Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Modelling the interaction between recovery, recrystallization and precipitation in AA6111 Go, Johnson 2006

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-ubc_2007-267219.pdf [ 17MB ]
Metadata
JSON: 831-1.0078561.json
JSON-LD: 831-1.0078561-ld.json
RDF/XML (Pretty): 831-1.0078561-rdf.xml
RDF/JSON: 831-1.0078561-rdf.json
Turtle: 831-1.0078561-turtle.txt
N-Triples: 831-1.0078561-rdf-ntriples.txt
Original Record: 831-1.0078561-source.json
Full Text
831-1.0078561-fulltext.txt
Citation
831-1.0078561.ris

Full Text

M O D E L L I N G THE INTERACTION B E T W E E N R E C O V E R Y , R E C R Y S T A L L I Z A T I O N A N D PRECIPITATION IN AA6111 by  JOHNSON GO B . A . Sc., University of British Columbia, 1998 M . A . Sc., University of British Columbia, 2001  A THESIS S U B M I T T E D IN P A R T I A L F U L F I L L M E N T OF T H E REQUIREMENTS FOR THE D E G R E E OF  DOCTOR OF PHILOSOPHY in  THE F A C U L T Y OF G R A D U A T E STUDIES (Materials Engineering)  T H E U N I V E R S I T Y OF B R I T S H C O L U M B I A July 2006  © Johnson Go, 2006  ABSTRACT  The present work investigates the evolution o f microstructure during the annealing o f an industrial precipitation hardened aluminum alloy A A 6 1 1 1 . Special emphasis is placed on understanding the interaction between recovery, recrystallization and precipitation through a combination o f experimental and modelling approaches.  Experimentally, extensive heat  treatments were carried out to study the effect o f varying initial precipitate conditions on the isothermal annealing behaviour o f the alloy in the temperature range o f 250-445°C. A total o f four prior aging conditions were considered: naturally aged (T4), peak aged ( P A ) , overaged (OA) and severely overaged ( S O A ) . It was found that recrystallization was severely retarded at the annealing temperature o f 325°C irrespective o f prior precipitate conditions. Microscopic evidence confirmed that the growth o f recrystallizing grains is directly related to the nonuniform spatial distribution o f precipitates. Subsequently, a new microstructure model was developed to link the changes in the microstructure to the mechanical properties o f the alloys. The model which was developed based on the internal state variable approach is capable o f translating quantitatively the interaction between recovery, subgrain growth, recrystallization and precipitation into a yield stress vs. time relationship. The effect  o f non-uniform  distribution o f precipitates was considered explicitly by using a simple rule o f mixtures. The validity o f the model was verified b y comparing the model calculations to the experimental data obtained from overaged 40% cold rolled A A 6 1 1 1 .  ii  TABLE OF CONTENTS ABSTRACT  ii  T A B L E OF CONTENTS  iii  LIST OF T A B L E S  vi  LIST OF FIGURES  vii  LIST OF S Y M B O L S  xii  ACKNOWLEDGEMENTS  xiv  Chapter 1  INTRODUCTION  1  Chapter 2  L I T E R A T U R E REVIEW.  4  2.1 Recovery 2.1.1 General Observations 2.1.2 Recovery Modelling 2.2 Recrystallization 2.2.1 General Observations 2.2.2 Recrystallization Modelling 2.3 Interaction Between Recovery and Recrystallization 2.4 Precipitation 2.4.1 Precipitation Hardening Behaviour o f A A 6 1 1 1 2.4.2 Precipitation Modelling 2.5 Interaction Between Precipitation and Recovery 2.6 Interaction Between Precipitation and Recrystallization 2.6.1 Precipitate Pinning 2.6.2 Solute Drag 2.7 Critical Assessment o f the Literature  5 5 6 10 10 10 14 15 16 20 22 24 25 33 38  Chapter 3  SCOPE A N D OBJECTIVES  40  Chapter 4  EXPERIMENTAL METHODOLOGY  42  4.1 Starting Materials 4.2 Sample Preparations 4.3 Heat-treatment Experiments 4.3.1 Solution Heat-treatments 4.3.2 Artificial A g i n g  42 42 45 45 46  iii  Chapter 5  4.3.3 Isothermal Annealing 4.4 Sample Characterization 4.4.1 Sample Preparation 4.4.2 Optical Metallography 4.4.3 Scanning Electron Microscopy 4.4.4 Electron Back Scattered Diffraction 4.4.5 Transmission Electron Microscopy 4.4.6 Resistivity Measurements 4.4.7 Tensile Measurements  47 47 49 51 52 52 53 53 54  E X P E R I M E N T A L RESULTS A N D DISCUSSION  56  5.1 Experimental Results 57 5.1.1 Solution Heat Treatments 57 5.1.2 Artificial A g i n g 60 5.1.3 The Deformed State 67 5.1.4 Isothermal Annealing at 3 2 5 ° C 76 5.1.4.1 Evolution of Y i e l d Stress 76 5.1.4.2 Evolution o f Resistivity 78 5.1.4.3 Evolution o f Microstructure 78 5.1.5 The Effect o f Annealing Temperature on Overaged Samples 93 5.1.6 T E M Studies o f the Annealing Behaviour o f Overaged Samples.... 97 5.2 Discussion o f Experimental Results 100 5.2.1 F l o w Stress Addition L a w 105 5.2.2 Evolution o f Resistivity 106 5.2.3 The Effect o f Prior A g i n g Conditions 110 5.3 Concluding Remarks 114  Chapter 6  M O D E L L I N G OF MICROSTRUCTURE E V O L U T I O N IN O V E R A G E D AA6111 6.1 6.2 6.3 6.4  M o d e l Development - The Internal State Variable Approach Recovery Subgrain Growth Recrystallization 6.4.1 Nucleation 6.4.2 Growth Rate 6.5 Precipitation 6.5.1 Dissolution/Growth 6.5.2 Coarsening 6.6. Parameter Identification 6.6.1 Solubility Product for Q' Precipitates 6.6.2 M o l a r Volume o f Q' Precipitates 6.7 M o d e l Implementation 6.8 Comparison with Experimental Results 6.9 Discussion o f Modelling Results iv  115 116 121 125 128 130 132 135 135 138 140 140 141 141 144 151  6.9.1 Interaction Between Recovery and Precipitation 6.9.2 Interaction Between Recovery, Precipitation and Recrystallization 6.9.3 Composite Microstructure 6.10 Summary and Limitations o f the Overall M o d e l  Chapter 7  S U M M A R Y A N D CONCLUSIONS 7.1 Future W o r k  151 155 155 157  161 164  REFERENCES  165  V  LIST OF TABLES Table 2.1. The value o f ideal J M A K exponent as a function o f growth dimensionality  13  Table 2.2. The effect o f prior precipitate conditions on the recrystallization completion time for a 70% cold rolled high purity A l - M g - S i alloy  30  Table 4.1. Chemical composition o f A A 6 1 1 1 in wt%  43  Table 4.2. Four step procedure for grinding and polishing aluminum alloys using a Phoenix 4000 automatic polisher  50  Table 5.1. Comparison o f the recrystallization behaviour o f 40% cold rolled A A 6 1 1 1 with varied precipitate conditions after annealing for 2 weeks at 325°C  82  Table 5.2.  Summary o f the flow stress contributions from precipitates and dislocations as a function o f precipitation state  Table 5.3. Summary o f the softening and recrystallization behaviour o f 40% cold rolled A A 6 1 1 1 with various precipitate conditions at the annealing temperature o f 325°C  107  Ill  Table 6.1. List o f internal state variables for recovery, subgrain growth, recrystallization and precipitation considered in the present modelling approach 117 Table 6.2. Reported diffusion data for M g , C u and S i atoms and self diffusion in bulk aluminum  124  Table 6.3. Comparison between calculated and measured R from T E M  145  Table 6.4. List o f adjustable parameters and their optimized values  146  Table 6.5. List o f physical parameters which were fixed i n the model  147  p  vi  LIST OF FIGURES Fig. 2.1. Recovery kinetics o f industrial processed A A 6 111  7  Fig. 2.2. Sigmoidal plot o f typical recrystallization kinetics during isothermal annealing. ... 11 Fig. 2.3. Evolution o f yield stress vs. aging time o f A A 6 1 1 1 i n the temperature range o f 160-220°C  17  Fig. 2.4. Bright field T E M image showing the precipitate structure i n A A 6 1 1 1 after aging for 7 hours at 180°C. N l and N 2 denote B" needles seen end-on and edge-on respectively  19  Fig. 2.5. Schematic showing the effect o f precipitate size, volume fraction and prior strain (s) on recrystallization kinetics and mechanism.  26  Fig. 2.6. Isothermal recrystallization kinetics showing the effect o f precipitation which occurs at various stages during recrystallization  28  Fig. 2.7. Schematic representation o f grain boundary migration controlled by (a) the transformation o f B' to /?precipitates and (b) local coarsening o f B precipitates at the recrystallization front  32  Fig. 2.8. The effect o f copper concentration on the migration rate o f boundaries i n aluminum at various temperature  35  Fig. 2.9. The effect o f M g contents on the time to achieve 50% recrystallization at 275°C o f a 95% cold rolled A l - M g alloy  36  Fig. 4.1. Optical micrograph showing the elongated grain structure i n the as received hot rolled A A 6 1 1 1  ;  44  Fig. 4.2. Schematic o f the heat treatment and rolling experiments  48  Fig. 4.3. The effect o f natural aging on annealed samples. Samples G l and G 2 were overaged prior to 40% cold rolled  55  Fig. 5.1. (a) Optical micrograph showing the solution treated microstructure with average grain size o f - 4 5 um, (b) E B S D micrograph o f the same sample with grain size o f ~42 u m  58  Fig. 5.2. S E M micrograph showing the solution treated microstructure  59  vii  Fig. 5.3. A g e hardening curve showing the as aged yield stress o f samples with varied precipitate conditions:  61  Fig. 5.4. Plastic portion o f the stress strain curves for (a)supersaturated solid solution (SSS), naturally aged and peak aged samples and (b) overaged and severely overaged samples. Note the serrated flow in the SSS and S O A samples  62  Fig. 5.5. (a) Bright field T E M image showing the lath shaped Q' precipitates (Li and L seen end on and edge on respectively) i n the O A sample and (b) corresponding diffraction pattern taken along the [001] zone axis o f aluminum  64  Fig. 5.6. Bright field T E M images showing (a) the lath shaped Q' precipitates and (b) large square shaped Mg2Si particles in the S O A sample  65  Fig. 5.7. Optical micrographs showing the microstructure o f the as quenched sample after aging for 7 days at 250°C ( O A ) and 325°C ( S O A ) . The average grain size in both micrographs is ~43 um  66  Fig. 5.8. Precipitation hardening curves o f A A 6 1 1 1 at 300 and 325°C. The as solution heat treated yield stress is indicated at the intercept with the vertical axis  68  Fig. 5.9. The as aged and as cold rolled yield stress o f samples with varied precipitate conditions. Note the significant increase in yield stress i n the T4 sample after 40% cold rolling  70  F i g . 5.10. Optical micrograph showing the deformed microstructure o f a 4 0 % cold rolled O A sample  71  Fig. 5.11. S E M micrograph showing the deformed microstructure o f a 4 0 % cold rolled O A sample  72  Fig. 5.12. Dislocation structures in (a) S O A and (b) O A samples after 40% cold deformation  73  2  Fig. 5.13. T E M micrographs showing segments o f fractured Q' precipitates in 40% cold rolled S O A sample. Courtesy of Dr. X. Wang  74  Fig. 5.14 (a) Distribution o f insoluble Fe-rich constituent particles i n the deformed matrix o f a deformed T 4 specimen, (b) close up view o f one o f the particles and (c) X - r a y spectrum indicates the presence o f Fe, S i , M n , and C u in the particle shown i n (b)  75  Fig. 5.15. Isothermal evolution o f yield stress during annealing at 325°C for 40% cold rolled (a) T 4 and P A samples and (b) O A and S O A samples  77  viii  Fig. 5.16. Evolution o f resistivity during annealing o f A A 6 1 1 1 with various precipitate conditions. The prior aging conditions are indicated i n the inset and the resistivity o f the as cold rolled and as solution treated samples are the intercepts with vertical axis  79  Fig. 5.17. Optical micrographs showing the recovered microstructure o f 40% cold rolled T4, P A and O A specimens annealed for 1 minute at 325°C  80  Fig. 5.18. E B S D maps showing the partially recrystallized microstructures o f 4 0 % cold rolled A A 6 1 1 1 with varied precipitate conditions after annealing for 2 weeks at 325°C  83  Fig. 5.19. Recrystallized grain size distribution in partially recrystallized (a) T4, (b) P A and (c) O A samples after annealing for 2 weeks at 3 2 5 ° C  84  Fig. 5.20. E B S D map showing the colonies o f large recrystallized grains in 4 0 % cold rolled O A sample annealed for 2 weeks at 325°C  85  Fig. 5.21. E B S D maps showing the partially recrystallized microstructures o f 4 0 % cold rolled A A 6 1 1 1 with varied precipitate conditions after annealing for 40 d a y s a t 3 2 5 ° C  87  Fig. 5.22. Evolution o f (a) fraction recrystallized (b) recrystallized grain size and (c) number o f recrystallized grains per unit area during isothermal annealing at325°C  88  Fig. 5.23. Spatial distribution o f precipitates in (a) T4 and (b) O A samples annealed for 2 weeks at 325°C  89  Fig. 5.24. (a) S E M micrograph showing the boundary between precipitate and precipitate free zones i n 40% cold rolled O A sample annealed for 2 weeks at 325°C. (b) X - r a y spectrum showing the presence o f M g , S i and C u i n one o f the precipitates  91  Fig. 5.25. (a) S E M micrograph showing the partially recrystallized microstructure o f 40% cold rolled O A sample after annealing for 2 weeks at 325°C. (b) E B S D band contrast map showing the same area o f the microstructure  92  Fig. 5.26. S E M micrograph using back scattered electrons showing a recrystallized grain nucleated from a Fe-rich intermetallic particle surrounded by precipitate free zones i n 4 0 % cold rolled O A sample annealed for 2 weeks at 325°C Fig. 5.27. The effect o f annealing temperature on the softening behaviour o f 40% cold rolled (a) O A sample and (b) S O A sample. The as cold rolled yield stress is indicated at the intercepts with the vertical axis  ix  94  95  Fig. 5.28. Isothermal recrystallization kinetics o f 40% cold rolled A A 6 1 1 1 at (a) 325°C and (b) 4 4 5 ° C with varied precipitate conditions  96  Fig. 5.29. F u l l y recrystallized microstructure o f the 40% cold rolled (a) O A and (b) S O A samples annealed for 100 minutes at 4 4 5 ° C  98  Fig. 5.30. T E M micrograph showing the formation o f cell structure i n 40% cold rolled O A sample annealed for 2 minutes at 325°C. Courtesy of Dr. X. Wang  99  Fig. 5.31. T E M micrograph showing the pinning o f dislocations by precipitates in 40% cold rolled O A sample annealed for 2 minutes at 325°C  101  Fig. 5.32. T E M micrograph showing the transformation o f cell structure into subgrains in 40%) cold rolled O A sample annealed for 7 days at 325°C  102  Fig. 5.33. T E M micrographs showing subgrains formation in 4 0 % cold rolled S O A sample after annealing for 100 minutes at 325°C. Courtesy of Dr. X. Wang  103  Fig. 5.34. (a) T E M micrographs showing a recrystallized grain embedded i n the deformed matrix o f the O A samples annealed for 7 days at 325°C. T E M micrographs showing segment o f the migrating grain boundaries are shown in(b)and(c)  104  Fig. 6.1. Schematic outline o f the overall model framework  142  Fig. 6.2. Comparison between model calculated and experimental (a) softening and (b) recrystallization curves for 4 0 % cold rolled overaged A A 6 1 1 1 during isothermal annealing at 325 and 445°C  149  Fig. 6.3. Comparison between predicted and experimental (a) softening and (b) recrystallization kinetics for 40% cold rolled severely overaged A A 6 1 1 1 during isothermal annealing at 325 and 445°C  150  Fig. 6.4. Softening due to recovery and precipitate coarsening i n the precipitate zones o f 40% cold rolled overaged A A 6 1 1 1 isothermally annealed at 325°C  152  Fig. 6.5. (a) Evolution o f precipitate radius during isothermal annealing o f 40% cold rolled overaged A A 6 1 1 1 at 325 and 445°C and (b) corresponding evolution o f concentration and precipitate volume fraction at 325°C  154  Fig. 6.6. Plots showing the time evolution o f Zener pinning pressure vs. the stored energy i n the precipitate zones o f 40% cold rolled overaged A6111 annealed at 325°C  156  x  Fig. 6.7. Comparison o f (a) softening kinetics and (bj recrystallization kinetics in the precipitate and precipitate free zones during the isothermal annealing o f 40% cold rolled overaged A A 6 1 1 1 at 325°C  xi  1  LIST OF SYMBOLS Symbols A a b c c  CM  c  P  Mg ^eq Cu ^eq Si ^eq r  r  r  Q Co  Definitions/Values A r e a o f a critical recrystallization nucleus (m ) Lattice parameter for Q' precipitates, 1.04 nm Magnitude o f Burger's vector, 0.286 nm Lattice parameter for Q' precipitates, 0.405 nm Residual solute concentration in matrix (CMS+CCU+CSI) Solute concentration in Q' precipitates, 81 at.% 2  Equilibrium concentration o f M g in solid solution, at. % Equilibrium concentration o f C u l n solid solution, at. % Equilibrium concentration o f Si i n solid solution, at. % Solute concentration at precipitate-matrix interface, at. % N o m i n a l solute concentration o f in A A 6 1 1 1 , 1.76 at.% N o m i n a l concentration o f M g i n A A 6 111, 0.88 at.%  Cu  n C  0  Nominal concentration o f C u in A A 6 1 1 1 , 0.30 at.% N o m i n a l concentration o f Si in A A 6 1 1 1 , 0.58 at.%  CM%  Ccu Csi D Do d d drex E F F F G eQ  s  c  D  K, k k la M M M N N c  b  0  A  D  Instantaneous concentration o f M g in solid solution, at. % Instantaneous concentration o f C u in solid solution, at. % Instantaneous concentration o f Si i n solid solution, at. % Effective diffusivity o f solute atoms (m /s) Diffusion coefficient for solute atoms (m /s) Grain diameter (m) Solution treated grain size (m) Recrystallized grain size (m) Y o u n g ' s modulus, 70 M P a Volume fraction o f precipitate free materials Coarsening fraction Precipitate volume fraction Shear modulus o f aluminum, 26 G P a Constant used to determine the equilibrium concentrations o f solutes i n solution, 2 . 8 x 1 0 2  2  28  Constant that determines the potency o f nucleation sites for recrystallization Constant i n the coarsening fraction equation Activation length for dislocation motions during recovery Taylor factor ~ 3.1 Grain boundary mobility (m /N-s) Pre-exponential factor for mobility (m /N-s) 3  3  Avogadro's number, 6.023x10 mol" Number o f precipitate particles per unit volume (m" ) 23  1  3  xii  Nats Nrex N  Number o f dislocation nodes,, assumed ~ 0.5p Number o f recrystallized nuclei per unit volume (m" ) Number o f recrystallized grains per unit area (m ) Number o f Fe-rich particles per unit volume ( m ) Number o f atoms per unit cell for Q' precipitates, 21 D r i v i n g pressure from dislocations (stored energy per unit volume) (Pa) Activation energy for solutes diffusion (J/mol) Recrystallization activation energy (J/mol) Recovery activation energy (J/mol) Recrystallized grain radius (m) Fe-rich particle radius (m) Gas constant (J/mol-K) Precipitate radius (m) Deformed grain boundary area per unit volume (m" ) Fe-rich particles surface area per unit volume (m" ) Temperature ( K ) Time Activation volume for recovery (b ) l5  J  2  r  N  3  Fe  n Pd QD  Qrex  Qo R  RFe RP Sv,gb Sv.Fe  T t V  1  1  J  v  M o l a r volume o f Q' precipitates, 1.09xl0" m V m o l Volume fraction o f recrystallized grains Volume fraction o f recrystallized grains i n precipitate free regions Volume fraction o f recrystallized grains i n precipitate regions Standard enthalpy o f Q' phase dissolution/precipitation reactions, 495 kJ/mol Constant i n the order o f 0.3 5  m  X  x,  X„  AH a  0  a  p  Constant used to determine the intrinsic grain boundary mobility Effective pinning parameter  a  Shape factor (~1)  8b  Average subgrain radius (m)  s  S  K  Geometrical constant o f order o f unity H i g h angle grain boundary velocity (m/s)  pd  Debye frequency, 8.11 x 1 0 s" Dislocation density (m" )  Q  A l u m i n u m atomic volume (m )  12  1  2  3  °i  F l o w stress o f precipitate free regions (Pa)  On  F l o w stress o f precipitate regions (Pa)  Odis  Dislocation contributions to flow stress (Pa)  Oi  Intrinsic flow stress o f aluminum alloy, 10 M P a  Ob  Precipitation hardening yield stress (Pa)  Ore  Instantaneous recovered yield stress (Pa)  Orex  Precipitate-free fully recrystallized flow stress, 40 M P a  Yi  Precipitate-matrix interfacial energy, 0.35 J / m  Ysb  L o w angle grain boundary energy, 0.16 J/m H i g h angle grain boundary energy, 0.324 J / m  Yzb  rj  xiii  2 1,1  2  "  •••• •  ' "  ACKNOWLEDGEMENTS  I can't begin to describe m y deep gratitude to m y supervisors, Professors Warren Poole and Matthias Militzer. M a n y o f the ideas in the model were conceived during many hours o f stimulating discussion with Professor Poole. I am indebted to Professor Militzer who first offered me the opportunity to work on a. project in recrystallization. I have benefited immensely on both personal and professional level under their guidance over the past few years. O f course, I cannot forget the advice provided by D r . M a r y Wells who is always so generous in sharing her thoughts and knowledge.  The financial support from A l c a n and N S E R C is gratefully acknowledged. Special thanks are extended to Dr. X i a n g Wang at McMaster University for carrying out the T E M work. I wish to acknowledge m y roommates in A M P E L 260, especially D r . Fateh Fazeli for being so patient with me on many occasions. I would also like to thank Babak Raeisinia and Sujay Sarkar for their help i n printing this thesis.  This thesis is dedicated to the memory o f m y father. I want to thank m y family for their love i n particular m y wife Lee Leng for her constant encouragement throughout the course o f my P h D studies.  xiv  Chapter 1  Introduction  The drive to produce high quality advanced aluminum sheet metals for the automotive industry has been intensifying over the past two decades, primarily due to the fierce competition with the steel industry. The aluminum sheet metal producers are faced by a number o f significant challenges which can be grouped into two major categories. First, there are increased demands from car manufacturers for improved strength and formability. Strength is required for structural applications where steel has been traditionally the dominant material. On the other hand, highly formable aluminum sheets are required for body-in-white applications which offer the greatest potential for weight reduction. Unfortunately, from a metallurgical point o f view, strength and formability are two incompatible properties; an increase i n strength i n the materials is usually associated with some degree o f loss i n formability or vice versa. The second major challenge facing the industry lies i n the ability to manufacture high quality products consistently at minimum cost.  The key to overcoming these challenges is through innovative product and process improvements. After years o f intensified research, advanced aluminum alloys with good combination o f strength and formability are now available specifically for automotive applications, for example, the A A 5 7 5 4 and A A 6 1 1 1 aluminum alloys. The heat treatable 6xxx series alloys were developed specifically for outer panel applications due to its high dent resistance. For this alloy, it is critical to control the development o f texture i n the materials  1  Chap.  11ntroduction  throughout the entire processing chain since the surface quality after painting is directly related to the distribution o f texture near the sheet surface. Furthermore, the isotropy o f the materials in terms o f mechanical properties can be significantly enhanced b y the presence o f favourable texture components.  One o f the most effective means to control texture is b y modifying the recrystallization behaviour o f the materials. For example, a more random recrystallized texture can be obtained i f particle-stimulated-nucleation (PSN) is the dominant nucleation mechanism. Hence, in order to exploit the full potential o f these advanced alloys through thermomechanical processing, sheet metal producers are required to have an increasingly sophisticated understanding o f the linkage between processing conditions and the evolution o f microstructure in the materials. Consequently, much o f recent collaborative research between academia and industry have been directed towards developing quantitative models based on the concept o f microstructure engineering. This modelling concept which has been developed since the 1970s focuses on applying fundamentally based mathematical models to predict the product properties as a function o f processing parameters by modelling microstructure evolution. A n accurate microstructure model, once established and verified, can be employed to systematically manipulate all existing processing parameters with material properties as a result. Therefore it provides a valuable tool for the industry to tailor their forming and heat treatment operations to achieve the most desirable product properties without the need to carry out expensive and time-consuming plant trials which are often based on the trial and error approach.  Comprehensive microstructure models are currently available for the hot rolling o f aluminum alloys [Sellars, 1997 ,Wells et al., 1998]. However, comparatively little attention has been "2  Chap.  11ntroduction  given to the annealing o f cold rolled alloys. This is somewhat surprising because the annealing process constitutes one o f the most critical processing steps i n the production o f sheet metals. It is usually the final heat treatment step where the microstructure o f the alloys can be modified before the products are shipped to customers. M o r e recently, microstructure models capable o f predicting softening behaviour and recrystallized grain size have been developed for the continuous annealing o f non-heat-treatable aluminum alloys [Go et al., 2003]. However, modelling work o f a similar nature has not yet been extended to the annealing o f precipitation-hardenable alloys. Hence, the goal o f the present work is to develop a basic modelling framework based on the concept o f microstructure engineering for the annealing o f cold rolled precipitation strengthened  alloys. The commercially significant A l - M g - S i - C u  A A 6 1 1 1 aluminum alloys has been chosen as the subject o f the present investigation. The experimental data generated from the present study represents the first systematic set o f recovery and recrystallization data for cold rolled A A 6 1 1 1 with a wide range o f precipitate conditions. Based on these data, a first generation microstructure evolution model is proposed that is focused on the interaction between recovery, recrystallization and precipitation. Texture evolution is beyond the scope o f the present work. The microstructure model developed in the present work can be seen as an important step towards the development o f a comprehensive process model for the annealing o f heat-treatable aluminum alloys.  3  Chapter 2  Literature Review  Prior to annealing, sheet metals undergo a cold rolling process where the strength o f the material is greatly enhanced due to the accumulation o f crystalline defects i n the structure, mainly i n the form o f dislocations. During annealing, the deformed microstructure which is highly loaded with dislocations is eliminated through the processes o f recovery and recrystallization. In materials o f medium or high stacking fault energy, significant subgrain growth may also occur prior to the onset o f recrystallization. A l l these microstructural processes are significantly influenced by the precipitate condition i n the deformed state. Depending on the annealing temperature, the pre-existing precipitates can either dissolve or coarsen  concurrently  with recovery  and recrystallization. I f the deformed  matrix is  supersaturated with solid solution, nucleation and growth o f new precipitates becomes viable during annealing. Hence, annealing o f cold rolled precipitation hardening alloys represents a complex process which may involve the interaction o f various metallurgical phenomena. In this chapter, we w i l l focus on the three principle microstructural processes o f recovery, recrystallization and precipitation. O f particular importance is the interaction between the various processes and their effect on the properties o f the materials. The literature review is organized  i n the following  order:  First, the individual  processes  o f recovery and  recrystallization are reviewed i n sections 2.1 and 2.2, respectively. The competing nature o f recovery and recrystallization is delineated  i n section 2.3. Section 2.4 reviews the  precipitation hardening behaviour o f A l - M g - S i - C u A A 6 1 1 1 aluminum alloy (2.4.1) and  4  Chap. 2 Literature Review  existing theoretical models for precipitation (2.4.2). The interaction between precipitation and recovery is discussed i n section 2.5. In Section 2.6 the two most commonly observed interaction between precipitation and recrystallization are assessed. The chapter concludes with a critical assessment o f the literature i n an effort to accentuate the importance o f integrated modelling and identify areas where improvement is most needed (section 2.7).  2.1  Recovery  2.1.1 General Observations  Recovery refers to a process that involves the rearrangement and annihilation o f dislocations into  lower  energy  configurations.  recrystallization is that the former  The palpable  difference  between  does not involve the sweeping  recovery and  o f the deformed  microstructure b y migrating grain boundaries. The dislocation motions can be accomplished by either glide, climb or cross-slip [Nes, 1995, Kuhlmann-Wilsdorf, 2000]. In alloys o f medium to high stacking fault energy, the rearrangement o f dislocations often leads to the formation o f subgrain structures with substantial size [Humphreys and Hatherly, 1995]. Several authors have suggested that subgrains that acquire a critical size eventually become the nuclei o f subsequent recrystallization [Doherty et al., 1997]. However, more research is still required to clarify the underlying mechanism for the transition to occur. Unlike recrystallization which can be quantified by measuring fraction transformed, recovery kinetics is usually followed by measuring the changes in the physical or mechanical properties o f the materials, mainly because direct quantification o f changes i n dislocation density is difficult.  5  Chap. 2 Literature Review  The recovery behaviour o f industrial processed A A 6 1 1 1 has been investigated previously at U B C as part o f a strategic project aimed at studying the continuous annealing behaviour o f aluminum alloys [Go et al., 2001a]. The results are shown i n Fig. 2.1 where the recovery kinetics is characterized by the softening in yield stress as a function o f annealing time. From Fig. 2.1a,  it can be observed that the degree o f softening due to recovery increases  significantly with increasing annealing temperatures. The effect o f prestrain on softening is shown in Fig. 2.1b.  It is evident that all the softening curves, irrespective o f annealing  temperatures or prior reduction, follow a logarithmic time decay. This logarithmic time dependence o f softening is typical o f the recovery process which has been observed in both steel [Mukunthan and Hawbolt, 1996] and aluminum alloys [Barioz et al., 1992, Burger et al., 1995, Verdier et al., 1996, G o et al., 2001b].  2.1.2  Recovery Modelling  During recovery, the annihilation and rearrangement  o f dislocations into lower energy  configurations can be accomplished by a combination o f glide, climb and cross slip. Hence, in order to formulate a rate equation to describe the logarithmic time decay o f flow stress during recovery, the concern becomes to identify the correct rate controlling mechanism. In addition to the three basic mode o f dislocation migration, solute drag becomes an alternative rate controlling mechanism i n solute containing alloys. In the literature, a variety o f quantitative models based on the four different rate controlling mechanisms: glide, thermally activated climb and cross slip and solute drag have been developed [Friedel, 1964, Humphreys and Hatherly, 1995, Nes and Saeter, 1995, Kuhlmann-Wilsdorf, 2000]. However, many o f the assumptions in these models are difficult to verify by experimental observations, mainly 6  Chap. 2 Literature Review  280  (a)  • O •  260 H 03  175°C 200°C 225°C 250°C  Q= 240 jg 220 co ? 200 > 180  60% cold rolled  160  <-*-f—  10 260  10  1  2  10  3  10  5  Time (s) (b)  Annealing Temp. = 200°C  240 03  Q_  220 CO  200  60%  180  160  40%  I i  1111  10  "" 1  I  n  1111  10  10  2  1— 3  n  10  4  Time (s) Fig. 2.1. Recovery kinetics o f industrial processed A A 6 1 1 1 : (a) effect o f annealing temperatures and (b) effect o f prestrain. The as cold rolled yield stress is 230 and 253 M P a for 40% and 60% cold reduction, respectively [Go et al., 2001a].  .7  Chap. 2 Literature Review  due to the difficulties in directly observing dislocation motion during recovery. Consequently, the models are often fitted to experimental results such as recovery softening curves by using a large number  o f adjustable  parameters. A comprehensive  review o f these modelling  approaches can be found i n a paper b y Nes (1995).  There are two dominant physically based models i n the literature that have been developed to describe the characteristic logarithmic time dependence o f recovery. The first approach is a single structural parameter model based on the overall dislocation density developed by Verdier et al. (1999). The mathematical formulation o f the model follows the original theory proposed by Friedel (1964) in which recovery is assumed to occur by thermally activated dislocation motion. In this model, the instantaneous yield stress o f the material, cr, during recovery is given by a kinetic law o f the form:  In Equation 2.1, Q  0  da,  64  o\  dt  9M a  E  6  l  (  2  Q\ Q  { kTJ  . ,  (cjy\ \kT  )  and V denote the activation energy and volume o f the elementary  recovery event, respectively. v is the Debye frequency, M is the Taylor factor and E is the D  Young's modulus. The parameter a is a constant o f the order o f 0.3 for aluminum. B y using Qo and V as fitting parameters, the model has been shown to be accurate i n describing the recovery softening o f A l - M g alloys with different amounts o f prestrain [Verdier et al., 1999, G o e r al, 2003].  8  Chap. 2 Literature Review  The second modelling approach is more rigorous in terms o f the number o f structural parameters used. According to Nes (1995), recovery softening is best modelled by following the evolution o f two parameters, namely, the cell/subgrain size, S and the dislocation density, s  Pd- The general form o f the model is given by [Nes and Saeter, 1995]:  (2.2)  where cr is the frictional stress o f aluminum and b is the magnitude o f the Burger's vector, ccj 0  and 0(2 are constants with values around 0.3-0.5 and 2-3, respectively. This model has been successfully employed to interpret the recovery behaviour o f high purity iron, aluminum and A l - M g alloys [Nes, 1995].  Although it appears that the model proposed by Nes is more complete in describing the recovered microstructure, implementation o f the model can become very complex since additional assumptions must be postulated in order to separate the flow stress contributions from dislocation density and subgrains. Consequently, additional adjustable parameters are required in order to fit the model to experimental data. In contrast to the argument by Nes, Verdier and coworkers have convincingly shown that recovery subgrain growth in commercial purity A l - M g alloys does not change the logarithmic time dependence o f yield stress [Verdier .et al., 1997a, 1997b, 1998]. Hence, they concluded that a single parameter approach based on dislocation density is sufficient to model recovery softening. The advantage o f the Verdier et al.'s model is that it can be easily integrated and applied to non-isothermal conditions with only two fitting parameters, the activation energy and volume, as demonstrated by G o et al., (2003). 9  Chap. 2 Literature Review  2.2  Recrystallization  2.2.1  General Observations  Recrystallization is accomplished by the migration o f high angle grain boundaries into the deformed or recovered matrix leaving behind a new set o f dislocation free grains. Hence, the progress o f recrystallization can be followed directly by plotting the evolution o f volume fraction recrystallized grains as a function o f annealing time. Such a plot has the characteristic sigmoidal form o f Fig. 2.2. A s indicated in Fig. 2.2, an incubation time is usually observed prior to the start o f recrystallization. Nucleation is followed by an increasing rate o f recrystallization and then a decreasing recrystallization rate when recrystallizing grains start to impinge on their neighbours. Experimentally, the volume fraction o f recrystallized grains can be measured directly from optical micrographs. A comprehensive analysis o f the quantitative metallography technique for recrystallization has been provided by Orsetti-Rossi and Sellars (1997). Due to the recent advancement in electron-backscattered diffraction ( E B S D ) , there has been a surge in using E B S D data to estimate fraction o f recrystallized grains [Humphreys, 2001]. In addition to these microstructural techniques, recrystallization kinetics can also be quantified from softening measurements provided that the effect o f recovery is separated [Chen et al, 2002, G o et al, 2003].  2.2.2  Recrystallization Modelling  The most widely used analytical approach to describe the evolution o f volume fraction o f recrystallized grains, X with respect to time, t follows the theory developed independently by 10  Chap. 2 Literature Review  1.0 H 3  0  Impingement of growing grains  8  N  1  0.6  o CD  (£  0.4  c  o  I  0.2 0.0 J  Nucleation Incubation time  Log Time  Fig. 2.2. Sigmoidal plot o f typical recrystallization kinetics during isothermal annealing.  11  Chap. 2 Literature Review  Kolmogorov (1937), Johnson and M e h l (1939) and A v r a m i (1940). The model is commonly known as the  JMAK  model. Assuming random  distribution o f nuclei, the  standard  mathematical form o f the model is written as  (2.3)  where B is a temperature dependent parameter and n is known as the J M A K exponent. The effect o f nucleation and growth rates are embedded in the kinetic parameter B. Equation 2.3 was derived based on the assumption that growth rate is constant during recrystallization. There are two limiting cases in terms o f nucleation: in the case o f site saturation, i . e., all nucleation events effectively take place at the onset o f recrystallization, then n = 3. If the nucleation rate is constant during recrystallization, then n = 4. The effect  o f growth  dimensionality o f the recrystallizing grains on the J M A K exponent is summarized in Table 2.1 [Humphreys and Hatherly, 1995].  The application o f the J M A K approach to model recrystallization has been critically assessed in a recent review article by Vandermeer (2001). Overall, there are two main criticisms associated with the J M A K model. First, the experimentally determined J M A K exponent is often less than 3 even though the recrystallized grains are essentially equaixed (i.e., 3-d growth). Secondly, the assumption o f constant growth rate is not expected to hold i f the driving force for recrystallization diminishes as recrystallization proceeds. B y reviewing a large body o f experimental data i n the literature, Humphreys and Hatherly (1995) have concluded that the cause o f these inconsistencies can be directly attributed to the heterogeneity  12  Chap. 2 Literature Review  Table 2.1. The value o f ideal J M A K exponent as a function o f growth dimensionality.  Growth dimensionality  Site saturation  Constant nucleation rate  3-d  3  4  2-d  2  3  1-d  1  2  13  Chap. 2 Literature Review  of the deformed structure. Inhomogeneous distribution o f stored energy leads to variation o f growth rate during recrystallization. Furthermore, recrystallization nucleation occurs first in regions with the highest stored energy and this contradicts the basic assumption o f random distribution o f nuclei in the J M A K model. In view o f these shortcomings, relaxed J M A K models in which the growth rate is a decreasing function o f time were subsequently developed by various authors [Vandermeer and Rath, 1989, Furu et al., 1990, Rios, 1997]. However, the requirement o f a random distribution o f nuclei remains as a serious limitation o f the J M A K model.  2.3  Interaction Between Recovery and Recrystallization  During annealing, recovery and recrystallization compete for the same dislocation stored energy accumulated i n the matrix during the cold working process. The classic early work b y Vandermeer and Gordon provides the first direct experimental evidence to show that the driving force for recrystallization o f aluminum alloys containing small amounts o f copper is severely reduced by recovery [Vandermeer and Gordon, 1962]. In the literature, recovery and recrystallization are frequently treated as sequential processes but many aspects o f the transition from recovery to recrystallization are still poorly understood. Several authors have suggested that recovery facilitates the nucleation o f recrystallized grains by the mechanism o f subgrain coalescence [Humphreys and Hatherly, 1995, Doherty et al., 1997]. However, careful analysis o f experimental data has revealed that in most cases, recrystallization nucleation is close to being site saturated [Vandermeer and Rath 1989, Orsetti-Rossi and Sellars, 1999]. This is particularly the case for industrial alloys which have been severely cold rolled. In this case, the competing nature between recovery and recrystallization can be readily modelled by 14  Chap. 2 Literature Review  using a time dependent growth rate, G without the need to consider i n detail the nucleation mechanism [Furu et al, 1990, Zurob et al, 2002]:  ^3  X = 1 - exp  -nN\ \Gdt  G is directly proportional to the driving pressure, P  d  (2.4)  exerted on the grain boundary o f  recrystallizing grains by the difference in dislocation density, p  d  across the recrystallization  front:  G = MP = d  -MGb p {t)  l  2  d  (2.5)  The constant o f proportionality, M is defined as the mobility o f the grain boundary. The magnitude o f the time dependent dislocation density in Equation 2.5 decreases as recovery proceeds. Therefore, recovery slows down recrystallization by lowering the driving pressure for the grain boundary to consume the deformed or recovered matrix.  2.4  Precipitation  Precipitation has been the subject o f numerous studies in the literature. In this work, the focus is on the effect o f precipitate conditions in the deformed microstructure on the recovery and recrystallization behaviour o f the alloys during subsequent annealing. O f particular interest is  15  Chap. 2 Literature Review  the precipitation behaviour o f the A l - M g - S i - C u A A 6 i l l alloy. The precipitation behaviour o f this alloy has been extensively studied in the past in an effort to improve its age hardening response during the paint bake cycle. Some o f these important observations are summarized i n the next section. Existing precipitation models are examined i n section 2.4.2.  2.4.1  Precipitation Hardening Behaviour of AA6111  In North America, the A l - M g - S i - C u A A 6 1 1 1 alloy is the main aluminum choice for automotive sheet skin applications, mainly due to its excellent paint bake response and high formability. Due to its significant commercial relevance, the precipitation hardening behaviour of the alloy i n the intermediate temperature range o f 160-220°C has been extensively characterized in many studies [Bryant, 1999, Quainoo et al., 2001, Esmaeili et al, 2003a, Wang et al., 2003]. M o r e recently, a yield strength model specifically for the aging o f A A 6 1 1 1 has been developed in the doctorate thesis o f Esmaeili (2002). In Fig. 2.3, the age hardening curves o f the material in the temperature range o f 160-220°C is shown in terms o f the evolution o f yield stress as a function o f aging time. It can be observed that the peak strength obtained at different aging temperatures is similar (-340 M P a ) but it took much longer for samples aged at lower temperatures to reach the peak strength: ~20 hours at 160°C vs. ~1 hour at 2 2 0 ° C . According to L l o y d et al., (2000), the corresponding precipitation sequence can be presented as  SSS -> G P zones/clusters -» j3" + Q' -> equilibrium Q + M g S i 2  16  Chap. 2 Literature Review  0.01  0.1  1  10  100  Fig. 2.3. Evolution o f yield stress vs. aging time o f A A 6 1 1 1 in the temperature range of 160220°C [Esmaeili., 2002].  17  Chap. 2 Literature Review  where SSS represents the supersaturated solid solution state. Several authors have suggested that the precipitation sequence o f A l - M g - S i - C u alloys is dependent on the M g : S i ratio and the concentration o f C u i n solid solution [Miao and Laughlin, 2000, Murayama et al, 2001]. The formation o f Guiner-Preston (GP) zones and solute clusters provides the increase i n strength during aging at room temperature which is commonly known as the T4 condition. These clusters have been characterized by atom probe field ion microscopy and found to primarily contain co-clusters o f M g and S i [Murayama et al., 2001]. The strength o f the alloy can be significantly enhanced by aging at elevated temperatures due to the precipitation o f the two main hardening phases, B" and Q'. Quantitative T E M measurements have shown that approximately 80% o f the total volume fraction o f precipitates are B" while the remaining fraction belongs to the Q' phase after peak aging at 180°C for 7 hours [Wang et al., 2003]. The corresponding precipitate structure o f the sample is depicted i n the bright  field  transmission electron micrograph shown i n Fig. 2.4. It is observed that the two metastable phases J3" and Q' have a needle and lath shaped morphology, respectively and they both form with the long axis o f the precipitate parallel to the <100> direction o f the aluminum matrix [Chakrabarti and Laughlin, 2004]. The crystal structure o f the B" and Q' precipitates have been identified as monoclinic and hexagonal, respectively [Perovic et al., 1999]. The Q' phase can be seen as a precursor for the equilibrium Q phase (some authors have used directly the notation Q instead o f Q' for the lath shaped precipitates, for example i n Weatherly et al., 2001). Based on the T E M work o f Wang and Embury (2002), the predominant precipitate after overaging for 7 days at 250°C is the Q' phase with lengths up to 350 nm. The length o f Q' precipitates increased significantly to - 6 0 0 nm after overaging for 10 minutes at 315°C [Perovic et al, 1999].  18  Chap. 2 Literature Review  Fig. 2.4. Bright field T E M image showing the precipitate structure in A A 6 1 1 1 after aging for 7 hours at 180°C. N l and N 2 denote B" needles seen end-on and edge-on respectively. L I and L 2 corresponds to Q' laths seen end-on and edge-on respectively. [Esmaeili, 2002].  19  Chap. 2 Literature Review  During transformation  from Q' to Q i n the later stages or at higher temperatures, the  precipitates maintain their lath shaped morphology and hexagonal crystal structure, only the size increases [Chakrabarti et al, 1998].  2.4.2  Precipitation Modelling  There are numerous kinetic models i n the literature for the precipitation o f second phase particles. In general, the precipitation process in a supersaturated solid solution can be divided into three distinct stages: nucleation, growth and coarsening. Theoretical models for each o f these individual processes are long available in the literature [Martin et al., 1997]. The recent trend in modelling precipitation kinetics is to couple the nucleation, growth and coarsening processes within  one  comprehensive  modelling framework.  This approach  has  been  successfully applied by several researchers to model the precipitation kinetics in aluminum alloys [Deschamps and Brechet, 1999, M y h r et al. 2001,] as w e l l as i n microalloyed steels [Dutta et al, 2001, Zurob et al, 2002].  In the model developed by Deschamps and Brechet (1999), the precipitation process is divided into two regimes. The first regime corresponds  to the nucleation and growth o f new  precipitates. The growth and coarsening o f these precipitates are considered in the second regime. A progressive transition from the first to second regime takes place and the transition occurs when the diminution o f the precipitate density, N due to coarsening is larger than the p  increase in precipitate density due to nucleation, i . e.:  20  Chap. 2 Literature Review  dN  p  dt  > growth+coctrs  dN  p  dt  (2.6) Enucleation  The mathematical formulation o f the models is based on classical nucleation and growth theories [Martin et al., 1997]. In terms o f precipitate coarsening, the standard L S W law is applied [Lifshitz and Slyozov, 1961, Wagner, 1961]. In the second regime, a coarsening fraction is used to integrate the individual contribution o f growth and coarsening to the overall average precipitate radius.  The model was subsequently coupled with a yield stress model and applied to describe the precipitation hardening behaviour o f A l - Z n - M g alloys. There are a number o f important assumptions i n the model. First, the diffusion o f Z n and M g in bulk aluminum is described b y an equivalent diffusivity. However, no diffusion equation is given i n the paper on how the equivalent diffusivity was calculated. It appears that the diffusivity  at a given aging  temperature is simply taken as a fitting parameter. Other fitting parameters i n the precipitation model include the interfacial energy o f the precipitate-matrix interface and the activation energy for precipitate nucleation. Secondly, the model does not consider directly the precipitation sequence, i n other words, only one type o f precipitate is considered. In spite o f these simple assumptions, this model is considered as one o f the most comprehensive model frameworks for precipitation kinetics currently available i n the literature. The model has also been extended to account for heterogeneous precipitation on dislocations and its interaction with the surrounding matrix [Deschamps and Brechet, 1999].  21  Chap. 2 Literature Review  2.5  Interaction Between Precipitation and Recovery  There have been few investigations into the interaction between recovery and precipitation. However, it is believed that fine and stable precipitates retard recovery i n a similar fashion as retarding recrystallization during annealing [Humphreys and Hatherly, 1995]. In the case o f recovery, segments o f dislocations may be pinned by precipitates thus render them immobile during recovery. O n the other hand, concurrent recovery lowers the dislocation density in the materials. This may i n turn delay the progress o f precipitation b y reducing the number o f available nucleation sites [Gomez-Ramirez and Pound, 1973].  Following Humphreys and Hatherly (1995), the pinning effect o f particles on dislocations can be treated based on a force balance approach. In this approach, the dislocation structure is assumed to be in the form o f a three dimensional dislocation network o f mesh size R^. The dislocation velocity is proportional to the change in scale o f the network. The driving force, Fj for coarsening o f a 3-D dislocation network by dislocation migration can be approximated by  Gb d=-T~  2  r, F  (2-7)  In a matrix with a random dispersion o f precipitate particles, the dislocation motion is opposed by a pinning force, F o f the order o f p  (2.8)  22  Chap. 2 Literature Review  where X is the spacing between the particles along the dislocation lines and c; is a constant. It should be noted that Equation 2.8 is based on the Orowan process i . e., dislocation lines pass through the particles b y leaving behind dislocation loops (Orowan loops) around the particles. Humphreys and Hatherly (1995) have also considered the situation i n which the recovery is dominated b y subgrain growth. In this case, the pinning o f subboundaries b y precipitates is treated as a special case o f Zener pinning. The recovery is then expected to proceed at a rate controlled by the coarsening o f precipitates.  A simplified approach to combine the pinning effect o f precipitates on dislocations with Verdier et al.'s recovery model (Equation 2.1) has recently been proposed b y Zurob (2003b). In this model, the ratio o f the net driving force to the total driving force is thought o f as the unpinned fraction o f the dislocation network, £ U s i n g Equations 2.7 and 2.8, <f is given as  d~ p t =— ^ F  F  e  . C^R -T  d  J  L  = l  J  (2-9)  L  The mesh size R can be estimated from the dislocation density, R = (3/p ) , and the average 05  d  d  pinning spacing A, is equal to p /N d  p  d  where N is the number o f precipitates per unit volume. p  Combining these expressions with Equation 2.9, one gets  P  where  dis  ly d  is the number o f dislocation nodes and approximately equal to 0.5p . 5  d  23  Finally,  Chap. 2 Literature Review  Verdier et. al's recovery model is modified to account for the pinning effect, i.e.:  -r  L  dt  Y 2 - ^  =  9M a i  2  E  v  D ^ P  ~  \  s  kT)  m  h  -hr  \ kT ){  (2-11)  N ) dis  Equation 2.11 assumes that the recovery kinetics is proportional to the fraction o f the network that is not available for recovery. It can be seen that recovery ceases when N is equal to TV^. p  This simple approach has been shown to be sufficient i n explaining the softening behaviour o f austenitic iron alloys containing various amounts o f N b and C during annealing [Zurob et al, 2003a].  •rf  2.6  Interaction Between Precipitation and Recrystallization  Most o f the existing studies on the interaction between precipitation and recrystallization focus on hot rolling o f microalloyed steels [Jonas and Weiss, 1979, K w o n and DeArdo, 1991, Kang et al, 1997, Medina et al., 1999, Lee, 1999, Abad et al., 2001]. B y comparison, there has been very limited research, i f any, aimed at studying the precipitation-recrystallization interaction i n commercial heat treatable aluminum alloys. This is unfortunate since Burger and co-workers have clearly shown that the microstructure and properties o f an industrial cold rolled annealed 6000 series aluminum alloys can be optimized by manipulating the thermomechanical history of the alloy (which determines the precipitate conditions i n the material) prior to annealing [Burger et al., 1995, 1996]. In the following, the interaction between precipitation and recrystallization is examined i n terms o f precipitate pinning (section 2.6.1) and solute drag  (section 2.6.2). 24  Chap. 2 Literature Review  2.6.1  Precipitate Pinning  During recrystallization, grain boundaries  are attracted to precipitates because when a  boundary intersects a particle, a region o f boundary equal to the intersection area is effectively removed which leads to a reduction in the energy o f the overall system. In general, precipitation has four important effects on recrystallization [Humphreys and Hatherly, 1995]:  1. The presence o f precipitates during cold deformation may lead to an increase in the stored energy and hence the driving force for recrystallization. 2. Large precipitates may act as nucleation sites for recrystallization via particlestimulated-nucleation (PSN). 3. Precipitation decreases the matrix solute content and therefore reduces the effect o f solute drag on the mobility o f grain boundaries. 4. Fine and closely spaced precipitates may exert a significant pinning force on high angle grain boundaries.  The first three effects tend to promote recrystallization, whereas the last tends to retard recrystallization. The importance o f these effects during annealing is dependent on the nature of the precipitates. In principle, three simple parameters can be considered: volume fraction, size and spacing o f the precipitates. The effect o f the precipitate volume fraction and size on recrystallization kinetics is schematically illustrated i n Fig. 2.5. The effect o f prior strain is also indicated. The graph can be analyzed in terms o f the ratio between precipitate volume fraction and radius, i . e. F IR . B y examining a number o f experimental investigations, P  P  Humphreys and Hatherly (1995) have concluded that to a first approximation, the retardation 25  Chap. 2 Literature Review  Fig. 2.5. Schematic showing the effect o f precipitate size, volume fraction and prestrain on recrystallization kinetics and mechanism [after Humphreys and Hatherly, 1995].  26  Chap. 2 Literature Review  o f recrystallization is most likely to occur when F IR P  is greater than 0.2 urn" . If the ratio is 1  P  less than 0.2 um" , recrystallization is often accelerated i n comparison with precipitate free 1  materials. The increase i n the rate o f recrystallization can be attributed to the increased driving force that arises from the additional dislocations generated by the precipitates during deformation and to particle stimulated recrystallization (PSN). The critical diameter for P S N to occur has been found to be in the range o f 1 p m for steel and aluminum alloys [Leslie et al, 1961, Humphreys, 1977, L l o y d , 1985]. Furthermore, because the solutes solubility varies with temperature, it is probable that precipitation may precede or accompany recrystallization during annealing. Fig. 2.6 shows the effect o f precipitation occurring at various stages during recrystallization on the shape o f the isothermal recrystallization curves [ L i u et al, 1996]. Type I and III occur during annealing at high and low temperatures, respectively. A t high annealing temperatures, precipitation does not interfere with recrystallization (in this case,  the  retardation effect would then primarily be one o f solute drag w h i c h w i l l be discussed later). A t low annealing  temperatures (type III kinetics) where precipitation takes place  before  recrystallization, the onset o f recrystallization is greatly delayed by the precipitates induced pinning force on grain boundaries. Recrystallization is only allowed to proceed after sufficient coarsening o f the precipitates has occurred. In type II kinetics, a halt i n the recrystallization process is observed w h i c h coincides with the precipitation process. This momentary cessation o f the recrystallization process appears as a plateau on the recrystallized fraction curve. Recrystallization resumes after precipitation is completed. It has been suggested by a number o f authors that type II and III recrystallization kinetics are controlled by the local coarsening o f precipitates at the recrystallization front. [Hansen et al., Wilshynsky-Dresler et al, 1992, Lillywhite et al, 2000].  27  1980, Lotter et al.,  1980,  Chap. 2 Literature Review  Log Time  Fig. 2.6. Isothermal recrystallization kinetics showing the effect o f precipitation which occurs at various stages during recrystallization [after L i u et al, 1996].  28  Chap. 2 Literature Review  Mechanistically, this is believed to occur as the migration rate o f the recrystallization fronts are retarded by a pinning force due to fine precipitates situated on the grain boundaries. A s long as the pinning force is larger than the magnitude o f the driving force for recrystallization, the grain boundaries w i l l be completely arrested. Once the precipitates begin to grow and coarsen due to Ostwald ripening, the pinning force w i l l start to decrease. A s soon as the pinning force becomes sufficiently weak, the high angle grain boundaries w i l l start to move and consume the neighbouring deformed grains, albeit at some reduced overall velocity.  To  date, the most  systematic  study on the influence o f prior precipitation state on  recrystallization behaviour o f aluminum alloys was conducted on a high purity A l - M g - S i alloy by Lillywhite et al. i n 2000. [Lillywhite et al., 2000]. In this work, a series o f heat treatments were carried out before cold rolling in order to produce samples with different precipitate conditions. The samples were cold rolled to 70% reduction i n thickness prior to annealing. The corresponding initial precipitate conditions are summarized in Table 2.2 along with the completion time for recrystallization obtained from isothermal annealing at 300°C. The experimental results i n Table 2.2 show that the samples with coarse and widely spaced J3 particles (solution treated then furnace cooled) displays the most rapid recrystallization kinetics  promoted  by  particle  stimulated  nucleation.  In  the  as-quenched  samples,  recrystallization took an intermediate time to complete. The slowest recrystallization rate is observed i n samples that have been preaged to produce fine metastable /?' particles. These metastable f3' particles were broken up and made partially incoherent by the deformation process. U p o n annealing, before the onset o f recrystallization, the broken /?' particles transform to the stable /? phase. Based on the results o f an extensive microstructural analysis,  29  Chap. 2 Literature Review  Table 2.2. The effect o f prior precipitate conditions on the recrystallization completion time for a 70% cold rolled high purity A l - M g - S i alloy [Lillywhite et al, 2000]. Heat treatment before  Initial precipitate  Recrystallization  conditions  completion time  cold rolling  Solution treated, water quenched  Supersaturated solid solution  Solution treated, furnace cooled  Stable  spheres  10 hours  0.2 hours  Solution treated, water quenched and then preaged at 300°C for 1 hour  Fine metastable B' rods  30  1600 hours  Chap. 2 Literature Review  Lillywhite et al. concluded that the rate determining step for recrystallization in the asquenched samples is the transformation o f the metastable B' phase to the equilibrium B phase while recrystallization in the preaged samples is controlled by the local coarsening o f P particles  at  the  recrystallization front. These  two  rate  controlling mechanisms  are  schematically illustrated i n Fig. 2.7.  Quantitatively, the retarding effect o f precipitates can be readily modelled by incorporating the retarding pressure, P that arises from precipitates into Equation 2.5: z  G=  M{P -P ) d  (2.12)  z  The term (Pd - P ) represents the net pressure acting on the grain boundaries. Therefore, z  recrystallizing grains w i l l only grow i f the net pressure is positive. P is commonly known as z  Zener pinning pressure due to Zener's seminal contribution to this subject. The mathematical derivation o f the pinning pressure arising from precipitates has been performed in many studies i n the past but unfortunately not always i n a totally correct way [Nes et al, 1985]. The complete derivation leads to an expression o f the pinning pressure, P  z  which is directly  proportional to the volume fraction o f precipitates and inversely proportional to the mean radius o f the precipitates [Humphreys and Hatherly, 1995]:  3F  rb 2R  P  g  p  31  (2.13)  Chap. 2 Literature Review  Fig. 2.7. Schematic representation o f grain boundary migration controlled by (a) the transformation o f /?' (grey rectangles) to J3 (dark circles) precipitates and (b) local coarsening of P precipitates at the recrystallization front. Arrows indicate the direction o f boundary migration [after Lillywhite et al., 2000].  32  Chap. 2 Literature Review  where y b refers to the grain boundary energy. F and R denote the volume fraction and radius g  p  p  o f the precipitates, respectively. Equation 2.13 is derived for a planar boundary intersecting an array o f precipitates which are randomly distributed i n the matrix. A n additional requirement for Equation 2.13 to be valid is that the grain size must be much larger than the average precipitate spacing. It should be noted that i n the original paper, the pinning pressure was half that o f Equation 2.13. The reason behind this discrepancy is unclear but Nes et al. have speculated that it is probably because Zener has assumed only the particles behind the boundary w i l l act against the forward motion o f the boundary thus obtaining a lower pinning pressure [Nes et al., 1985]. A more rigorous treatment o f the pinning pressure involves the incorporation o f precipitate shape and non-random distribution o f precipitates, as shown b y Nes et al. (1985). In a recent review article b y Manohar et al. (1998), it has been shown that a more comprehensive treatment o f the particle-grain boundary interaction leads to considerably higher P than original Zener's estimate. However, Humphreys and Hatherly (1995) have z  concluded that more sophisticated calculations do not result i n relationships which differ significantly from Equation 2.13. The Zener equation remains the most widely used approach in the estimation o f particle pinning pressure.  2.6.2 Solute Drag  In addition to precipitate pinning, the presence o f a significant amount o f solutes can retard recrystallization by reducing the grain boundary mobility and evidence o f this has been found in a number o f studies [Gordon and Vandermeer, 1966, Humphreys and Hatherly, 1995, Cahn, 1996]. A t high solute concentrations, the grain boundary mobility is low and decreases with  33  Chap. 2 Literature Review  increasing solute concentrations. This behaviour is illustrated i n Fig. 2.8 where the reciprocal velocity o f boundaries is plotted against the copper concentration i n aluminum. Assuming a constant driving force, it can be seen that the boundary velocity is inversely proportional to the solute concentration. Fig. 2.8 also shows that the retarding effect o f solutes diminishes with increasing temperatures.  The aforementioned effect o f solute on recrystallization is not observed in all materials. A n example is given i n Fig. 2.9 where the time to achieve 50% recrystallization, f % o f a 95% 50  cold rolled A l - M g alloys at 275°C is shown as a function o f M g content. It can be seen that the rate o f recrystallization is significantly lower when the M g content is increased from 0.5 to 1 wt%. However, at M g contents above 1 wt%, recrystallization is remarkably accelerated with increasing M g content up to 5% [Koizumi et al., 2000]. The accelerated recrystallization behaviour can be explained by the presence o f excess solutes during deformation which strongly inhibit dynamic recovery. A s a consequence, higher stored energy is available to drive subsequent recrystallization. Apparently, the increase i n stored energy is more than enough to. overcome the inhibiting effect o f solutes.  Modern quantitative theory o f grain boundary mobility i n a dilute solid solution is largely based on that developed by Cahn (1962) and Liicke and Detert (1957). In this model, the grain boundary velocity is divided into two regimes. The first regime corresponds to boundaries with high velocity for large driving force. In this case, the solutes have little effect on the boundary mobility and it is thought that the boundary has escaped from its solute atmosphere [Humphreys and Hatherly, 1995]. In the low mobility regime for small driving force, an atmosphere o f solute atoms is associated with the grain boundary. Under this condition, the  34  Chap. 2 Literature Review  (x10°)  7• v* /  s  /  6*  /  125°C 139°C 155°C 170°C 189°C  / /  /  o  1 O  4/  O  Id  / / /  *.  o OH  /  /  /  S  1 • 00 I  <_.  M M  •  •f I —  * TI . . * ? . r : . n1  »1  »  50  100 150 200 250 (xlO")  1  6  Cu concentration (at. fraction) Fig. 2.8. The effect o f copper concentration on the migration rate o f boundaries in aluminum at various temperatures [after Gordon and Vandermeer, 1966].  35  Chap. 2 Literature Review  14000 12000 Temp. = 275°C  10000 £  8000 -  Jp  6000 H 4000 2000  0  1  2  3  4  5  6  Mg (wt%) Fig. 2.9. The effect o f M g contents on the time to achieve 50% recrystallization at 275°C o f a 95% cold rolled A l - M g alloy [after K o i z u m i et al, 2000].  36  Chap. 2 Literature Review  mobility o f the grain boundary, M is inversely proportional to the concentration o f the solutes, CM according to:  M =\  J_  + cc C  (2.14)  m  where Mo is the intrinsic mobility o f the grain boundary and oc is a temperature dependent m  parameter. Both o f these quantities are difficult to specify, i n particular the constant a  m  requires an accurate estimation o f the solute-boundary binding energy. T o evaluate M , pure  as it the  grain boundary diffusion data is required since the mobility is controlled by the rate o f diffusion o f solute atoms i n the boundary region [Zurob et al., 2002]. A n interesting analysis of the effect o f solute drag on recrystallization kinetics has recently been provided by Brechet and Purdy (2003). Based on their analysis, it can be shown that the general assumption that recrystallization kinetics samples the high mobility regime may not always be correct. According to their theory, i f the driving force is low and the number o f recrystallization nuclei is larger than a critical value, each grain might always stay in the low mobility regime before the condition o f hard impingement can be reached.  Finally, since the motion o f high angle grain boundaries during recrystallization is thermally activated, the effect o f temperature on mobility is often found to obey an Arrhenius relationship o f the form [Humphreys and Hatherly, 1995]:  M  = MQ  exp  Q  where Q is the activation energy for boundary migration.  37  (2.15)  Chap. 2 Literature Review  2.7  Critical Assessment of the Literature  A s delineated i n the beginning o f this chapter, the microstructural evolution during annealing o f a cold rolled precipitation hardened alloys is a result o f the complex interplays between recovery, recrystallization and precipitation. In the literature, precipitation is studied more extensively than the processes o f recovery and recrystallization. One o f the main hurdles in studying recovery and recrystallization is the lack o f understanding i n the deformed state. This has prohibited the development o f a quantitative theory for the nucleation o f recrystallized grains. Recovery, on the other hand, has only received cursory attention i n the literature and as a result many aspects related to the dislocation reactions are still poorly understood. For example, it is still not yet possible to establish, by either experiments or modelling, the rate controlling mechanism during recovery.  In terms o f modelling, comprehensive mathematical models are available to couple the nucleation, growth and coarsening kinetics o f precipitates. For recrystallization modelling, the J M A K model is at present the most widely used analytical approach. This is simply due to the lack o f alternative models in the literature. B y comparison, the development o f quantitative theories for recovery is still i n its infancy. A unified theory o f recovery and recrystallization based on the stability and growth o f cellular microstructures has been proposed b y Humphreys (1997, 1999). However, this concept still requires significant development before it can be applied to model industrial alloys.  In order to develop a realistic model framework for the annealing o f precipitation hardened alloys, the interaction between recovery, recrystallization and precipitation must be captured  38  Chap. 2 Literature Review  based on sound physical theories. The Zener approximation is available as a quantitative tool to describe the retarding effect o f precipitates on recrystallization and it has been verified i n many studies. But much less is known about the effect o f precipitation on recovery. The quantitative approach proposed by Zurob et al. (2002) is reasonable but verification o f the model's assumption is difficult, mainly due to the lack o f direct experimental observations on the local interaction between subboundaries and precipitates.  In the current literature, the most comprehensive model i n coupling the effect o f recovery, recrystallization and precipitation was developed by Zurob et al. (2002) for the hot deformation o f microalloyed steels. The experimental results provided by Lillywhite et al. (2000), clearly indicate that the preexisting precipitate conditions i n the deformed structure have an enormous effect on subsequent recrystallization behaviour o f a cold rolled A l - M g - S i alloy during annealing. However, quantitative physically based microstructure models for the annealing o f cold rolled precipitation hardened aluminum alloys is still lacking i n the literature. The present work is carried out to address this deficiency. The scope and objective are delineated in the next chapter.  39  Chapter 3  Scope and Objectives  The primary objective o f the present work is to obtain a fundamental understanding o f the effect o f simultaneous recovery and precipitation on the recrystallization behaviour o f cold rolled A A 6 1 1 1 through a combination o f experimental investigation and microstructure modelling.  Experimentally, the goal is achieved through: •  artificial aging o f solution treated materials at 20, 180, 250 and 325°C to obtain specimens with varied precipitate conditions prior to cold rolling,  •  isothermal annealing o f the cold worked materials i n the temperature range, i.e. 250445°C where recovery, dissolution/precipitation and recrystallization are expected to occur concurrently,  •  thorough characterization o f the annealed specimens using appropriate metallography techniques to identify on a microscopic scale the interaction mechanisms between the various microstructural phenomena,  •  measuring the yield stress o f the specimens at various time intervals during annealing in order to relate the evolution o f microstructure to the mechanical properties o f the materials.  40  Chap. 3 Scope and Objectives  In terms o f modelling, the goal is to develop a comprehensive microstructure model to translate a qualitative description o f the interaction between recovery, recrystallization and precipitation into a quantitative prediction i n terms o f softening i n yield stress as a function o f annealing time. The overall model w i l l be constructed by adopting physically based models in the literature for the individual processes o f recovery, recrystallization and precipitation. The individual submodels w i l l be coupled based on well established physical theories in order to provide a realistic description for the complex behaviour o f industrial alloys. Throughout the modelling exercise, a minimum number o f adjustable parameters is sought and all the parameters used have a transparent physical meaning. Validation o f the model w i l l be carried out by comparing the model output with the experimental data obtained from overaged 40% cold rolled A A 6 1 1 1 .  The present work provides the first scientific approach to consider recovery, recrystallization and precipitation as well as their, interaction within a single model framework for the annealing o f A A 6 1 1 1 . The knowledge acquired from the experiments as w e l l as modelling work w i l l make significant contributions to the development o f a through process model for the production o f heat treatable aluminum alloys.  41  Chapter 4  Experimental Methodology  The primary objective o f the experimental work is to generate a series o f recovery and recrystallization data using deformed samples with varied precipitate conditions. The asreceived materials were subjected to a series o f thermal and rolling processes. microstructures  of  the  specimens  were  extensively  examined  using  a  The  variety  of  characterization tools. The details o f these experiments are described in this chapter.  4.1  Starting Materials  A l l the samples used in this investigation were obtained from industrially hot rolled sheets (coil #38752) supplied by A l c a n . The as-received A l - M g - S i - C u A A 6 1 1 1 alloy was ingot cast, homogenized and hot rolled to a final thickness o f 3.5 mm. Table 4.1 outlines the composition of the A l - M g - S i - C u alloy A A 6 1 1 1 i n wt%. A n optical micrograph showing the microstructure of the as received hot rolled sheet is given i n Fig. 4.1. The highly elongated grain structure clearly indicates that recrystallization did not take place during or after hot rolling.  4.2  Two  Sample Preparation  sets o f samples were prepared for subsequent  heat-treatment experiments.  Small  rectangular sheet specimens were sheared from the as-received hot rolled sheets to be used  42  Chap. 4 Experimental Methodology  Table 4.1. Chemical composition o f A A 6 1 1 1 in wt%.  Mg  Si  Cu  Fe  Mn  Cr  Ti  Al  0.75  0.63  0.75  0.25  0.2  0.05  0.06  bal.  43  Chap. 4 Experimental Methodology  Chap. 4 Experimental Methodology  primarily for metallography examinations. A second set o f rectangular strip samples measuring 105 m m i n length and 19 m m in width were sheared with the longitudinal direction parallel to the rolling direction o f the sheets. Tensile samples with 40 m m gauge length were subsequently punched out from these strips after cold rolling using a manual die. In addition to tensile and metallography samples, a small number o f square coupons (25 x 25 mm) were prepared for resistivity measurements.  4.3  Heat-treatment Experiments  For each combination o f rolling and heat-treatment conditions, the tests were carried out once using two identical samples. Heat-treatments that were shorter than two days were carried out in low temperature molten salt baths (60% potassium nitrate + 4 0 % sodium nitrite). A n o i l bath was used for a limited number o f tests at 250°C. In order to minimize the heat up time, the o i l and salt baths were stirred vigorously throughout the duration o f the experiments. For heat-treatments longer than two days, either a tube or box furnace was utilized. In this case, samples were placed as close as possible to the thermocouples i n the furnace. Temperatures o f the baths and furnaces were checked periodically using a Fluke K-type  thermometer.  Differences between the thermometer and controller readings were typically within ± 4 ° C .  4.3.1 Solution Heat-treatments  A l l heat-treatment experiments were started with a solution heat-treatment at 560°C for 10 minutes in a salt bath followed by quenching in water at room temperature. The combination  45  Chap. 4 Experimental Methodology  o f time and temperature was chosen to dissolve all the pre-existing precipitates formed during hot rolling and coiling processes and hence restore the maximum solid solution in the materials. The solution heat-treatment is also carried out to eliminate the elongated grain structure seen i n F i g . 4.1. A previous study at U B C has shown that the elongated grain structure may complicate the cold rolling process and increase the driving force for subsequent recovery and recrystallization processes during annealing [Go et al., 2001].  4.3.2 Artificial Aging  After the solution heat treatment, the samples were artificially aged to produce four different precipitate conditions: (i) naturally aged (T4), (ii) peak aged ( P A ) , (iii) overaged ( O A ) and (iv) severely overaged ( S O A ) . The T4 conditions were achieved by aging the samples at room temperature for 8 days. The P A samples were obtained by aging the samples at 180°C for 7 hours. The overaged and severely overaged samples were obtained b y aging for 7 days at 250 and 325°C, respectively. Precautions were taken to minimize the time gap (usually within minutes) between quenching (from solutionizing temperature) and artificial aging in order to prevent natural aging from occurring. The formation o f solute clusters/GP zones prior to artificial aging has been found to have an adverse effect on subsequent precipitation behaviour [Poole etal, 1997].  In addition to aging the materials to specific precipitate conditions, two precipitation hardening curves were generated. The evolution o f yield stress as a function o f aging time was measured at 300 and 325°C for times up to 7 days.  46  Chap. 4 Experimental Methodology  4.3.3  Isothermal Annealing  Prior to isothermal annealing, the T4, T6, O A and S O A specimens were rolled at room temperature to a reduction o f 40% in thickness (from 3.50 to 2.09mm) using a laboratory scale rolling m i l l . Generally, a total o f 4 passes (reverse rolling) were applied to achieve the required thickness for all the specimens. Annealing experiments were carried out immediately after cold rolling in order to prevent the occurrence o f room temperature recovery. In order to study the effect o f prior aging condition, all the samples were annealed isothermally at 325°C. The effect o f annealing temperature was investigated by annealing the O A samples at 250 and 4 4 5 ° C and the S O A samples at 445°C. The high annealing temperature o f 445°C was chosen specifically to study the effect o f precipitate dissolution. The holding time was varied from 1 minute up to 40 days. A t the end o f the annealing cycle, the samples were quenched in water at room temperature. A summary o f the overall thermal and mechanical processing applied to the as-received materials is schematically illustrated in Fig. 4.2.  4.4  Sample Characterization  The microstructures were characterized using a variety o f experimental, techniques including optical microscopy ( O M ) , scanning electron microscopy ( S E M ) , electron back-scattered diffraction ( E B S D ) , and resistivity measurements. Transmission electron microscopy ( T E M ) was also carried out i n collaboration with researchers from the Brockhouse Institute o f Materials Research at McMaster University.  47  Chap. 4 Experimental Methodology  Fig. 4.2 Schematic o f heat treatment and rolling experiments.  48  Chap. 4 Experimental Methodology  AAA  Sample Preparation  A l l microstructural examinations were done on sections parallel to the rolling direction revealing the through thickness microstructures.  To prepare the surface o f interest for  microstructural examination, specimens were cold mounted in an acrylic resin and polished to 0.05 p m finish using a Phoenix 4000 automatic polisher. Due to the ductile nature o f aluminum alloys, deformation induced damage is a common problem during the grinding and polishing process. T o overcome this problem, a four step grinding and polishing procedure developed by Buehler specifically for aluminum alloys was adopted. B y following the steps outlined in Table 4.2, a mirror like surface finish can be obtained consistently with minimal fine polishing scratches.  Specimens for electron microscopy examination were further electropolished i n order to remove the thin deformed  layer on the surface caused by mechanical polishing. The  composition o f the electropolishing solution was 100 m l perchloric acid (60%) + 500 m l denatured ethyl alcohol. The samples were made the anode by immersing in the solution for about 1 minute at a bath temperature o f below -10°C. A steel cup which contains the solution was used as the cathode. Power is provided by a rectified power supply. The current density was controlled by adjusting the voltage until the ampere meter on the power supply reads 1 A .  49  Chap. 4 Experimental Methodology  Table 4.2. Four step procedure for grinding and polishing aluminum alloys using a Phoenix 4000 automatic polisher.  Surface  Abrasive/Size  Load Lb.  Base Speed  (N)/Specimen (rpm)/Direction *  Time (min:sec)  Abrasive disc  240 or 320 grit S i C with water cooled  5(22)  240-300 Comp.  Until plane  Ultra-Pol cloth  6 p m diamond suspension  6(27)  120-150 Comp.  6:00  Trident cloth  1 p m diamond suspension  6(27)  120-150 Comp.  4:00  M i c r o cloth  0.05 p m colloidal silica suspension  6(27)  120-150 Contra.  2:00  *Comp. = platen and specimen holder both rotate i n the same directions Contra. = platen and specimen holder rotate in opposite directions  50  Chap. 4 Experimental Methodology  4.4.2  Optical Microscopy  In order to reveal the microstructures under optical microscope, the samples were first anodized using the Baker's reagent (200 m l distilled H 0 + 6 m l H B F 2  4  (48 wt%)). A thin  layer o f oxide film was deposited on the surface after anodization allowing the microstructures to be revealed under crossed-polarized illumination. Photomicrographs o f the microstructures were taken using a N i k o n E P I P H O T 300 series inverted metallurgical microscope equipped with a digital camera. Post processing o f the micrographs was completed employing the Clemex Professional Imaging and Adobe Photoshop 6 software.  The volume fraction o f recrystallized grains was quantified using the ImageTool software developed by the researchers from The University o f Texas Health Science Centre. Before analyzing the microstructures i n ImageTool, recrystallized grain boundaries were outlined on transparency  and the  image scanned  into a P C . Recrystallized grains i n a partially  recrystallized structure were selected primarily based on their shape. H i g h l y elongated grains are identified as deformed matrix and grains with aspect ratio o f equal or less than 3 were considered recrystallized grains. The ImageTool software individual recrystallized grain, A . rex  calculates the area o f each  The sum o f all the recrystallized grain areas divided by the  total area o f the micrograph gives the volume fraction o f recrystallized grains. Typically, a minimum total area o f 6.3x10" m m was measured for each sample.  The recrystallized grain size, d , was estimated by calculating the equivalent area diameter rex  assuming spherical grains i n 2-d [Orsetti-Rossi and Sellars, 1997], i.e.,  51  Chap. 4 Experimental Methodology  (4.1)  The number o f grains included in the analysis ranges from 200 to 700 depending on the degree of recrystallization i n the sample.  4.4.3  Scanning Electron Microscopy (SEM)  A l l S E M micrographs were taken on a Hitachi S-3000N electron microscope. The accelerating voltage was varied from 5 k e V up to 20keV. L o w voltage is generally applied for taking backscattered electron ( B S E ) images. In order to obtain the best quality B S E images, the contrast was increased to maximum and brightness adjusted to its lowest level.  4.4.4  Electron Back Scattered Diffraction (EBSD)  E B S D scans were carried out on a Hitachi scanning electron microscope ( S E M ) S570 operating at 20 k e V . After inserting the sample into the S E M chamber, the sample holder was tilted 70° towards the detector. The H K L Channel 5 suite o f programs was used to acquire and process the diffraction data. E B S D mapping o f the grain structures was carried out at a step size o f 2 um unless otherwise noted. The indexing quality ranges from a minimum o f 85% up to as high as 95%. To reconstruct the microstructure from the E B S D data, it is convenient to divide grain boundaries into low and high angle grain boundaries. In this study, the transition from low to high angle grain boundaries is taken as 15° [Humphreys and Hatherly, 1995].  52  Chap. 4 Experimental Methodology  4.4.5  Transmission Electron Microscopy (TEM)  Initial characterization o f the as aged specimens was carried out at U B C . T o prepare the T E M thin foils, small discs measuring 3 m m in diameter were cut from the sheet samples using electron discharging. The discs were then mechanical polished to reduce the thickness to approximately 100-120 urn. The ground discs were then electropolished to perforation in a Struers Tenupol-2 jet polishing unit using an electrolyte o f 10% perchloric acid, 20% glycenol and 70%> methanol at around -20°C. The operating voltage o f the jet polisher was 2 0 V . The microscope is a Hitachi 800 scanning transmission electron microscope operating at 200keV.  Additional T E M observations were performed by Dr. X . Wang from the Brockhouse Institute o f Materials Research at McMaster University using a conventional Philips C M - 1 2 electron microscope operating at 120keV. T E M thin foils were prepared b y mechanically polishing the samples to approximately 100 um and then jet polishing i n a solution o f perchloric acid and methanol at -35°C. The averaged dimensions o f the precipitates were determined from bright field images. The measurements o f cross-sectional area were converted to an equivalent diameter using an equation similar to Equation 4.1 assuming spherical precipitates.  4.4.6  Resistivity Measurements  The resistivity o f the specimens, p were calculated from conductivity data measured using a r  portable Verimet M 4 9 0 0 C conductivity tester. The tester was calibrated to measure the electrical conductivity o f a specimen and display the result i n percent I A C S (International  53  Chap. 4 Experimental Methodology  Annealed Copper Standard, 100% LACS copper = 58 M Q m ) . A l l measurements were carried out at room temperature i n C O M P mode to compensate for any temperature effects.  4.4.7  Tensile Measurements  The mechanical response o f the samples at a given annealing temperature was followed by the evolution o f yield stress with respect to annealing time. A l l tensile tests were carried out at a strain rate o f 0.002 s" on a M T S servo-hydraulic tensile machine with the tensile axis parallel 1  to the rolling direction o f the sample. A n extensometer with gauge length o f 40 m m was attached to the reduced section o f the samples to measure the elongation during straining. The yield stress, <j , was measured from engineering stress-strain curves employing the standard y  0.2% offset method. T w o tests were conducted for each experimental condition. The average values between the two measurements  were taken. The difference between the two  measurements is typically within ± 5 M P a .  Tensile tests were carried out immediately (within a few minutes) after annealing to prevent natural aging from occurring. This step is critical particularly at high annealing temperature, since significant amount o f solutes can be dissolved during annealing and the structure becomes unstable upon quenching. A n example is given i n Fig. 4.3 where the tensile curves o f two annealed samples were compared. The two overaged ( O A ) and cold rolled samples were annealed for 1.75 hours at 445°C. However, the yield stress o f sample G l was measured 2 days after the annealing was completed. It can be seen that the yield stress increased drastically (from 50 to 80 M P a ) due to the effect o f natural aging.  54  Chap. 4 Experimental Methodology  200  150 G1, YS = 80 MPa 03  co co cu  100  CO  50  0 0.00  0.06  Fig. 4.3. The effect o f natural aging on annealed samples. Sample G l was tested immediately after annealing at 4 4 5 ° C for 1.75 hours while sample G 2 was tested 2 days after the annealing heat treatment. Both samples were i n their overaged conditions prior to 40% cold rolling.  55  Chapter 5  Experimental Results and Discussions  In this chapter, the experimental results are presented by following the sequence o f the experimental procedures illustrated in Fig. 4.2. Prior to cold rolling, the as received materials underwent a series o f heat treatments i n order to achieve the desire starting microstructure. The effect o f solution heat treatment and artificial aging is presented first i n sections 5.1.1 and section 5.1.2, respectively. The deformed microstructure is analyzed i n the next section (5.1.3). In section 5.1.4, the isothermal annealing behaviour o f the deformed specimens with various precipitate conditions are presented in terms o f the evolution o f yield stress, resistivity and microstructure as a function o f annealing time. The second part o f this chapter is devoted to the discussion o f the experimental results. In section 5.2.1, a simple nonlinear addition law is employed to examine the work hardening behaviour o f the various samples. Then, i n section 5.2.2, resistivity measurements are analyzed i n terms o f nucleation, growth and coarsening o f precipitates. The effect o f prior aging conditions on the isothermal annealing behaviour is discussed in section 5.2.3 with special attention given to the overaged samples.  56  Chap. 5 Experimental Results and Discussio  5.1  Experimental Results  5.1.1  Solution Heat Treatments  The solution heat treatment step was carried out to recrystallize the elongated grain structure and dissolve all the preexisting precipitates in the as received hot band. Fig. 5.1a shows the through thickness microstructure o f the as quenched sample after solution heat treatment (supersaturated solid solution). The fully recrystallized microstructure comprises grains which are slightly elongated in the rolling direction. Using E B S D mapping, the fully recrystallized microstructure is reproduced in Fig. 5.1b with the same magnification. In this micrograph, high angle grain boundaries with a minimum o f 15° misorientation are represented by black lines and boundaries between 2-15° misorientation are represented by grey lines. It can be seen that the recrystallized grains are essentially free o f internal substructures. The average grain size measured from the E B S D map (d ~42pm) agrees very well with the grain size s  measured from the optical micrograph (d ~45um). This is interpreted as a validation o f the s  use o f 15° misorientation as the criterion for high angle grain boundaries. Fig. 5.2 shows a S E M micrograph depicting the fully recrystallized microstructure at higher magnification. The most notable feature o f this micrograph is the random dispersion o f coarse and irregularly shaped intermetallic particles throughout the microstructure. The chemistry and distribution o f these particles are analyzed in section 5.1.3.  57  Chap. 5 Experimental Results and Discuss  Fig. 5.1. (a) Optical micrograph showing the solution treated microstructure with average grain size o f - 4 5 urn, (b) E B S D micrograph o f the same sample with grain size o f - 4 2 um (black lines represent high angle grain boundaries > 15 misorientation).  58  c  Chap. 5 Experimental Results and Discussi  Fig. 5.2. S E M micrograph showing the solution treated microstructure. Irregularly shaped Ferich intermetallic particles as indicated in the micrograph are randomly distributed throughout the microstructure.  59  Chap. 5 Experimental Results and Discussi  5.1.2 Artificial Aging  To prepare the solution treated specimens for cold rolling, the samples were subjected to a series o f artificial aging processes as outlined i n section 4.3.2. Four precipitate conditions were studied: (1) naturally aged, T4, (2) peak aged, P A , (3) overaged, O A and (4) severely overaged, S O A . The yield stress o f the as quenched samples with varied precipitate conditions can be compared conveniently by plotting the data on a typical age hardening curve. This is shown i n Fig. 5.3 where the horizontal axis is used to represent the precipitate state o f the samples instead o f aging time. Starting from the supersaturated solid solution (SSS) condition, the yield stress increases from 58 to 139 M P a after 8 days o f natural aging (T4). The outstanding precipitation hardening potential o f this alloy is illustrated by the P A sample where the solution treated yield stress was increased by nearly six fold (from 58 to 334 M P a ) . The yield stress decreases progressively to 153 and 92 M P a as the aging temperature is increased to 250 and 325°C, respectively.  The plastic portions o f the stress strain curves for the as aged samples with varied precipitate conditions are shown i n Figs. 5.4. The stress strain curve o f the supersaturated solid solution is included in Fig. 5.4a for comparison. In contrast with the smooth flow observed i n the T4, P A and O A samples, the plastic stress strain curves for the SSS and S O A samples exhibit substantial evidence o f serrated flow. The serration is a well known effect i n A l - M g alloys which is associated with the pinning o f dislocations by M g atoms i n solution [Lloyd, 1980, Inagaki and Komatsubara, 2000, Tian, 2003]. Therefore, the appearance o f serration i n the  60  Chap. 5 Experimental Results and Discussio  400 334  co  300  -  200  -  CL  a>  \  O  c <D  139  /  153  CT  5  100  0  92 58  i  sss  T4  PA  OA  SOA  Precipitate Conditions  Fig. 5.3. A g e hardening curve showing the as aged yield stress o f samples with varied precipitate conditions: S S S : supersaturated solid solution, T 4 : naturally aged, P A : peak aged, O A : overaged and S O A : severely overaged. This corresponds to heat treatment o f 10 minutes at 560°C, 8 days at room temperature, 7 hours at 180°C, 7 days at 2 5 0 ° C and 7 days at 325°C, respectively. The corresponding values o f the as aged o are indicated on the curve. y  61  Chap. 5 Experimental Results and Discussi  co CL  Peak aged  0.00  0.03  0.06  0.09  0.12  0.15  0.18  0.15  0.18  Plastic strain 180 (b)  150  CO Q_  Overaged  Severely Overaged  0.00  0.03  0.06  0.09  0.12  Plastic strain Fig. 5.4. Plastic portion o f the stress strain curves for (a)supersaturated solid solution (SSS), naturally aged and peak aged samples and (b) overaged and severely overaged samples. Note the serrated flow in the SSS and S O A samples.  62  Chap. 5 Experimental Results and Discuss  stress strain curve o f the S O A sample suggests that significant amount o f solute atoms remained i n solid solution after aging for 7 days at 325°C.  The precipitate structures o f the T4 and P A samples have been extensively studied in the past and these results have been summarized in section 2.4.1. Hence, only the precipitate structures of the O A and S O A samples are characterized i n the present work. Bright field T E M micrographs depicting the precipitate structure i n the O A and S O A samples are shown in Figs. 5.5a and 5.6a, respectively. In contrast with the P A sample (Fig. 2.4) where 80% o f the total volume fraction o f precipitates are B", the majority o f the precipitates i n the O A and S O A specimens are the lath shaped Q' precipitates (indicated as L i and L i n Fig. 5.5a). The 2  corresponding diffraction pattern for the Q' precipitates is shown i n Fig. 5.5b. In addition to the fine Q' precipitates, square shaped M g S i particles with size i n the order o f several 2  microns are also observed in the S O A sample (Fig. 5.6b). N o M g S i particles were found i n 2  the O A sample. From the T E M micrographs, the average equivalent diameter o f the Q' precipitates are estimated as 13 n m and 35 nm for the O A and S O A samples, respectively. Not surprisingly, the dimensions o f the precipitates increased significantly after aging at higher temperature leading to a coarser precipitate spacing. The corresponding optical micrographs o f the as aged O A and S O A samples are shown in Fig. 5.7a and 5.7b. The average grain size is measured as ~43 p m i n both samples. This is similar to the recrystallized grain size found in the as solution treated microstructure shown i n Fig. 5.1 thus confirming that no grain growth has occurred i n the aging process.  63  Chap. 5 Experimental Results and Discussi  (a)  Fig. 5.5. (a) Bright field T E M image showing the lath shaped Q' precipitates (Li and L 2 seen end on and edge on respectively) in the O A sample and (b) corresponding diffraction pattern taken along the [001] zone axis o f aluminum.  64  Chap. 5 Experimental Results and Discussi  400 nm  3.8 um  . 5.6. Bright field T E M images showing (a) the lath shaped Q' precipitates and (b) large square shaped M g S i particles in the S O A sample. Courtesy of Dr. X. Wang. 2  65  Chap. 5 Experimental Results and Discussi  Fig. 5.7. Optical micrographs showing the microstructure o f the as quenched sample after aging for 7 days at 250°C ( O A ) and 325°C ( S O A ) . The average grain size in both micrographs is - 4 3 pm.  66  Chap. 5 Experimental Results and Discuss  In addition to aging the specimens to specific precipitate conditions, the age hardening behaviour o f the solution treated samples was investigated at 300 and 325°C. The results are shown i n Fig. 5.8 where the age hardening response o f the material is characterized by measuring the evolution o f yield stress with respect to aging time. It can be seen that the yield stress increases rapidly and attains its peak value i n less than 1 minute at 325°C. A t the lower aging temperature o f 300°C, the peak strength was reached after about 200 seconds. Beside the difference in precipitation kinetics, the magnitudes o f the peak strength are also different. The initial yield stress which represents the yield stress o f supersaturated solid solution was more than doubled from 58 to - 1 5 0 M P a at 325°C. The peak strength obtained at 300°C is even higher, - 1 7 0 M P a . This behaviour conforms to the typical age hardening response o f a heat-treatable alloy where higher peak strength is usually observed at lower aging temperature at the expense o f longer time. After the peak strength is reached, the precipitates entered their coarsening phase which leads to the gradual decrease i n yield stress shown i n the aging curves. Precipitate coarsening occurs at a much slower rate than the nucleation and growth o f precipitates. This behaviour is evident in the time it took for the samples to soften: it took nearly 44 and more than 65 hours for the samples to give up 90% o f the gain i n yield stress at 325 and 300°C, respectively.  5.1.3 The Deformed State  It is important to examine the deformed state because it sets the stage for subsequent recovery and recrystallization processes. Following aging heat treatment, the specimens with varied precipitate states were cold rolled to a reduction o f 40% in thickness. This corresponds to an  67  Chap. 5 Experimental Results and Discussio  250 Aging Temp.  200  03  CL b  - • -  300°C  - • -  325°C  150  ^ 100 50  0  "j""  0  I • I I • 11  I  10  1  I  • I I 1111  I  10  2  T V  I'TTTfp  I  10  3  I  I I I 11 If  " - ^  10  4  |  |  | | 11||  |  10  5  I  I I I III  10  6  Time (s) Fig. 5.8. Precipitation hardening curves of A A 6 1 1 1 at 300 and 325°C. The as solution heat treated yield stress is indicated at the intercept with the vertical axis.  68  Chap. 5 Experimental Results and Discuss  equivalent strain o f 0.58. The yield stress o f the various as deformed samples are given i n Fig. 5.9 along with the as aged yield stress. It can be seen that the yield stress o f the T4 sample was markedly increased by more than 200 M P a while the increase i n yield stress for the P A , O A and S O A samples is in the order o f - 1 0 0 M P a . This work hardening behaviour w i l l be further analyzed in section 5.2.1.  A n optical micrograph showing the as deformed microstructure o f the O A specimen is given i n Fig. 5.10. A closer view o f the deformed grains is shown i n the S E M micrograph appearing in Fig. 5.11. The major microstructural change is that the slightly elongated recrystallized grains seen i n Figs. 5.7 become more elongated i n the rolling direction after deformation. Macroscopic shear bands which extend across several grains are also observed (Fig. 5.10). The dislocation structures after cold rolling are shown in the T E M micrographs o f Fig. 5.12a and 5.12b for the as cold rolled O A and S O A samples, respectively. The lath shaped Q' precipitates were fractured into small segments during deformation. This is shown i n Fig. 5.13 where the precipitate structure o f the as cold rolled S O A sample is given as an example.  Another important aspect o f the deformed microstructure is the distribution o f insoluble Ferich particles which act as potential nucleation sites for recrystallized grains. Fig. 5.14a shows the typical spatial distribution o f these particles in the deformed matrix o f a T4 specimen. One o f the larger particles is shown at higher magnification i n Fig. 5.14b. The X-ray spectrum (Fig. 5.14c) indicates that significant amounts o f S i , C u and M n are present i n the Fe rich particle. Based on quantitative metallography, the average equivalent diameter o f the particles was determined as 2.5 ± 0.05 u m and the number density is approximately 820 mm" . 3  69  Chap. 5 Experimental Results and Discussion  500 400  A  300  A  OL  ^  200 100 0 T4  PA  OA  SOA  Precipitate Conditions Fig. 5.9. The as aged and as cold rolled yield stress o f samples with varied precipitate conditions. Note the significant increase in yield stress i n the T 4 sample after 40% cold rolling.  70  Chap. 5 Experimental Results and Discussi  200 um  Fig. 5.10. Optical micrograph showing the deformed microstructure o f a 40% cold rolled O A sample. The slightly elongated grains shown in F i g . 5.11 become more elongated in the rolling direction after deformation.  71  Chap. 5 Experimental Results and Discuss  Fig. 5.11. S E M micrograph showing the deformed microstructure o f a 40% cold rolled O A sample.  72  Chap. 5 Experimental Results and Discuss  Chap. 5 Experimental Results and Discuss  1 um  Fig. 5.13. T E M micrographs showing segments of fractured Q' precipitates in 40% cold rolled  S O A sample. Courtesy of Dr. X. Wang.  74  Chap. 5 Experimental Results and Discussi  0  2  4  6  8  k«V  Fig. 5.14. (a) Distribution o f insoluble Fe-rich constituent particles in the deformed matrix o f a deformed T4 specimen, (b) close up view o f one o f the particles and (c) X-ray spectrum indicates the presence o f Fe, S i , M n , and C u in the particle shown in (b).  75  Chap. 5 Experimental Results and Discussi  5.1.4  Isothermal Annealing at 325°C  After cold rolling, all the deformed  samples  with varied precipitate  conditions were  isothermally annealed at 325°C. The results o f these experiments are presented i n three parts: First, the material response to the annealing heat treatment is characterized by following the softening i n yield stress as a function o f annealing time. The second part compares the evolution o f resistivity i n the deformed samples during annealing with the evolution o f resistivity i n the solution treated sample during artificial aging. In the third part, the isothermal recrystallization  behaviour  is  described  by  comparing  the  partially  recrystallized  microstructures o f the T4, P A and O A samples.  5.1.4.1  Evolution of Yield Stress  Fig. 5.15 shows the softening behaviour o f the samples with varied precipitate conditions after annealing at 325°C for time up to 40 days. The uncertainty  associated  with these  measurements is estimated to be in the order o f 5-10 M P a . It can be seen that the yield stress decreased rapidly in the initial stage o f annealing irrespective o f prior aging condition. The initial softening is particularly severe for the P A sample which lost about 60-70% o f its as deformed yield stress after only 1 minute o f annealing. The rate o f decrease in yield stress slows down considerably after the first few minutes o f annealing. This can be seen i n the softening curve o f the S O A sample where the yield stress decreases by only 15 M P a (from 120 to 105 M P a ) between 5 minutes and 48 hours o f annealing time. The softening kinetics o f the T4 and P A samples is basically the same with both curves eventually reaching a plateau at - 7 0 M P a after 2 weeks o f annealing (Fig. 5.15a).  76  Chap. 5 Experimental Results and Discussion  500 Prior Aging Conditions • T4 (8 days, Room Temp.)  400-1  b  • P A (7 hrs, 180°C)  ^ 200 -I  100  0  A A~""i  0 300  * •  10  1  i  II  10  2  i ilium  10  i  10  3  (b)  i  n  10  4  s  i  10  |  i in  10  s  7  10  8  Prior Aging Conditions  250  • -  O A (7 days, 250°C)  • -  S O A (7 days, 325°C)  200 150 •{ 100 50 H  0  T"  0  ™l  ;  I—  10  1  10  2  "I—  i|  10  |  10  3  4  | — i i i mill—i i  10  5  10  6  10  7  |  10  8  Time (s)  Fig. 5.15. Isothermal evolution o f yield stress during annealing at 325°C for 40% cold rolled (a) T4 and P A samples and (b) O A and S O A samples. The prior aging conditions are indicated in the inset and the as cold rolled yield stress is indicated at the intercepts with vertical axis.  77  Chap. 5 Experimental Results and Discuss  The final yield stress o f the O A and S O A samples annealed for 40 days is 73 and 41 M P a respectively (Fig. 5.15b). This represents an overall softening o f 285, 359, 147 and 153 M P a for the T4, P A , O A and S O A samples, respectively. The onset o f recrystallization (determined by following the changes i n microstructure) for the respective samples is indicated on the softening curves.  5.1.4.2  Evolution of Resistivity  Fig. 5.16 shows the evolution o f resistivity in the T4, P A and O A specimens with respect to annealing time at 325°C. The resistivity curve o f an artificially aged sample at 325°C is included for comparison. It can be observed that prior aging conditions did not affect significantly the evolution o f resistivity during annealing. A l l the curves seem to collapse onto one another i n the early stage o f annealing and eventually follow closely the change i n resistivity o f the solution treated sample during artificial aging. The implication o f these results is important since resistivity is directly related to the solutes concentration i n solid solution. This aspect w i l l be further discussed in section 5.2.2.  5.1.4.3  Evolution of Microstructure  Optical micrographs showing the recovered microstructures o f the T 4 , P A and O A samples annealed for 1 minute at 325°C are shown i n Fig. 5.17. The recovered microstructures are essentially the same as the as deformed structure (Fig. 5.10) thus confirming that no recrystallization took place in the initial stage o f annealing i n all o f the samples. B y following  78  Chap. 5 Experimental Results and Discussi  50 Annealing temp. = 325°C  Prior Aging Conditions • A - T4 (8 days, Room Temp.) • • - OA (7 days, 250°C) e - PA (7 hrs, 180°C) Q - Artificially aged 325°C  45 \  a f  \  \  40 H  \  \  \  w "<> /  35  T  -a lSS  30 0  '•III  I  10  1  I  I '""I  I  10  2  I I  I  10  I  10  3  I  4  10  I  5  10  6  10  7  Time (s)  Fig. 5.16. Evolution o f resistivity during annealing o f A A 6 1 1 1 with various precipitate conditions. The prior aging conditions are indicated in the inset and the resistivity o f the as cold rolled and as solution treated samples are the intercepts with vertical axis (time = 0).  79  Chap. 5 Experimental Results and Discussi  Fig. 5.17. Optical micrographs showing the recovered microstructure o f 40% cold rolled T4, P A and O A specimens annealed for 1 minute at 325°C.  80  Chap. 5 Experimental Results and Discussio  the change in the grain structure with respect to annealing time, the onset o f recrystallization was determined to occur after approximately 12 hours i n the T4 and P A samples and 48 hours in the O A sample. This is summarized in Table 5.1 along with several key microstructural parameters describing the partially recrystallized microstructures obtained after annealing for 2 weeks at 325°C. These parameters include the average recrystallized grain size d , density rex  of recrystallized grains per unit area and fraction o f recrystallized grains. The corresponding E B S D maps o f the partially recrystallized microstructures are shown i n Fig. 5.18a to 5.18c. It is difficult to identify the preferential nucleation sites for recrystallization. However, it can be observed that some o f the recrystallized grains are located on the boundaries o f deformed grains indicating that grain boundary nucleation is a possible mechanism. It w i l l be shown later that in addition to grain boundary nucleation, evidence o f particle-stimulated-nucleation can also be found i n the microstructure. Based on quantitative microscopy, the mean recrystallized grain size d  rex  is measured as 14.6, 11.5, and 18.6 urn for the T 4 , P A and O A  samples, respectively. The bar charts o f Fig. 5.19 show the distribution o f recrystallized grain size i n the various samples normalized by the averaged grain size. The distribution o f normalized grain size in the O A sample is slightly wider than i n the T4 and P A specimens which show relatively narrow distributions. It is also interesting to compare the density o f recrystallized grains per unit area listed in Table 5.1. W h i l e the number o f recrystallized grains i n the O A sample is less than one half o f the number o f recrystallized grains i n the T4 and P A samples, these grains have grown to a larger size. These relatively large recrystallized grains are distributed heterogeneously in the microstructure. This is shown i n Fig. 5.20 where colonies o f large recrystallized grains (on the order o f 100 um i n diameter) can be seen to congregate i n the centre o f the micrograph.  81  Chap. 5 Experimental Results and Discussi  Table 5.1. Comparison o f the recrystallization behaviour o f 40% cold rolled A A 6 1 1 1 with varied precipitate conditions after annealing for 2 weeks at 325°C.  Prior aging conditions  Average Onset of No. of Fraction recrystallized recrystallized recrystallization at recrystallized grain size, d grains per mm 325 V (hours)  2  rex  T4  12  0.37  14.4 p m  1387  PA  12  0.32  11.5 p m  1946  OA  48  0.30  18.6 p m  617  82  Chap. 5 Experimental Results and Discuss  100pm  Fig. 5.18. E B S D maps showing the partially recrystallized microstructures o f 40% cold rolled A A 6 1 1 1 with varied precipitate conditions after annealing for 2 weeks at 325°C. The corresponding prior aging conditions are (a) T4, (b) P A and (c) O A . Black lines represent grain boundaries which are > 1 5 ° and grey lines represent boundaries between 2-15°.  83  Chap. 5 Experimental Results and Discussion  30  (a) 25 20. 15 £  10  0 0.1  10  (  (b)  30 25 ^- 20  (T  (U LL 10 5 0 0.1  10  (  (c)  30 25 5- 20  515 cr <u £  10 5; 0:0.1  10  d ex / ^rect r  Fig. 5.19. Recrystallized grain size distribution in partially recrystallized (a) T4, (b) P A and (c) O A samples after annealing for 2 weeks at 3 2 5 ° C .  84  Chap. 5 Experimental Results and Discussi  100 um  Fig. 5.20. E B S D map showing the colonies o f large recrystallized grains in 40% cold rolled O A sample annealed for 2 weeks at 325°C. Black lines represent grain boundaries which are >15° and grey lines represent boundaries between 2-15°.  85  Chap. 5 Experimental Results and Discuss  Lastly, the average internal misorientation o f the substructure i n the deformed grains is found to be i n the range o f 5-6° for a l l the samples based on E B S D measurements. This value is i n agreement with the measurements b y Vatne et al. (1996) in hot deformed aluminum alloys.  Generally, recrystallization proceeds at a very sluggish rate at 325°C irrespective o f prior aging conditions. The recrystallization kinetics o f the T 4 and P A specimen are similar: It took 2 weeks o f annealing for the recrystallized grains to consume - 3 7 % o f the deformed microstructure (Figs 5.18a and b). The recrystallization kinetics i n the O A sample is by far the slowest with only - 3 0 % o f the microstructure recrystallized after 2 weeks o f annealing (Fig. 5.18c). In an attempt to fully recrystallize the deformed microstructure, the annealing time for the T 4 and O A samples was subsequently increased to 40 days. The resulting partially recrystallized microstructures are shown i n Figs. 5.21a and 5.21b for the O A and T 4 samples respectively. The volume fraction o f recrystallized grains in the T 4 samples increased to - 4 8 % while only - 3 7 % o f the microstructure i n the O A samples were recrystallized after 40 days o f annealing. Fig. 5.22a compares the recrystallization kinetics o f the two samples i n terms o f the fraction recrystallized vs. annealing time. The evolution o f recrystallized grain size and number o f recrystallized grains per unit area are shown i n Figs. 5.22b and 5.22c, respectively. The magnitude o f the error bars shown i n all the figures represents the standard deviations between multiple fields o f measurements obtained from different areas o f the microstructure. There is a considerable scatter i n the recrystallized fraction data indicating that the recrystallization occurred heterogeneously i n the microstructure. The spatial distribution o f precipitates was examined i n S E M and the micrographs are shown i n Fig. 5.23a and 5.23b for the T4 and O A samples, respectively. Both samples were obtained after annealing for 2 weeks  86  Chap. 5 Experimental Results and Discussion  100 um  Fig. 5.21. E B S D maps showing the partially recrystallized microstructures o f 40% cold rolled A A 6 1 1 1 with varied precipitate conditions after annealing for 40 days at 325°C. The corresponding prior aging conditions are (a) O A and (b) T4. Black lines represent grain boundaries which are > 1 5 ° and grey lines represent boundaries between 2-15°.  87  Chap. 5 Experimental Results and Discussion  0  200  400  600  800  1000  1200  Time (hrs) oo  •  (b) 30 •  Annealing Temp. = 325°C  E  a.  Avei aged  5  25 •  OA  J  -l-—  20 •  JU 15  -i-—  10 200  400  600  800  1000  1200.  Time (hrs) JUUU •  E E  (c)  2500 •  Annealing Temp. = 325°C  2000 • CD L_  D)  T3  CD  T4  1500 -  N  o  j  I  1000 OA  0)  500 0• 0  •  •III—•—i—i—•  200  i  i  -I—1 1 1 I I I ! 1 • • • • • •  400  600  800  1000  1 1 1  1200  Time (hrs)  Fig. 5.22. Evolution o f (a) fraction recrystallized (b) recrystallized grain size and (c) number o f recrystallized grains per unit area during isothermal annealing at 325°C.  88  Chap. 5 Experimental Results and Discussion  Fig. 5.23. Spatial distribution o f precipitates in (a) T4 and (b) O A samples annealed for 2 weeks at 325 °C. Note the absence o f precipitate clusters in the T4 sample.  89  Chap. 5 Experimental Results and Discussion at 325°C. Precipitates can be found along grain boundaries as w e l l as i n the matrix. The main difference between the two samples is the spatial distribution o f the precipitates. In the case o f the T 4 sample, relatively coarse particles are homogeneously distributed throughout the microstructure resulting i n a more uniform distribution o f particle spacing (Fig. 5.23a). O n the other hand, localized clusters o f relatively fine and closely spaced precipitates are observed i n the O A sample, as shown i n Fig. 5.23b. These precipitated clusters are not distributed uniformly throughout the microstructure. Precipitate free zones can be found i n the matrix adjacent to some o f the precipitate clusters. In the example shown i n Fig. 5.23b, precipitate free zones comprise approximately 15-25% o f the microstructure. A clearer view o f the boundary between precipitate and precipitate free zones is shown in Fig. 5.24a. The X-ray spectrum confirms the presence o f M g , Si and C u in the precipitates in the precipitate zones (Fig. 5.24b).  In order to assess the effect o f the spatial distribution o f precipitates i n the O A sample, specifically the precipitate free zones on the recrystallization process, it is necessary to link the precipitate structure seen i n the S E M micrographs to the partially recrystallized microstructures as observed in E B S D (Fig. 5.23b vs. Fig. 5.18c). This is illustrated in Fig. 5.25 where the same area o f the O A sample annealed for 2 weeks are shown employing the two different experimental techniques. The E B S D micrograph in Fig. 5.25b is obtained by utilizing the band contrast function which shows the indexing quality in terms o f grayscale: the darker the grains the lower the indexing quality. Recrystallized grains which are free o f internal substructures are shown i n white and indicated b y the letters A , B and C . B y using a hardness indent as a marker, the precipitate structure o f the same area is then examined in  90  Chap. 5 Experimental Results and Discussion  0  2  4  6  8  keV  Fig. 5.24. (a) S E M micrograph showing the boundary between precipitate and precipitate free zones in 40% cold rolled O A sample annealed for 2 weeks at 325°C. (b) X-ray spectrum showing the presence o f M g , S i and C u in one o f the precipitates.  91  Chap. 5 Experimental Results and Discussion  Fig. 5.25. (a) S E M micrograph showing the partially recrystallized microstructure o f 40% cold rolled O A sample after annealing for 2 weeks at 325°C. (b) E B S D band contrast map showing the same area o f the microstructure. The recrystallized grains A , B and C i n the E B S D map are associated with precipitate free zones in the S E M micrograph. The precipitate clusters are marked by D , E , F and associated with deformed grains i n the E B S D map.  92  Chap. 5 Experimental Results and Discuss  S E M employing the back-scattered electron mode as shown i n Fig. 5.25a. It can be seen that the recrystallized grains are clearly associated with precipitate free zones while the deformed grains (marked b y the letters D , E and F) are related to the precipitate clusters i n the S E M micrograph. Further evidence o f this is shown i n Fig. 5.26 which shows a growing recrystallized grain nucleated in the vicinity o f a Fe-rich intermetallic particle surrounded b y precipitate free zones.  5.1.5 The Effect of Annealing Temperature on Overaged Samples  The softening behaviour o f the O A sample at 250, 325 and 4 4 5 ° C is illustrated in Fig. 5.27a. Fig. 5.27b shows the softening curves for the S O A specimens obtained at the annealing temperatures o f 325 and 4 4 5 ° C . It can be observed that the yield stress o f the S O A sample decreases rapidly to - 5 0 M P a after only 1 minute o f annealing at 4 4 5 ° C and remains constant after that. The decrease i n yield stress for the O A sample is slower with the yield stress reaching 50 M P a i n about 30 minutes. A t the lower annealing temperature o f 250°C, the decrease in yield stress o f the O A sample appears to reach a plateau at around 180 M P a after 5 minute before decreasing to 160 M P a after 3 hours o f annealing.  The effect o f annealing temperature on the recrystallization kinetics is shown i n Fig. 5.28. It is observed that recrystallization is faster i n the S O A sample for the two temperatures investigated. The main difference is observed at the annealing temperature o f 325°C where recrystallized grains were detected after - 1 0 hours o f annealing i n the S O A sample compared to 48 hours i n the O A sample. O n increasing the annealing time to 40 days, 80% o f the  93  Chap. 5 Experimental Results and Discuss  Fig. 5.26. S E M micrograph using back scattered electrons showing a recrystallized grain nucleated from a Fe-rich intermetallic particle surrounded by precipitate free zones i n 40% cold rolled O A sample annealed for 2 weeks at 325°C.  94  Chap. 5 Experimental Results and Discussion  250  o  io  io  1  4  10  2  10  3  io : 5  io  8  10  6  10  7  Time (s)  Time (s) Fig. 5.27. The effect o f annealing temperature on the softening behaviour o f 40% cold rolled (a) O A sample and (b) S O A sample. The as cold rolled yield stress is indicated at the intercepts with the vertical axis. 95  Chap. 5 Experimental Results and Discuss  (a)  1.0 -  Annealing Temp. = 325°C 0.8 /  SOA /  0.6 -  /  / /  /  0.4  /  •  10  m  A  / / / / /  1  0.2 H 0.0  O  r  i  i i i i 11  10  4  i  i  i  i  i i i 11  10  5  I  I  I  I  I  I I I  10  6  7  Time (s) 1.0 -  (b)  SOA 0.8 ! OA X  0.6 0.4 -  TI  I  0.2 Annealing Temp. = 445°C 0.0  i  10  1  i  10  22  i  10  33  i  • 111  10  44  I I  10  5  Time (s) Fig. 5.28. Isothermal recrystallization kinetics of 40% cold rolled A A 6 1 1 1 at (a) 325°C and (b) 445°C with varied precipitate conditions.  96  Chap. 5 Experimental Results and Discussion  deformed microstructure i n the S O A sample was consumed b y recrystallized grains but only 30% o f fraction recrystallized was achieved in the O A sample. The recrystallization kinetics i n both o f the samples increases considerably as the annealing temperature was increased to 445°C. In the S O A sample, 80%> o f the microstructure was recrystallized within 10 minutes o f annealing while it took 30 minutes for recrystallization to reach the same fraction i n the O A sample. Fig. 5.29  shows the fully recrystallized microstructure o f the two samples  after  annealing for 100 m i n at 4 4 5 ° C . The average recrystallized grain size was determined to be 57 and 52 u m for the O A and S O A samples, respectively. Finally, it is noted that no recrystallization was observed i n the O A samples annealed at 2 5 0 ° C .  5.1.6  TEM Studies of the Annealing Behaviour of Overaged Samples  The objective o f the T E M experiments was to gain additional insight on the annealing behaviour o f the overaged materials, i n particular the mechanism o f interaction between recovery, recrystallization and precipitation. The experiments focused on examining selected O A and S O A samples annealed at 325°C. A l l the T E M work presented i n the following was carried out in collaboration with Dr. X . Wang from the Brockhouse Institute o f Materials Research at M c M a s t e r University.  The T E M micrograph o f Fig. 5.30 shows the recovered microstructure o f the O A sample after annealing for 2 minutes at 325°C. It can be seen that cell structures consisting o f diffuse cell walls with high density o f tangled dislocations begin to form i n the early stage o f annealing. Precipitates are observed to pin low angle grain boundaries during recovery as shown in Fig.  97  Chap. 5 Experimental Results and Discussion  Fig. 5.29. Fully recrystallized microstructure of the 40% cold rolled (a) O A and (b) SOA samples annealed for 100 minutes at 445°C.  98  Chap. 5 Experimental Results and Discuss  Chap. 5 Experimental Results and Discussion  5.31. Fig. 5.32 shows that the tangles o f dislocations in cell walls transformed into subgrain boundaries as the annealing time was increased to 7 days. The formation o f subgrains is more prominent i n the S O A sample where well defined subgrains with boundaries made up o f multiple sets o f dislocations are observed after 100 mins o f annealing, as shown i n Fig. 5.33.  A series o f T E M images is shown i n Fig. 5.34 to illustrate the interaction  between  precipitation and recrystallization in the O A sample annealed for 7 days at 325°C. Fig. 5.34a shows a growing recrystallized grain embedded in the deformed matrix. In Fig. 5.34b, a T E M image is shown across the recrystallization front for the growing grain. Precipitates are observed to pin the migrating grain boundaries thus causing segments o f the boundaries to curve forward (Fig. 5.34c).  5.2  Discussion of Experimental Results  The experimental results are analyzed in detail in the next three subsections: First, a nonlinear addition law is employed to quantify the contributions o f dislocations and precipitates to the as cold rolled yield stress. Then, the evolution o f resistivity i n the T 4 , P A and O A samples during isothermal annealing is interpreted i n terms o f the nucleation, growth and coarsening o f the precipitates. In the end, the effect o f prior aging condition o n the isothermal annealing behaviour is analyzed with special attention given to the O A sample.  100  Chap. 5 Experimental Results and Discussion  101  Chap. 5 Experimental Results and Discussion  102  Chap. 5 Experimental Results and Discussion  Chap. 5 Experimental Results and Discussion  (a)  Fig. 5.34. (a) T E M micrographs showing a recrystallized grain embedded in the deformed matrix o f the O A samples annealed for 7 days at 325°C. T E M micrographs showing segment of the migrating grain boundaries are shown in (b) and (c). Courtesy of Dr. X. Wang.  104  Chap. 5 Experimental Results and Discussion  5.2.1 Flow Stress Addition Law  Previous studies on A A 6 1 1 1 have shown that the work hardening behaviour o f A A 6 1 1 1 is strongly influenced by the precipitation states i n the material [Cheng et al., 2003]. This is evident i n the data presented i n Fig. 5.9 which shows the remarkable increase i n yield stress i n the naturally aged materials after 40% cold rolling. O n a macroscopic level, one can quantify this effect b y carefully considering the manner i n which the contributions from precipitates and dislocations are summed. In general, the summation o f the solid solution strengthening component, cr precipitate contribution, <j and dislocation hardening contribution, cr^ can be ss  p  described b y using a nonlinear addition law with the following form [Cheng et al., 2003]:  \_  <j  y  = CTi+cj  ss  +(a " p  +cr "Y dis  (5.1)  where cr, is the intrinsic strength o f aluminum and n is a constant. Taking 10 M P a as a reasonable estimate for the intrinsic strength o f aluminum [Wang et al., 2003] and assuming negligible contributions from  solid  solution for the aging conditions examined, the  precipitation hardening contributions can be calculated from the as aged yield stress, i. e., cr = p  <?as-aged  - oj. The latter assumption is valid i f most o f solutes are precipitated out which is the  case i n the present analysis. The results o f this simple calculation are tabulated i n Table 5.2 for each o f the precipitate conditions. Furthermore, b y using an appropriate value for the constant n i n Equation 5.1, the contribution from dislocation hardening to the flow stress can be calculated. The value o f n depends on the strength and density o f the obstacles. Typically, n  105  Chap. 5 Experimental Results and Discussion  varies from 1 for weak obstacles (e.g. solid solution or clusters) to a value o f 2 for strong obstacles (e.g. large precipitates). For intermediate cases, the value o f n is expected to fall between these extremes. In the present case, the strengths o f the precipitates in the T4 and P A samples can be classified as weak (n - 1) and moderate (n = 1.5) obstacles respectively while the precipitates i n the O A and S O A samples can be considered as strong obstacles (n = 2). Based on these assumptions, the magnitudes o f cfe can be calculated and the results are summarized in Table 5 . 2 . B y comparison, the T4 sample work hardened to a much larger extent than the rest o f the samples. The magnitude o f Orf, which is directly responsible for the s  stored energy for subsequent recovery and recrystallization processes is considerably higher in the T4 and P A samples as compared to the O A and S O A samples. It should, however, be noted that the current interpretation o f the as deformed yield stress represents a greatly simplified approach as the work hardening process is expected to be strongly dependent on whether the precipitates can be sheared by dislocations. Additional complications may arise due to the fracture o f large precipitates i n the O A and S O A samples during the cold working process. Improvements are possible by adopting a more complicated work hardening model [Sevillano, 1993]. However, with the current modelling objective i n mind, this does not appear to be justified.  5.2.2 Evolution of Resistivity  A n y factors that tend to distort the regularity o f the crystal lattice w i l l increase the resistivity of the materials, p by scattering the conducting electrons [Stanley, 1963]. In the present case, r  there are three relevant factors that may contribute to the increase o f resistivity in the  106  Chap. 5 Experimental Results and Discussion  Table 5.2. Summary o f the flow stress contributions from precipitates and dislocations as a function o f precipitation state. Initial precipitation state n  ^As-aged ^As-cold rolled  0~dis  T4  1  139  356  129  217  PA  1.5  334  430  324  197  OA  2  153  220  143  154  SOA  2  92  194  82  165  107  Chap. 5 Experimental Results and Discussion  materials: i) dislocation density, ii) solute atoms i n solid solution and iii) precipitates. The contribution o f these three factors can be summed linearly according to Matthiessen's law:  Pr=P( ) T  + Ti Pi i i C  +  Pppt  +  (5 -2)  Pdis  In Equation 5.2, p(T) represents the resistivity o f pure A l w h i c h is a constant at a given measuring temperature, C, is the concentration o f a solute element and p is the corresponding t  resistivity coefficient. p  ppt  and pdi are the resistivity contributions due to precipitate and S  dislocations respectively. In cold worked materials, the magnitude o f pdi is expected i n the S  order o f - 0 . 3 n Q m . Furthermore, it is not far from reality to assume that the term  p , pp  diminishes rapidly upon annealing at elevated temperature due to the significant increase i n both precipitate size and spacing. Therefore, based on Equation 5.2, the variation in resistivity can be directly related to the variation i n the concentration o f solute i n solid solution. This can be verified b y careful examination o f the resistivity curves shown i n Fig. 5.16 i n terms o f nucleation, growth and coarsening o f precipitates:  1) During the artificial aging o f solution treated samples, the nucleation and growth o f fine scale precipitates which significantly deplete the matrix o f solute atoms caused the resistivity to decrease sharply i n the early stage o f annealing. This corresponds to the initial rise i n the age hardening curve to peak strength at 3 2 5 ° C (Fig. 5.8). The depletion o f solute atoms appears to continue slowly until - 3 0 0 0 seconds at which point the value o f resistivity becomes identical to the O A sample. A t this annealing time, the precipitates are well into their coarsening stage. During coarsening, the 108  Chap. 5 Experimental Results and Discussion  variation o f solute concentration is not significant and this is reflected in the resistivity curve which shows very small variations. 2) The evolution o f resistivity o f the T4 and P A samples can be explained in a similar way as the artificially aged samples. The initial rapid nucleation and growth o f the Q' phase caused the resistivity to drop by drawing solutes from solid solution. The effect o f this nucleation and growth processes is again short lived (up to ~3000s). After that the precipitation process is dominated by the coarsening o f precipitates. 3) The resistivity o f the O A sample remains virtually unchanged i n the initial stage o f annealing. This behaviour is expected since the stable precipitates are well into the coarsening stage prior to cold rolling. In other words, there is no supersaturation in the solution to drive the nucleation and growth o f new precipitates upon annealing. The flat resistivity curve also confirms that the reduction o f dislocation density due to recovery did not influence the resistivity measurements.  It is less clear why all the resistivity curves slowly decrease in the later stage o f annealing. One possible explanation for this is that the precipitation o f equilibrium phases reduces slightly the concentration o f solute i n the matrix after long annealing time. Finally, it should be noted that while the resistivity measurements indicate that the precipitation process during isothermal annealing at 3 2 5 ° C is mostly dominated b y the coarsening o f precipitates, the kinetics o f the process  might be different  for different  initial precipitate  conditions.  Furthermore, the spatial distribution o f precipitates is expected to play an influential role in the recrystallization process.  109  Chap. 5 Experimental Results and Discussion  5.2.3 The Effect of Prior Aging Conditions  The effect o f varying the initial precipitate conditions on the isothermal annealing behaviour at 325°C is summarized i n Table 5.3. Two important observations are noted: i) the overall recrystallization kinetics is sluggish; the fastest recrystallization is observed i n the S O A sample while the O A sample recrystallized at the slowest rate, ii) the majority o f softening is due to the simultaneous occurrence o f recovery and precipitate coarsening, especially i n the T4 and P A samples. These observations can be explained by examining the combined effect o f recovery, recrystallization and precipitation.  T4 (naturally aged) It is expected that the clusters and G P zones formed during the natural aging process started to dissolve rapidly during heat up to the annealing temperature. Some o f the clusters may act as potential nucleation sites for the subsequent precipitation o f Q' phase. A significant amount o f this precipitation took place preferentially at the elongated grain boundaries and substructures (Fig. 5.23a), thereby pinning these boundaries and also pinning any new recrystallized grains that may form. The inhibiting effect diminishes as precipitates coarsen which ultimately leads to the onset o f recrystallization.  P A (peak aged): The isothermal softening kinetics o f the T4 and P A samples is essentially identical as shown i n Fig. 5.15a. The dramatic drop i n yield stress o f the P A sample can be attributed to the rapid transformation o f the fine fi" precipitates to the coarser Q' phase. The fraction o f  110  Chap. 5 Experimental Results and Discussion  Table 5.3. Summary o f the softening and recrystallization behaviour o f 40% cold rolled A A 6 1 1 1 with various precipitate conditions at the annealing temperature o f 325°C.  Initial heat treatment  Initial precipitate phases  Softening  Recrystallization  As deformed Final a a (MPa) (MPa)  y  j  Onset time  y  Fraction recrystallized  1  T4 (8 days at room temperature)  Solute clusters and G P zones  356  71  12 hours  ~ 48%  P A (7 hours at 180°C)  Fine P" (80% by volume fraction) + Q'  430  73 after 2 weeks  12 hours  ~ 35% after 2 weeks  220  73  48 hours  ~ 37%  194  41  10 hours  ~ 90%  O A (7 days at 250°C)  S O A (7 days at 325°C)  Lath shaped Q' Lath shaped Q' + some square shaped Mg Si 2  After 40 days o f annealing unless otherwise noted  111  Chap. 5 Experimental Results and Discussion  recrystallized grains i n the two samples is also found to.be similar after 2 weeks o f annealing at 325°C (see Figs. 5.18a and 5.18b).  O A (overaged) and S O A (severely overaged) The precipitates in the O A and S O A samples are already i n their stable configuration prior to annealing. These relatively large precipitates were fractured into small segments i n the cold working process and as a result the number density o f precipitates was significantly increased (Fig. 5.13). U p o n annealing, coarsening resumes but the high density o f the precipitates pins grain boundaries making recrystallization a difficult process. However, the recrystallization rate was greatly enhanced b y raising the annealing temperature to 4 4 5 ° C as shown i n Fig. 5.28b. A n important consideration with regard to raising the annealing temperature is the effect o f precipitate dissolution. Based on the studies b y Burger et al. (1996) o n A A 6 1 1 1 , significant dissolution o f precipitates was observed to occur at temperatures above 430°C. Hence, it is likely that the number density o f precipitates quickly diminishes upon annealing at 445°C. This coupled with the fact that recrystallization being a thermally activated process results i n the rapid recrystallization seen i n Fig. 5.28b. Lastly, it should be mentioned that recrystallization is found to occur at two commonly observed sites i n aluminum alloys: i) deformed grain boundaries (Fig. 5.18) and ii) deformation zones around large intermetallic particles (Fig. 5.26).  It is interesting to further compare the recrystallization behaviour o f the O A and T 4 samples based on the data presented i n Fig. 5.22. There are a number o f notable differences i n the development o f recrystallizing microstructures i n the two samples. First, it is clear that  112  Chap. 5 Experimental Results and Discussion  recrystallization is faster i n the T4 samples. One possible reason behind this is the difference in the stored energy accumulated during cold rolling. It has been shown i n section 5.2.1 that samples with T 4 condition work hardened to a much larger extent than the O A samples. O n increasing the annealing time to 2 weeks, the resultant average recrystallized grain size in the O A sample is larger than the grain size found i n the T4 sample (20 vs. 15 um). Colonies o f large recrystallized grains with a diameter as large as 100 urn can be observed i n the O A sample (Fig. 5.20) whereas smaller but more evenly distributed recrystallized grains are found in the T 4 sample (Fig. 5.18a). This difference can be explained b y comparing the spatial distribution o f precipitates in the two samples since the limiting grain size is directly related to the spacing between precipitates. The large precipitate free zones i n the O A sample has been shown to correlate with recrystallizing grains (Fig. 5.25). In the case o f the T4 sample, reprecipitation o f Q' phase occurred in the matrix and along grain boundaries during annealing. These precipitates then coarsen resulting i n a much finer distribution o f precipitate spacing  (Fig. 5.23a).  Additional insight on the recrystallization process can be gained b y carefully examining the T E M micrographs presented i n Fig. 5.34. It is apparent from the curvature o f the migrating front, the boundary is subjected to two opposing pressures. The subgrains surrounding the recrystallization  front  exert  a forward pressure  i n order to consume  the recovered  microstructure. But segments o f the grain boundary are immobile due to the pinning pressure exerted by precipitates. The consequence o f these competing pressures is that the segment o f the migrating front which is i n contact with the subgrains bow forward and where the boundary is pinned by the precipitates, it is bowed back (Fig. 5.34c).  113  Chap. 5 Experimental Results and Discussion  5.3  Concluding Remarks  The aging heat treatments carried out prior to cold rolling encompass a wide range o f possible precipitate conditions i n A A 6 1 1 1 . In the next chapter, a microstructure model based on the internal state variable approach is developed for the overaged samples based on the knowledge acquired in this chapter.  114  Chapter 6  Modelling of Microstructure Evolution for Overaged AA6111  In this chapter, the internal state modelling approach is adopted to develop a comprehensive microstructure model for the annealing o f overaged A A 6 1 1 1 . Special emphasis is placed on integrating existing physically based models for the various elementary  microstructural  reactions: recovery, subgrain growth, recrystallization and precipitation. The chapter is organized in the following order: i n the first part o f this chapter, section 6.1, the internal state variable modelling approach is introduced along with the internal state variables that have been selected to represent the individual processes o f recovery, subgrain growth, precipitation and recrystallization. In the formulation o f material response equations, a modelling strategy based on the rule o f mixtures is employed to account for the effect o f heterogeneous spatial distribution o f precipitates i n the deformed microstructure. F r o m sections 6.2 to 6.5, the respective evolution laws for recovery, subgrain growth, recrystallization and precipitation are derived and coupled using physically sound theories i n the literature. Material specific parameters which are required as input to the model are calculated in section 6.6. Section 6.7 explains the implementation o f the model and gives a schematic outline o f the overall model framework.  Section 6.8 is devoted to compare the model predictions with available  experimental data i n terms o f softening and recrystallization kinetics. In section 6.9 the model is employed to analyze quantitatively the interaction between the various microstructural processes. Finally, this chapter concludes with a brief discussion i n section 6.10 on the limitations o f the present model.  115  Chap. 6 Modelling of Microstructure Evolution for Overag  6.1  Model development - The Internal State Variable Modelling Approach  The concept o f microstructural modelling based on internal state variables was originally proposed by Richmond (1986) and applied to deformation processes.  Since then, this  modelling method has been expanded and widely applied to other industrial processes o f commercial alloys which includes casting, cooling after hot forming, aging heat-treatment and welding [Grong and Shercliff, 2000]. The internal state variable modelling approach is particularly suited for modelling industrial thermomechanical processes because it is capable of relating changes i n product properties to the changes i n microstructure resulting from changes in processing parameters. Hence, an accurate internal state variable model developed based on physically sound mathematical equations is extremely useful in process design where operational parameters are optimized to achieve desired product properties.  The first step i n the development o f an internal state variable model is to identify appropriate state variables to represent the most significant aspect o f the microstructure. In general, a microstructural evolution phenomenon can be well described by one variable. It is unusual to consider more than three variables for a given microstructure process [Grong and Shercliff, 2000]. These internal state variables are, i n principle, measurable physical quantities although some o f them are measured indirectly in practice; for example, dislocation density is often quantified based on flow stress measurements. Table 6.1 lists the internal state variables that have been selected to represent the four principal metallurgical reactions considered in the present model.  116  Chap. 6 Modelling of Microstructure Evolution for Overag  Table 6.1. List o f internal state variables for recovery, subgrain growth, recrystallization and precipitation considered i n the present modelling approach.  Microstructural Process  Internal State Variables  Recovery  Dislocation density, pdi *  Subgrain growth  Subgrain size, S b  Recrystallization  Volume fraction o f recrystallized grains, X  Precipitation  s  s  Precipitate radius, R and density, p  Followed indirectly by the evolution o f flow stress  117  Chap. 6 Modelling of Microstructure Evolution for Overaged AA6111  The next step involves the formulation o f a series o f mathematical equations to capture the evolution o f internal state variables as a function o f reaction time at a given reaction temperature. Mathematically, it is most convenient to formulate the evolution laws based on a system o f coupled, in general non-linear first-order differential equations:  ^ L = (T,S S gl  h  2  .S^  (6.1)  where T is the instantaneous temperature, and Si, S2,---Si are the instantaneous values o f the internal state variables. Each internal state variable, Si, evolves with increasing time and may be a function o f other state variables for a given set o f processing conditions such as temperature and amount o f prior cold reduction. Equation 6.1 is strictly applicable to a thermally controlled process where the evolution o f each internal state variable in the next time increment is uniquely defined by these instantaneous values and the current temperature. Hence, introduction o f some initial conditions, i.e., the condition at time, t = 0 is required. These evolution laws can be integrated over the time and temperature history o f the heat treatment cycle using an appropriate numerical method thereby determining the internal state variables o f the resulting microstructure. In the present work, established models in the literature are adopted to devise the evolution laws for the individual processes o f recovery, subgrain growth, recrystallization and precipitation.  The final step i n the development o f an internal state variable model is to construct appropriate material response equations to link the output o f the evolution laws, i.e., the resulting microstructure parameters to the physical or mechanical properties o f the materials. In the  118  Chap. 6 Modelling of Microstructure Evolution for Overa  present modelling approach, the evolution o f internal state variables is linked to the softening in flow stress as a function o f isothermal annealing time. One simple approach is to model the microstructure as consisting o f a mixture o f precipitate and precipitate-free zones. Based o n this composite model, the overall flow stress o f the material, <y at any time during annealing is y  obtained by a simple rule o f mixtures:  cr =cr F + y  *  I  I  (6.2)  ( l - F )  I  The subscripts / and II indicate the quantities o f interest i n the precipitate-free and precipitate zones, respectively. A s a first approximation, Equation 6.2 is assumed to be valid since the volume fraction o f the material that is free o f precipitates, F, is relatively small (F - 0.15 estimated from S E M micrographs) and the microstructure is dominated by the precipitate zones. Furthermore, the strength levels o f the softer (precipitate free zones ) and the harder (precipitate zones) fractions are expected to be within one order o f magnitude. Following Equation 6.2, the overall volume fraction recrystallized grains is also given b y the rule o f mixtures: X  = XF I  +  X  I  (6.3)  ( \ - F )  I  It is straightforward to determine the flow stress o f the precipitate free zones, o/. It contains a contribution from the flow stress o f the fully recrystallized fraction, cr  rex  (-40 M P a ) and a  contribution from the recovered flow stress, o- in the unrecrystallized fraction. Again using rc/  the rule o f mixtures, 07 is calculated as follows: a-1 = a , + cr Xj rex  + a  119  r  c  I  (l-Xj)  (6.4)  Chap. 6 Modelling of Microstructure Evolution for Overag  where a is the intrinsic strength o f A l (-10 M P a ) . cr t  rex  is larger than cr, b y 3 0 M P a due to  residual contributions from precipitation hardening and at the highest annealing temperature o f 445°C there is also an additional contribution from solid solution strengthening ass • However, changes i n ass during annealing heat treatment is considered o f minor importance i n the present analysis since ass scales with the solute concentration, C in a non-linear manner, i.e., &ss ~  with q < 1 [Esmaeili, 2002]. The determination o f the flow stress o f the precipitates  region, an is more complicated. It contains an additional contribution from precipitates, a . p  This can be determined b y combining a series o f non-linear addition laws with the rule o f mixtures:  ° 7 / = °7 + Vrex-matrixXll  ° rex-matrix  + Unrex-matrix G  ~ \ rex  r  G  I Unrex-matrix  G  =  \ rcIl G  0 ~ ll)  (- )  X  6  p  5a  (6.5b)  +<T  2  2~ p  (6.5c)  +<T  The initial flow stress is assumed to be the same for precipitate and precipitate free zones, i.e., aj=an at t - 0. In Equations 6.4 and 6.5c, the recovered flow stress, a j and a n are obtained rc  rc  directly b y numerical integration o f the evolution law for recovery over the time and temperature history o f the annealing heat-treatment. Given that the precipitates are well into their overaged conditions, particle bypass is expected to be the dominant precipitatedislocation interaction mechanism. Based on the work by Esmaeili et al. (2003b) on A A 6 1 1 1 , the precipitation contributions to the flow stress i n the precipitate zones, a , under this p  condition is given by:  120  Chap. 6 Modelling of Microstructure Evolution for Overaged AA6111  MGbF  l p  (6.6)  (2x) R l/2  p  where M is the Taylor factor, G is the shear modulus and b the magnitude o f the Burgers vector. The quantities R  p  and F represent the average radius and volume fraction o f the p  precipitates respectively.  6.2  Recovery  It is assumed that the dislocation density, pd is directly related to the flow stress o f the material according to the classical forest work hardening theory [Taylor, 1934]:  (6.7)  where or is a constant i n the order o f 0.3.  In the present modelling treatment, the recovery model developed b y Verdier et al. (1999) is adopted to describe the recovery kinetics. This model is favored for two reasons: Firstly, the model relates the reduction i n flow stress to the lowering o f the average dislocation density and thus fits well with the internal state variable approach. Secondly, the model allows only for two adjustable parameters, namely the activation energy and activation volume, thus i n line with the current modelling objective in keeping the unknown parameters to a minimum.  121  Chap. 6 Modelling of Microstructure Evolution for Overaged AA6111  The mathematical formulation o f the Verdier et a/.'s model for the precipitate free zones is shown i n Equation 6.8a. In the precipitate zones, the retarding effect o f precipitates on recovery is captured b y combining the model with the approach proposed b y Zurob et al. (2002), as shown in Equation 6.8b.  Precipitate free zones:  d{cr -cr ) rcI  _  rex  dt  64(a -a ) y 2  rcI  rex  D  9M a E 3  2  sink NA(°rd-°rex)  V  exp  (6.8a)  RT g  Precipitate zones:  di^rd! -^rex) dt  exp  9M a E 3  2  sink N (<7rcII-<7rex)V^ A  RT g  Qo  a  1—  »  N  dis  N  ^  (6.8b)  J  In Equations 6.8a and 6.8b, R denotes the gas constant and T is the temperature i n K e l v i n . g  The effective pinning parameter, a which has a value o f less than 1, is introduced i n p  Equation 6.8b to estimate the fraction o f precipitates that are available to pin the dislocation networks. The magnitude o f the parameter a is determined b y fitting the model calculation to p  experimental data. Complete retardation o f the recovery process, i.e., da /dt rc  = 0, is expected  when cCpN = Ndi . The number o f dislocation nodes, Ndis is approximated as 0.5p></' [Dutta et 5  p  S  al, 2001, Zurob et al, 2002].  122  Chap. 6 Modelling of Microstructure Evolution for Overaged AA6111  The key parameters in Equations 6.8a and 6.8b are the two activation parameters, i.e. the recovery activation energy, Q and activation volume, V. Estimation o f the magnitude o f these 0  two parameters is problematic simply because Verdier et a/.'s recovery model does not discriminate between thermally activated cross slip, climb or solute drag as the rate determining process. However, the activation energy is likely to be approximated by the activation energy for self diffusion (-142 kJ/mol for A l [Smithells and Brandes, 1976]) i f dislocation climb is the rate controlling process since it involves the formation and movement of vacancies. O n the other hand, i f solute drag is the rate controlling mechanism, then Qo is expected to lie within the range o f the activation energy for solute diffusion i n aluminum, i.e. 130-140 kJ/mol. The reported values o f the activation energy o f diffusion o f the various species in aluminum are listed i n Table 6.2. The values for the self diffusion o f aluminum is included for comparison.  The second activation parameter, i.e. the activation volume is a quantity which is difficult to specify except for being o f the order o f b . In the case o f thermally activated mechanism, 3  the activation volume can be written as V - b l where l is an activation length associated 2  a  a  with the dislocation motion. In the case o f solute drag as rate controlling mechanism, the activation length is a physical parameter defined as the distance between solute pinning points along the dislocation lines. Hence, /„ is inversely proportional to the concentration o f solutes i n the solution, C  M  [Nes, 1995]:  123  Chap. 6 Modelling of Microstructure Evolution for Overaged AA6111  Table 6.2. Reported diffusion data for M g , C u and S i atoms and self diffusion in bulk aluminum.  Elements  Diffusivity in Aluminum  Mg  D = 2.2 x 10" m /s, Q = 130 kJ/mol  M y h r and Grong, (2000), M y h r et al, (2001)  Si  D = 2.0 x 10" m /s, Q = 137 kJ/mol  Burachynsky and Cahoon, (1997), Fujikawa et al, (1978)  Cu  Do = 6.5 x 10" m /s, Q =136.1 kJ/mol  Burachynsky and Cahoon, (1997), Fujikawa and Hirano, (1989)  Al  Do = 1.7 x 10" m /s, &> = 142 kJ/mol  Smithells and Brandes, (1976)  4  2  0  D  4  2  0  D  5  2  D  4  2  124  Chap. 6 Modelling of Microstructure Evolution for Overaged AA6111  where K is a geometrical constant o f order o f unity and Q is the atomic volume o f aluminum (1.65xl0"  29  m ) . In A A 6 1 1 1 , the concentration o f residual solutes typically ranges from 0.263  0.74 atomic% after overaging at temperatures i n the range o f 200 to 4 0 0 ° C . Therefore, based on Equation 6.9, the activation volume is expected to be i n the order o f 6-\2b . In the present 3  modelling approach, the activation volume is taken as a constant and set equal to an average value o f 9b . This consideration amounts to the fact that bulk solute concentrations do not change significantly during annealing o f overaged alloys. In summary, the two adjustable parameters i n the recovery model are the activation energy (allowed to vary between 130-142 kJ/mol) and the effective pinning cc (0 < cc < 1). p  6.3.  p  Subgrain Growth  The formation o f a w e l l defined subgrain structure such as the one shown i n Fig. 5.34 is promoted b y the delay i n the onset o f recrystallization. A s annealing time increases, these subgrains may grow and coarsen i n order to lower the stored energy o f the recovered structure via the reduction o f grain boundary area. Following 0rsund and N e s (1989), i f the substructure can be approximated b y an array o f subgrains o f radius S b then the driving pressure for s  subgrain growth, P b may be estimated from s  P  s  b  = ^  125  (6-10)  Chap. 6 Modelling of Microstructure Evolution for Overaged AA6111  where a  }  is a geometrical factor i n the order o f 1.5 and y  sb  is the energy o f the low angle  subgrain boundaries. The magnitude o f y b is dependent on the misorientation o f the boundary s  and may be estimated from the Read-Shockley equation [Vatne et al, 1996, Humphreys and Hatherly, 1995, Furu et al, 1999]:  (6.11)  where v is the Poisson ratio (-0.33) and 6 is the critical misorientation angle for a high angle C  grain boundary (commonly taken as 15° [Humphreys and Hatherly, 1995]). Hence, by taking an average subgrain misorientation o f 5° (obtained from E B S D measurements o f the internal substructure o f the deformed grains), the value o f y b is calculated as 0.16 J/m . 2  s  The rate o f subgrain growth is assumed to be proportional to the driving pressure, P , as S B  shown in Equation 6.12a i n the precipitate free zones. The constant o f proportionality being the mobility o f the subgrain boundaries, M'. In the precipitate zones, the retarding effect o f fine particles on the rate o f growth o f subgrains is considered based on a simple approach proposed by Humphreys and Hatherly (1995). In this approach, the driving pressure for subgrain growth is modified by a pinning term as shown in Equation 6.12b.  Precipitate free zones: W d  =  M  ,  \Ysb  a  sb,l  t  S  126  (6.12a) (0  Chap. 6 Modelling of Microstructure Evolution for Overaged AA6111  Precipitate zones: dS,'sb,II  3^(0  dt  <W/(0  (6.12b)  (t)j  2R P  If the motion o f the subgrain boundaries is thermally activated, then the mobility, M' can be assumed to vary with temperature in accordance with an Arrhenius relationship o f the form:  M'  - M'Q  exp \ Q * } (  K  R  (6.13)  8 J T  where Q b is the activation energy for subgrain growth and M'Q is the intrinsic mobility o f the S  subgrain boundary. Admittedly, this calculation is not rigorous since a  comprehensive  approach i n modelling subgrain growth should include the effect o f misorientations on the mobility o f the boundaries [Furu et al., 1995, Humphreys and Hatherly, 1995]. Nonetheless, this simplified approach allows us to maintain the simplicity o f the model and yet obtain a reasonable description o f the underlying microstructure evolution. In the present model, both the parameters, Q b and M'Q are treated as fitting parameters. s  Lastly, it is important to note that the contribution o f subgrain size is not considered i n the flow stress equations (Equations 6.4 and 6.5). In doing so, we have attributed the recovery softening during annealing solely to the annealing out o f dislocations described in section 6.2. This is consistent with the approach proposed by Verdier and co-workers (1999) who showed that recovery subgrain growth does not effect the logarithmic time decay o f yield stress in A l -  127  Chap. 6 Modelling of Microstructure Evolution for Overa  M g alloys. A single internal state variable based on dislocation density is sufficient to describe the softening curve. This is i n contrast with the approach b y Nes and Saeter (1995) who consider the flow stress o f the material at any time during recovery is a function o f both dislocation density, pd and subgrain size, 8 b- However, it should be noted that the relative s  importance o f these two internal state variables i n determining the flow stress is still a question o f much debate i n the literature [Nes, 1995].  6.4  Recrystallization  The present description o f the evolution o f volume fraction recrystallized grains, X with respect to annealing time is derived based on the J M A K approach. Assuming that the recrystallized grains are distributed randomly throughout the volume, then there is a simple mathematical equation to relate the real volume fraction recrystallized to the extended volume fraction recrystallized, X : ext  dX  " J-x)  dX  =  ( 6 1 4 )  Differentiating Equation 6.14 with respect to time and rearranging gives:  dX  dX , /, „ \ x  128  Chap. 6 Modelling of Microstructure Evolution for Overa  Assuming isotropic growth o f spherical grains, the extended volume fraction is related to the volume o f the growing grains and number o f recrystallization nuclei per unit volume, N  rex  * . = f * * X ,  by  (6-16)  where R is the average radius o f recrystallizing grains i n the absence o f hard impingement. Equation 6.16 can be differentiated with respect to time to obtain the term dX /dt i n ext  Equation 6.15:  Finally, the evolution o f volume fraction recrystallized grains as a function o f time is obtained by combining Equations 6.15 and 6.17:  §  dt  =4 ^ § N j l - X )  dt  (6.18)  Equation 6.18 allows recrystallizing grains to grow isotropically i n three dimensions until impingement b y neighbouring grains. This hard impingement effect is taken into account b y the term (l-X). Therefore, as recrystallization proceeds to completion (X-> 1), dX/dt w i l l tend to become 0. It can be seen from Equation 6.18 that the evolution o f volume fraction recrystallized grains depends on three factors: (a) the instantaneous grain radius, R (b) the recrystallized grain growth rate, dRJdt and (c) the number density o f recrystallization nuclei, 129  Chap. 6 Modelling of Microstructure Evolution for Overag  N . The growth rate depends critically on the stored energy i n the deformed structure and rex  therefore is a function o f both the recovery and precipitate processes. The number density o f recrystallized nuclei can be calculated from the amount o f rolling reduction applied to the as aged materials. These two quantities are evaluated in separate sections below.  6.4.1  Nucleation  It is difficult to formulate a physical description o f the nucleation process for recrystallization primarily due to lack o f understanding o f the deformed structure. The first major problem one encounters is the definition o f recrystallized "nuclei" because recrystallized grains do not "nucleate" as totally new grains v i a the classical random atomic fluctuation mechanism proposed for phase transformations [Cahn, 1950, Humphreys and Hatherly, 1995, Doherty et al, 1997]. However, it is now widely accepted that new recrystallized grains originate from pre-existing sites i n the deformed microstructure. A common feature among these pre-existing sites is high local misorientations, for examples, highly misoriented deformation zones around large particles and deformed grain boundaries [Doherty et al, 1997]. Another important consideration is the role o f recovery i n facilitating the nucleation o f recrystallization [Ray et al., 1975, B a y and Hansen,  1979, Humphreys and Hatherly, 1995]. Unfortunately, a  theoretical model is presently not available for recrystallization nucleation. Hence, under the prevailing circumstances, it is assumed that all nucleation events effectively take place at the onset o f recrystallization, i.e., site saturated nucleation. This assumption has been shown to be satisfactory for industrial alloys with large prior deformation [Furu et al., 1990, Humphreys and Hatherly, 1995]. The number o f recrystallization nuclei per unit volume, N , is assumed rex  130  Chap. 6 Modelling of Microstructure Evolution for Overa  to be proportional to the sum o f the grain boundary area and Fe-containing particles surface area:  A  where A is the area o f the critical nucleus (~R )- The basic assumption o f Equation 6.19 is 2  c  C  that both grain boundary area and area i n the vicinity o f Fe-containing particles have the same potency for the nucleation o f recrystallized grains. The critical nuclei radius, R is assumed to c  be i n the order o f 0.5 urn based o n estimation o f subgrain size from T E M micrographs. From Equation 6.19, it can be seen that the maximum number o f possible nuclei is given by the ratio between the total surface area per unit volume and the critical nucleus area. The nucleation parameter k (0 < k < 1) determines the potency o f the nucleation sites which i n the present modelling treatment needs to be treated as a fitting parameter.  In Equation 6.19, two possible nucleation sites are considered:  1. Area adjacent to the Fe-rich constituent particles: The total surface area per unit volume, S Fe, can be calculated from the number density, N  ViFe  Vw  and the averaged radius  o f the Fe-rich particles, Rp ,'e  S =A7tR N 2  vFe  Fe  131  Fe  (6.20)  Chap. 6 Modelling of Microstructure Evolution for Overaged AA6111  The values for A V and R e  Fe  are determined from experimental measurements (see  section 5.1.3). 2. Deformed grain boundary area: The total deformed grain boundary area per unit volume, S , b after cold rolling can be estimated from the solutionized grain size, d (~ v g  s  42pm). B y assuming that the shape o f the solutionized grains resembles a regular tetrakaidecahedron, S b is obtained as follows [Chen et al., 2002]: v>g  —  2d [ s  a + 3flJl + -^-+3  i  a  2  42 + 2a' <  a  I  (6.21)  a  where a = exp(s ). The true strain, s is related to the amount o f prestrain, r (in % T  T  reduction) according to  f £j = ln  1  ^  vl-r/100,  6.4.2  (6.22)  Growth rate  The growth rate o f the recrystallizing grains is given b y the w e l l known relationship o f  ~- = d MP  d  132  (6-23)  Chap. 6 Modelling of Microstructure Evolution for Overaged AA6111  where M is the mobility o f the high angle grain boundary and Pd is the driving pressure for recrystallization. The calculation o f the driving pressure is somewhat complicated because the recovered microstructure is composed o f well defined subgrain structure and deformed structure. The subgrain boundaries are made up o f multiple sets o f well defined dislocation networks while the interior o f the subgrains are relatively free o f dislocations (Fig. 5.33). Outside the subgrains i n the deformed regions, more or less uniformly distributed dislocations can be identified (Fig. 5.34). Following Vatne et al. (1996), the average stored energy per unit volume o f such a composite structure can be defined as follows:  Pd=\pdGb +^L 2  ( 6 > 2 4 )  °sb  2  The growth rate o f the recrystallizing grain i n the precipitate free zones is obtained b y combining Equations 6.23 and 6.24, as shown i n Equation 6.25a. The dislocation density is time dependent due to the effect o f concurrent recovery. In the precipitate zones, the driving pressure for recrystallization is modified b y a Zener retarding term under the condition o f evolving precipitate size and density. This is shown in Equation 6.25b.  Precipitate free zones:  dt  \ 2  P  d  J  ^  {t)Gb W  133  2  - ^ a  +  <W(0.  (6.25a)  Chap. 6 Modelling of Microstructure Evolution for Overaged AA6111  Precipitate zones: dRn dt  .2 , a\Ysb $sb,n{t)  IrgbFpi*) 2R (t) p  (6.25b)  J  In Equation 6.25b, y b denotes the high angle grain boundary energy (-0.324 J / m [Murr, 2  g  1975]). The high angle grain boundary mobility, M i s a complex function o f the concentration of the solutes due to the solute drag effect as discussed i n section 2.6.2. Since recrystallization is a thermally activated process, a simplified approach is to assume that the mobility obeys an Arrhenius relationship, i.e.:  M  = MQ exp  -  (6.26)  V  Here, Q  rex  denotes the activation energy for recrystallization and M is a pre-exponential 0  factor. Equation 6.26 has been found to work generally w e l l w i t h many materials including both steel and aluminum alloys [Huang and Humphreys, 1999, Humphreys and Hatherly, 1995]. A s a first approximation, the magnitude o f Q  rex  is set equal to 200 kJ/mol based on the  recrystallization data from Vatne (1995). The value for Mo is found b y fitting the model to experimental data.  134  Chap. 6 Modelling of Microstructure Evolution for Overaged AA6111  6.5  Precipitation  In the precipitate zones, an evolution law is required to follow the change in the precipitate size and density during annealing. In the present work, the evolution laws for dissolution and precipitation are mainly derived from the models developed by Cheng et al. (2000) and Deschamps and Brechet (1999). Since the model is only applicable for overaged materials, the nucleation and growth o f new precipitates are not considered. The present precipitation model primarily deals with concurrent dissolution/growth and coarsening o f Q' precipitates. The complexity o f the precipitation sequence involving various intermediate phases is not accounted for i n the model. For mathematical simplicity, the progress o f precipitates dissolution/growth and coarsening are monitored by following the changes i n the average values o f the precipitate density, N and radius, R . Furthermore, it is assumed that individual p  p  segments o f fractured Q' precipitates (Fig. 5.13) can be represented b y spherical precipitates. This greatly simplifies  the mathematical formulation o f the  evolution equations  for  dissolution/growth and coarsening.  6.5.1  Dissolution/Growth  In the first stage o f annealing, pre-existing precipitates i n the deformed matrix can either grow or dissolve. Whether the precipitates may dissolve or grow depends on its initial size and the annealing temperature. The rate at which this occurs can be expressed by a growth law for spherical particles [Cheng et al., 2000]:  135  Chap. 6 Modelling of Microstructure Evolution for Overa  dR  dt  ~Q  M  C  p  Cp-Q  \d/g  eq  I eq  R  y nt  D  p  xl/2  D  (6.27)  where C and C, denotes the solute concentration i n the precipitate and at the precipitateP  matrix interface, respectively. CM represents the average solute concentration i n the matrix and is the equivalent diffusivity. Following Deschamps and Brechet (1999), it is assumed that the precipitate composition is a fixed combination o f A L j C ^ M g g S i ? and that one can describe the diffusion kinetics for this combination o f species using an equivalent diffusivity. The temperature dependence o f the diffusion process is expressed by an Arrhenius type o f equation:  f eq = 0  D  D  P  ex  -  (6.28)  where QD is the activation energy for diffusion and Do is a pre-exponential factor. A s a first approximation, the magnitude o f Q  D  is set equal to the activation energy o f self diffusion  aluminum, i.e., QD = 142 kJ/mol (Table 6.2). The magnitude o f the pre-exponential factor (between ~10" to 10" m /s) is found by fitting the model to experimental data. 4  5  2  It can be seen from Equation 6.27 that the precipitates w i l l dissolve i f C, > CM and grow i f C, < CM- The effect o f curvature on dissolution and growth kinetics enters Equation 6.27 v i a the Gibbs-Thompson equation [Martin et al, 1997]:  136  Chap. 6 Modelling of Microstructure Evolution for Overa  l-C  Cj — C q exp *0_ e  C  Rr,  (6.29)  -C  ^eq J  with  R,=^ff  (6.30)  RT g  In Equation 6.30,  y denotes the precipitate-matrix interfacial energy and V  m  volume o f the Q' precipitates. C  eq  is the molar  is the equilibrium solute concentration at the annealing  temperature. The magnitude o f the precipitate-matrix interfacial energy, y is a function o f the coherency between the precipitates and the matrix. Incoherent precipitates are expected to have higher interfacial energy due to larger structural distortions at the interface. However, experimental determination o f the interfacial energy is a difficult problem. A s a result, y is usually taken as a fitting parameter in most modelling approaches. For example, in the age hardening model o f M y h r et al. (2000, 2001), the Mg2Si-matrix interfacial energy was varied from 0.2 to 0.26 J / m in order to fit the model calculations to experimental data obtained from 2  A l - M g - S i alloys. In another precipitation model developed by Deschamps and Brechet (1999) for A l - Z n - M g alloy, value as high as 0.3 J / m  2  was used for the interface between r/'  precipitates and the matrix. In the present modelling exercise, y is taken as a constant i n the t  order o f 0.3 J/m . 2  137  Chap. 6 Modelling of Microstructure Evolution for Overa  6.5.2  Coarsening  It is expected that the majority o f the precipitates entered the coarsening regime i n the early stage o f annealing since the precipitates are well into the coarsening stage prior to cold rolling. Following Deschamps and Brechet (1999), the standard Lifshitz-Slyozor-Wagner ( L S W ) coarsening law is used to describe the evolution o f average precipitate radius [Lifshitz and Slyozor, 1961, Wagner, 1961]:  dRp_  _ 4  dt  ^ ( i - Q ^ J V ^  27 ( r \Cp-C j  \  r  coars  eg  2  R *p  2  In the coarsening regime, precipitates that are larger than the average radius w i l l grow and those that are below w i l l dissolve. The corresponding average solute concentration is given b y replacing Q with CM i n Equation 6.29. Differentiating CM with respect to time, one gets  dC  _  M  1 - C eq  RpC  M  dt  R  2  C  -C  dR,  (6.32)  dt  Subsequently, the evolution equation for the number density o f precipitate is obtained b y differentiating the mass balance equation:  CM  l-^N R n  n  3  )= C --nN„R C P^p ^p 3  'P"P  n  138  (6.33)  Chap. 6 Modelling of Microstructure Evolution for Overag  and combining it with Equations 6.31 and 6.32 which leads to  dN  4 Ceq ( l ~ Ceq ) Rd^eff  r  dt  "(c -c f  coars  P  RQ  C  M { \ - C  P  M  )  (c -c )  R  Finally, under the  v  etl  P  K  M  conditions o f simultaneous  J~ P N  4nR  •3N  r  (6.34)  p  dissolution/growth and coarsening,  the  contribution from the respective processes to the overall precipitate distribution is weighted by a coarsening fraction, F [Deschamps and Brechet, 1999]: c  dR —E- = (I_F dt  dR  p  v  + F,  )—^  dt  0 1  V  dN  K  =  d/g  dN  f  dt  dt  dR  p  (6.35a)  p  dt  R  coars  (6.35b) coars  with (  •  F =\-erf c  K  A h  CM  r  -1  (6.36)  K eq J  where k = -0.1 i f Q > C c  M  and k = 0.1 i f C, < C . c  M  Equation 6.36 provides a smooth transition  from the dissolution/growth stage to the coarsening stage. Deschamps and Brechet (1999)  139  Chap. 6 Modelling of Microstructure Evolution for Overaged AA6111  have shown that the exact form o f the coarsening function is not critical to the overall coarsening kinetics as long as F  C  approaches 1 when the matrix solutes concentration  approaches the equilibrium condition, i.e., CM -> C EQ  6.6  Parameter Identification  A n inherent requirement in all microstructure modelling work is the need to identify a wide spectrum o f physical parameters. The values o f some o f the known parameters such as the Young and shear modulus are given i n the list o f symbols on page x i i . However, there are two material specific parameters which are required as model input, namely, the solubility product and molar volume for Q' precipitates. These two quantities are evaluated below.  6.6.1  Solubility Product for Q' Precipitates  A n important assumption in the precipitation model is that all particles are spherical with uniform thermodynamic properties and identical chemical composition. In addition, the model does not consider directly the complex precipitation sequence. A l l the pre-existing precipitates are assumed to be in Q' phase which has a H C P crystal structure with a fixed chemical composition o f A L j C ^ M g g S i y . The solubility product for the Q' phase within the aluminum rich corner o f the quaternary A l - M g - S i - C u phase diagram can be expressed as [Raeisinia, et al, 2004]:  ^eq  Si C;eq  Cu  C.eq  = K\ exp  AHo V  140  ,  (6.37)  Chap. 6 Modelling of Microstructure Evolution for Overa  where C^ , 8  solution,  and  are the equilibrium concentrations (in at. %) o f M g , C u and S i i n  respectively.  AHo is the standard  enthalpy  o f the reversible  Q' phase  dissolution/precipitation reaction (-495 kJ/mol) and Kj is a constant ( ~ 2 . 8 x l 0 ) . The nominal 28  solute concentration, Co i n A A 6 1 1 1 is given by the sum o f the nominal concentrations o f the elements i n the alloy, c{f , 8  6.6.2  CQ and C§'. U  Molar Volume of Q' Precipitates  The molar volume, V o f the Q' precipitates is obtained from the lattice parameters reported m  by Chakrabarti et al. (1998). F o r H C P crystal structure, the volume o f a unit cell, V is given c  by a c(sin!20°) 2  where a and c are the lattice parameters. U s i n g a = 1.04 n m and c = 0.405 nm,  the molar volume is computed as follows [Gladman, 1997]:  V =^J^ m  = \.09x\0- — 5  n  mol  (6.38)  where n is the number o f atoms per unit cell (n - 21).  6.7  Model Implementation  The overall model framework is constructed by connecting a series o f differential equations, as shown i n Fig. 6.1. The internal state variables that were used to link the various submodels are highlighted to emphasize the interaction between the various microstructural processes.  141  Chap. 6 Modelling of Microstructure Evolution for Overage  Precipitate Free Zones (I) Recovery I.  =  exp, -—  Subgrain growth I:  - j '  4  ^7(7)  M  Recrystallization I:  —  I  Precipitate Zones (II)  Subgrain growth II: —=f^ = A T » ' \dR, dt Precipitate radius: dR,  V-g  f  C  4 Cqjl-Cg)  27  $  r  P~ >  C  Cp-C f eq  - j f - O - S ) -dt  Precipitate density:  2R {t)j  Cu-C,  dt  Overall:  ^bjl(')  4 « r  27  Precipitation II  XyDtf  Recrystallization II:  *t dR„ dt  Cjl-CeylRoDtf  RQC {1-C^)\  3  M  !>  ^*  •  F"  —  E  Fp,R  P  Fig. 6.1. Schematic outline o f the overall model framework.  142  Chap. 6 Modelling of Microstructure Evolution for Overa  The numerical integration o f these equations is performed i n twelve stages using the RungeKutta method: at each calculation time step, the rate o f variation o f the five internal state variables (R , N , <j , S b and X) is calculated as a function o f the current value o f a l l p  p  rc  s  parameters. A mass balance is also carried out at each time step to evaluate the residual solute concentration i n the matrix. The outcome o f the integrations is then fed into the appropriate material response equations (Equations 6.2 to 6.6) to obtain the instantaneous flow stress and volume fraction o f recrystallized grains.  Before the model can be implemented, the conditions o f the as deformed material must be specified. In the precipitate zones, the respective contributions o f precipitates and dislocation to the as deformed yield stress were determined accordingly using Equations 6.5 and 6.6. The precipitate size at t = 0 is determined by assuming that after 7 days o f aging at 250 and 325°C, the precipitate conditions are reasonably close to the equilibrium conditions. In this case, the volume fractions o f precipitate i n the materials can be related to the residual solute concentrations (in atomic%) in the matrix according to [Raeisinia et al., 2006]:  C  Mg  = 0.9-0.35F  C =0.6-0.3lF Si  (6.39a) (6.39b)  p  C =0.3-0.09F Cu  p  p  (6.39c)  Equations 6.39a to 6.39c were derived using a mass balance between each solute i n the precipitate and i n the matrix and the stoichiometry o f the precipitate. The volume fraction o f precipitate at a given temperature is obtained b y inserting Equations 6.39 into the solubility 143  Chap. 6 Modelling of Microstructure Evolution for Overa  product o f Q' (Equation 6.37) determined as aged yield stress,  and solving for F . U s i n g F p  <J -aged, as  p  and the experimentally  the precipitate radius, R at t = 0 is estimated from p  Equation 6.6. Following that, the initial number density o f precipitates is given b y N = p  3F /4nR/. p  Table 6.3 compares the calculated precipitate radius after 7 days o f aging at 250  and 325°C with the measurements from T E M . It can be seen that the values o f calculated R  p  are reasonable considering that T E M measurements are regarded as only crude estimations o f the true values. It should be noted that no fitting parameter is used to obtain the calculated R . p  These results confirmed the validity o f using Equation 6.6 to calculate the precipitate contributions to flow stress.  6.8  Comparison with Experimental Results  The model is evaluated i n terms o f the time evolution o f yield stress and fraction recrystallized. First, the model is fitted to the experimental data (both softening and recrystallization curves) o f the O A samples b y adjusting the values o f seven parameters. These adjustable parameters are physically motivated and therefore are allowed to vary between a prescribed range, for instance, the activation energy for recovery is allowed to vary between 130-142 kJ/mol. The optimized values o f these parameters are listed i n Table 6.4. Table 6.5 lists other physical parameters which were fixed i n the model. These parameters were obtained either from literature or estimated from experimental data.  The quality o f the fit was determined by a least square iteration method b y minimizing the difference between the model output and the softening and recrystallization data o f the O A  144  Chap. 6 Modelling of Microstructure Evolution for Overa  Table 6.3. Comparison between calculated and measured R from T E M . p  Aging conditions  Calculated R  Measured (TEM) R  7 days at 250°C  8.6 nm  6.6 nm  7 days at 325°C  14.2 nm  17.5 nm  p  *Equivalent radius  145  p  Chap. 6 Modelling of Microstructure Evolution for Overag  Table 6.4. List o f adjustable parameters and their optimized values.  Model  Parameter  Value  Recovery  Effective pinning parameter, ct  9 x 10"  Recovery  Activation energy, Q  140 kJ/mol  Subgrain growth  L o w angle grain boundary mobility, MQ  5 x 10" m /N-s  Subgrain growth  Activation energy, Q  155kJ/mol  Precipitation  Diffusion coefficient, D  5.5 x 1 0 m / s  Recrystallization  Nucleation parameter, k  5 x 10"  Recrystallization  H i g h angle grain boundary mobility, M  p  0  SB  3  _5  0  2  8  1 x 10 m /N-s 2  0  146  6  2  3  Chap. 6 Modelling of Microstructure Evolution for Overag  Table 6.5. List o f physical parameters which are fixed i n the model.  Model  Parameter  Value  Source  Recovery  Activation volume, V  9b  Calculated (Equation. 6.9)  Subgrain growth  Critical misorientation angle, 0  15°  Humphreys and Hatherly, 1995  L o w angle grain boundary energy, y  0.16 J / m  3  C  Subgrain growth  Calculated (Equation. 6.11)  2  sb  Recrystallization  Activation energy, Q  200 kJ/mol  Vatne, 1995  Recrystallization  H i g h angle grain boundary energy, y  0.324 J / m  Murr, 1975  Recrystallization  Critical nuclei radius, R  0.5 p m  Precipitation  Interfacial energy, y  0.3 J / m  rex  2  gb  c  147  Estimated from T E M subgrain size  2  Deschamps and Brechet, 1999  Chap. 6 Modelling of Microstructure Evolution for Overa  samples. The results are shown i n Figs. 6.2a and 6.2b. In terms o f softening, it can be seen that good agreement between the model calculations and experimental data is obtained at the annealing temperatures o f 250 and 445°C. The slow down i n recovery rate at 250°C due to precipitate pinning indicated b y the plateau in the softening curve between ~ 1 0 to 10 seconds 2  4  is well captured b y the model. A t the annealing temperature o f 3 2 5 ° C , the model appears to have overestimated the decrease i n yield stress i n the later stage o f annealing. Deviation between model and experimental results is also observed i n the recrystallization curves i n Fig. 6.2b after ~5 x 10 seconds o f annealing. Nevertheless, the model gives good predictions i n 6  the initial stage o f annealing. The magnitude o f the activation energy for recovery, 140 kJ/mol, is fully i n the possible range o f solute diffusion i n aluminum (Table 6.2). But the activation energy for subgrain growth, 155 kJ/mol, is somewhat higher than the values given i n Table 6.2. The values o f the diffusion parameters utilized i n the precipitation model, i.e., D - 5.5 x 0  10" J / m and QD - 142 k/mol are reasonably close to the values for the self diffusion o f 5  2  aluminum reported i n the literature. The magnitude o f the effective pinning parameter is small indicating that only a small fraction o f the precipitates are available to p i n dislocations during recovery.  Further validation o f the model is carried out by applying the model to predict the softening curves o f the S O A samples using the same set o f parameters listed i n Table 6.4. The results are shown i n Figs. 6.3a and 6.3b. It is obvious that the model is capable o f predicting the softening curves at 325°C accurately. However, at the higher annealing temperature o f 445°C, the model predictions are less satisfactory, especially i n the early stage o f annealing.  148  Chap. 6 Modelling of Microstructure Evolution for Overa  250  200 H 03  CL  150 H CO CO  CO T3 g> >-  100  10-  3  10"  2  10"  1  10°  10  10  1  2  10  3  10  4  10  10  5  6  10  7  10  8  10  9  T i m e (s)  10  1  10  2  10  3  10  4  10  5  10  6  10  7  10  8  Time (s)  Fig. 6.2. Comparison between model calculated and experimental (a) softening and (b) recrystallization curves for 40% cold rolled overaged A A 6 1 1 1 during isothermal annealing at 325 and 445°C. 149  Chap. 6 Modelling of Microstructure Evolution for Overag  Time (s) Fig. 6.3. Comparison between predicted and experimental (a) softening and (b) recrystallization kinetics for 40% cold rolled severely overaged A A 6 1 1 1 during isothermal annealing at 325 and 4 4 5 ° C . 150  Chap. 6 Modelling of Microstructure Evolution for Overa  It is believed that the rapid transformation o f Q' precipitates to the relatively coarse Mg2Si particles may have contributed the initial drop i n yield stress i n the S O A samples which is not accounted for i n the present model. This postulation is reasonable because significant number of Mg2Si particles were detected i n the S O A samples even before annealing (see Fig. 5.6b). It is also possible that the recrystallization rate is enhanced due to the presence o f these particles which are not effective i n pinning grain boundaries.  6.9  Discussion of Modelling Results  The most significant aspect o f the present model is that it is capable o f translating a qualitative description o f the interaction between recovery, recrystallization, subgrain growth and precipitation into a quantitative prediction i n terms o f softening i n yield stress vs. time relationships. In the ensuing discussion, the isothermal annealing behaviour o f the overaged samples at 325°C as predicted by the model is used as an example to illustrate the efficacy o f the present model.  6.9.1  Interaction between Recovery and Precipitation  In Fig. 6.4, the contributions from recovery, <j and precipitates, <T to the overall yield stress rc  P  is plotted as a function o f annealing time. Initially, recovery proceeds at a rate given by Equation 6.8b with little interference from the precipitates. A s recovery proceeds, the number o f dislocation nodes, Ndt decreases and consequently the rate o f recovery is gradually reduced s  151  Chap. 6 Modelling of Microstructure Evolution for Overa  200  150  Precipitate coarsening  H  CO Q_  CO  S 100 (/) T3  Recovery  0)  50  H  0  i  10-  2  10-  1  10°  r  10  1  10  2  10  3  10  4  10  5  10  6  10  7  Time (s) Fig. 6.4. Softening due to recovery and precipitate coarsening in the precipitate zones o f 40% cold rolled overaged A A 6 1 1 1 isothermally annealed at 325°C.  152  Chap. 6 Modelling of Microstructure Evolution for Overag  by the pinning term in Equation 6.8b. Recovery is completely halted when the number o f dislocation nodes is equal to about 10% (a ~ 0.09) o f the total number o f precipitates. This p  occurs at about 100 seconds into annealing at 325°C which corresponds very well with the T E M observations shown i n Fig. 5.31. Complete retardation o f the recovery process continues until the onset o f precipitate coarsening. In the precipitate coarsening regime, recovery proceeds at a rate dictated by the precipitate coarsening process. Hence, in the intermediate stage o f annealing the overall softening o f the material i n the precipitate zones represents a convoluted effect o f recovery and precipitate coarsening.  The evolution o f precipitate radius with annealing time is shown i n Fig. 6.5a for the annealing temperatures o f 325 and 445°C. It can be seen that precipitate dissolution causes the average radius to decrease initially. The dissolution process is promoted by the increase in solubility during annealing since both the annealing temperatures are higher than the prior aging temperature o f 250°C. Obviously, the effect o f dissolution is more apparent at 445°C due to higher solubility. Nonetheless, i n both cases precipitate coarsening quickly takes over as annealing progresses. The corresponding evolution o f matrix solute concentrations and volume fraction o f precipitates are shown in Fig. 6.5b for the annealing temperature o f 325°C. The onset o f precipitate coarsening can be identified b y following the change in the matrix solute concentration as indicated in Fig. 6.5b. The initial small increase i n solute concentration and a corresponding minute decrease in the precipitate volume fraction is the consequence o f precipitate dissolution.  153  Chap. 6 Modelling of Microstructure Evolution for Overag  12  / /  11  / /' i  co ,3  i  2 <i)  9  I  8  03  /325°C  i i i-  =TZZ  /  CD  \ . ^ . . ^ . / 445°C 7 6 101  2  10-1  1 Q  0  1 Q  102  1  1 Q  3  1 0  4  1 Q  5  Time (s) 1.0  0.05  0.8  Coarsening  0.04  Dissolution o  0.6 -  0.03  0.4 -  0.02  E o  0.2  h 0.01  'M Annealing Temp. = 325°C  0.0 -I 10"  1  . 10°  . 10  1  . 10  2  , 10  3  1 10  4  . 10  , s  10  6  1- 0.00 10 7  Time (s)  Fig. 6.5. (a) Evolution o f precipitate radius during isothermal annealing o f 40% cold rolled overaged A A 6 1 1 1 at 325 and 445°C and (b) corresponding evolution o f concentration and precipitate volume fraction at 325°C.  154  Chap. 6 Modelling of Microstructure Evolution for Overa  6.9.2  Interaction between Recovery, Precipitation and Recrystallization  Both recovery and subgrain growth reduces the driving pressure for high angle grain boundaries during recrystallization according to Equation 6.25. O n the other hand, precipitate coarsening leads to lower pinning pressure thus promotes recrystallization. The best way to illustrate this delicate balance o f pressure at the recrystallization front is to plot the stored energy per unit volume vs. the Zener retarding pressure. This is shown i n Fig. 6.6. It can be seen that in the early stage o f annealing, the dislocation density i n the deformed microstructure is quickly consumed b y the recovery process which leads to the initial drop i n stored energy. A s annealing time increases, the decrease i n stored energy slows down which corresponds to the pinning o f dislocations by precipitates. However, it can be observed that the Zener pressure quickly diminishes as precipitates coarsen thus allowing the driving pressure to overcome the pinning pressure. Upon further annealing, precipitate coarsening accelerates and releases the subgrain structure. The combination o f subgrain growth and recrystallization cause the stored energy i n the microstructure to rapidly decrease i n the later stage o f annealing. In essence, the development o f recrystallized microstructure is the consequence o f complex interplays between various microstructure phenomena.  6.9.3  Composite Microstructure  A novel feature o f the present model is the description o f the deformed microstructure as a composite model composed, o f a mixture o f precipitate and precipitate free zones. This assumption provides some interesting implications i n the description o f microstructure evolution during annealing. The most important one being that different parts o f the 155  Chap. 6 Modelling of Microstructure Evolution for Overa  1.2  10-1  1  0  o  1 0  1  10  2  10  3  10  4  10  5  10  6  10  7  10  8  Time (s) Fig. 6.6. Plots showing the time evolution o f Zener pinning pressure vs. the stored energy in the precipitate zones o f 40% cold rolled overaged A6111 annealed at 325°C.  156  Chap. 6 Modelling of Microstructure Evolution for Overa  microstructure w i l l assume different recovery and recrystallization rates during annealing. For instance, the recovery rate is expected to be faster i n the precipitate free zones due to the absence o f the pinning term (Equations 6.8a), leading to variation i n stored energy for recrystallization i n different parts o f the microstructure. This behaviour is illustrated in Figs. 6.7a and 6.7b where the softening and recrystallization kinetics o f the precipitate free zones are compared to those i n the precipitate zones. It is obvious that deformed grains that are located i n the precipitate free zones recover and recrystallize faster than the deformed grains i n the precipitate zones. This type o f inhomogeneous recovery and recrystallization behaviour is a commonly observed behaviour i n many industrial alloys [Vandermeer and Gordon, 1962, Furu et al., 1990, Humphreys and Hatherly, 1995, Vandermeer, 2001]. However, this behaviour is often neglected i n many previous work on the modelling o f recovery and recrystallization [Humphreys and Hatherly, 1995]. The present model provides a physical basis  to relate  the effect  o f non-uniform spatial distribution o f precipitates  to the  heterogeneous recovery and recrystallization behaviour o f cold deformed alloys.  6.10  Summary and Limitations of the Model  It is important to recognize that the current modelling approach represents an attempt to describe a highly complex microstructure based on some greatly simplified assumptions. Having said that, the model is capable o f addressing the challenge to quantitatively link the response o f the material in terms o f mechanical properties to the various microstructural changes that occur during isothermal annealing. The novel feature o f the present modelling approach lies i n its ability to explicitly take into account the spatial distribution o f precipitate on recovery and recrystallization kinetics. The interaction between the various microstructure 157  Chap. 6 Modelling of Microstructure Evolution for Overa  1  ~  1  10"  2  1  10"  1  10°  1  10  1 1  10  1 2  10  1 3  10  1 4  10  1 5  10  1 6  10  7  1 10  8  Time (s)  Time (s)  Fig. 6.7. Comparison o f (a) softening kinetics and (b) recrystallization kinetics in the precipitate and precipitate free zones during the isothermal annealing o f 40% cold rolled overaged A A 6 1 1 1 a t 3 2 5 ° C .  Chap. 6 Modelling of Microstructure Evolution for Overag  phenomena are considered based on physically sound principles and all the parameters utilized in the model have transparent physical meaning. The model framework which is constructed based on the internal state variable approach is versatile i n a sense that additional microstructure phenomena, for example, grain growth, can be easily integrated, thus allowing the model to be easily adopted to other alloy system. Throughout the modelling exercise, attempts were made to keep the number o f adjustable parameters to the minimum and eliminate any unknown parameters. However, in order to apply the model to a specific alloy system, experimental softening curves are required to calibrate the model i n order to verify the magnitudes o f the adjustable parameters listed in Table 6.4. T w o parameters which are expected to be highly alloy dependent are the effective pinning parameter, a in the recovery model and the  nucleation parameter, k, in the  recrystallization model. Furthermore,  microstructure analysis needs to be carried out to estimate the volume fraction o f precipitate free zones i n the deformed microstructure.  Te model suffers three main limitations:  1. Since the precipitation model considers only one type o f precipitate, i.e., the Q' phase, the model loses its validity at high annealing temperatures or after prolonged annealing time i f significant number o f the Q' precipitates is transformed into the Mg2Si phase. 2. The yield stress model does not take into account the effect o f subgrain size. It is assumed that the annealing out o f dislocations in the deformed microstructure controls the recovery softening during annealing.  159  Chap. 6 Modelling of Microstructure Evolution for Overag  The recrystallization model  lacks a detailed nucleation  model. Nucleation o f  recrystallized grains is simply assumed to be site saturated and nucleation sites are limited to deformed grain boundary area and Fe-containing intermetallic particles.  160  Chapter 7  Summary and Conclusions  The present work investigates the evolution o f microstructure during the annealing o f cold rolled precipitation hardened aluminum alloys. Through a combination o f experimental and modeling approaches, the interaction between recovery, subgrain growth, recrystallization and precipitation and their effect on the mechanical properties o f the materials were studied in detail. Experimentally, the isothermal recrystallization behaviour o f 40% cold rolled aluminum alloy A A 6 1 1 1 was examined as a function o f the precipitate conditions in the deformed state. A total o f four prior aging conditions were included in the study: naturally aged (T4), peak aged ( P A ) , overaged ( O A ) and severely overaged ( S O A ) . The material response to annealing heat treatment in the temperature range o f 2 5 0 - 4 4 5 ° C was quantified by following the softening i n yield stress and the evolution o f volume fraction o f recrystallized grains with annealing time. Experimental results obtained at the annealing temperature o f 325°C indicate that the recrystallization kinetics were extremely sluggish irrespective o f the starting precipitation state, the slowest being the overaged samples. The T4  and  PA  samples  displayed  similar behaviour  during  annealing.  The  fastest  recrystallization rates were observed in the S O A samples. U s i n g a combination o f S E M and E B S D techniques, it was shown that the development o f recrystallized microstructure i n the overaged samples can be directly correlated to the heterogeneous spatial distribution o f precipitates in the deformed structure. Significant subgrain growth was observed prior to the onset o f recrystallization. In all cases, the combined effect o f recovery and precipitate  161  Chap. 7 Summary and Conclusions  coarsening were found to be responsible for the majority o f the softening experienced by the samples during annealing. Increasing the annealing temperature to 4 4 5 ° C significantly enhances both the softening and recrystallization kinetics i n the O A and S O A samples. A t 250°C, no recrystallization was observed in the overaged samples.  Based on the knowledge gained i n the experimental work, a comprehensive microstructure model was developed for the annealing o f overaged alloys. The model which draws on the concept o f internal state variables adopts a simple rule o f mixtures to divide the microstructure into two parts: precipitate and precipitate free zones. This distinguish approach allows the model to describe the inhomogeneous recovery and recrystallization behaviour i n the materials i n a physical way. The overall model framework is constructed by coupling a series o f submodels for recovery, subgrain growth, precipitate coarsening and recrystallization. The development o f submodels relies on those already established i n the literature. The linkages between various submodels are provided b y following the evolution of internal state variables representing the respective microstructure phenomena, namely, dislocation density, subgrain size, precipitate size and density and volume fraction o f recrystallized grains. It has been demonstrated that the model provides a unique tool to translate a qualitative description o f the interaction between recovery, recrystallization, subgrain growth and precipitation into a quantitative prediction i n terms o f softening i n yield stress vs. time relationships. The model has been shown to be accurate i n describing the softening and microstructure evolution during the annealing o f 4 0 % cold rolled overaged and severely overaged A A 6 1 1 1 . Less satisfactory results were obtained i f  162;  Chap. 7 Summary and Conclusions  significant precipitate phase transformations occur during annealing since the model only considers one type o f precipitates. This remains one o f the limitations o f the model.  Lastly, the most significant contributions o f the present work are summarized i n the following:  •  The experimental data gathered i n the present study represents the first generation o f recovery and recrystallization data for cold rolled A A 6 1 1 1 with a wide range o f precipitate conditions.  •  The microstructure model developed in the present work represents a novel approach to relate directly the effect o f inhomogeneous spatial distribution o f precipitates to the recovery and recrystallization processes.  •  For the first time, quantitative descriptions o f the interaction between recovery, subgrain growth, precipitation and recrystallization are considered explicitly within a single model framework for cold rolled A A 6 1 1 1 .  In conclusion, the present model can be seen as an important step towards the development of a comprehensive through process model for the industrial production o f precipitation hardenable alloys. The model framework is not limited to aluminum alloys. In principle, it can be applied to other alloy systems as well. Further advancement o f the model can be achieved i n future work and these are discussed i n the next section.  163  Chap. 7 Summary and Conclusions  7.1  Future Work  The following future work is proposed:  •  A natural extension o f the present model is to extend the precipitation model to take into account the entire sequence o f precipitation, i.e., nucleation, growth and coarsening o f precipitates. This w i l l greatly expand the applicability o f the model to cold rolled alloys with varied precipitate conditions. The model is currently limited to overaged alloys.  •  Another development o f the present model which could be considered is to couple the microstructure model with a work hardening model w h i c h w i l l provide the deformed conditions o f the materials. This w i l l significantly expand the model capability to study the effect o f prestrain on the interaction between recovery, precipitation and recrystallization. The model is, i n its present state, limited to 40% cold rolled materials.  •  The applicability o f the model can be further expanded to study the effect o f nonisothermal heat treatments on the interacting phenomena. These situations  are  extremely common i n the industrial processing o f sheet alloys. Mathematically, the model which consists o f a series o f differential equations can be readily integrated over the thermal histories o f the alloys. However, this should be carried out i n a pragmatic manner i n which a minimum number o f adjustable parameters is sought.  164  REFERENCES Abad, R., Fernandez, A . I., Lopez, D . and Rodriguez-Ibabe, J. M . (2001), ISIJInt., 41, 13731382. Avrami, M . (1940), J. Chem. Phys., 8, 212-224. Barioz, C , Brechet, Y . , Legresy, J. M . , Cheynet, M . C , Courbon, J., Guyot, P. and Ratnaud, G . M . (1992), i n Proc. 3 Int. Conf. On Aluminum Alloys, eds. Arnberg et al. Trondheim. 347354. rd  Bay, B . and Hansen, N . (1979), Metall. Trans., A 1 0 , 279-288. Brechet, Y . J. M . and Purdy, G . R . (2003), Can. Metall. Quarterly, 42, 121-124. Bryant, J. D . (1999), Metall. Mater. Trans. A, (1999), 3 0 A , 1999-2006. Burachynsky, V . and Cahoon, J. R . (1997), Metall. Mater. Trans. A, 2 8 A , 563-582. Burger, G . B . , Gupta, A . K . , Jeffrey, P. W . and L l o y d , D . J. (1995), Mater. Characterization, 35, 25-39. Burger, G . B . , Gupta, A . K . , Sutak, L . and L l o y d , D . J. (1996), Mat. Sci. Forum, 217-222, 471-478. Cahn, J. W . (1962), Acta Metall, 10, 789-798. Cahn, R . W . (1996), i n Physical Metallurgy, eds. Cahn and Haasen, North-Holland, N e w York, N Y , 2440-2448. Chakrabarti, D . J., Cheong, B . and Laughlin, D . E . (1998), i n Automotive Alloys II, ed. Das, S. K . , T M S , 27-44. Chakrabarti, D . J. and Laughlin, D . E . (2004), Prog, in Mat. Sci., 49, 389-410. Chen, S. P., Hanlon, D . N . , Pei, Y . T. and Dehosson, H . T h . M . (2002), J. of Mat. Sci., 37, 989-995. Chen, S. P., Todd, I. and V a n der Zwaag, S. (2002), Metall. Mater. Trans. A, 3 3 A , 529-537. Cheng, L . M . , Hawbolt, E . B . and Meadowcroft, T. R . (2000), Metall. Mater. Trans. A, 31 A . 1907-1916. Cheng, L . M . , Poole, W . J., Embury, J. D . and L l o y d , D . J. (2003), Metall. Mater. Trans. A, 34A, 2473-2481.  165  Deschamps, A . and Brechet, Y . (1999), Acta Mater., 47, 293-305. Doherty, R. D . , Hughes, D . A . , Humphreys, F. J., Jonas, J. J., Jensen D . J., Kassner, M . E . , K i n g , W . E . , M c N e l l e y , T. R., McQueen, H . J. and Rollett, A . D . (1997), Mat. Sci. Eng. A, 238, 219-274. Dutta, B . , Palmiere, E . J . and Sellars, C . M . (2001), Acta Mater., 49, 785-794. Esmaeili, S. (2002), P h D Thesis, University o f British Columbia, Vancouver, Canada. Esmaeili, S., Wang, X . , L l o y d , D . J. and Poole, W . J. (2003a), Metall. Mater. Trans. A., 34A, 751-763. Esmaeili, S., L l o y d , D . J . and Poole, W . J. (2003b), Acta Mater., 5J_, 2243-2257. Friedel, J. (1964), Dislocations, Pergamon Press, U K . Fujikawa, S., Hirano, K . and Fukushima, Y . (1978), Metall. Trans. A, 9 A , 1811-1815. Fujikawa, S. and Hirano, K . (1989), Def. Diffus. Forum, 66-69, 447-452. Furu, T., Marthinsen, K . and Nes, E . (1990), Mat. Sci. and Technol, 6, 1093-1102. Furu, T., 0rsund, R . and Nes, E . (1995), Acta Mater., 43, 2209-2232. Furu, T., Shercliff, H . R., Baxter, G . J. and Sellars, C . M . (1999), Acta Mater., 47, 2377-2389. Gladman, T. (1997), The Physical Metallurgy of Microalloyed Steels, The Institute o f Materials, London, U K . Go, J., Poole, W . J., Militzer, M . and W e l l , M . A . (2001a), Unpublished work on AA6111, N S E R C Strategic Grant Project N o . 101772, University o f British Columbia, Vancouver, Canada. Go, J., Militzer, M . , Wells, M . A . and Poole, W . J. (2001b), i n Proc. of the I ' Int. Conf. on Recrystallization and Grain Growth, eds. Gottstein and M o l o d o v , R W T H Aachen, Germany, 995-1000. s  Go, J., Poole, W . J., Militzer, M . and Wells, M . A . (2003), Mat. Sci. Technol., 19, 1361-1368. Gomez-Ramirez, R . and Pound, G . M . (1973), Metall. Trans., 4, 1563-1570. Gordon, P. and Vandermeer, R . (1966), in Recrystallization, Grain Growth and Textures, A S M , Metals Park, Ohio, 205-266. Grong, O and Shercliff, H . R . (2000), Prog, in Mat. Sci., 47,163-282.  166  Hansen, S. S., Vander Sande, J. B . and Cohen, M . (1980), Metall. Trans. A, 11 A . 387-402. Huang, Y . and Humphreys F. J. (1999), Acta Mater., 47, 2259-2268. Humphreys, F . J. (1977), Acta Metall, 25, 1323-1344. Humphreys, F . J. and Hatherly, M . (1995), Recrystallization and Related Annealing Phenomena, 1 edition, Pergamon Press, U K . st  Humphreys, F. J . (1997), Acta Mater., 45, 4231-4240. Humphreys, F . J. (1999), Mat. Sci. Technol, 15, 37-44. Humphreys, F . J. (2001), J. Mat. Sci., 36, 3833-3854. Inagaki, H . and Komatsubara, T. (2000), Mat. Sci. Forum, 331-337. 1303-1308. Johnson, W . A . and M e h l , R. F . (1939), AIME Trans., 135, 416-442. Jonas, J. J. and Weiss, I. (1979), Met. Sci., 13, 238-245. Kang, K . B . , K w o n , O., Lee, W . B . and Park, C . G . (1997), Scrip. Mater., 36, 1303-1308. K o i z u m i , M . , Kohara, S. and Inagaki, H . (2000), Z. Metallkd., 91, 460-467. Kolmogorov, A . N . (1937), Izv. Akad. Nauk. USSR. Ser. Mathmat., 1, 335. Kuhlmann-Wilsdorf, D . (2000), Mat. Sci. Forum, 331-337. 689-702. K w o n , O. and DeArdo, A . J . (1991), Acta Metall. Mater., 39, 529-538. Lee, K . (1999), Scrip. Mater., 40, 837-843. Leslie, W . C , Michalak, J . T. and A u l , F. W . (1961), i n Proc. Conf. on Iron and its Dilute Solution, eds. Spencer and Werner, John W i l e y and Sons, N e w Y o r k , 119-216. Lifshitz, I. M . and Slyozov, V . V . (1961), J. of Phys. Chem. Solids, 19, 35-50. Lillywhite, S. J., Pragnell, P. B . and Humphreys F. J. (2000), Mat. Sci. Technol, 16,11121120. L i u , C , Burghardt, J.C., Jacobs, T. H . and Scheffer, J. J. F . (1996), i n Proc. 37 MWSP Conf, vol. X X X I I I , ISS, Warrendale, P A . th  L l o y d , D . J . (1980), Metall. Trans. A, UA, 1287-1294.  167  L l o y d , D . J. (1985), i n Microstructural Control in Aluminum Alloys: Deformation, Recovery and Recrystallization, eds. C h i a and McQueen, The Metallurgical Society o f A I M E , N e w York, 45-66. Lloyd, D . J., Evans, D . R . and Gupta, G . K . (2000), Can. Met. Quarterly, 39, 475-482. Lotter, U . , Miischenborn W . and Thieman, E . (1980), i n Recrystallization and Grain Growth of Multiphase and Particle Containing Materials, eds. Hansen et al., Ris0 National Laboratory, Roskilde, Denmark, 133-138. Liicke, K . and Detert, K . (1957), Acta Metall, 5, 628-637. Manohar, P. A . , Ferry, M . and Chandra, T. (1998), ISIJInt., 38, 913-924. Martin, J . W . , Doherty, R . D . and Cantor, B . (1997), Stability of Microstructure in Metallic Systems, Cambridge University Press, U K . Medina, S. F., Quispe, A . , Valles, P. and Bahos, J. L . (1999), ISIJInt., 39, 913-922. M i a o , W . F . and Laughlin D . E . (2000), Metall. Mater. Trans. A, 3 1 A , 361-371. Mondolfo, L . F . (1979), Aluminum Alloys: Structure and Properties, Butterworth, London. Mukunthan, K . and Hawbolt, E . B . (1996), Metall. Mater. Trans. A. 2 7 A , 3410-3423. Murr, L . E . (1975), Interfacial Phenomena in Metals and Alloys, Addison-Wesley, Reading, M A , 131. Murayama, M . , Hono, K . , M i a o , W . F . and Laughlin D . E . (2001), Metall. Mater. Trans. A, 32A, 239-246. Myhr, O. R . and Grong, 0 . (2000), Acta Mater., 48, 1605-1615. Myhr, O. R . and Grong, 0 . and Andersen, A . J. (2001), Acta Mater., 49, 65-75. Nes, E . , Ryum, N . and Hunderi, O . (1985), Acta Metall, 33, 11-22. Nes, E . (1995), Acta Metall Mater., 43, 2189-2207. Nes, E . and Saeter, J. A . (1995), in Proc. of the 16 Ris0 Int. Symposium on Mat. Sci.: Microstructural and Crystallographic Aspects of Recrystallization, eds. Hansen et al, Ris0 National Laboratory, Denmark, 169-192. th  Orsetti-Rossi, P. L . and Sellars, C . M . (1997), Acta Mater., 45, 137-148. Orsetti-Rossi, P. L . and Sellars, C . M . (1999), Mat. Sci. Technol, 15, 185-192.  168  0rsund, R. and Nes, E . (1989), Scripta Metall, 23, 1187. Perovic, A . , Perovic, D . D . , Weatherly, G . C . and L l o y d , D . J . (1999), Scripta Mater., 41, 703708. Poole, W . J., L l o y d , D . J. and Embury, J . D . (1997), Mat. Sci. and Eng., A234-236, 306-309. Quainoo, G . K . , Yannacopoulos, S. and Gupta, A . K . (2001), Can. Metall. Quarterly, 40, 211220. Raeisinia, B . , Poole, W . J . and Lloyd, D . J. (2006), Mat. Sci. Eng. A, 420, 245-249. Ray, R. K . , Hutchinson, W . B . and Duggan, B . J. (1975), Acta Metall, 23, 831-840. Richmond, O . (1986), J. of Met., 38, 16-18. Rios, P. R . (1997), Metall. Mater. Trans. A, 2 8 A , 939-946. Sellars, M . C . (1997), i n Thermec '97, eds. Chandra et al., T M S , Warrendale, 3-11. Sevillano, J. G . (1993), in Mat. Sci. and Technol, A Comprehensive Treatment, eds. Cahn et al., V C H , Weinheim, 6, 19-88. Smithells, C . J. and Brandes, E . A . (1976), Metals Reference Handbook, 5 edition, Butterworth, London. t h  Stanley, J. K . (1963), Electrical and Magnetic Properties of Metals, A S M , Metals Park, Ohio. Suehiro, M . , L i u , Z . K . and Argen, J. (1998), Metall. Mater. Trans. A, 29A, 1029-1034. Taylor, G . I. (1934), Proc. Royal. Soc. A, 145, 362. Tian, B . (2003), Mat. Sci. Eng., A360, 330-338. Vandermeer, R . A . and Gordon, P. (1962), in Recovery and Recrystallization of Metals, ed. Himmel, L . , Interscience, N Y , 221-240. Vandermeer, R. A . and Rath, B . B . (1989), Metall. Trans. A, 2 0 A , 391-401. Vandermeer, R . A . (2001), i n Recrystallization and Grain Growth: Proc. of the First Joint Int. Conf, eds. Gottstein et al., Aachen, Germany, 645-657. Vatne, H . E . (1995), P h D Thesis, The Norwegian Inst, o f Technol., Trondheim, Norway. Vatne, H . E . , Furu, T., 0rsund, R . and Nes, E . (1996), Acta Mater., 44, 4463-4473.  169  Verdier, M . , Saeter, J. A . , Janecek, M . , Brechet, Y . , Guyot, P., D u l y , D . and Nes, E . (1996), Mat. Sci. Forum, 217-222, 435-440. Verdier, M . , Groma, I., Flandin, L . , Lendvai, J., Brechet, Y . and Guyot, P. (1997a), Scripta Mater., 37, 449-454. Verdier, M . , Bley, F., Janecek, Livet, F., Simon, J. P. and Brechet, Y . (1997b), Mat. Sci. Eng., A234-236, 258-262. Verdier, M . , Janecek, M . , Brechet, Y . and Guyot, P. (1998), Mat. Sci. Eng., A 2 4 8 , 187-197. Verdier, M . , Brechet, Y . and Guyot, P. (1999), Acta Mater. 47, 127-134. Wagner, C . (1961), Z. Electrochem., 65, 581-591. Wang, X . and Embury, J. D . (2002), Unpublished TEM work on AA6111, McMaster University, Hamilton, Canada. Wang, X . , Poole, W . J . , Esmaeili, S., L l o y d , D . J . and Embury, J . D . (2003), Metall. Mater. Trans. A. 3 4 A , 2913-2924. Weatherly, G . C , Perovic, A , Mukhopadhyay, N . K . , L l o y d , D . J. and Perovic, D . D . (2001), Metall. Mater. Trans. A, 3 2 A , 213-218. Wells, M . , L l o y d , D . J., Samarasekera, I. V . , Brimacombe, J . K . and Hawbolt, E . B . (1998), Metall. Mater. Trans. B, 2 9 B , 709-719. Wilshynsky-Dresler, D . O., Krauss, G . and Matlock, D . K . (1992), in Developments in the Annealing of Sheet Metals., eds. Pradhan and Gupta, T M S , Warrendale, P A , 189-218. Zurob, H . S., Hutchinson, C . R . , Brechet, Y . and Purdy, G . (2002), Acta Mater., 50, 30753092. Zurob, H . S., Hutchinson, C . R., Brechet, Y . and Purdy, G . (2003a), i n Austenite Formation and Decomposition, eds. D a m m and Merwin, T M S , Warrendale, P A , 121-138. Zurob, H . S. (2003b), P h D Thesis, McMaster University, Hamilton, Canada.  170  

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0078561/manifest

Comment

Related Items