UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Annealing behaviour of cold deformed AA3003 aluminum alloys Babaghorbani, Payman 2015

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

Item Metadata

Download

Media
24-ubc_2015_november_babaghorbani_payman.pdf [ 4.84MB ]
Metadata
JSON: 24-1.0166650.json
JSON-LD: 24-1.0166650-ld.json
RDF/XML (Pretty): 24-1.0166650-rdf.xml
RDF/JSON: 24-1.0166650-rdf.json
Turtle: 24-1.0166650-turtle.txt
N-Triples: 24-1.0166650-rdf-ntriples.txt
Original Record: 24-1.0166650-source.json
Full Text
24-1.0166650-fulltext.txt
Citation
24-1.0166650.ris

Full Text

ANNEALING BEHAVIOUR OF COLD DEFORMED AA3003 BASED ALUMINUM ALLOYS  by  PAYMAN BABAGHORBANI  M.Sc., National University of Singapore, Singapore, 2008 B.Sc. University of Tehran, Iran, 2006   A THESIS SUBMITTED IN PARTIAL FULFILLMENT  OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (MATERIALS ENGINEERING)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  August 2015  © Payman Babaghorbani, 2015    ii  Abstract AA3xxx series aluminum alloys which are used in automotive heat exchangers usually experience a complicated thermomechanical history with a number of processing steps including homogenization, extrusion, cold deformation and then annealing. The cold deformation can involve a wide range of strains, for example, a few percent strain for micro-multiport tubing and large strains for tube drawing. Often the parts are annealed either as a separate processing step or in conjunction with the brazing operation. Results from industry suggest that a wide range of microstructures can be observed after brazing, ranging from coarse multi-crystals to fine grained polycrystalline microstructures. As such, annealing behaviour of cold deformed AA3003 based alloys after extrusion was investigated in this work. Experimental work was conducted on two alloys homogenized prior to extrusion: 3003 (0.54 wt% Fe) and low Fe 3003 (0.09 wt% Fe). A variety of homogenization heat treatments were examined in order to produce the starting materials. Microstructure, yield stress, work hardening and recrystallization behavior of these alloys with different initial microstructures were investigated. A wide range of pre-strain (1-80%) was applied at room temperature using tensile test and rolling. Although most of the annealing treatments were done at 600 °C, samples with pre-strains larger than 0.1 were also annealed at 350-600 °C to study the effect of temperature on microstructure evolution. The minimum strain required to initiate recrystallization was    iii  experimentally measured for each condition using tapered samples. As expected, it was found that dispersoids significantly inhibit recrystallization process and can change the critical strain for recrystallization as high as 18%. In addition, contribution from different strengthening mechanisms on the yield stress and work hardening behaviour was calculated and then a model was developed to describe the stress-strain response. The model represents experimental data within ±10% for both yield stress and UTS over a wide range of conditions. Consequently, a physically based model was developed for the critical strain required to initiate recrystallization. This is the first attempt, to the author’s best knowledge, to model critical strain in a system with distribution of fine and relatively large precipitates.           iv  Preface This dissertation is original and some work has been published [P. Babaghorbani, W.J. Poole, M.A. Wells and N.C. Parson, ICAA13, Pittsburgh, Pennsylvania, USA (2012) and P. Babaghorbani, W.J. Poole, M.A. Wells and N.C. Parson, ICAA12, Yokohama, Japan (2010)]. Starting materials used in this study were provided by RTA R&D and extrusion trials were done by Dr. Nick Parson at RTA R&D in Jonquiere, Quebec. The experimental and modelling work presented in this thesis has been carried out in the Department of Materials Engineering at the University of British Columbia (Vancouver). This includes all the experimental design, sample preparation, deformation, heat treatment and microstructural characterization. All the experimental and modelling work of this work is done by the author, Payman Babaghorbani, except: (i) transmission electron microscopy work on dispersoids of AA3003 samples was performed by Dr. Reza Roumina at UBC and (ii) characterization of constituent particles in AA3003 samples was carried out by Yuanyuan Geng at UBC.     v  Table of Contents Abstract ............................................................................................... ii Preface ................................................................................................iv Table of Contents .................................................................................. v List of Tables ........................................................................................ix List of Figures .......................................................................................xi List of Symbols .................................................................................. xvii Acknowledgments ............................................................................... xix CHAPTER 1   Introduction ..................................................................... 1 CHAPTER 2   Literature Review .............................................................. 5 2.1   Industrial Processing and Microstructure of 3xxx Alloys ..................... 6 2.1.1 Casting .............................................................................................. 7 2.1.2 Homogenization .................................................................................. 8 2.1.3 Extrusion ......................................................................................... 10 2.1.4 Post Extrusion Deformation and Heat Treatment .................................... 10 2.2 Yield Strength of 3xxx Alloys ........................................................ 11 2.2.1 Solid Solution Strengthening ............................................................... 11 2.2.2 Grain Size Strengthening .................................................................... 13 2.2.3 Precipitation Strengthening ................................................................. 14 2.2.4 Strengthening from Large Second Phase Particles .................................... 16 2.2.5 Superposition of Strengthening Components ........................................... 17    vi  2.3  Macroscopic Work Hardening Bahaviour ........................................ 18 2.4  The Deformed State ................................................................... 25 2.4.1   Microstructural Features ................................................................... 25 2.4.2   Stored Energy of Cold Work ............................................................... 26 2.5  Recovery after Deformation ......................................................... 30 2.5.1   General Observations ........................................................................ 30 2.5.2   The Extent of Recovery...................................................................... 32 2.6   Recrystallization ....................................................................... 33 2.6.1   General Observations ........................................................................ 33 2.6.2   Recrystallization Nucleation .............................................................. 34 2.6.3   Critical Plastic Strain ........................................................................ 37 2.7    Effect of Particles on Grain Boundary Movement ............................ 38 CHAPTER 3   Research Scope and Objectives ............................................ 41 CHAPTER 4   Methodology ................................................................... 43 4.1   Materials and Homogenization .................................................... 43 4.2   Sample Preparation ................................................................... 45 4.3  Metallography .......................................................................... 45 4.4  Deformation............................................................................. 47 4.5 Post Deformation Heat Treatments ................................................ 50 4.6 Sample Characterization .............................................................. 51 4.6.1 Optical Microscopy ............................................................................ 51 4.6.2 Scanning Electron Microscopy (SEM) ................................................... 53    vii  4.6.3 Electron Back Scattered Diffraction (EBSD) ........................................... 53 4.6.4 Electrical Conductivity Measurements ................................................... 53 CHAPTER 5   Experimental Results and Discussion ................................... 55 5.1   Characterization of Initial Microstructure ...................................... 55 5.1.1   AA3003 .......................................................................................... 55 5.1.2   Low Fe AA3003 .............................................................................. 62 5.2   Tensile Behaviour ..................................................................... 68 5.2.1 AA3003 ........................................................................................... 68 5.2.2 Low Fe 3003 ..................................................................................... 72 5.2.3 Discussion ........................................................................................ 75 5.3   Annealing Behaviour ................................................................. 76 5.3.1  Critical Plastic Strain for Recrystallization in AA3003 ............................ 76 5.3.2 Critical Plastic Strain for Recrystallization in Low Fe 3003 ....................... 82 5.3.3 Discussion ........................................................................................ 83 5.3.4   Annealing Behaviour of AA3003 after Large Strain Rolling ..................... 87 5.3.5 Discussion ........................................................................................ 97 5.4   Concurrent Precipitation ............................................................ 97 CHAPTER 6   Modeling ........................................................................ 102 6.1 Yield Stress Model .................................................................... 102 6.1.1 Discussion of Yield Stress Model ......................................................... 110 6.2 Work Hardening Behaviour ........................................................ 112 6.2.1 Discussion of Work Hardening Model ................................................. 119    viii  6.3 Critical Strain for Recrystallization .............................................. 122 6.3.1 Discussion of Critical Strain Model ..................................................... 128 6.4 Summary of Modeling ............................................................... 130 7   Concluding Remarks ........................................................................ 133 7.1 Summary ................................................................................ 133 7.2 Future Work ........................................................................... 134 References ......................................................................................... 136                 ix  List of Tables Table 4.1. Chemical composition of experimental alloys (wt%)  ................................. 44 Table 5.1. Initial microstructural characteristics of extruded strips used to study critical plastic strain for onset of recrystallization .................................................................. 65 Table 5.2. Initial microstructural characteristics of extruded strips used to study recrystallization behaviour after rolling ..................................................................... 66 Table 5.3. Initial microstructural characteristics of AA3003 un-extruded samples used to study tensile behaviour of these alloys ................................................................... 67 Table 5.4. Experimental values of yield stress and engineering UTS for different conditions of AA3003 .............................................................................................. 69 Table 5.5. Electrical resistivity before and after annealing of samples with fine initial grains, 12-14 µm (values are in nΩ.m) ....................................................................... 77 Table 5.6. Electrical resistivity before and after annealing of samples with large initial grains, 98 µm (values are in nΩ.m) ............................................................................ 78 Table 5.7. Critical plastic strain for recrystallization of AA3003 samples (initial grain size: 12 µm for H1 and H1-7h samples and 14 µm for H24 samples). .......................... 80 Table 5.8. Critical plastic strain for recrystallization of AA3003 samples (initial grain size: 98 µm). ............................................................................................................. 81 Table 5.9. Critical plastic strain range for recrystallization of AA3003 samples. .......... 81 Table 5.10. Critical plastic strain for recrystallization of Low Fe 3003 samples. .......... 84 Table 5.11. f/r  ratios of dispersoids and constituent particles and critical plastic strains for AA3003 and Low Fe 3003 samples ..................................................................... 85 Table 6.1. Values for microstructure state variables used in the yield stress model .... 108 Table 6.2. Values used in the yield stress model to estimate constituent particles contribution. .......................................................................................................... 110    x  Table 6.3. Contribution from different strengthening mechanisms on yield stress (values are in MPa) ............................................................................................................ 111 Table 6.4. Yield stress in each condition and fitting parameters used in the work hardening model .................................................................................................... 114 Table 6.5. Critical recrystallization strain range obtained from experiments and model .............................................................................................................................. 127                         xi  List of Figures Figure 1.1.  Microstructure of a micro-multiport tube after: (a) low level of cold deformation and (b) brazing treatment [5]. ................................................................ 11 Figure 2.1. As-cast grains of AA3003 with a dendrite structure (100 mm DC cast billet) [17] ............................................................................................................................ 8 Figure 2.2. Yield stress as a function of Mn and Mg level in solid solution, illustrating that Mn in solid solution has a much stronger effect on the yield stress than Mg [6] .... 13 Figure 2.3. Schematic diagram showing the elasto-plastic transition and the stages of work hardening [63]. ................................................................................................ 20 Figure 2.4. Comparison between the original Kocks-Mecking model and the Bouaziz approach (Experimental data taken from [63]) .......................................................... 24 Figure 2.5. The microstructure in a polycrystalline metal deforming by slip. The various features are shown in increasing scale: (a) Dislocations, (b) Dislocation boundaries, (c) Deformation and transition bands within a grain, (d) Specimen and grain-scale shear band and (e) Deformation zone around a particle in a rolled polycrystal [65]. ............ 29 Figure 2.6. Calorimetric readings during heating of different metals after deformation in torsion at -196 ºC to different surface shear strain (s) [65] .......................................... 30 Figure 2.7. Different stages in the recovery of a plastically deformed material: (a) dislocation tangles, (b) cell formation, (c) annihilation of dislocations within cells, (d) subgrain formation, (e) subgrain growth [65] ............................................................. 32 Figure 2.8. Formation of recrystallization nucleation site by SIBM consisting of (a) subgrain growth to reach the critical size and (b) growth of nucleus by high-angle boundary movement [81].......................................................................................... 36 Figure 4.1.  Tapered sample used in this study .......................................................... 46 Figure 4.2.  Grains are revealed using Poulton’s reagent (note: this is a conventional sample)  ................................................................................................................... 47    xii  Figure 4.3.  (a) A tapered sample with a shaded region in which strain measurement was carried out and (b) strain along the shaded section using digital image correlation technique ................................................................................................................. 49 Figure 4.4.  (a) K type thermocouple attached to the sample and (b) heating rate in a salt bath ......................................................................................................................... 52 Figure 5.1.  Micrographs showing microstructure of extruded samples (plate) homogenized at 600 °C for: (a) 1 hr and (b) 24 hr ...................................................... 56 Figure 5.2. (a) Bright field TEM image and (b) corresponding diffraction pattern taken from samples with high density of dispersoids (Work done by Dr. Roumina at UBC) .............................................................................................................................. ..57 Figure 5.3.  A FEGSEM micrograph showing dispersoids in 3003 samples with high density of dispersoids ............................................................................................... 58 Figure 5.4.  Size distribution (3D diameter) of dispersoids in AA3003 samples homogenized for 1 hr ............................................................................................... 58 Figure 5.5. Optical images showing grain structure in AA3003 extruded strips with: (a) high density of dispersoids and (b) almost no dispersoids ........................................... 60 Figure 5.6. EBSD maps and pole figures of extruded strips in AA3003 system homogenized at 600 °C for (a) 1hr and (b) 24 hr ........................................................ 61 Figure 5.7. Back scattered images showing constituent particles in Low Fe 3003 samples homogenized at 600 °C for: (a) 1hr and (b) 24 hr .......................................... 63 Figure 5.8.  FEGSEM micrograph showing dispersoids in low Fe 3003 samples homogenized for 1h at 600 °C .................................................................................. 64 Figure 5.9.  Size distribution (3D diameter) of dispersoids in Low Fe AA3003 samples homogenized for 1 hr ............................................................................................... 64 Figure 5.10.  True stress-true strain curves for AA3003 samples. ................................ 69 Figure 5.11. Manganese solubility in solid solution as a function of temperature calculated using Thermo-Calc (TTAL6 database) for both alloys ............................... 71    xiii  Figure 5.12.  Work hardening rate vs stress curves for AA3003 samples. Yield stress for each condition is shown on the curves. For 375C-24h condition, since the first stage of work hardening is very large, the yield stress cannot be illustrated (yield stress=70 MPa) ................................................................................................................................ 72 Figure 5.13.  True stress-true strain curves for H1 samples with different initial grain size (spherical diameter of dispersoids = 104 nm, volume fraction of dispersoids = 1.01%) ..................................................................................................................... 73 Figure 5.14.  True stress-true strain curves for H24 samples with different initial grain size (almost no dispersoids in the microstructure). ..................................................... 73 Figure 5.15.  True stress-true strain curves for Low Fe 3003 samples (initial grain size: H1-LF=32 µm and H24-LF = 20 µm) ....................................................................... 74 Figure 5.16.  Work hardening rate of Low Fe 3003 samples ...................................... 74 Figure 5.17.  Boundary between recrystallized and unrecrystallized regions in (a) macroscopic (Poulton’s reagent) and (b) microscopic scale (anodized). Please note, these images are taken from two different H24 samples ............................................. 78 Figure 5.18.  Strain along a tapered specimen at different times of loading, i.e. t1<t2<t3<t4<t5 (note: this curve is extracted from DaVis software) ............................... 80 Figure 5.19.  Recrystallized grain size versus strain along tapered H1 and H24 samples with small initial grain sizes (12 µm for H1 and 14 µm for H24 specimens)................. 82 Figure 5.20.  Critical strain for onset of recrystallization in low Fe 3003 samples homogenized at 600 °C for (a) 1 hr and (b) 24hr (note: samples were loaded up to the same load in order to get very similar strain gradient along them) .............................. 84 Figure 5.21.  Critical plastic strain versus total f/r ratio for AA3003 and low Fe 3003 alloys (initial grain size: 12 and 14 µm for H1 and H24 specimens – 32 and 20 µm for H1-LF and H24-LF samples) .................................................................................... 85 Figure 5.22.  Initial grain structure of: (a) H1 and (b) H24 samples with very large grains (VLG), 0.5-3 mm ..................................................................................................... 87    xiv  Figure 5.23. Optical micrographs showing the recrystallization behaviour of H1 samples (initial grain size: 12 µm) cold rolled for: (a) 10%, (b) 20%, (c) 40%, (d) 65% and (e) 80% (note: cold rolled samples were annealed at 600 °C for 1 min) ................................... 89 Figure 5.24. Optical micrographs showing the recrystallization behaviour of H24 samples (initial grain size: 14 µm) cold rolled for: (a) 10%, (b) 20%, (c) 40%, (d) 65% and (e) 80%. (note: cold rolled samples were annealed at 600 °C for 1 min) ................ 90 Figure 5.25.  Effect of dispersoids density on recrystallized grain size of AA3003 samples with fine initial grain size, 12 µm for H1 and 14 µm for H24 (note: error bars are showing smallest and largest grain size measured) ............................................... 91 Figure 5.26. Optical micrographs illustrating the recrystallization behaviour of H1-VLG samples (initial grain size: 0.5-3 mm), cold rolled for: (a) 10%, (b) 20%, (c) 40% and (d) 80%. (note: cold rolled samples were annealed at 600 °C for 1 min) ........................... 93 Figure 5.27. Optical micrographs illustrating the recrystallization behaviour of H24-VLG samples (initial grain size: 0.5-3 mm), cold rolled for: (a) 10%, (b) 20%, (c) 40% and (d) 80% (note: cold rolled samples were annealed at 600 °C for 1 min) ................ 94 Figure 5.28.  Effect of dispersoids density on recrystallized grain size of AA3003 samples with large (0.5-3 mm) initial grain size (note: error bars are showing smallest and largest grain size measured) ............................................................................... 95 Figure 5.29.  Effect of initial grain size (fine: 12 µm and large: 0.5-3 mm) on recrystallized grain size of AA3003 samples with high density of dispersoids (H1).  Error bars are showing smallest and largest grain size measured ................................ 96 Figure 5.30.  Effect of initial grain size (fine: 14 µm and large: 0.5-3 mm) on recrystallized grain size of AA3003 samples with very low density of dispersoids (H24). Error bars are showing smallest and largest grain size measured ................................ 96 Figure 5.31. Optical micrographs of fully recrystallized microstructure of samples homogenized for 1 hr at 600 °C (AA3003) cold rolled for 80% followed by annealing at different temperatures; (a) as-rolled microstructure, (b) 100 min at 350 °C, (c) 30 min at 400 °C and (d) 1 min at 500 °C ................................................................................. 99 Figure 5.32.  Electrical resistivity of samples rolled for 20% and then annealed at 400 °C (AA3003) ............................................................................................................... 100    xv  Figure 5.33.  Optical micrographs of AA3003 samples cold rolled for 20% and then annealed at 400 °C: (a) H1 samples annealed for 1440 min and (b) H24 samples annealed for 3 min ................................................................................................. 101 Figure 6.1. Yield strength as a function of Mn in solid solution in Al-Mn alloys (grain size of 500 to 1000 µm), this figure is plotted based on data published in reference [6] ....  ……………………………………………………………………………………………..104 Figure 6.2. Schematic microstructure of AA3003 samples homogenized for 1 hr at 600 °C .......................................................................................................................... 112 Figure 6.3. Keff  as a function of volume fraction of constituent particles ................... 115 Figure 6.4. ξ as a function of Mn level in solid solution ........................................... 116 Figure 6.5. Comparison of the measured (symbols) and the predicted (lines) stress-strain curves for: (a) H24, (b) H1, (c) H1-7h, (d) As-cast, (e) 375C-24h, (f) H24-LF and (g) H1-LF .................................................................................................................. 117/118 Figure 6.6. Comparison between engineering ultimate tensile stresses (UTS) and yield stresses predicted by the model with the ones measured experimentally ................... 119 Figure 6.7. True UTS obtained from work hardening rate- and true stress-true strain curves. Both curves are plotted from the model ....................................................... 120 Figure 6.8. Comparison of the modeled forest hardening and the experimental result for an Al-Mn alloy contained coarse particles but very few dispersoids (Mn in solid solution: 0.48 wt%, grain size: 65 µm) [6, 77] .......................................................... 123 Figure 6.9. Predicted range of critical strain for onset of recrystallization for: (a) H24, (b) H1, (c) H1-7h, (d) H24-LF and (e) H1-LF ................................................... 125/126 Figure 6.10.  Comparison between predicted critical strains for recrystallization and experimentally measured values. Red squares are average values for each approach .............................................................................................................. …………..127 Figure 6.11. Schematic of microstructure in AA3003 alloy showing constituent particles and recrystallized grains (shaded grains) pinned by dispersoids ................................ 130    xvi  Figure 6.12. Micrographs showing annealing sequence of Al-Si using in-situ High Voltage Electron Microscopy (HVEM): (a) initiation of recrystallization in the arrowed region of the deformation zone close to the particle and (b) the recrystallized grain consumed the deformation zone and did not grow further [65, 105] ......................... 131                  xvii  List of Symbols Symbols Definitions/Values σss Solid solution (S.S.) contribution to yield stress (MPa) Kss Constant which relates S.S. contribution to amount of Mn is S.S. (i.e. 38 MPa/wt%)    CMn Amount of Mn in S.S. (wt%) σgb Grain size contribution to yield stress (MPa) σ0 Intrinsic strength of a single crystal of high purity aluminum (<1 MPa) k Constant used in the Hall-Petch equation (0.068 MPa.m1/2) d Grain diameter σdisp Dispersoids strengthening contribution to yield stress M Taylor factor (3.07 for randomly oriented FCC metals) F Average interaction force between the dislocation line and the precipitate b Magnitude of the Burgers vector (0.286 nm) λeff Mean planar precipitate-spacing which dislocation travels Г Average line tension βC Precipitate strength (varies between 0 and 1) μ Shear modulus υ Poisson’s ratio (~0.33) δ Angle between the dislocation line and its burgers vector Λ Outer cut-off distances used in calculating the line energy of the dislocation r0 Inner cut-off distances used in calculating the line energy of the dislocation r Average particle radius f Volume fraction of the precipitates σconst Constituent strengthening contribution to yield stress γ Accommodation factor µ Shear modulus of matrix ε* Unrelaxed plastic strain µ* Shear modulus of relatively large particles σdis Strengthening contribution of dislocations to yield stress α Geometrical constant of the order 0.3 εp Plastic strain k1 Rate of dislocation accumulation k2 Rate of dynamic recovery σs Scaling stress θ0 Initial work hardening    xviii  Symbols Definitions/Values θIV Work hardening rate at large strains Keff Constant describing the dislocation accumulation ξ Capture distance for dynamic recovery α* Constant with a value approximately 2-3 δs Cell/subgrain size ρm Mobile dislocation density ρi Immobile dislocation density in the cell interior ρw Immobile dislocations in the cell walls V Volume fraction of the cell walls Es Stored energy rsubgrain Subgrain radius γ Boundary energy Pz Zener pinning pressure A Area of particles calculated by Clemex Professional Imaging software           xix  Acknowledgments First and foremost, I would like to offer my deep gratitude to my supervisor, Professor Warren Poole, for his excellent support, guidance and encouragement throughout my research. He continually helped me to develop my ability and skills to perform independent research as a graduate student.  I would like to thank Dr. Mary Wells for her useful comments, encouragement and kindness. I am also grateful to Dr. Nick Parson for his help and valuable suggestions, and to Rio Tinto Alcan for funding the project and supplying the material for this study.  I would like to express my gratitude to Dr. Guillaume Badinier for his help in measuring strain along tapered specimens using image correlation software. Gratitude is also extended to Mr. Ross McLeod, Mr. Carl Ng and Mr. David Torok for their expertise and the countless samples they prepared for me. My special thanks to Professor David Embury, Dr. Qiang Du, Dr. Leo Colley, Dr. Babak Raeisinia, Dr. Reza Roumina, Dr. Hamid Azizi-Alizamini, Dr. David Marechal, Dr. Fateh Fazeli and all my other friends at UBC for their help and support.  This work would not have been possible without the phenomenal love, sacrifice and support of my parents, Zohreh and Mohammad, and my sister, Parisa.    1  CHAPTER 1   Introduction Aluminum is one of the most versatile and sustainable materials used in the global economy. Between 1990 and 2010, its production in the Canadian aluminum industry nearly doubled [1]. As a result of international competition, there is an increased awareness by companies such as Rio Tinto Alcan, a global leader in the aluminum industry, that they must focus on high-value-added products, for example, alloys used to fabricate heat exchangers for the automotive industry.  After casting (direct chill casting), alloys for heat exchanger applications undergo a complicated thermomechanical history with a number of processing steps including homogenization, high temperature extrusion, ambient temperature deformation and then annealing. The final stage of the manufacturing process of these alloys (ambient temperature deformation + annealing) has been the least studied step. Typically, ambient temperature deformation includes two regimes of deformation, low level of deformation (e.g. 1-8%) for sizing and straightening purposes or large strains (more than 10%) for tube drawing and rolling purposes. Subsequent annealing of cold deformed samples is conducted as a separate processing step or in a conjunction with a brazing operation.  There are a number of parameters that can affect resulting microstructure such as pre-strain level, fine and coarse precipitates, annealing heating rate, annealing temperature and annealing holding time. All these parameters can consequently affect product’s properties. From an industrial point of view, a relatively coarse grain size (70-   2  120 µm) is preferred for most heat exchanger applications, as this gives a high corrosion resistance, high sagging resistance, and good brazeability [2]. In contrast, a fine grain size is desirable for products that require high formability, for example, thin wall tubes. As such, grain-size control is essential for heat exchanger applications [2].  Since the middle of the 1990s, the trend with automotive heat exchangers is to replace mechanical assembly by brazing of aluminum alloys because of cost, safety and recycling issues. For instance, micro-multiport (MMP) tubing, made from 1xxx or 3xxx, is a flat body with a row of side-by-side passageways, which are separated by upright webs. Processing of this product involves extrusion, straightening, cutting, assembly and furnace brazing. The straightening operation imposes a small amount of cold work and brazing is generally done at 600-605 °C (about 91% of the melting point for the alloy). One of the main motivations for the current study was the resulting microstructure after lightly deforming these products (1% to 10%) at room temperature followed by brazing heat treatment which typically takes place at a very high temperature, i.e. 600 ºC. In this case, there is very little knowledge available in the literature on the effect of room temperature deformation and subsequent annealing on the microstructure of extruded AA3xxx. Results from industry suggest that a wide range of microstructures can be observed ranging from coarse multi-crystals to fine grained polycrystalline microstructures. Figure 1.1 shows an example from industry with a fine and coarse grain structure in a multi-port extrudate. Poor sagging resistance (creep on    3  grain boundaries) and poor corrosion resistance (corrosion along grain boundaries) are expected for the microstructure with very large grains shown in Figure 1.1b. Therefore, one primary goal of the current study was to understand how the processing of the alloy affects the final microstructure for a wide range of processing routes in a commercially important 3xxx aluminum alloys.    (a) (b) Figure 1.1.  Microstructure of a micro-multiport tube after: (a) low level of cold deformation and (b) brazing treatment [3]. The commercially significant alloy AA3003 and a low Fe 3003 variant have been chosen as the alloys of interest in the present investigation. The experimental data generated from the present study represents the first systematic set of post extrusion thermo-mechanical processing of AA3003 aluminum alloys. Experimental work was carried out at small and large strain regimes in order to understand the annealing behaviour of these alloys. Based on these data, a model for the critical plastic strain necessary for recrystallization is proposed. It is focused on the competition between    4  stored energy and pinning pressure from large (1-5 µm) and fine (40-200 nm) particles. It is also worth indicating that the work on low strains followed by annealing has received almost no attention in the literature. The major significance of this work is the integration of the industrial processing conditions with structure-property relationships and the close linkage between modeling activities and experimental work.     5  CHAPTER 2   Literature Review A key aspect in design of optimal processing routes is a fundamental understanding of the effect of processing history on the evolution of microstructure. During the complex manufacturing route of heat exchangers fabricated from AA3xxx series, it is increasingly important to develop quantitative knowledge of the microstructure evolution at each stage of the process as it affects the final product microstructure and its properties. Therefore, it is important to understand how the homogenization treatment and extrusion process affect the microstructure evolution during the subsequent manufacturing stage, cold deformation followed by annealing.  This chapter provides background information and details research relevant to the current research study. Thus, the literature review is organized in the following order: First, industrial processing and microstructure of 3xxx alloys are described. Then, strengthening mechanisms in 3xxx aluminum alloy system are discussed. Also, work hardening behaviour of these alloys is presented. This chapter reviews microstructural features of the deformed state and the energy stored due to deformation. The individual processes of recovery and recrystallization are delineated here. Recrystallization mechanisms and critical plastic strain required for recrystallization initiation are also incorporated. Finally, effect of particles on grain boundary movement is reviewed.    6  Models for microstructure/property evolution during thermomechanical process are summarized with an emphasis on the internal state variable approach which will be used in this work. Then, the relevant metallurgical phenomenon (e.g. cold working, formation of the deformed state, recovery and recrystallization of deformed microstructure) will be briefly reviewed. Finally, as the resulting microstructure of AA3xxx is significantly influenced by prior homogenization and extrusion, the knowledge in the literature for these processes will be summarized. 2.1   Industrial Processing and Microstructure of 3xxx Alloys AA3xxx aluminum alloys contain manganese (Mn), iron (Fe) and silicon (Si) as alloying elements. In commercial 3xxx aluminum alloys, composition range of alloying elements is 0.3-1.5 wt% Mn, 0.1-0.7 wt% Fe, 0.1-0.6 wt% Si, 0-0.30 wt% Cu, 0.1 wt% Ti and many contain other additions such as Mg, Cr, and Zn [4, 5]. In general, the yield strength of 3xxx aluminum alloys is low, i.e. 20-60 MPa [5, 6]. AA3003 alloy is a preferable choice for automotive heat exchanger applications due to its good combination of strength, corrosion resistance, workability and high melting temperature [5-8]. These properties allow heat exchanger fabricators to easily deep draw, extrude and braze these alloys [5-8]. The solubility of Fe and Si in aluminum is very low and, therefore, the addition of Fe into the system will promote formation of Fe intermetallics which result in a fine recrystallized grain structure after cold drawing and annealing [5, 7]. The presence of Mn along with Fe and Si as alloying elements leads to the     7  formation of complex quaternary-phase Al-Mn-Fe-Si such as Al12(Fe,Mn)3Si, Al15(Fe,Mn)3Si2,or the α-Al(Fe,Mn)Si [9, 10]. The manufacturing steps of alloy AA3003 are typically casting, homogenization, extrusion, cold deformation and annealing. The following sections provide more details on each fabrication step. 2.1.1 Casting The typical feedstock for extrusion operations are Direct Chill (DC) cast billets. Solidification of the DC cast metal starts in the water-cooled mold [10]. The melt flows into the mold cavity through a trough and a vertical nozzle. The melt flow is controlled by a floating valve increasing the outlet opening of the spout when the melt level goes down or decreasing it when the melt level goes up [10]. Solidification under these conditions produces equiaxed grains with a dendrite structure as shown in Figure 2.1. An average grain size of ≈64 µm has been reported for AA3003 by Grajales [5]  for a 100 mm diameter billet produced by DC casting. In AA3xxx series alloys, the main intermetallic phases (known as constituent particles) after solidification are Al6(Fe, Mn) and α-Al(Mn, Fe)Si. Further, the as-cast state is supersaturated in manganese (Mn) and iron (Fe) at room temperature due to non-equilibrium cooling and the low solubility of these elements in aluminum [6, 11-13]. There are models in the literature for the solidification behavior of 3xxx alloys during DC casting [14-16].    8   2.1.2 Homogenization The cast billets undergo what is known in the industry as a homogenization treatment. This consists of heating the billet up slowly (50-250 °C/hr) to 500-630 °C and holding it for 4-5 hr followed by a slow cool down to room temperature [18]. The whole homogenization process, including the heat-up, holding and cool-down, typically takes approximately 10 hours [18]. During heating, no microstructure change can be observed until approximately 400 °C, when the eutectic networks of constituent particles begin to break up [12]. Depending on the chemistry of the 3xxx alloy, at approximately 400°C and above, some of the Al6(Mn,Fe) constituent particles transform to the α-Al(Mn,Fe)Si  Figure 2.1. As-cast grains of AA3003 with a dendrite structure (100 mm DC cast billet) [17].    9  phase with the resulting change in composition of the particles [12] but no significant change in the area fraction of the constituent particles can be measured [11]. On the other hand, the supersaturation of Mn in solid solution during heating drives precipitation of fine dispersoids in the intra-granular region [12, 19]. As the solubility of Mn increases with temperature, a complex interplay between dissolution, growth, coarsening of dispersoids and long range diffusion of Mn to the constituent particles occurs. The composition and crystal structure of the dispersoids have been found to depend on chemistry [11]. In an experimental study of an AA3003 alloy (1.15 wt%Mn, 0.58 wt% Fe, 0.2 wt% Si and 0.08 wt% Cu) [11], the dispersoids were identified as the α-Al(Mn,Fe)Si phase. It was observed that the α-phase dispersoids could grow/coarsen to sizes of 100-200 nm and the peak number density can exceed 1000/μm3 [11]. On the other hand, Hansen et al. [20] studied precipitation behaviour in a strip-cast Al–1.59Mn–0.29Fe–0.09Si alloy which was cold rolled and annealed at 400 °C for a short time. These authors found a quasi crystal icosahedral phase together with α-Al(Mn,Fe)Si and Al6(Mn,Fe) dispersoids precipitate from the matrix. It was suggested that the quasicrystal phase was a precursor to the α-Al(Mn,Fe)Si and Al6(Mn,Fe) dispersoids [20]. Models have been proposed by researchers to simulate microstructure evolution during homogenization, see the references [15, 19, 21].     10  2.1.3 Extrusion After the homogenization step, the billets are reheated in an induction or gas fire furnace to the extrusion temperature [7]. The billet is then placed in the heated extrusion container along with a dummy block. Then, the ram pushes the pre-heated billet through a die which determines the cross-sectional geometry of the extruded product. The billets undergo a wide range of extrusion ratios 10:1 to greater than 300:1 [5]. The important processing parameters of extrusion are the ram speed and the incoming billet temperature. Ram speed ranges from 1 to 50 mm/s and the billet temperature is usually between 400 to 550 °C [22]. Finite element packages such as QForm, Hyperextrude and Deform have been used to simulate the extrusion process (e.g. temperature, strain rate, strain distribution, etc) [23-25]. 2.1.4 Post Extrusion Deformation and Heat Treatment The final stage of the processing route of AA3xxx alloys involves room temperature deformation with the objective of controlling the final dimensions of the products followed by annealing or brazing operation. A wide range of strains can be applied to the extruded products. Often a low level of strain (e.g. 1-8%) is applied to the extruded samples for straightening/sizing before the final heat treatment step. Brazing is conducted at high temperatures, e.g. 600 °C, and under certain conditions a dramatic coarsening of the microstructure via a highly inhomogeneous recrystallization process can occur. Figure 1.1 shows an example from industry where an extrusion with a fine    11  grain size was cold deformed to a low strain and then subjected to a brazing simulation where recrystallization resulted in very large grains. These large grains are not desirable as they lead to poor sagging resistance (creep on grain boundaries) and poor corrosion resistance (localized corrosion along grain boundaries). At a general level, it is known that the recrystallized grain size depends on level of cold work, the starting microstructure (grain size, solute content, distribution of 2nd phases), annealing temperature and annealing time [22]. However, the detailed examination of this problem has not been investigated in the literature. 2.2 Yield Strength of 3xxx Alloys The yield strength is an important design criterion for heat exchangers because of the weight-saving advantages of minimizing fin and tube wall thicknesses. Four strengthening mechanisms can be identified in AA3xxx alloys: i) solid solution strengthening, ii) grain size strengthening, iii) precipitation strengthening due to dispersoids and iv) strengthening from the relatively large constituent particles.  2.2.1 Solid Solution Strengthening Solid solution hardening results from the interaction between dislocation motion and solute atoms [6, 26, 27]. The size difference between the solute atoms and the matrix atoms creates a strain field around the solute atom which leads to strengthening of the material. Solid solution hardening depends on: i) the nature of dislocation-solute atom    12  interaction which depends on size, modulus and/or chemical effects, ii) changes in the nature of dislocation (i.e. possible changes in stacking fault energy) and iii) the statistics of how a dislocation interacts with a large number of solute atoms. There are a number of theories for solid solution strengthening in metals, including the Fleischer model (∆σ ∝ c1/2) [28], which treats the solute atoms as point obstacles; the Labusch theory (∆σ ∝ c2/3) [29], which is a statistical model that accounts for interactions of solute atoms above and below the glide plane. It is usually difficult to discriminate between these models based on experimental data. For industrial alloys, a linear dependence of strength on solute level often provides an acceptable description of solid solution hardening. For example, Ryen et al. [6] investigated the effect of Mn and Mg in solid solution on the yield stress in binary alloys. As shown in Figure 2.2, to a first approximation the compositional dependence of yield stress is linearly related to the Mn solute level.     13   Figure 2.2. Yield stress as a function of Mn and Mg level in solid solution, illustrating that Mn in solid solution has a much stronger effect on the yield stress than Mg [6].     2.2.2 Grain Size Strengthening Grain boundaries have a significant effect on the plastic deformation of polycrystalline materials. At low temperatures, in particular, the boundaries act as strong obstacles to dislocation movement due to discontinuity in the orientation of the slip plane at the grain boundaries [30]. Further, compatibility should exist among the neighboring grains during the deformation of polycrystals such that the development of voids or cracks is not permitted [30]. The grain size effects are usually accounted for using the Hall-Petch relationship [31, 32], i.e.  210 kdgb   (2.1)    14  where σ0 is related to the intrinsic strength and k is a constant and d is grain diameter. The intrinsic strength of a single crystal of high purity aluminum is less than 1 MPa [33] and k  value ranges 0.065-0.07 MPam1/2 for pure aluminum [30, 34, 35]. However, there have been many reports showing that once the grain size is reduced down below a critical value, a breakdown in the Hall-Petch trend is observed [36-39]. Nevertheless, experimental results on different materials clearly indicate that the Hall-Petch equation is applicable for grain sizes of 500 nm to 100’s μm [36-39]. As such, the Hall-Petch relationship is applicable for the engineering alloys of relevance in this study which have grain sizes in the range of 10-100 μm [30].  2.2.3 Precipitation Strengthening  Precipitates can effectively act as barrier to the dislocation motion which leads to strengthening of alloys. One can treat precipitates as being of two types, i.e. shearable or non-shearable. The nature of interaction between dislocations and precipitates in a complex manner depends on a number of factors: i) anti phase boundary energy in the precipitate, ii) matrix-precipitate interfacial energy, iii) elastic misfit stresses, iv) modulus misfit effect and v) coherency stresses [30, 40]. When the precipitates are not sheared, the stress required is related to the expansion of a dislocation between the particles, i.e. the Orowan stress [30, 40]. In the case of a shearable precipitate, however, the extra stress necessary for particle shear is less than that of the Orowan stress and will depend on the spacing of precipitates and strength of dislocation-precipitate interaction    15  [30]. In AA3003 alloy, α-Al(Mn,Fe)Si dispersoids are considered to be partially coherent with Al matrix [13, 41, 42] and it has been reported that dispersoids can be treated as non-shearable particles [13, 43]. The contribution from this mechanism on the yield strength can be described by [30]  effdisp bMF8.0 (2.2) where M is the Taylor factor (3.07 for randomly oriented FCC metals), b is the magnitude of the Burgers vector, λeff is the mean planar precipitate-spacing which a dislocation travels and F denotes the precipitate strength which represents the average interaction force between the dislocation line and the precipitate. The precipitate strength can be normalized with respect to the dislocation line tension, resulting in  cF  2  (2.3) where Г is the average line tension. The value of βC varies between 0 and 1 with the latter value representing the maximum strength obtained when the precipitates become non-shearable.  In general, line tension Г depends on the nature of dislocation (i.e. edge and screw represent the extremes) and can be represented by [40]    )/ln(1sin314 022rb    ( .4)    16  where μ is shear modulus, υ is Poisson’s ratio, δ is the angle between the dislocation line and its Burgers vector and Λ and r0 are the outer and inner cut-off distances used in calculating the line energy of the dislocation. An average line tension of αµb2 is often used in models where α ~0.25-0.5. For non-shearable spherical particles, λeff can be calculated based on the average particle radius, r, and volume fraction, f [44]:  rfeff2132  (2.5)  2.2.4 Strengthening from Large Second Phase Particles  When a ductile matrix with a distribution of relatively large particles (>1 µm) and a volume fraction range of 1-10% is plastically deformed, elastic and plastic incompatibility stresses develop in both the matrix and particles [45-48]. At small strain, the strain hardening rate is very high and also the plastic incompatibility stresses increase linearly with the strain [45-47]. The high initial work hardening regime at low strains reduces with the onset of plastic relaxation around particles [45, 47]. This type of strengthening mechanism has been extensively studied for a range of systems and interpreted in terms of Eshelby theory [48-50]. The analysis of spherical particles in Mg-Al alloys by Caceres et al. [50] has been examined in this framework and it was shown that the contribution to the yield stress can be estimated as [50]:    17   *4  fconst   (2.6) where γ is an accommodation factor, µ is the shear modulus of matrix, ε* is the unrelaxed plastic strain, f is the volume fraction of the precipitates and γ depends on the particles shape (for more detail see reference [51]). For spherical particles embedded in a matrix, γ is given by [51]:   )1(1557  (2.7)  In Equation 2.6, φ can be calculated using the following equation [49, 50]:  )( ***  (2.8) where µ* is the shear modulus of relatively large particles.  2.2.5 Superposition of Strengthening Components The strengthening mechanisms discussed above contribute independently to the yield stress measured on the macroscopic scale. A large number of studies have been dedicated to determine the superposition law [52-59]. As such, an empirical superposition law has been proposed: σq =Σσiq, where σi is the flow stress produced by the strengthening mechanism, i, and 1≤ q ≤2. Ebeling and Ashby [58] reported that for Cu alloys containing incoherent SiOs particles, the q in the equation equals unity. Also, Kocks et al. [53] concluded that q is equal to 1.0 when the interaction of dislocations    18  with “point obstacles” gives rise to a “friction stress”. Moreover, Hirsch and Humphreys [59] strengthened a Cu alloy by incoherent Al2O3 particles and came up with the value of 1.0 for q. However, there are some other studies [52, 60] in which the researchers reported q>1.0. Kocks [60] concluded that q value depends on the relationship between the flow stress associated with each mechanism and the respective obstacles density in the glide plane. Recently, Vaucorbeil et al. [61] investigated the superposition of strengthening contributions in engineering alloys for different sets of obstacles and derived a new expression for the exponent q. This expression is an analytical function of only the breaking angle of the respective obstacle sets [61]. 2.3  Macroscopic Work Hardening Bahaviour Work hardening refers to the increase in stress with strain required to continue plastic deformation. The phenomenology of work hardening has been extensively studied over the past 50 years for both single crystals and polycrystals [62]. It has been observed that work hardening behaviour at homologous temperatures below 0.3 of melting point, Tmp, can be divided into 4 stages [62]. Stage I behaviour relates to the deformation of single crystals oriented for glide on a single slip system and is not observed in polycrystals.  Stage II is observed in single crystals when more than one slip system is activated or in polycrystalline samples when elasto-plastic transition is complete [62]. For high purity FCC metals, the Stage II work hardening rate is approximately µ/20 i.e. 1200 to 1500 MPa for aluminum [63]. Stage II is observed to be    19  almost temperature and strain rate independent. In Stage III, the hardening rate decreases as the flow stress increases. At larger strains, a final stage of work hardening known as Stage IV is often observed [63]. In stage IV the hardening rate is often constant but at a low hardening rate. The stages of work hardening in polycrystals can be conveniently analyzed by plotting the work hardening rate as a function of the flow stress (often referred to as Kocks-Mecking plots) as schematically shown in Figure 2.3. Hence, Stage II is associated with the initial work hardening rate. Stage III is the regime where the hardening rate decreases linearly with stress. Stage III behavior is strongly dependent on the temperature and stacking fault energy but weakly dependent on the strain rate [63]. During deformation at low homologous temperatures, dislocation density increases with strain. The process of work hardening can be viewed as a competition between dislocation accumulation and dislocation annihilation, often referred to as dynamic recovery [64]. Often an inhomogeneous distribution of dislocations (e.g. in cell structure) is observed making the dislocation density measurement difficult [65].     20   Figure 2.3. Schematic diagram showing the elasto-plastic transition and the stages of work hardening [63]. The deformed state will be discussed in detail in section 2.4. Physically based work hardening models typically consist of two parts: (a) a model relating the flow stress to the appropriate state variables (e.g. dislocation density, cell/subgrain size, misorientation of subgrain boundaries) and (b) a model for the evolution of these variables with strain.  The following reviews some of the various physically based models: Single Parameter Models  The Taylor equation, given below, offers a framework to simply relate the flow stress (σ) to the average dislocation density (ρ) [66-70]   bMdis   (2.9)    21  where M is the Taylor factor (3.07 for randomly oriented FCC metals), α is a geometrical constant of the order 0.3 and b is the magnitude of the Burgers vector. The Kocks-Mecking model [62, 71] is the most developed and commonly used single parameter model. In this model, the evolution of dislocation density with plastic strain, εp, is described by a differential equation, i.e.:  2211 kkddp  (2.10) where k1 and k2 are constants which describe the rate of dislocation accumulation and dynamic recovery, respectively. The constant k1 is athermal and rate insensitive while k2 is strongly temperature and weakly rate dependent [62]. In this equation, the first term represents hardening due to dislocation accumulation and the second term corresponds to the effect of dynamic recovery. The flow stress as a function of plastic strain can be calculated by integrating Equation 2.10 and substituting into 2.9 to obtain [72]:   pss  0exp1 (2.11) where σs is the scaling stress and results from an extrapolation of the work hardening in stage III to a zero work hardening rate and θ0 is the initial work hardening. Equation 2.11 is sometimes referred to as the Voce equation. It should be noted that this equation requires modification if stage IV work hardening is to be taken into account. To account for stage IV in a phenomenological manner, Tomé et al. [73] have modified the Voce equation as follows:     22    pspIVs  0exp1)( (2.12) where θIV is defined as the large strain work hardening rate.  Recently, Bouaziz [74] introduced a modified differential equation describing the evolution of dislocation density with strain:    )exp( bKMdd effp (2.13) where εP is the plastic strain, Keff is a constant describing the dislocation accumulation due to the interaction with forest dislocations as obstacles, b is the magnitude of the Burger’s vector (0.286 nm) and ξ can be interpreted as the capture distance for dynamic recovery. It is noted that Equation 2.13 asymptotically approaches Equation 2.10 if ξ√ρ<< 1. The work hardening rate can now be expressed by   spdd exp0 (2.14) which can be integrated to [74]:    ss01ln (2.15) This modification of the original Kocks-Mecking model has the advantage of being able to capture stage IV work hardening without introducing additional fitting    23  parameters. Figure 2.4, for example, shows how well the new approach captures the stress-strain curve for high purity aluminum compared to the original Kocks-Mecking (KM) model [63].  Multiple Parameter Models The single variable models such as Kocks-Mecking do not always capture the complexity of microstructure development. This is especially important when details of the dislocation arrangement are important, e.g. in problems of stored energy and nucleation of recrystallization. For example, Nes and co-workers [75] have proposed a work hardening model based on the cell/subgrain size, δs and dislocation density ρ. The mathematical form of the model is given by [75-77]  sMGbbM *210  (2.16) where σ0 is the frictional stress of aluminum and α* is a constant with a value of approximately 2-3. In this case, the description of the stress-strain behavior requires the differential equations to describe the evolution of ρ and δs as a function of strain, temperature and strain rate. Another approach is proposed by Gottstein and co-workers [78] in which three variables are defined to describe the spatial distribution of dislocations (mobile dislocation density ρm, immobile dislocation density ρi in the cell interior and the    24  immobile dislocations in the cell walls ρw). As such, the resulting flow stress on the slip system can be calculated by [79]    21210 1 wi MGbVMGbV    (2.17) where V is defined as the volume fraction of the cell walls . In this case, evolution laws for these internal variables must be developed.     Figure 2.4. Comparison between the original Kocks-Mecking model and the Bouaziz approach (Experimental data taken from [63]).    25  2.4  The Deformed State After understanding the work hardening phenomenon and the related models, it is essential to understand the microstructural changes due to the deformation as it affects the microstructure evolution after annealing. The seminal book of Humphreys and Hatherly provides a comprehensive review of this topic. The following is a brief summary emphasizing the essential features. 2.4.1   Microstructural Features Metals with high or moderate stacking fault energy such as aluminum, nickel and copper deform by dislocation mediated slip. The deformation in these metals is heterogeneous and regions of different orientation develop within the original grains due to orientation change during deformation. The main features of the microstructures in deformed metals of medium and high stacking fault energy are summarized according to the scale of the heterogeneity as shown schematically in Figure 2.5. Dislocations- Particularly after low strains, dislocations may exist in the deformed microstructure as tangles or other rather random structures (Figure 2.5a). Cells and subgrains- As shown in Figure 2.5b, equiaxed micron-sized volumes bounded by dislocation walls are cells or subgrains. These walls are either tangled (cell) or are well-ordered low angle boundaries (subgrain).    26  Deformation and transition bands- Individual grains within the sample subdivide on a large scale during deformation into regions of different orientation as a consequence of either inhomogeneous stresses transmitted by neighbouring grains or the intrinsic instability of the grain during plastic deformation. The resulting deformation bands (Figure 2.5c) deform on different slip systems. Moreover, the narrow regions between the deformation bands, which may be either diffuse or sharp, are termed transition bands. Shear bands- As a consequence of plastic instability, intense shear can occur in a polycrystalline sample. The shear bands, which are non-crystallographic in nature, may pass through several grains and even extend through the specimen (Figure 2.5d). Deformation zones around particles- At large strains and large particles, complex dislocation structures are formed which are associated with local rotation/distortion close to the particles. Such regions are commonly termed deformation zones shown in Figure 2.5e. The form and distribution of such dislocations at particles primarily depend on the strain and particle size. 2.4.2   Stored Energy of Cold Work Most of the work expended in deforming a metal is converted to heat and only a very small amount remains as energy stored in the material (typically less than 5%), which is the source for property changes during annealing. Although this stored energy    27  is derived from point defects and dislocations, at ambient temperature almost all of the stored energy is derived from the accumulation of dislocations [65]. Hence, the essential difference between the deformed and annealed states lies in the dislocation content and arrangement. The stored energy due to cold deformation of metals is an important parameter in microstructure evolution during annealing [65, 80, 81].  Stored energy is difficult to be measured experimentally but there are number of studies in which researchers have attempted to measure stored energy or dislocation densities using indirect measures such as the flow stress increment, resistivity measurements and hardness tests or direct measures such as differential scanning calorimetry (DSC) and transmission electron microscope (TEM)  [67, 82-86]. For example, Figure 2.6 illustrates the energy release during heating of different metals previously deformed in torsion at -196 ºC.   At low strains, there is a gap in knowledge in order to estimate the energy stored since most of the direct methods (e.g. TEM, Calorimetry, etc) cannot be used due to their limitations, i.e. the heat released during recrystallization is too small to be measured and the dislocation density is low making statistically representative TEM measurements very difficult. Often, an acceptable estimate of stored energy can be made from a simple estimate of the dislocation density, ρ, and the dislocation energy per line length as follows. An estimate of the dislocation density is calculated by inverting the Taylor equation (Equation 2.9).     28  After estimating dislocation density (ρ), the stored energy, Es can be related to the dislocation density according to [65]   02ln4)(rfbEs   (2.18) where  Λ is the upper cut-off radius (usually taken to be the separation of dislocations, ρ-1/2) [64] r0 is the inner cut-off radius (usually taken to be between b and 5b)    f(υ) is a function of Poission’s ratio, υ, which, for an average population of edge and screw dislocations is ~ (1-υ/2)/(1-υ) Humphreys and Hatherly [65] argue that for typical values of cut-off radii and for average dislocation populations, the logarithmic term can be replaced by an average value of ½. Therefore, the stored energy of cold work can be calculated as [65, 80, 81]  221 bEs  (2.19)  where ρ can be estimated from the Taylor equation (Equation 2.9).       29   Figure 2.5. The microstructure in a polycrystalline metal deforming by slip. The various features are shown in increasing scale: (a) Dislocations, (b) Dislocation boundaries, (c) Deformation and transition bands within a grain, (d) Specimen and grain-scale shear band and (e) Deformation zone around a particle in a rolled polycrystal [65]. Sshhhhhhhhhh    30   Figure 2.6. Calorimetric readings during heating of different metals after deformation in torsion at -196 ºC to different surface shear strain (s) [65].  2.5  Recovery after Deformation 2.5.1   General Observations Recovery refers to changes in the properties of a deformed material which occur prior to recrystallization. Recovery is primarily related to changes in the dislocation structure of the material [87-97]. Recovery is not confined to plastically deformed materials and may occur in any crystal into which a non–equilibrium, high concentration of point or line defects has been introduced. As most of the excess point    31  defects will anneal out at low temperatures, point defects produced during deformation are not considered further. Dislocation recovery is not a single microstructural process but a series of micromechanisms which are schematically shown in Figure 2.7. Whether any or all of these occur during annealing will depend on a number of parameters including the material, purity, strain, deformation temperature and annealing temperature [65]. Although the recovery stages tend to occur in order shown, there may be significant overlap between them.    Annihilation of dislocations and rearrangement of dislocations into lower energy configurations are the two primary processes happening during recovery [65, 98]. Glide, climb and cross slip of dislocations are the possible ways to reach lower energy systems [95, 99]. For instance, dislocations of opposite sign on the same glide plane annihilate by gliding towards each other which can occur even at low temperature. A combination of climb and glide gives rise to annihilation of the dislocations of opposite Burgers vector on a different glide plane [64]. This process can only occur at high homologous temperatures because climb requires thermal activation [65].  Recovery and recrystallization are competing processes since the stored energy produced during deformation is the driving force in both phenomena [65]. As the deformed structure is consumed during recrystallization, no further recovery can occur. Hence, the extent of recovery depends on the ease with which recrystallization occurs. On the other hand,    32  since recovery lowers the driving force for recrystallization, a significant amount of prior recovery may in turn influence the nature and kinetics of recrystallization.      (a) (b) (c) (d)  (e) Figure 2.7. Different stages in the recovery of a plastically deformed material: (a) dislocation tangles, (b) cell formation, (c) annihilation of dislocations within cells, (d) subgrain formation, (e) subgrain growth [65].  During recovery, the microstructural changes in a material are subtle and occur on a small scale. Recovery is often measured indirectly using the change in some physical (e.g. density and electrical resistivity) and mechanical properties (e.g. hardness and yield stress). 2.5.2   The Extent of Recovery Complete recovery of polycrystalline metals can only occur when the material has been lightly deformed [100, 101]. However, single crystals of cubic metals, if oriented for single slip and deformed in stage I of work hardening, may also recover almost completely on annealing [101]. Although the amount of recovery is usually found to    33  increase with strain at a constant annealing temperature [102], this trend is reversed in more highly strained materials because of the earlier onset of recrystallization. Annealing temperature is another factor affecting the rate of recovery. Results of annealing of lightly deformed iron indicate that more complete recovery occurs at higher temperatures [101, 103]. Since stacking fault energy γSFE affects the dissociation of dislocation into partials, it determines the mechanisms controlling the rate of recovery, i.e. the rate of dislocation climb and cross slip. In metals of high stacking fault energy such as aluminum, climb and cross-slip can occur easily compared to low/medium stacking fault materials which lead to significant recovery [101, 104]. However, solute may inhibit recovery by pinning dislocations or affecting the concentration and mobility of vacancies. Pinning of dislocations leads to a higher stored energy which promotes the recovery and also inhibits the recovery. As such, it is difficult to predict the net effect of solute on recovery [65]. 2.6   Recrystallization 2.6.1   General Observations Recovery progresses gradually with time and there is no readily identifiable beginning or end of the process. In contrast, recrystallization involves the formation of dislocation-free grains in certain parts of the specimen and the subsequent growth of these grains consumes the deformed or recovered microstructure [105].    34  Recrystallization is a microstructure transformation, which can be directly measured by quantitative metallography. The microstructure at any time is divided into recrystallized and non-recrystallized regions. The progress of recrystallization, therefore, can be followed directly by plotting the evolution of volume fraction recrystallized as a function of annealing time. 2.6.2   Recrystallization Nucleation For recrystallization nucleation, it is generally accepted that first nuclei form in the microstructural heterogeneities possessing large orientation gradient or sharp lattice curvatures, such as grain boundaries [106, 107], transition bands [108] and shear bands [108-111]. The recrystallization nuclei, which form therein, must fulfill the condition of thermodynamic stability which is lowering the energy of this region with respect to their immediate environment [109]. The mechanisms for initiation of recrystallization are not fully understood. However, several mechanisms have been proposed for the nucleation of recrystallization. These mechanisms will be introduced as follows: Strain Induced Boundary Migration (SIBM) This mechanism was first described by Bailey and Hirsch [112] and is expected to be dominant in single-phase materials at small and medium strains [113]. SIBM takes place if the driving force for growing a subgrain due to stored energy is sufficient to overcome the retarding pressure due to boundary curvature, 2γ/r, where γ is the    35  boundary energy and r is the radius of subgrain. Hence, a cell/subgrain needs to reach a critical radius, rc, in order to become a viable nucleus. This critical size increases with time as stored energy decreases due to recovery   )(2)( tEtr sc (2.20) In high SFE materials, the subgrain structure is well defined and contains most of dislocations present in the deformed state. A subgrain with lower stored energy compared to its surroundings is a nucleation site as shown in Figure 2.8. In Figure 2.8a, the subgrain initially grows within Grain I. When the subgrain reaches the critical size, part of a pre-existing grain boundary bulges into Grain II because it benefits from a very mobile high-angle boundary (Figure 2.8b). The competition between the rate at which the critical subgrain radius increases and the rate at which a given subgrain can grow (boundary mobility) to reach the critical size determines the occurrence of nucleation. Particle-Stimulated Nucleation (PSN) PSN is a likely recrystallization mechanism in many engineering alloys as they contain second-phase particles greater than 1 µm. PSN only occurs if the prior deformation is carried out below a critical temperature or above a critical strain rate because the interaction between particles and dislocations is temperature dependent [65].    36  Local deformation of the matrix, termed the deformation zone, due to presence of a particle gives rise to an orientation gradient and accumulation of dislocations in the vicinity of the particle, particularly the large particles [65]. For instance, Liu et al. [114]   (a) (b) Figure 2.8. Formation of recrystallization nucleation site by SIBM consisting of (a) subgrain growth to reach the critical size and (b)  growth of nucleus by high-angle boundary movement [81].  investigated lattice rotation adjacent to constituent particles in AA3104 and found that the average lattice rotation is about 5°, 7°, 9° and 10° at 10%, 30%, 50% and 70% cold rolling reduction, respectively. As such, recrystallization originates by the growth of subgrains within the deformation zone. As a subgrain grows in an orientation gradient, its misorientation with neighbouring subgrains increases. When this misorientation reaches that of a high angle boundary (e.g. 10-15°), a potential recrystallization nucleus forms. This nucleus with high angle boundary energy is subjected to retarding and driving pressures due to its radius and dislocation density, respectively. Hence, the    37  critical condition for onset of recrystallization by PSN is that at which the nucleus has at least the critical radius as given by Equation 2.20. The minimum diameter of second phase particles to make PSN an effective recrystallization mechanism has been found to be in the range of 1 μm for steel and aluminum [65].  2.6.3   Critical Plastic Strain A critical plastic strain is the minimum strain at which recrystallization occurs. At this value, the dislocation density makes it statistically favorable to form only a few nuclei, which can then grow at the expense of the unrecrystallized material [115]. Using this concept, a strain-anneal technique to make single crystals of iron, aluminum, and titanium has been developed [116-120]. The strain-anneal technique is based upon the recrystallization of deformed materials where new grains of the stable phase grow at the expense of the deformed grains. However, its mechanism/concept can lead to drastic undesirable coarsening of the microstructure [121] as shown in Figure 1.1 in industrial alloys. In this figure, the material was deformed for 1-5% and subsequently annealed. As such, a very low number of nuclei are activated in the web (or intersection of web and flange) and then spread out into the flange. One method to estimate critical strain is through the use of a tapered tensile sample. For example, Bailey and Brewer [117] employed a tapered sample in order to determine critical strain for crystal growth in α-iron specimen. When stretched in tension, a range of strains is produced in the specimen. Upon annealing, the strain at which recrystallization initiates can then be    38  found from a single sample. It is worth noting that here is a gap in knowledge to estimate the critical strain for recrystallization and, to the best knowledge of the author, no work has been done to determine critical strain to initiate recrystallization in 3xxx aluminum alloys. 2.7    Effect of Particles on Grain Boundary Movement When a boundary intersects a particle, a region of boundary equal to the intersection area is effectively removed which leads to a reduction in the energy of the overall system. Hence, grain boundaries are attracted to particles during recrystallization. The migration rate of recrystallization fronts are retarded by a pinning pressure, named Zener drag, due to fine particles situated on the grain boundaries. A comprehensive review on Zener pinning pressure, Pz, has been done by Manohar et al. [122]. This review paper summarizes several modifications to the original equation proposed by C.S. Smith in 1948 [123]. Based on discussions on the modified versions of the pinning pressure equation from several studies such as [122, 124], there is a range in which analytical models have a good agreement with experiments using the following equation [122, 124, 125]  rfP zz (2.21)    39  where αz is a constant with a value of 1.1-1.37, γ refers to grain boundary energy, f is particle volume fraction and r is the particle radius.  Dispersed second-phase particles exert a retarding pressure on the low- and high-angle boundaries which significantly affects the recovery, recrystallization and grain growth during annealing of deformed structures [65]. Zener drag is a complex function of the interface, shape, size, interspacing and volume fraction of dispersed particles [65, 126]. Homogenization treatment is applied to direct-chill cast aluminum alloys before hot deformation in order to form small dispersoids which act as recrystallization inhibitors during deformation and annealing or solution treatments [126]. For instance, Mn-bearing dispersoids in 3xxx series aluminum alloys play an important role in controlling the recrystallization behavior of the alloys [126, 127]. In AA6xxx aluminum alloys, Zr-, Mn- and Cr-containing dispersoids significantly inhibit the recrystallization process [128-132]. By examining a number of experimental investigations, Humphreys and Hatherly [65] have concluded that to a first approximation, the retardation is most likely to occur when f/r is greater than 0.2 μm-1. If the ratio is less than 0.2 μm-1, recrystallization is often accelerated in comparison with particle-free material due to the increased driving force that arises from the additional dislocations generated by the particles during deformation.    40  During thermomechanical processing or annealing of a deformed and supersaturated material, recovery as well as recrystallization may be influenced by the precipitation reaction, a phenomenon which is commonly referred to as concurrent precipitation. The different precipitation phenomena that may occur in the concurrent precipitation regime were first reported by Hornbogen [133] and Köster [134], while Nes and Embury [135] reported on the abnormal grain size that may result from this reaction. Later works by Nes and co-workers [136, 137] focused on the texture aspects associated concurrent precipitation. Also, Tangen and co-workers [2] showed that concurrent precipitation of Mn-bearing dispersoids in Al-Mn alloy strongly affects recrystallization kinetics as well as recrystallized grain size and shape.  2.8    Summary This chapter has summarized some of the previous works conducted on the AA3xxx or similar systems. Also, this chapter provides some principles and information required to understand tensile response and annealing behaviour of AA3xxx system. As discussed in this chapter, post extrusion deformation followed by annealing has been the least studied step which is the main focus of the current work. Chapter 3 describes the scope and objectives of the current study to increase the knowledge of the annealing behaviour of AA3xxx after extrusion.     41  CHAPTER 3   Research Scope and Objectives To date, the effect of post extrusion deformation followed by heat treatment on the microstructure and mechanical properties is the least studied step in the processing of extrusion alloys. As discussed in the literature review, there are knowledge gaps on the recrystallization behaviour of 3xxx aluminum alloys, especially at small strains, i.e. less than 10%.  Thus, the range of conditions examined in the current work encompassed alloys with different level of Fe, i.e. AA3003 (0.54 wt% Fe) and low iron 3003 (0.09 wt% Fe) as Fe affects the volume fraction and size of constituent particles. Also, different level of Mn in solid solution, 0.05 wt% to 1.2 wt%, was studied. Dispersoids and constituent particles volume fraction ranges 0% to 3% and 1% to 4%, respectively. Annealing of cold deformed samples was carried out at 350 °C to 600 °C.  The broad objective of the present work is to obtain a fundamental understanding of post-extrusion thermomechanical processing of AA3003 alloys in order to improve the properties and quality of these alloys. The following objectives are sought in this work:   To study the conditions under which abnormally large grains are produced after low level of deformation at room temperature followed by annealing at very high temperature, 600 ºC    42   To examine the effect of initial microstructure (e.g. dispersoids density/level of manganese in solid solution/grain size) on the yield stress, grain size and critical strain required to initiate recrystallization of these alloys  To determine the critical plastic strain required to initiate recrystallization at 600 °C. There are two main reasons for determining the critical strain at 600 °C: (i) industrial practice of brazing for these alloys is done at this temperature and (ii) homogenization is done at 600 °C, hence, almost no changes in dispersoids and constituents was observed and then no additional microstructure variable came into the picture.  To develop a physically based model using the internal state variable approach to translate a qualitative description of the interaction between recrystallization and second-phase particles into a quantitative description of critical strain required for onset of recrystallization.  The present work would provide the first scientific approach to consider strain hardening, recrystallization and precipitates (dispersoids) as well as their interaction within a single model framework for annealing behavior of AA3xxx.    43  CHAPTER 4   Methodology The primary objective of the experimental work was to generate a series of data in order to study mechanical property and recrystallization behavior of 3xxx aluminum alloys. The as-received materials were subjected to a series of thermomechanical processes. The microstructures of the specimens were examined using a variety of characterization tools. The details of these experiments are described in this chapter. 4.1   Materials and Homogenization The starting material for the experiments was DC cast as 100 mm diameter billets of AA3003 and low Fe AA3003. The billets were cast at Rio Tinto Alcan’s Arvida Research and Development Research Centre. Table 4.1 shows chemical composition of these alloys. Prior to high temperature extrusion, for both alloys, the material underwent different homogenization treatments, i.e. 1 and 24 hr at 600 °C followed by water quenching which give rise to high and very low density of dispersoids, respectively. Homogenization heat treatment were performed with a heating rate of 150 °C/h and a heating rate of 50 °C/h for the last hour to the homogenization soaking temperature. In order to produce another microstructure with different size and volume fraction of dispersoids, extruded AA3003 samples homogenized for 1 hr (with high density of dispersoids) were heated to 400 °C (using a salt bath) and held for 7 hr. This heat treatment prompts the pre-existing Mn-bearing dispersoids to grow. For simplicity,    44  the homogenization conditions have been designated as: 3003 samples homogenized for 1 hr at 600 °C (H1), those homogenized for 24 hr at 600 °C (H24), H1 samples heat treated at 400 °C for 7 hr (H1-7h), Low Fe 3003 samples homogenized for 1h at 600 °C (H1-LF) and Low Fe 3003 samples homogenized for 24 hr at 600 °C (H24-LF). In addition to the above conditions, two more conditions were also studied in this work: (i) as-cast 3003 samples and (ii) the as-cast samples first heat treated to 500 °C with a heating rate of 50 °C/h, quenched and then reheated to 375 °C (using salt bath) and held for 24 hr (labeled: 375C-24h). Extrusion was done with a billet temperature of 480 °C and container temperature was 450 °C. Ram speed was 8 mm/s (an exit speed of 100 m/min). Extrusion ratio was 210:1 and billets were extruded to produce plates 30 mm in width and 1.3 mm in thickness. In order to study effect of grain size on the critical strain required for onset of recrystallization, extruded samples homogenized for 1 and 24 hours with a large initial grain size were examined. As-received extruded 3003 samples (with 12 and 14 µm grains) were cold rolled for 25% and 10%, respectively and then annealed for 1 min at 600 °C in salt bath.  Table 4.1. Chemical composition of experimental alloys (wt%). Alloy Mn Fe Si Ti Cu Al AA3003 1.27 0.54 0.1 0.02 <0.01 Bal. Low Fe AA3003 1.16 0.09 0.07 0.02 <0.01 Bal.    45  4.2   Sample Preparation Characterization of the material was conducted along the extrusion direction. Hence, micrographs are taken from normal direction-extrusion direction plane (ND-ED). Tensile samples with 40 mm gauge length and 6.35 mm width were taken out along the extruded strip using wire cut electrical discharge machining (EDM).  In order to have a gradient of strain along a sample, tapered samples were also used with 40 mm gauge length, 6.35 mm largest width and 4.00 mm smallest width. Figure 4.1 shows a tapered sample used in this study. Some tensile tests were also carried out on as-cast samples. The as-cast samples were cylindrical in shape with 5.4 mm diameter and 40 mm reduced section.  4.3  Metallography  To prepare the surface of interest for microstructural examination, specimens were cold mounted and then mechanical ground (120/320/400/600 grade SiC) was performed followed by diamond polishing using 6 μm (~8 min) and 1 μm (~5 min) suspension. After diamond polishing, samples were polished chemically and/or anodized with the intention of revealing intermetallic phases and/or grain structure, respectively. Chemical polishing was carried out in hydrofluoric acid (0.5% volumetric HF) for 60 seconds. Barker’s reagent, i.e. 3% HBF4 in distilled water (48% HBF4 concentrate) was employed at room temperature to anodize the material to reveal    46  grains. Pure aluminum was used as the cathode and the sample as the anode hooked up to the power supply (0-60 V and 0-2 A DC Power Supply). Sample was immersed in the reagent at an angle to prevent formation of air bubbles at the surface. Once aluminum piece and sample in the solution, the voltage was slowly turned up to 30 to 34 V. Anodizing time was varied from 30 to 60 seconds as it depends on sample size and freshness of solution. Poulton’s reagent (60 ml HCl/30 ml HNO3/5 ml HF/5 ml H2O) was also used to reveal very large grains. Samples were mechanically ground using 320 grade SiC grinding paper and then warmed by hair dryer for 45 seconds followed by immersion into the Poulton’s reagent for 20-50 seconds (depends on how fresh the solution was). Figure 4.2 shows very large grains after revealed by Poulton’s reagent.   Figure 4.1.  Tapered sample used in this study. Cvncvncncncncncvncnfgg w1= 4.00 mm  w2= 6.35 mm 40 mm    47   Figure 4.2.  Grains are revealed using Poulton’s reagent (note: this is a conventional tensile sample). 4.4  Deformation All the samples were uniaxially deformed in tension at room temperature. Two approaches were employed: (a) normal tensile specimen and (b) tapered sample to provide a continuous range of strains. Tests were conducted using Instron screw-driven machine with a 5 kN load cell, at a nominal strain rate of 2 × 10-3 s-1. An extensometer was attached to the samples in order to measure the change in length, ∆L, of the sample within the guage length of the extensometer (L0=12.5 mm). Engineering stress, S, and strain, e were calculated as S=F/A0 and e=∆L/L0 (F: Load and A0: initial area of the section bearing the load). True strain (ε) and true stress (σ) were calculated using the following equations:   e 1ln  (4.1) and   eS  1  (4.2)    48  The yield stress was determined based on a 0.2% offset strain method. To extract work hardening rate, a 3rd order exponential decay curve was fit to the true stress-true strain curve (R2>0.999) using the Origin software and then the equation was mathematically differentiated in order to obtain the work hardening rate. To achieve a strain gradient using one sample (a range of 1% to 10%), a tapered sample was used as shown in Figure 4.1. A series of images were captured (1 image per second) using digital camera (QImaging QICAM fast 1394). Afterwards, post processing of images was carried out using DaVis digital image correlation software (La Vision Inc., Ypsilanti, USA). Multi-pass correlation strategy with a final interrogation window size of 128×128 pixels with 75% overlap was chosen to compute the in-plane displacement fields and finally in-plane strain field. Interrogation window is the area used to search corresponding patterns between images. It is worth noting that LaVision digital image correlation system uses a cross-correlation algorithm to track the movement of a speckle pattern on the specimen surface from a sequence of recorded images. From the algorithm, deformation vectors of the speckle pattern are calculated and the strains within the material can be evaluated. As such, a speckle pattern was applied (fine black spots on white colour) on the tapered samples. In order to apply this pattern, specimens first painted with white colour and then very fine spots were applied by spraying black colour from some distance on the white surface. Figure 4.3a    49  illustrates the selected area on a tapered sample in which strain was calculated using DaVis software and Figure 4.3b shows strain gradient along a tapered sample.  Cold rolling (roll diameter: 154 mm) was also conducted in order to apply large strains. Thickness reductions were accomplished in few passes depending on the target     (a)                              (b)  Figure 4.3.  (a) A tapered sample with a shaded region in which strain measurement was carried out and (b) strain along the shaded section using digital image correlation technique.    50  reduction. The extruded materials were rolled at room temperature to 10, 20, 40, 65 and 80% thickness reduction. The von-Mises equivalent strain can be calculated from the thickness reduction, r, according to    r11ln32 (4.3)  As such, strains of ~ 0.12, 0.25, 0.54, 1.21 and 1.86 were obtained after rolling. 4.5 Post Deformation Heat Treatments  Thermal treatments of deformed samples were conducted using a salt bath having a composition of 40% NaNO3 + 60% KNO3 in order to have high heating rate. Heating rate in a salt bath was measured experimentally by attaching a K-type thermometer to a AA3003 sample, 100 mm (L) × 30 mm (W) × 1.3 mm (T), and put it in a salt bath pre-heated to 600 °C. Figure 4.4a illustrates thermocouple attached to an extruded sample to measure the heating rate of salt bath. The heating rate is measured and shown in Figure 4.4b (heating rate of 97.4 °C/s ~100 °C/s). Annealing was done at 600 °C with a holding time of 1 min to have minimal changes in dispersoids density. Annealing was also carried out at other temperatures ranges from 350 to 600 °C with the purpose of studying annealing behavior of these alloys. All these annealing were conducted in the salt bath.      51  4.6 Sample Characterization The microstructures were characterized using a variety of experimental techniques including optical microscopy (OM), scanning electron microscopy (SEM), electron back-scattered diffraction (EBSD), Field emission gun SEM (FEGSEM), and electrical conductivity measurements.  4.6.1 Optical Microscopy Photomicrographs of the microstructures were taken using a Nikon EPIPHOT 300 series equipped with a digital camera. Polarizer slide and analyzer slide were put in the light path in order to observe grain in anodized samples. Post processing of the micrographs was completed employing Clemex Professional Imaging software. Micrographs were printed out and then the grain boundaries were manually traced on a transparent plastic sheet. Afterwards, the transparent sheets were scanned into computer and analyzed by the Clemex software. Grain size measurement was done based on ASTM E 112 [138].      52    (a)   (b)  Figure 4.4.  (a) K type thermocouple attached to the sample and (b) heating rate in a salt bath 97.4 ºC/s     53  4.6.2 Scanning Electron Microscopy (SEM) To examine constituent particles, SEM micrographs were taken on a Hitachi S-3000N SEM operating at 20 keV. Back scattered electron (BSE) images were taken in order to reveal constituent particles with sharp and clear edges.  Also, a ΣIGMATM ZEISS FEGSEM operating at 20 keV was used in order to study dispersoids size. Images obtained from SEM and FEGSEM were printed out. The particles’ boundaries were manually traced on a transparent plastic sheet, which was then scanned into computer.  Scanned images were analyzed by Clemex Image Analysis software. 4.6.3 Electron Back Scattered Diffraction (EBSD) EBSD was used to determine the microtexture. The measurements were carried out on a Hitachi S-570 SEM equipped with a electron back scattered detector. The operating conditions were as follows: accelerating voltage 20 keV, Samples tilt 70°, working distance 23 mm, step size 1-2 μm. The indexing rate ranged from a minimum of 85% up to as high as 96%. The HKL Channel 5 software was used to obtain the EBSD patterns. A medium level (five neighbouring points) of zero solution extrapolation has been applied to the data to remove non-indexed points. 4.6.4 Electrical Conductivity Measurements Electrical conductivity of samples was measured using a Sigmatest® 2.069 (by Foerster Instruments Inc.TM) with an 8 mm probe. Standard samples were used to    54  calibrate the unit each time before use. Measurements were made using a frequency of 60 KHz. The data was output in units of MS/m. The electrical conductivity of the extruded samples before and after annealing was measured. The units were converted using the following equation. Electrical conductivity, δ, was converted to resistivity, ρelec according to  ].[1013 mnelec   (4.4)               55  CHAPTER 5   Experimental Results and Discussion In this chapter, experimental results are presented by following the sequence of the experiments. Prior to deformation and annealing, characterization of the as-received materials (extruded samples homogenized prior to extrusion) was carried out in order to study the effect of initial microstructure on the annealing behaviour. First, the characterization of AA3003 and low Fe 3003 is presented. Second, tensile behaviour of these alloys and then annealing behaviour of 3003 and low Fe 3003 was studied. Afterwards, critical strains for recrystallization were experimentally determined. In addition, the effect of large pre-strains on the recrystallization behaviour is presented. Finally, concurrent precipitation during recrystallization of these alloys is discussed. 5.1   Characterization of Initial Microstructure 5.1.1   AA3003 Constituent particles, Al6(Fe, Mn), and dispersoids, α-Al(Mn,Fe)Si, are the main intermetallic phases of AA3xxx series [11, 19]. Since these phases have a significant effect on the annealing behaviour, metallographic examinations were conducted in order to characterize them. Grajales [5] reported that as-cast 3003 samples have grain size of 60-68 µm (circular diameter). Figures 5.1a and 5.1b show optical images of HF etched 3003 samples homogenized for 1 hr and 24 hr at 600 °C followed by high    56  temperature extrusion. All the micrographs in this work are taken from the extrusion-normal direction plane (ED-ND plane) unless otherwise noted. The fine grey spots are  50 μm50 μm (a) (b) Figure 5.1.  Micrographs showing microstructure of extruded samples (plate) homogenized at 600 °C for: (a) 1 hr and (b) 24 hr.  etch pits  which form near dispersoids and the darker, larger particles are the constituent particles. Constituent particles are aligned with the extrusion direction. As discussed in the literature review, during a homogenization treatment, dispersoids first nucleate and grow in the primary aluminum dendrites, but for longer times, long range diffusion of Mn to the constituent particles causes the dispersoids to dissolve. As such, samples homogenized for 1hr had a large density of dispersoids while samples homogenized for 24 hr had almost no dispersoids. TEM images of dispersoids in H1 samples and their crystal structure are shown in Figure 5.2 (TEM work was done by Dr. Reza Roumina at UBC). Diffraction pattern confirmed that dispersoids are α phase, Al(Mn,Fe)Si and    57  have a body centered cubic (BCC) crystal structure. FEGSEM was utilized in order to measure the average size of dispersoids (Figure 5.3). Area of each particle (A) was estimated using Clemex Professional Imaging software on FEGSEM micrographs and then equivalent circle diameter (2D) was calculated using this equation, D=2 (A/π)0.5. A factor of 1.273 was used to convert 2D mean size to 3D mean size [139]. sdfjkhsfjkhsfkjshdl  R. Roumina, UBC (2010) (a) (b) Figure 5.2. (a) Bright field TEM image and (b) corresponding diffraction pattern taken from samples with high density of dispersoids (Work done by Dr. Roumina at UBC). Djgasdkjhgadjsdasdad The dispersoids in H1 samples were measured and have an average 3D diameter of 104 nm (over 200 dispersoids were examined). The 3D diameter size distribution of dispersoids in H1 samples is shown in Figure 5.4. The volume fraction of dispersoids in H1 samples was calculated using the model developed by Du et al. [19, 140]. This mathematical model was developed to simulate the precipitation kinetics during heat    58  treatment of multi component aluminum alloys. The model is based on the general numerical framework proposed by Kampmann and Wagner and features a full coupling with CALPHAD software [19, 140].    Figure 5.3.  A FEGSEM micrograph showing dispersoids in 3003 samples with high density of dispersoids. jhgajg hjksa gkjsag ksjg hak   Figure 5.4.  Size distribution (3D diameter) of dispersoids in AA3003 samples homogenized for 1 hr.    59  Regarding the constituent particles, Geng [17] conducted measurements on these particles for samples homogenized for 1 hr and 24 hr (on extruded samples). Constituent particles were found to have an average 3D diameter of 1.2 μm and 1.6 μm for H1 and H24 samples, respectively (Geng [17] reported the diameters in 2D - A factor of 1.273 was used to convert them to 3D mean size [139]). The area fraction of constituent particles in H1 and H24 samples was measured to be 2.9% and 3.8%, respectively [17]. A minimal change in the characteristics of the constituent particles is expected in H1 samples held for 7 hr at 400 °C since Mn solute atoms come out of the solution in the form of dispersoids. In other words, there is no long range diffusion and only growth of dispersoids occurs during this heat treatment. Hence, constituent particles in H1-7h samples will be assumed to have the same size and volume fraction as the ones in H1 samples. Figure 5.5 shows the equiaxed grain structure in H1 and H24 samples extruded at high temperature (i.e. strips, 30 mm × 1.3 mm). An average grain size of 12 and 14 μm (circular diameter) was measured for H1 and H24 samples, respectively. The grain structure for the starting materials was also characterized by EBSD as shown in Figure 5.6. Pole figures of the two conditions show a relatively strong cube texture which is a common texture for a recrystallized microstructure after plane strain deformation (i.e. while the extrusion done in this work was not plane strain, the width strain was much less than the thickness strain so the deformation did tend towards plane strain rather than uniaxial deformation) [65]. No grain growth is expected for H1 samples held for 4    60  hours at 400 ºC because: (i) there is a small growth of grains in H24 samples annealed for 24 hr at 600 ºC compared to H1 samples homogenized for 1 hr, ~ 2 µm and (ii) this treatment was done at much lower temperature, 400 ºC, than the annealing temperature, 600 ºC for only 7 hr. 50 μm (a) 50 μm (b) Figure 5.5. Optical images showing grain structure in AA3003 extruded strips with: (a) high density of dispersoids and (b) almost no dispersoids.    61                        100 μm {111} EDTD (a)  100 μm  {111} EDTD  (b) Figure 5.6. EBSD maps and pole figures of extruded strips in AA3003 system homogenized at 600 °C for (a) 1 hr and (b) 24 hr    62  5.1.2   Low Fe AA3003 Characterization was also carried out on low Fe 3003 specimens, and constituent particles of samples homogenized for 1 hr and 24 hr had an average spherical diameter of 3.0 μm and 4.6 μm, respectively. Figure 5.7 shows these constituent particles in these two homogenization conditions. The area fraction of constituent particles measured experimentally in H1-LF and H24-LF samples is approximately 1.5% and 1.7%, respectively.  Figure 5.8 provides micrographs obtained from FEGSEM showing dispersoids in H1-LF samples. Dispersoids have an average spherical diameter of 72 nm (over 100 particles were examined). The size distribution of dispersoids in H1-LF samples is illustrated in Figure 5.9. For the extruded strips, grain size of 32 μm and 20 μm were obtained for H1-LF and H24-LF samples, respectively.  Tables 5.1, 5.2 and 5.3 summarize all the characteristics of the initial microstructure of samples used to study critical plastic strain for recrystallization and recrystallization behaviour after rolling and tensile behaviour, respectively. All the values in these tables will be discussed in this section.       63  Jhgadasddfsfsfkadfadf  (a)  (b) Figure 5.7. Back scattered images showing constituent particles in Low Fe 3003 samples homogenized at 600 °C for: (a) 1 hr and (b) 24 hr.  Sdsadadadasdsadasdsdad    64   Figure 5.8.  FEGSEM micrograph showing dispersoids in low Fe 3003 samples homogenized for 1h at 600 °C. hgfasghdfhasdgfhasdgfhsagdfhad  Figure 5.9.  Size distribution (3D diameter) of dispersoids in Low Fe AA3003 samples homogenized for 1 hr. 65  Table 5.1. Initial microstructural characteristics of extruded strips used to study critical plastic strain for onset of recrystallization  Material Grain Size (µm) EQAD Constituent Particle Radius (µm) 3D Constituents Area Fraction (%) Dispersoids Radius (nm) 3D Dispersoids Area Fraction (%) Mn Level in Solid Solution (wt%)# H1 12+ 0.6+ 2.9+ 52+ 1.01@ 0.5 H1-7h$ 12* 0.6* 2.9* 69 2.31 0.07 H24 14+ 0.8+ 3.8+ - - 0.5 H1-LF 32+ 1.5+ 1.5+ 36+ 0.21@ 0.76 H24-LF 20+ 2.3+ 1.7+ - - 0.76 H1-LG& 98+ 0.6* 2.9* 52* 1.01* 0.5 H24-LG& 98+ 0.8* 3.8* - - 0.5 # Obtained from equilibrium phase diagram. + Experimentally measured. @ Estimated from the model developed by Du et al [19, 140] $ These samples are the result of holding H1 samples for 7 hours at 400 °C. *Assumed unchanged from the original condition. & These conditions were examined to study the effect of initial grain size on critical strain for onset of recrystallization (LG: Large Grains ~ 98  µm)    66  Assasasasassas Table 5.2. Initial microstructural characteristics of extruded strips used to study recrystallization behaviour after rolling  Material Grain Size  Constituents Radius (µm) Constituents Area Fraction (%) Dispersoids Radius (nm) Dispersoids Area Fraction (%) Mn Level in Solid Solution (wt%)# H1 12+ µm 0.6+ 2.9+ 52+ 1.01@ 0.5 H24 14+ µm 0.8+ 3.8+ - - 0.5 H1-LG 0.5-3.0 mm  0.6* 2.9* 52* 1.01* 0.5 H24-LG 0.5-3.0 mm 0.8* 3.8* - - 0.5 # Obtained from equilibrium phase diagram. + Experimentally measured. @ Estimated from the model developed by Du et al [19, 140] *Assumed unchanged from the original condition.  67   Dasadadaadad Table 5.3. Initial microstructural characteristics of AA3003 un-extruded samples used to study tensile behaviour of these alloys  Material Grain Size (µm)  Constituents Radius (µm) Constituents Area Fraction (%) Dispersoids Radius (nm) Dispersoids Area Fraction (%) Mn Level in Solid Solution (wt%)# As-cast 60-68§  - 2.4+ - - 1.2 375C-24h& 60-68* - 2.4* 21@ 2.75‡ 0.055 # Obtained from equilibrium phase diagram. § Experimentally measured by Grajales [5] + Experimentally measured by Geng [17] & As-cast samples first heat treated to 500 °C with a heating rate of 50 °C/h and for the second heat treatment, they were heated to 375 °C and held for 24hours. *Assumed unchanged from the original condition. @ Reported by Li et al. [13] ‡ Calculated by keeping the Mn balance constant in the system   68  5.2   Tensile Behaviour As described before, the extruded materials were deformed in the small and large strains regimes. A uniaxial tensile test on conventional tensile specimens and tapered samples were performed. A tensile test on a tapered sample allows for a range of strain to be imposed to a single sample (1-10%). To examine large strains, cold rolling was conducted (up to a true strain of 1.86). Before conducting deformation to study annealing behaviour, it is useful to examine the tensile behaviour of these alloys as it sets the stage for subsequent recovery and particularly recrystallization processes. Hence, this behaviour is examined here as follows: 5.2.1 AA3003  True stress-strain curves of AA3003 samples are illustrated in Figure 5.10. Yield stress and UTS values obtained for each condition are reported in Table 5.4. As-cast samples with the highest amount of Mn in solution have much higher yield stress compared to H1, H24 and H1-7h samples. There is a small difference between H1 and H24 samples, although H1-7h samples show lower values for mechanical properties compared to H1 and H24 samples.        69  adadasdsaasdd  Figure 5.10.  True stress-true strain curves for AA3003 samples. Sadsadsadasdad Table 5.4. Experimental values of yield stress and engineering UTS for different conditions of AA3003.    Material H1 H24 H1-7h As-cast 375-24h Yield Stress (MPa) 48 46 37 59 70 UTS (MPa) 114 104 98 138 143     70  This result is consistent with the work done by Ryen and co-workers [6] showing that the amount of manganese in solid solution has a significant effect on yield stress (see section 2.2.1 for more information). In order to obtain the phase diagram, Thermo-calc software with TTAL6 database was used. Then, the components of the system, i.e. elements (Al, Fe, Mn and Si) and possible equilibrium phases, FCC matrix and the second phases, i.e. Alpha and Al6Mn were chosen. Afterwards, thermodynamic equilibrium calculation was performed over a range of temperature. Output of these calculations is the Mn content in the FCC matrix at different temperatures as illustrated in Figure 5.11. There is a significant drop in solubility of manganese in aluminum by changing the temperature from 600 °C to 400 °C. As such, holding H1 samples for 7h at 400 °C gives rise to growth of pre-existing Mn-bearing dispersoids. Although 375C-24h samples has the lowest level of Mn in solid solution, they possess the highest yield strength. These samples are the result of heating the as-cast samples to 500 °C (heating rate: 50 °C/h), quenching and then reheating and holding them at 375 °C for 24 hr which leads to precipitation of very high density of dispersoids. It has been reported that precipitation hardening (see section 2.2.3) is a relevant strengthening mechanism for AA3xxx alloys although they are in the class of non-heat-treatable alloys [5, 12, 43]. For example, Li et al. [12] examined two conditions in commercial 3003 alloys quite similar to the H24 and 375C-24h conditions in this work and they found quite similar effect    71   Figure 5.11. Manganese solubility in solid solution as a function of temperature calculated using Thermo-Calc (TTAL6 database) for both alloys. regarding dispersoids on the yield strength (~52% increment). The author will return to this point in Chapter 6 where a model for the yield stress and work hardening will be described.  Figure 5.12 shows work hardening behaviour of AA3003 samples for different conditions. Elastic-plastic transition followed by Stages II, III and IV (a breakdown of the linear decrease in the work hardening rate with stress) are observed in all conditions. Also, Figures 5.13 and 5.14 illustrate the mechanical response of H1 and H24 samples with different initial grain sizes. These figures show the effect of fine dispersoids on the flow stress of H1 samples compared to H24 samples where there are almost no α + Al6Mn α     72  dispersoids. In other words, grain size effect is more noticeable in H24 samples compared to H1 samples.    Figure 5.12.  Work hardening rate vs stress curves for AA3003 samples. Yield stress for each condition is shown on the curves. For 375C-24h condition, since the first stage of work hardening is very large, the yield stress cannot be illustrated (yield stress=70 MPa). 5.2.2 Low Fe 3003 The stress-strain response and work hardening rate of Low Fe 3003 samples are shown in Figures 5.15 and 5.16, respectively. Similar to AA3003 samples, Stage II, III and IV were observed. There is a small difference between the samples homogenized for 1 and 24 hr and this discrepancy is probably associated with the dispersoids with diameter of 72 nm and volume fraction of 0.21%. Yield stress of 46 and 45 MPa was achieved for H1-LF and H24-LF samples, respectively.     73   Figure 5.13.  True stress-true strain curves for H1 samples with different initial grain size (spherical diameter of dispersoids = 104 nm, volume fraction of dispersoids = 1.01%). Gjdagsdjhasdjghjdghjh  Figure 5.14.  True stress-true strain curves for H24 samples with different initial grain size (almost no dispersoids in the microstructure).    74  nahdmdjfajsdfadfhajdhfajdhfadjh  Figure 5.15.  True stress-true strain curves for Low Fe 3003 samples (initial grain size: H1-LF=32 µm and H24-LF = 20 µm). Hgfghkjfdkjdsdfsdsdfsdfssfsfsfsfsfsfsfsfsfkj  Figure 5.16.  Work hardening rate of Low Fe 3003 samples. Hgadhjgadjadghadjghajdgaadgakdja     75  5.2.3 Discussion As described in Chapter 2, there are four main mechanisms that affect the yield stress of 3003 and low Fe 3003 alloys: (i) level of Mn in solid solution, ii) grain size strengthening, (iii) precipitation hardening due to dispersoids and (iv) constituent particles strengthening. All these factors should be taken into consideration in order estimate the yield strength on these alloys. For example, as-cast samples with almost no dispersoids but with a maximum amount of Mn in solid solution, 1.2 wt%, have the second highest yield stress and work hardening rate. Further, H1-7h samples have the lowest yield stress and work hardening rate as they have very low Mn in the solid solution. Comparing the yield stress values for these alloys (Table 5.4) shows that Mn in solid solution can increase the yield stress by more than 50%. Solid solution hardening is a result of interaction between mobile dislocations and solute atoms. Dispersoids play an important role in the stress-strain response of AA3003 samples compared to the initial grain size of this alloy. For instance, 375C-24h samples show the highest yield stress and work hardening rate due to very fine dispersoids, 21 nm in radius and a high volume fraction of dispersoids, 2.75%, as shown in table 5.3. The enhancement of the work hardening rate in samples with a high density of dispersoids (non-shearable precipitates) can be attributed to: (i) the storage and relaxation of additional geometrically necessary dislocations [44] and (ii) the development of internal stresses due to non-deformable particles [46, 47]. For AA3003 alloys, there are three factors    76  affecting work hardening rate: (i) geometrically necessary dislocations produced around dispersoids, (ii) storage of elastic energy around constituent particles and (iii) interaction of solute atoms with dislocations related to the Mn solid solution level. Grain size effect on the mechanical response of 3003 was also examined. In H1 samples with different initial grain size (12 µm vs 98 µm), no significant difference in stress-strain response is observed. However, in H24 samples where there is almost no dispersoids, difference in flow stress is more noticeable. One can speculate that dispersoids have a strong effect on tensile behaviour of AA3003 alloy and also minimize effect of grain size on the stress-strain response. On the other hand, grain size effect on the tensile response can be realized once there are no dispersoids in the microstructure. It should also be noted that further study is required in order to fully understand this behaviour and make a firm conclusion.  5.3   Annealing Behaviour  5.3.1  Critical Plastic Strain for Recrystallization in AA3003 The deformed tapered samples with different initial microstructure were annealed at 600 °C for 60 seconds in a salt bath which has a high heating rate, ~100 °C/s. In order to see if any microstructural changes occurred during annealing, electrical resistivity of samples before and after annealing was measured. The resistivity measurements before and after annealing on samples with fine (12-14 µm) and large    77  (~98 µm) initial grains show almost no change (See Table 5.5 and 5.6). This suggests minimal change in the constituents and dispersoids particles in the microstructure during the 60s anneal.  Figures 5.17a and 5.17b show the boundary between recrystallized (very large grains) and unrecrystallized regions in an annealed tapered sample in macro- and micro-scale, respectively. As described in the methodology section, Poulton’s reagent was used to reveal the large recrystallized grains on the tapered samples. In the recrystallized part of the sample (right side of the arrow), grains get finer as we move towards the narrowest section due to the higher pre-strain in this section. This boundary represents the critical strain required to recrystallize the microstructure at 600 °C.  Dfhgdsjhjkhkhfhgfdfhgf  Table 5.5. Electrical resistivity before and after annealing of samples with fine initial grains, 12-14 µm (values are in nΩ.m).  Material Before Annealing After Annealing H1 48.0 ± 0.3 48.2 ± 0.3 H24 46.1 ± 0.3 46.0 ± 0.3 Bcvbcvbcvznbc     78  Table 5.6. Electrical resistivity before and after annealing of samples with large initial grains, 98 µm (values are in nΩ.m).  Material Before Annealing After Annealing H1/LG 48.0 ± 0.3 47.9 ± 0.3 H24/LG 46.1 ± 0.3 45.9 ± 0.3 asdsadasdadsadasdasdasd 10 mm (a) 10 mm10 mm (b) Figure 5.17.  Boundary between recrystallized and unrecrystallized regions in (a) macroscopic (Poulton’s reagent) and (b) microscopic scale (anodized). Please note, these images are taken from two different H24 samples. Adasdaddadadsasdd    79  In order to determine the critical plastic strains, each tapered sample was marked at 3 locations with known distances from the narrow side. These marks were detectable in the images obtained from the DaVis software. Afterwards, distance between one mark and the boundary was measured and then corresponding strain was obtained from the DaVis software. Please note, the strain recorded in the software was plastic strain as after deformation because digital image correlation was used on unloaded samples.  Figure 5.18 shows development of pre-strain along a tapered sample as time passes. Strain increases rapidly at the small width section of a tapered sample compared with the larger width. The critical plastic strain for each condition was determined from at least 4 samples and is shown in Tables 5.7 and 5.8 for 3003 samples with fine and large initial grain size. Table 5.9 shows a summary of the critical strains range for AA3003 samples in each condition. The results of Table 5.9 suggest that there is a very small difference in critical plastic strains in H1 samples with different initial grain size, i.e. slightly higher strains for samples with large grains. For H24 samples, there is almost no change in critical plastic strain for onset of recrystallization.     80   t 2 t 1 t 3 t 4 t 5 Tapered sample Figure 5.18.  Strain along a tapered specimen at different times of loading, i.e. t1<t2<t3<t4<t5 (note: this curve is extracted from DaVis software) Hjsadgjhdgjahdgjkad Table 5.7. Critical plastic strain for recrystallization of AA3003 samples (initial grain size: 12 µm for H1 and H1-7h samples and 14 µm for H24 samples). Material Sample 1 Sample 2 Sample 3 Sample 4 Sample 5  Sample  6 Sample 7 Sample 8 H1 9.4% 8.0% 8.5% 8.8% 10.0% 9.8% 9.7% 10.0% H24 1.8% 2.0% 2.0% 1.9% 2.0% 1.9%   H1-7h 18.5% 17.5% 19.0% 19.0%        81  Vxvxnzbvx Table 5.8. Critical plastic strain for recrystallization of AA3003 samples (initial grain size: 98 µm). Material Sample 1 Sample 2 Sample 3 Sample 4 H1 9.7% 9.0% 10.0% 10.6% H24 1.8% 2.0% 2.0% 2.2% Vxvxnzbvkjkljlkjjlx Table 5.9. Critical plastic strain range for recrystallization of AA3003 samples. Material H1 H24 H1-7h Critical Plastic Strain (initial grain: 12 & 14 µm) 8.0-10.0% 1.8-2.0% 17.5-19.0% Critical Plastic Strain (initial grain: 98 µm) 9.0-10.6% 1.8-2.2% _ Jadghajkdgajkdgadjagd  Figure 5.19 shows the result for the recrystallized grain size as a function of applied plastic strain in tapered H1 and H24 samples. Larger recrystallized grain size was achieved for H1 samples suggesting the important effect of dispersoids on pinning the recrystallization front.     82  5.3.2 Critical Plastic Strain for Recrystallization in Low Fe 3003 The same trend observed in AA3003 material was obtained for the low iron 3003 samples. Figure 5.20 shows the boundary between recrystallized and unrecrystallized regions for samples with a different density of Mn-bearing dispersoid. It should be noted that test of these samples stopped at the same point in order to have similar strain gradients along the tapered samples. Four samples were examined for this system, as shown in Table 5.10. Larger critical strain for samples with a higher density of dispersoids (H1-LF) was required for onset of recrystallization which directly reflects   Figure 5.19.  Recrystallized grain size versus strain along tapered H1 and H24 samples with small initial grain sizes (12 µm for H1 and 14 µm for H24 specimens).    83   the pinning pressure of dispersoids on recrystallization behavior of these alloys.  As discussed in Chapter 2, f/r ratio is an important factor as it defines dragging pressure on the recrystallization front (see Equation 2.21). As such, the critical strain range with respect to f/r ratio for low Fe 3003 and 3003 samples is summarized in Table 5.11. At least 4 samples were tested in order to determine the critical strain for initiation of recrystallization. Figure 5.21 shows the critical plastic strain required for recrystallization onset versus the total amount of f/r ratio (dispersoids + constituents). 5.3.3 Discussion The stored energy in the aluminum polycrystal is almost completely derived from accumulation of dislocations for the case of deformation at ambient temperature. A detailed understanding of density and spatial distribution of dislocations as a function of applied strain is a complex problem, particularly in the case of engineering alloys. This is affected by second phase particles such as constituent particles and dispersoids the accumulation and recovery of the deformed structure critically depends on their size and volume fraction. For example, lattice rotation occurs adjacent to constituent particles during deformation and the amount of this rotation depends on deformation level and size of particles. As such, a deformation zone around large constituent particles is created and hence, local stored energy and local misorientations can play a        84    Asdghajdgjdkgadjkgadkjad  20mm4% (a) 20mm1.2% (b) Figure 5.20.  Critical strain for onset of recrystallization in low Fe 3003 samples homogenized at 600 °C for (a) 1hr and (b) 24hr (note: samples were loaded up to the same load in order to get very similar strain gradient along them.)  Sada dasdada dad Table 5.10. Critical plastic strain for recrystallization of Low Fe 3003 samples. Material Sample 1 Sample 2 Sample 3 Sample 4 H1-LF 3.4% 4.0% 4.5% 4.7% H24-LF 1.4% 1.0% 1.4% 1.2% Jhdjasbhdajdbhjdbajdba d         85    Table 5.11. f/r  ratios of dispersoids and constituent particles and critical plastic strains for AA3003 and Low Fe 3003 samples. Material H1 H1-7h H24 H1-LF H24-LF f/rdispersoids (µm-1) 0.19 0.33 0.00 0.06 0.00 f/rconstituents (µm-1) 0.05 0.05 0.05 0.01 0.01 Critical Plastic Strain Range 8.0-10.0% (for small grains) 9.0-10.6% (for large grains) 17.5-19.0% 1.8-2.0% (small grains) 1.8-2.2% (large grains) 3.4-4.7% 1.0-1.4% Jdhgajkdgadjgadgadadadad    Figure 5.21.  Critical plastic strain versus total f/r ratio for AA3003 and low Fe 3003 alloys (initial grain size: 12 and 14 µm for H1 and H24 specimens – 32 and 20 µm for H1-LF and H24-LF samples).     86  critical role in the initiation of recrystallization (i.e. particle stimulated nucleation). On the other hand, these nuclei can be pinned by dispersoids and may not become large enough grains to be detectable using optical microscopy and Poulton’s reagent. It is this complex interplay which must be considered to rationalize the current study. For example, in 3003 and the Low Fe 3003 samples with dispersoids, depending on the size and volume fraction, much larger strain was required to initiate recrystallization suggesting strong pinning pressure on the nuclei boundaries (see Table 5.11). In other words, dispersoids effectively pin the nuclei boundary and hence larger stored energy is required to have viable nuclei. It is well known that f/r value is a measure to predict recrystallization behaviour shown in Table 5.11. Details on how these values were calculated/measured will be discussed in the next chapter. It was found that larger f/r value leads to larger critical plastic strain for onset of recrystallization consistent with previous studies and researches [65]. Due to pinning of cell boundaries, only few nuclei can grow and become a recrystallized grain. As a result, larger recrystallized grain size is observed in samples with dispersoids.  Grain boundaries and constituent particles can act as nucleation sites. Hence, samples with large grains (~98 µm) were examined the same way as samples with small grains (12-14 µm) to study the effect of grain boundary on recrystallization behaviour. Results showed there is a small change (~ 1%) in the critical strain especially for H1 samples, i.e. higher critical strain for samples with large grains. This suggests small    87  effect of grain boundaries on recrystallization nucleation and hence, strong effect of constituent particles on recrystallization nucleation.   5.3.4   Annealing Behaviour of AA3003 after Large Strain Rolling  As discussed before, AA3xxx alloys are used for rolling and extrusion applications, mainly for thin walled components such as beverage cans, building plates and heat transfer tubes. In tube drawing, samples experience large strains followed by annealing. Hence, the annealing behavior of these alloys after large strain deformations was studied. The main objectives of this part of the work was to investigate: (a) the recrystallization behavior and recrystallized grain size for cold deformed material that had experienced different homogenization treatments and annealing temperatures and (b) the effect of the initial grain size on the recrystallized grain size as a function of the level of cold work. First, we consider samples with no or minimal change in 2nd phase particles during annealing. 5 mm 5 mm (a) (b) Figure 5.22.  Initial grain structure of: (a) H1 and (b) H24 samples with very large grains (VLG), 0.5-3 mm.    88  In order to study the effect of initial grain size on annealing behaviour, some samples were deformed to critical strains estimated from previous experiments (~10 pct and ~2 pct pre-strain for samples homogenized for 1 hr and 24 hr at 600 °C, respectively) and then recrystallized at 600 °C for 1 min. This produced samples with very large grains (VLG), 0.5-3 mm, as shown in Figure 5. 22. For AA3003 samples, therefore, two different initial grain sizes (small and large) were examined as well as different dispersoid densities. Figure 5.23 shows the recrystallization behaviour of H1 samples with fine initial grain size (~12 µm) rolled for 10-80% and then annealed at 600 °C for 1 min. As expected, finer recrystallized grains are formed by increasing the deformation. Annealing behaviour of H24 samples (very low dispersoid density) with fine initial grain size is also shown in Figure 5.24 with a similar trend observed.          89    200 μm    200 μm  (a) (b)   200 μm   (c) (d)   200 μm  (e) Figure 5.23. Optical micrographs showing the recrystallization behaviour of H1 samples (initial grain size: 12 µm) cold rolled for: (a) 10%, (b) 20%, (c) 40%, (d) 65% and (e) 80% (note: cold rolled samples were annealed at 600 °C for 1 min) Wwkhkjhkjhwww 200 μm    90    (a) (b)   (c) (d)  (e) Figure 5.24. Optical micrographs showing the recrystallization behaviour of H24 samples (initial grain size: 14 µm) cold rolled for: (a) 10%, (b) 20%, (c) 40%, (d) 65% and (e) 80%. (note: cold rolled samples were annealed at 600 °C for 1 min) Hdgkjadghkajdhakjdhakj   100 μm    91  Figure 5.25 plots the recrystallized grain size as a function of the percent of cold work for the samples with high density (H1) and low density (H24) of dispersoids. The effect of dispersoids on recrystallized grains was observed. For all deformation levels, the recrystallized grain size is larger in the H1 compared to the H24 samples. This difference is noticeable in samples deformed for 10% and 20%. It appears that the effect of pinning on recrystallization from dispersoids is more significant when the level of deformation is relatively low, i.e. 10% and 20%. For instance, at strain 0.14, the ratio of grain sizes is 5.3 but at strain 1.21, this ratio is 1.2.    Figure 5.25.  Effect of dispersoids density on recrystallized grain size of AA3003 samples with fine initial grain size, 12 µm for H1 and 14 µm for H24 (note: error bars are showing smallest and largest grain size measured).    92  Figure 5.26 and 5.27 illustrate the recrystallization behaviour of AA3003 samples with large initial grain size and a high or low dispersoids density, respectively. Larger recrystallized grains were produced in H1-VLG samples suggesting that dispersoids pin recrystallization nuclei boundaries and so some of the nuclei do not reach the critical size to become a viable nuclei. Therefore, as also observed before in samples with fine initial grains, samples with a high density of dispersoids have larger recrystallized grains compared to those with almost no dispersoids.  As shown in Figure 5.28, the recrystallized grain size in the H1 samples is still larger than those with a very low density of dispersoids (H24 samples), but the difference in recrystallized grain size is not as large as in samples with small initial grain size. Figure 5.29 shows the effect of initial grain size on recrystallized grain size in H1 samples where there is a high density of dispersoids. Forming finer grains in samples with small initial grains suggests the important role of grain boundaries in recrystallization. For instance, a recrystallized grain size of 65 µm (large initial grain size) and 40 µm (fine initial grain size) is obtained for samples with the same pre-strain, 0.52. Samples with large grains have less grain boundary area and it is speculated that this gives rise to a lower number of nucleation sites for recrystallization. Relatively, there is a small effect of initial grain size on recrystallized grains of samples with high density of dispersoids suggesting strong boundary pinning by these fine particles.     93    200 μm   (a)    200 μm  (b)   200 μm  (c)   200 μm  (d) Figure 5.26. Optical micrographs illustrating the recrystallization behaviour of H1-VLG samples (initial grain size: 0.5-3 mm), cold rolled for: (a) 10%, (b) 20%, (c) 40% and (d) 80%. (note: cold rolled samples were annealed at 600 °C for 1 min)        94    (a)   (b)  (c)  (d) Figure 5.27. Optical micrographs illustrating the recrystallization behaviour of H24-VLG samples (initial grain size: 0.5-3 mm), cold rolled for: (a) 10%, (b) 20%, (c) 40% and (d) 80%. (note: cold rolled samples were annealed at 600 °C for 1 min) Sdasdsadasdasdasd     95  Sadasdasdadadada  The measurements for recrystallized grain size in H24 samples with different initial grain sizes (14 μm vs 0.5-3 mm) are illustrated in Figure 5.30. One can observe the strong effect of initial grain size especially at lower strains suggesting that grain boundary nucleation mechanisms may be relevant here (e.g. boundary buldging). Comparing Figures 5.29 and 5.30 confirms that initial grain size has much less effect on recrystallized grain size in samples with a high density of dispersoids. In other words, dispersoids exert an effective and significant pinning pressure on recrystallization front and affect the density of favorable sites for recrystallization nucleation.   Figure 5.28.  Effect of dispersoids density on recrystallized grain size of AA3003 samples with large (0.5-3 mm) initial grain size (note: error bars are showing smallest and largest grain size measured).    96  dfsdfsdffsdfsdfsdff  Figure 5.29.  Effect of initial grain size (fine: 12 µm and large: 0.5-3 mm) on recrystallized grain size of AA3003 samples with high density of dispersoids (H1).  Error bars are showing smallest and largest grain size measured.  Figure 5.30.  Effect of initial grain size (fine: 14 µm and large: 0.5-3 mm) on recrystallized grain size of AA3003 samples with very low density of dispersoids (H24). Error bars are showing smallest and largest grain size measured.    97  5.3.5 Discussion Effect of dispersoids and initial grain size on recrystallization behavior of AA3003 samples rolled at room temperature were studied. Similar to small strain deformation level, finer recrystallized grains were achieved by increasing the level of cold work as it leads to a higher level of stored energy. In samples with fine initial grains, cold rolled H1 samples produced larger recrystallized grain size compared to H24 samples. Hence, dispersoids effectively impede the formation of viable recrystallization nuclei and just a few of new grains are formed leading to large grains. Effect of dispersoids on recrystallized grain size is specifically more significant in strains less than 0.4. It can be speculated that at strains larger than 0.4, another nucleation mechanism such as shear bands is another active mechanism. Also, results showed relatively small effect of initial grain size when dispersoids are present. In H24 samples, on the other hand, strong effect of initial grain size on recrystallization was realized particularly at strains less than 0.4, suggesting that grain boundary bulging is relevant.   5.4   Concurrent Precipitation AA3xxx alloys are also used for rolling and extrusion applications, mainly for thin walled components such as beverage cans, building plates and heat transfer tubes. In tube drawing, samples experience large strains at room temperature followed by annealing. As such, annealing behaviour of these alloys after large pre-strains is an    98  important subject to examine carefully and more in depth. To begin with, extruded AA3003 samples were rolled at room temperature to 10%, 20%, 40% and 80% thickness reduction and then annealed at different temperatures ranging from 350 to 600 °C. Figure 5.11 shows that precipitation is expected at these temperatures. The micrographs in Figure 5.31 are showing microstructure evolution of H1 samples cold rolled for 80% and then annealed at different temperatures. In order to get a fully recrystallized microstructure, samples were held for 100 min, 30 min and 1 min at 350 °C, 400 °C and 500 °C, respectively. Significantly different recrystallized grain size has been observed for these samples. It is well understood that concurrent precipitation can affect recovery and particularly recrystallization behavior which is the main reason of these results [141-143]. As solubility of manganese atoms drops drastically by reducing temperature, the Mn atoms come out of the solution in the form of dispersoids. Results show that there is a critical annealing temperature below which coarse and inhomogeneous recrystallized microstructure is achieved. On the other hand, if the deformed samples are annealed above the critical temperature, the structure recrystallizes into finer and more homogeneous grain sizes because no concurrent precipitation is taking place. The result is consistent with the work done by Tangen and co-workers [141] in which they also observed concurrent precipitation of Mn-bearing dispersoids which retards recrystallization and consequently, leads to undesirable and coarse-grained structures.      99  50 µm  (a)  50 µm (b) 50 µm (c) 50 µm (d) Figure 5.31. Optical micrographs of fully recrystallized microstructure of samples homogenized for 1 hr at 600 °C (AA3003) cold rolled for 80% followed by annealing at different temperatures; (a) as-rolled microstructure, (b) 100 min at 350 °C, (c) 30 min at 400 °C and (d) 1 min at 500 °C.  Electrical conductivity measurements were also carried out in order to further study concurrent precipitation of dispersoids. Hence, samples were cold rolled for 20% and then annealed at 400 °C for 4 hr. Samples were taken out after 10, 30, 90 and 240    100  minutes for conductivity measurement. Figure 5.32 illustrates changes in resistivity during annealing at 400 °C. Electrical resistivity decreases as time goes on which confirms precipitation of Mn along with recrystallization process.  It should be noted that the degree of concurrent precipitation increases with increasing the prior cold reduction due to an enhanced diffusion rate (diffusion along dislocations) and higher number of heterogeneities available for nucleation of dispersoids [141]. A 2.5 percent decrease in electrical resistivity defines as the start of precipitation [141]. As such, after 10 minutes, precipitation of Mn-bearing dispersoids begins (see Figure 5.32) and if recrystallization is not fully complete in less than 10 minutes, concurrent precipitation of dispersoids will retard the recrystallization process. In fact, dispersoids resulting from concurrent precipitation pin recrystallization nuclei  Figure 5.32.  Electrical resistivity of samples rolled for 20% and then annealed at 400 °C (AA3003).    101  and so prevent the nuclei from reaching their critical size and become viable nuclei. For instance, Figure 5.33 shows that recrystallization is complete in H24 samples after 3 minutes at 400 °C (before onset of dispersoids precipitation) while H1 samples are not fully recrystallized even after 24 hr (1440 min) at 400 °C due to retardation of recrystallization process by precipitation of dispersoids.  As such, all the annealing treatments were done at 600 °C for 1 minute in salt bath as this temperature is fairly above the critical temperature and no concurrent precipitation is expected. Also, minimal change in dispersoid size/density is expected due to the high heating rate in salt bath. 100 μm (a) 100 μm (b) Figure 5.33.  Optical micrographs of AA3003 samples cold rolled for 20% and then annealed at 400 °C: (a) H1 samples annealed for 1440 min and (b) H24 samples annealed for 3 min.    102  CHAPTER 6   Modeling  In this chapter, the internal state variable model approach is adopted to develop a model which describes the critical plastic strain required to initiate recrystallization in a AA3003 based alloys. Special emphasis is placed on using physically based models as well as keeping the number of fitting parameters to a minimum. First, in Section 6.1, the yield stress for a wide range of conditions is modeled using microstructural features such as the amount of Mn in solid solution, the grain size, the dispersoid density and size, the dislocation density and the constituent size and volume fraction as inputs. Section 6.2 is devoted to develop a model for work hardening using the recent approach of Bouaziz which captures Stage IV work hardening behaviour [74]. In Section 6.3, the critical strain for recrystallization initiation is calculated using the work hardening model to estimate stored energy and a physically based equation to estimate Zener drag from precipitates (dispersoid and constituent particles). Finally, this chapter concludes with a brief discussion in Section 6.4 on the strengths and limitations of the present work. 6.1 Yield Stress Model As discussed in the literature review, there are four main sources of strengthening contributions in AA3xxx alloys: (i) Mn solid solution, (ii) grain size, (iii) precipitate    103  hardening from dispersoids and (iv) constituent particles. This section describes how each of the contributions was calculated and how they were summed together.  The effect of Mn in solid solution on the yield stress of a binary Al-Mn alloy has been studied by Ryen et al. [6]. In that work, the fit to the data reported showed a significant deviation at high Mn contents which are relevant to the current study. As such, the results were re-plotted as shown in Figure 6.1. To a first approximation, the compositional dependence of yield stress is linearly related to the Mn solute level as follows:  Mnssss CK  (6.1) where Kss  for Mn is 38 MPa/wt% and CMn is the weight percent of Mn in solid solution (R2=0.89 - Note: R2 is a statistical calculation used with regressions when analyzing a collected set of data points. The R2 is a measure of how well the function fits the data. The closer the R2 value is to 1.0, the better chance that the fit produces values closer to the data points). It is worth noting that the current fit to the data of Ryen et al. [6] shows a stronger dependence of solid solution hardening on composition than Ryen et al. [6] reported, i.e. 38 MPa/wt% vs. 26.9 MPa/wt%, respectively. The method used by Ryen et al. [6] is not described in detail but if one fits the data using a least squares regression without the data point at 0.8 wt% Mn, then a value of 26.6 MPa/wt% is achieved (i.e. almost the same as Ryen et al. [6] who reported a value of 26.9 MPa/wt%). On the other hand, if one includes all the experimental data, then one gets    104  38 MPa/wt%. As the majority of the cases in the current work are closer to the higher Mn levels, it is proposed that this is the more relevant fit to the experimental data. It is also well known that grain boundaries can act as an obstacle to dislocation motion. This effect on yield stress can be captured using the Hall-Petch relationship [31, 32], i.e.  210 kdgb   (6.2) where k is a constant and d is grain diameter. Since intrinsic stress is less than 1 MPa for high purity aluminum [33], the term σ0 can be ignored. In the literature, to the best knowledge of the author, no data on the effect of Mn on the constant k is reported. Hence, the value of 0.068 MPa.m1/2 for high purity aluminum [35] is used in the current application.  Figure 6.1. Yield strength as a function of Mn in solid solution in Al-Mn alloys (grain size of 500 to 1000 µm), this figure is plotted based on data published in reference [6].    105   Since the fine dispersoids can also act as obstacles to dislocation movement, the yield strength increment due to dispersoids should also be taken into consideration. In AA3003 alloys, α-Al(Mn,Fe)Si dispersoids can be treated as non-shearable particles [13, 43], and the contribution from this mechanism on the yield strength can be described by [30, 44]  effdisp bMF8.0 (6.3) where M is the Taylor factor (3.07 for randomly oriented FCC metals), b is the magnitude of the Burgers vector (0.286 nm), λeff is the mean planar precipitate-spacing which dislocation travels and F denotes the precipitate strength which represents the average interaction force between the dislocation line and the precipitate. The precipitate strength obtained for non-shearable particles can be equated to twice the dislocation line tension, i.e.   2F  (6.4) where Г is the average line tension.  In general, line tension Г depends on the nature of dislocation (i.e. edge and screw represent the extremes) and can be represented by [40]   )/ln(1sin314 022rb    (6.5)    106  where μ is shear modulus, υ is Poisson’s ratio, δ is the angle between the dislocation line and its Burgers vector and Λ and r0 are the outer and inner cut-off distances used in calculating the line energy of the dislocation. The line tension has been estimated assuming an inner cutoff ratio of 2b. The outer cutoff ratio is more difficult to estimate but should lie between the limits of 2r and λeff. In the current work, a value of a constant line tension of 0.27 µb2 has been adopted which lies between the upper and lower bounds obtained using the outer cutoff limits described above.  For non-shearable spherical particles, λeff can be calculated based on the average particle radius and volume fraction, f  [13, 40, 44]:  rfeff2132  (6.6) Volume fraction of dispersoids could be experimentally measured but it is difficult to get statistically relevant data. Therefore, in the present case, the model developed by Du et al. [19, 140] was employed to determine volume fraction of dispersoids. This mathematical model was developed to simulate the precipitation kinetics during heat treatment of multi component aluminum alloys. The model is based on the general numerical framework proposed by Kampmann and Wagner and features a full coupling with CALPHAD software [19, 140] and has been comprehensively validated with experimental measurements [19]. Using the model, volume fractions of 1.01% and 0.21% for dispersoids were obtained in H1 and H1-LF samples, respectively. For the    107  H1-7h and 375C-24h samples, the same model cannot be used because: (i) the parameters such as number of nucleation sites and growth rate used in the model are specifically for the heat treatment practices applied to H1 and H1-LF and (ii) this model is not validated for heat treatments that H1-7h and 375C-24h experienced. In this case, the dispersoids volume fraction was calculated from the ternary phase diagram using TTAL6 database, i.e. it is assumed that equilibrium is reached. Further, it is known that manganese atoms are distributed in constituent particles, dispersoids and matrix (solid solution). Hence, distribution of Mn in  each component was ensured to satisfy a Mn mass balance where the density of dispersoids and constituent particles used for this calculation were 3.59 g.cm-3 and 3.45 g.cm-3, respectively [144, 145]. In order to estimate the dispersoid size in the H1-7h samples, it is assumed that pre-existing dispersoids in H1 samples coarsen during heat treatment and no nucleation is occurring. The same heat treatment steps and similar alloy composition used by Li et al. [13] were employed in this study to produce 375C-24h samples. As such, it was assumed that dispersoids had the same size as the ones reported by Li and co-workers [13] in a similar alloy. Finally, the dispersoids size distribution for H1 and H1-LF samples were measured using FEGSEM micrographs. Values are reported in 3D and a factor of 1.273 was used to convert 2D mean size to 3D mean size [139]. Volume fraction and size of dispersoids used in the current calculations are summarized in Table 6.1.     108  Table 6.1. Values for microstructure state variables used in the yield stress model. Material H24 H1 H1-7h As-cast 375C-24h H24-LF H1-LF Mn solid solution level (wt%) 0.5 0.5 0.07  1.2 0.055 0.76 0.76 Grain size (µm) 14 12 12 64 64 20 32 Dispersoids volume fraction (%) - 1.01 2.31 - 2.75 - 0.21 Dispersoids radius (nm) - 52 69 - 21 - 36 Constituents volume fraction (%) 3.8 2.9 2.9 2.4 2.4 1.7 1.5 Constituents radius (µm) 0.8 0.6 0.6 - - 2.3 1.5 Finally, the presence of relatively large (>1 µm) elastic constituent particles in the microstructure led to the development of elastic and plastic incompatibility stresses [45-48] which can contribute to the yield stress. This type of strengthening mechanism has been extensively studied for a range of systems and can be described in terms of Eshelby theory [48-50]. The analysis of spherical particles in Mg-Al alloys by Caceres et al. [50] is of particular relevance to the current study. In this work, the contribution to the yield stress can be estimated as [50]:    109   *4  fconst   (6.7) where γ is an accommodation factor, µ is the shear modulus of matrix, ε* is the unrelaxed plastic strain and f is the volume fraction of the precipitates and γ depends on particles shape (see reference [51] for more details). Kljfljkflkfjldkfsjflkj For spherical particles embedded in a matrix, γ is given by [51]:   )1(1557  (6.8) ʋ is Poisson’s ratio (~0.33). In Equation 6.4, φ can be calculated using the following equation [49, 50]:  )( ***  (6.9) where µ* is the shear modulus of relatively large particles, i.e. constituent particles. Shear modulus of constituent particles can be estimated by [50]   )1(2)21(3*  const (6.10) where µconst is the bulk modulus of constituent particles. Value of parameters used to calculate the constituent particles contribution is shown in Table 6.2. The volume fraction and size of constituent particles were measured using the micrographs taken by SEM and optical metallography reported by Geng [17] and reported in Table 6.1.     110  Table 6.2. Values used in the yield stress model to estimate constituent particles contribution. Symbol Description Value µ* Shear modulus of constituent particles 42 GPa µ Shear modulus of matrix 26 GPa ε* Unrelaxed plastic strain 0.002 µconstituents Bulk modulus of constituent particles 109.76 GPa [146] Incorporating the microstructure parameters reported in Table 6.1 and the various strengthening contribution equations gives a contribution from each mechanism as shown in Table 6.3. It should be noted that contribution from different mechanisms were added linearly (See section 2.2.5 for more details). Comparing the model and experimental values shows that the model well captures the yield stress. It appears that in H1 and H1-LF conditions, there is a slightly higher difference between the model and experimental values (~7 MPa). 6.1.1 Discussion of Yield Stress Model This model well predicts the yield stress values for each condition and the highest difference between experiments and model prediction observed for H1 and H1-LF conditions, approximately 7 MPa. This difference can be correlated to the model    111  assumption which is the uniform distribution of dispersoids everywhere within the matrix. However, there is an area around constituent particles in H1 and H1-LF samples where there is almost no dispersoids, called a dispersoids free zone (DFZ) which is not considered in the model and should have a yield stress similar to H24 samples where no dispersoids present. In fact, DFZ starts to form after 500 °C during homogenization since dispersoids start to dissolve and long range diffusion of manganese atoms to constituent particles is taking place [19]. It has been shown by Du et al. [19] that there is a dispersoids free zone in AA3003 samples homogenized for 1 hour. A schematic of the microstructure of these samples is illustrated in Figure 6.2.  Table 6.3. Contribution from different strengthening mechanisms on yield stress (values are in MPa). Material H24 H1 H1-7h As-cast 375C-24h H24-LF H1-LF Solid solution 19.0 19.0 2.7 45.6 2.1 28.9 28.9 Grain boundaries 18.2 19.6 19.6 8.5 8.5 15.2 12.0 Precipitation hardening 0.0 12.8 14.6 0.0 52.6 0.0 8.3 Constituent hardening 5.2 4.0 4.0 3.3 3.3 2.3 2.1 Yield stress (Model) 42.4 55.4 40.9 57.4 66.5 46.4 51.2 Yield stress (Experiment) 46 48 37 59 70 45 46 Lklklkkkkkkkk    112   The hypothesis is that the material within DFZ starts to yield while the remaining material containing dispersoids is still elastically deforming. Hence, it is proposed that the experimental value is lower than that predicted by model.  constituentsdispersoidsDFZDFZDFZDFZ Figure 6.2. Schematic microstructure of AA3003 samples homogenized for 1 hr at 600 °C.  6.2 Work Hardening Behaviour The recent approach proposed by Bouaziz [74] is an improvement to the classical Kocks-Mecking approach as it captures Stage IV work hardening, at least in a phenomenological manner, i.e. :    )exp( bKMdd effp (6.11) where εP is the plastic strain, Keff is a constant describing the dislocation accumulation during work hardening, b is the magnitude of the Burger’s vector (0.286 nm) and ξ can be interpreted as the capture distance for dynamic recovery. However, his approach does not account for accumulation of dislocations around non-shearable precipitates.    113  As such, Equation 6.11 has been revised in a similar manner to the Estrin-Mecking modification to the original Kocks-Mecking model for forest hardening of FCC metals [62, 147], i.e. by adding a term for dislocation accumulation around non-shearable particles:   GppteffpKbKMdd )exp( (6.12) where Kppt is a scaling parameter for the role of non-shearable precipitates and λG denotes the geometric slip distance on the glide plane and is related to the volume fraction (fdisp) and the radius of non-shearable dispersoids (rdisp), i.e. λG = rdisp/fdisp [44].  Equation 6.12 can be integrated numerically in order to find dislocation density evolution as a function of plastic strain. For the numerical integration, different step sizes were used (0.1, 0.01, 0.001, 0.0001 and 0.00001) to examine its effect. It was found that for strain step sizes less than 0.001 no change in the results was observed. To be conservative, a strain step size of 0.0001 was used to numerically integrate Equation 6.12. After determining the dislocation density, the flow stress from dislocation hardening can be calculated using the Taylor relationship , i.e. σ=Mαμbρ0.5. The fit parameters used in this model are summarized in Table 6.4. One additional consideration is important here. The term, Keff, in Equation 6.11 is related to the initial work hardening rate in a particle free alloy. In the present work, we have used Keff as an effective parameter which takes into account dislocation accumulation and the build-up    114  of elastic energies around constituent particles. As such, Keff has been made as a function of the volume fraction of constituent particles and includes data for high purity Al where Kpure Al = 0.0274 [63, 74]. It was found that the effective value of Keff was exponentially dependent on the volume fraction of constituent particles as shown in Figure 6.4, i.e.:  )395.0(exp0281.0 tconstitueneff fK   (6.13) A least squares regression was determined where the coefficient of determination was found to be, R2=0.99.   sdfsdffffffffffffffffff  Table 6.4. Yield stress in each condition and fitting parameters used in the work hardening model. Materials σyield (MPa) Fitting Parameters Keff ξ Kppt H24 42.4 0.126 3.00×10-7 0 H1 54.0 0.088 3.00×10-7 3×108 H1-7h 39.5 0.088 3.86×10-7 3×108 As-cast 57.0 0.072 1.60×10-7 0 375C-24h 66.1 0.072 3.89×10-7 3×108 H24-LF 46.4 0.055 2.48×10-7 0 H1-LF 51.2 0.051 2.48×10-7 3×108    115   Figure 6.3. Keff  as a function of volume fraction of constituent particles. In addition, it is generally understood that solute atoms affect dynamic recovery [6, 148, 149]. In order to examine the effect of Mn on dynamic recovery, four conditions with very different Mn in solid solution levels were chosen, i.e. as-cast, H1-7h, H24 and H24-LF.  In these four conditions, then, ξ values were determined in order to obtain a good fit to experimental stress-strain curves (Table 6.4 provides a summary of the relevant fit parameters for the individual stress-strain curves). Then, the values of ξ were plotted as a function of manganese in solid solution (see Figure 6.4). As can be seen, there is an almost linear dependency of ξ on the Mn solute level and the data again includes data for high purity aluminum. A linear regression of the data (R2=0.97) provides the following description:    116   77 104)102(   c  (6.14) This equation leads to lower values for ξ in samples as the Mn solute level increases, and thus dynamic recovery becomes more difficult.   Figure 6.4. ξ as a function of Mn level in solid solution. For all the conditions, the same value is used for Kppt relevant to the nature and strength of non-shearable dispersoids. Stress-strain curves obtained from the model are plotted versus experimental data (see Figure 6.5). As shown in Figure 6.5, the model provides a good description of the stress-strain response for all conditions with some exceptions. For example, in the case of the 375C-24h condition (Figure 6.5e), while the model describes the initial hardening rate well, there is an increasing deviation between the model and the experiments at larger strains.     117      (a) (b)   (c) (d)           118     (e) (f)  (g) Figure 6.5. Comparison of the measured (symbols) and the predicted (lines) stress-strain curves for: (a) H24, (b) H1, (c) H1-7h, (d) As-cast, (e) 375C-24h, (f) H24-LF and (g) H1-LF. Figure 6.6 illustrates that the model predicts the yield stress and UTS for all seven conditions within +/-10%. To determine the UTS from the model: (i) the true strain-true stress from the model and the work hardening rate vs. true strain from the model were plotted, (ii) the point where true stress is equal to the work hardening rate is the    119  necking point as shown in Figure 6.7 (the UTS but in true strain), i.e. the Considere condition, (iii) true strain at necking was converted to engineering strain using Equation 4.1, εT = ln (1 + εeng), and then engineering UTS was calculated using Equation 4.2, σT = σeng (1 + εeng).   Figure 6.6. Comparison between engineering ultimate tensile stresses (UTS) and yield stresses predicted by the model with the ones measured experimentally. Jhdkjhadkjhdakldh  6.2.1 Discussion of Work Hardening Model In this section, some of the strengths and limitations of the work hardening model are discussed. First, a strength of the model is its simplicity, i.e. model has five fitting parameters Keff (two parameters in its equation), ξ (two parameters in its equation) and Kppt. It is also worth noting that recently proposed dislocation storage model by Bouaziz    120  (Equation 6.7) [74] describes the work hardening behavior at larger strains (above 10%) much better than the Kocks-Mecking model. However, Bouaziz’s model [74] does not take into account presence of second phase particles, especially non-shearable particles, i.e. dispersoids in AA3003 system [13, 43]. Due to additional dislocation loops formed around dispersoids, initial work hardening significantly increases. There are two   Figure 6.7. True UTS obtained from work hardening rate- and true stress-true strain curves. Both curves are plotted from the model.  mechanisms proposed to explain this increase: (i) the overall dislocation evolution law for dislocation density in terms of the accumulation of dislocations and their effect on dynamic recovery [45, 63, 150] and (ii) the development of the local storage of elastic energy due to the storage of loops around precipitates and these can play an important    121  role in plastic deformation of these alloys during reversed strain paths, e.g. Bauschinger tests [46, 63, 151, 152]. It is worth noting that the internal stress increases rapidly at the initial stage of deformation but saturates at strains larger than 5% [152]. In addition, Zhao et al. [77, 152] concluded that the internal stress makes a small contribution to the work hardening and during monotonic loading at strains larger than 5%, this contribution is less than 10%. In terms of present model, therefore, the first mechanism has been considered by adding the term Kppt/λG to the dislocation density evolution law proposed by Bouaziz. The second mechanism, i.e. development of elastic internal stresses can also contribute to the work hardening behavior [152]. In the case of the 375C-24h condition (Figure 6.5e) this might be one explanation for the observed deviation between the model and the experiments at strains larger than 1%. Zhao et al. [77] suggested that the internal stress developed due to dispersoids could not be neglected when there is a high volume fraction. In the current study, it was estimated that the volume fraction of dispersoids was 2.75%, i.e. even higher than the constituent particles volume fraction of 2.4%. As such, the deviation observed in the current work may be related to the internal stress due to the dispersoids which was not accounted for in the present study.  The second simplification in the model is the use of effective value for Keff which is a function of the volume fraction of constituent particles. The effect of the constituent particles on the stress-strain behavior primarily derives from the storage of elastic    122  stresses (indeed, this term is included in the yield stress model). In order to include this effect in the work hardening model would have required additional fitting parameters and additional experiments (for example, Bauschinger tests to assess internal stresses).  This simplification was made for these pragmatic reasons. It would be interesting for future work to examine this question in more detail. Finally, it is of interest to compare the current model with the recent proposal of  Zhao and Holmedal [77, 152]. Figure 6.8 shows the experimental curve (plastic strain versus flow stress) of an Al-Mn alloy and the model prediction [77]. This model [77] is based on a balance of storage and dynamic recovery of geometrically necessary dislocations (GNDs) around dispersoids and has six parameters. The alloy used in Figure 6.8 is quite similar to the H24 and H24-LF conditions in this study, containing coarse particles but very few dispersoids. Comparing Figure 6.8 with Figure 6.5a and 6.5f (with very similar micro-features) shows the model developed in the current study better captures experimental data and does so with five fitting parameters.  6.3 Critical Strain for Recrystallization After predicting stress-strain curves for each condition, an estimate of the energy stored due to the storage of dislocations can be determined as [65, 80, 81]:   221 bEs  (6.15)    123  where ρ can be estimated from integration of Equation 6.12. As such, an estimate for the driving pressure for onset of recrystallization process can be calculated. On the other hand, the pinning pressure from the second phase particles on the grain boundaries should be considered as it inhibits or stops recrystallization process.   Figure 6.8. Comparison of the modeled forest hardening and the experimental result for an Al-Mn alloy contained coarse particles but very few dispersoids (Mn in solid solution: 0.48 wt%, grain size: 65 µm) [6, 77]. As discussed in more details in section 2.7, a range of pinning pressure can be calculated using the following formula [122, 124, 125]     brfParfP GBUpperzGBLowerz 37.1,1.1  (6.16) where γGB refers to grain boundary energy, i.e. 324 mJ/m2 for aluminum [65], f is particle volume fraction and r is the particle radius. This equation is employed in order    124  to calculate a range of possible pinning pressure on recrystallization front in each condition depending on size and volume fraction of dispersoids and constituent particles.  Eivani et al. [126] investigated Zener drag pressure from nano-scale dispersoids on AA7020 alloy and they linearly added the pressure from different size distribution of dispersoids in order to calculate total drag pressure. To the best knowledge of the author, there is no work to consider effect of pressure pinning from nano- and micro-scale precipitates for total pinning pressure. As such, Zener pinning pressure from both dispersoids and constituent particles acting on moving boundaries were considered and the pinning pressures were added together linearly to estimate the total pinning pressure. Stored energy can be calculated as a function of plastic strain using Equation 6.16. And, a range of pinning pressure was also obtained using Equation 6.15. Figures 6.9 illustrate stored energy and Zener pinning pressures in AA3003 and Low Fe 3003 samples. A range of critical plastic strain (i.e. where stored energy = Zener drag) reported in these curves were obtained using the following equation   Es (εP) = Pz total = Pz (dispersoids) + Pz (constituents) (6.17) Table 6.5 summarizes range of critical plastic strain for recrystallization in all conditions obtained from experiments and the model. Very good prediction of critical recrystallization strain using the simple physically based model was achieved as shown    125  in Table 6.5. Based on different experiments (i.e. some variation in repeat experiments) a range of coefficient was obtained for fγ/r (Equation 6.16). The results achieved in the current study suggest a coefficient of 1.37 gives the best fit for the critical strain over a range of conditions. Figure 6.10 illustrates how well this model predicts critical plastic strain. Green line shows where model and experimental values are exactly the same. 1.2% - 1.5%Pz(Constituents) = 17-21  kPa (a) 8.4% - 11.4%Pz(Dispersoids) = 69-85  kPaPz(TOTAL) = 86-106  kPaPz(Constituents) = 17-21  kPa (b)    126  >18.1%Pz(Dispersoids) = 119-148  kPaPz(TOTAL) = 136-169  kPaPz(Constituents) = 17-21  kPa (c) 0.7%-0.9%Pz(Constituents) = 3-4  kPa (d) 3.1%-3.8%Pz(Dispersoids) = 20-25  kPaPz(TOTAL) = 23.6-29.4  kPaPz(Constituents) = 3.6-4.4  kPa (e) Figure 6.9. Predicted range of critical strain for onset of recrystallization for: (a) H24, (b) H1, (c) H1-7h, (d) H24-LF and (e) H1-LF.    127   Tuyteuyteuyeteqgdbbkcjbkjbskcb Table 6.5. Critical recrystallization strain range obtained from experiments and model. Material Experiment Model H24 1.8-2.0 pct 1.2-1.5 pct H1 8.0-10.0 pct 8.4-11.4 pct H1-7h 17.5-19.0 pct >18.1 pct H24-LF 1.0-1.4 pct 0.7-0.9 pct H1-LF 3.4-4.7 pct 3.1-3.8 pct asdhdGkgkkjhlkjlnlbnjgkjgkgkgk  Figure 6.10.  Comparison between predicted critical strains for recrystallization and experimentally measured values. Red squares are average values for each approach.    128  6.3.1 Discussion of Critical Strain Model Extensive investigations have been carried out in order to understand and model recrystallization [65, 80, 81, 98]. Several mechanisms have been proposed for initiation of recrystallization (see Section 2.6.2 for more details): (i) strain-induced boundary migration (SIBM) and (ii) particle-stimulated nucleation (PSN). In this modeling work, dislocations created in the vicinity of constituent particles were not taken into account and an average dislocation density was taken into consideration. Hence, stored energy estimated in this study does not include local energy storage due to presence of constituent particles and global stored energy was estimated. There are several reasons for the assumption of not including energy storage in the deformation zones (other than for sake of simplicity), i.e.  (a) It is difficult to accurately measure dislocation density at very low strains especially limitation of using different techniques to measure stored energy at low strains (less than 10%).  (b) Another challenge that should be considered at these low deformation levels is the possibility of development of the deformation zones around constituent particles. Lattice rotation adjacent to constituent particles in AA3104 alloy was examined [114] and it was found that the average lattice rotation is about 5° at 10% cold rolling reduction. As such, it can be speculated that the minimum diameter of second phase particles to be an effective source of recrystallization at    129  low strain levels is no longer 1 μm (this value is reported by [65]) and should be larger in order to get larger lattice rotation. Likewise, global drag pressure was calculated assuming uniform distribution of dispersoids without presence of DFZ’s as explained in Section 6.1.1 and shown in Figure 6.2. Considering the assumptions made to estimate stored energy and pinning pressure, there is a possibility that recrystallization nuclei form near constituent particles but these nuclei cannot grow in-between the constituent particles due to the presences of dispersoids. As shown schematically in Figure 6.11, there may be some recrystallized grains in the microstructure which did not have enough driving pressure to overcome the drag pressure by dispersoids. The hypothesis is that new grains grew in the DFZ and then pinned once they reached dispersoids. This is quite similar to a situation reported by Humphreys [105] where a recrystallized area next to a constituent particle could not grow due to the gradient of stored energy. Figure 6.12 illustrates that a recrystallization nuclei formed in the deformation zone close to the particle (Figure 6.12a) and then grew into the zone and once consumed the deformation zone, growth stopped (Figure 6.12b). It would be interesting for future work to examine regions which were not recrystallized at the macroscopic level with high resolution EBSD to search for evidence of this hypothesis.  Another assumption made when calculating the pinning pressure was addition of two Zener drag (from dispersoids and constituent particles) linearly. This is consistent    130   Figure 6.11. Schematic of microstructure in AA3003 alloy showing constituent particles and recrystallized grains (shaded grains) pinned by dispersoids. with the recent approach by Eivani et al. [126] where they linearly added Zener drag pressures from two different size distribution of dispersoids. But, this question remains poorly understood and could be an area of interest for future work. 6.4 Summary of Modeling It is important to recognize that the current modeling approach represents an attempt to describe a complex microstructure based using relatively simplified assumptions. Nevertheless, the current model is capable of addressing the challenge to quantitatively link mechanical response of the material to the various microstructural features and consequently, critical plastic strain for recrystallization is determined. The model consists of three submodels: (i) yield stress (ii) work hardening and (iii) critical plastic strain for recrystallization which are linked together and output of each submodel is     131    (a) (b) Figure 6.12. Micrographs showing annealing sequence of Al-Si using in-situ High Voltage Electron Microscopy (HVEM): (a) initiation of recrystallization in the arrowed region of the deformation zone close to the particle and (b) the recrystallized grain consumed the deformation zone and did not grow further [65, 105]  used as an input for the next submodel. The present work is based on average properties, average drag pressure (average size for dispersoids and constituents) and average stored energy (average dislocation density) in the system. Since physically sound principles are considered in the model, all the parameters utilized here have transparent physical meaning. Throughout the modeling exercise, attempts were made to keep the number of adjustable parameters to the minimum and eliminate any    132  unknown parameters. It should be noted that all the experimental work carried out in this study were designed in such a way to minimize any change in volume fraction, size and density of dispersoids and constituent particles during annealing process. As such, one should be careful when using this model to predict critical strain required to initiate recrystallization as this model is sensitive to the number of parameters and conditions e.g. alloying element amount, annealing heating rate and temperature, annealing holding time, etc. These parameters significantly affect volume fraction, size and density of dispersoids and constituent particles. For instance, depending on the heating rate, temperature of annealing and annealing holding time, dissolution or precipitation of dispersoids can occur which affects size and volume fraction of constituent particles and eventually onset of recrystallization. In this case, examination of critical strain for recrystallization would be quite complicated and current simplified model would not capture these complexities.           133  7   Concluding Remarks  7.1 Summary The present work investigated the annealing behaviour of cold worked AA3003 based aluminum alloys. The interaction between precipitates and recrystallization was examined in detail through a combination of experiments and rationalized using a simple model. Mechanical response of these alloys was also studied. The major findings of this study can be summarized as follows: 1. Critical strains for onset of recrystallization in AA3003 based alloys were experimentally obtained. Tapered samples were successfully used to measure the critical strains. It was found that the critical strain varied from approximately 1% to 18% depending on the volume fraction and size of dispersoids.  3. Using tensile test results, a physically based model was developed for the yield strength and work hardening behaviour of AA3003 based alloys. The yield stress model includes the contributions from Mn in solid solution, grain size, dispersoids and constituent particles. The work hardening model is a modified form of Bouaziz formulation. The models represent the data within ±10% for both yield stress and UTS over a wide range of conditions. 4. A physically based model to predict the critical plastic strain to initiate recrystallization is presented. Recrystallization is considered to occur under conditions    134  where stored energy is greater than Zener drag. To the author’s best knowledge, this is the first attempt to model critical strain in a system with distribution of fine and relatively large precipitates.  5. At large pre-trains, e.g. cold rolled, annealing behaviour of AA3003 alloys with different initial dispersoids density and grain size were also studied. The results suggest that at strains less than 0.54, grain boundary bulging mechanism is relevant in samples with almost no dispersoids. Also, the effect of initial grain size on recrystallized grain size is much smaller when dispersoids present. 7.2 Future Work There are some interesting areas identified during this work which could be proposed for future work: 1. Study microstructure of the regions which were not recrystallized at the macroscopic level with high resolution EBSD in order to see if there is evidence that some recrystallization nuclei were formed but could not grow. 2. Investigate effect of dispersoids free zones (DFZ) on mechanical response of AA3003 based alloys which eventually affect stored energy and recrystallization behaviour of these alloys.    135  3. Investigate further how to estimate Zener drag pressure in the case of two different size distributions of second-phase particles in the microstructure. 4. Examine annealing behaviour of AA3003 based alloys when heating rate during annealing is similar to the industrial practices (e.g. 20-minute heat up). In this work, heating rate was quite fast (~100 °C/s) in order to minimize any microstructural changes in dispersoids and constituent particles. 5. Study shear band formation during cold rolling and the nature of shear banding which can very well be dependent on grain size and dispersoid density. Shear bands can be a dominant source of recrystallization nucleation due to the large orientation gradient.           136  References [1] J. Nyboer, M. kniewasser, Canadian Industrial Energy End-use Data and Analysis Centre, (2012). [2] S. Tangen, K. Sjolstad, T. Furu, E. Nes, Metall. Mater. Trans. A, 41 (2010) 2970. [3] W.J. Poole, M.A. Wells, N.C. Parson, 13th International Conference on Aluminum Alloys (ICAA13), Pennsylvania, USA, (2012), 293. [4] H. Ekstrom, Al-Mn Brazing Sheet for Heat Exchangers,  Virtual Fabrication of Aluminum Products: Microstructural Modeling in Industrial Aluminium Fabrication Processes), John Wiley & Sons, Inc, (2006), 20. [5] L.M. Grajales,  Department of Materials Engineering, UBC, Vancouver, (2013). [6] O. Ryen, O. Nijs, E. Sjolander, B. Holmedal, H. Ekstrom, E. Nes, Metall. Mater. Trans. A, 37 (2006) 1999. [7] N.C. Parson, R. Ramanan, Extrusion Technology for Aluminum Profiles Foundation, (2008). [8] M. Dehmas, E. Aeby-Gauttier, P. Archambault, M. Serriere, Metall. Mater. Trans. A, 44A (2012) 1059. [9] J.R. Davis, ASM Specialty Handbook: Aluminum and Aluminum Alloys, ASM International, (1993). [10] D.G. Eskin, Physical metallurgy of direct chill casting of aluminum alloys, Taylor & Francis Group, (2008). [11] Y.J. Li, L. Arnberg, Acta Mater., 51 (2003) 3415.    137  [12] Y.J. Li, L. Arnberg, Mater. Sci. and Eng. A, 347 (2003) 130. [13] Y.J. Li, A.M.F. Muggerud, A. Oslen, T. Furu, Acta Mater., 60 (2012) 1004. [14] Q. Du, A. Jacot, Acta Mater., 53 (2005) 3479. [15] A. Jacot, M. Rappaz, Acta Mater., 50 (2002) 1909. [16] R. Nadella, D.G. Eskin, Q. Du, L. Katgerman, Porg. Mater. Sci., 53 (2008) 421. [17] Y. Geng,  Materials Engineering Department, UBC, Vancouver, (2011). [18] A.L. Dons, Y. Li, S. Benum, C.J. Simensen, A. Johansen, and E.K. Jensen, Aluminum, 81 (2005) 1038. [19] Q. Du, W.J. Poole, M.A. Wells, N.C. Parson, JOM, 63 (2011) 44. [20] V. Hansen, J. Gjonnes, B. Andersson, mater. Sci. Lett., 8 (1989) 823. [21] A.L. Dons, J. Light Metals, 1 (2001) 133. [22] N.C. Parson, Rio Tinto Alcan (Arvida R&D Centre), Private Discussion (2013). [23] W.H. Van Geertruyden, H.M. Browne, W.Z. Misiolek, P.T. Wang, Metall. Mater. Trans. A, 36 (2004) 1049. [24] M. Verdier, Y. Brechet, P. Guyot, Acta Mater., 47 (1999) 127. [25] T. Sheppard, L. Niu, X. Velay, Mat. Sci. Tech., 29 (2013) 60. [26] R.L. Fleischer, W.R. Hibbard,  The Relation Between the Structure and Mechanical Properties of Metals, Her Majesty’s Stationary Office, London, (1963), 262. [27] P. Haasen,  Physical Metallurgy, Elsevier Science BV, (1996), 2009.    138  [28] R.L. Fleischer, in: D. Peckner (Ed.) Solid-solution hardening, Reinhold Publishing Corp., New York, (1964), 93. [29] R. Labusch, Phys. Status Solidi, 41 (1970) 659. [30] M.A. Meyers, K.K. Chawla, Mechanical behavior of materials, Cambridge University Press, Cambridge (UK), (2009). [31] E.O. Hall, Porc. Phys. Soc. London B, 64 (1951) 747. [32] N.J. Petch, J. Iron Steel Inst., 174 (1653) 25. [33] N. Hansen, Acta Metall., 25 (1977) 863. [34] M. Tiryakioglu, J.T. Staley, Handbook of aluminum: Vol. 1: physical metallurgy and processes, Marcel Dekker Inc., New York, (2003). [35] J.D. Embury, Strengthening methods in crystals, Wiley, New York, (1970). [36] K. Lu, W.D. Wei, J.T. Wang, Scripta Metall. Mater., 24 (1990) 2319. [37] A.H. Chokshi, A. Rosen, J. Karch, H. Gleiter, Scripta Mater., 23 (1989) 1679. [38] H.J. Hofler, R.S. Averback, Scripta Metall. Mater., 24 (1990) 2401. [39] M.A. Meyers, A. Mishra, D.J. Benson, Prog. Mater. Sci., 51 (2006) 427. [40] A.J. Ardell, Metall. Mater. Trans. A, 16 (1985) 2131. [41] E. Nes, S.E. Naess, R. Hoier, Z. Metall., 63 (1972) 248. [42] P. Donnadieu, G. Lapasset, T.H. Sanders, Phil. Mag. Lett., 70 (1994) 319. [43] A.M.F. Muggerud, E.A. Mortsell, Y.J. Li, H. R., Mat. Sci. Eng. A, 567 (2013) 21.    139  [44] F. Fazeli, W.J. Poole, C.W. Sinclair, Acta Mater., 56 (2008) 1909. [45] M.F. Ashby, Strengthening methods in crystals, Elsevier, Amesterdam, (1971). [46] L.M. Brown, W.M. Stobbs, Phil. Mag., 23 (1971) 1185. [47] L.M. Brown, W.M. Stobbs, Phil. Mag., 23 (1971) 1201. [48] J.D. Eshelby, Proc. Roy. Soc. A, 241 (1957) 376. [49] L.M. Brown, D.R. Clarke, Acta Metall., 25 (1977) 563. [50] C.H. Caceres, W.J. Poole, A.L. Bowles, C.J. Davidson, Mater. Sci. and Eng. A, 402 (2005) 269. [51] L.M. Brown, D.R. Clarke, Acta Metall., 23 (1975) 821. [52] J. Friedrichs, P. Haasen, Phil. Mag., 31 (1975) 863. [53] U.F. Kocks, A.S. Argon, M.F. Ashby, Porg. Mater. Sci., 19 (1975) 1. [54] T.J. Koppenaal, D. Kuhlmann-Wilsdorf, Appl. Phys. Lett., 4 (1964) 59. [55] U. Lagerpusch, V. Mohles, D. Baither, B. Anczykowky, E. Nembach, Acta Mater., 48 (2000) 3647. [56] E. Nadgornyi, Prog. Mat. Sci., 31 (1988) 1. [57] R.C. Picu, R. Li, Acta Mater., 58 (2010) 5443. [58] R. Ebeling, M.F. Ashby, Phil. Mag., 13 (1966) 805. [59] P.B. Hirsch, F.J. Humphreys, Porc. Roy. Soc. Lond. A, 318 (1970) 45. [60] U.F. Kocks, Proc 5th intl conf on strength of metals and alloys, (1979).    140  [61] A. Vaucorbeil, W.J. Poole, C.W. Sinclair, Mat. Sci. Eng. A, 582 (2013) 147. [62] U.F. Kocks, H. Mecking, Prog. Mat. Sci., 48 (2003) 171. [63] W.J. Poole, J.D. Embury, D.J. Lloyd, Work hardening in aluminum alloys, in: R. Lumley (Ed.) Fundamentals of aluminum metallurgy, Woodhead Publishing Limited, (2011), 307. [64] D. Hull, D.J. Bacon, Introduction to dislocations, 4th ed., Butterworth-Heinemann, (2001). [65] F.J. Humphreys, M. Hatherly, Recrystallization and related annealing phenomena, 2nd ed., Pergamon, Oxford, UK, (2004). [66] D. Mandal, I. Baker, Scripta Metall. et Mater., 33 (1995) 645. [67] I. Baker, L. Liu, D. Mandal, Scripta Metall. et Mater., 33 (1995) 167. [68] D. Mandal, I. Baker, Scripta Metall. et Mater., 33 (1995) 813. [69] G. Mohamedi, B. Bacroix, Acta Mater., 48 (2000) 3295. [70] F.R.N. Nabarro, Z.S. Basinski, D.B. Holt, Adv. Phys., 13 (1964) 193. [71] H. Mecking, U.F. Kocks, Acta Metall., 29 (1981) 1865. [72] E. Voce, J. Inst. Met., 74 (1948) 537. [73] C.N. Tome, G.R. Canova, U.F. Kocks, N. Christodoulou, J.J. Jonas, Acta Metall., 32 (1984) 1637. [74] O. Bouaziz, Adv. Eng. Mater., 14 (2012) 759. [75] E. Nes, Porg. Mater. Sci., 41 (1998) 129.    141  [76] E. Nes, J.A. Saeter,  The 16th Riso Intl. Symposium on Mat. Sci.: Microstructure and Crystallographic Aspects of Rrecrystallization, Denmark, (1995), 169. [77] Q. Zhao, B. Holmedal, Phil. Mag., 93 (2013) 3142. [78] F. Roters, D. Raabe, G. Gottstein, Acta Mater., 48 (2000) 4181. [79] G.V.S.S. Prasad, M. Goerdeler, G. Gottstein, Mater. Sci. and Eng. A, 400-401 (2005) 231. [80] J.W.C. Dunlop, Y.J.M. Brechet, L. Legras, H.S. Zurob, J. Nucl. Mater., 366 (2007) 178. [81] H.S. Zurob, Y. Brechet, J. Dunlop, Acta Mater., 54 (2006) 3983. [82] W.B. Hutchinson, S. Jonsson, L. Ryde, Scripta Metall., 23 (1989) 671. [83] A. Zahia, F. Salhi, J. Aride, D. Monya-Siesse, G. Moya, J. Alloys Compd., 188 (1992) 264. [84] T. Knudsen, W.Q. Cao, A. Godfrey, Q. Liu, N. Hansen, Metall. Mater. Trans. A, 39 (2008) 430. [85] M. Verdier, I. Groma, L. Flandin, J. Lendvai, Y. Brechet, P. Guyot, Scripta Mater., 217-222 (1997) 449. [86] J. Go, W.J. Poole, M. Militzer, M.A. Wells, Mat. Sci. Tech., 19 (2003) 1361. [87] R. Sandstrom, B. Lehtinen, E. Hedman, I. Groza, S. Karlsson, J. Mater. Sci., 13 (1978) 1229. [88] R.W. Cahn, J. Inst. Metals, 76 (1949) 121. [89] B. Bever, Proceedings Seminar on Creep and Recovery, Cleveland, (1957), 14.    142  [90] E.C.W. Perryman, Proceedings Seminars on Creep and Recovery, Cleveland, (1956), 14. [91] J. Friedel, Dislocations, Addison-Wesley, London, (1964). [92] J.C.M. Li, Recrystallization, grain growth and texture, ASM, (1965). [93] R. Sandstrom, Acta Metall., 25 (1977) 897. [94] R. Sandstrom, Acta Metall., 25 (1977) 905. [95] E. Nes, Acta Metall., 43 (1995) 2189. [96] P.A. Beck, Adv. Phys., 3 (1954) 245. [97] A.L. Titchener, M.B. Bever, Prog. Metal. Phys., 7 (1958) 247. [98] R.D. Doherty, D.A. Hughes, F.J. Humphreys, J.J. Jonas, D.J. Jensen, M.E. Kassner, W.E. King, T.R. McNelley, H.J. McQueen, A.D. Rollett, Mater. Sci. and Eng. A, 238 (1997) 219. [99] D. Kuhlmann-Wilsdorf, Mater. Sci. Forum, 331-337 (2000) 689. [100] G. Masing, J. Raffelsieper, Z. Metallk., 41 (1950) 65. [101] J.T. Michalak, H.W. Paxton, Trans. Metall. Soc. AIME, 221 (1961) 850. [102] W.C. Leslie, J.T. Michalak, F.W. Aul, Iron and its dilute solid solutions, Wiley Inter-Science, New York, (1963). [103] R. Drouard, J. Washburn, E.R. Parker, Trans. Metall. Soc. AIME, 197 (1953) 1226.    143  [104] L.M. Clarebrough, M.E. Hargreaves, M.H. Loretto, Recovery and recrystallization of metals, Wiley Inter-Science, New York, (1963). [105] F.J. Humphreys, Acta Metall., 25 (1977) 1323. [106] J.H. Driver, H. Paul, J.C. Glez, C. Maurice, 21st Intl. Rios Symposium, Denmark, (2000), 35. [107] W.B. Hutchinson, Acta Metall., 37 (1989) 1047. [108] J. Hjelen, R. Orsund, E. Nes, Acta Metall., 39 (1991) 1377. [109] H. Paul, J.H. Driver, Z. Jasienski, Acta Mater., 50 (2002) 815. [110] A. Duckham, O. Engler, R.D. Knutsen, Acta Mater., 50 (2002) 2881. [111] O. Engler, Scripta Mater., 44 (2001) 229. [112] J.E. Bailey, P.B. Hirsch, Proc. R. Soc., A267 (1962) 11. [113] P. Gerber, J. Tarasiuk, T. Chauveau, B. Bacroix, Acta Mater., 51 (2003) 6359. [114] Q. Liu, Z. Yao, A. Godfrey, W. Liu, J. Alloys Compd, 482 (2009) 264. [115] J.C. Lashley, M.G. Stout, R.A. Pereyra, M.S. Blau, J.D. Embury, Scripta Mater., 44 (2001) 2815. [116] D.J. Bailey, E.G. Brewer, US, ( (1972)). [117] D.J. Bailey, E.G. Brewer, Metall. Trans. A, 6 (1975) 403. [118] G.K. Williamson, R.E. Smallman, Acta Metall., 1 (1953) 487. [119] D.F. Stein, J.R. Low, Trans. Metall. Soc. AIME, 221 (1961) 744.    144  [120] M. Sugano, C.M. Gilmore, Metall. Trans. A, 10 (1979) 1400. [121] N. Parson, Alcan International Ltd., Kingson, ON, (2008). [122] P.A. Manohar, M. Ferry, T. Chandra, ISIJ International, 38 (1998) 913. [123] C.S. Smith, Trans. AIME, 175 (1948) 15. [124] P.M. Hazzledine, P.B. Hirsch, N. Louat,  Proc. 1st Int. Symp. on Metallurgy and Materials Science, Riso National Laboratory, Roskilde, Denmark, (1980), 159. [125] E. Nes, N. Ryum, O. Hunderi, Acta Metall., 33 (1985) 11. [126] A.R. Eivani, S. Valipour, H. Ahmed, J. Zhou, J. Duszczyk, Metall. Mater. Trans. A, 42 (2011) 1109. [127] O. Daaland, E. Nes, Acta Mater., 44 (1996) 1389. [128] M. Cabibbo, E. Evangelista, C. Scalabroni, E. Bonetti, Mater. Sci. Forum, 503-504 (2006) 841. [129] L. Lodgaard, N. Ryum, Mater. Sci. Eng. A, 283 (2000) 144. [130] L. Lodgaard, N. Ryum, Mater. Sci. Tech., 16 (2000) 599. [131] R.A. Jeniski, B. Thanaboonsombut, T.H. Sanders, Metall. Mater. Trans. A, 27 (1996) 19. [132] D.H. Lee, J.H. Park, S.W. Nam, Mater. Sci. Tech., 15 (1999) 450. [133] E. Hornbogen, Praktischee Metallographie, 9 (1970) 349. [134] O. Koster, Recrystallization of Metallic Materials, Stuttgart, (1971). [135] E. Nes, J.D. Embury, Z. Metallkd., 66 (1975) 589.    145  [136] O. Daaland, E. Nes, Acta Mater., 44 (1996) 1413. [137] H.E. Vatne, O. Engler, E. Nes, Mater. Sci. Tech., 13 (1997) 93. [138] Annual book of ASTM standards-ASTM Designation E-112-88, ASTM, Philadelphia, PA, (1998). [139] M.Y. Kong, R.N. Bhattacharya, C. James, A. Basu, Geol. Soc. Am. Bull., 117 (2005) 244. [140] Q. Du, W.J. Poole, M.A. Wells, Acta Mater., 60 (2012) 3830. [141] S. Tangen, K. Sjolstad, T. Furu, E. Nes, Metall. Mater. Trans. A 41 (2010) 2970. [142] M. Somerday, F.J. Humphreys, Mat. Sci. Tech., 19 (2003) 20. [143] K. Huang, Y. Li, K. Marthinsen, Mat. Sci. Forum, 783-786 (2014) 174. [144] M. Cooper, Acta Cryst., 23 (1967) 1106. [145] L.K. Walford, Acta Cryst., 18 (1965) 287. [146] J.F. Chinella, TMS 2012, Florida, USA, (2012), 445. [147] Y. Estrin, Unified Constitutive Laws of Plastic Deformation, Academic Press, Orlando, (1996). [148] D.A. Hughes, Acta Metall. Mater., 41 (1993) 1421. [149] D. Park, M. Niewczas, Mater. Sci. Eng. A, 491 (2008) 88. [150] M.F. Ashby, Phil. Mag., 21 (1970) 399. [151] L.M. Brown, R.K. Ham, Dislocation-particle interactions. Strengthening Methods in Crystals, 3rd ed., Wiley and Sons, 1971, (1971).    146  [152] Q. Zhao, B. Holmedal, Y. Li, Phil. Mag., 93 (2013) 2995.   

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.24.1-0166650/manifest

Comment

Related Items