bhadeshia et al.46 who were able to account for the combined effect of temperature and steel chemical composition on the growth kinetics. However, in order to illustrate the competition between the different variables that contribute to the formation of grain boundary ferrite in as-deposited steel weld metals, the simplified treatment of Liu and Olson47 and Fleck et al.4S has been adopted here. As a starting point the Avrami equation17 is considered for the limiting case of zero nucleation rate by assuming early site saturation. If subsequent growth of the grain boundary ferrite allotriomorphs occurs in both directions perpendicular to the austenite grain boundaries at a rate which is controlled by diffusion of carbon in austenite, the time dependence of the ferrite thickness, AZa, is given by equation (6-17): (6-44)
where E1 is the one-dimensional parabolic thickening constant (defined in equation (6-18)). The corresponding growth rate of allotriomorphic ferrite Ua is then obtained by differentiating equation (6-44) with respect to time: (6-45) From a stereological standpoint, the grain boundary surface area per unit volume Sv cannot be calculated without further assumptions regarding the shape of the columnar austenite grains. Bhadeshia et al.31*46*49 solved this problem by representing the grain morphology by a uniform, space-filling array of hexagonal prisms. However, with the precision aimed at here, it is sufficient to assume that Sv is equal to the surface area per unit volume of an inscribed cylinder whose volume is equivalent to that of the hexagonal prisms (see Fig. 6.30). Noting that each grain boundary is shared by two adjacent grains, the expression for Sv (in the absence of end effects) becomes:47'48 (6-46)
where dy and I1 are the diameter and length of the inscribed cylinder, respectively. By substituting the above expressions for Ua and Sv into equation (6-34), we obtain:
(6-47)
In practice, the one-dimensional parabolic thickening constant in equation (6-47) varies both with temperature and steel chemical composition, as shown by the data of Bhadeshia et aL46 reproduced in Fig. 6.31. However, if we instead use a reasonable average value for E1 within the characteristic transformation temperature range for allotriomorphic ferrite (i.e. E1 = E1), the integral I2 in equation (6-47) has the following analytical solution: x Growth direction of columnar grains
Fig. 6.30. Hexagonal prism model for the columnar austenite grain morphology in low-alloy steel weld metals. The inscribed cylinder in the figure has approximately the same surface to volume ratio as the hexagonal prisms.
Parabolic thickening constant (E1), ^m/s1/2
Temperature, 0C Fig. 6.31. Effect of temperature and steel chemical composition on the one-dimensional parabolic thickening constant for allotriomorphic ferrite. (1): 0.03 wt% C, (2): 0.06 wt% C, (3): 0.08 wt% C and (4): 0.10 wt% C. Data from Bhadeshia et al.46
(6-48) from which (6-49)
Equation (6-49) predicts that the volume fraction of grain boundary ferrite in the as-deposited weld metal depends on the combined action of the following three main variables: (i) The one-dimensional parabolic thickening constant ei which is determined by the weld metal chemical composition (i.e. the content of austenite and ferrite stabilising elements). (ii) The columnar austenite grain size dy which is controlled by the weld metal solidification microstructure (i.e. the weld metal chemistry, the weld pool geometry, and the thermal conditions under which solidification occurs). (iii) The retention time within the critical transformation temperature range for allotriomorphic ferrite, as determined by the applied heat input and the mode of heat flow (i.e. thick plate, medium thick plate, or thin plate welding, respectively).
It can be seen from the microstructure data of Grong et al.50 reproduced in Fig. 6.32 that the influence of these variables are adequately accounted for in the present model. However, the calculated volume fractions of grain boundary ferrite are consistently lower than the measured ones. This discrepancy can probably be attributed to the use of constant values for the onedimensional parabolic thickening constant. Consequently, if proper corrections are made for the inherent variation in E1 with temperature and steel chemical composition, the agreement between theory and experiments is significantly improved, as shown by the data of Bhadeshia et al.46 reproduced in Fig. 6.33. Example (6.7)
Consider GMA welding on a thick plate of a low-alloy steel under the following conditions:
Suppose that the grain boundary allotriomorphs form within the temperature range from 750 to 6000C at a constant rate ei of 3 jam s~1/2. Estimate on the basis of the theory developed in the previous section the volume fraction of allotriomorphic ferrite in the weld deposit when the columnar austenite grain size is 80|Lim. In these calculations we shall assume that the equilibrium volume fraction offerritef®q~Fe in the fully transformed steel is 0.9. Thermal data for low-alloy steels are given in Table 1.1 (Chapter 1). Solution
The situation is described in Fig. 6.34. In this case the problem is to estimate the retention time /Str within the critical temperature range for ferrite formation from the Rosenthal thick plate solution (Chapter 1). From equation (1-66), we have:
Volume fraction of GF
Regression line
C-Mn steel weld metals Si content: 0.50-1.03 wt% Mn content: 0.33-2.72 wt%
x
*
.
^
)
Fig. 6.32. Experimental verification of equation (6-49). Data from Grong et al.5Q
Measured volume fraction of GF
C-Mn steel weld metals
Line of unit slope
Calculated volume fraction of GF
Temperature
Fig. 6.33. Comparison between measured and predicted volume fractions of grain boundary ferrite in C-Mn steel weld metals. Data from Bhadeshia et al.46
log time Fig. 6.34. Conditions for allotriomorphic ferrite formation in low-alloy steel weld metals (Example 6.6).
By inserting this value into equation (6-49), we obtain:
Although experimental data are not available for a direct comparison, the calculated value of fa'Fe is reasonable and of the expected order of magnitude. 6.3.4 Widmanstdtten ferrite With increasing degree of undercooling the redistribution of carbon becomes insufficient to maintain a planar growth mode, and hence, further growth of the ferrite can only take place by lateral movement of ledges along a low-energy interface*.120 This, in turn, implies a Kurdjumow-Sachs-type orientation relationship between the austenite and the ferrite, i.e. {Ill }1_Fe parallel with {110}a_F6, and <110> 7 .^ parallel with <11 l>a_Fe, which is a characteristic feature of the Widmanstatten ferrite structure. The ferrite sideplates, once nucleated, grow very rapidly under the prevailing conditions because of an efficient redistribution of carbon to the sides of the advancing interface.1 As a result, parallel arrays of ferrite laths of high aspect ratios (typically 10:1 to 20:1) are often found in the areas adjacent to the austenite grain boundaries, as shown by the optical micrographs in Fig. 6.19(b) and (c). Following the treatment of Bhadeshia et al.,46 the lengthening rate of Widmanstatten ferrite can be estimated using the Trivedi theory9 for diffusion-controlled growth of parabolic cylinders with correction for the assumed displacive character of the Widmanstatten ferrite transformation. As shown in Fig. 6.35, the pertinent growth rates are normally so large that the formation of Widmanstatten ferrite is essentially complete within a fraction of a second. This implies that the transformation, for all practical purposes, can be treated as being isothermal.37 When the growth rate is known, the volume fraction of Widmanstatten ferrite in the asdeposited weld metal may be estimated by assuming that the ferrite sideplates nucleate at a constant rate at the yFelaFe boundaries and subsequently grow into the interior of the columnar austenite grains until they physically impinge with intragranularly nucleated acicular ferrite or allotriomorphic ferrite.46 It is seen from the microstructure data of Bhadeshia et al.46 reproduced in Fig. 6.36 that the calculated volume fractions of Widmanstatten ferrite are in reasonable agreement with experiments, although the discrepancy in certain cases is admittedly large. *A different view is suggested by Bhadeshia et al.31'46'51'52 who claim that growth of Widmanstatten ferrite occurs in a displacive manner analogous to that documented for martensite in steel, with the exception that carbon must diffuse during growth.
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b
Growth rate of WF, u,m/s
a
Temperature, 0C Fig. 6.35. Predicted growth rates of Widmanstatten ferrite in C-Mn steel weld metals; (a) Growth rate calculations for weld compositions listed in Fig. 6.31, (b) Growth rate calculations after modifying compositions to allow for carbon enrichment due to grain boundary ferrite formation. Data from Bhadeshia
etai46
6.3.5 Acicular ferrite in steel weld deposits Simultaneously with or immediately after the formation of Widmanstatten ferrite at the austenite grain boundaries, acicular ferrite may start to nucleate intragranularly at non-metallic inclusions. This phase is commonly observed in low-alloy steel weld metals, where the fine dispersion of oxide inclusions provides favourable sites for heterogeneous nucleation.3653 There seems to be general agreement that microstructures primarily consisting of acicular ferrite provide optimum weld metal mechanical properties, both from a strength and toughness point of view, by virtue of its small lath size and high dislocation density. 365354 Consequently, the formation of this particular microconstituent is of significant commercial importance and has therefore attracted substantial research interest over the years. 363746 " 58 In spite of all this effort, the acicular ferrite transformation in low-alloy steel weld metals is still a subject of considerable controversy. 6.3.5.1 Crystallography of acicular ferrite It is well established that acicular ferrite nucleates in the transformation temperature range between Widmanstatten ferrite and lower bainite.55"59 Based on conventional diffraction pattern analyses in the transmission electron microscope (TEM), Bhadeshia 6tf a/.54'59have shown that the acicular ferrite plates exhibit an orientation relationship with the austenite grain in which they grow. The observed orientation relationship lies within the Bain orientation region27 and can approximately be described as:
Previous Page
b
Growth rate of WF, u,m/s
a
Temperature, 0C Fig. 6.35. Predicted growth rates of Widmanstatten ferrite in C-Mn steel weld metals; (a) Growth rate calculations for weld compositions listed in Fig. 6.31, (b) Growth rate calculations after modifying compositions to allow for carbon enrichment due to grain boundary ferrite formation. Data from Bhadeshia
etai46
6.3.5 Acicular ferrite in steel weld deposits Simultaneously with or immediately after the formation of Widmanstatten ferrite at the austenite grain boundaries, acicular ferrite may start to nucleate intragranularly at non-metallic inclusions. This phase is commonly observed in low-alloy steel weld metals, where the fine dispersion of oxide inclusions provides favourable sites for heterogeneous nucleation.3653 There seems to be general agreement that microstructures primarily consisting of acicular ferrite provide optimum weld metal mechanical properties, both from a strength and toughness point of view, by virtue of its small lath size and high dislocation density. 365354 Consequently, the formation of this particular microconstituent is of significant commercial importance and has therefore attracted substantial research interest over the years. 363746 " 58 In spite of all this effort, the acicular ferrite transformation in low-alloy steel weld metals is still a subject of considerable controversy. 6.3.5.1 Crystallography of acicular ferrite It is well established that acicular ferrite nucleates in the transformation temperature range between Widmanstatten ferrite and lower bainite.55"59 Based on conventional diffraction pattern analyses in the transmission electron microscope (TEM), Bhadeshia 6tf a/.54'59have shown that the acicular ferrite plates exhibit an orientation relationship with the austenite grain in which they grow. The observed orientation relationship lies within the Bain orientation region27 and can approximately be described as:
Measured volume fraction of WF
Calculated volume fraction of WF Fig. 6.36. Comparison between measured and predicted volume fractions of Widmanstatten ferrite in CMn steel weld metals. Data from Bhadeshia et al.46
This corresponds to the well-known Kurdjumow-Sachs (K-S) orientation relationship* and suggests that growth of the AF plates occurs either by a ledge mechanism or by a pure shear transformation similar to that reported for upper bainite in steel. 1^0-60"62 6.3.5.2 Texture components of acicular ferrite Kluken et al.63 have studied the development of transformation textures in as-deposited steel weld metals containing acicular ferrite, using the electron backscattering pattern (EBSP) technique. Referring to the (200) stereographic projection in Fig. 6.37, the measured acicular ferrite orientations form a symmetrical and consistent pattern and disclose evidence of a coupled solidification/solid state transformation texture in the weld metal. A closer examination of the data reveals the existence of three major texture components within the acicular ferrite microstructure, i.e. one <100> component and two complementary <111> components.63 The former component includes acicular ferrite plates which have a <100> direction approximately *The orientation relationship can alternatively be described by the Nishiyama-Wasserman (N-W) correspondence which also lies within the Bain orientation region. However, since the K-S and the N-W orientation relationships only differ from each other by a 5.26° rotation of the close packed planes, they can be regarded as equivalent.
(a)
(b)
Fig. 6.37. The development of transformation textures in as-deposited steel weld metals containing acicular ferrite; (a) (200) pole figure showing the crystallographic orientations of acicular ferrite referred to the original cell/dendrite growth direction, (b) Backscattered electron channeling contrast image of delta ferrite/austenite columnar grain (the metallographic section is normal to the cell/dendrite growth direction). After Kluken et al.63 parallel with the cell/dendrite growth direction (Fig. 6.38(a)). The other plates have a <111> direction aligned in the same crystal growth direction (Fig. 6.38(b)). These data can be represented by two sub-components which are displaced with respect to each other by a 60° rotation about a common <111> axis. It is evident from the measurements of Kluken et al.63 that the acicular ferrite plates in asdeposited steel weld metals exhibit an orientation relationship with both the austenite and the prior delta ferrite columnar grains in which they grow. This 'memory' effect arises from the characteristic solidification pattern and transformation behaviour of low-alloy steel welds (e.g. see discussion in Section 3.8.2, Chapter 3). As shown schematically in Fig. 6.39, the columnar grain region will exhibit a sharp <100> solidification texture which has its origin in the phenomenon of preferred crystal growth. At the onset of the peritectic reaction, the austenite adopts a K-S type of orientation relationship with the delta ferrite in order to minimise the energy barrier against nucleation.64 The austenite subsequently grows around the periphery of the primary phase until impingement occurs on neighbouring columnar grain boundaries. During the yFe to aFe transformation, this memory effect gives rise to the formation of acicular ferrite plates which have a <100> direction approximately parallel with the original cell/dendrite growth direction. The presence of the two other texture components within the weld metal is thus a result of complementary crystal rotations taking place within the same orientation region. The proposed sequence of reactions is in excellent agreement with the texture analysis of Hu65 who made theoretical calculations of the resulting orientations of iron after §Fe to yFe and yFe to aFe transformations in succession according to the scheme outlined in Fig. 6.39. 6.3.5.3 Nature of acicular ferrite Currently, the mechanisms of acicular ferrite formation in low-alloy steel weld metals are not
Cell/dendrlte growth direction
(a)
(b)
Fig. 6.38. Schematic diagrams showing the three main texture components in acicular ferrite according to the Kurdjumow-Sachs orientation relationship; (a) The <100> texture component, (b) The two complementary <111> texture components. After Kluken et a/.63 fully understood. However, detailed TEM studies performed by Bhadeshia et aL37>59>62>66 have clearly demonstrated that acicular ferrite is a form of intragranularly nucleated bainite. In practice, this means that the microconstituent may be present either as 'upper' or 'lower' acicular ferrite in the weld deposit (depending on the carbon concentration), as shown schematically in Fig. 6.40. In general, the ferrite component of upper bainite is composed of groups of thin parallel laths (subplates) with a well-defined crystallographic habit.2061 Although the growth mechanism of upper bainite is still a subject of considerable controversy, it has been postulated that the subplates advance into the austenite with their own tip configurations. One model is shown in Fig. 6.41, where each subplate forms as a ledge upon the adjacent subplates through a nucleation and growth process. These ferrite laths possess the same variant of the K-S orientation relationship, which means that they are separated by low-angle grain boundaries. A typical austenite grain will contain numerous sheaves of bainitic ferrite exhibiting different variants of the K-S orientation relationship. This implies that the boundary between adjacent plates of acicular ferrite should alternately be of the low-angle and high-angle type, a feature which also has been observed experimentally (see data in Fig. 6.42). Hence, both the morphology and the crystallography of acicular ferrite bear a close resemblance to upper bainite.
Columnar grain Fig. 6.39. Schematic diagram showing the sequence of reactions occurring during cooling of a low-alloy steel weld through the critical transformation temperature ranges. After Kluken et al.63
6.3.5.4 Nucleation and growth of acicular ferrite Since the thickening rate of plate-like precipitates is very high, the acicular ferrite laths, once nucleated, will grow into the austenite phase until they physically impinge with neighbouring plates. At present, there exist no models which allow the acicular ferrite content to be calculated from first principles. The reason for this is quite obvious, since the final weld metal microstructure generally depends on complex interactions between a number of different variables, including:36 (i) (ii) (iii) (iv) (v)
The total alloy content. The concentration, chemical composition, and size distribution of non-metallic inclusions, The solidification microstructure. The prior austenite grain size, The weld thermal cycle.
Carbon supersaturated plate Carbon diffusion into austenite and carbide precipitation in ferrite
Carbon diffusion into austenite
Carbide precipitation from austenite
'Upper' acicular ferrite
'Lower' acicular ferrite
Fig. 6.40. Schematic illustration of the transition from 'upper' to 'lower' acicular ferrite in low-alloy steel weld metals. The diagram is based on the ideas of Bhadeshia and Svensson.37 Successive nucleation and growth of parallel plates
Misorientation, degrees
Fig. 6.41. Proposed model for nucleation and growth of upper bainite in steel (schematic). After Verhoeven.61
Plate number Fig. 6.42. Measured spatial misorientation between adjacent plates of acicular ferrite in a low-alloy steel weld. Data from Kluken et a/.63
A more realistic approach would be to estimate the volume fraction of acicular ferrite via the equation:37 (6-50) where f%FFe and f%FFe are the corresponding volume fractions of grain boundary ferrite and Widmanstatten ferrite, respectively (note that in equation (6-50) the formation of microphases has been disregarded). The method outlined above has shown to work well for numerous welds (e.g. see Fig. 6.43), but fails when the primary microstructure consists of a mixture of acicular ferrite and martensite, as is the case in high strength steel weld deposits6768 In spite of this shortcoming, equation (650) expresses in an explicit manner the real essence of the problem, namely that the evolution of the acicular ferrite microstructure depends on the interplay between several competing nucleation and growth processes which occur consecutively during cooling from the Ae3-temperature. This important point is often overlooked when discussing the conditions for acicular ferrite formation in low-alloy steel weld metals. Size effects in heterogeneous nucleation The important influence of second-phase particles on the austenite to ferrite transformation has been examined theoretically by Ricks et al69 using classical nucleation theory. By assuming inert, incoherent, and non-deformable inclusions and constant values for the volume free energy change and the surface free energy of both the yFe /yFe and yFe /aFe boundaries, the normalised energy barrier to nucleation has been calculated and plotted against the particle radius as shown in Fig. 6.44. It can be seen from the figure that the nucleation of ferrite at inclusions is always energetically more favourable than homogeneous nucleation, but less favourable than nucleation at austenite grain boundaries, irrespectively of the inclusion size. The most potent nucleation sites are particles of a radius greater than about 0.2-0.5 jum, which
Volume fraction
Allotriomorphic ferrite
Widmanstatten ferrite Acicular ferrite
Carbon content, wt% Fig. 6,43. Predicted variation in microstructure as a function of carbon concentration in C-Mn steel weld deposits (SMAW-IkJ mm~ l). Data from Bhadeshia and Svensson.37
AG* /AG* het. horn.
Inclusion , Austenite grain boundary
Inclusion radius, jim Fig. 6.44. Effect of particle radius on the normalised energy barrier against ferrite nucleation at inclusions. The corresponding energy barrier against nucleation of ferrite at austenite grain boundaries is indicated by the horizontal broken line. Data from Ricks et al.69
is within the typical size range of most weld metal inclusions (see Figs. 2.57-2.61 in Chapter 2). This finding is in excellent agreement with the results of Barbaro et al.70 reproduced in Fig. 6.45, showing that a certain minimum inclusion size (say 0.2-0.3 jam) is required for acicular ferrite nucleation in steel weld deposits. It should be noted, however, that Ricks et al69 omitted a consideration of the effects of plastic strain produced as a result of differences in thermal contraction between the austenite and the particles as well as the possibility for the ferrite to adopt reasonable orientation relationships with both the austenite and the catalyst particles. Based on nucleation theory it can be argued that these factors will influence the transformation process.1 This, in turn, may explain why certain types of inclusions appear to be more favourable nucleation sites for acicular ferrite than other (to be discussed below). Catalyst effects in heterogeneous nucleation As mentioned above, there is considerable circumstantial evidence available in the scientific literature that intragranular nucleation of acicular ferrite is preferentially associated with specific types of non-metallic inclusions (i.e. 7-Al2O3, MnOAl2O3, TiN). 365571 " 78 Different mechanisms have been proposed over the years to explain these phenomena, including:3655'73'76'77 (i)
Nucleation resulting from a small lattice disregistry between the inclusions and the ferrite.
(ii)
Nucleation in the vicinity of inclusions caused by local compositional inhomogeneity in the steel matrix.
(iii) Nucleation in the vicinity of inclusions resulting from favourable strain or dislocation arrays due to differences in the thermal contraction between the particles and the matrix.
Probability of nucleation
Inclusion radius, JLX m Fig. 6.45. Effect of inclusion size on the probability of acicular ferrite nucleation in steel weld deposits. Data from Barbara et al.10
Because of the complexity of the weld metal inclusions, and the experimental difficulties involved in performing controlled in situ measurements, it cannot be stated with certainty which of these three mechanisms that are operative during the acicular ferrite transformation. However, based on simple theoretical calculations it can be argued that the contribution from the elastic strain fields around the particles due to differential contraction effects probably is too insignificant to influence the free energy of transformation and that the resulting punchingstress at the particle/matrix interface is well below the critical value required to generate new dislocations in the austenite.47'81'82 Moreover, detailed STEM/EDS microanalyses have failed to reveal detectable variations in the matrix composition in the vicinity of the inclusions.83 Hence, nucleation resulting from a small lattice disregistry between the inclusions and the ferrite appears to be the most likely explanation to the observed effects of deoxidation practice on the weld metal transformation behaviour. From a theoretical standpoint, the development of a faceted ferrite nucleus which exhibits a rational orientation relationship with both the austenite and the inclusions would require that the substrate and the austenite have similar crystal structures and identical lattice orientations. The catalyst particles must therefore be cubic and bear an orientation relationship with the austenite which lies within the Bain region.27 However, considering the fact that the weld metal inclusions form in the liquid state prior to the solidification process, the latter requirement cannot generally be met.37 Nevertheless, even if the orientation of the inclusions were perfectly random, it is apparent that orientation relations within the Bain region would be observed purely by chance. In view of the high symmetry of the cubic system, the probability of this happening must be calculated. An approximative estimate is given below for single phase cubic inclusions, based on the method described by Ryder et al?4 Figure 6.46 contains a standard stereographic projection of the austenite crystal, showing the <100> rFe -poles (squares) and the <110>rFe-poles (dots). The Bain orientation region is represented by small circles of radius 11° centered on the <100> r / v - and the <110> rFe -poles.84
Fig. 6.46. Stereographic projection of Bain regions represented by 11° circles, round <100>7_Fe-poles (squares) and <110>7_Fe-poles (dots) of the austenite lattice. After Ryder et aiS4 The austenite/inclusion(i) orientation relationship is within the orientation region derived from the Bain correspondence if one <100>rpole lies within a <100>7_Fe-region and the other two <100>rpoles lie within <110>rFrpole lies within a given <100> r ^-region is (o/47T, where o> is the solid angle enclosed by one <100> r ^-region (equal to 27t(l-cos 11°) = 0.115). Since there are three <100>/ directions and six <100>7_Fe-regions, the probability that at least one <100>rpole lies within a <100>7_F£,-region is equal to: (6-51) Imagine now that the inclusion lattice is rotated through 360° about the <100>raxis which lies within a <100> y . Fe -region. The other two <100> r poles will then lie within <110>7.Fe-regions for at the most 4 X 22° = 88° of this rotation, since the diameter of the <100>7_Fe-regions is 22°. Hence, the probability P2 that, if one <100> r pole lies within a <100>7.Fe-region, the other two will lie within <110>7.Fe-regions is given in the upper limit by: (6-52) The total probability that a given orientation relationship lies within the Bain region purely by chance is thus: (6-53) Therefore, assuming random orientation, about 4% of the weld metal inclusions would lie within the Bain region purely by chance if they were single phase cubic crystals. In practice, however, inclusions commonly found in low-alloy steel weld metals are of a very heterogeneous chemical and crystalline nature. As shown in Fig. 2.72 in Chapter 2, a typical inclusion may contain up to six different constituent phases, including the three cubic phases 7-Al2O3, MnOAl2O3, and TiN. This implies that at least 12% of the inclusions may contain a cubic phase which lies within the Bain orientation region.
Measurements of orientation relationships between specific inclusion constituent phases (i.e. 7-Al2O3, MnOAl2O3, and TiN) and contiguous acicular ferrite plates performed by Grong et a/.85 support the above interpretation (see Table 6.3). Referring to the standard stereographic projections in Fig. 6.47, a very high proportion of the ferrite/inclusion orientations falls within the Bain region. In addition, two other variants (i.e. No. 5 and 6) are indicated for TiN which do not meet this requirement. They are therefore regarded as spurious (in the sense that the observed orientation relationships do not stem from a catalyst nucleation event) and should be ignored. Hence, it may be concluded that the observed orientation relationships between acicular ferrite and specific inclusion constituent phases are not fully reproducible in the true meaning of the word, since only those combinations which satisfy the inherent crystallography of the acicular ferrite microstructure are acceptable. An interesting observation from the data in Table 6.3 is that nucleation of acicular ferrite on inclusions is always associated with low-index planes of the {100} or the {110} type, which indicates a faceted growth morphology of the inclusions. Faceted growth may occur as a result of anisotropy in the growth rates between high-index and low-index crystallographic planes, and can in the extreme case lead to a morphology of the type shown in Fig. 6.48. Consequently, formation of faceted inclusions in the liquid steel during deoxidation appears to be an intrinsic feature of low-alloy steel weld metals. Simple verification on the basis of classic nucleation theory shows that the associated reduction of the energy barrier to nucleation, AGlet , is the primary cause for the ferrite nucleus to develop epitaxial orientation relationships with the substrate and the austenite.8687 Referring to Fig. 6.49, a qualitative ranking of the different inclusion constituent phases with respect to nucleation potency of acicular ferrite can be made from the data presented in Table 6.3. It is evident that both 7-Al2O3, MnOAl2O3, and TiN reveal a good lattice matching with the ferrite phase in one crystallographic direction. In addition, nucleation of acicular ferrite at TiN offers Table 6.3 Observed orientation relationships between acicular ferrite and different inclusion constituent phases in a SA low-alloy steel weld. Data from Grong et al.85 Substrate
Orientation Relationship
(s)
No.
Plane Combinations
Ratio^
(100) s ~//(011) a _ Fe [011]s ~ // [533] a . Fe
1
{011}a_Feand{400}s
1.02
MnOAl2O3
(200) s ~//(110) a F e
2
{110}a_Feand {400}s
0.99
(spinel)
(011)s // (010)a Fe [Oil],//[QOlLp 6
3
{200}a Fe and {440}s
0.99
(TlO) 8 // (100)a Fe (112)s//(011)a_Fe [lll] s //[011] a . F e
4
{200}a Fe and {220}s {011} a . Fe and{112} s
0.97 1.17
(101) s //(103) a _ Fe (320)s//(112)a_Fe [232] s //[351] a _ Fe
5
{310} a . Fe and{330} s {112}a.Fe and {320}s
0.91 0.99
{133} aFe and{550} s {200}a.Feand {221 }s
1.10 1.01
7-Al2O3 (distorted spinel)
TiN (NaCl)
Variant
Interplanar Spacing
(101) s //(133) a _ Fc [221]s//[200]a_Fe Defined as d(hkl)a.Fe /d(hkl)s
6
Fig. 6.47. Standard (100) stereographic projections of the orientation relationships listed in Table 6.3; (a) Variant (1) and (3), (b) Variant (4), (5) and (6). The Bain orientation region is indicated by the 11° circles in the graphs (see Fig. 6.46 for details). the advantage of partial lattice coherence in a second (independent) direction, which further contributes to a reduction of AG^e/ through a minimisation of the interfacial energy between the two phases. This makes TiN an extremely efficient nucleant for acicular ferrite. Microstructure data available for submerged arc (SA) steel weld deposits clearly support the above findings that nucleation of acicular ferrite occurs preferentially at inclusions which contain aluminium or titanium. As shown in Fig. 6.50, a high volume fraction of acicular ferrite is always achieved when sufficient amounts of titanium are added either through the filler wire or the flux, irrespectively of the aluminium and oxygen concentrations. This is in sharp contrast to welds produced with welding consumables containing low levels of titanium, where the acicular ferrite content drops rapidly with decreasing [A%Al]weld/[%O]anal ratios
Fig. 6.48, Example of a faceted crystal delimited by {100} and {110} planes (schematic).
TiN
MnOAI2O3
T-Al2O3
AG
;et.
Austenite grain boundary
Nucleation site Fig. 6.49. Qualitative ranking of different inclusion constituent phases with respect to nucleation potency of acicular ferrite. due to the presence of lower fractions of 7-Al2O3 and MnOAl2O3 in the inclusions (see Fig. 2.72 in Chapter 2). Similar observations have also been made by other investigators.3672" 76,78,79
It should be noted that the weld metal transformation behaviour in practice depends on complex interactions between a number of important variables, including alloying and deoxidation practice, the solidification microstructure, the prior austenite grain size, and the weld thermal cycle.36'5358 This means that the presence of 7-Al2O3, MnOAl2O3 or TiN at the surface of the inclusions is perhaps a necessary but not a sufficient criterion for formation of acicular ferrite in steel weld metals. Example (6.8)
Consider a partly Ti-Al deoxidised steel weld metal which contains a total number of 4 X 107 inclusions per mm 3 . Based on Fig. 2.72 in Chapter 2 and the theory developed above, estimate an upper limit for the volume of a typical plate of acicular ferrite when the weld metal [A%Al]weld/ \y°O\anaL r a t i o i s °- 80 -
Vol% AF
[A%A|lweld/[%o]anal Fig. 6.50. Effect of deoxidation practice (inclusion chemistry) on the acicular ferrite transformation in low-alloy steel weld metals. Data compiled from miscellaneous sources. Solution
From Fig. 2.72 it is seen that the total number of constituent phases in the inclusions is six, including the three cubic phases 7-Al2O3, MnOAl2O3, and TiN. If we assume a random orientation and only one nucleation event per inclusion, the following upper limit for the acicular ferrite plate volume is obtained:
The above volume corresponds to an acicular ferrite plate which has the shape of a square lath of side lOjim and thickness 2|im. Although this estimate is in reasonable agreement with experimental observations,37 the prediction is conservative in the sense that it assumes only one nucleation event per inclusion. In practice, an oxide inclusion which is orientated within the Bain region has the capability of nucleating several acicular ferrite plates, as shown by the SEM micrograph in Fig. 6.51. In addition, the acicular ferrite plates may nucleate autocatalytically at aFe /yFe boundaries, a process which also is referred to as sympathetic nucleation in the literature.36'37'7083 At present, it is not clear to what extent autocatalytic nucleation plays a role in the development of the acicular ferrite microstructure. Hardenability effects Since acicular ferrite is one of the last phases to form after the growth of allotriomorphic and Widmanstatten ferrite, it is bound to be influenced by the prior transformation products, as indicated by equation (6-50). The strong dependence of the acicular ferrite content on the austenite grain size must therefore be understood on this basis. 3747 ' 48 ' 7088 " 90 It is evident from the data of Barbaro et al.70 reproduced in Fig. 6.52 that a coarse austenite grain size favours intragranular nucleation of acicular ferrite at the expense of formation of allotriomorphic and
Fig. 6.51. SEM micrograph of a carbon extraction replica showing evidence of multiple nucleation of acicular ferrite at a weld metal inclusion. Widmanstatten ferrite. This effect is most pronounced during slow cooling, since the combination of a small austenite grain size and a slow cooling rate implies that much of the yFephase already has transformed to allotriomorphic ferrite before the temperature for intragranular nucleation of acicular ferrite is reached. Example (6.9)
Consider a low-alloy steel weld metal which contains a total number of 5 X 107 inclusions per mm3 with an average radius of 0.25 Jim. Use this information to evaluate the conditions for acicular ferrite formation within the as-deposited weld metal and the low-temperature reheated region of the weld when the austenite grain size is 100 and 10 |iim, respectively. In these calculations we shall assume that the equilibrium volume fraction of ferrite ff~Fe in the fully transformed steel is 0.9. Solution
First we need to estimate the total surface area per unit volume available for ferrite nucleation at austenite grain boundaries, Sv (GB), and non-metallic inclusions, Sv (/), respectively. As-deposited weld metal
Reheated weld metal
(as before)
Volume fraction of AF
Austenjte grain size,jim Fig. 6.52. Effect of austenite grain size on the acicular ferrite transformation in low-alloy steel weld deposits. Data from Barbara et al.70 From the above calculations it is apparent that the conditions for intragranular nucleation of acicular ferrite at inclusions are particularly favourable within the as-deposited weld metal, since SV(I) > SV(GB), whereas nucleation and growth of ferrite at austenite grain boundaries will dominate within the reheated region of the weld (SV(GB)» SV(I)). This conclusion is also consistent with predictions based on the Avrami equation (equation (6-49)). If we, as an illustration, assume that the volume fraction of grain boundary ferrite in the as-deposited weld metal is 0.3, the corresponding fraction of GF in the reheated weld metal becomes:
On this basis it is not surprising to find that the microstructure within the grain refined region of low-alloy steel welds is usually polygonal ferrite, while the as-deposited weld metal also contains high proportions of acicular ferrite (see Fig. 6.19(c) and (d), respectively). It is important to realise, however, that the presence of allotriomorphic ferrite at the austenite grain boundaries has the benefical effect of suppressing the formation of bainitic sheaves at the austenite grain boundaries, which, in turn, allows the acicular ferrite to develop on intragranular nucleation sites.9091 Consequently, due to the number of competing nucleation and growth processes involved, the volume fraction of acicular ferrite is often seen to pass through a maximum when the weld metal hardenability is successively increased by additions of alloying elements, as shown in Fig. 6.53.
Microstructural component, %
GF and PF WF
Fertile with aligned second phase (FS)
Chromium content, wt% Fig. 6.53. Effect of chromium additions on the C-Mn primary weld metal microstructure. After Babu and Bhadeshia.91
6.3.6 Acicular ferrite in wrought steels In recent years a new class of low-carbon microalloyed steels has emerged to meet the need for improved weldability, particularly with respect to the HAZ toughness. 70'92 These steels are not aluminium-killed (they usually contain less than 30 ppm Al), but are instead deoxidised with titanium (120-140 ppm) to produce a relatively coarse distribution of submicroscopic Ti oxide inclusions within the base metal (presumably Ti 2 O 3 ). During high heat input welding (> 5 kJ mm"1), the oxides will not retard austenite grain growth but instead act as favourable nucleation sites for acicular ferrite within the interior of the austenite grains, as shown schematically in Fig. 6.54(a). However, since the inclusion number density is quite low (<106 particles per mm3), the microstructure is significantly coarser than that normally observed in steel weld deposites.92 Nevertheless, their presence contributes to suppress the formation of Widmanstatten ferrite and upper bainite within the grain coarsened HAZ, which is a common problem with the traditional Al-Ti microalloyed steels22 (see Fig. 6.54(b)).
63.7 Bainite Bainitic microstructures (besides acicular ferrite) are frequently observed during welding, particularly in the HAZ of low-carbon microalloyed steels,22'93"95 but also within the fusion region of the weld if the nucleation conditions are favourable.37'55'5991 Two main forms can be identified, i.e. upper and lower bainite, as indicated in Fig. 6.19(a). 6.3.7.1 Upper bainite In general, the morphology of upper bainite bears a close resemblance to Widmanstatten ferrite (both are typical sideplate structures), while its crystallography is more like that of lowcarbon martensite (the K-S orientation relationship is usually less precise than for WF).20 In spite of this similarity, the formation of upper bainite cannot be fully understood in terms of
HAZ
WF/UB
HAZ Fig. 6.54. Schematic illustration of the HAZ transformation behaviour during high heat input welding; (a) Ti-oxide containing steel, (b) Conventional Al-Ti microalloyed steel. The diagrams are based on the ideas of Homma et al.92
the classic theory of martensite nucleation assuming a pure invariant plane strain deformation.1'20'61 HAZ transformation behaviour As shown in Fig. 6.19(a), upper bainite is frequently observed within the grain coarsened HAZ of low-carbon microalloyed steels. The bainite sheaves nucleate preferentially at austenite grain boundaries and subsequently grow into the interior of the grains until they physically impinge with other transformation products such as martensite or Widmanstatten ferrite. Because of these competitive nucleation and growth processes, the highest volume fractions of upper bainite are normally attained at an intermediate cooling rate, as indicated by the microstructure data in Fig. 6.55. Weld metal transformation behaviour Upper bainite may also form within the columnar grain region of high heat input SA steel welds, as shown by the optical micrograph in Fig. 6.56. The indications are that the observed
Microstructural component, %
iUBj
Ferrite with aligned second dhase (FS)
WF
Mill Cooling time, At 8/5 , s Fig. 6.55. Effect of cooling time, Af8/5, on the grain coarsened HAZ transformation behaviour (simulated thick plate heat cycles, Tp « 13500C). Data from Akselsen et al96
Fig. 6.56. Optical micrograph showing formation of upper bainite within the columnar grain region of a SA steel weld.
shift in the weld metal transformation behaviour is related to a change in the deoxidation practice which alters the kinetics of the subsequent solid state transformation reactions through a modification of the solidification microstructure.64 Solidification induced phosphorus segregations are of particular interest in this respect, since previous examinations have shown that phosphorus can strongly enhance the formation of grain boundary ferrite by raising the local Ae3 temperature of the steel97 (see also Example 6.5). Following the discussion in Section 6.3.5.4, the evolution of allotriomorphic ferrite at the austenite grain boundaries has the beneficial effect of suppressing the formation of bainitic sheaves at these sites, which, in turn, allows the acicular ferrite to develop on intragranular
Microstructural component, %
Carbides
Lower bainite
Martensite Fig. 6.58. TEM micrograph showing the formation of lower bainite within the HAZ of a low-carbon microalloyed steel.
6.3.8 Martensite At very high undercoolings, the austenite decomposes to martensite by means of an invariant plane strain deformation, which implies that there is no change in the steel chemical composition. The reaction product will either be lath or plate (twinned) martensite, depending on the alloy level. Lath martensite is commonly found in plain carbon and low-alloy steels up to about 0.5wt% C, and is formed by a slip mechanism, as shown schematically in Fig. 6.59(a). When the carbon content exceeds this threshold, the martensite transformation occurs rather by formation of deformation twins (Fig. 6.59(b)). The crystal structure of plate martensite is bet (body-centred tetragonal), while lath martensite reveals a bcc (body-centred cubic) structure,61 which becomes increasingly distorted with increasing steel carbon contents.20 Both transformation products exhibit the characteristic Kurdjumow-Sachs orientation relationship with the austenite, but this relationship tends to be less precise at high carbon levels.1'20 6.3.8.1 Lath martensite Lath martensite is frequently observed within the grain coarsened HAZ during low heat input welding of microalloyed steels. As shown in Fig. 6.60, the microstructure will be fully martensitic for values of Ar875 up to about 5-10s, depending on the steel hardenability. The hardness of the martensite formed is usually below 400 VPN, which is significantly lower than the corresponding peak value achieved after water-quenching.98 This means that considerable autotempering occurs during cooling from the M^-temperature, which in the case of low-carbon microalloyed steels can be as high as 5000C. 6.3.8.2 Plate (twinned) martensite In the intercritical HAZ (i.e. partly transformed region), carbon-rich austenite, formed by decomposition of pearlite or isolated carbides, may transform to high carbon (twinned) martensite on cooling, as shown schematically in Fig. 6.61. However, since the Mf temperature in this case will be far below room temperature, significant amounts of retained austenite may be present in the areas adjacent to the martensite islands. This transformation product is therefore
Slip
Twin
b
a
Fig. 6.59. Mechanisms of martensite formation in steel (schematic); (a) Slip along parallel planes, (b) Generation of deformation twins. The diagram is based on the ideas of Verhoeven.61
Steel A
Martensite content, vol%
Steel B Steel C
Cooling time, At0._ ,s 8/5 Fig. 6.60. Effect of cooling time, Af8/5, on the volume fraction of lath martensite within the grain coarsened HAZ of microalloyed steels (simulated thick plate heat cycles). Data from Akselsen et «/.98
frequently referred to as the martensite-austenite (M-A) constituent in the scientific literature.99"103 Kinetics of austenite formation In general, the formation of austenite during intercritical annealing of low-carbon microalloyed steels can be separated into three main stages:99 (i)
Rapid growth of austenite into pearlite until the dissolution process is completed.
(ii)
Slower growth of austenite into ferrite at a rate which is either controlled by carbon diffusion in the austenite or by diffusion of substitutional elements such as manganese in the ferrite, depending on the applied annealing temperature.
T
T
t
wt% C
Fig. 6.61. Schematic illustration of the formation of plate (twinned) martensite within the intercritical HAZ of low-carbon microalloyed steels; Heating leg of thermal cycle: Pearlite -> -yFe (>0.5 wt% C), Cooling leg of thermal cycle: yFe(> 0.5 wt% C) -> a'Fe (twinned martensite).
(iii) Very slow final equilibration of solute concentration gradients within the austenite or the ferrite through diffusion. At temperatures above say 7700C, the rate of pearlite decomposition is sufficiently high for complete dissolution, even during low-heat input welding. Hence, in hot rolled and normalised steels all pearlite will transform to austenite when the peak temperature of the thermal cycle exceeds this threshold. However, if the starting microstructure is a mixture of martensite and upper bainite (as often will be the case in multi-pass welding), the austenite will nucleate both at prior austenite grain boundaries and along the interfaces between laths of bainite or martensite, as shown by the optical micrographs in Fig. 6.62. A similar pattern has also been observed during intercritical annealing of dual-phase steels.104'105 Considering the kinetics, carbides precipitated within autotempered low-carbon martensite or between the laths of bainite would be expected to dissolve at a rate comparable with that of pearlite.105 Hence, it is reasonable to assume that no retained carbides will be present intragranularly after reheating to say Tp « 7700C when the starting microstructure is a mixture of martensite and bainite. Further growth of the austenite into the ferrite requires, however, that the peak temperature of the thermal cycle is raised significantly above 7700C in order to reach the kinetic (paraequilibrium) stage where the reaction is controlled by diffusion of carbon in austenite." Consequently, the possibilities of obtaining growth of the austenite colonies within the low peak temperature regions of the intercritical HAZ are strongly limited, which implies that the carbon content of the austenite islands in these regions should be close to the saturation level of carbon in austenite at the temperature of dissolution. Conditions for M-A formation On subsequent cooling, the carbon-rich austenite can decompose to a variety of microstructures (ranging from twinned martensite to pearlite) or remain untransformed, depending on the base plate hardenability, the weld cooling programme, and the initial size of the austenite islands.102103'106 When the starting microstructure is a mixture of ferrite and pearlite (as frequently observed in normalised steels), twinned martensite forms readily along the prior base
(a)
(b)
Fig. 6.62. Optical micrographs showing favourable sites for austenite formation during two-pass weld thermal simulation. (First cycle: Tp « 13500C, Atm « 12 s, Second cycle: Tp « 775°C, Atm « 12 s); (a) Intergranular, (b) Intragranular. After Akselsen et aim
metal pearlite bands or within isolated pearlite colonies at high cooling rates, as shown by the TEM micrographs in Fig. 6.63(a) and (b). With decreasing cooling rates, however, the transformation product shifts from twinned martensite to predominatly pearlite (see Fig. 6.63(c) and (d)) in the absence of strong hardenability elements such as molybdenium and boron which can stabilise the M-A constituent.102'107"109 In controlled rolled and accelerated cooled steels, where the carbides are mainly present in the form of submicroscopic colonies or isolated particles located at ferrite/ferrite grain boundaries (see Fig. 6.64(a)), the situation becomes slightly more complex. Under such conditions, the majority of the austenite islands formed within the low peak temperature region of the intercritical HAZ will be of a size below 1 jam. It has been verified experimentally that such
(a)
(C)
(b)
(d)
Fig. 6.63. Examples of transformation products formed after intercritical thermal cycling of a ferritic/ pearlitic starting microstructure to a peak temperature of 775°C; (a) M-A islands (black areas) surrounded by ferrite (At6/4 ~ 5 s), (b) Close-up of twinned martensite within a M-A island (At6/4 ~ 5 s), (c) Isolated pearlite colony formed at an intermediate cooling rate (Ar674 ~ 12 s), (d) Pearlite colonies formed during slow cooling (At614 ~ 35 s). After Akselsen et al.103
small particles do not readily transform to martensite, but will largely remain in the steel in the form of retained austenite.100'103'110'111 This can be explained by the lack of nucleation opportunities for martensite or by the volume restraint provided by the surrounding ferrite matrix.1 x x Consequently, twinned martensite in controlled rolled and accelerated cooled steel is seen to form within a few, relatively large austenite islands which stem from decomposition of single carbide colonies, as illustrated by the TEM micrograph in Fig. 6.64(b). During multipass welding, the initial carbide distribution in the base plate will be of less importance because of the transformations imposed by the heat of previous weld passes. Hence, after full reaustenitising of the steel the M-A constituent may form both intergranularly and intragranularly, depending on the starting microstructure, as shown previously in Fig. 6.62(a) and (b). An example of intergranularly nucleated twinned martensite is contained in Fig. 6.65. Volume fraction of M-A constituent At present, an adequate kinetic model for partial reaustenitising of steel during continuous heating and cooling is lacking. However, in view of the previous discussion it is obvious that the volume fraction of the M-A constituent within the intercritical HAZ of single pass steel weldments must be closely related to the initial base plate pearlite content. This is also in agreement with experimental observations (see Fig. 6.66).
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(a)
(b)
Fig. 6.64. Conditions for martensite formation within the intercritical HAZ of a controlled rolled and accelerated cooled steel containing copper and nickel; (a) TEM micrograph of the initial base plate carbide distribution, (b) TEM micrograph showing evidence of twinned martensite within a l(im large austenite colony formed during intercritical thermal cycling to T « 775°C (Ar674 « 35 s). After Akselsen etal^
6.4 Austenitic Stainless Steels Simple austenitic stainless steels generally contain between 18 and 30 wt% chromium, 8 to 20 wt% nickel, and between 0.03 to 0.1 wt% carbon.20 Since the solubility of carbon decreases rapidly with temperature (see Fig. 6.67), reheating of the steels within the temperature range from 500 to 9000C will lead to the rejection of carbon from solid solution, usually by chromium carbide precipitation (Cr23C6). These carbides nucleate preferentially at the austenite grain boundaries, which, in turn, results in depletion of the regions adjacent to the grain boundaries with respect to chromium, as shown schematically in Fig. 6.68. The presence of such chromium-depleted regions within the steel makes it sensitive to intergranular corrosion in service.20'112
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(a)
(b)
Fig. 6.64. Conditions for martensite formation within the intercritical HAZ of a controlled rolled and accelerated cooled steel containing copper and nickel; (a) TEM micrograph of the initial base plate carbide distribution, (b) TEM micrograph showing evidence of twinned martensite within a l(im large austenite colony formed during intercritical thermal cycling to T « 775°C (Ar674 « 35 s). After Akselsen etal^
6.4 Austenitic Stainless Steels Simple austenitic stainless steels generally contain between 18 and 30 wt% chromium, 8 to 20 wt% nickel, and between 0.03 to 0.1 wt% carbon.20 Since the solubility of carbon decreases rapidly with temperature (see Fig. 6.67), reheating of the steels within the temperature range from 500 to 9000C will lead to the rejection of carbon from solid solution, usually by chromium carbide precipitation (Cr23C6). These carbides nucleate preferentially at the austenite grain boundaries, which, in turn, results in depletion of the regions adjacent to the grain boundaries with respect to chromium, as shown schematically in Fig. 6.68. The presence of such chromium-depleted regions within the steel makes it sensitive to intergranular corrosion in service.20'112
Content of M-A constituent, vol%-
Fig. 6.65. TEM micrograph showing evidence of intergranularly nucleated twinned martensite in double-cycled specimens (First cycle: Tp ~ 13500C, A;6/4 -12s, Second cycle: Tp - 775°C, A;6/4 - 12s) After Akselsen et al.103
Base plate pearlite content, v o l % •
Fig. 6.66. Effect of base plate pearlite content on the volume fraction of M-A constituent in thermally cycled specimens (simulation conditions: Tp -775°C, Atm « 5s). Data from Akselsen et al.m
Temperature, 0C
Carbon content, wt% Fig. 6.67. Solvus temperatures for different types of carbides in 304 austenitic stainless steel as a function of carbon content. Data from Kou.112 Cr depleted zone
Grain boundary
Cr carbide precipitate Fig. 6.68. Schematic illustration OfCr23C6 precipitation at grain boundaries in austenitic stainless steels. The diagram is based on the ideas of Kou.112
6.4.1 Kinetics of chromium carbide formation Precipitation of Cr23C6 in austenitic stainless steels is a typical nucleation and growth process. The temperature-time transformation curve is therefore C-shaped, and can be modelled according to the general principles outlined in Section 6.2.2.3. As an illustration, we shall assume that the parameters listed in Table 6.4 are representative of nucleation of Cr23C6 in a 304 type austenitic stainless steel containing 0.07 wt% C. If we at the same time allow for the variation in austenite grain size with distance from the fusion boundary, the shape and position of the C-curve in temperature-time space at different locations within the HAZ is given by equation (6-35):
(6-54)
A graphical representation of equation (6-54) in Fig. 6.69 shows that the nose of the C-curve for the reference steel (characterised by Teq = T*eq and D1 = D 7 ) is strongly shifted to the left in the IT-diagram, thereby providing favourable conditions for Cr23C6 precipitation in the heat affected zone during welding. The problem becomes less imminent if the base plate carbon content is reduced from say 0.07 to 0.04 wt%. In that case the associated reduction in the solvus temperature Teq from 920 to 8000C will displace the C-curve towards longer times in the diagram which by far exceed the duration of a typical weld thermal cycle, as shown in Fig. 6.69. 6.4.2 Area of weld decay Experience shows that corrosion attact within the HAZ of single pass austenitic stainless steel welds usually starts in regions where the peak temperature of the thermal cycle has been close to the nose of the C-curve in Fig. 6.69. This observation cannot be explained by just considering the HAZ temperature-time pattern, since the retention time within the critical temperature range for chromium carbide precipitation is virtually the same for both high and low peak temperature thermal cycles, as indicated in Fig. 6.70. The explanation is, of course, that the C-curve becomes increasingly shifted to the right in the IT-diagram as the peak temperature increases due to austenite grain growth occurring during welding. This point is more clearly illustrated below. Example (6.10)
Consider single pass butt welding of 2mm sheets of 304 austenitic stainless steels with covered electrodes under the following conditions:
Evaluate on the basis of equations (6-32), (6-33), and (6-54) in combination with the grain growth diagram in Fig. 5.30(b) (Chapter 5) the conditions for chromium carbide formation within the HAZ during welding when the base plate carbon content is 0.07 and 0.04 wt% C, respectively. Thermal data for austenitic stainless steels are given in Table 1.1 (Chapter 1).
Temperature, 0C
Time, s Fig. 6.69. Effect of carbon content on the isothermal precipitation of C ^ C 6 in 304 austenitic stainless steels. Broken curve: 0.07 wt% C, Solid curve 0.04 wt% C. The diagrams are constructed on the basis of equation (6-54). T
t
Grain growth Area of weld zone decay Fig. 6.70. Schematic illustration of thermal cycles and sensitisation region within the HAZ of an unstabilised austenitic stainless steel. Table 6.4 Input data used to construct C-curve for Cr23C6 precipitates in reference steel. Parameter
Value
T
tr
T*q
A0
Q/
£>*
(K)
(s)
(K)
(Jmol- 1 )
(kJmol-1)
(jxm)
923
60
1193
150
200
18
[• Activation energy for grain boundary diffusion of Cr in austenite.
Solution
If we, as a first approximation, neglect the contribution from heat flow in the welding direction, the temperature-time pattern is given by equation (1-100) in Chapter 1. Taking n = 4 and (1 — Xc) = 0.98 (assuming interface-controlled growth), the extent of chromium carbide precipitation occurring within the HAZ of the weld can be calculated from equations (6-32) and (6-33) by numerical integration over the actual thermal cycles. The results of such computations are presented graphically in Fig. 6.71. As expected, precipitation of chromium carbides occurs readily within the low peak temperature region of the weld when the carbon content is 0.07 wt%. For points located within the grain growth zone, the resulting displacement of the C-curve towards longer times in the CCT-diagram will gradually retard the reaction, which implies that the fraction transformed starts to decline when the peak temperature of the thermal cycle exceeds about 11500C. In contrast, the low-carbon steel reveals no sign of chromium carbide precipitation within the HAZ. This result is in good agreement with general experience, and explains why the carbon content of modern austenite stainless steels has been gradually lowered to values below 0.03 wt % in step with the progress in the steel manufacturing technology.20112
6.5 Al-Mg-Si Alloys
Austenite grain size, pm
Grain growth zone
Unaffected base metal
Fraction transformed
Age-hardenable Al-Mg-Si alloys are widely used as structural components in welded assemblies. They offer tensile strength values higher than 350 MPa in the artificially aged T6 condition owing to the presence of very fine, needle shaped (3"(Mg2Si) precipitates along <100> directions in the aluminium matrix.113 Although Al-Mg-Si alloys are readily weldable, they suffer from severe softening in the heat affected zone (HAZ) because of reversion (dissolution) of the 3"(Mg2Si) precipitates during the weld thermal cycle. 6112 This type of mechanical impairment represents a major problem in engineering design.114
Peak temperature, 0C Fig. 6.71. Conditions for Cr23C6 precipitation within the HAZ of a single pass austenitic stainless steel butt weld (Example 6.10).
6.5.1 Quench-sensitivity in relation to welding High strength alloys such as AA 6082 contains manganese in addition to magnesium and silicon. Manganese is added to control recrystallisation and grain growth in the material during hot forming. The disadvantage is that it increases the quench sensitivity of the alloy.115 The reason for this is that the Mn-bearing dispersoids (which form during homogenisation) provide favourable nucleation sites for the non-hardening (3'(Mg2Si) phase, as shown by the TEM micrograph in Fig. 6.72. The resulting reduction in the solute content leads to a reduced HAZ strength both in the naturally aged TA and peak aged T6 conditions. 56116 6.5.1.1 Conditions for (3 '(Mg2Si) precipitation during cooling Myhr and Grong6 have shown how the quench-sensitivity concept can be applied to welding of Al-Mg-Si alloys. Their model has later been refined and extended to heat treatment of AA 6082 alloys by Shercliff et al.ni and Bratland et a/.118119 As an illustration, we shall assume that the parameters listed in Table 6.5 are representative of nucleation of (3'(Mg2Si) particles in an AA 6082 alloy homogenised at 5800C. If we further assume that the P'(Mg2 Si) particles only form at Mn-bearing dispersoids, the (N* /Nv) term in equation (6-14) may be replaced by the corresponding (5* / Sv) ratio, where S* and Sv refer to the total surface area per unit volume of dispersoids in the reference and the actual aluminium alloy, respectively. This leads to the following expression for t*:
Fig. 6.72. TEM micrograph showing nucleation of non-hardening (3'(Mg2Si) precipitates at Mn-bearing dispersoids in an AA 6082 alloy. Table 6.5 Input data used to construct C-curve for p' (Mg2Si) precipitates in reference aluminium alloy. Parameter
Value
Tr
t\
T*q.
A0
(K)
(s)
(K)
(Jmol"1)
573
20
766
350
f" Activation energy for diffusion of Mg in aluminium.
Qj
S^
(kJmol"1) (mm2 per mm3) 130
100
(6-55) A graphical representation of equation (6-55) in Fig. 6.73 shows that the nose of the Ccurve for the reference alloy (characterised by Teq = r and Sv = S^ is strongly shifted to the left in the IT-diagram, thereby providing favourable conditions for (3'(Mg2Si) formation dunng welding. In general, an increase in T or Sv will enhance the quench-sensitivity of the material because of the resulting increase in the nucleation rate. This will be the case if the alloy contams large amounts of excess silicon in solid solution or is homogenised at a temperature lower than 5800C.118119 Example (6.11)
Consider plasma-MIG butt welding of a 10 mm thick Al-Mg-Si plate under the following conditions: qo = 10 kW, v = 10 mm s~\ T0 = 200C Evaluate on the basis of equations (6-32), (6-33), and (6-55) the conditions for P'(Mg,Si) precipitation within the high peak temperature region of the HAZ during welding (T7 > T ) In these calculations we shall assume that the transformation behaviour of the base'metafis similar to that of the reference alloy in Table 6.5. Relevant thermal data for Al-Mg-Si alloys are given in Table 1.1 (Chapter 1). Solution
Temperature,°C
Referring to Fig. 1.43 in Chapter 1, the mode of heat flow becomes essentially one-dimensional if the net arc power is kept sufficiently high compared with the plate thickness (i.e.
Time, s Fig. 6.73. C-curve for precipitation of 3'(Mg2Si) in the reference AA 6082 alloy. The diagram is constructed on the basis of equation (6-55).
qold>0.05 kW mm"1). Since this requirement is met in the present case, the HAZ temperaturetime pattern is given by equation (1-100).Taking n = 0.75 and (1 - Xc) = 0.84 for precipitation of p'(Mg2Si) in AA6082 aluminium alloys,118 we obtain after integration of equations (6-32) and (6-33) over the weld cooling cycle:
and
The above calculations show that precipitation of (3'(Mg2Si) particles at dispersoids is, indeed, a significant process under the prevailing circumstances. Since the mode of heat flow during single pass butt welding of aluminium plates is essentially one-dimensional, it is possible to construct general transformation diagrams which give the fraction transformed as a function of the applied heat input. An example of such a diagram is contained in Fig. 6.74.
Fraction transformed
6.5.1.2 Strength recovery during natural ageing Myhr and Grong6 have shown how equation (6-15) can be applied for modelling of the HAZ room temperature ageing characteristics. Figure 6.75 shows a typical natural ageing curve for AA 6082 alloys after full solution heat treatment. Due to enhanced precipitation of GP-zones, the hardness will increase from about 42 VPN to a maximum of 80 VPN after a period of 5 to 7 days. However, this ultimate hardness is significantly reduced if solute is lost during the weld cooling cycle because of precipitation of non-hardening (3'(Mg2Si) particles at dispersoids.6117 The relationship between the solute content, C0, and the maximum fraction of hardening precipitates which form during natural ageing, AXp, can be obtained from a simple
T
logt Net heat input ( q /vd), kJ/mm2 Fig. 6.74. Conditions for 0'(Mg2Si) precipitation within the HAZ of single pass AA 6082 butt welds (Tp>Teq).
Hardness (VPN)
Water-quenched specimens
5-7 days
Log time Fig. 6.75. Typical ageing curve for an AA 6082 aluminium alloy at room temperature (schematic). 2-D kinetic (cell) model, assuming that the reaction is interface-controlled. Let r denote the radius of the growing precipitates (defined in Fig. 6.76(a)). Since we are only interested in the terminal value of r at a fixed temperature, the time t in the expression for r can be regarded as constant. Hence, we may write (when C0 » Ca and Cp » C0): (6-56) where C4 is a kinetic constant. If the distribution of the precipitates is approximated by that of a 2-D face-centered cubic space lattice (see Fig. 6.76(b)), the parameter, AXp, is simply given as:
(6-57)
where rm denotes the maximum particle radius which forms within the system if all alloying elements are present in solid solution at the onset of the ageing reaction (C0 = C*). Because of the stoichiometry of the precipitation reaction, C0 and C* in the expression for AXp may be taken proportional to the magnesium concentration in solid solution. Hence, we may write: (6-58)
Equation (6-58) predicts that AXp is a simple power function of CMg. The magnesium concentration in solid solution can be obtained from electrical resistivity measurements, and is given by the following equation:6118 (6-59) where pm is the measured resistivity, pss is the resistivity in the as-quenched condition, while p0
is the corresponding resistivity in the fully annealed condition (i.e. when all Mg and Si are tied up in precipitates). A comparison between equation (6-58) and the electrical resistivity data in Fig. 6.77 confirms the relevance of this power-law-relationship, although the deviation in certain cases in admittedly large. Example (6.12)
Consider plasma-MIG butt welding of a 10 mm thick Al-Mg-Si plate under conditions similar to those employed in Example 6.11. Estimate on the basis of equation (6-58) the relative (b)
Concentration
(a)
Distance
AXp
Fig. 6.76. Simplified 2-D kinetic (cell) model for precipitation of hardening particles in Al-Mg-Si alloys during natural ageing; (a) Particle/matrix concentration profile, (b) Cell geometry.
C
Mg /C*Mg
Fig. 6.77. Experimental verification of equation (6-58).
fraction of hardening precipitates which forms within the fully reverted region of the HAZ after prolonged room temperature ageing. Solution
Referring to Example (6.11), the relative fraction of (3'(Mg2Si) precipitates which forms at dispersoids during the weld cooling cycle amounts to:
from which
This gives:
Since the resulting precipitation strength increment is directly proportional to AXp,ul loss of solute in the form of (3'(Mg2Si) particles during the weld cooling cycle will inevitably lead to a reduced HAZ strength in the naturally aged (T4) condition.6 We shall return to this question in Chapter 7 (Section 7.4.3). 6.5.2 Sub grain evolution during continuous drive friction welding Continuous drive friction welding is a solid-state joining process that produces coalescence by the heat developed between two surfaces by mechanically induced rubbing motion. When the appropriate rotation velocity is reached, the two workpieces are brought together and an axial force is applied. The two surfaces are held under pressure, and due to the heat developed, a plasticised layer forms at the interface. After a predetermined time the rotation stops and the pressure is increased to facilitate forging or local upsetting of the heated metal. Filler metal, flux, or shielding gas is not required with this process. The structural changes within the fully plasticised region of friction welded Al-Mg-Si alloys arise from the combined action of work hardening and softening due to dynamic recovery. When the steady state conditions for deformation in friction welding are reached, the rate of dislocation generation in the plasticised material balances the dislocation annihilation rate, which means that large strains can be imposed without any changes in theflowstress or subgrain size. Referring to Fig. 6.78, the subgrain structure within the fully plasticised region consists of sheaves of virtually equiaxed grains (2-3 |jim in size) that are separated from each other by low-angle grain boundaries. This type of microstructure is characteristic of hot worked aluminium alloys.120 In general, the Zener-Hollomon (Zh) parameter provides a basis for evaluating the evolution of the subgrain structure during hot working. As shown by McQueen and Jonas,121 the following relationship exists between the subgrain diameter ds and the Z^-parameter in aluminium alloys: (6-60)
Partly deformed region
Fully plasticized region
Partly deformed region
(a)
(b)
Fig. 6.78. Micrographs showing the subgrain structure within the fully plasticised and partly deformed region of a friction welded Al-Mg-Si alloy; (a) Overview, (b) Close-up of the subgrain structure (EBSP image).
where (6-61)
The peak temperature T and the strain rate i distributions within the fully plasticised region of a friction weld can be computed on the basis of the generic models developed by Midling and Grong.122 Examples of such calculations are shown in Fig. 6.79(a). Plots of the resulting Zener-Hollomon parameter and subgrain diameter at different locations within the HAZ are contained in Fig. 6.79(b).
Partly deformed region
Strain rate, s"1
Radial position:
Peak temperature, 0C
Fully plasticized region
Radial position:
Fully plasticized region
Subqrain diameter, urn
Zener-Hollomon parameter, s
l
Axial distance, mm
Partly deformed region
Axial distance, mm Fig. 6.79. Modelling of the subgrain evolution in the fully plasticised region of a friction welded AA 6082 aluminium alloy; (a) Predicted peak temperature Tp and strain rate (e) distributions, (b) Plots of the Zener-Hollomon Zh parameter and resulting subgrain diameter ds at different locations within the HAZ. Data from Midling and Grong.122
It is evident from the graphs that the value of the Zener-Hollomon parameter is of the order of 1014-1012 s"1 within the fully plasticised region of the HAZ during continuous drive friction welding of Al-Mg-Si alloys. The predicted range in Zh corresponds to a subgrain size of 2-3 jam, in agreement with experimental observations (see EBSP image in Fig. 6.78(b)). Outside the fully plasticised region the Zener-Hollomon parameter drops from about 1012 to 1010 s"1 due to a sudden change the strain rate from 102 to 10° s"1 as the contribution from the material flow field in the rotational direction ceases. This value is outside the validity range of equation (6-60), and leads to the formation of coarse subgrains at the boundary between the fully plasticised and the partly deformed region, as shown by the TEM micrographs in Fig. 6.80.
Fig. 6.80. TEM micrographs showing evidence of coarse subgrains at the boundary between the fully plasticised and partly deformed region of a friction welded AA 6082 aluminium alloy.
References 1. 2. 3. 4.
D. A. Porter and K.E. Easterling: Phase Transformations in Metals and Alloys, 1981, Wokingham (England), Van Nostrand Reinhold. M.E. Fine: Phase Transformations in Condensed Systems, 1964, New York, The Macmillian Company. N. Ryum: Compendium in Physical Metallurgy, 1973, Trondheim (Norway), The University of Trondheim, The Norwegian Institute of Technology. G.F. Vander Voort (ed.): Atlas of Time-Temperature Diagrams for Nonferrous Alloys, 1991, Materials Park (Ohio), ASM International.
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RE. Marth, H.I. Aaronson, G.W. Lorimer, T.L. Bartel and K.C. Russell: Metall. Trans., 1976, 7A, 1519-1528. CM. Dallam and D.L. Olson: Weld. J., 1989, 68, 198s-2O5s. G. Thewlis: HW Doc. IXJ-165-90 (1990). R.A. Farrar, Z. Zhang, S.R. Bannister and G.S. Barrite: J. Mater. ScL, 1993, 28, 1385-1390. S.S. Babu and H.K.D.H. Bhadeshia: Mater. ScL Technol, 1990, 6, 1005-1020. H. Homma, S. Ohkita, S. Matsuda and K. Yamamoto: Weld. J., 1987, 66, 301s-309s. R.E. Dolby: Weld. J., 1979, 58, 225s-238s. B.C. Kim, S. Lee, NJ. Kim and D.Y. Lee: Metall Trans., 1991, 22A, 139-149. R.H. Phillip: Weld. J., 1983, 62, 12s-18s. O.M. Akselsen, J.K. Solberg, G. R0rvik and AJ. Paauw: Technical Report STF34 F87013, 1987, Trondheim (Norway), Sintef-Division of Metallurgy. A.O. Kluken and 0. Grong: Proc. Int. Conf. on Recent Trends in Welding Science and Technology, Gatlinburg, TN, May, 1989, pp. 781-786. Publ. ASM International, Materials Park, OH, 1990. O.M. Akselsen, G. R0rvik, M.I. Ons0ien and 0. Grong: Weld. J., 1989, 68, 356s-362s. G.R. Speich, V.A. Demarest and R.L. Miller: Metall. Trans., 1981,12A, 1419-1428. C.A.N. Lanzillotto and FB. Pickering: Metal ScL, 1982, 16, 371-382. J.H. Chen, Y. Kikuta, T. Araki, M. Yoneda and Y. Matsuda: Acta Metall, 1984, 32, 1779-1788. M. Ramberg, O.M. Akselsen and 0 . Grong: Proc. Int. Conf. on Advances in Welding Science and Technology, Gatlinburg, TN, May, 1986, pp. 679-684. Publ. ASM International, Materials Park, OH, 1986. O.M. Akselsen, 0. Grong and J.K. Solberg: Mater. ScL Technol, 1987, 3, 649-655. X, -L. Cai, AJ. Garratt-Reed and W.S. Owen: Metall. Trans., 1985, 16A, 543-557. JJ. YI, LS. Kim and H.S. Choi: Metall. Trans., 1985, 16A, 1237-1245. O.M. Akselsen, J.K. Solberg and 0 . Grong: Stand. J. Metall, 1988,17, 194-200. A.R. Marder: Metall. Trans., 1981, 12A, 1569-1579. X.P Shen and R. Priestner: Metall Trans., 1990, 21 A, 2547-2553. NJ. Kim and YG. Kim: Mater. ScL Eng., 1990, A129, 35-44. K.R. Kinsman, G. Das and R.F Hehemann: Acta Metall, 1977, 25, 359-365. N.K. Balliger andT. Gladman: Met. ScL, 1981, 15, 95-108. S. Kou: Welding Metallurgy, 1987, Toronto (Canada), John Wiley & Sons. J.E. Hatch (ed.): Aluminium — Properties and Physical Metallurgy, 1984, Metals Park (Ohio), American Society for Metals. FM. Mazzolani: Aluminium Alloy Structures, 1985, Boston (USA), Pitman Publish. Inc. O. Lohne and A.L. Dons: Scand. J. Metall, 1983, 12, 34-36. R.P Martukanitz: Proc. Int. Conf. on Advances in Welding Science and Technol, Gatlinburg (Tenn.), May, 1986, pp. 193-201. Publ. ASM International, Materials Park (OH). 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. 357369. Publ. The Norwegian Institute of Technology, Trondheim, Norway. D.H. Bratland, 0. Grong, O.R. Myhr and H.R. Shercliff: Proc. Int. Conf on Computer-Assisted Materials Design and Process Simulation, Tokyo (Japan), September, 1993, pp. 135-141. Publ. The Iron and Steel Institute of Japan. D.H. Bratland, 0 . Grong, H.R. Shercliff, O.R. Myhr and S.Tjotta:,4cta Metall Mater., Overview No. 124,1997,45,1-22. CM. Sellars: Proc. 3rd Int. Conf. on Aluminium Alloys—Their Physical and Mechanical Properties, Trondheim (Norway), June, Vol. Ill, pp. 89-106. Publ. The Norwegian Institute of Technology, Trondheim, Norway. HJ. McQueen and JJ. Jonas: Treatise on Mater. ScL Technol, 1975,6, 393-493. O.T. Midling and 0 . Grong: Acta Metall Mater., 1994,42,1595-1609: ibid., 1611-1622.
Appendix 6.1 Nomenclature start temperature of ferrite to austenite transformation (0C or K)
concentration of solute at particle/matrix interface (at.% or wt%)
end temperature of ferrite to austenite transformation (0C or K)
concentration of solute inside the precipitates (at.% or wt%)
equilibrium 7/a solvus temperature (0C or K) interfacial area per unit volume (jLim2 per |um3 or m2 per m3) material constant related to the potency of the heterogeneous nucleation sites (J mol"1) difference between total and acid soluble aluminium in weld metal (wt%)
concentration of solute in matrix (at.% or wt%) maximum concentration of solute in matrix (at.% or wt%) continuous cooling transformation cooling rate (0C s"1 or K s 1 ) plate thickness (mm) subgrain diameter (jum or m)
acicular ferrite integration parameter
average diameter of columnar austenite grains (\xm or m)
bulk concentration of free boron in steel (ppm)
ferrite grain size (\xm or m)
amount of boron which segregates to austenite grain boundaries on cooling (ppm) amount of boron which segregates to austenite grain boundaries in reference steel on cooling (ppm)
austenite grain size (jum or m) austenite grain size in reference material (jum or m) element diffusivity (JLim2 s"1 or !!TV1) complementary error function
fraction of boron atoms associated with vacancies (ppm) various kinetic constants and temperature-dependent parameters
vacancy-boron binding energy (J mol"1 or kJ mol"1) vacancy formation energy (J mor 1 or kJ mol"1)
electron backscattering pattern
arbitrary function of (T)
electron dispersive system
amperage (A)
volume fraction of transformation product
kinetic strength of thermal cycle with respect to p-precipitation
equilibrium volume fraction of transformation product
modified Z1 integral
ferrite with aligned second phase
integral in equation (6-47)
molar free energy of a-phase (J mol"1 or J m"3)
kinetic constant in Avrami equation (variable units)
molar free energy of p-phase (J mol"1 or J nr 3 )
time constant in Avrami equation (s)
arbitrary function of X
Kurdjumow-Sachs orientation relationship
molar free energy of transformation (J mol"1 or J m~3)
isothermal transformation
free energy donated to the system when nucleation occurs heterogeneously (J mol"1 or J nr 3 ) increase in strain energy resulting from lattice distortion (J mol 1 or J m 3 ) increase in surface energy due to nucleus formation (J mol"1 or J ITT3)
interledge spacing (nm) length of columnar austenite grains (|Lim or m) lower bainite proportionality constant in boron diffusion model martensite
volume free energy change associated with transformation (J mol"1 or J m 3 )
mobility parameters related to the jump-frequency of atoms across a particle/matrix interface (variable units)
energy barrier against heterogeneous nucleation (J or J mol"1)
end temperature of martensite transformation (0C or K)
energy barrier against homogeneous nucleation (J or J mol"1)
start temperature of martensite transformation (0C or K)
grain boundary ferrite gas metal arc welding
martensite-austenite constituent metal inert gas
time exponent in Avrami equation
two-dimensional radius vector in y-z plane (mm)
number of nucleation sites per unit grain boundary area (irr 2 or finr 2 )
isothermal zone width referred to the fusion boundary (mm)
Avogadro constant (6.022 X 1023 moH) rate of heterogeneous nucleation (m-3 s-1)
universal gas constant (8.314 J mol-1 K"1) grain boundary or particle surface area per unit volume (m2 per m3 or mm2 per mm 3 )
rate of grain boundary nucleation (rrr2 s"1 or CITT2 s"1)
shape factor related to the wetting conditions at nucleus/ substrate interface
total number of heterogeneous nucleation sites per unit volume (rrr3)
submerged arc welding
total number of heterogeneous nucleation sites per unit volume in reference material (m~3)
shielded metal arc welding scanning transmission electron microscope time (s)
Nishiyama-Wasserman orientation relationship analytical weld metal oxygen content (wt%) probability
time taken to precipitate a certain fraction of P at an arbitrary temperature T (s) time taken to precipitate a certain fraction of (3 at a chosen reference temperature Tr (s)
polygonal ferrite
integration limits (s)
net arc power (W or kW)
cooling time from 600 to 4000C (S)
activation energy for diffusion (J mol"1 or kJ mol 1 )
cooling time from 800 to 5000C (S)
radius of precipitates (nm, Jim or m)
retention time (s) temperature (0C or K)
maximum particle radius following prolonged room temperature ageing (nm, fim or m)
undercooling or temperature interval (0C or K)
equilibrium solvus temperature (0C or K)
integration parameter half thickness of plate (jam, m)
ambient temperature (0C or K) Zener-Hollomon parameter (s"1) 0
peak temperature ( C or K) frequency factor (s"1) chosen reference temperature (0C or K)
interfacial energy between nucleus and matrix (J irr 2 )
naturally aged condition wetting angle (degrees) peak-aged condition transmission electron microscope
non-hardening (metastable) precipitates in Al-Mg-Si alloys hardening (metastable) precipitates in Al-Mg-Si alloys
voltage (V) migration rate of incoherent interface (|im s"1)
strain rate (s~!)
migration rate of semi-coherent interface (jam s"1)
parabolic thickening constant for plate-like precipitates (jam s~1/2 or m s-1/2)
upper bainite 1
welding speed (mm s" )
average value of E1 within a specific temperature range (|im s~1/2 or m s"1/2)
volume (|iim3, mm3, or m3) Vickers pyramid number
parabolic thickening constant for spherical precipitates (|im s~1/2 or m s"1/2)
Widmanstatten ferrite arc efficiency fraction transformed (corrected for physical impingement of adjacent volumes) fraction transformed (not corrected for physical impingement of adjacent volumes) fraction transformed defined by the C-curve maximum fraction of hardening precipitates which form during natural ageing
solid angle enclosed by one <100>7_Fe-pole in a standard stereographic projection of the Bain region measured electrical resistivity (nQm) electrical resistivity in solutedepleted matrix (nQm) electrical resistivity in asquenched condition (nQm)
Appendix 6.2 Additivity in relation to the Avrami Equation In order to prove that equation (6-32) is the isokinetic version of the Avrami equation, we first need to rewrite it in a differential form. From equation (6-25), we have: (A6-1)
Substituting (A6-2)
(A6-3)
into equation (A6-1) then gives:
(A6-4)
(A6-5) Provided that equation (A6-5) contains separable variables of X and t* (T), it can be integrated as follows: (A6-6)
Taking b = 1 - XIn, y = 1 - X and dy = - dX, we get:
Rearranging equation (A6-7), gives: (A6-8) where (A6-9)
Equation (A6-8) is identical with equation (6-32) in the text.
7 Properties of Weldments
7.1 Introduction Weldments are prime examples of components where the properties obtained depend upon the characteristics of the microstmcture. Since failure of welds often can have dramatic consequences, a wealth of information is available in the literature on structure-property relationships. However, in order to fit some of the apparently conflicting results into a more consistent picture, a theoretical approach is adopted here rather than a review of the literature. This procedure also involves the use of phenomenological models for the quantitative description of structure-property relationships in cases where a full physical treatment is not possible.
7.2 Low-Alloy Steel Weldments The symbols and units used throughout the chapter are defined in Appendix 7.1. The major impetus for developments in high-strength low-alloy (HSLA) steels has been provided by the need for: (i) higher strength, (ii) improved toughness, ductility, and formability, and (iii) increased weldability. In order to meet these contradictory requirements, the steel carbon contents have been progressively lowered to below 0.10 wt% C. The desired strength is largely achieved through a refinement of the ferrite grain size, produced by the additions of microalloying elements such as aluminium, vanadium, niobium, and titanium in combination with various forms for thermomechanical processing.1 This procedure has made it possible to improve the resistance of steels to hydrogen-assisted cold cracking, stress corrosion cracking, and brittle fracture initiation in the weld heat-affected zone (HAZ) region, without sacrificing base metal strength, ductility, or low-temperature toughness.2 Controlled rolled HSLA steels are currently produced with a minimum yield strength in the range from 350-550 MPa. Above this strength level, quenched and tempered steels are commonly employed. 72.1 Weld metal mechanical properties The recent progress in steel plate manufacturing technology has, in turn, called for new developments in welding consumables to produce weld metal deposits with mechanical properties essentially equivalent to the base metal.3 From the large volume of literature dealing with HSLA steel filler metals, it appears that the bulk of weld metal research over the past decade has been concentrated on the achievement of a maximum toughness and ductility for a given strength level by control of the weld metal microstructure.34 There seems to be general agreement that microstructures primarily consisting of acicular ferrite provide optimum weld metal mechanical properties, both from a strength and toughness point of view, by virtue of its high
dislocation density and small lath size. The formation of large proportions of upper bainite, Widmanstatten ferrite, or grain boundary ferrite, on the other hand, are considered detrimental to toughness, since these structures provide preferential crack propagation paths, especially when continuous films of carbides are present between the ferrite laths or plates. Attempts to control the weld metal acicular ferrite content have led to the introduction of welding consumables containing complex deoxidisers (Si, Mn, Al, Ti) and balanced additions of various alloying elements (Nb, V, Cu, Ni, Cr, Mo, B). The final weld metal microstructure will depend on complex interactions between several important variables such as:3"5 (i) (ii)
The total alloy content. The concentration, chemical composition, and size distribution of non-metallic inclusions. (iii) The solidification microstructure. (iv) The prior austenite grain size, (v) The weld thermal cycle. Although the microstructural changes taking place within the weld metal on cooling through the critical transformation temperature range in principle are the same as those occurring during rolling and heat treatment of steel, the conditions existing in welding are significantly different from those employed in steel production because of the characteristic strong nonisothermal behaviour of the arc welding process. For example, in steel weld deposits the volume fraction of non-metallic inclusions is considerably higher than that in normal cast steel products because of the limited time available for growth and separation of the particles. Oxygen is of particular interest in this respect, since a high number of oxide inclusions is known to influence strongly the austenite to ferrite transformation both by restricting the growth of the austenite grains as well as by providing favourable nucleation sites for various types of microstructural constituents (e.g. acicular ferrite). Moreover, during solidification of the weld metal, alloying and impurity elements tend to segregate extensively to the centre parts of the interdendritic or intercellular spaces under the conditions of rapid cooling.67 The existence of extensive segregations further alters the kinetics of the subsequent solid state transformation reactions. Accordingly, the weld metal transformation behaviour is seen to be quite different from that of the base metal, even when the nominal chemical composition has not been significantly changed by the welding process.3"5 This, in turn, will affect the mechanical integrity of the weldment. 7.2.1.1 Weld metal strength level In low-alloy steel weld metals there are at least four different strengthening mechanisms which may contribute to the final strength achieved. These are: (i) (ii) (iii) (iv)
Solid solution strengthening, Dislocation strengthening, Grain boundary strengthening, Precipitation strengthening.
The relative contribution from each is determined by the steel chemical composition and
the weld thermal history. Because of the number of variables involved, a full physical treatment of the problem is not possible. Consequently, the simplified treatment of Gladman and Pickering8 has been adopted here. Figure 7.1 shows the individual strength contributions in low-carbon bainite, which is the dominating microconstituent in as-deposited steel weld metals (includes both upper and lower bainite as well as acicular ferrite). Firstly, there are the solid solution strengthening increments from alloying and impurity elements such as manganese, silicon and uncombined nitrogen, which in the present example correspond to a matrix strength of about 165 MPa. Secondly, the grain size contribution to the yield stress is shown as a very substantial component, the magnitude of which is determined by the bainite lath size. Finally, a typical increment for dispersion strengthening is indicated. This contribution is negligible at large lath sizes typical of upper bainite, but becomes significant at small grain sizes because of a finer intralath carbide dispersion.8 Hence, in steel weld deposits containing high proportions of acicular ferrite or lower bainite carbides will make a direct contribution to strength, even at relatively low carbon levels. The results in Fig. 7.1 are of significant practical importance, since they show the inherent limitations of the system with regard to the maximum strength that can be achieved through control of the microstructure. As shown in Section 6.3.5.4 (Chapter 6), the typical lath size (width) of acicular ferrite in low-alloy steel weld metals is about 2 jam. According to Fig. 7.1, this corresponds to a maximum yield strength of approximately 650 MPa, which is in good agreement with the observed threshold strength of acicular ferrite containing steel weld deposits.9 If higher strength levels are required, it is necessary to decrease the grain (lath) size through a refinement of the microstructure, i.e. by replacing acicular ferrite with either lower
Yield strength, MPa
p 1/4 -f/o Number of carbides per mm Nv (mm" )
Dispersion
Grain size
Matrix strength
-1/2 Bainitic ferrite grain size, mm
Fig. 7.1. Contributions to strength in low-carbon bainite. Data from Gladman and Pickering.8
bainite or martensite. Development along these lines has led to the introduction of a new generation of high strength steel weld metals with a yield strength in the range from 650 to 900 MPa.10'11 7.2.1.2 Weld metal resistance to ductile fracture It is well established that the weld metal resistance to ductile fracture is strongly influenced by the volume fraction, shape, and size distribution of non-metallic inclusions.12"15 Although a verified quantitative understanding of the fracture process is still lacking, there seems to be general agreement that it involves the following three basic steps:16 (i)
Nucleation of internal cavities during plastic flow, preferentially at non-metallic inclusions. (ii) Growth of these cavities with continued deformation, (iii) Final coalescence of the cavities to produce complete rupture. Details of these three stages may vary widely in different materials and with the state of stress existing during deformation. Similarly, the fractographic appearance of the final fracture surface is also influenced by the same factors. Effect of inclusion volume fraction The primary variables affecting the true strain at fracture 8/ are the inclusion diameter dv, and the inclusion volume fraction Vv. The relation between Ef and Vv has been determined experimentally for a wide variety of materials, and can most simply be expressed as:17 (7-1) where c\ is an empirical constant. The tensile test data of Widgery12 reproduced in Fig. 7.2 reveal a strong dependence of £/ on Vv, but the relationship appears to be linear rather than non-linear, as predicted by equation (7-1). Due to a similar fracture mechanism, a correlation also exists between the Charpy Vnotch (CVN) upper shelf energy and the true fracture strain in tensile testing, as shown in Fig. 7.3. For this reason, the weld metal impact properties are normally seen to decrease with increasing oxygen concentrations when testing is performed in the upper shelf region. From Fig. 7.4 we see that the CVN upper shelf energy is a linear function of the weld metal oxygen content. This observation is not surprising, considering the fact that the inclusion volume fraction is directly proportional to the oxygen level (see equation (2-75) in Chapter 2). Effect of inclusion size distribution Void nucleation may occur both by cracking of the inclusions and by interface decohesion. In the former case, the critical stress for particle cracking ap is given by:16
(7-2)
where 7^ is the surface energy of the particle, Ep is the Young's modulus of the particle, A is the stress concentration factor at the particle, and dv is the particle diameter.
True fracture strain
GMAW (E=1.6kJ/mm)
Inclusion volume fraction
CVN upper shelf energy, J
Fig. 7.2. Variation of true fracture strain £/with inclusion volume fraction Vv. Data from Widgery.12
SAW and FCAW
True fracture strain Fig. 7.3. Correlation of CVN upper shelf energy with true fracture strain in tensile testing. Data from Akselsen and Grong.20 Equation (7-2) predicts that large inclusions will tend to form voids first as the stress required for initiation is proportional to (l/dv )1/2. This result is also in agreement with experimental observations. As shown in Fig. 7.5, the size distribution of inclusions located in the centre of voids at the fracture surface is significantly coarser than the corresponding particle size distribution in the material. In particular, large, angular shaped aluminium oxide (AI2O3)
CVN upper shelf energy, J
SAW
Oxygen content, wt% Fig. 7.4. Correlation of CVN upper shelf energy with analytical weld metal oxygen content. Data from Devillers et aL 13
inclusions appear to be preferential nucleation sites for microvoids in low-alloy steel weld metals (see Fig. 7.5(b)). Although the combined effect of particle size and local stress concentration on the ductile fracture behaviour cannot readily be accounted for in a mathematical simulation of the process, the CVN data in Fig. 7.6 suggest that the content of large inclusions (e.g. of a diameter greater than about 1.5 Jim) should be minimised in order to maintain a high resistance against dimpled rupture. In practice, this requires careful control of the weld metal aluminium-oxygen balance and the heat input applied during welding (see Section 2.12 in Chapter 2). Effect of strength level The toughness of a material reflects its ability to absorb energy in the plastic range. One way of looking at toughness is to assume that it scales with the total area Uj under the stress-strain curve. Several mathematical expressions for this area have been suggested. For ductile materials we may write:19 (7-3) where Rm is the ultimate tensile strength (UTS). If Uj is regarded as a material constant, one would expect that Rm and £y are reciprocal
Total inclusion population
SAW
Frequency, %
Frequency, %
Inclusions associated with dimples
Inclusion diameter, jum
Frequency, %
Total inclusion population
(b)
SAW
Inclusions associated with dimples
Frequency, %
(a)
Inclusion diameter, jum
Fig. 7.5. Histograms showing the size distribution of non-metallic inclusions in the weld metal and in the centre of microvoids at the fracture surface, respectively; (a) Low aluminium level (Al-containing manganese silicate inclusions), (b) High aluminium level (AI2O3 inclusions). Data from Andersen.18
High Ti levels CVN upper shelf energy, J
Medium Ti levels Low Ti levels
SAW
Nv (d v >1.5 um)-105 Fig. 7.6. Correlation of CVN upper shelf energy with number of particles per mm3 greater than 1.5 urn, Nv(dv > 1.5 um). Data from Grong and Kluken.15
True fracture strain
SAW and FCAW
Ultimate tensile strength, MPa Fig. 7.7. Correlation of true fracture strain with ultimate tensile strength (low-alloy steel weld metals). Data from Akselsen and Grong.20 quantities, i.e. an increase in Rm is always associated with a corresponding decrease in Ef, according to the equation: (7-4) where c^ is a constant which is characteristic of the alloy system under consideration.
It is evident from the tensile test data in Fig. 7.7 that the fracture strain is a true function of Rm, although the relationship appears to be linear rather than non-linear, as predicted by equation (7-4). These results are of considerable practical importance, since they imply that the upper shelf energy absorption, and hence, the shape of the CVN transition curve is strongly affected by the weld metal strength level. Accordingly, control of the weld metal microstructure becomes particularly urgent at high strength levels to avoid problems with the cleavage fracture resistance (to be discussed below). 7.2.1.3 Weld metal resistance to cleavage fracture Cleavage fracture is characterised by very little plastic deformation prior to the crack propagation, and occurs in a crystallographic fashion along planes of low indicies, i.e. of high atomic density.1 Body-centred cubic (bcc) iron cleaves typically along {100} planes, which implies that the cracks must be deflected at high angle grain (or packet) boundaries, as shown schematically in Fig. 7.8. Consequently, in steel weld metals the ferrite grain size and the bainite packet width are the main microstructural features controlling the resistance to cleavage crack propagation. Since the microstructure which forms within each single austenite grain will not be uniform but a complex mixture of two or more constituent phases, it is difficult, in practice, to define a meaningful grain size or packet width. For this reason, most investigators have attempted to correlate toughness with the presence of specific microconstituents in the weld metal.3"5 For example, an increase in the volume fraction of acicular ferrite will result in a corresponding increase in toughness (i.e. decrease in the CVN transition temperature), as shown in Fig. 7.9.
(a)
(b) Fig. 7.8. Schematic diagrams showing cleavage crack deflection at interfaces; (a) High angle ferriteferrite grain boundaries, (b) High angle packet boundaries (bainitic microstructures).
Transition temperature, 0C
SAW (E = 5.2-6.2 kJ/mm)
Al: 0.018-0.062 wt% Ti: 0.005 - 0.065 wt% O: 0.018-0.058 wt%
Acicular ferrite content, vol% Fig. 7.9. Correlation between the weld metal 35J CVN transition temperature and the acicular ferrite content. Data from Grong and Kluken.15 This observation is not surprising, considering the extremely fine lath size of the acicular ferrite microstructure (typically less than 5jim). Moreover, results obtained from fractographic examinations of SMA and FCA steel weld metals have demonstrated that large non-metallic inclusions (> l|im) can strongly influence the cleavage fracture resistance, either by acting as cleavage cracks themselves of by providing internal sites of stress concentration which facilitate carbide-initiated cleavage in the adjacent matrix.21'22 In the former case, the critical stress required for crack propagation in the matrix, Cf(M), is given by the Griffith's equation:19
(7-5)
where En is the Young's modulus of the matrix, ye^ is the effective surface energy (equal to the sum of the ideal surface energy and the plastic work), and c is the half crack length. Since c is proportional to the particle diameter dv, equation (7-5) predicts that welds containing large inclusions should be more prone to cleavage cracking than others. This result is also in agreement with general observations. For example, in self-shielded FCA steel weld metals it has been demonstrated that cleavage crack initiation is usually associated with large aluminium-containing inclusions which form in the molten pool before solidification (see Fig. 7.10). Consequently, control of the inclusion size distribution is essential in order to ensure an adequate low-temperature toughness. 7.2.1.4 The weld metal ductile to brittle transition In addition to the parameters mentioned above, there are several other factors, some interrelated, which play an important part in the initiation of cleavage fracture. These are:1 (i)
The temperature dependence of the yield stress.
(a)
(b)
(C)
Fig. 7.10. Initiation of cleavage fracture in a self-shielded FCA steel weld from an aluminium-containing inclusion; (a) Initiation site short distance ahead of the notch, (b) Detail of initiation site showing cracked inclusion, (c) Detail of cracked inclusion (remnants of particle are left in the hole). (ii) (iii) (iv)
Dislocation locking effects caused by interstitials or alloying elements in solid solution (e.g. nitrogen and silicon), Nucleation of cracks at twins, Nucleation of cracks at carbides.
In general, this picture is too complicated to establish a physical framework within which the various theoretical models for the ductile to brittle transition in steel can be embedded. We are therefore forced to base our judgement and understanding of how key parameters affect the position and shape of the CVN transition curve solely on scattered phenomenological observations and empirical models (e.g. see the reviews of Grong and Matlock3 or Abson and Pargeter4). An example of how far the latter approach has been developed is given below. Akselsen and Grong20 have established a series of empirical equations which relates toughness to the weld metal acicular ferrite content and the ultimate tensile strength (UTS). Figures 7.11 and 7.12 show how each of these parameters influences the CVN transition curve. It is evident from the diagrams that control of the weld metal acicular ferrite content becomes particularly important at high strength levels to avoid problems with the fracture toughness. In cases where undermatch is aimed at (i.e. a weld metal to base plate strength ratio less than unity), the weld metal tensile strength is typically of the order of 450 to 550 MPa. Within this range a volume fraction of acicular ferrite beyond 25 vol% will generally be sufficient to meet current toughness requirements (35 J at -40 0 C). If overmatch is desired, the volume fraction of acicular ferrite becomes more critical, partly because of a higher weld metal strength level and partly because of more stringent toughness requirements (e.g. 45 J rather than 35 J at -40 0 C). Process diagrams of the type shown in Figs. 7.11 and 7.12 can therefore serve as a basis for proper selection of consumables for welded steel structures. It should be noted that Akselsen and Grong20 in their analysis omitted a consideration of the important influence of free (uncombined) nitrogen and non-metallic inclusions on the CVN transition curve. Based on the experimental data in Fig. 7.13 it can be argued that such compositional variations can be equally detrimental to toughness as a decrease in the acicular ferrite content. Consequently, further refinements of the models are required if a verified quantitative understanding of the ductile to brittle transition in low-alloy steel weld metals is to be obtained. Example (7.1)
Consider multipass FCA steel welding with two different electrode wires, one with titanium additions and one without. Table 7.1 contains a summary of weld metal chemical compositions. Provided that the microstructure and the inclusion size distribution are similar in both cases, use this information to evaluate the low-temperature toughness of the welds, as revealed by CVN testing. Solution
Since the nitrogen content of both welds is quite high (0.011 wt%), the risk of a toughness deterioration due to strain ageing is imminent, particularly at low Ti levels. Taking the atomic weight of titanium and nitrogen equal to 47.9 and 14.0 g mol"1, respectively, the stoichiometric amount of titanium that is necessary to tie-up all nitrogen as TiN can be calculated as follows:
WeIdA In weld A most of the nitrogen is free (uncombined) due to an unbalance in the titanium content. This means that the risk of a toughness deterioration due to strain ageing is high.
(a)
Absorbed energy, J
Tensile strength: 600 MPa Vol% acicular ferrite
35 Joules
Test temperature, 0C
(b)
Absorbed energy, J
Tensile strength: 800 MPa
Vol% acicular ferrite
35Joules.
Test temperature, 0C Fig. 7.11. Predicted effect of weld metal acicular ferrite content on the CVN transition curve at two different tensile strength levels; (a) Rm = 600 MPa, (b) Rm = 800 MPa. Data from Akselsen and Grong.20
WeIdB Weld B contains 0.030 wt% Ti, which is not far from the stoichiometric amount of titanium necessary to tie-up all nitrogen. Although some titanium also is bound as Ti2O3, it is reasonable to assume that the free nitrogen content in this case is sufficiently low to eliminate problems with strain ageing. Consequently, weld B would be expected to exhibit the highest toughness (i.e. the lowest CVN transition temperature) of the two, as indicated in Fig. 7.14.
(a) 25 vol% acicular ferrite Absorbed energy, J
UTS
35 Joules
Test temperature, 0C
(b)
Absorbed energy, J
75 v o l % acicular ferrite
UTS
-..35J.Q.ute$-
Test temperature, 0 C
Fig. 7.12. Predicted effect of weld metal ultimate tensile strength (UTS) on the CVN transition curve at two different volume fractions of acicular ferrite; (a) 25 vol% AF, (b) 75 vol% AF. Data from Akselsen and Grong.20 Table 7.1 Chemical composition of FCA steel weld metals considered in Example (7.1). Element Weld
wt% C
wt% Si
wt% Mn
wt% Al
wt% Ti
wt% S
wt% N
wt% O
A
0.10
0.40
1.50
0.005
0.006
0.008
0.011
0.031
B
0.10
0.40
1.50
0.005
0.030
0.008
0.011
0.031
(a) SMAW (basic electrodes) Absorbed energy, J
95% confidence interval
Testing temperature: -400C
Nitrogen content, ppm (b)
Absorbed energy, J
Low content of coarse inclusions
High content of coarse inclusions ( > 1}im )
Self-shielded FCA steel weld metals Test temperature, 0C Fig. 7.13. Effect of impurities on weld metal CVN toughness; (a) Nitrogen content, (b) Inclusion level. Data from ESAB AB (Sweden) and Grong et al. 22
7.2.1.5 Effects of reheating on weld metal toughness In principle, improvement of weld properties can be achieved through a post-weld heat treatment (PWHT). This may have the benefits of:3 (i)
Enhancing the fatigue strength through a general reduction of welding residual stresses.
Absorbed energy
WeIdB
WeIdA
35 J
Test temperature, 0C Fig. 7.14. Schematic drawings of the CVN transition curves for welds A and B (Example (7.1)).
(a)
(b)
Fig. 7.15. Typical low-temperature fracture modes of Ti-B containing steel weld metals; (a) Quasicleavage (as-welded condition), (b) Intergranular fracture (after PWHT).
(ii)
Increasing the toughness by recovery (i.e. removal of strain-aged damage) and martensite tempering.
For these reasons local PWHTs are commonly required for all structural parts above a specified plate thickness (e.g. 50 mm according to current North Sea offshore specifications). Post-weld heat treatment is usually carried out in the temperature range from 550 to 6500C. In practice, however, the toughness achieved will depend on the weld metal chemical composition, and in some cases deterioration rather than improvement of the impact properties is observed after PWHT. In such cases the reduction in toughness can be ascribed to:3'4 (i)
Precipitation hardening reactions. Present experience indicates that elements such as vanadium, niobium, and presumably titanium can produce a marked deterioration in toughness because of precipitation of carbonitrides in the ferrite, provided that these elements are present in the weld metal in sufficiently high concentrations.
(ii)
Segregation of impurity elements (e.g. P, Sn, Sb and As) to prior austenite grain boundaries, which, in turn, can give rise to intergranular fracture. The indications are that this type of embrittlement is strongly enhanced by the presence of second phase particles at the grain boundaries.
Experience shows that Ti-B containing steel weld metals often fail by intergranular fracture in the columnar grain region after PWHT,23 as evidenced by the SEM fractographs in Fig. 7.15. The observed shift in the fracture mode is associated with a significant drop in toughness (Fig. 7.16) and arises from the combined action of solidification-induced phosphorus segregations and borocarbide precipitation along the prior columnar austenite grain bounda-
ACVN, J
SAW
Open symbols: 5 - 8 ppm B Filled symbols: 20 - 25 ppm B
Base line
Titanium content, wt% Fig. 7.16. Observed displacement in the CVN toughness after PWHT (ACVN) as a function of the weld metal boron and titanium contents. Negative values indicate loss of toughness. Data from Kluken and Grong.23
Fig. 7.17. TEM micrograph showing precipitation of borocarbides, Fe23(B,C)6, along prior austenite grain boundaries in a Ti-B containing steel weld metal after PWHT (600 0 C-Ih).
ries (Fig. 7.17). Since borocarbides are brittle and partly incoherent with the matrix, they can be regarded as microcracks (of length dp) ready to propagate. In such cases there is virtually no plastic deformation occurring before crack propagation, which implies that the intergranular fracture stress is given by the Griffith's equation:24 (7-6)
where 7 ^ is again the effective surface energy (equal to the sum of the ideal surface energy and the plastic work), and dp is the particle diameter. Although the value of yeg_ would be expected to be low in the presence of solidificationinduced phosporus segregations,24 this alone is not sufficient to initiate intergranular fracture in the weld metal. However, during PWHT the borocarbides will start to grow from an initially small value to a maximum size of about 0.1 to 0.2jim (Fig. 7.17), following the classic growth law for grain boundary precipitates dpatl/4?5 This implies that the intergranular fracture stress, Oj(I), will gradually decrease with increasing annealing times, as indicated in Fig. 7.18. When the matrix fracture strength, Cj(M), is reached, the fracture mode shifts from predominantly quasi-cleavage in the as-welded condition (Fig. 7.15(a)) to intergranular rupture after PWHT (Fig. 7.15(b)). This is observed as a marked reduction in the CVN toughness, as shown previously in Fig. 7.16. 7.2.2 HAZ mechanical properties The last twenty years have seen a revolution in the metallurgical design of steel. Whereas old steels relied on the use of carbon for strength, the trend today is to rely more on grain refinement in combination with microalloy precipitation to meet the current demand for an improved weldability. This includes both the sensitivity to weld cracking and the HAZ mechanical properties required by service conditions and test temperatures. The latter aspect is of particular interest in the present context and will be discussed later.
Stress
Intergranular fracture mode
Quasi-cleavage fracture mode Particle diameter
[Annealing time]174 Fig. 7.18. Schematic illustration of the mechanisms of temper embrittlement in Ti-B containing steel weld metals (Gf(M): matrix fracture strength, (*/(/): intergranular fracture strength).
p0.2> R nv M P a R
HV 5 ,kp/mm 2
Martensite content, vol%
7.2.2.1 HAZ hardness and strength level The HAZ hardness and strength level is of significant practical importance, since it influences both the cracking resistance and the toughness. Although the peak strength is mainly controlled by the martensite content (see Fig. 7.19), the relationship is generally too complicated to allow reliable predictions to be made from first principles. This implies that our understanding of the HAZ strength evolution, at best, is semi-empirical.
Cooling time, At 8 / 5 , s Fig. 7.19. Structure-property relationships in the grain coarsened HAZ of low-carbon microalloyed steels (vol% M: martensite content, Rp : 0.2% proof stress, Rm: ultimate tensile strength, HV5: Vickers hardness, A%5.* cooling time from 800 to 5000C). Data from Akselsen et al.26
A number of different empirical models exist in the literature for prediction of HAZ peak hardness and strength.26"31 However, the aptness of some of these models is surprisingly good, which justifies construction of iso-hardness and iso-strength diagrams for specific grades of steels.32 Examples of such diagrams are given in Fig. 7.20. It is evident from Fig. 7.20 that the HAZ peak strength is controlled by two main variables, i.e. the steel chemical composition and the weld cooling programme. The compositional effect is allowed for by the use of an empirical carbon equivalent, which ranks the influence of the various alloying elements on the steel hardenability. According to Yurioka et al.,2* the CEn-equivalent is given as:
(7-7) where all compositions are given in wt%. Moreover, the cooling time from 800 to 5000C, Af8/5, is used as an abscissa in Fig. 7.20. This parameter is widely accepted as an adequate index for the weld cooling programme, and can be read from nomograms of the type shown in Fig. 1.49 (Chapter 1). The axes of Fig. 1.49 are dimensionless, but they can readily be converted into real numbers through the use of the following conversion factors:33 Ordinate: (7-8)
Abscissa: (7-9) The different parameters in equations (7-8) and (7-9) are defined in Appendix 7.1. The results in Fig. 1.49 are interesting, since they show that the cooling time, A%5, depends on the mode of heat flow during welding. In this case the transition from 'thick' to 'thin' plates, corresponding to an abscissa of about 0.64, is clearly not represented by a single plate thickness d, but will be a function of both the net heat input r\E and the ambient temperature T0. Accordingly, the HAZ strength level is seen to vary between wide limits, depending on the steel chemical composition and the operational conditions applied (Fig. 7.20). Example (7.2)
Consider stringer bead deposition (GMAW) on two low-alloy steel plates of similar composition but different thickness under the following conditions: I = 250A, U = 30V, v = 5mm s"1, r| = 0.8, T0 = 200C According to the steel mill certificate the CEn carbon equivalent is equal to 0.46 wt%. Use this information together with the diagrams in Figs. 1.49 and 7.20 to estimate the peak HAZ strength level when the plate thickness is 10 and 30 mm, respectively.
CEn, wt%
(a)
Cooling time, A t 8 / 5 , s
CE||f wt%
(b)
Cooling time, At 8 7 5 , s Fig. 7.20. HAZ iso-property diagrams for HSLA steels; (a) Iso-hardness contours, (b) Iso-yield strength contours. Data from Kluken et al.32
Solution
First we calculate the net heat input per unit length of the weld r\E:
From equation (7-9) we have:
Readings from Fig. 1.49 then give: d = 10 mm:
from which
d = 30 mm:
from which
We can now use the diagrams in Fig. 7.20(a) and (b) to obtain the peak HAZ hardness and yield strength, respectively. This gives: d = 10 mm:
d = 30 mm:
It is evident from the above calculations that the HAZ strength level is sensitive to variations in the welding conditions. Normally, the HAZ hardenability is high enough to facilitate
a local strength increase adjacent to the fusion boundary, as shown in Fig. 7.21. An exception is high heat input welding on quenched and tempered steels (Fig. 7.2l(b)), where the presence of large amounts of Widmanstatten ferrite and polygonal ferrite within the grain coarsened and grain refined region, respectively can lead to a severe HAZ softening. This type of mechanical impairment represents a problem in engineering design, since it puts a restriction on the use of high strength steels in welded structures.
BM"
IR"
JfL Gf[R. GCR
BM
High strength steels.
GCR GRR
Medium strength steels
R p02 and R m ,
(a)
Low heat input welding: E^ 1 -2 kJ/mm
Medium strength steels
High strength steels
SR" BM"
TR"
GCR "GRR
,BM [SR JfL, ^GRR. QQR.
R
p0.2 and R m> MPa
(b)
High heat input welding: E^4 kJ/mm Fig. 7.21. Effects of steel chemical composition and welding conditions on the HAZ strength level (BM: base metal, SR: subcritical region, IR: intercritical region, GRR: grain refined region, GCR: grain coarsened region); (a) Low heat input, (b) High heat input. Data from Akselsen and R0rvik.34
7.2.2.2 Tempering of the heat affected zone Certain regulations for offshore structures require that no part of the welded joint shall be harder than a specified limit, e.g. 280, 300 or 325 VPN, to reduce the risk of hydrogen cracking. Such requirements cannot always be met by a suitable choice of preheating and welding conditions. In practice, a reduction in the HAZ strength level can be achieved by applying a PWHT. The tempering effect of different temperature-time combinations can be described by the Hollomon-Jaffe parameter:35 (7-10) where T is in K (absolute temperature). In Fig. 7.22 the isothermal hardness data reported by Olsen et al.36 have been plotted against the empirical Hollomon-Jaffe parameter. In this particular case the best fit is obtained if the constant B* in equation (7-10) is equal to 16.5 (with t in seconds). It is evident from Fig. 7.22 that tempering at, say, 6000C for 1 h is more than sufficient to reduce the HAZ peak hardness to values below 280 VPN. This implies that PWHT is an effective (but expensive) way of reducing the HAZ strength level. Deposition of temper weld beads has been suggested as an alternative means of reducing the hardness of the HAZ.36"38 This procedure is indicated schematically in Fig. 7.23, showing two temper beads (black) in the lower sketch. If the beads are properly positioned with respect to the fusion line, the outer Ac\ contour of the HAZ produced by the temper bead should just touch the fusion line of the last filler pass, as indicated in the upper sketch of Fig. 7.23. The material reaustenitised by the temper bead would then be weld metal, while the HAZ remaining from the last filler pass would be tempered below the transformation range.
Vickers hardness, VPN
Filled symbols: t = 10 seconds
Steel chemical composition (wt%)
F> = T(16.5 + logt) Fig. 7.22. Hollomon-Jaffe type plot of isothermal hardness data. After Olsen et al.36
Temper bead
Last filler pass
Fusion line Ac3 line Ac1 line
Fig. 7.23. Schematic illustration of weld bead tempering. Since the Hollomon-Jaffe parameter is an empirical criterion developed for isothermal tempering of medium and high carbon steels, it cannot readily be applied to pulsed tempering. A better approach would be to use the so-called Dorn parameter,39 which in an integral form can be written as:39'40 (7-11)
where Qapp. is the apparent activation energy for the controlling diffusion reaction. The Dorn parameter has proved useful to compare isothermal and pulsed tempering data on the assumption that the kinetics of softening, in the actual range of hardness, are controlled by diffusion of carbon in ferrite. Qualitatively, the aptness of equation (7-11) can be illustrated in a plot of measured hardness against the diffusional parameter P^ ( s e e Fig- 7.24). It is evident from Fig. 7.24 that the isothermal data points can be represented by a smooth curve which coincides with the upper boundary of the scatter band obtained in pulsed tempering. The slightly higher hardness observed after isothermal tempering arises probably from a brief period of heating that makes the effective time somewhat less than 10 s. Case Study (7.1)
As an illustration of principles, Fig. 7.25 shows a case of identical welding parameters for the last filler pass and the temper bead, the latter one being positioned so as to give a peak temperature of 7200C at the fusion line of the former one. The temperature field around the two
^s
1
'
Vickers hardness. VPN
Hardness ratio HV/HVmax, %
Isothermal 10 s Series 1 " 2 " 3 " 4 Double pulse
2
Fig. 7.24. Measured hardness ratio HVIHVmax. vs the Dorn parameter P2 (Qapp. = 83.14 kJ mol *). Data fromOlsentf/tf/.36
beads is clearly the same. In Fig. 7.25 an estimate has been based on the simplified Rykalin thick plate solution, which applies to a fast moving high power source on a semi-infinite body (see equation (1-73) in Chapter 1). At T-T0 ~ 15000C, a fusion line radius of about 4.4 mm is obtained for a net heat input of 0.8 kJ mm"1. The corresponding Ac\ radius is 6.5 mm. The temperature-time pattern is shown in the lower left graphs of Fig. 7.25 for three different positions in the HAZ, i.e. y = 0 (former fusion line), y = 1 mm, and y = 2 mm (z = 0). The corresponding plots of dP2 ldt vs t are shown to the right. Taking the area P2 under each curve and reading the hardness ratio at TJP^ from Fig. 7.24, an expected hardness profile is obtained, as shown in the upper diagram of Fig. 7.25. The expected effect of tempering is seen to range from a hardness of about 65% (HV « 265 VPN) at the fusion line to about 80% (HV « 340 VPN) close to the outer boundary of the HAZ (y = 2 mm). If the centre-line displacement had been different from the chosen optimum of 2.1 mm (e.g. say 3 mm), the predicted hardness curve would be shifted to about 75% and 90% of the peak hardness at y = 0 and y = 2 mm, respectively. On the other hand, if the centre-line distance had been shorter, say 1 mm, a narrow zone of the original HAZ would be re-austenitised and therefore about as hard as before deposition of the temper bead. The results from the above modelling exercise show that the HAZ hardness of weld toes and cap layers can be reduced by applying an appropriate temper bead technique. However, this requires an extremely good process control, since the temper beads must be positioned very precisely for a successful result. Consequently, the use of temper beads for improvement of the HAZ properties has not found a wide application in the industry.3641 7.2.2.3 HAZ toughness In spite of the recent developments in steel plate manufacturing technology, there is still concern about the HAZ toughness of low-carbon microalloyed steels because of their tendency to
max
HV/HV
last filter pass
temper bead
y, mm
HA2
Parent plate
106exp(-10000/T)
T, 0C
We d metal
t,s
t,s
Fig. 7.25. Application of Dorn parameter to weld bead tempering (Case Study (7.1)). form brittle microstructures within specific thermal regions of the weld. 4142 Moreover, improvement of the HAZ toughness through PWHT is sometimes found to be difficult in contrast to experience with more traditional C-Mn steels.41'43 Consequently, the increasing use of lowcarbon microalloyed steels in various welded structures has introduced new problems related to the HAZ brittle fracture resistance which formerly did not appear to be of particular concern.44 Fully transformed region Specific effects of peak temperature on HAZ toughness, as assessed on the basis of thermally cycled CVN specimens, are shown in Fig. 7.26. It is apparent from the graph that embrittlement in the fully transformed part of the HAZ is often located in the grain coarsened region adjacent
I SR R
G C R
G R R
-3
(D
c O
I
Sn igel cycel 0
Peak e tmperau tre,C Fig. 7.26. Effects of peak temperature on the CVN energy absorption at -400C (SR: subcritical region, IR: intercritical region, GRR: grain refined region, GCR: grain coarsened region). Data from Akselsen et a/.45 to the fusion boundary where the peak temperature of the thermal cycle has been above about 12000C. The problem can mainly be ascribed to the presence of low-toughness microstructures such as upper bainite and Widmanstatten ferrite which form typically at intermediate and slow cooling rates (see Fig. 6.55 in Chapter 6). In contrast, the grain refined region will almost always exhibit a satisfactory low-temperature toughness owing to the characteristic fine polygonal ferrite microstructure.41 An exception is low heat input welds produced from steels with a heavily banded pearlite/ferrite microstructure, where the risk of a toughness deterioration is imminent due to martensite formation along the prior base metal pearlite bands.45'46 In recent years a new class of low-carbon microalloyed steels has emerged which is characterised by an excellent low temperature HAZ toughness, even at high heat inputs (see Fig. 7.27). This particular grade is frequently referred to as Ti-O steels due to their content of indigenous titanium oxide inclusions (presumably Ti2O3). Although the mechanisms involved are not yet fully understood, it is reasonable to assume that the improved toughness at high heat inputs arises from a refinement of the HAZ microstructure, as discussed previously in Section 6.3.6 (Chapter 6). It is interesting to note that the major effect of the titanium oxide inclusions in this case appears not to be control of the austenite grain size (which in some cases can exceed 500 |im at the fusion boundary), but is rather to act as favourable nucleation sites for acicular ferrite intragranularly.4748 Similar phenomena are well known from transformation kinetics of low-alloy steel weld deposits, where non-metallic inclusions play an important role in the development of the acicular ferrite microstructure.3"5 Intercritical region The microstructural evolution in the intercritical HAZ of low-carbon steels has previously been discussed in Section 6.3.8.2 (Chapter 6). In order to understand the origin of embrittlement in the intercritical region, consideration must be given to the stress fields and the transformation strains developed in the ferrite matrix
Transition temperature, 0C
Ti-O steel Ti-N steel
Peak temperature, 0C Fig. 7.27. Response of modern Ti-O steels and traditional Ti-N steels to CVN testing following weld thermal simulation. Data from Homma et al.41 as a result of the martensite formation.49 It follows from Fig. 7.28 that the hard martensiteaustenite (M-A) islands will give rise to significant stress concentrations at the martensite/ ferrite interface owing to the pertinent difference in the yield strength (stiffness) between the two phases. At the same time, the volume expansion associated with the austenite to martensite transformation leads to significant elastic and plastic straining of the ferrite.50 At moderately high temperatures and deformation strains, many of the matrix dislocations will be mobile, which means that the ferrite will maintain its ductility, while the stiffer M-A islands are exposed to cracking and debonding. With increasing strain, the cracks can grow into voids and further develop into deep holes, until final rupture occurs by hole/void coalescence due to internal necking.49 However, when mechanical testing is performed at subzero temperatures under high strain rate conditions (> 102 s"1 for CVN testing), the flow strength of the ferrite increases significantly because of the reduced mobility of the screw dislocations.51 In addition, strain partitioning between the M-A islands and the ferrite may also occur, which further enhances the stress concentrations at the M-A/ferrite interface.52 Accordingly, the local stress level at the interface will eventually exceed the cleavage strength of the ferrite, with consequent initiation of brittle fracture. This conclusion is consistent with observations made from tensile testing of dual-phase steels, showing that failure of dual-phase microstructures often is caused by fracture in the ferrite region.52"54 Because the intercritical HAZ toughness is closely related to the volume fraction of the M-A constituent in the matrix, 4 5 5 1 5 5 embrittlement can normally be avoided by decreasing the cooling rate through the critical transformation temperature range to facilitate pearlite formation (see Fig. 7.29). An exception is boron-containing steels, where the HAZ hardenability is high enough to stabilise the M-A constituent, even at slow cooling rates (see CVN data for steel B in Fig. 7.29).
Normalized stress Stiff particle Normalized distance
Absorbed energy, J
Fig. 7.28. Stress distribution in matrix caused by stiff inclusion (or: radial stress, (5$: tangential stress, tmax.' maximum shear stress). Data from Chen et al.49
Open symbols: Filled symbols:
Steel A (T-L)
(L-T) Steel B
(T-L)
Cooling time, At 6 / 4 , s Fig. 7.29. Effect of cooling time Ar674 on the intercritical HAZ toughness at -20 0 C (thermally cycled specimens). Steel A: 11 ppm B, Steel B: 26 ppm B. Data from Ramberg et al.55
Effect of PWHT Considering the intercritical HAZ, a significant improvement of the CVN toughness can be achieved by applying a PWHT, as shown by the data of Akselsen et al51 This effect arises partly from a reduction of the stress concentrations at the M-A/ferrite interface as a result of martensite tempering and partly from relaxation of transformation strains within the ferrite matrix.51 Such recovery reactions will start to occur when the temperature is raised above about100 0 C.
(a)
CTOD at -1O0C, mm
(b)
P content, wt% Fig. 7.30. Effects of PWHT on the grain coarsened HAZ toughness; (a) Example of intergranular fracture along prior austenite grain boundaries after PWHT (6000C - 1 h), (b) Measured CTOD vs base plate phosphorus content for post weld heat treated specimens (6000C - 4 h). Data quoted by Grong and Akselsen.41
In contrast to the behaviour described above for the intercritical HAZ, the reported effect of PWHT on the grain coarsened HAZ toughness is much more complicated and rather confusing. However, experience has shown that particularly niobium-vanadium containing steels are sensitive to PWHT due to the strong precipitation hardening potential of Nb(C,N) and V(C,N).43'56 In addition, a toughness deterioration may occur as a result of segregation of impurity elements such as phosphorus, tin, and antimony to prior austenite grain boundaries. This, in combination with a tempered martensitic microstructure, can lead to intergranular
fracture when testing is performed at subzero temperatures (see Fig. 7.30(a)). The detrimental effect of phosphorus on the HAZ toughness of low carbon microalloyed steels after PWHT is shown in Fig. 7.30(b). Example (7.3)
Consider procedure test SA welding on a thick plate of a Nb-microalloyed steel under the following conditions: / = 500A, U = 30V, v = 6mm s"1, r\ = 0.95, T0 = 200C Table 7.2 contains data from CVN testing of the base plate and thermally cycled specimens. The weld thermal simulation experiments were carried out at three different peak temperatures (i.e. 13500C, 10000C, and 7800C) under cooling conditions similar to those employed in the SA welding trial. Based on the data in Table 7.2 and the simplified Rykalin thick plate solution (equation (1-73) in Chapter 1), estimate the locations of the brittle zones (referred to the fusion boundary) within the HAZ of the SA procedure test weld considered above. Solution
It is evident from the CVN data in Table 7.2 that the HAZ toughness would be expected to be low in positions of the weld where the peak temperature has been close to 780 and 13500C, conforming to the intercritical and grain coarsened region, respectively. Based on the simplified Rykalin thick plate solution, the following expression can be derived for an arbitrary isothermal zone width, Ar*m, referred to the fusion boundary (see equation (5-47) in Chapter 5):
Taking pc and Tm equal to 0.005 J mm"3 0C"1 and 15200C, respectively for low-alloy steels (from Table 1.1 in Chapter 1), we obtain: Table 7.2 Results from CVN testing of base metal, thermally cycled specimens, and procedure test weld (Example (7.3)) Test results
Absorbed energy at -40 0 C (J)
Base metal Thermally cycled specimens Weld HAZ* 1
320, 310, 305; average: 312 0
Tp = 780 C T = 10000C 7;= 13500C
40, 36, 34; average: 37 225, 220, 219; average: 221 50, 46, 40; average: 46
GCR: 63, GRR: 225, IR: 53
GCR: grain coarsened region; GRR: grain refined region; IR: intercritical region.
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Intercritical HAZ (Tp « 7800C):
Grain coarsened HAZ (Tp « 13500C):
From this we see that the brittle zones are located 3.5 and 0.5 mm from the fusion boundary, respectively. A comparison with the procedure test results in Table 7.2 shows that the measured CVN toughness after welding at these locations is slightly higher than that inferred from the weld thermal simulation experiments. This observation is not surprising, considering the fact the CVN specimens extracted from the procedure test weld, in practice, include a wide spectrum of thermal regions which have undergone highly different temperature-time programmes, whereas the microstructure within the thermally cycled CVN specimens is more homogeneous due to a similar temperature-time pattern across the whole gauge length (see Fig. 7.31). Hence, weld thermal simulation cannot replace procedure testing carried out on real welds. Nevertheless, it is a useful method of evaluating the microstructural stability and mechanical response of materials to reheating, as experienced in welding. 7.2.3 Hydrogen cracking Hydrogen embrittlement as a problem is mainly associated with ferritic steels and the risk of crack initiation in the grain coarsened HAZ following welding.5758 As shown in Fig. 7.32, these cracks are usually situated at weld toes, weld root, or in an underbead position. Occationally, hydrogen cracks can also develop in the weld metal. A characteristic feature of hydrogen-induced cracking is that the process is time-dependent, i.e. the crack may first appear after several minutes or hours from the time of arc extinction. Consequently, the phenomenon is also referred to delayed cracking or cold cracking in the scientific literature. 7.2.3.1 Mechanisms of hydrogen cracking Hydrogen embrittlement in steels in characterised by:59'60 (i)
The crystal structure dependence Hydrogen embrittlement is mainly associated with materials which exhibit a bcc or a bet crystal structure, i.e. ferritic and martensitic steels. Austenitic stainless steels and aluminium alloys with a fee crystal structure are usually not sensitive to hydrogen.
(ii)
The microstructure dependence A martensitic steel is generally more prone to hydrogen cracking than a ferritic steel, but a martensitic microstructure is not a requirement for crack initiation.
Previous Page
Intercritical HAZ (Tp « 7800C):
Grain coarsened HAZ (Tp « 13500C):
From this we see that the brittle zones are located 3.5 and 0.5 mm from the fusion boundary, respectively. A comparison with the procedure test results in Table 7.2 shows that the measured CVN toughness after welding at these locations is slightly higher than that inferred from the weld thermal simulation experiments. This observation is not surprising, considering the fact the CVN specimens extracted from the procedure test weld, in practice, include a wide spectrum of thermal regions which have undergone highly different temperature-time programmes, whereas the microstructure within the thermally cycled CVN specimens is more homogeneous due to a similar temperature-time pattern across the whole gauge length (see Fig. 7.31). Hence, weld thermal simulation cannot replace procedure testing carried out on real welds. Nevertheless, it is a useful method of evaluating the microstructural stability and mechanical response of materials to reheating, as experienced in welding. 7.2.3 Hydrogen cracking Hydrogen embrittlement as a problem is mainly associated with ferritic steels and the risk of crack initiation in the grain coarsened HAZ following welding.5758 As shown in Fig. 7.32, these cracks are usually situated at weld toes, weld root, or in an underbead position. Occationally, hydrogen cracks can also develop in the weld metal. A characteristic feature of hydrogen-induced cracking is that the process is time-dependent, i.e. the crack may first appear after several minutes or hours from the time of arc extinction. Consequently, the phenomenon is also referred to delayed cracking or cold cracking in the scientific literature. 7.2.3.1 Mechanisms of hydrogen cracking Hydrogen embrittlement in steels in characterised by:59'60 (i)
The crystal structure dependence Hydrogen embrittlement is mainly associated with materials which exhibit a bcc or a bet crystal structure, i.e. ferritic and martensitic steels. Austenitic stainless steels and aluminium alloys with a fee crystal structure are usually not sensitive to hydrogen.
(ii)
The microstructure dependence A martensitic steel is generally more prone to hydrogen cracking than a ferritic steel, but a martensitic microstructure is not a requirement for crack initiation.
(a)
Specimen holder [Homogeneous zone CVN-specimen Notch location
(b)
Notch location
Weld metal
CVNspecimen
Base metal
Grain coarsened HAZ Grain refined HAZ Fig. 7.31. Methods for evaluation of HAZ toughness (schematic); (a) Weld thermal simulation, (b) Weld procedure testing. (b)
(a)
HAZ
Root crack
Toe crack Underbead crack
Transverse crack
Toe irack Underbead crack HAZ
Fig. 7.32. Schematic diagrams showing hydrogen-induced cracks in different types of welds; (a) Fillet weld, (b) Butt weld. The diagrams are based on the ideas of Coe.57
True fracture strain
5%/min
Uncharged
104%/min Uncharged
Charged Charged
5x105%/min Uncharged
1.9x106%/min
Charged
Charged Uncharged
Test temperature, 0C Fig. 7.33. Variation of true fracture strain with nominal strain rate and test temperature for charged and uncharged specimens. Data from Brown and Baldwin.59
(iii) The strain rate dependence Hydrogen embrittlement is most prominent at low strain rates typical of tensile testing, as shown in Fig. 7.33. At high strain rates the hydrogen diffusion is not fast enough to keep pace with the fracture development. (iv)
The temperature dependence Hydrogen cracking occurs usually within the temperature range from -150 to +2000C. This temperature dependence reflects the fact that both the hydrogen concentration and the stress intensity at the crack tip must exceed some critical value before crack propagation occurs.
(v)
The time dependence Since hydrogen embrittlement is a diffusion-controlled process, the cracks will propagate in a stepwise manner to allow for supply of hydrogen from the surrounding matrix to the crack tip (see Fig. 7.34).
Over the years a number of mechanisms have been proposed to explain the origin of hydrogen embrittlement. The three most important are:
Fracture
Fracture
-8 Resistance change x 10 ,Q.
Applied stress: 1240MPa Applied stress: 1100MPa
Time, min Fig. 7.34. Example of stepwise crack propagation in notched tensile specimens, as inferred from electrical resistivity measurements. Data from Steigerwald et a/.60
(a)
The hydrogen gas pressure model, originally proposed by Zapfee and Sims,61 which postulates that atomic hydrogen will diffuse to microvoids where it recombines to form molecular hydrogen. In ferritic steels the equilibrium H2(g) pressure within the microvoids is typically of the order of 106 to 107 atm, which is more than sufficient to bring about a local fracture development.
(b)
The surface energy model (Petch62). According to this model hydrogen will reduce the effective surface energy of the crack. Under such conditions the crack can propagate at a lower nominal stress in the presence of hydrogen, in agreement with the Griffith's theory (equation (7-5)).
(c)
The slip softening model of Beachem,63 which accounts for the experimental observation that hydrogen-charged specimens generally exhibit a lower flow stress than hydrogen-free specimens. This suggests that hydrogen interfers with dislocations in a manner which facilitates different types of fracture, including micro void coalescence (or dimpled rupture), quasicleavage fracture, and intergranular fracture.64
Currently, it cannot be stated with certainty which of these three mechanisms that are operative under the conditions existing in welding. However, this question is of minor importance in the present context, since we here are mainly concerned with the factors responsible for hydrogen cracking in steel weldments.
7.2.3.2 Solubility of hydrogen in steel Since hydrogen is the smallest of all atoms, it is readily soluble in iron. In general, both octahedral and tetrahedral lattice sites are potential traps for interstitials, as indicated in Fig. 7.35. In the case of hydrogen it is believed that the dissolved atoms are mainly present in tetrahedral positions in the form of protons.65 Because of the pertinent difference in the size of the fee and the bcc interstices (see Fig. 7.35), the hydrogen solubility in iron will change stepwise with temperature following the bfe —> yFe and yFe —> aFe transformations, as shown previously in Fig. 2.7(c) (Chapter 2). (a)
Metal atom Octahedral interstices (Size: 0.15 aQ)
Metal atom Tetrahedra! interstices (Size: 0.08 aQ)
Metal atom Octahedral interstices (Size: 0.07 a0)
Metal atom Tetrahedral interstices (Size: 0.13 a 0)
(b)
Fig. 7.35. Schematic representation of octahedral and tetrahedral lattice sites in different crystal structures; (a) Face-centred cubic (fee) structures, (b) Body-centred cubic (bcc) structures.
In addition to the interstitial fraction, hydrogen may be present in the form of molecular (gaseous) hydrogen trapped in micro voids or plane lattice defects. This amount is frequently referred to as residual hydrogen, and can in many cases overshadow the equilibrium hydrogen content. For example, at room temperature the maximum solubility of atomic hydrogen in the iron lattice is estimated to be 0.001 to 0.01 ppm, while the analytical hydrogen content of steels varies typically from 1 to 10 ppm. This supersaturation is formidable and provides the necessary driving force for trapping of gaseous hydrogen in the microstructure. 7.2.3.3 Diffusivity of hydrogen in steel Published data for the diffusivity of hydrogen in steels are summarised in Fig. 7.36. At high temperatures, the diffusivity of hydrogen in ferritic steels is in reasonable agreement with the reported value for lattice diffusion of hydrogen in bcc iron. However, when the temperature drops below say 2000C, both the scatter and the discrepancy become more apparent due to the phenomenon of hydrogen trapping. Inclusion of the trapping effect has led to the introduction of an apparent diffusion coefficient for hydrogen in ferritic steels, D%pp , which according to Oriani66 is given by:
(7-12)
where D^ is the lattice diffusion coefficient for hydrogen in bcc iron, K is the density of trap sites (i.e. number of trap sites per number of lattice sites), and EB is the binding energy between hydrogen and the trap site. A graphical representation of equation (7-12) is shown in Fig. 7.36. A closer inspection of the graph reveals that the predicted temperature dependence of the apparent diffusion coefficient is in fair agreement with the reported diffusivity data for hydrogen in steel. Moreover, it is interesting to note that the hydrogen diffusion coefficient in austenite is nearly two orders of magnitude lower than the corresponding value for the ferrite phase at a given temperature. This observation is not surprising, considering the pertinent difference in the packing density between the fee iron lattice and the bcc iron lattice (74% and 68%, respectively). Thus, for diffusion of hydrogen in austenite, we have:57 (7-13) where T is the absolute temperature (in K). 7.2.3.4 Diffusion of hydrogen in welds The thermodynamics and kinetics of hydrogen absorption in the weld pool have previously been discussed in Section 2.8 (Chapter 2). Since hydrogen is a very mobile atom (and therefore is easily lost to the surroundings), the hydrogen concentration will vary both in the longitudinal direction and in the through thickness direction of the weld, as shown in Fig. 7.37. This process will continue even after the weld has cooled down to room temperature due to the characteristic high diffusivity of atomic hydrogen in ferrite (see Fig. 7.38).
Hydrogen diffusion coefficient, m2/s
Temperature, 0C
Ferritic steels Trapping theory
Austenitic steels
1000/T1K'1 Fig. 7.36. Summary of reported diffusion coefficients of hydrogen in iron and steel. Data compiled by Coe57 and Yurioka and Suzuki.58 Several successful attempts have been made in the past to model hydrogen diffusion in welds by means of numerical methods.68"70 Unfortunately, none of these solutions are simple enough to get a good overall indication of the hydrogen redistribution during cooling and subsequent PWHT. As an illustration of principles, we shall therefore present a simplified analytical solution to the hydrogen diffusion problem in welding, based on an analogy between diffusion and heat conduction. Diffusion model The idealised model considers a butt weld of uniform hydrogen concentration in the longitudinal direction, as shown in Fig. 7.39. The width of the fusion zone is 2L, while the initial hydrogen concentration at the time of solidification (i.e. at t = 0) is Q. The hydrogen concentration in the base metal outside the fusion zone is C0. If element losses to the surroundings are neglected, the problem can be treated as uniaxial diffusion in an isotropic solid analogous to that described in Section 1.7 (Chapter 1) for heat conduction in thermit welding. Thus, in the limiting case where the diffusion coefficient can be regarded as constant, the hydrogen concentration ( Q as a function of time (t) and distance (y) is given by equation (1-22):
ml H 2 /10Og
Deposited metal
Fused metal
Position x, mm ml H 2 /100g
Mean value
10 mm
Diffusible Residual
Fig. 7.37. Measured longitudinal and lateral distributions of hydrogen in a single pass SMA weld quenched right after welding. Data from Christensen et al.61
(7-14)
where D** is the hydrogen diffusivity, and erf(u) is the Gaussian error function (defined previously in Appendix 1.3, Chapter 1). In practice, it is necessary to rewrite equation (7-14) in a differential form to allow for the variation in the hydrogen diffusion coefficient with temperature. After some manipulation, we obtain: (7-15)
H I/cm3
15 mm p. I/cm3
a)
b)
Fig. 7.38. Redistribution of hydrogen following welding (numerical calculations); (a) Right after welding, (b) After 12 h at room temperature (ljil cm"3 = 0.0115 ppm). Data from Christensen.68
Fusion zone
Fig. 7.39. Sketch of idealised hydrogen diffusion model.
This differential equation can be integrated numerically in temperature-time space when the weld thermal programme is known. The boundary conditions are as follows:
when
when
when
when Case Study (7.2)
Although the above model does not give a true physical picture of the hydrogen redistribution in butt welds, it may provide valuable quantitative information about the extent of hydrogen diffusion occurring during cooling from the solidification temperature under different welding conditions. Figure 7.40(a) shows a sketch of a 2mm thick single pass butt steel weld made by means of the GTA process. For the purpose of convenience we shall assume that the temperature field around the heat source is given by the simplified Rykalin thin plate solution (equation (1-100) in Chapter 1). Thus, at (T-T0)= 15000C a total width of the fusion zone of about 4.3mm is obtained for a net heat input of 67.2 J mm"2. The corresponding distance from the weld centre-line to the 13500C HAZ isotherm is 2.5mm. Figure 7.40(b) shows computed temperature and hydrogen concentration profiles at the centre of the weld (y = 0) and in the grain coarsened HAZ (y = 2.5mm) for a chosen ambient temperature of 200C (no preheating). As expected, the hydrogen concentration within the fusion zone itself (v < L) decreases in a monotonic manner as the weld cools down. In contrast, the hydrogen concentration outside the fusion zone (y > L) is seen to pass through a local maximum. In the absence of preheating this maximum is attained after very long times, which may initiate hydrogen cracking in the grain coarsened HAZ if the microstructure is martensitic. The picture is completely changed if the ambient temperature is raised to 1000C (moderate preheating). As shown in Fig. 7.40(c), the main effect of preheating is to decrease the cooling rate in the low-temperature regime (i.e. below 5000C) after the completion of the austenite to ferrite transformation. The HAZ microstructure is therefore not significantly altered, but instead more hydrogen is allowed to diffuse out of the weld region before the temperature drops below the critical value where hydrogen cracking may occur. This is seen as a shift in the peak hydrogen concentrations towards lower absolute values and shorter times in Fig. 7.40(c). 7.2.3.5 Factors affecting the HAZ cracking resistance Safety against hydrogen cracking is an important aspect of weldability. In spite of the knowledge accumulated and the improvements made over the past decades, the current trends towards stronger steels and heavier sections still require continuous attention to the risk of cracking. Cold cracking test methods In principle, a proper weldability criterion should enable the user to select combinations of steel, consumables and operational conditions that will ensure sufficient crack safety at a minimum of total cost. It should also enable him to examine the effects of these main variables separately and establish a quantitative grading system for safety which takes into account the consequences of failure. In recognition of this situation, a number of empirical cracking test methods has been de-
HAZ
iaiMMlTOMsl
Tp = 1 3500C
(b) Solid curves: Centre - line Broken curves: HAZ T0 = 200C
Hydrogen concentration
(C-C0)Z(C1-C0)
Temperature, 0C
Temperature-time programme
Time, s (C) Solid curves: Centre - line Broken curves: HAZ T0 = IOO0C
Hydrogen concentration1
(C-C0)Z(C1 -C 0 )
Temperature, 0C
Temperature-time programme
Time, s Fig. 7.40. Computed temperature and hydrogen concentration profiles during GTA butt welding of a 2mm thin steel sheet (Case Study (7.2)); (a) Sketch of weld, (b) Redistribution of hydrogen in the absence of preheating, (c) Redistribution of hydrogen after preheating to 1000C.
veloped over the years to study the mechanisms of hydrogen cracking in weldments (e.g. see the review of Yurioka and Suzuki58). Broadly speaking, the cold cracking tests fall into either one of the two categories, i.e. self-restrained tests or externally loaded tests. Examples of the former type are the Tekken (oblique Y-groove) cracking test, the CTS (controlled thermal severity) cracking test, and the cruciform cracking test. Well-known externally loaded tests are the implant cracking test, the TRC (tensile restraint cracking) test, and the RRC (rigid restraint cracking) test. The implant method The implant technique is a good example of a cracking test method which allows separate assessment of the various metallurgical and operational factors that contribute to hydrogen cracking in welds. As shown in Fig. 7.41 the Scandinavian version of the implant test employs a cylindrical test bar made from the steel to be examined which is notched (threaded) at some distance from one of its ends.71 The bar is inserted into a reamed hole in the backing plate of a similar grade of steel, so that the threaded end is flushed with the plate surface. In order to execute a test, the hole is sealed off with a single weld bead deposited on the plate under carefully controlled conditions. After a specified delay of 60 s per kJ mm"1 gross heat input, the implant assembly is quenched and put under a static tensile load at room temperature. The stress applied is subsequently reported on the nominal cross-section of the bar. After a specified loading time (if no rupture has occurred), the assembly backing plate with the test bar may be sectioned and examined with respect to microcracks in the HAZ. The implant test may be performed at different stress levels, cooling rates and hydrogen contents. The implant rupture strength, RIR, is obtained in a programme of stepwise loading, going down or up by a fixed amount depending on rupture or not. It is then defined as the nominal stress at which the statistically probability of rupture is 50% when the load is applied for a long period. Implant test results The critical stress for rupture in the Scandinavian version of the implant test may be written in a differential form as a sum of four contributions: Test weld
Implant test
Tensile load Fig. 7.41. Schematic representation of the implant test method.
Backing plate
(7-16)
The CEW parameter in equation (7-16) refers to the so-called HW carbon equivalent, originally developed for C-Mn steels: (7-17) Moreover, A/333 is a hydrogen diffusional parameter which takes into account variations in the measured implant rupture strength after various thermal treatments (including preheating and PWHT). According to Christensen and Simonsen,71 the extent of hydrogen diffusion which occurs in the low-temperature regime can be reported in the form of an equivalent isothermal hold time at 6O0C (or 333K), defined as:
(7-18)
where Tc refers to the local HAZ temperature at the moment of quenching (usually taken as 1000C). It follows from equation (7-16) that the two first members reflect the influence of microstructure upon the implant rupture strength, and is therefore related to the HAZ peak hardness. The two last members take into account the effect of analytical HFM and local hydrogen concentrations. As shown in to Fig. 7.42, the numerical values of the partial derivatives dRIR/ dCEw, dRIR/dAts/5, 3RIR/3 log HFM, and dRIR I B^At333 may vary within relatively wide limits, depending on the steel chemical composition and the operational conditions applied. Nevertheless, the concept is still useful for quantitative predictions of the HAZ cracking resistance, as illustrated below. Example (7.4)
Experience has shown that conventional pipeline steels with carbon equivalent CEW up to 0.4% can be welded with basic electrodes (Af8/5 ~ 8-9 s) without the use of external preheating, provided that the weld metal hydrogen content is kept sufficiently low (HFM ~ 4 ppm). Suppose that the same procedure shall be employed in hyperbaric welding of pipeline steels at a depth of 320 m (33 bar total pressure). Based on the implant test data in Fig. 7.42, estimate the minimum reduction in the steel carbon equivalent (ACEW) which must be incorporated in the specifications to compensate for the increased hydrogen absorption observed at such depths (#FM-10ppm). Solution
The concept of partial derivatives implies that we will have the same safety against hydrogen cracking if there is no net change in the implant rupture strength (i.e. ARm = 0). Since the weld
(a)
R|R,MPa
HSLA steels
CEW,% (b)
R|R, MPa
HSLA steel
At8/5, S Fig. 7.42. Examples of implant test results: (a) Rm vs CEW, (b) RIR vs Ar8/5. cooling programme is similar in both cases, the variation in A/8/5 and ^At333 Hence, equation (7-16) reduces to:
can be neglected.
(C)
R1R, MPa
HSLA steel
HFM, ppm
R|R, MPa
(d)
Quenched and tempered steels
^ • • " Fig. 7.42. Examples of implant test results (continued); (c) RIR vs HFM, (d) RIR vs -^Ar333 . Data from Christensen and Simonsen.71
In the present example the total change in the weld metal hydrogen content between 1 and 33 bar is equal to:
Moreover, the numerical values of dRIR/dCEw and dRIR/d log HFM can be read from Fig. 7.42(a) and (c), respectively. When A/8/5 ~ 8.6 s, we obtain:
and
This gives:
The above calculations suggest that the CEW carbon equivalent of pipeline steels should not exceed 0.35% if hydrogen cracking is to be avoided under hyperbaric welding conditions. 7.2.4 H2S stress corrosion cracking Hydrogen sulphide (H2S) stress corrosion cracking is a well-known phenomenon taking place in steels in environments containing sour oil and gas. As shown in Fig. 7.43 this type of cracking arises from corrosion reactions with subsequent absorption of hydrogen in the metal. The embrittlement mechanisms are therefore similar to those reported for hydrogen cracking in steels, and can be evaluated from standard test methods.72 7.2.4.1 Threshold stress for cracking For a given combination of steel, microstructure and H2S concentration there exists a lower limit for the imposed stress where cracking no longer will occur. Experience has shown that the threshold stress, vth, is related to the yield strength RpQ2 through the following equation:73 (7-19) Equation (7-19) predicts that the threshold stress (and thus the steel cracking resistance) passes through a local maximum as the yield strength increases. The locus of this peak stress is obtained by setting dath/dRpo2 = 0, which gives Rpo2 ~ 600MPa and crth (max) ~ 360MPa. In practice, a hardness criterion rather than a yield strength criterion is used for ranking of steels with regard to H2S stress corrosion cracking resistance. According to Dieter,19 the following relation exists between Rpo and HV: (7-20) where m is the strain hardening exponent in the Ludwik equation. The value of m may vary between wide limits, depending on the steel chemical composition and the heat treatment conditions applied, but for HSLA steels m ~ 0.15 is a reasonable compromise.19 In that case the observed maximum in the cracking resistance at Rp02 ~600MPa
Short distance between anode and cathode sites Stress Anode:
Crack
Embrittled zone Cathode:
Stress Fig. 7.43. Mechanisms of hydrogen absorption in cathodic stress corrosion cracking (schematic). corresponds to a hardness of about 250VPN. This value should be compared with the maximum hardness level of 22HRC (Rockwell C) or 248VPN incorporated in many offshore specifications. 7.2.4.2 Prediction of HAZ cracking resistance Prediction of the H2S stress corrosion cracking resistance based on equation (7-19) requires quantitative information about the HAZ strength level. The peak strength for various combinations of steels and welding conditions can easily be read from diagrams of the type shown in Fig. 7.20 or calculated from diverse empirical formulae.2674 Figure 7.44 shows examples of computed cr^ - At^ profiles for three different types of steels spanning a range in the CEn carbon equivalent from 0.41 to 0.50%. It is evident from these plots that the cooling time required to obtain the maximum threshold stress depends on the steel chemical composition. In general, ultra-low-carbon steels will exhibit the highest resistance against stress corrosion cracking, since a low HAZ hardenability will eliminate problems with martensite formation in the grain coarsened region during the 7 to a transformation. On the other hand, these steels suffer from a severe HAZ softening during high heat input welding, with consequent reduction in the threshold stress. Under such conditions it may be safer to use ordinary low-carbon microalloyed steels or C-Mn steels with a higher HAZ hardenability to compensate for the observed strength loss. Equation (7-19) can also be employed for assessment of the relevance of current hardness requirements. Figure 7.45 shows the same types of plots as in the preceding figure (on a normalised scale) where typical ranges for the HAZ hardness are indicated. It is evident that the threshold stress is rather insensitive to small variations in the hardness level. Only in cases where the HAZ hardness exceed 300VPN or drops below say 220VPN a significant deterioration in the H2S stress corrosion cracking resistance is to be expected. This suggests that the maximum hardness requirement of 248VPN incorporated in many offshore specifications is too stringent, since it imposes severe restrictions on the use of steels in welded structures without improving the service performance to any great extent.
Threshold stress, MPa
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Ultra-low-carbon steel Low-carbon steel C-Mn steel
A
WS
Normalized threshold stress
Fig. 7.44. Computed a f/l -A% 5 profiles for selected steels.
Ultra-low-carbon steel Low-carbon steel C-Mn steel
A
w
s
Fig. 7.45. Effect of peak hardness on the HAZ stress corrosion cracking resistance.
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7.3 Stainless Steel Weldments Stainless steels are widely used in various industries where corrosion is of particular concern. These materials can be classified into four main categories, based on their microstructure: (i) (ii) (iii) (iv)
Austenitic stainless steels. Austenitic-ferritic (duplex) stainless steels. Ferritic stainless steels. Martensitic stainless steels.
As shown in Table 7.3, the welding of stainless steels is encumberred by a number of different metallurgical problems, including solidification cracking, hydrogen cracking, precipitation reactions, and grain growth. Some of these problems will be discussed below in the light of information available in recent literature.75"78 7.3.1 HAZ corrosion resistance Austenitic stainless steels containing about 0.07 wt% carbon or more are often susceptible to intergranular corrosion in the weld HAZ due to chromium carbide precipitation (see Section 6.4 in Chapter 6). This phenomenon is frequently referred to as the 'weld decay' in the scientific literature.76
Table 7.3 Characteristics of stainless steel weldments. Chemical Composition Material
Major Elements
Austenitic stainless steels1"7'
Cr: 17-25 wt% Ni: 8-20 wt% Mn: ~2 wt% C: 0.03-0.15 wt%
Duplex stainless steels1"'*''
Cr: 18-27 wt% Ni: 7-8 wt% Mo: \-A wt% C:<0.1 wt%
Ferritic stainless steels1"*
Cr: 12-30 wt% Mn: 1-1.5 wt% C:<0.15wt%
Al, V, Zr
Martensitic stainless steels1"'*'5
Cr: 11-18 wt% Mn:~1.0wt% C: 0.15-1.2 wt%
Ni, Mo, W, V
Minor Elements
Welding Problems
Mo, Ti, Al, Nb
• HAZ chromium carbide precipitation • HAZ grain growth • Solidification cracking
Ti, N
• Shift in the HAZ austenite/ferrite balance • Reduced HAZ toughness • Precipitation of o-phase, Cr2N etc. • HAZ grain growth • Low HAZ toughness • HAZ chromium carbide precipitation • Hydrogen cracking • High HAZ hardness and transformation stresses • Low HAZ toughness
High resistance against general corrosion High resistance against stress corrosion cracking (in the presence of chlorides) High strength Adequate low-temperature toughness
Like weld decay, knife-line attack is also related to intergranular C^Q-precipitation, but it differs from the former type in that the corrosion attack occurs in a narrow region adjacent to the fusion boundary following multipass welding of Ti/Nb stabilised stainless steels. As shown in Fig. 7.46, the origin of knife-line attack can be attributed to dissolution of TiC or NbC during the initial weld thermal cycle in regions of the HAZ where the peak temperature has been above say 12500C. Since the cooling rate within the high temperature regime is very high, reprecipitation of TiC or NbC does not take place on cooling. This leaves carbon free to react with chromium during subsequent reheating to peak temperatures of about 700-8000C following deposition of the second layer (filler pass). Knife-line corrosion attack is usually observed in weldments where the second pass (top)
(a)
Temperature
Dissolution of TiC or NbC C-curve for precipitation of TiC or NbC
1st thermal cycle Time
Temperature
(b)
C-curve for precipitation of TiC or NbC C-curve for precipitation OfCr C 23 6 2nd thermal cycle Time
Fig. 7.46. Mechanisms of knife-line corrosion attack in austenitic stainless steel weldments (schematic); (a) Dissolution of TiC or NbC during the initial weld thermal cycle, (b) Precipitation of Cr23C6 in the low peak temperature region of the weld HAZ following deposition of the second layer. (The corresponding C-curves for precipitation of TiC/NbC and Cr23C6 in the grain growth zone are displaced far to the right in the diagram.)
overlaps the lower part of the fusion boundary of the first (root) pass, as indicated in Fig. 7.47(a). In practice, the problem can be eliminated by simply reversing the welding sequence or by changing the welding procedure so that the second pass overlaps the middle rather than the lower part of the root pass. The latter point is illustrated in Fig. 7.47(b).
732 HAZ strength level In single phase materials such as austenitic stainless steels, the primary grain size will make a direct contribution to strength. In general, the grain size dependence of the yield stress (<3O) is well described by the Hall-Petch relation:19 (7-21) where ct is the friction stress (representing the overall resistance of the crystal lattice to dislocation movement), k is the locking parameter (which measures the relative hardening contribution of the grain boundaries), and D is the average grain diameter. It follows from the analysis in Section 5.4.2.5 (Chapter 5) that the grain size across the HAZ of austenitic stainless steel weldments may vary by a factor of three to five, depending on the
(a)
Cr-depleted region
Knife-line corrosion attack
(b)
Cr-clepleted region No corrosion attack Fig. 7.47. Effect of welding performance on the corrosion resistance of Ti/Nb-stabilised austenitic stainless steels; (a) Low resistance against knife-line corrosion attack, (b) High resistance against knife-line corrosion attack. The diagrams are based on the ideas of Kou.76
applied heat input. This means that a permanent soft zone will form adjacent to the fusion boundary after welding, which may reduce the overall load-bearing capacity of the joint. Example (7.5)
Consider plasma arc butt welding of a 5mm thick plate of type 316 austenitic stainless steel under the following conditions:
Provided that the conditions for one dimensional heat flow are met, estimate on the basis of the nomograms in Fig. 5.30(b) (Chapter 5) the variation in the austenite grain size across the HAZ after welding. Calculate then via the Hall-Petch relation (equation (7-21)) the expected reduction in the HAZ strength level due to this change in the microstructure. Input data: Base metal yield strength: 300 MPa Locking parameter in Hall-Petch relation: k = 227 MPa (im1/2 Solution
First we need to calculate the net heat input per mm2 of the weld:
Readings from the nomograms in Fig. 5.30(b) give the HAZ grain size profile shown in Fig. 7.48. In order to obtain the resulting HAZ strength distribution, it is necessary to fix the value of the friction stress, Oi, in the Hall-Petch relation. In the present example, we have:
from which
It follows from the graphical representation of the Hall-Petch relation in Fig. 7.48 that the variation in the yield strength across the HAZ is rather small under the prevailing circumstances. In fact, the maximum HAZ strength reduction which may occur in such materials because of grain growth is about 18%, corresponding to high heat input welding conditions. This implies that welding does not impose severe restrictions on the design stress as long as the steel is used in the fully annealed condition. 7.3.3 HAZ toughness All body-centred cubic metals (including ferritic and martensitic stainless steels) show a marked temperature dependence of the fracture toughness, as indicated in Fig. 7.49. At high temperatures fracture occurs normally by ductile rupture, whereas cleavage is the dominating fracture mode at low temperatures. This type of behaviour makes both ferritic and martensitic stainless
Yield strength, MPa
Austenite grain size, \im
Peak temperature, 0C
Absorbed energy
Fig. 7,48. Computed HAZ grain size and yield strength profiles in a 5mm thick butt weld of type 316 austenitic stainless steel (Example (7.5)).
Test temperature Fig. 7.49. Effect of temperature on notch toughness (schematic). steels unsuitable for many structural applications where the HAZ toughness is of particular concern. In contrast, medium- and high-strength fee metals have usually such high toughness that brittle fracture is not a problem at low temperatures, unless there is some special reactive chemical environment. Austenitic stainless steels and aluminium alloys fall within this category. When it comes to duplex stainless steel weldments, the situation is more complex. Here the HAZ toughness is determined by the austenite/ferrite balance in the weld, which, in
turn, depends on the steel chemical composition and the operational conditions applied.78"80 As shown in Fig. 7.50, complete ferritisation is normally achieved in regions close to the fusion boundary during the initial heating leg of the thermal cycle. Provided that the cooling rate through the critical transformation temperature range is kept reasonably low, a significant proportion of the ferrite may retransform back to austenite on cooling (see Fig. 7.51). This will contribute to a high HAZ toughness, even at subzero temperatures, as indicated by the CVN transition curves in Fig. 7.52. In general, an austenite content of about 30 vol% is sufficient to avoid problems with the HAZ toughness in duplex stainless steel welds. 7.3.4 Solidification cracking When a high alloy steel solidifies, a variety of microstructures can developed, depending on the steel chemical composition and the cooling conditions applied. Referring to the Fe-Ni-Cr phase diagram in Fig. 7.50, compositions on the Ni-rich side of the peritectic/eutectic liquidus solidify as primary austenite, while those on the Cr-rich side solidify as primary delta ferrite. The former condition is known to promote solidification cracking in welds due to partitioning of low-melting-point segregates of sulphur and/or phosphorus to the ^Fe-IFe grain boundaries.76"78 Since the solubility of sulphur and phosphorus is higher in delta ferrite than in austenite (0.18 and 2.8 wt%, respectively vs 0.05 and 0.25 wt% in austenite), the cracking susceptibility can normally be reduced if delta ferrite is present in sufficient amounts.76 At the same time, the interfacial Vetting' conditions are significantly improved owing to the formation of a low-
Peak temperature
Weld metal Partly melted zone
Liquid (L)
Delta ferrite grain growth zone
9 §
Partly transformed zone
I I
Unaffected base metal
Chromium content, wt%
Fig. 7.50. Schematic diagram defining different thermal regions within the HAZ of a single pass duplex stainless steel weld.
30-45sat1300°C
Fe-26.0 wt% Cr - 6.9 wt% Ni
Temperature, 0C
A4- temperature: 1260 0C
% 5 - ferrite at RT
Time, s Fig. 7.51. CCT-diagram for a duplex stainless steel. Data from Mundt and Hoffmeister.79 energy interface between yFe and o>e, which prevents spreading of the liquid along the grain boundaries.82 For these reasons, a minimum weld metal delta ferrite content of about 5 to 10 vol% is usually specified for austenitic stainless steels. The quantitative relationship between the delta ferrite content and the weld metal chemical composition in austenitic stainless steels has been determined first by Schaeffler83 and later by Delong et a/.84'85 The constitution diagram of Delong is shown in Fig. 7.53. Here the alloying elements are grouped into ferrite formers (i.e. Cr, Mo, Si, and Nb) and austenite formers (i.e. Ni, C, N, and Mn) to determine the corresponding chromium and nickel equivalents for a given alloy. The Delong diagram differs from the Schaeffler diagram in that the important nitrogen contribution also is included in the former, thus allowing a more accurate prediction of the weld metal delta ferrite content. Example (7.6)
Consider plasma arc butt welding of a 5mm thick plate of austenitic stainless steel under conditions similar to those employed in Example (7.5). Data for the base metal (BM) and the filler wire (FW) chemical compositions are given in Table 7.4. Use this information together with the Delong diagram in Fig. 7.53 to determine which of the two filler wires (I or II) that provides the highest resistance against weld metal solidification cracking under the prevailing circumstances. In the present example we shall assume that the mixing ratio B/(B+D) is 0.57 (the mixing ratio is defined in Section 1.10.8, Chapter 1). Solution
In the absence of oxidation losses, the weld metal chemical composition is given by the 'rule of mixtures':
Peak temperature: 13000C
Absorbed energy, J
3-D heat flow conditions
Test temperature, 0C Fig. 7.52. CVN transition curves for a duplex stainless steel after weld thermal simulation. Data from Videm.81 Table 7.4 Chemical composition of base plate and filler wires used in Example (7.6). Material1
wt% C
wt% Cr
wt% Ni
wt% Mo
wt% Mn
wt% Si
Baseplate
0.03
17.0
12.0
2.0
2.0
0.9
Filler wire I
0.03
18.0
11.5
2.7
0.8
0.9
0.07
Filler wire II
0.03
18.0
15.5
-
0.8
0.9
0.07
wt% N
Max. 0.015 wt% S and 0.03 wt% P
This leads to the weld metal chemical compositions shown in Table 7.5. We can now calculate the Cr- and Ni-equivalents for both welds:
Nickel equivalent (%Ni+30x%C+30x%N+0.5x%Mn)
Austenite
Schaeffler A+M line Austenite+ martensite
Austenite+ferrite
Chromium equivalent (%Cr+%Mo+1.5x%Si+0.5x%Nb) Fig. 7.53. The Delong diagram85 showing the relationship between delta ferrite content and weld metal chemical composition for stainless steels.
Table 7.5 Computed weld metal chemical compositions (Example (7.6)). Weld No.
wt% C
wt% Cr
wt% Ni
wt% Mo
wt% Mn
wt% Si
wt% N
I
0.03
17.4
11.8
2.3
1.5
0.9
0.03
II
0.03
17.4
13.5
1.1
1.5
0.9
0.03
Readings from Fig. 7.53 then give: Weld I : About 93 vol% austenite and 7 vol% delta ferrite Weld IP. 100 % austenite From this we see that wire I provides the highest resistance against weld metal solidification cracking for the combination of steel and operational conditions considered above. It should be emphasised that the Delong diagram gives no information about the real solidification microstructure, since it is based on measurements of retained delta ferrite at room temperature. Also, the important effect of cooling rate on the weld metal transformation behaviour is neglected in the present analysis. Consequently, the use of such empirical diagrams for selection of steel and welding consumables is a keenly debated question in the scientific literature.
7.4 Aluminium Weldments Aluminium alloys are to an increasing extent used as structural components in welded assemblies because of their high strength, low density, and good resistance against general corrosion. In certain cases the application of aluminium is restricted by a low HAZ strength level due to softening reactions occurring during welding. In other cases the cracking resistance or the fatigue strength becomes the limiting factor, depending on the design criterion. Table 7.6 summarises typical problems associated with welding of aluminium and its generic alloys. In the following, we shall focus on the structural and mechanical response of age-hardenable aluminium alloys to the heat of welding processes, with particular emphasis on Al-Mg-Si alloys and Al-SiC metal matrix composites. 7.4.1 Solidification cracking Conventional filler metals for aluminium welding are based on the binary Al-Si or Al-Mg systems. It follows from Fig. 7.54 that maximum cracking sensitivity occurs somewhat between pure Al and 2 to 4 wt% Si and Mg in aluminium, respectively. This behaviour arises from the competitive influence of two different processes.76 In pure aluminium, on the one hand, the solidification cracking problem does not exists, since there is no low-melting-point eutectic present at the grain boundaries. In solute-rich aluminium alloys, on the other hand, the eutectic liquid is so abundant that it backfills and 'heals' the incipient cracks, which results in a low cracking sensitivity. Somewhere in between the two composition limits, the amount of eutectic liquid may be just large enough to form continuous films at the grain boundaries. This, in combination with high shrinkage or thermal contraction stresses, may lead to solidification cracking, as indicated in Fig. 7.55. Normally, aluminium-based filler metals contain between 4 to 5 wt% Si or Mg. This solute content is usually high enough to prevent solidification cracking during welding. Problems Table 7.6 Characteristics of aluminium weldments. Chemical Composition Minor Elements
Welding Problems
Material
Major Elements
Al-Mg alloys (5 XXX-series)
Mg: 1-5 wt%
Si, Fe, Mn
• Solidification cracking • Reduced HAZ strength level (work-hardened materials)
Al-Mg-Si alloys (6xxx-series)
Mg: 0.5-1.3 wt% Si: 0.4-1.4 wt%
Mn, Cr, Fe
• Solidification cracking • Hot cracking • Reduced HAZ strength level
Al-Zn-Mg alloys (7xxx-series)
Mg: 0.5^4 wt% Zn: 2-8 wt%
Cu, Cr, Mn, Fe
Al-SiC metal matrix composites (10-15% vol% SiC)
Si: -7.5 wt% Mg: -0.5 wt%
Fe, Ti
• Solidification cracking • Hot cracking • Low HAZ stress corrosion cracking resistance • Conventional fusion welding is not recommended • High-quality joints can be produced by means of friction welding or diffusion bonding
Relative crack sensitivity
AI-Si system
Al-Mg system
Composition of weld, wt% Fig. 7.54. Solidification cracking sensitivity of binary Al-Si and Al-Mg alloys. Data from Dudas and Collins.86 may arise, however, if the weld metal becomes heavily depleted with respect to Si or Mg due to dilution with the parent metal. Welds of a high B/(B+D) ratio fall within this category. In such cases it may be necessary to use over-alloyed filler wires to obtain crack-free welds. Example (7.7)
Consider plasma arc butt welding of a 10mm thick aluminium plate of type AA 6082-T6 (containing 0.7 wt% Mg and 0.9 wt% Si) under the following conditions: qo = 2OkW, v = 10mm s"1, T0 = 200C Experience shows that the bead reinforcement amounts to 10% of the groove cross section (details of the groove geometry are given in Fig. 7.56). Two different filler wires are available, wire I with 5 wt% Si and wire II with 5 wt% Mg. Use this information along with the diagrams in Fig. 7.54 to determine which of the two filler wires (I or II) that provides the highest resistance against weld metal solidification cracking under the prevailing circumstances. In these calculations we shall assume that the temperature field around the heat source is given by the simplified Rykalin thin plate solution (equation (1-100) in Chapter 1). Thermal data for AlMg-Si alloys are contained in Table 1.1. Solution
First we need to estimate the mixing ratio BI(B+D). The total width of the fusion zone (2ym) can be obtained from equation (1-100):
(a)
(b) Fig. 7.55. Examples of solidification cracking in aluminium weldments (Varestraint test coupons); (a) Al-I wt% Si, (b) Al-I wt% Mg. After Cross.87
Fig. 7.56. Groove geometry for a single pass Al-Mg-Si butt weld (Example (7.7)). This gives:
and
from which
In the absence of oxidation losses, the weld metal chemical composition is given by the 'rule of mixtures':
If wire I is used, the weld metal Mg and Si concentrations become:
Similarly, in the case of wire II, we get:
A comparison with Fig. 7.54 shows that wire I provides the highest safety against weld metal solidification cracking under the prevailing circumstances, while wire II is unacceptable. The lower cracking resistance of the Al-Mg wire compared with the Al-Si wire at high dilution ratios arises from the pertinent difference in the fraction of eutectic liquid which forms during weld metal solidification. For pure binary alloys the eutectic fraction feuL is given by equation (3-46) in Chapter 3:
where CeuL is the eutectic concentration, and ko is the equilibrium partitioning coefficient (given by the binary Al-Si and Al-Mg phase diagrams). If the contribution from the accompanying alloying element is neglected, the values of feuL become: Weld I (1.80 wt% Si):
Weld II (1.65 wt% Mg):
From this we see that the fraction of eutectic liquid in weld I is so abundant that it backfills and 'heals' all incipient cracks, while feut in weld II is just large enough to form continuous films at the columnar grain boundaries which, in turn, promotes solidification cracking. 7.4.2 Hot cracking Hot cracking is a phenomenon occurring within the high peak temperature regions of the HAZ during welding of aluminium alloys. In spite of the difference in location, hot cracking like solidification cracking is intergranular and arises from the combined action of grain boundary liquation and stresses induced by solidification shrinkage and thermal contraction. The formation of liquid phases within a weld HAZ can readily be explained with the help of a simple binary phase diagram of the type shown in Fig. 7.57. If the composition of the binary alloy is
Temperature
Liquid (L)
Composition Fig. 7.57. Schematic binary phase diagram defining the equilibrium conditions for partial melting during reheating.
higher than Cmax^ and the alloy is heated to a temperature above TeuU partial melting will occur. Since the eutectic phase is usually located at the grain boundaries, these sites become immediately covered with liquid films if the wetting conditions are favourable. 7.4.2.1 Constitutional liquation in binary Al-Si alloys Experience shows that even binary alloys with a nominal composition lower than Ceut can undergo incipient melting at the eutectic temperature. This will obviously be the case if the alloy contains segregations so that the concentration locally exceeds the critical composition. Another possibility is melting due to 'constitutional liquation', a mechanism originally proposed by Pepe and Savage8889 for the formation of hot cracking in 18-Ni maraging steel weldments at temperatures well below the bulk solidus of the alloy. The same theory has later been applied by Reiso et al.90~93 and Lohne and Ryum94 to explain incipient melting during homogenisation heat treatment of aluminium alloys. In the following, the treatment of Lohne and Ryum94 is adopted to illustrate the principles of constitutional liquation in binary Al-Si alloys under conditions applicable to welding. The theory is later extended to ternary Al-MgSi alloys. Figure 7.58 shows a section of the Al-rich corner of the binary Al-Si phase diagram. Consider next a pure Al-1.2 wt% Si alloy that first is brought to equilibrium at a lower temperature to form 10|um large Si particles (Fig. 7.59(a)) and then is rapidly heated to a higher temperature slightly above Teut. If local equilibrium is maintained at the particle/matrix interface during heating, the composition is given by the Al-Si solvus boundary in Fig. 7.58. When Ceut is reached incipient melting will take place by formation of eutectic liquid (according to the reaction Al + Si —» liquid), as shown in Fig. 7.59(b). The process will continue until the whole Si particle has dissolved (Fig. 7.59(c)). Depending on the density/location of the Si particles and the interfacial wetting conditions, grain boundary liquation may eventually occur, as indicated in Fig. 7.59(d).
Liquid
Temperature, 0C
Liquid+solid ss
Al+Si
Silicon content, wt% Fig. 7.58. Section of the Al-rich comer of the binary Al-Si phase diagram. Data from Ref. 95.
(a)
(b)
(C)
(cO
Fig. 7.59. Optical micrographs showing the microstructural evolution during homogenisation heat treatment of binary Al-Si alloys; (a) Isolated Si particle embedded in a matrix of Al, (b) Partially melted Si particle surrounded by Al-Si eutectic (25s at 582°C), (c) Globular Al-Si eutectic structure formed after complete dissolution of the Si particle (60s at 582°C), (d) Spreading of eutectic liquid along a grain boundary (25s at 582°C). Courtesy of O. Lohne, Sintef - Division of Metallurgy, 7034 Trondheim, Norway.
7.4.2.2 Constitutional liquation in ternary Al-Mg-Si alloys Constitutional liquation in ternary Al-Mg-Si alloys has been investigated by Reiso et al.96 Figure 7.60 shows a section of the Al-rich corner of the quasi-binary Al-Mg2Si phase diagram. When an alloy of composition C < Ceut is heated up rapidly, as in the case of welding, the primary Mg2Si particles do not have enough time to dissolve. When the quasi-binary eutectic temperature is reached at about 593°C, incipient melting will occur, according to the reaction:96 liquid (7-22) Further heating to a higher temperature (T > 593°C) provides additional time for dissolution of Mg2Si and formation of more liquid of variable composition. In practice, reaction (7-
Temperature, 0C
Mg2Si concentration, wt% Fig. 7.60. Quasi-binary section of the Al-rich corner of the ternary Al-Mg-Si phase diagram. Data from Reiso et al.96 and Phillips.97 22) may also proceed below the quasi-binary eutectic temperature Teut, since the diffusion rate of Mg is higher than that of Si.96 By considering the kinetics it can be shown that the interface concentration will gradually move towards the silicon side of the quasi-binary line in the phase diagram as the Mg2Si particles dissolve, thereby reducing the temperature at which liquation occurs (from 593 down to about 5800C). Moreover, in alloys containing excess amounts of silicon, two other side reactions can take place:96 liquid
(7-23)
and liquid
(7-24)
The former is analogous to the melting reaction in binary Al-Si alloys (Fig. 7.58), while the latter corresponds to the eutectic reaction in the ternary Al-Mg-Si system (Teut varies from 555 to 559°C, depending on the source). Since this eutectic temperature represents the lowest temperature at which a melt can exist within the system, it means that local melting of second phase particles cannot take place below, say, 555 to 559°C during welding of Al-Mg-Si alloys.
7.4.2.3 Factors affecting the hot cracking susceptibility In addition to the thermodynamic and kinetic effects mentioned above, there are several other factors, some interrelated, which play an important part in the formation of hot cracks in Al-Mg-Si weldments. These are:76 (i)
The number density and size distribution of Mg2Si and Si particles in the base metal.
(ii)
The total grain boundary area per unit volume available for absorption of eutectic liquid (determined by the HAZ grain size).
(iii) The interfacial wetting conditions. (iv) The local tensile stress level in the partially melted region. It follows that the hot cracking susceptibility may be significantly altered by a change in one of these parameters, but, in practice, there is very little that can be done to prevent grain boundary liquation if the base material already contains second phase particles. In fact, the only useful way of eliminating the cracking problem is to reduce the tensile stress in the partially melted HAZ through proper selection of welding consumables. This is because the composition of the weld metal can be adjusted so that solidification is completed first in the partially melted region and then in the fusion zone, thus avoiding hot cracking in the former. As an illustration of principles, the diagrams of Gittos and Scott98 (reproduced in Fig. 7.61) will be considered. These diagrams show the variation of the weld metal solidus temperature with base metal dilution for two commercial filler wires (wire I: Al-5 wt% Si, and wire II: Al5 wt% Mg). It is evident that the risk of hot cracking is highest when wire II is used, particularly at high B/(B+D) ratios, since solidification occurs first in the weld metal and then in the partially melted region. In contrast, wire I provides a good HAZ cracking resistance over the whole composition range because of the resulting lower solidus temperature. In the latter case the weld metal solidification and thermal contraction stresses are imposed on the HAZ at a stage where liquid no longer exists at the grain boundaries. Example (7.8)
Consider plasma arc butt welding of a 10mm thick aluminium plate of AA6082-T6 (containing 0.7 wt% Mg and 0.9 wt% Si) under conditions similar to those employed in Example (7.7). Use the diagrams in Fig. 7.61 to determine which of the two filler wires (I or II) that provides the highest resistance against hot cracking in the partially melted region under the prevailing circumstances. Solution
In the previous example the base metal dilution ratio, BI(B+D), was found to be 0.78. Under such conditions wire I provides the highest resistance against hot cracking, since solidification first occurs in the partially melted region and then in the weld metal. This explains why Al-Si based filler wires are usually recommended for single pass butt welding of Al-Mg-Si extrusions if the strength level is not of particular concern.
Solidus temperature, 0C
(a)
liquid
B/(B+D), %
Solidus temperature, 0C
(b)
liquid
B/(B+D), % Fig. 7.61. Variation of weld metal solidus temperature with dilution for 6082 aluminium alloys (Al-0.7 wt% Mg-0.9 wt% Si); (a) Wire I (Al-5 wt% Si), (b) Wire II (Al-5 wt% Mg). The melting temperature for different base metal constituent phases are indicated by the horizontal broken lines in the diagrams. Data from Gittos and Scott98 and Reiso et al.96
Peak temperature
Partly reverted region:
HAZ-
Unaffected base metal
Fully reverted region
Hardness
(a)
Distance from fusion line (b)
Temperature
C-curve for precipitation of (3'(Mg2 Si)
Weld thermal cycle Time
Fig. 7.62. Schematic diagrams showing the sequence of reactions occurring in the HAZ of 6082-T6 aluminium welds; (a) Hardness distribution following p"(Mg2Si) dissolution; (b) Precipitation of P'(Mg2Si) at dispersoids during the weld cooling cycle.
7A3 HAZ microstructure and strength evolution during fusion welding The age-hardenable Al-Mg-Si alloys have been widely studied, to the extent that most of the underlying physical processes are well established. They offer tensile strength values higher than 350 MPa in the artificially aged (T6) condition owing to the presence of very fine, needleshaped 3"(Mg2Si) precipitates along <100> directions in the aluminium matrix." Although Al-Mg-Si alloys are readily weldable, they suffer from severe softening in the heat affected zone (HAZ) because of reversion (dissolution) of the (3"(Mg2Si) precipitates during the weld thermal cycle.76100"103 This type of mechanical impairment represents a major problem in engineering design, since it reduces the load-bearing capacity of the joint.104 7.4.3.1 Effects of reheating on weld properties Microstructural changes in the HAZ of Al-Mg-Si alloys have been examined by several investigators,100"103 and the main results are summarised in Fig. 7.62. It is evident from Fig. 7.62(a) that reversion of [3"(Mg2Si) precipitates will occur to an increasing extent in the peak temperature range from 250 to 5000C. This is associated with a continuous decrease in the HAZ hardness until the dissolution process is completed. During cooling of the weld, some solute recombines to form coarse, metastable (3'(Mg2Si) precipitates which do not contribute to strengthening (Fig. 7.62(b)). However, close to the fusion boundary a large fraction of alloying elements will remain in solid solution at the end of the thermal cycle, thereby giving conditions for extensive age-hardening at room temperature over a period of 5 to 7 days (Fig. 7.62(c)). In general, enhanced HAZ strength recovery can be achieved by the use of artificial ageing in the temperature range from 150 to 1800C,76 but this possibility will not be considered here. Peak temperature
(C)
Hardness
Contribution; from natural: ageing \ Resulting hardness profile
Distance from fusion line
Fig. 7.62. Schematic diagrams showing the sequence of reactions occurring in the HAZ of 6082-T6 aluminium welds (continued); (c) Hardness distribution after prolonged room temperature ageing.
7.4.3.2 Strengthen ing mechan isms in A l-Mg-Si alloys Due to the lack of experimental evidence of coherency strains around (3"(Mg2Si) precipitates in Al-Mg-Si alloys," it has been suggested that the increased resistance to dislocation motion accompanying the presence of these structures arises from the high energy required to break Mg-Si bonds in the particles as dislocations shear through them. Assuming that this strengthening effect is associated with order hardening, the net precipitation strength increment, Aop, can be calculated from the equation originally derived by Kelly and Nicholson:105 (7-25) where 7/ is the internal interface (or antiphase) boundary energy, b is the Burgers vector,/is the particle volume fraction, and c$ is a kinetic constant. By introducing the relative particle volume fraction, f/fo, we obtain: (7-26) where fo is the initial volume fraction of (3"(Mg2Si) precipitates in the alloy, and C4 is a new kinetic constant (equal to c 3 / o ). It is evident from equation (7-26) that Aop = Aap (max) = c4 when/7/ o = 1. Hence, this equation can be rewritten as: (7-27) Here amin denotes the intrinsic matrix strength after complete particle dissolution, while dmax is the original base metal strength in the artificially aged (T6) condition. Provided that a linear relationship exists between yield strength and hardness, equation (727) can be rewritten as:102 (7-28) Equation (7-28) provides a basis for assessing the reaction kinetics through simple hardness measurements. Typical values for amax, HVmax, omin, and HVmin are given in Table 7.7. 7.4.3.3 Constitutive equations The kinetics of (3"(Mg2Si) dissolution during reheating of 6082-T6 aluminium alloys have been considered in Section 4.4.2 (Chapter 4). Table 7.7 Properties of some Al-Mg-Si and Al-SiC weldments. Type of Weld
Material
HVmax [VPN]
HVmin [VPN]
omax [MPa]
<5min [MPa]
®
Fusion welds
6082-T6
110
42
282
78
0.56
Friction welds
6082-T6
115
47
297
93
0.49
0.43
Al-SiC-T6
137
55
342
83
0.55
0.43
W
Reversion model When the 3"(Mg2Si) particles dissolve, the volume fraction falls from its initial value f0, according to equation (4-36). A combination of equations (4-36) and (7-28) leads to the following expression for the dimensionless strength parameter within the partly reverted region of the HAZ: (7-29)
where t\ is the maximum hold time required for complete particle dissolution at a given temperature (defined by equation (4-31) in Chapter 4), and n is a time exponent (< 0.5). The variation of n with/// o is shown in Fig. 4.20. Natural ageing model In general, the fraction of hardening (3"(Mg2Si) precipitates which forms during natural ageing (flfo) depends on the amount of remnant solute present in the matrix material after cooling of the weld. By considering the kinetics of the C-curve for precipitation of essentially nonhardening 3'(Mg2Si) particles at dispersoids during the weld cooling cycle, Myhr and Grong102 arrived at the following relationship for flfo' (7-30) where (7-31)
Here O is a material constant (defined in Table 7.7), and t\ is the critical time required to precipitate a certain fraction of $'(X = Xc) at an arbitrary temperature (T). The variation of t*2 with temperature is given by equation (6-55) in Chapter 6. The net precipitation increment following natural ageing (a2) can therefore be written as:
(7-32) Coupling of models Based on equations (7-29) and (7-32) it is possible to calculate the HAZ strength distribution after welding and subsequent natural ageing when the weld thermal programme is known. Figure 7.63 shows a sketch of the superimposed hardness profiles, as evaluated from these equations. Since the resulting strength level in the partly reverted region depends on the interplay between two competing processes (i.e. dissolution and reprecipitation), it is convenient to define the 'boundary' between the two models on the basis of the intersection point in Fig. 7.63 where a\ = a 2 , i.e.: (7-33) and (7-34)
Hardness
Fully reverted region
Peak temperature
Partly reverted region
Reversion model Intersection point , Natural ageing model
Distance from fusion line Fig. 7.63. Coupling of reversion and natural ageing models. It follows that this locus also defines the minimum HAZ strength level, which is an important parameter in engineering design. 7.4.3.4 Predictions of HAZ hardness and strength distribution The predictions are based on computer programmes which utilise the medium thick plate heat flow solution described in Section 1.10.4 (Chapter 1) and the kinetic models outlined above to calculate the HAZ hardness distribution for specific welding conditions (details are given in Ref. 106). Accuracy of predictions Examples of measured and predicted HAZ hardness profiles are shown in Figs. 7.64 and 7.65. When stringer bead welding is carried out on a plate of medium thickness, the hardness distribution in the transverse y direction will vary with distance from the plate surface due to a continuous change in the heat flow conditions. A comparison between observed and predicted hardness profiles in Fig. 7.64 shows that such effects are readily accounted for in the present model. In contrast, a full penetration butt weld will always reveal a similar HAZ hardness distribution in the transverse section of the weld, as shown in Fig. 7.65. This situation arises from the lack of a temperature gradient in the through-thickness z direction of the plate. Moreover, it is evident from Figs. 7.64 and 7.65 that the final dimensions of the HAZ are strongly influenced by variations in welding parameters and operational conditions. Hence, it is difficult to justify the use of a constant safety factor for the width of the HAZ as recommended in current design rules for welded Al-Mg-Si alloys.104 Aptness of models Based on the kinetic models described in the proceding sections, it is possible to construct two-dimensional (2-D) maps which show characteristic hardness and peak temperature contours in the HAZ of 6082-T6 aluminium weldments. Examples of such diagrams are given in
(a)
Hardness, VPN
Peak temperature, 0C
HV (predicted)
Aym, mm (b)
Hardness, VPN
Peak temperature. 0C
HV (predicted)
ym,mm Fig. 7.64. Comparison between measured and predicted HAZ hardness profiles in a stringer bead GMA weld; (a) Upper plate surface, (b) Lower plate surface. The peak temperature distribution is indicated by the broken lines in the graphs. (Operational conditions: qo = 9.1 kW, v = 5.1 mm s"1, d = 15mm). Data from Myhr and Grong.102 Fig. 7.66. Included is also a 3-D plot of the HAZ hardness distribution in the transverse section of the weld. The results in Fig. 7.66 reveal a direct relationship between the HAZ isothermal contours on the one hand and the resulting HAZ hardness/strength distribution on the other. In this particular example the soft zone closely follows the contour of the 4000C isotherm. This, in turn, implies that the minimum HAZ strength level is fairly constant and virtually independent of choice of welding parameters (i.e. close to 60 VPN for single pass welds).
Hardness, VPN
Peak temperature. 0C
HV (predicted)
A y m , mm Fig. 7.65. Comparison between measured and predicted HAZ hardness profiles in a single pass plasma arc butt weld. The peak temperature distribution is indicated by the broken line in the graph. (Operational conditions: qo = 14.0 kW, v = 5.8 mm s"1, d = 13mm). Data from Myhr and Grong.102 In practice, the HAZ hardness can be converted into an equivalent yield or ultimate tensile strength through the following regression formulae:102 (7-35) and (7-36) From equation (7-35) we see that a minimum HAZ hardness of about 60 VPN corresponds to a strength reduction factor of:
This value is in good agreement with the recommended strength reduction factor of 0.49 incorporated in many welding specifications and standards.104'107 Process diagrams for single pass butt welds Because of the complex temperature-time pattern in aluminium welding, it is not possible to condense general information about the HAZ strength distribution into 2-D process diagrams. An exception is single pass butt welding of plates, where the medium thick plate solution described in Section 1.10.4 (Chapter 1) can largely be simplified if the net arc power is kept sufficiently high compared with the plate thickness (e.g. qold > 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 mm"2 (see equation (1-100) in Chapter 1).
y, mm
z, mm
Hardness code
Fusion zone
(a)
(b)
Fig. 7.66. Computed HAZ hardness and peak temperature contours in the transverse section of a stringer bead GMA weld; (a) 2-D graphical representation, (b) 3-D graphical representation. (Operational conditions as in Fig. 7.64). Data from Myhr and Grong.102
Figure 7.67 shows plots of the HAZ hardness/strength profiles for different values of qo Ivd. It follows that a narrow width of the HAZ requires the use of a low energy input per mm2 of the weld. In practice, this can be achieved by the choice of an efficient welding process (e.g. electron beam or laser welding) which allows deposition of a full penetration butt weld without employing a groove preparation (i.e. eliminates the need for filler metals). Multipass welding The present process model can also be extended to multipass welding if it is assumed that reversion of indigenous (3'(Mg2Si) precipitates occurs instantaneously on reheating above the phase boundary solvus temperature (here taken equal to 5200C).
Rm [MPa]
Hardness, VPN
V2[MPa]
Scale: 10 mm
Distance from fusion line Fig. 7.67. Process diagram for single pass 6082-T6 butt welds. Data from Myhr and Grong.102 Figure 7.68 shows 2-D and 3-D plots of computed HAZ hardness and peak temperature contours for a simulated two-pass butt weld. This model system consists of two imaginary stringer beads which are placed symmetrically on each side of a 15mm thick plate. Comparable hardness data for a single pass weld of same thickness are contained in Fig. 7.66. It is evident from Figs. 7.66 and 7.68 that deposition of a second pass will neither increase the width nor reduce the strength of the HAZ to any great extent. The explanation lies in the fact that the temperature field around each heat source tends to overlap with increasing distance from the fusion boundary due to symmetry effects (see Fig. 7.68(a)), which prevents excessive strength loss during reheating of the weld. Similar observations have also been made from actual testing of multipass Al-Mg-Si weldments.108 Example (7.9)
Consider plasma arc butt welding of a 10mm thick aluminium plate of type AA 6082-T6 under conditions similar to those employed in Example (7.7). Estimate on the basis of the process diagram in Fig. 7.67 and the simplified Rykalin thin plate solution (equation (1-100) in Chapter 1) both the minimum HAZ strength level, the total width of the reduced strength zone after welding, as well as the lower temperature limit for dissolution of the (3"(Mg2Si) precipitates during the weld thermal cycle. Thermal data for Al-Mg-Si alloys are given in Table 1.1 (Chapter 1). Solution
First we need to calculate the net heat input per mm2 (q ol vd). In the present example, we have:
Hardness code
z, mm
y, mm
Fusion zone (a)
(b) Fig. 7.68. Computed HAZ hardness and peak temperature contours for a simulated two-pass butt weld (the second pass is deposited immediately after cooling of the first pass); (a) 2-D graphical representation, (b) 3-D graphical representation. (Operationalconditions: qo = 9A kW, v = 5.1 mms~ l ,d- 15mm). Data from Myhr and Grong.102
Readings from Fig. 7.67 then give:
and
Similarly, by considering the extension of the HAZ and the corresponding length of the scale bar in Fig. 7.67, the total width of the reduced strength zone becomes:
The relationship between peak temperature T- Tp and distance y = ym from the heat source can now be obtained by differentiating equation (1-100) with respect to time. After some manipulation, we obtain:
By substituting qo/vd = 200 J ram"2, pc = 0.0027 J mm"3 0C"1, and Tm = 652°C into the above equation, the following temperature for incipient dissolution of the p"(Mg2Si) precipitates is obtained:
It is obvious from the above calculations that the degree of HAZ softening occurring during welding is substantial under the prevailing circumstances. This explains why, for instance, high heat input deposition is usually not recommended for Al-Mg-Si alloys. 7.4.4 HAZ microstructure and strength evolution during friction welding Friction welding is a solid state joining process that involves both heating and plastic deformation of the parent material under extreme thermal and strain rate conditions.109"113 During the welding operation the material is deformed at high temperatures, initially at low strain rates, but due to the axial displacement of the specimen, the material is subsequently brought into the fully plasticised region where the strain rate may exceed 103 s"1 (e.g. see Fig. (6.79) in Chapter 6). Although the resulting microstructural changes are similar to those observed in many hot working processes, it is obvious that transient effects must play a more dominant role in friction welding because of the rapid temperature and strain rate fluctuations. This, in turn, increases the complexity of the analysis. 7.4.4.1 Heat generation in friction welding A major problem in modelling of heat flow phenomena in friction welding is to obtain an accurate description of the energy input at the faying interface. This is because the friction coefficient L| L is changing continuously during the welding cycle from |i > 1 at the dry sliding start, towards zero when the temperature for asperity melting is reached at the interface.113 However, for the ideal case considered in Fig. 7.69, the torque required to rotate two circular shafts relative to one other under the action of an axial load pressure is given by: 114115
(7-37)
where M is the interfacial torque, R* is the surface radius, and P(r) is the pressure distribution across the interface (here assumed constant and equal to P).
Pressure
Pressure
Fig. 7.69. Schematic arrangement of friction welding of a solid rod. If all the shearing work at the interface is assumed to be converted into frictional heat, the average heat input per unit area and time becomes:114
(7-38) where qo is the net power (in W), P is the friction pressure (in N mm"2), A is the cross section (in mm2), and wmax. is the maximum surface velocity at the outer edge (in m s"1). Equation (7-38) provides a basis for estimating the heat generation at the interface during continuous drive friction welding in the absence of asperity melting. 7.4.4.2 Response ofAl-Mg-Si alloys and Al-SiC MMCs to friction welding In friction welding of aluminium alloys and Al-SiC metal matrix composites, the deformation is maintained throughout the steady state period.113 The microstructural changes that take place at this stage of the process can be classified as dynamic changes, since they occur under the action of variable plastic straining. Similarly, those taking place after the forge operation (when the weld cools) are referred to as static changes due to the lack of external plastic deformation. The former includes the generation of recovered subgrains and reversion of constituent precipitates in the area of high temperature and high deformation, whereas the latter involves precipitation reactions, e.g. formation of hardening [3"(Mg2Si) particles in the heat affected zone following natural ageing.109"113 In order to assemble an adequate model for the microstructural evolution during friction welding, it is necessary to divide the HAZ into different reaction zones. Referring to Fig. 7.70, the following three main regions are of specific interest in this context: (i)
The fully plasticised region, ZpL, where the material is able to accommodate the plastic strain by dynamic recovery (or recrystallisation) of the microstructure.
Contact section
Z Fig. 7.70. Schematic diagram showing the three main reaction zones within a friction welded component (Zpi/. fully plasticised region, Zpd\ partly deformed region, Zud: undeformed region). (ii)
The partly deformed region, Zpd., where the degree of plastic deformation is accommodated by an increase in the dislocation density of the matrix grains. In this region the temperature is sufficiently high to facilitate dissolution of the base metal hardening precipitates.
(iii) The undeformed region, Z1^., characterised by partial reversion of the base metal precipitates. Aspects of HAZ subgrain evolution during continuous drive friction welding have been described in Section 6.5.2 (Chapter 6). In the following, the structural and mechanical response of T6 heat treated Al-Mg-Si alloys and Al-SiC metal matrix composites to the imposed heating and plastic deformation will be considered more in detail. 7.4.4.3 Constitutive equations Since the HAZ strength level in both types of materials is mainly controlled by dissolution and precipitation reactions occurring within the aluminium matrix during the weld thermal cycle,109"113 we can use equations (7-29) and (7-32) with minor modifications to describe the reversion and the natural ageing characteristics of the weld components (see Table 7.7). In addition, it is necessary to allow for the plastic deformation introduced during friction welding, because dislocations will be generated in the matrix material to accommodate the strain.113 In general, work hardening of metals and alloys is a very complex problem which has not yet been properly solved. However, with the precision aimed at here it is sufficient to assume that this strength contribution is given by: (7-39) where 1F is a constant which is characteristic of the material under consideration (given in Table 7.7). The form of equation (7-39) indicates that the hardness is essentially constant within the plasticised regions of the weld HAZ. 7.4.4.4 Coupling of models Based on equations (7-29), (7-32), and (7-39) it is possible to calculate the HAZ strength distribution after friction welding and subsequent natural ageing when the weld thermal programme is known. Figure 7.71 (a) and (b) show schematic representations of the superim-
posed hardness profiles, as evaluated from these models. The resulting HAZ hardness distribution is indicated by the solid curve in the graphs for short and long duration thermal cycles, respectively. Since the present treatment oversimplifies the problem by only considering the strongest contribution with no interaction, the justification of this assumption relies on a good correlation between theory and experiments. It follows from Fig. 7.71 that particle dissolution is the major softening mechanism in friction welding of Al-Mg-Si alloys and Al-SiC metal matrix composites. At the same time a substantial strength recovery will occur as a result of external plastic straining in combination with intrinsic precipitation of hardening (3"(Mg2Si) particles following prolonged room temperature ageing. Depending on the operational conditions applied, this may give rise to differences in the shape of the HAZ hardness profiles, as shown in Fig. 7.71. (a)
Hardness
Reversion model
Work hardening model
Natural ageing model Unaffected base material Axial distance, Z (b)
Hardness
Reversion model
Work hardening model
Natural ageing model
Unaffected base material
Axial distance, Z Fig. 7.71. Schematic representation of the HAZ hardness distribution after friction welding and subsequent natural ageing; (a) Short duration thermal cycle, (b) Long duration thermal cycle. The parameters Zp/., Zp(L and Zud% are defined in Fig. 7.70.
7.4.4.5 Prediction of the HAZ hardness distribution The predictions are based on computer programmes which utilise the heat and material flow models described in Ref.113 in combination with the constitutive equations given above to calculate the HAZ hardness distribution for specific welding conditions. Accuracy of predictions Examples of measured and predicted hardness profiles are given in Figs. 7.72 and 7.73. A closer inspection of the graphs reveals a good agreement between theory and experiments in all three cases. It is interesting to note that there is no clear distinction in the shape of the HAZ hardness profiles between friction welded Al-Mg-Si alloys and Al-SiC metal matrix composites when comparison is made on the basis of a similar temperature-time pattern (see Fig. 7.73). However, large diameter weld components will normally reveal a different hardness distribution, as shown in Fig. 7.72, because longer welding times will increase the total heat input. Under such conditions the contribution from the plastic deformation becomes negligible, which means that the resulting HAZ hardness profile will closely resemble that observed during conventional gas metal arc (GMA) and plasma arc welding of Al-Mg-Si alloys (see Figs. 7.64 and 7.65).
Hardness, VPN
Process diagrams Based on the above process model, it is possible to construct a series of diagrams which summarise information about the effect of important welding variables in a systematic and illustrative manner. Examples of such diagrams for 6082-T6 aluminium alloys and T6 heat treated Al-SiC metal matrix composites are given in Fig. 7.74(a) and (b), respectively.
Predicted Measured
Unaffected base material Axial distance, mm Fig. 7.72.Comparison between measured and predicted HAZ hardness profiles in a <£26mm Al-Mg-Si weld component. (Assumed input data: <E> = *F = 0.56, HVmax= 110, HVmin = 42). Operational conditions: qJA = 17W m m 2 and ts = 6s. Data from Midling and Grong.113
Hardness, VPN
(a)
Predicted Measured
Unaffected base material Axial distance, mm
Hardness, VPN
(b)
Predicted Measured
Axial distance, mm Fig. 7.73.Comparison between measured and predicted HAZ hardness profiles; (a) 4> 16mm Al-Mg-Si weld component. (Operational conditions: qJA - 25W mrrr2 and ts = 0.9s), (b) 16mm friction welded Al-SiC metal matrix composite. (Operational conditions: qJA = 25W mirr 2 and ts= 3.8s). Data from Midling and Grong.113
Hardness, VPN
(a)
Axial distance, mm •
Hardness, VPN
(b)
Axial distance, mm Fig. 7.74. Process diagrams for friction welding; (a) 6082-T6 aluminium alloys. (Operational conditions: umax_ = 2.5m s"1 and [i = 0.5), (b) Al-SiC-T6 metal matrix composites. (Operational conditions: Umax. = 2.5m s"1 and \x = 0.5). Data from Midling and Grong.113
It is evident from these diagrams that the HAZ hardness distribution depends on the total heat input applied during friction welding. Although the controlling parameters qo IA and ts (welding time), in practice, are kept within relatively narrow limits, it is obvious that a small width of the HAZ requires the use of a high specific power (qol A) in combination with a short duration heating cycle (ts < 2 s). This is also in agreement with general experience.109"112 Example (7.10)
Consider continuous drive friction welding of a T6 heat treated Al-SiC metal matrix composite under the following conditions:
Use the process diagram in Fig. 7.74(b) to estimate the minimum HAZ hardness level as well as the total width of the strength reduced zone after welding. In this example we shall assume that the friction coefficient Ji is equal to 0.5. Solution
First we need to calculate the frictional heat per unit area of the weld. From equation (7-38), we have:
A comparison with Fig. 7.74(b) shows that a specific power of 25 W mm"2 corresponds to a minimum HAZ hardness of about 90 VPN, i.e. a reduction of 45 VPN compared with the base material. At the same time the total width of the reduced strength zone is seen to be 12 mm. It should be emphasised that the observed strength loss is not permanent, since the resulting HAZ strength level is mainly controlled by dissolution reactions taking place within the aluminium matrix during the weld thermal cycle. Consequently, a full HAZ strength recovery can be achieved by the use of an appropriate post weld heat treatment, as shown by the tensile test data in Table 7.8.
Table 7.8 Mechanical properties of friction welded Al-SiC metal matrix composites. Data from Midling and Grong109'113 HV
Material
R
p0 2
R
m
e
B
[VPN]
[MPa]
[MPa]
[%]
Al-SiC-T6 (base material)
135
315
352
3.6
Al-SiC-T6 (as-welded condition)
90
207
268
3.0
Al-SiC-T6 (PWHT condition)!
135
313
348
3.1
Solution heat treated at 535°C for 3 h followed by water-quenching and artifical ageing at 1600C for 10 h.
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56. 57. 58. 59. 60. 61. 62. 63. 64.
65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81.
O.D. Sherby and J.E. Dorn: Trans. AIME, 1953,197, 324-330. T. Reti, M. Gergely and R Tardy: Mater. ScL Technol., 1987, 3, 365-371. 0 . Grong and O.M. Akselsen: Metal Constr., 1986,18, 557-562. C. Thaulow, AJ. Paauw, A. Gunleiksrud and OJ. Naess: Metal Constr, 1985,17, 94R-99R. O.M. Akselsen, 0. Grong and G. R0rvik: Scand. J. MetalL, 1990,19, 258-264. C. Thaulow, AJ. Paauw and K. Guttormsen: Weld J, 1987, 66, 266s-279s. O.M. Akselsen, J.K. Solberg and 0. Grong: Scand. J. MetalL, 1988,17, 194-200. O.M. Akselsen, 0 . Grong and P.E. Kvaale: MetalL Trans., 1986,17A, 1529-1536. H. Homma, S. Ohkita, S. Matsuda and K. Yamamoto: Weld J, 1987, 66, 301s-309s. Y-T. Pan and J-L. Lee: Proc. 3rd. Int. Conf. on Trends in Welding Research, Gatlinburg (Tennessee), June, 1992, pp. 539-543. Publ. ASM International, Materials Park, Ohio (1993). J.H.Chen,Y.Kikuta,T.Araki,M.YonedaandY.Matsuda: ActaMetalL, 1984,32,1779-1788. C.A.N. Lanzillotto and RB. Pickering: Met. ScL, 1982,16, 371-382. O.M. Akselsen, 0 . Grong and J.K. Solberg: Mater. ScL Technol., 1987, 3, 649-655. H.P. Shen, T.C. Lei and J.Z. Liu: Mater. ScL Technol., 1986, 2, 28-33. NJ. Kim and G. Thomas: MetalL Trans., 1981,12A, 483-489. A.F. Szewezyk and J. Garland: MetalL Trans., 1982,13A, 1821-1826. M. Ramberg, O.M. Akselsen and 0. Grong: Proc. 1st Int. Conf. on Trends in Welding Research, Gatlinburg, TN, May, 1986, pp. 679-685. Publ. ASM International, Metals Park, Ohio (1987). N.E. Hannertz: Schweissen & Schneiden, 1976, 28, 379-382. RR. Coe: Welding Steels Without Hydrogen Cracking, 1973, Abington (Cambridge), The Welding Institute. N. Yurioka and H. Suzuki: Int. Mater. Rev., 1990, 35, 217-249. LT. Brown and W.M. Baldwin: Trans. AIME, 1954, 200, 298-303. E.A. Steigerwald, RW. Shaller and A.R. Troiano: Trans. AIME, 1959, 215, 1048-1052. CA. Zapffe and CE. Sims: Trans. AIME, 1941,145, 225-237. NJ. Petch: Phil. Mag., 1956,1, 331-337. CD. Beachem: MetalL Trans., 1972, 3, 437-451. A.W. Thompson and LM. Bernstein: In Effects of Hydrogen on the Behaviour of Metals (Eds LM. Bernstein and A.W. Thompson), 1980, Warrendale, PA, Metallurgical Society of AIME, pp. 291-308. J.D. Fast: Gases in Metals, 1976, London, Macmillan Press Ltd. R.A. Oriani: Ada MetalL, 1970,18, 147-157. N. Christensen, K. Gjermundsen and R. Rose: Brit. WeIdJ., 1958, 5, 272-281. N. Christensen: Svetsen, 1975, 34, 22-32. N. Yurioka and S. Ohshita: HW Doc. IX-1161-80 (1980). C Zhang and J.A. Goldak: HW Doc. IX-1662-92 (1992). N. Christensen and T. Simonsen: Scand. J. MetalL, 1981,10, 120-126. NACE Standard MR-01-75 (1975). M.I. Ons0ien, O.M. Akselsen, 0. Grong and P.E. Kvaale: WeIdJ., 1990, 69 (No. 1), 45-51. H. Suzuki: Trans. Jap. Weld. Soc, 1981,16, 25-32. D.L. Olson: Weld J, 1985, 64, 281s-295s. S. Kou: Welding Metallurgy, 1987, New York, John Wiley & Sons, Inc. R.D. Campbell: In Ferrous Alloy Weldments (Eds D.L. Olson and T.H. North), 1992, Zurich, Trans. Tech. Publications Ltd., pp. 167-216. I. Varol, J.C Lippold and W.A. Baeslack: ibid., pp. 217-252. R. Mundt and H. Hoffmeister: Arch. Eisenhuttenwes., 1983, 54, 253-256; ibid. 333-336. S. Atamert and J.E. King: Mater. ScL Technol., 1992, 8, 896-911. M. Videm: MSc. Thesis, 1985, Department of Metallurgy, The Norwegian Institute of Technology, Trondheim, Norway.
82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93.
94. 95. 96. 97. 98. 99. 100. 101. 102. 103. 104. 105. 106. 107. 108. 109.
110.
111. 112. 113. 114. 115.
J.A. Brooks, A.W. Thompson and J.C. Williams: WeldJ, 1984, 63, 71s-83s. A.L. Schaeffler: Metal Prog., 1949, 56, 680-680B. W.T. Delong, G. Ostrom and E. Szumachowski: WeIdJ., 1956, 35, 526s-533s. CJ. Long and W.T. Delong: WeIdJ., 1973, 52, 281s-297s. J.H. Dudas and RR. Collins: Weld J, 1966, 45, 241s-249s. CE. Cross: Ph.D Thesis, 1986, Colorado School of Mines, Golden, Colorado, USA. JJ. Pepe and W.F. Savage: Weld J, 1967, 46, 41 ls-422s. JJ. Pepe and W.F. Savage: Weld J, 1970, 49, 545s-553s. O. Reiso: Proc. 3rd. Int. Conf. on Aluminium Extrusion Technology, Atlanta, GA, 1984, vol. 1, pp. 31-40. Publ. Aluminium Association (1984). O. Reiso: Proc. 4th Int. Aluminium Extrusion Technology Seminar, Chicago, IL, 1988, vol. 2, pp. 287-295. Publ. Aluminium Association (1988). O. Reiso, H.G. 0verlie and N. Ryum: Metall. Trans., 1990, 21A, 1689-1695. H. Gjestland, A.L. Dons, O. Lohne and O. Reiso: In Aluminium Alloys — Their Physical and Mechanical Properties, 1986, Warley (UK), Engineering Materials Advisory Service Ltd., pp. 359-370. O. Lohne and N. Ryum: Proc. 4th Int. Aluminium Extrusion Technology Seminar, Chicago, IL, 1988, vol. 2, pp. 303-308. Publ. Aluminium Association (1988). Metals Handbook, 8th Edition (vol. 8). O. Reiso, N. Ryum and J. Strid: Metall. Trans. A, 1993, 24A, 2629-2641. H.W.L. Phillips: Annotated Equilibrium Diagrams of Some Aluminium Alloy Systems, 1959, London, The Institute of Metals, pp. 65-71. N.F. Gittos and M.H. Scott: WeIdJ, 1981, 60, 95s-103s. J.E. Hatch (Ed.): Aluminium — Properties and Physical Metallurgy, 1984, Ohio (USA), American Society for Metals. T. Enjo and T. Kuroda: Trans. JWRI, 1982,11, 61-66. S.D. Dumolt: Ph.D Thesis, 1983, Carnegie-Mellon University, USA. O.R. Myhr and 0. Grong: Ada Metall. Mater., 1991, 39, 2693-2702; ibid, 2703-2708. 0 . Grong and O.R. Myhr: In Mathematical Modelling of Weld Phenomena, (Eds H. Cerjak and K.E. Easterling), 1993, London, The Institute of Materials, pp. 300-311. FM. Muzzolani: Aluminium Alloy Structures, 1985, Boston (USA), Pitman Publishing Inc. A. Kelly and R.B. Nicholson: Progr. Mat. ScL, 1963,10, 151-156. O.R. Myhr, Ph.D Thesis, 1990, Division of Metallurgy, The Norwegian Institute of Technology, Trondheim, Norway. European Recommendations for Aluminium Alloy Structures, 1978. G. Steidl and R. Mossinger: Aluminium, 1977, 53, 199-203. O.T. Midling, 0. Grong and M. Camping: Proc. 12th Riso Int. Symp. on Materials Science: Metal Matrix Composites—Processing, Micro structure and Properties, Roskilde, Denmark, 1991, pp. 529-534. Publ. Riso National Laboratory (1991). O.T. Midling, 0. Grong and D.H. Bratland: Proc. 3rd Int. Conf. on Aluminium Alloys — Their Physical and Mechanical Properties, Trondheim, Norway, 1992, pp. 99-105. Publ. The Norwegian Institute of Technology, Department of Metallurgy (1992). O.T. Midling and 0. Grong: Proc. 3rd Int. Conf. on Trends in Welding Research, June, 1992, Gatlinburg, TN, pp. 1147-1151. Publ. ASM International (1993). O.T. Midling and 0. Grong: Proc. Int. Conf Advanced Composites '93, Wollongon, Australia, February 1993, pp. 1221-1226. Publ. The Minerals, Metals & Materials Society (1993). O.T. Midling and 0. Grong: Acta Metall. Mater., 1994, 42, 1595-1609; ibid, 1611-1622. N.N. Rykalin, A.I. Pugin, V.A. Vasil'eva: Weld. Prod, 1959, 6, 42-52. B. Crossland: Cont. Phys., 1971,12, 559-574.
Appendix 7.1 Nomenclature lattice parameter (nm)
particle diameter (Jim, m)
cross section (mm2, m 2 )
inclusion diameter (jJm, m)
start temperature of ferrite to austenite transformation (0C, K)
amount of deposited metal (mm2) diffusivity (mm2 s"1, m2 s"1)
end temperature of ferrite to austenite transformation (0C, K)
average grain size ((Xm, m) lattice diffusion coefficient (mm2 s"1, mV1)
Burgers vector (nm, m) body-centred cubic
elongation (%) body-centred tetragonal gross heat input (kJ mm"1)
amount of fused parent metal (mm2)
binding energy between hydrogen and trap site (J mol"1, kJ mol"1)
kinetic constant in Hollomon-Jaffe parameter
Young's modulus of matrix (MPa, GN m-2)
base metal half crack length (jum, m)
Young's modulus of particle (MPa, GN m-2)
various kinetic and empirical constants Gaussian error function element concentration (ppm, ml per 100 g, |il cm-3)
particle volume fraction
eutectic concentration (wt%)
volume fraction of hardening precipitates in natural ageing model
initial element concentration (ppm, ml per 100 g, |il cnr 3 )
initial particle volume fraction
maximum solid solubility (wt%)
eutectic fraction
base metal or weld metal element concentration (wt%, ppm, ml per 100 g,
flux-cored arc welding face-centred cubic
jil cm"3)
filler wire Yurioka carbon equivalent grain coarsened region HW carbon equivalent 1
gas metal arc welding
crack tip opening displacement grain refined region Charpy V-notch gas tungsten arc welding plate thickness (mm)
hydrogen content related to fused metal (ml per 100 g or g per ton)
post weld heat treatment net power (W)
Rockwell C hardness Vickers hardness (kg mm"2 or VPN) Vickers hardness in the artificially aged condition (kg mm"2 or VPN) matrix Vickers hardness in the absence of hardening precipitates (kg mm"2 or VPN)
apparent activation energy for softening reaction (J mol"1, kJ mol"1) radius vector (mm, m) isothermal zone width referred to fusion boundary (mm) universal gas constant (8.314 J mol"1 K-i)
kinetic strength of thermal cycle with respect to P' (Mg2Si) formation
friction surface radius (mm, m)
intercritical region
implant rupture strength (MPa)
locking parameter in Hall-Petch equation (MPa |im 1/2 )
ultimate tensile strength (MPa)
equilibrium partitioning coefficient density of trap site half length of fusion zone in hydrogen diffusion model (mm, m) longitudinal direction (notch perpendicular to plate rolling direction) strain hardening exponent in Ludwik equation interfacial torque (Nm)
0.2% proof stress (MPa) scanning electron microscope shielded metal arc welding subcritical region time (s) maximum hold time required for complete particle dissolution at T (s) critical hold time required to precipitate a certain amount of P'(Mg2Si) at T (S)
martensite-austenite constituent metal matrix composite time exponent
welding time (s) cooling time from 600 to 4000C (s) cooling time from 800 to 5000C (s)
dimensionless operating parameter in heat flow model
cooling time from 1200 to 8000C (s)
friction pressure (N mm"2, MPa)
equivalent isothermal hold time at 333K (s)
Hollomon-Jaffe parameter
temperature (0C, K)
Dorn parameter (s)
chosen reference temperature (0C, K)
pressure distribution across weld interface (MPa)
eutectic temperature (0C, K)
melting point (0C, K)
strength (MPa)
ambient temperature (0C, K)
yield stress (MPa)
0
peak temperature ( C, K)
intergranular fracture strength (MPa)
artificially aged condition
matrix fracture strength (MPa)
transmission electron microscope transverse direction (notch parallel with plate rolling direction) velocity (m s"1) surface velocity (ms"1) area under stress-strain curve (J m~3)
friction stress (MPa) yield strength in artificially aged condition (MPa) matrix yield strength in the absence of hardening precipitates (MPa) critical stress for particle cracking (MPa)
ultimate tensile strength radial stress (MPa) welding speed (mm s"1) inclusion volume fraction
threshold stress for H2S stress corrosion cracking (MPa)
Vickers pyramid number
tangential stress (MPa)
welding direction (mm, m)
effective surface energy (J irr 2 )
transverse direction (mm, m)
internal interface (or antiphase) boundary energy (J m~2)
y-coordinate at maximum width of isotherm (mm)
surface energy of particle (J m~2)
isothermal zone width (mm, m)
friction coefficient
through-thickness direction (mm, m)
maximum shear stress (MPa)
partly deformed region in friction welding model (mm)
dimensionless cooling time from 800 to 5000C
fully plasticised region in friction welding model (mm)
dimensionless temperature conforming to 8000C
undeformed region in friction welding model (mm)
dimensionless temperature conforming to 5000C
stress concentration factor
arc efficiency factor
true fracture strain
dimensionless supersaturation
dimensionless plate thickness
) non-hardening precipitates in Al-MgSi alloys and Al-SiC MMCs
material constants volume heat capacity (J mm"3 0C"1)
) hardening precipitates in Al-Mg-Si alloys and Al-SiC MMCs
dimensionless strength parameter dimensionless strength parameter in reversion model dimensionless strength parameter in natural ageing model dimensionless strength parameter in work hardening model
net precipitation strength increment (MPa) maximum precipitation strength increment (MPa) HAZ strength reduction factor angular velocity (rad/s)
8 Exercise Problems with Solutions
8.1 Introduction This chapter contains a collection of different exercise problems which the author has adopted in his welding metallurgy course for graduate (mature) students. They illustrate how the models described in the previous chapters can be used to solve practical problems of more interdisciplinary nature. Each of them contains a 'problem description' and some background information on materials and welding conditions. The exercises are designed to illuminate the microstructural connections throughout the weld thermal cycle and show how the properties achieved depend on the operating conditions applied. Solutions to the problems are also presented. These are not complete or exhaustive, but are just meant as an aid to the reader to develop the ideas further.
8.2 Exercise Problem I: Welding of Low Alloy Steels Problem description Consider gas metal arc (GMA) welding of low allow steels under the following conditions: (i) (ii) (iii) (iv)
Tack welding of a T-joint (Fig. 8.1) Root pass deposition in a single V-groove (Fig. 8.2) Root pass deposition in a X-groove (Fig. 8.3) Deposition of cap layer during multipass welding (Fig. 8.4)
The materials to be welded are a C-Mn steel and a Nb-microalloyed low carbon steel with chemical compositions and properties as listed in Tables 8.1 and 8.2. Details of welding parameters and operational conditions are given in Table 8.3 and 8.4, respectively. Table 8.1 Exercise problem I: Base plate chemical compositions (in wt%). Steel C-Mn
1
LC-Nb 1
1
C
Si
Mn
P
S
Nb
Al
0.20
0.35
1.46
0.003
0.002
-
0.037
0.08
0.26
1.44
0.003
0.003
0.020
0.025
Ti: -0.008, N: 0.0027, Ca: 0.0040, B: 0.0002.
Table 8.2 Exercise problem I: Mechanical properties of base materials. Steel
1
Rp02 (MPa)
I
Rm (MPa)
I
El. (%)
I
CVN - 4 0 (J)
C-Mn
328
525
33
150
LC-Nb
430
525
32
225
Table 8.3 Exercise problem I: Welding parameters. Parameter
/ (A)
U (V)
v (mm s"1)
Value
150
21
4
f
The arc efficiency factor may be taken equal to 0.85 (see Table 1.3). No preheating is applied (T0 = 20 0C).
Table 8.4 Exercise problem I: Operational conditions and filler wire characteristics K Shielding gas:
Pure CO2
Gas flow rate:
15 Nl per min
Wire diameter:
1.0 mm
Wire feed rate:
6.0 m per min
Wire composition:
C: 0.1 wt%, Si: 1.0 wt%, Mn: 1.7 wt%
Weld metal* composition:
C: 0.09 wt%, Si: 0.7 wt%, Mn: 1.2 wt%
Weld metal* properties:
Rp02: 460 MPa, Rm: 560 MPa, El.: 26%, CVN _40: 50 J
f
Data compiled from dedicatedfillerwire catalogues and welding manuals. * Values refer to all weld metal deposit.
Fig. 8.1. Tack welding of a T-joint.
Fig. 8.2. Root pass deposition in a single V-groove.
Fig. 8.3. Root pass deposition in a X-groove.
Fig. 8.4. Deposition of cap layer during multipass welding.
Analysis: The students should work in groups (3 to 4 persons) where each group select a specific combination of base material and welding conditions (e.g. deposition of a cap layer on the top of a thick multipass C-Mn steel weld). The problem here is to evaluate the response of the base material to heat released by the welding arc. The analysis should be quantitative in nature and based on sound physical principles. The following points shall be considered: (a) Select an appropriate heat flow model for the system under consideration. (b) Estimate the minimum bead length which is required to achieve pseudo-steady state (i.e. a temperature field that does not vary with position when observed from a point located in the heat source). (c) Estimate the value of the deposition coefficient kx (in gA " 1 S" 1 ), the weld cross section areas D and B (in mm2), and the mixing ratio DI(B + D) during welding. (d) Estimate the weld metal chemical composition. Calculate then the following quantities: - Total loss of Si and Mn in the arc column - Total oxygen pick-up in the weld pool - Residual oxygen level and total amount of oxygen rejected from the weld pool during deoxidation - Total amount of slag formed during welding (in g per 100 gram weld metal) (e) Carry out a total oxygen balance for the system, and estimate the resulting CO content in the welding exhaust gas. (f) Estimate the chemical composition, volume fraction, and mean size (diameter) of the
oxide inclusions which form in the cold part of the weld pool. Calculate then the following inclusion characteristics: -
Number of particles per unit volume Number of particles per unit area Total surface area of particles per unit volume Mean particle centre to centre volume spacing
(g) Estimate the weld metal solidification mode and the resulting columnar grain morphology. Indicate also the type of substructure which form at different positions from the weld centre line. (h) Evaluate the thermal stability of the base metal grain boundary pinning precipitates. At which temperature will these precipitates dissolve? (i) Calculate the austenite grain size profile across the HAZ. Estimate also the size of the columnar austenite grains in the weld metal. (j) Estimate the primary reaction products which form in the weld metal and the HAZ after the austenite to ferrite transformation. (k) Estimate the maximum hardness in the HAZ after welding. Use this information to evaluate the risk of hydrogen cracking and H2S stress corrosion cracking during service. (1) Estimate the CVN toughness both in the weld metal and the HAZ after welding. (m) Based on the results obtained explain why the carbon content of modern structural steels has been gradually lowered to values below 0.1 wt% in step with the progress in steel manufacturing technology. Solution: In all cases we can use stringer bead deposition on thick plates as a model system. It follows from the analysis in Section 1.10.7 (Chapter 1) that the pertinent difference in the effective heat diffusion area between a bead-on-plate weld and a groove weld may conveniently be accounted for by introducing a correction factor/, which depends on the geometry of the groove (see Fig. 1.68). Thus, in the general case the net (effective) power of the heat source can be written as:
In the following, we shall only consider deposition of a cap layer on a thick plate where / = 1, but the analysis can readily be applied to other combinations of steels and welding conditions as well (e.g./< 1). In the former case, we get:
Table 1.1 (Chapter 1) contains relevant input data for the steel thermal properties. (a) The problem of interest is whether we must use the general (but complex) Rosenthal
thick plate solution (equation (1-45)) or can adopt the simplified solution for a fast moving high power source (equation (1-73)). Fig 1.24 provides a basis for such an evaluation. The most critical position will be the fusion line. If we neglect the latent heat of melting, the QJn3 ratio at the melting point becomes:
Readings from Fig. 1.24 suggest that the error introduced by neglecting the contribution from heat flow in the welding direction is sufficiently small that it can be disregarded in the calculations of the HAZ thermal programme. This means that equation (1-73) can be used in replacement of equation (1-45) if that is desirable. (b) The duration of the transient heating period depends on the actual point of observation (i.e. the distance from the heat source). If we, as an illustration of principles, would like to apply the pseudo-steady state solution down to a peak temperature of, say, 7000C, the corresponding nJQ ratio at that temperature becomes:
From Fig. 1.21 we see that this ratio corresponds to a dimensionless radius vector a3m of about 5. The duration of the transient heating period may now be read from Fig. 1.18. A crude extrapolation gives:
from which
The minimum bead length is thus 25 mm, which is surprisingly short, (c) The value of the deposition coefficient may be estimated from the data in Table 8.4.
This value corresponds to a kVp ratio of about 0.65 mm 3A 1 S \ which is in excellent agreement with the data quoted in Table 1.7. The area D of deposited metal thus becomes (see equation (1-120)):
The corresponding area of fused parent metal is most conveniently read from Fig. 1.21. Taking the n3/Q ratio at the melting point equal to (1/0.22) ~ 4.5, we obtain:
from which
The mixing ratio is thus:
This value is somewhat lower than the expected mixing ratio, which for low heat input welding is close to 0.67. (d) The composition data in Table 8.4 refer to all weld metal deposit. Since the dilution with respect to the base material in this case is small, the weld metal composition would be expected to be close to that given in Table 8.4. An estimate of the total burn-off of alloying elements during welding can be obtained by considering the difference in chemical composition between the filler wire and the weld metal. In the present case we get:
Loss of silicon As shown in Section 2.10.1.3 (Chapter 2), the silicon loss can partly be ascribed to SiO(g) formation in the arc column (with consequent fume formation), and partly to reactions with oxygen in the weld pool during the deoxidation stage (with consequent silicate slag formation). The former loss can be estimated from the fume formation data presented in Table 2.6. Taking the fume formation rate (FFF) of silicon equal to 63 mg min"1, the total loss of silicon in the arc column amounts to:
The corresponding oxidation loss of silicon in the weld pool is thus:
Loss of manganese As shown in Section 2.10.1.4 (Chapter 2), manganese is partly lost in the arc column due evaporation and partly in the weld pool due to deoxidation reactions. Taking the fume formation rate of manganese equal to 14 mg min"1 (from Table 2.6), the total loss of Mn in the arc column amounts to:
The corresponding oxidation loss of manganese in the weld pool is thus:
Oxygen pick-up in the weld pool When the oxidation losses of silicon and manganese in the weld pool are known, it is possible to calculate the total oxygen pick-up in the hot spot of the pool immediately beneath the root of the arc, according to the procedure outlined in Section 2.10.1.5 (Chapter 2). However, first we need to estimate the residual weld metal oxygen content on the basis of the thermodynamic model presented in Fig. 2.56. In the present example, the numerical value of the deoxidation parameter is:
Reading from Fig. 2.56 gives a residual oxygen content of about 0.07 wt%. The total oxygen pick-up in the weld pool is thus:
Rejected oxygen from the weld pool The amount of rejected oxygen is equal to the difference between the total and the residual oxygen level:
From this we see that most of the oxygen which is picked up at elevated temperatures is rejected again during cooling in the weld pool due to deoxidation reactions and subsequent phase separation. Manganese silicate slag formation The weld pool deoxidation reactions give rise to the formation of a top bead slag, as shown in Section 2.10.1.5 (Chapter 2). In the present example the amount of slag per 10Og weld metal is equal to:
A comparison with Fig. 2.35 shows that the calculated weight of slag is in reasonable agreement with experimental observations. (e) The oxygen balance is carried out in accordance with the procedure outlined in Section 2.10.1.7 (Chapter 2). First we need to estimate the total mass of weld metal produced per unit time:
The total CO2 consumption is thus: Oxidation of carbon:
Oxidation of silicon:
Oxidation of manganese:
Increase in the weld metal oxygen content:
The total CO evolution is equal to the sum of these four contributions:
The resulting CO content in the welding exhaust gas is thus:
A comparison with the experimental data in Table 2.2 shows that the calculated CO content is of the expected order of magnitude. (f) The deoxidation model in Section 2.12.4.1 (Chapter 2) can be used to estimate the inclusion composition. From Fig. 2.68 we see that the inclusions are essentially pure manganese silicates with an overall composition close to MnSiO3. When the inclusion composition is known, it is possible to convert the residual weld metal oxygen content into an equivalent inclusion volume fraction according to the procedure outlined in Section 2.12.1.Taking the stoichiometric conversion factor equal to 5.0 X 10~2 for manganese silicate slags, we obtain:
Moreover, we can use equation (2-79) in Section 2.12.2.2 to calculate the mean diameter of the inclusions:
The different inclusion characteristics may now be estimated from equations (2-80) to (2-83): Number of particles per mm3:
Number of particles per mm2:
Total surface area of particles per mm3:
Mean particle centre to centre volume spacing:
A comparison with Table 2.11 shows that the calculated inclusion characteristics are in reasonable agreement with those reported for C-Mn steel weld metals. (g) The characteristic growth pattern of columnar grains in bead-on-plate welds is shown schematically in Fig. 3.33. The first phase to form will be delta ferrite which subsequently decomposes to austenite via a peritectic transformation (see Fig. 3.72). The important question is whether re-nucleation of the grains will occur during solidification. In practice, this depends on the interplay between a number of variables which cannot readily be accounted for in a simplified analysis, including the weld pool geometry, the cooling rate and the nucleation potency of the non-metallic inclusions. Broadly speaking, the energy barrier associated with nucleation of delta ferrite at manganese silicates is rather high (e.g. see Fig. 3.30), which suggests that formation of new grains ahead of the advancing solid/liquid interface is not very likely under the prevailing circumstances. Hence, the columnar grain zone would be expected to extend entirely from the fusion line towards the centre of the weld, as frequently observed in this type of welds. Moreover, Fig. 3.43 provides a basis for estimating the substructure of the weld metal columnar grains. Close to weld centre-line the local crystal growth rate will approach the welding speed (i.e. RL ~ 4 mm s"1). At the same time a simple analytical solution exists for the thermal gradient in the weld pool (equation (3-28)):
From this we see that a cellular-dendritic type of substructure is likely to form within the central parts of the fusion zone, in agreement with general experience (see Fig. 3.36). (h) Fig. 5.25 shows the location of the cap layer. Since the base plate is a Nb-microalloyed steel, the important grain boundary pinning precipitates within the HAZ are either NbC, NbN or a mixture of these. In the former case the equilibrium dissolution temperature may be estimated from the solubility product of the pure binary compounds. From equation (4-4) and Table 4.1, we have:
and
This shows that NbC is thermodynamically more stable than NbN. In practice, the real dissolution temperature may be significantly higher than that predicted from equation (4-4) because of the kinetic superheating (see discussion in Section 4.4, Chapter 4). The grain growth diagram in Fig. 5.21 (a) provides a basis for estimating the effect of heating rate (heat input) on the dissolution kinetics. Taking the ordinate qo /v equal to 2678/4000 = 0.67 kJ mm"1, we obtain:
This corresponds to a kinetic superheating of about 2000C in the case of NbC. In the HAZ on the weld metal side (see Fig. 5.25), oxide inclusions may act as effective grain boundary pinning precipitates. These will be thermodynamically stable up to the melting point of the steel. (i) The austenite grain size profile across the base plate HAZ can be read from Fig. 5.21(a). Taking the ordinate q/v equal to 0.67 kJ mm"1, we see that the maximum austenite grain size at the fusion boundary will exceed 100 /mm because of dissolution of the base metal grain boundary pinning precipitates. In the HAZ on the weld metal side, the situation is different. Here the stable weld metal oxide inclusions will impede austenite grain growth to a much larger extent.The limiting austenite grain size may be calculated from equation (5-21).Taking the Zener coefficient equal to 0.5 for oxide inclusions in steel (Fig. 5.4), we obtain:
Because of the phenomenon of epitaxial grain growth (see Section 3.3, Chapter 3), the initial size of the weld metal delta ferrite/austenite columnar grains would be expected to be comparable to the size of the HAZ austenite grains adjacent to the fusion boundary. Since the latter varies along the periphery of the fusion boundary at the same time as competitive grain growth leads to a general coarsening of the solidification microstructure with increasing distance from the fusion boundary, an average columnar austenite grain size of about 50 /mm seems reasonable under the prevailing circumstances. (j) As an illustration of principles, we shall assume that the CCT diagram in Fig. 6.27(a) provides an adequate description of the base plate transformation behaviour during welding. The cooling time from 800 to 500 0C can be calculated from equation (1-67):
from which
Readings from Fig. 6.27(a) give the following microstructures within the grain coarsened and grain refined region of the HAZ, respectively: Grain coarsened region (T ~ 13500C): Microstructure : 100% lath martensite Transformation start temperature: ~ 470 0C Grain refined region (Tp «10000C): Microstructure : ferrite + pearlite Transformation start temperature: ~ 600 0C It follows that the observed difference in the HAZ transformation behaviour can mainly be attributed to a corresponding difference in the prior austenite grain size, which according to Fig. 5.21(a) is about 50 /im at Tp « 1350 0C and below 10 ^m at Tp « 10000C. In addition, small islands of plate martensite will form within the intercritical (partly transformed) HAZ, where the peak temperature of the thermal cycle has been between Ac1 and Ac3 (see discussion in Section 6.3.8.2, Chapter 6). Just above the Ac1 temperature the volume fraction of the M-A (martensite-austenite) constituent is approximately equal to the base plate pearlite content (Fig. 6.66), which in the present case is about 8 vol%, as judged from the steel carbon content. Considering the weld metal, the situation is different. Here the oxide inclusions will strongly affect the microstructure evolution by promoting intragranular nucleation of acicular ferrite (see discussion in Section 6.3.5, Chapter 6). In practice, the role of inclusions in weld metal transformation kinetics is difficult to assess and hence, we will take a more simplistic (pragmatic) approach to this problem by just comparing the total surface area available for nucleation of ferrite at prior austenite grain boundaries and inclusions, respectively (SJGB) versus SJI)). The following three regions of the weld are considered: As-deposited weld metal:
Reheated weld metal (close to fusion line):
Reheated weld metal (far from fusion line): In this case an estimate will be made for dy = 10 /mi.
From the above calculations it is apparent that the conditions for acicular ferrite formation are particularly favourable within the as-deposited weld metal (Sx(I) > SJGB)), and somewhat less favourable within the high peak temperature region of the weld HAZ (SJGB) > SJI)). In contrast, acicular ferrite would not be expected to form within the low peak temperature region of the HAZ, since nucleation of ferrite at austenite grain boundaries in this case will completely override nucleation at inclusions (SJGB) » SJI)).This is also in agreement with general experience (e.g. see photographs of typical microstructures in Fig. 6.19(c) and (d)). (k) The maximum hardness/strength level within the grain coarsened region of the HAZ can be estimated from the diagrams presented in Section 7.2.2 (Chapter 7) if the steel composition and welding parameters fall within the specified range. Alternatively, we can use Fig. 7.19, which applies to low carbon microalloyed steels. Taking the cooling time from 800 to 500 0C, Ar8/5, equal to 3.3 s, we obtain: HVmax = ~ 380 VPN and Rp02 (max) = ~ 980 MPa In general, a hardness rather than a strength criterion is used as a basis for evaluation of the risk of hydrogen cracking and H2S stress corrosion cracking during service. In the former case an upper limit of about 300 to 325 VPN is incorporated in many welding specifications to avoid problems with hydrogen cracking, but this restriction can be relaxed if specific precautionary actions are taken during the welding operation to reduce the supply of hydrogen as shown in Section 7.2.3 (Chapter 7). Considering the H2S stress corrosion cracking resistance a maximum hardness level of 248 VPN is strictly enforced in many welding specifications, as discussed previously in Section 7.2.4 (Chapter 7). Hence, significant tempering of the martensite would be required if the weldment is going to be used in environments containing sour oil or gas. (1) In general, the toughness requirements vary with the type of application, but for offshore structures a minimum CVN toughness of 35J at — 400C is frequently specified. From the CVN data in Tables 8.2 and 8.4 it apparent that both the base plate and the weld metal meet this requirement. Moreover, auto-tempered low carbon martensite and polygonal ferrite, which form within the grain coarsened and grain refined region of the HAZ, respectively are known to have an adequate cleavage resistance.This means that the intercritical HAZ is the most critical region of the joint when it comes to toughness due to the presence of high carbon plate martensite within the ferrite matrix (see Figs. 6.61 through 6.65 and discussion in Section 7.2.2.3, Chapter 7). In practice, the problem may be solved by applying an appropriate post weld heat treatment (PWHT). (m) Since the properties of martensite depend on the carbon content, C-Mn steel weldments will generally be more prone to hydrogen cracking, H2S stress corrosion cracking and brittle fraction initiation in the HAZ than low carbon microalloyed steel weldments. This explains
why the base plate carbon content has been gradually lowered to values well below 0.1 wt% in step with the progress in steel plate manufacturing technology.
8.3 Exercise Problem II: Welding of Austenitic Stainless Steels Problem
description:
Consider GTA welding of 2 mm thin sheets of AISI 316 austenitic stainless steel with chemical composition as listed in Table 8.5. The base plate has an average grain size of 18 /xm in the fully annealed condition, which conforms to a tensile yield strength of about 300 MPa. The sheets shall be butt welded in one pass, using a simple I-groove with 3 mm root gap. In this case the addition of filler wire is adjusted so that the area of the weld reinforcement amounts to 50% of the groove cross section. Details of welding parameters and operational conditions are given in Table 8.6 and 8.7, respectively. Table 8.5 Exercise problem II: Base plate chemical composition (in wt%). Steel
C
Mn
Cr
Ni
AISI316
0.03
2.0
16
12
Table 8.6 Exercise problem II: Welding parameters*. Parameter Value
/ (A)
U (V)
200
15
+
v (mm s"1) 5 0
The arc efficiency factor may be taken equal to 0.4. No preheating is applied (T0 = 20 C).
Table 8.7 Exercise problem II: Operational conditions and filler wire characteristics1. Shielding gas:
Argon
Wire composition: Weld metal* properties: Data compiled from dedicatedfillerwire catalogues and welding manuals. Values refer to all weld metal deposit.
Analysis: The problem here is to evaluate the response of the base material to welding under the conditions described above. The analysis should be quantitative in nature and based on sound physical principles. The following input data are recommended:
Specific questions: (a) Select an appropriate heat flow model for the system under consideration. (b) Estimate the minimum bead length which is required to achieve pseudo-steady state down to a peak temperature of 1000 0C. (c) Estimate the deposition rate (in gA^s" 1 ), the weld cross section areas D and B (in mm2), and the dilution ratio B/(B + D) during welding. (d) Estimate the weld metal chemical composition for the given combination of base plate, filler wire and dilution ratio. (e) Sketch the contour of the weld pool and the resulting columnar grain morphology in the x-y plane after solidification. Estimate also the weld metal delta ferrite content. (f) Evaluate the risk of solidification cracking during welding. (g) Calculate the austenite grain size profile across the HAZ. Estimate also the size of the columnar grains in the weld metal. (h) Evaluate the risk of chromium carbide formation in the HAZ during welding. (i) Estimate on the basis of the Hall-Petch relation the maximum load bearing capacity of the joint during service. Solution: (a) The problem of interest is whether we must use the general (but complex) Rosenthal thin plate solution (equation (1-81)) or can adopt the simplified solution for a fast moving high power source (equation (1-100)). Fig 1.43 provides a basis for such an evaluation. The most critical position will be the fusion line. If we neglect the latent heat of melting, the BJn^ ratio at the melting point becomes:
Similarly, the dimensionless plate thickness is equal to:
Readings from Fig. 1.43 show that we are outside the validity range of the simplified 1-D model close to the fusion line, but that this solution is a good approximation within the low peak temperature region of the HAZ. Here equation (1-100) may be used in replacement of equation (1-81). (b) The duration of the transient heating period depends on the actual point of observation (i.e. the distance from the heat source). If we would like to apply the pseudo-steady state solution down to a peak temperature of 1000 0C, the corresponding nJ8B ratio becomes:
From Fig. 1.31 we see that this ratio corresponds to a dimensionless radius vector a5m of about 5. The duration of the transient heating period may now be read from Fig. 1.28. A crude extrapolation gives:
from which
(c) First we need to calculate D:
This gives the following deposition rate:
The total area of fused metal can be read from Fig. 1.31. At the melting point the n3/0p8 ratio is close to 2, which gives:
and
This gives:
Note that in these calculations we have assumed that A2 is equal to the sum of (B+D) in order to achieve realistic numbers. (d) The weld metal composition can be calulated from a simple 'rule of mixtures':
By using input data from Tables 8.5 and 8.7, we get:
(e) The bead morphology can be read from Fig. 1.29. Taking the 68In3 ratio at the melting point equal to 0.5, it is easy to verify that the geometry of the weld pool in this case is tearshaped. The columnar grain structure is therefore similar to that shown in Fig. 3.11(b). When the composition is known the weld metal microstructure can be read from Fig. 7.53 by considering the resulting chromium and nickel equivalents:
This gives a delta ferrite content of about 7 vol%. (f) Normally, a minimum delta ferrite content of about 5 to 10 vol% is specified to avoid problems with solidification cracking in the weld metal (see discussion in Section 7.3.4, Chapter 7). This requirement is clearly met under the prevailing circumstances. (g) The HAZ austenite grain size in different positions from the fusion boundary can be read from Fig. 5.30(b). In the present example the net heat input per mm2 of the weld is equal to:
This corresponds to a maximum austenite grain size of about 60/mi close to the fusion boundary, which also is a reasonable estimate of the weld metal columnar grain size. (h) The most critical position is the low peak temperature region of the weld HAZ where Tp is between 800 and 1000 0C, as shown in Section 6.4.2 (Chapter 6). However, it is evident from Fig. 6.69 that the risk of chromium carbide formation in this case is negligible because of the low base plate carbon content. Hence, the corrosion resistance will not be significantly affected by the welding operation. (i) The minimum HAZ strength level may conveniently be calculated from equation (7-21), using input data from Example 7.5 (page 530):
This gives the following strength reduction factor for the joint:
8.4 Exercise Problem III: Welding of Al-Mg-Si Alloys Problem
description:
Consider G M A welding of 5 mm A A 6082 extrusions with chemical composition as listed in Table 8.8. The base material has a Vickers hardness and tensile yield strength of 110 VPN and 280 MPa, respectively in the T6 temper condition. The extrusions shall be butt welded in one pass, using a simple I-groove with no root gap. Two different filler wires are available, one Al-Si wire and one Al-Mg wire (in the following designated wire I and II, respectively). Details of welding parameters and operational conditions are given in Table 8.9 and 8.10, respectively. Table 8.8 Exercise problem III: Base plate chemical composition (in wt%). Alloy AA 6082
Si
Mg
Mn
Fe
0.98
0.64
0.52
0.19
Table 8.9 Exercise problem III: Welding parameters1. Parameter Value
/(A)
(/(V)
200
28
v (mm s"1) 10 0
|The arc efficiency factor may be taken equal to 0.8. No preheating is applied (T = 20 C).
Table 8.10 Exercise problem III: Operational conditions and filler wire characteristics1. Shielding gas:
Argon
Gasflowrate:
20 Nl per min
Wire diameter:
1.6 mm
Wire feed rate:
5.5 m per min
Wire composition:
Wire I : Al + 5 wt% Si Wire II: Al +5 wt% Mg
Weld metal* properties:
Wire I: Rp02 : 55 MPa, Rn; 165 MPa, El.: 18% Wire II: Rp02 : >130 MPa, Rn;. >280 MPa, El.: >17%, CVN+20: >30 J
Data compiled from dedicated filler wire catalogues and welding manuals. Values refer to all weld metal deposit.
Analysis: The problem here is to evaluate the response of the base material to welding under the conditions described above. The analysis should be quantitative in nature and based on sound physical principles. The following input data are recommended:
Specific questions:
Temperature, 0C
Atomic percent silicon
Weight percent silicon Fig. 8.5. The binary Al-Si phase diagram.
Temperature, 0C
Atomic percent magnesium
Weight percent magnesium Fig. 8.6. The binary Al-Mg phase diagram.
(a) Select an appropriate heat flow model for the system under consideration. (b) Estimate the minimum bead length which is required to achieve pseudo-steady state down to a peak temperature of 200 0C. (c) Estimate the value of the deposition coefficient k' (in gA^s" 1 ), the weld cross section areas B and Z) (in mm2), and the dilution ratio BI(B + D) during welding. (d) Estimate the content of Mg and Si in the weld metal. (e) Sketch the weld metal columnar grain structure and the segregation pattern during solidification. Indicate also the type of substructure which forms at different positions along the periphery of the fusion boundary. Relevant binary phase diagrams are given in Figs. 8.5 and 8.6. (f) Evaluate the risk of solidification cracking during welding. (g) Evaluate the risk of liquation cracking in the HAZ during welding. (h) Sketch the sequence of reactions occurring within the HAZ during welding. Then estimate the following quantities: - The temperature for incipient dissolution of /3". - The total width of the HAZ (referred to the fusion boundary). - The temperature for full dissolution of /3". - The total width of the fully reverted HAZ (referred to the fusion boundary). (i) Estimate for each combination of filler wire and parent material an overall strength reduction factor which determines the load bearing capacity of the joint. (j) Imagine now that the same extrusion instead is used in the fully annealed (O- temper) condition with a Vickers hardness and tensile yield strength of 50 VPN and 100 MPa, respectively. To what extent will the temper condition affect the microstructure and strength evolution during welding? Solution: (a) The problem of interest is whether we must use the general (but complex) Rosenthal thin plate solution (equation (1-81)) or can adopt the simplified solution for a fast moving high power source equation (1-100)). Fig 1.43 provides a basis for such an evaluation. The most critical position will be the fusion line. If we neglect the latent heat of melting, the 6 In3 ratio at the melting point becomes:
Similarly, the dimensionless plate thickness is equal to:
Readings from Fig. 1.43 show that we are outside the validity range of the simplified 1-D solution close to the fusion line, but that equation (1-100) may be used (with some reservations) within the low peak temperature region of the HAZ. (b) The duration of the transient heating period depends on the actual point of observation (i.e. the distance from the heat source). If we would like to apply the pseudo-steady state solution down to a peak temperature of 200 0C, the corresponding n/86p ratio becomes:
From Fig. 1.31 we see that this ratio corresponds to a dimensionless radius vector
from which
It follows that the minimum bead length required to achieve pseudo-steady state during aluminium welding is much longer than in steel welding due to the pertinent differences in the heat 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 agreement with the data quoted in Table 1.7. The area D of deposited metal thus becomes (see equation (1-120)):
The total area of fused metal can be read from Fig. 1.31. At the melting point the nJ0p8 ratio 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) in order to achieve realistic numbers. (d) The weld metal composition can be calulated from a simple 'rule of mixtures':
By using input data from Tables 8.8 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 melting point equal to 1, it is easy to verify that the shape of weld pool in this case is elliptical. The columnar 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 metal columnar grains. Close to weld centre-line the local crystal growth rate will approach the welding speed (i.e. RL ~ 10 mm s"1). At the same time a simple analytical solution exists for the 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 the central 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 Scheil equation (equation (3-46)) may be used for an analysis of the segregation pattern during solidification. 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 sensitive 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 I In this case the fraction of eutectic liquid is so abundant that it backfills and 'heals' all incipient cracks. Hence, the hot cracking susceptibility is low. Wire II When the Al-Mg filler wire is used the fraction of eutectic liquid is just large enough to form continuous films at the columnar grain boundaries. Hence, the hot cracking susceptibility is high. (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 for evaluating the HAZ cracking susceptibility: Wire I In this case the risk of liquation cracking is small because the solidus temperature of the weld metal is lower than the actual melting temperatures of the base metal constituent phases. Wire II Due to the high Bi(B + D) ratio involved, the solidus temperature of the weld metal will exceed the actual melting temperatures of the base metal constituent phases. This may lead to liquation cracking in parts of the HAZ where the peak temperature is greater than, say, 555 to 559 0C. (h) The sequence of reactions occurring within the HAZ during welding of AA 6082-T6 aluminium 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 0.08 kJmm~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 for incipient dissolution of /3" is in good agreement with that obtained from the solubility product. (i) The yield strength in HAZ and the weld metal can be obtained from Fig. 7.67 and Table 8.10, 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 mechanical properties and should therefore be used, unless the cracking resistance is of particular concern. (j) When the material is present in the O-temper condition, it will contain an appreciable amount of the equilibrium /3-Mg2Si phase. This will tend to accelerate the problem with liquation 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 thermodynamically much more stable than the metastable /3" phase. In practice, this means that only a narrow solutionised zone will form adjacent to the fusion boundary. However, within this 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 80 VPN 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
Author Index
A Aaron, H.B. 320, 326, 398-9 Aaronson, H.I. 408, 429 Abson, DJ. 407, 428, 440, 477-8, 485,493, 504 Adams, CM. 26 Adrian, H. 301,303 Agren, J. 320-1,326 Akselsen, O.M. 97, 345, 347, 349, 367,406,414-15,419,444,446, 448-54, 481, 484, 488-90, 4956, 499, 502-7, 525 Alberry, RJ. 374, 500, 502 Alcock, CB. 159 AIi, A. 427-8 American Society for Testing Materials (ASTM) 364 Andersen, I. 483 Anderson, M.P. 380 Anderson, RD. 3 Ankem, S. 343,351 Apold,A. 174-5 Araki, T. 505-6 Ardeil, AJ. 494 Ashby, M.F. 26, 201, 314, 318, 329, 360, 363-4, 375, 377-8, 459, 461,464 Asthana, R. 326 Atlas of isothermal transformation and cooling transformation diagrams 403 Avrami, M. 403, 422
B Babu, S.S. 210,408,443-4 Bach, H. 138 Bain, E.C 408, 427, 436 Bakes, R.G. 15 Baldwin, W.M. 509,511 Balliger, N.K. 452 Bannister, S.R. 441,443 Barbara, FJ. 435-6, 441-4 Barin, I. 154 Barrie, G.S. 441,443 Barritte, G.S. 434-6,441 Baskes, M.I. 277-8 Beachem,CD. 512 Beaven, RA. 440 Bell, H.B. 171,204-5 Bentley, K.R 15
Berge, J.O. 229 Bernstein, LM. 512 Betzold,J. 413 Bhadeshia, H.K.D.H. 147, 206, 292, 408-9, 413, 422-9, 431, 4 3 3 ^ , 436,441,443-4 Bhatti,A.R. 208-10 Biloni, H. 229 Bjornbakk, B. 486,491 Blander, M. 171,173 Boiling, G.F. 290 Bonnet, C 435, 440 Bradstreet, BJ. 186 Bramfitt, B.L. 244 Bratland, D.H. 459-62, 556-8, 562 British Iron and Steels Research Association 3 Brody, H.D. 272, 276 Brooks, J.A. 277-8, 533 Brown, A.M. 345 Brown, LT. 509, 511 Brown, L.C. 314 Burck, R 289 Burgardt, R 229
C Cahn, J.W. 337, 340-1, 345 Cai, X.-L. 450 Cameron, T.B. 413 Camping, M. 556-8, 562 Capes, J.F. 251,292-3,412 Carslaw, H.S. 2, 4 Chai,CS. 171 Challenger, K.D. 434, 480 Chan, J.W. 403 Charpentier, F.R 435, 440 Chen, J.H. 505-6 Chew, B. 132, 135 Chipman, J. 414 Choi, H.S. 450 Christensen, N. 24, 26-7, 31-2, 80, 88,90-1,97,100, 116, 125, 132, 143,148-50,153,155,158,162, 170-1, 173-4, 176-9, 181-2, 186,189,193,207,345,347,349, 367,500,502,515-17,520-2 Christian, J.W. 329, 400-1, 403-4, 429,431 Cisse, J. 290 Claes, J. 180
Cochrane, R.C. 292-3, 407, 428 Coe,F.R. 128-9,509-10,515 Coleman, M.C 259, 263-4 Collins, F.R. 537 Corbett, J.M. 203, 428 Corderoy, DJ.H. 151, 155, 160-1 Cotton, H J.U. 496 Cottrell, CL.M. 496 Crafts, W. 190 Craig, I. 171 Cross, CE. 251,259,292-3,412,538 Crossland, B. 556 D Dallam, CM. 441 D'annessa, A.T. 280 Das. G. 452 Dauby, P. 180 David, S. A. 96,99,105,210,222,228, 236, 239-41, 250, 260, 272, 278, 290,478 Davis, GJ. 221, 240, 247, 250, 278, 279,292,478 Davis, V. deL. 162 DeArdo, AJ. 290 Deb, P. 434, 480 DebRoy,T.210 Delong,WT.533 Demarest, V. A. 449-50 Devillers, L. 435,440,480, 482 Devletian,J.H.279,285,413 Dieter, G.E. 482,486, 524-5, 529 Distin, PA. 157 Doherty,R.D.301,309,396 Dolby, R.E. 407,444 Dons, A.L. 438,459, 541 Dorn, XE. 501-2 Dowling, J.M. 203,428 Dube, CA. 408 Dudas, J.H. 537 Dumolt, S.D. 547 E Eagar, T.W. 26, 96, 99, 105, 171-2, 174,228 Easterling, K.E. 26, 226, 247, 301, 303, 309, 314, 318, 345, 360, 363-4, 367, 375, 377-8, 380, 389, 392, 403, 408, 427, 429, 435-6, 441-4, 448, 500, 502
Ebeling, R. 201 Edmonds, D.V. 409 Edwards, G.R. 227,259,422-3,425, 428,441 Eickhorn,F. 187-8 Elliott, J.F. 151, 162, 174-5, 179, 182, 184, 191 Engel,A. 187-8 Enjo, T. 547 Es-Souni, M. 440 European Recommendations for Aluminium Alloy Structures 552 Evans, G.M. 137-8, 192-3, 203, 420-1,435,440
F Fainstein, D. 320, 398-9 Farrar, R.A. 435, 441, 443,480 Fast, J.D. 513 Ferrar, R.A. 428,435,444,478,485, 504 Fine, M.E. 389, 403 Fischer, W. A. 162 Fisher, DJ. 221, 234, 242, 251, 259, 261,265-6,270,274 Fleck, N.A. 422-3, 428, 441 Flemings, M.C. 221, 234, 242, 265, 272,275-6 Fortes, M.A. 374-5, 380-1 Fountain, R.W. 414 Fradkov, V.E. 380 Franklin, A.G. 195,208 Fredriksson, H. 290 Frost, HJ. 380 Fruehan, RJ. 156 Fujibayashi, K. 146
G Garcia, C.I. 290 Garland, J. 505 Garland, J.G. 221,240,247,250,278, 279, 292-3, 478 Garret-Reed, AJ. 450 Gergely, M. 501-2 Giovanola, B. 260 Gittos, N.F. 544-5 Gjermundsen, K. 162, 516 Gjestland, H. 541 Gladman, T. 343-5, 452, 479 Gleiser,M. 151,162,174-5,179,191 Goldak,J.A. 515 Goolsby, R.D. 306 Greenwood, J.A. 15 Grest, G.S. 380 Gretoft, B. 147, 422-8 Grevillius, N.F. 182, 185, 188
Grewal, G. 343,351 Griffiths, E. 3,4 Grong, 0 , 26, 61, 73-5, 77, 80, 88, 90-2,116, 149-50,153,155,158, 161, 163-6, 170, 174, 176-9, 181-2, 185-6, 189, 192-204, 206-7, 209-11, 227, 247-8, 250-4, 256, 290, 292-4, 314, 327-30,345-7,349,355,360,364, 367-8, 371-2, 406, 412-15, 419, 422-3, 425, 428, 430-2, 435-6, 438, 440-1, 444, 446-54, 458-62, 464, 465-6, 477-8, 480-1, 484-6, 488-91, 493, 496, 502-7, 547-9, 551-8,560-3 Gunleiksrud, A. 503 Guo, Z.H. 405,420-1
H Habrekke, T. 229 Halmoy,E. 151 Hannertz, N.E. 507 Harris, D.R. 414 Harrison, P.L. 428, 435, 444, 478, 485, 504 Hatch, J.E. 3, 458, 547 Hawkins, D.N. 208-10, 435, 440 Hazzledine, P.M. 342-3 Heckel, R.W. 326 Hehemann, R.F. 429,452 Heile, R.F. 154, 156-7, 169 Heintze, G.N. 244, 247 Heiple, CR. 229 Hellman, P. 339, 343-5 Hemmer,H. 371-2 Hilbert, M. 339, 343-5 Hill,D.C. 154, 156-7, 169 Hillert, M. 290 Hilty, D.C. 190 Hjelen, J. 195, 292, 430-3, 438 Hocking, L.M. 196 Hollomon, J.H. 465, 500 H6llrigl-Rosta,F.413 Homma, H. 203, 444-5, 504-5 Hondros,E.D. 414 Honeycombe, R.W.K. 406,408,420, 429, 431, 444, 447-8, 453, 486 Horii,Y. 187-8 Houghton, D.C. 303, 323 Howden, D.G. 141 Howell, PR. 434-6, 441 Hu, H. 337-8, 342-3, 345,430 Hultgren, R. 3 Hunderi, O. 337, 341-2, 380
I Ibarra, S. 497 Indacochea, J.E. 171,173 International Institute of Welding 129, 152 Ion, J.C. 314, 318, 360, 3 6 3 ^ , 368 Ivanchev, I. 204-5
J Jackobs, F.A. 418 Jackson, CE. 89, 99, 100 Jaeger, J.C. 2, 4 Jaffe, L.D. 500 Janaf, ?. 154 Jelmorini, G. 156 Jonas, JJ. 464 Jones, W.K.C 374 Jordan, M.F. 143, 145, 259, 263-4 Joshi, Y. 96, 99, 105 Just, E. 413
K Kaplan, D. 435, 440, 480, 482 Kasuya, T. 496 Kato, M. 233 Kawasaki, K. 380 Keene, BJ. 96, 99, 105,228 Kelly, A. 548 Kelly, K.K. 3 Kern, A. 380 Kerr, H.W. 203, 247, 273, 290, 428 Kiessling, R. 202^4 Kihara,H. 131, 133, 134 Kikuchi, T. 1 4 2 ^ Kikuta, Y. 505-6 Kim, B.C. 444 Kim, LS. 450 Kim, NJ. 444,451,505 Kim, YG. 451 Kinsman, K.R. 429, 452 Kirkwood, RR. 292-3 Kluken, A.O. 182, 186, 194-204, 206,209-11,247-8,250-4,256, 290, 292-4, 371-2, 430-3, 4356,438,440,446-7,479-80,484, 486,491,493,497 Knacke, O. 154 Knagenhjem, H.O. 229 Knott, J.F. 486 Kobayashi, T. 1 4 2 ^ Kotler, G.R. 320, 326, 398-9 Kou, S. 27, 75-6, 96, 99, 105, 228, 250, 264-5, 272, 377, 453, 455, 458 Krauklis, P. 435-6, 441-4 Kraus, H.G. 228
Krauss, G. 418 Kubaschewski, O. 159 Kuroda, T. 547 Kurz, W. 221, 234, 242, 251, 259, 260-1,265-6,270,274 Kuwabara, M. 146 Kuwana, T. 142-4 Kvaale, FE. 414-15, 419, 504
L Lancaster, J.F. 118, 120, 162, 187 Lanzillotto, C.A.N. 452, 505 Le, Y. 27, 75-6, 265 Lee, D.Y. 444 Lee, J.-L. 504 Lei, T.C. 505 Li, W.B. 345, 367 Lifshitz, J.M. 314, 351 Lindborg,U. 170, 182-3, 185 Liu, J.Z. 505 Liu, S. 251, 292-3,412,422-3,428, 435-6,441,497 Liu, Y. 339 Loberg, B. 303 Lohne, O. 380,459,541 Long, CJ. 533, 535 Lucke,K. 337, 340-1,345 Lutony, MJ. 380
M Maitrepierre, Ph. 414 Marandet, B. 435, 440, 480, 482 Marder,A.R.451 Marthinsen, K. 380 Martins, G.P. 182, 185-6, 192-3 Martukanitz, R.P. 459 Matlock, D.K. 193, 195, 201, 413, 422-3, 428, 432, 435, 440-1, 477-8, 480, 485, 488, 491, 493, 504 Matsuda, F. 131, 133, 134, 233, 271 Matsuda, S. 203, 208, 319, 444-5, 504-5 Matsuda, Y. 505-6 Matsunawa, A. 96, 99, 105 Mazzolani, F.M. 458 McKnowlson, P 15 McMahon, CJ. 418 McPherson, R. 244, 247 McQueen, HJ. 464 McRobie, D.E. 486 Mehl, R.F. 408, 436-7 Metals Handbook 3, 545 Midling, O.T. 465-6, 556-8, 560-3 Miller, R.L. 449-50 Mills, A.R. 435, 440
Mills, K.C. 96, 99,105,228 Milner, D.R. 141 Miranda, R.M. 374-5 Mitra, U. 171-2 Mizuno, M. 284 Moisio, T. 290 Mondolfo, L.F. 2A2-A Mori, N. 187-8 Morigaki, 0.146 Morral, J.E. 413 Mossinger, R. 554 Mundra, K. 210 Munitz, A. 267 Murray, J.L. 203 Muzzolani, F.M. 547,550,552 Myers, RS. 26 Myhr, O.R. 26, 61, 73-5, 77, 314, 327-30, 360, 458-62, 464, 496, 547-9,550-5 N Naess, OJ. 503 Nagai, T. 380 Nakagawa,H. 131, 133, 134 Nakata, K. 271 Nes,E. 337, 341-2, 380 Nicholson, R.B. 548 Niles, R.W. 89 Nilles,P. 180 Nordgren, A. 303 North, T.H. 171 Nowicki,A. 171 Nylund, H.K. 438 O O'Brien, J.E. 143, 145 Odland, PT. 480 Ohkita, S. 203, 444-5, 504-5 Ohno, S. 143 Ohshita, S. 103, 104,496,515 Ohta, S. 380 Okumura, M. 103, 104 Okumura, N. 208, 319 Olsen, K. 500, 502 Olson, D.L. 171,173-4,176-9,1812, 185-6, 192-3, 422-3, 428, 436,441,480,497,500,502 Onsoien, M.I. 479, 448-9, 495-6, 525 Oreper, G.M. 96, 99, 105, 228 Oriani, R.A. 514 Orr, R.L. 3 Ostrom, G. 533 0verlie, H.G. 541 Owen, W.S. 450 Ozturk,B. 156
P Paauw, AJ. 446, 503 Pabi, S.K. 326 Pakrasi, S. 413 Pan, Y-T. 504 Pande, C S . 339 Pardo, E. 247, 273 Pargeter, RJ. 428, 440, 477-8, 485, 493, 504 Patterson, B.R. 339 Pepe,JJ. 541 Petch,NJ. 512 Petty-Galis, J.L. 306 Phillip, R.H. 444 Phillips, H.W.L. 543 Pickering, RB. 301, 303, 452, 479, 505 Pitsch, W. 436-7 Plockinger, E. 186 Porter, D.A. 247,309,389,392,403, 408,413,427,429,435,448 Pottore,N.S.290 Priestner, R. 451 Pugin, A.I. 556-7
R Ramachandran, S. 190-1, 204 Ramakrishna, V. 151, 162, 174-5, 179, 191 Ramberg, M. 450-1, 505-6 Ramsay, CW. 480 Rappaz, M. 236, 239, 241, 260 Rath, B.B. 337-8, 342-3, 345 Ravi Vishnu, P. 500, 502 Reif, W. 380 Reiso, O. 541-3 Reti,T. 501-2 Ribes, A. 435, 440, 480, 482 Riboud, PV. 480, 482 Ribound, PV. (Riboud ?) 435, 440 Ricks, R.A. 434-5, 436, 441 Ringer, S.P. 345, 367 Rollett, A.D. 380 Roper, J.R. 229 Rorvik, G. 247-8, 250-4, 256, 2924, 430, 446-9, 495-6, 499,503, 507, 525 Rose, R. 516 Rosenthal, D. 26, 28, 31, 33, 38, 41, 48, 51, 56, 59-61, 76, 98, 133, 360 Roux, R. 140 Rykalin, N.N. 18, 21, 26, 41, 45, 56, 93,95, 556-7 Ryum, N. 326,337,341-2,345,347, 349,367,380,382,390,396,403, 541-3
S Saetre, T.O. 380, 382 Saggese, ME. 208-10, 435,440 Sagmo, G. 97 Saito, S. 103, 104 Sakaguchi, A. 284 Savage, W.F. 541 Schaeffler, A.L. 533 Scheil, E. 403 Schriever, U. 380 Schumacher, J.E 162 Schwan,M.21,25 Scott, MH. 544-5 Seah,MR414 Seay, E.B. 96, 99, 105 Senda, T. 233 Shackleton, D.N. 166-7 Shaller,F.W.509,512 Shen, H.P. 505 Shen,X.P.451 Sherby, O.D. 501-2 Shercliff, H.R. 314,329,459-62,464 Shinozaki, K. 131, 133, 134 Siewert, T.A. 182, 185-6, 192-3, 227,425,428 Sigworth, G.K. 162 Simonsen, T. 520-2 Sims, CE. 512 Skaland, T. 346 Skjolberg, E.M. 140-1 Slyozov,V.V. 314,351 Smith, A. A. 166-7, 169, 170 Soares, A. 380-1 Solberg, J.K. 446, 450-4, 504-6 Sommerville, LD. 204-5 Speich, G.R. 449-50 Srolovitz, DJ. 380 Staley, J.T. 394-5, 459 Steidl, G. 554 Steigerwald,E.A.509,512 Stjerndahl, J. 290 Stoneham, A.M. 414 Strangwood, M. 428-9, 431, 444 Strid, J. 303, 542-3 Stuwe,H. 337, 340-1,345 Sugden, A.A.B. 292,431 Suutala, N. 290 Suzuki, H. 406, 444, 477, 496, 509, 515,520 Suzuki, S. 303, 323 Svensson, L.E. 147, 206, 413, 4228, 431, 4 3 3 ^ , 441, 444, 536 Szekely, J. 96,99,105,120,162,183, 187,228,281,284 Szewezyk, A.F. 505 Szumachowski, E. 533
T Takalo,T.290 Tamehiro, H. 496 Tamura, 1.405,420-1 Tanigaki, T. 146 Tanzilli, R.A. 326 Tardy, P. 501-2 Tensi, H.M. 21,25 Thaulow, C. 503 Themelis, NJ. 120,162,183,187,281, 284 Therrien,A.E.434,480 Thewlis, G. 203,435,440-1 Thivellier, D. 414 Thomas, G. 505 Thompson, A.W. 480,512 Thompson, CV. 380 Tichelaar, G.W. 156 Tjotta, S. 459,460 Tomii,Y.284 Torsell, K. 182-3,185 Tricot, R. 414 Trivedi, R. 260, 400,427 Troiano,A.R.509,512 Tsai,N.S.26 Tsukamoto, K. 271 Tundal, UH. 326 Turkdogan, E.T. 126, 182, 184-6, 191-2,195-6,207,214 Turpin, M.L. 182,184
U Uda, M. 143 Udler, D.G. 380 UIe, R.L. 96, 99, 105 Umemoto, M. 405, 420-1 Underwood, E.E. 201, 338 Unstinovshchikov, J.I. 494
V Van Den Heuvel, G J P M . 156 Van Stone, R.H. 480 Vander Voort, G.F. 394, 403 Vandermeer, R.A. 341 Vasil'eva, VA. 556-7 Verhoeven, J.D. 286, 429, 431, 433, 448-9 Villafuerte, XC 247,273 Vitek, J.M. 96,99,105,210,222,228, 240,250,272,278,478
W Wagner, C 201, 314, 351 Wahlster, M. 186 Walsh, R. A. 190-1,204 Walton, D.T. 380 Wang, YH. 96, 99, 105, 228 Weatherly, G.C. 303, 323 Welding Handbook 24 Welz, W. 21,25 Whelan,MJ. 319, 356 Whiteman, J.A. 208-10, 435, 440 Widgery, DJ. 480-1 Willgoss, R.A. 132 Williams, J.C 533 Williams, TM. 414 Wolstenholme, D.A. 174 Woods, WE. 279, 285 Worner, CH. 342-3 Wriedt, H.A. 203
Y Yamamoto, K. 203, 444-5, 504-5 Yang, J.R. 428-9 Yi, JJ. 450 Yoneda, M. 505-6 Yurioka, N. 103, 104,496, 509,515, 520
Z Zacharia, T. 96, 99, 105, 228 Zapffe,CA.512 Zener, C 341-2,344,465 Zhang, C 515 Zhang, Z. 441,443
Index Index terms
Links
A absorption of elements see hydrogen, nitrogen, oxygen acicular ferrite in low-alloy steels
428
crystallography of
428
nature of
430
nucleation and growth of
432
texture components of
429
acicular ferrite in wrought steels
444
aluminium as alloying element in steel effect on inclusion composition
202
206
effect on solidification microstructure
246
272
effect on weld properties
481
486
solubility product of precipitates
303
aluminium weldments
458
age-hardenable alloys
458
quench sensitivity
459
precipitation conditions during cooling
459
strength recovery during natural ageing
461
subgrain evolution in friction welding
464
characteristics
293
536
536
constitutional liquation in Al-Mg-Si alloys
542
in Al-Si alloys
541
example (7.9) – minimum HAZ strength level
554
example (7.8) – weld metal hot cracking
544
example (7.7) – weld metal solidification cracking
537
example (7.10) – minimum HAZ hardness level
562
HAZ microstructure evolution
547
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595
596
Index terms
Links
aluminium weldments (Continued) constitutive equations
548
during friction welding
555
during fusion welding
547
hot cracking
540
factors affecting
544
solidification cracking
536
strength evolution during welding
547
constitutive equations
548
during friction welding
555
hardness and strength distribution
550
strengthening mechanisms in alloys
547
amplitude of weaving – definition arc atmosphere composition
80 132
see also shielding gases arc efficiency factors
26
definition
26
selected values
27
arc welding
24
definition of processes
24
austenite grain size in low-alloy steels
409
primary precipitation in fusion welds
292
austenite formation in low-alloy steels conditions for austenitic stainless steels
558
449 450 453
see also stainless steel weldments characteristics of
527
chromium carbide formation
456
grain growth diagrams for steel welding
375
weld decay area
456
This page has been reformatted by Knovel to provide easier navigation.
558 560
597
Index terms
Links
Avrami equation in solid state transformations see also solid state transformation and transportation kinetics additivity in
404
exponents in
401
475
B Bain orientation region
436
bainite in low-alloy steels
444
lower
447
upper
444
bead morphology
96
bead penetration
99
deposit and fused parent metal
96
example (1.16) – SA welding of steel
97
example (1.17) – SMAW welding of steel
98
example (1.18) – Jackson equation
99
Bessel functions – modified
46
47
boron in steel effect on transformation behaviour
413
segregation of
294
weld properties
493
bowing of crystal
240
Bramfitt’s planar lattice disregistry model
244
505
see also solidification of welds
C carbon equivalents
496
carbon as alloying element in steel austenitic stainless steels
453
weld deposits
424
carbon-manganese steel weld metals, grain growth in
370
casting, structural zones
221
This page has been reformatted by Knovel to provide easier navigation.
521
49
598
Index terms cell/dendrite alignment angle
Links 249
see also solidification of welds cellular substructure
251
see also solidification of welds chemical reaction model – overall
116
chromium carbide formation in austenitic stainless steels
456
chromium-molybdenum steel welds, grain growth in
372
columnar grains
228
see also solidification of welds columnar to equiaxial transition
268
see also solidification of welds competitive grain growth
234
see also solidification of welds concentration displacements during welding see oxygen, absorption of cooling condition during solidification
221
cooling rate, C.R. thick plate welding
37
thin plate welding
53
cooling time, ∆t8/5 thick plate welding
36
thin plate welding
53
cooling time, t100
103
D Delong diagram
535
delta ferrite, primary precipitation of
290
dendrite arm spacing
261
primary
261
secondary
264
dendrite fragmentation
250
see also solidification of welds
This page has been reformatted by Knovel to provide easier navigation.
292
599
Index terms dendrite substructure
Links 252
see also solidification of welds dendrite tip radius
260
see also solidification of welds deoxidation reactions in weld pools
180
example (2.9) – homogeneous nucleation of MnSiO3
182
growth and separation of oxide inclusions
184
buoyancy (Stokes flotation)
185
fluid flow pattern
186
separation model
188
nucleation model
182
nucleation of inclusions
182
overall deoxidation model
201
deposit – amount of weld metal
96
deposition rate
96
dissociation of gases in arc column
117
distributed heat sources
77
general solution
77
simplified solution (Gaussian heat distribution) simplified solution (planar heat distribution)
112 80
case study (1.2) – surfacing with strip electrodes
87
case study (1.3) – GTA welding with a weaving technique
87
dimensionless operating parameter
82
dimensionless time
82
dimensionless y- and z-coordinates
82
example (1.13) – effect of weaving on temperature distribution
83
implications of model
86
model limitations
86
2-D heat flow model
80
see also heat flow models Dorn parameter
219
501
This page has been reformatted by Knovel to provide easier navigation.
112
600
Index terms
Links
duplex stainless steels
531
HAZ toughness
532
HAZ transformation behaviour
532
E energy barrier to solidification
225
see also solidification of welds enthalpy of reaction
302
definition of
302
values
303
entropy of reaction
302
definition
302
values
303
epitaxial solidification
222
equiaxed dentritic growth
268
equilibrium dissolution temperature of precipitates
303
see also solidification of welds error functions see Gaussian error functions
F fluid flow pattern in weld pools
186
flux basicity index
171
friction welding
18
see also aluminium weldments dimensionless temperature
20
dimensionless time
20
dimensionless x-coordinate
21
example (1.4) – peak temperature distribution
23
heat flow model
18
temperature-time pattern
23
Fritz equation
281
This page has been reformatted by Knovel to provide easier navigation.
228
601
Index terms
Links
fume formation, rate of iron
157
manganese
156
silicon
152
fused parent metal – amount of
98
G gas absorption, kinetics of
120
rate of element absorption
121
thin film model
120
gas desorption, kinetics of
123
rate of element desorption
123
Sievert’s law
124
gas porosity in fusion welds
279
growth and detachment of gas bubbles
281
nucleation of gas bubbles
279
separation of gas bubbles
283
Gaussian error functions, definition
112
Gaussian heat distribution
112
see also distributed heat sources Gibbs-Thomson law
309
Gladman equation
344
grain boundary ferrite
408
crystallography of
408
growth of
422
nucleation of
408
grain detachment
250
see also solidification of welds grain growth computer simulation
337 380
diagrams construction of
360
This page has been reformatted by Knovel to provide easier navigation.
602
Index terms
Links
grain growth (Continued) axes and features of
363
calibration procedures
361
heat flow models
360
for steel welding
360
case studies
364
C-Mn steel weld metals
370
Cr-Mo low alloy steels
372
niobium-microalloyed steels
367
titanium-microalloyed steels
364
type 316 austenitic stainless steels
375
driving pressure for
339
example (5.3) – austenite grain size in niobium-microalloyed steels
358
example (5.2) – austenite grain size in Ti microalloyed steels
354
example (5.1) – limiting austenite grain size in steel weld metals
344
grain boundary mobility
337
drag from impurities
340
drag froma random particle distribution
341
driving pressure for growth
339
grain structures, characteristics
337
growth mechanisms
345
nomenclature
384
normal grain growth
343
size, limiting
343
Griffith’s equation
486
gross heat input – definition growth rate of crystals
37 230
local
234
nominal
230
see also solidification of welds
This page has been reformatted by Knovel to provide easier navigation.
342
494
603
Index terms
Links
H Hall-Petch relation
529
heat flow models distributed heat sources
77
grain growth diagrams
360
instantaneous heat sources local preheating
5 100
medium thick plate solution
59
thermal conditions during interrupted welding
91
thermal conditions during root pass welding
95
thick plate solutions
26
thin plate solutions
45
heat input see heat flow models Hellman and Hillert equation
344
Hollomon-Jaffe parameter
500
hydrogen, absorption of
128
content in welds
132
covered electrodes
134
combined partial pressure of
134
example (2.1) – hydrogen absorption in GTAW
133
example (2.2) – hydrogen absorption in SMAW
136
in gas-shielded welding
131
hydrogen determination
128
implications of Sievert’s law
140
reaction model
130
sources of hydrogen
128
in submerged arc welding
138
effect of water content in flux
138
example (2.3) – hydrogen absorption in SAW
139
hydrogen cracking in low-alloy steel weld metals
509
diffusion in welds
514
diffusivity in steel
514
This page has been reformatted by Knovel to provide easier navigation.
112
604
Index terms
Links
hydrogen cracking in low-alloy steel weld metals (Continued) HAZ cracking resistance
518
mechanisms of
509
solubility in steel
513
hydrogen in multi-run weldments
140
hydrogen in non-ferrous weldments
141
hydrogen sulphide corrosion cracking in low-alloy steel weld metals
524
prediction of
525
threshold stress for
524
hyperbaric welding
176
I implant testing
520
see also hydrogen cracking inclusions in welds – origin
192
constituent elements and phases in inclusions
202
example (2.10) – computation of inclusion volume fraction
194
example (2.12) – computation of total number of constituent phases in inclusions
211
prediction of inclusion composition
204
size distribution of inclusions
195
coarsening mechanism
196
effect of heat input
196
example (2.11) – computation of number density and size distribution of inclusions volume fraction stoichiometric conversion factors
201 193 194
instantaneous heat sources
5
line source
5
plane source
5
point source
5
interface stability
254
This page has been reformatted by Knovel to provide easier navigation.
605
Index terms interfacial energies
Links 242
see also solidification of welds interrupted welding, thermal conditions
91
example (1.14) – repair welding of steel casting
93
heat flow models
93
K Kurdjumow-Sachs orientation relationship
408 444
L latent heat of melting
3
lattice disregistry see Bramfitt’s planar lattice disregistry model local fusion in arc strikes
7
dimensionless operating parameter
7
dimensionless radius vector
7
dimensionless temperature
7
dimensionless time
7
example (1.1) – weld crater formation and cooling conditions
9
heat flow model
7
temperature-time pattern
8
low-alloy steel weldments
477
acicular ferrite in
428
crystallography of
428
nature of
430
nucleation and growth in
432
texture components of
429
austenite formation in
449
conditions for
450
bainite in
444
lower
447 This page has been reformatted by Knovel to provide easier navigation.
427 448
429
606
Index terms
Links
low-alloy steel weldments (Continued) upper
444
case study (7.1) – weld bead tempering
501
example (7.1) – low-temperature toughness of welds
488
example (7.2) – peak HAZ strength level
496
example (7.3) – location of brittle zones
508
HAZ mechanical properties
494
hardness and strength level
495
tempering
500
toughness
502
hydrogen cracking
509
diffusion in welds
514
diffusivity in steel
514
example (7.4) – hydrogen cracking under hyperbaric welding conditions
521
HAZ cracking resistance
518
implant testing
520
mechanisms of
509
solubility in steel
513
hydrogen sulphide corrosion cracking
524
prediction of
525
threshold stress for
524
martensite in
447
austenite formation, kinetics of
449
lath
447
M-A formation, conditions for
450
plate (twinned)
447
mechanical properties
477
ductile to brittle transition
486
reheating
491
resistance to cleavage fracture
485
resistance to ductile fracture
480
strength level
478
This page has been reformatted by Knovel to provide easier navigation.
607
Index terms
Links
low-alloy steel weldments (Continued) transformation behaviour
290
406
solidification primary precipitation of austenite
292
primary precipitation of delta ferrite
290
solid state acicular ferrite
428
bainite
444
grain boundary ferrite
408
martensite
447
microstructure classification
406
nomenclature for
406
Widmanstatten ferrite
427
Ludwik equation
524
M magnesium in aluminium alloys solubility product of precipitates
303
martensite in low-alloy steels
447
austenite formation, kinetics of
449
lath
447
M-A formation, conditions for
450
plate (twinned)
447
martensitic stainless steels, characteristics of
527
mass transfer in weld pool, overall kinetic model of
124
medium thick plate solution
59
see also heat flow models dimensionless maps for heat flow analysis
61
case study (1.1) – temperature distribution in steel and aluminium weldments
69
construction of maps
61
This page has been reformatted by Knovel to provide easier navigation.
292
608
Index terms
Links
medium thick plate solution (Continued) cooling conditions close to weld centre line
63
example (1.12) – aluminium welding
68
isothermal contours
65
limitation of maps
65
peak temperature distribution
61
retention times at elevated temperatures
63
experimental verification
72
peak temperature and isothermal contours
75
weld cooling programme
72
weld thermal cycles
72
general heat flow model
59
practical implications
75
melting efficiency factor
89
mixing ratio
98
moving heat sources
24
see also heat flow models net arc power, definition
26
niobium-microalloyed steels, grain growth in
367
nitrogen, absorption of
141
content in welds
143
covered electrodes
143
gas-shielded welding
142
nominal composition
147
sources of
142
submerged arc welding
146
example (2.4) – nitrogen content in weld metal deposit
146
N non-isothermal transformations additivity principle and Avrami equation
403 404
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609
Index terms
Links
non-isothermal transformations (Continued) isokinetic reactions
404
non-additive reactions
405
non-steady heat conduction biaxial conduction
2
triaxial conduction
2
uniaxial conduction
2
nucleation, energy barrier to
225
nucleation, homogeneous
182
219
see also deoxidation reactions in weld pools nucleation, potency of particles
242
see also solidification of welds nucleation, rate of heterogeneous during solidification
248
nucleation in solid state transformation kinetics
389
in C-curve modeling
390
nucleation of gas bubbles in fusion welds
279
nucleation of grain boundary ferrite in low-alloy steels
408
austenite grain size
409
boron alloying
413
factors affecting ferrite grain size
420
solidification-induced segregation
417
O operating parameter, dimensionless point and line heat source models
31
weaving model
82
Ostwald ripening see particle coarsening oxygen, absorption of
148
classification of shielding gases
166
overall oxygen balance
166
content in welds
148
covered electrodes
173
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272
610
Index terms
Links
oxygen, absorption of (Continued) absorption of carbon and oxygen
176
loss of silicon and manganese
177
the product [%C] [%O]
179
reaction model
174
effects of welding parameters
169
amperage
169
voltage
170
welding speed
170
example (2.8) – oxygen consumption and total CO evolution during GMAW gas arc metal welding
166 148
manganese evaporation
156
example (2.6) – fume formation rate of manganese
157
sampling of elevated concentrations
149
carbon oxidation
149
silicon oxidation
152
example (2.5) – fume formation rate of silicon
156
SiO formation
154
total oxygen absorption
162
transient oxygen concentrations
160
example (2.7) – slag formation in GMAW
164
submerged arc welding
170
concentration displacements
172
flux basicity index
171
total oxygen absorption
173
transient oxygen absorption
172
oxygen, retained in weld metal
190
implications of model
192
thermodynamic model of
190
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173
611
Index terms
Links
P particle coarsening
314
applications to continuous heating and cooling
314
example (4.4) – coarsening of titanium nitride in steel
315
kinetics
314
particle dissolution
316
analytical solution
316
case study (4.1) – solute distribution across HAZ
330
example (4.5) – isothermal dissolution of NbC in steel
320
example (4.6) – dissolution of NbC within fully transformed HAZ
323
numerical solution
325
application to continuous heating and cooling
329
process diagrams for aluminium butt welds
332
Peclet number for weld pools
186
peritectic solidification in welds
290
see also low alloy steel weldments primary precipitation of γp-phase
290
transformation behaviour
290
precipitate growth mechanisms liquid state
196
solid state
395
diffusion-controlled
397
interface-controlled
396
precipitate stability
301
see also particle coarsening and particle dissolution example (4.1) – equilibrium dissolution temperature of nitride precipitates
304
example (4.2) – equilibrium volume fraction of Mg2Si
307
example (4.3) – metastable β”(Mg2Si) solvus
312
nomenclature
334
solubility product
301
equilibrium dissolution temperature
303
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612
Index terms
Links
precipitate stability (Continued) stable and metastable solvus boundaries
304
thermodynamic background
301
preheating, local heat flow model
100 100
dimensionless half width of preheated zone
101
dimensionless temperature
101
dimensionless time
101
example (1.19) – cooling conditions during steel welding
102
time constant
101
pseudo-equilibrium, concept of pseudo-steady state temperature distribution, definition
122 24
R reversion see particle dissolution example (1.15) – cooling conditions during root pass welding
95
heat flow model
95
Reynold number definition
187
of gas bubbles
284
of particles
187
root pass welding, thermal conditions in
95
Rosenthal equations see thick and thin plate solutions
S Scheil equation
272
modified
276
original
272
separation of gas bubbles in fusion welds
283
shielding gases see oxygen, hydrogen and nitrogen, absorption of CO-evolution
166
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613
Index terms Sievert’s law
Links 124
140
silicon in aluminium solubility product of precipitates
303
solid state transformations in welds
387
Al-Mg-Si alloys
458
austenitic stainless steels
453
Avrami equation in, additivity in
404
high strength low-alloy steels
406
kinetics see transformation kinetics nomenclature solid state transformation kinetics
471 387
see also transformation kinetics driving force for
387
non-isothermal transformations
402
nucleation in solids
389
overall
400
precipitates, growth of
395
solidification cracking in weldments aluminium
536
stainless steel
532
solidification microstructures
251
columnar to equiaxed transition
268
dendrite tip radius
260
equiaxed dendritic growth
268
example (3.12) – equiaxed dendritic growth in Al-Si welds
270
example (3.13) – application of Scheil equation
276
interface stability criterion
254
example (3.6) – critical temperature gradient for planar solidification front in Al-Si welds example (3.7) – substructure characteristics of Al-Mg welds primary dendrite arm spacing
256 258 261
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475
614
Index terms
Links
solidification microstructures (Continued) example (3.8) – effect of heat input on primary dendrite arm spacing in welds
262
example (3.9) – variation of primary dendrite arm spacing across fusion zone secondary dendrite arm spacing example (3.10) – secondary dendrite arm spacing in thick plate GTA Al-Si welds
263 264 266
example (3.11) – secondary dendrite arm spacing in thin plate GTA Al-Si butt welds
267
local solidification time
265
substructure characteristics
251
cellular
251
dendritic
252
solidification of welds
221
columnar grain structures and morphology
228
epitaxial solidification
222
energy barrier to solidification
225
implications of
226
growth rate of columnar grains
230
example (3.1) – nominal crystal growth rate in thin sheet welding of austenitic stainless steels
234
example (3.2) – local dendrite growth rate in single crystal welds
237
local crystal growth rate
234
nominal crystal growth rate
230
renucleation of crystals
242
critical cell-dendrite alignment angle
249
dendrite fragmentation
250
example (3.4) – nucleation potency of TiN with respect to delta ferrite
245
example (3.5) – nucleation potency of γ-Al2O3 with respect to delta ferrite
246
grain detachment
250
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615
Index terms
Links
solidification of welds (Continued) nucleation potency of second phase particles rate of heterogeneous nucleation reorientation of columnar grains
242 247 239
bowing of crystal
240
example (3.3) – bowing by dendritic branching
240
structural zones solubility of gases in liquids and solids
221 125
hydrogen in Al
125
hydrogen in Cu
125
hydrogen in Fe
125
hydrogen in Ni
125
nitrogen in Fe
126
see also gas absorption and gas desorption solubility product
301
equilibrium dissolution temperature
303
stable and metastable solvus boundaries
304
thermodynamic background
301
solute redistribution in welds
272
example (3.14) – formation of hydrogen bubbles in weld pools
282
example (3.15) – separation of hydrogen bubbles in weld pools
284
example (3.16) – solute redistribution during cooling in austenite regime
287
gas porosity
279
homogenisation of microsegregations
286
macrosegregation
277
microsegregation
272
spot welding
10
dimensionless operating parameter
11
dimensionless radius vector
11
dimensionless time
11
example (1.2) – cooling conditions
12
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513
616
Index terms
Links
spot welding (Continued) heat flow model
11
refined model for
110
temperature-time pattern
12
stainless steel weldments
527
see also austenitic stainless steels austenitic characteristics of
527
chromium carbide formation
456
grain growth diagrams for steel welding
375
example (7.5) – variation in HAZ austenite grain size and strength level
530
example (7.6) – weld metal solidification cracking
533
HAZ corrosion resistance
527
HAZ strength level
529
HAZ toughness
530
solidification cracking
532
weld decay area
456
duplex HAZ toughness
532
HAZ transformation behaviour
532
stereometric relationships (number of particles per unit volume, number of particles per unit area, total surface area per unit volume, and mean particle volume spacing)
201
Stokes law
185
substructure of welds
251
187
see also solidification of welds
T texture in welds solidification
221
solid state
429
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290
284
617
Index terms
Links
thermal properties of metal and alloys
3
conductivity
3
diffusivity
3
heat content at melting point
3
latent heat of melting
3
melting point
3
volume heat capacity
3
thermit welding
14
dimensionless temperature
16
dimensionless time
16
dimensionless x-coordinate
16
example (1.3) – cooling conditions
16
heat flow model
14
temperature-time pattern
17
thick plate solutions
26
see also heat flow models pseudo-steady state temperature distribution
31
cooling conditions close to weld centre line
36
dimensionless operating parameter
31
dimensionless x-coordinate
31
dimensionless y-coordinate
31
dimensionless z-coordinate
31
distribution of temperatures
31
example (1.5) – duration of transient heating period in aluminium welding
30
example (1.6) – thermal contours
37
example (1.7) – weld geometry
39
isothermal zone widths
32
length of isothermal enclosures
34
simplified solution
41
example (1.8) – retention time in steel welding
44
temperature-time pattern
41
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618
Index terms
Links
thick plate solutions (Continued) 2-D heat flow model volume of isothermal enclosures transient heating period thin plate solutions
41 35 29 45
see also heat flow models example (1.9) – duration of transient heating period in aluminium welding
48
pseudo-steady state temperature distribution
49
cooling conditions close to weld centre line
53
example (1.10) – weld geometry and cooling rate
54
isothermal zone widths
49
length of isothermal enclosures
51
simplified solution
56
example (1.11) – retention time in steel welding
59
1-D heat flow model
56
temperature-time pattern
57
transient heating period
29
titanium as alloying element in steel effect on inclusion composition
203
208
effect on solidification microstructure
244
272
effect on grain growth
354
364
effect on transformation behaviour
435
444
effect on weld properties
488
solubility product of precipitates
303
titanium-microalloyed steels, grain growth in
364
see also low alloy steel weldments transformation kinetics
387
Avrami equation
400
475
additivity in
404
475
exponents in
401
driving force for
387
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619
Index terms
Links
transformation kinetics (Continued) example (6.1) – C-curve analysis
394
example (6.2) – conditions for ferrite formation within HAZ
410
example (6.3) – volume fraction of grain boundary ferrite in HAZ
412
example (6.4) – ferrite/martensite formation in HAZ
416
example (6.5) – displacement of ferrite C-curve due to segregation
418
example (6.6) – variation in ferrite grain size across HAZ
421
example (6.7) – volume fraction of allotriomorphic ferrite in weld deposit
425
example (6.8) – volume of acicular ferrite plate
440
example (6.9) – conditions for acicular ferrite formation
442
example (6.10) – conditions for chromium carbide formation
456
example (6.11) – conditions for β’(Mg2Si) precipitation
460
example (6.12) – ageing characteristics of aluminium weldments
463
non-isothermal transformations
402
nucleation in solids
389
overall
400
precipitates, growth of
395
type 316 austentitic stainless steels, grain growth in
375
see also stainless steel weldments
V volume of weld metal volume fraction of inclusions
36 193
volume heat capacity
3
W Wagner-Lifshitz equation
196
water content
137
in electrode coating
137
in welding flux
138
see also hydrogen absorption This page has been reformatted by Knovel to provide easier navigation.
314
351
620
Index terms weld pool shape and geometry
Links 228
elliptical weld pool
229
tear-shaped weld pool
229
see also solidification of welds welding processes, definitions
24
see also arc welding processes wetting conditions
222
242
interfacial energies
242
247
wetting angle
225
see also solidification of welds Widmanstätten ferrite in low-alloy steels
427
Z Zener drag, definition of in grain growth
341 341
Zener equation
342
Zener-Hollomon parameter
465
zinc in aluminium solubility product of precipitates
303
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344
