{"http:\/\/dx.doi.org\/10.14288\/1.0429369":{"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool":[{"value":"Applied Science, Faculty of","type":"literal","lang":"en"},{"value":"Materials Engineering, Department of","type":"literal","lang":"en"}],"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider":[{"value":"DSpace","type":"literal","lang":"en"}],"https:\/\/open.library.ubc.ca\/terms#degreeCampus":[{"value":"UBCV","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/creator":[{"value":"Kordmir, Setareh","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/issued":[{"value":"2023-04-04T18:52:26Z","type":"literal","lang":"en"},{"value":"2023","type":"literal","lang":"en"}],"http:\/\/vivoweb.org\/ontology\/core#relatedDegree":[{"value":"Master of Applied Science - MASc","type":"literal","lang":"en"}],"https:\/\/open.library.ubc.ca\/terms#degreeGrantor":[{"value":"University of British Columbia","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/description":[{"value":"Aluminum 6xxx extrusion alloys are attractive candidates for use in automotive applications to decrease vehicle weight. In this study, Al-Mg-Si alloys, and especially variants of AA6082 with two different Mn contents were extruded into 3 \u00d7 90mm strips on a pilot scale extrusion press with processing conditions designed to produce either recrystallized or unrecrystallized microstructures. The objectives of the study are to i) characterize the important microstructural features in the two alloys and ii) examine the relationship between orientation dependence of mechanical properties measured from uniaxial tensile and VDA bend tests with the microstructure.\r\nThe characterization of microstructure and crystallographic texture was done using scanning electron microscopy and electron back scatter diffraction. The mechanical anisotropy was measured by tensile and VDA bend testing conducted at 0, 45 and 90o to the extrusion direction. The characterization analysis shows presence of crystallographic anisotropy, morphological and topological anisotropy of second phase particles in the studied alloys. \r\nIt was found that the strength and fracture anisotropy in tension and bending were significantly affected by the microstructure. A linear correlation between the tensile true strain to fracture and the maximum bend angle prior to substantial damage was observed for the samples tested at 0 and 90o to the extrusion directions for the two alloys. However, the results for samples taken at 45o to the extrusion direction did not follow this trend.","type":"literal","lang":"en"}],"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO":[{"value":"https:\/\/circle.library.ubc.ca\/rest\/handle\/2429\/84140?expand=metadata","type":"literal","lang":"en"}],"http:\/\/www.w3.org\/2009\/08\/skos-reference\/skos.html#note":[{"value":" Anisotropy of Strength and Fracture Behavior in Al-Mg-Si-(Mn) Extrusion Alloys by Setareh Kordmir B.Sc. University of Tehran, 2018 M.Sc. University of Tehran, 2020 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF   MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (MATERIALS ENGINEERING) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  March 2023  \u00a9 Setareh Kordmir, 2023 ii  The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, a thesis entitled: Anisotropy of Strength and Fracture Behavior in Al-Mg-Si-(Mn) Extrusion Alloys  submitted by Setareh Kordmir                                       in partial fulfillment of the requirements for the degree of Master of Applied Science In                   Materials Engineering Examining Committee: Warren J. Poole, Professor, Department of Materials Engineering, UBC Supervisor Matthias Militzer, Professor, Department of Materials Engineering, UBC Supervisory Committee Member Steven Cockcroft, Professor, Department of Materials Engineering, UBC Supervisory Committee Member     iii  Abstract Aluminum 6xxx extrusion alloys are attractive candidates for use in automotive applications to decrease vehicle weight. In this study, Al-Mg-Si alloys, and especially variants of AA6082 with two different Mn contents were extruded into 3 \u00d7 90mm strips on a pilot scale extrusion press with processing conditions designed to produce either recrystallized or unrecrystallized microstructures. The objectives of the study are to i) characterize the important microstructural features in the two alloys and ii) examine the relationship between orientation dependence of mechanical properties measured from uniaxial tensile and VDA bend tests with the microstructure. The characterization of microstructure and crystallographic texture was done using scanning electron microscopy and electron back scatter diffraction. The mechanical anisotropy was measured by tensile and VDA bend testing conducted at 0, 45 and 90o to the extrusion direction. The characterization analysis shows presence of crystallographic anisotropy, morphological and topological anisotropy of second phase particles in the studied alloys.  It was found that the strength and fracture anisotropy in tension and bending were significantly affected by the microstructure. A linear correlation between the tensile true strain to fracture and the maximum bend angle prior to substantial damage was observed for the samples tested at 0 and 90o to the extrusion directions for the two alloys. However, the results for samples taken at 45o to the extrusion direction did not follow this trend.    iv  Lay Summary There is significant interest to replace steel components with aluminum in automotive industry to decrease vehicle weight and consequently, reduce environmental impact of conventional vehicles, e.g., greenhouse gas emissions. The deformation of aluminum extrusions in crash applications to absorb energy is of interest to industry. Thus, it is important for the design team to predict mechanical properties such as strength and fracture behavior of the material under different loading directions in order to engineer the material to meet the design requirements. This work focuses on mechanical response of two commonly used alloys in tension and bending deformation. An experimental study has been conducted to identify different sources of anisotropy in the material and then, explain the orientation dependence of strength and fracture behavior. The main finding of this work was that anisotropy induced by crystallographic texture or initiated due to spatial distribution of second phase particles affect the plastic response of material in different deformation orientations.        v  Preface The majority of this study was conducted by the author at The University of British Columbia under the supervision of Dr. Warren J. Poole. The extruded materials for this project were provided by Dr. Nick Parson from Rio Tinto Aluminum. Samples were machined at the UBC Machine Shop in the Materials Engineering department. Thermodynamic calculations using TTAl6 database in Thermo-Calc software were provided by Dr. Zhijun Zhang from the Materials Engineering department, The University of British Columbia.  A version of Chapters 5 was published in the conference proceedings: S. Kordmir, N.C. Parson and W. J. Poole, \u201cThe role of microstructure on strength and fracture anisotropy effects in Al-Mg-Si extrusion alloys\u201d, in 2023 TMS Annual Meeting & Exhibition, San Diego, California, USA, March 19\u201323, 2023.        vi  Table of Contents Abstract .......................................................................................................................................... iii Lay Summary ................................................................................................................................. iv Preface............................................................................................................................................. v Table of Contents ........................................................................................................................... vi List of Tables ................................................................................................................................. ix List of Figures ................................................................................................................................ xi List of Symbols ............................................................................................................................ xix List of Abbreviations .................................................................................................................. xxii 1 Introduction .............................................................................................................................. 1 2 Literature review ...................................................................................................................... 4 2.1 Review of Al-Mg-Si (6xxx) Aluminum Alloys ............................................................... 4 2.1.1 Extrusion route and age hardening of Al-Mg-Si (6xxx) aluminum alloys ............... 4 2.1.2 Chemical composition of Al-Mg-Si (6xxx) aluminum alloys .................................. 6 2.2 Deformation of Al-Mg-Si (6xxx) aluminum alloys ......................................................... 9 2.2.1 Phenomenology of work hardening ........................................................................ 10 2.2.2 Textures and microstructures (after Plane Strain Deformation) ............................. 12 2.2.3 Recrystallization texture and microstructure (after Plane Strain Deformation) ..... 15 2.2.3.1 Effect of second phase particles .......................................................................... 16 2.2.4 Sources of plastic anisotropy in 6xxx alloys........................................................... 17 vii  2.2.5 Models for simulation of deformation in polycrystals ............................................ 21 2.3 Fracture behaviour of Al-Mg-Si (6xxx) aluminum alloys ............................................. 24 2.3.1 Stress triaxiality ...................................................................................................... 26 2.3.2 Effect of anisotropy on fracture in 6xxx alloys ...................................................... 27 3 Scope and Objectives ............................................................................................................. 31 4 Methodology .......................................................................................................................... 32 4.1 Introduction .................................................................................................................... 32 4.2 Materials ......................................................................................................................... 32 4.3 Microstructure Characterization ..................................................................................... 36 4.3.1 Electron Backscatter Diffraction (EBSD) ............................................................... 36 4.3.2 Scanning Electron Microscope (SEM) ................................................................... 38 4.3.3 Optical Microscope (OM) ....................................................................................... 38 4.3.4 Characterization of Second Phase Constituent particles ......................................... 40 4.4 Mechanical Testing ........................................................................................................ 42 4.4.1 Tensile Test ............................................................................................................. 42 4.4.2 Three-point bend test .............................................................................................. 49 4.4.3 Hardness test ........................................................................................................... 52 4.5 Visco-plastic self-consistent (VPSC) model .................................................................. 53 5 Results and Discussion ........................................................................................................... 56 5.1 Material characterization ................................................................................................ 56 viii  5.1.1 Experimental results................................................................................................ 56 5.1.1.1 Texture and Microstructure ................................................................................. 56 5.1.1.2 Second phase Characterization............................................................................ 58 5.1.2 Discussion ............................................................................................................... 68 5.2 Tensile response of extruded strips ................................................................................ 71 5.2.1 Experimental results and simulation ....................................................................... 71 5.2.1.1 Simulations for tensile response .......................................................................... 82 5.2.2 Discussion ............................................................................................................... 88 5.2.2.1 Simulation and experimental comparison ........................................................... 90 5.3 Bending response of extruded strips .............................................................................. 91 5.3.1 Experimental results................................................................................................ 91 5.3.2 Discussion ............................................................................................................. 100 5.3.3 Correlation between tensile and bend test results ................................................. 102 5.3.4 Correlation between mechanical behavior and sources of anisotropy .................. 103 6 Summary and Future Work .................................................................................................. 106 6.1 Summary ...................................................................................................................... 106 6.2 Future Work ................................................................................................................. 107 References ................................................................................................................................... 108 Appendix A ................................................................................................................................. 115  ix  List of Tables Table 2-1 Crystallographic data of the phases in Al-Mg-Si alloys. ................................................ 7 Table 2-2 Crystallographic data of the phases after homogenization in Al-Mg-Si alloys. ............. 9 Table 4-1 Chemical composition of the AA6082 alloys in wt%, measured using optical emission spectroscopy (OES). ..................................................................................................................... 33 Table 4-2 Summary of the details of the extrusion trials conducted on the AA6082 alloys. ....... 33 Table 4-3 Summary of grinding and polishing procedures for sample surface preparation ......... 37 Table 5-1 Approximate volume fraction of orientations within 15\u00b0 away from ideal texture components ................................................................................................................................... 58 Table 5-2 Summary of mole and volume fractions for Fe-based phases at 20\u00b0C from equilibrium in Thermo-Calc (TTAl6) for both alloys based on Figure 5.3 ...................................................... 59 Table 5-3 Summary of results from log-normal fit to constituent particle distributions in Figure 5.6 and 5.9 (data presents average and the standard deviation of the normally distributed logarithm of the variables). ................................................................................................................................ 64 Table 5-4 Summary of mechanical properties from tensile tests. Variations are based on the standard deviation obtained for each variable in Appendix A (*R-value reported at an axial strain of 10% strain for T4 and 6% for T6) ............................................................................................ 73 Table 5-5 Summary of the slip system level fit parameters used in constitutive law for VPSC simulations of the ED tensile curves (\ud835\udf0f0 and \ud835\udf0f1 are the resolved shear stresses) ........................ 84 Table 5-6 Summary of R-values from experiment and VPSC simulation (\u201c*\u201d value reported at 10% strain for T4 and 6% strain for T6 state) .............................................................................. 86 x  Table 5-7 Summary of VDA test bend angles after springback (# of repeats= 3)........................ 92 Table A-1 Summary of AA7030 tensile test results obtained after 10% strain for variability estimation (measured R-values were obtained using a micrometer before and after the stretch)..................................................................................................................................................... 115                xi  List of Figures Figure 1-1 Photograph showing anisotropic fracture response for bend tests where the bend axis was a) perpendicular to the extrusion direction (ED) and b) parallel to the ED, in seven 6xxx aluminum alloys (reprinted with permission from Rio Tinto Aluminum). .................................... 1 Figure 2-1 Schematic temperature path of the aluminium heating process for AA6082 alloy during the production ................................................................................................................................. 5 Figure 2-2 Approximate compositions (at. %) ranges of commercial 6xxx series alloys, with guidelines for different Mg\/Si-ratios (adapted with permission from [11]). .................................. 8 Figure 2-3 Ideal texture components for FCC metals, represented in pole figures {001}, {011}, and {111} (adapted with permission from [35]). .......................................................................... 13 Figure 2-4 (a) orientation distribution function (ODF) figure showing the hot extruded texture of AA6082 (reprinted with permission from [38]) and (b) schematic representation of texture fiber (reprinted with permission from [35]). ......................................................................................... 14 Figure 2-5 (a) IPF grain maps for 350\u00baC extruded AA6063 profile, overall scan; (b) Texture, in the form of (001) and (111) pole figures for the centre region, and (c) for the near surface region (A2:TD direction, A1:ED direction) [reprinted with permission from [39]]. ............................... 15 Figure 2-6 (a,d) IPF maps of the profile cross-sections in the extrusion direction (ED), (b,e) IPFs, and (c,f) {001} PFs of (a,b,c) A6061 and (d,e,f) A6005C (reprinted with permission from [41])........................................................................................................................................................ 17 Figure 2-7 True stress versus logarithmic strain curves from the experiments on smooth tensile specimens of (a) AA6063 alloy (with recrystallized grain structure) and (b) AA6110 alloy (non-xii  recrystallized grain structure) under different tensile directions (reprinted with permission from [50])............................................................................................................................................... 20 Figure 2-8 Normalized yield stress versus tensile direction at a plastic work corresponding to 0.01 plastic strain (top) and  Lankford coefficient (R-value) versus tensile direction up to necking (bottom) for the (a) AA6063 alloy and (b) AA6110 alloy (reprinted with permission from [50])........................................................................................................................................................ 23 Figure 2-9 Intergranular vs transgranular fracture (reprinted with permission from [70]). .......... 24 Figure 2-10 Representative stress-strain curves from the tension tests on the smooth specimen for (a) AA6063 and (b) AA6110, in the extruded (EX) and the cast and homogenized (CH) conditions. The legend in sub-figure (a) is valid for both sub-figures (reprinted with permission from [2]). 28 Figure 2-11 Optical micrographs and SEM images of the fracture surface of the extruded commercial alloy AA7108 after three-point bend test. The bend axis was aligned along the ED in (a) and (b) and along the TD in (c) and (d). The arrows in (b) indicate stringers of particles aligned along the ED (reprinted with permission from [37]). ................................................................... 30 Figure 4-1 a) Illustrations of the geometry of the die, b) actual image of the die and c) expanded view of a). ..................................................................................................................................... 33 Figure 4-2 Optical images taken from ED-ND plane of the AA6082 alloys after Barker\u2019s etching containing a, a\u2019) 0 wt.% Mn and b, b\u2019) 0.5 wt.% Mn (figures a and b represent the front location, while a\u2019 and b\u2019 represent the back location of extrudate). ............................................................ 34 Figure 4-3 Optical images taken from ED-ND plane of the AA6082 alloys after HF etching containing a, a\u2019) 0 wt.% Mn and b, b\u2019) 0.5 wt.% Mn (figures a and b represent the front location, while a\u2019 and b\u2019 represent the back location of extrudate). ............................................................ 35 xiii  Figure 4-4 Vickers hardness of studied alloys as a function of aging time at 180\u00b0C in an oil bath....................................................................................................................................................... 36 Figure 4-5 Setup for the optical microscope for polarized light observations. ............................. 39 Figure 4-6 Sensitivity of area fraction measurement in 0Mn alloy using different image thresholding parameter grey scale from 0 (black) to 255 (white) on same image. ....................... 41 Figure 4-7 Photograph showing the different orientations of tensile samples with respect to the extrusion direction (ED). .............................................................................................................. 43 Figure 4-8 Dimensions for the tensile samples machined from extruded strips (in mm). ............ 43 Figure 4-9 Figure illustrating location of clip-on extensometers for measuring elongation in length and contraction in width of samples during the test. .................................................................... 44 Figure 4-10 Figure showing fracture area measurement method using the ImageJ software and secondary electron images. ........................................................................................................... 45 Figure 4-11 Ratio of model output to the input based on the measured as-received condition for stress triaxiality correction [93]. ................................................................................................... 46 Figure 4-12 Figure showing yield stress determination using the 0.2 % offset method from the Engineering stress-strain curve. .................................................................................................... 47 Figure 4-13 a) An example of stress and work hardening rate vs true strain curve used for work hardening rate measurement, b) An example showing reproducibility of stress-strain curve recalculated using the non-smoothed work hardening rate........................................................... 48 Figure 4-14 Figure showing different orientation of the bend samples with respect to the extrusion direction (ED) machined from the extruded strips (dashed line represents the bend axis). ......... 49 Figure 4-15 Dimensions for the bend test samples machined from extruded strips (in mm). ...... 50 xiv  Figure 4-16 Illustration of a) the general setup of VDA 238-100 bend test and b) the definition of the bend angle. .............................................................................................................................. 50 Figure 4-17 Schematic figure illustrating measurement variables from the experimental setup for the bend test (reprinted with permission from [95]). .................................................................... 51 Figure 4-18 Example of Force-Displacement curve showing springback estimation using the unloading curve. ............................................................................................................................ 52 Figure 4-19 Estimated error vs halfwidth angle study performed to determine optimal halfwidth angle for ODF calculation (for 0Mn alloy) in MTEX. ................................................................. 54 Figure 4-20 Voce hardening parameters (\ud835\udf0f0, \ud835\udf0f1, \ud835\udf030, \ud835\udf031) shown on stress strain curve (adapted with permission from [99]). .................................................................................................................. 55 Figure 5-1 EBSD analysis of 0Mn alloy. a) EBSD inverse pole figure (IPF) grain structure map from centre of the ED-ND plane, b) spatial distribution of ideal texture components (Note: for each texture component, the color represents those grains within 15\u00b0 of ideal components. White areas represent other orientations), c) grain size distribution histogram and d) 111 and 100 pole figures showing the macroscopic crystallographic texture. ...................................................................... 57 Figure 5-2 EBSD analysis of 0.5Mn alloy. a) EBSD inverse pole figure (IPF) grain structure map from centre of the ED-ND plane, b) spatial distribution of ideal texture components (Note: for each texture component, the color represents those grains within 15\u00b0 of ideal components. White areas represent other orientations), c) grain thickness distribution histogram and d) 111 and 100 pole figures showing the macroscopic crystallographic texture. .......................................................... 58 Figure 5-3 Thermo-Calc modeling result of different phases at various temperatures in equilibrium for a) 0Mn and b) 0.5Mn alloy (Note: dashed vertical line represents the liquid phase). ............ 59 xv  Figure 5-4 Backscatter electron images showing the Fe based particles in the a) 0Mn and b) 0.5Mn alloy............................................................................................................................................... 60 Figure 5-5 Example of stitched BSE images showing constituent particles in 0Mn alloy the three perpendicular surfaces aligned with a) ND-ED plane (along ED), b) ND-TD plane (along TD) and c) ED-TD plane (along ED) for particle size and orientation distribution analysis...................... 62 Figure 5-6 Normalized size distribution and orientation distribution of the constituent particles in 0Mn alloy the three perpendicular surfaces aligned with (a, d, g, j) ND-ED plane, (b, e, h, k) ND-TD plane and (c, f, i, l) ED-TD plane. .......................................................................................... 63 Figure 5-7 Normalized size distribution of a) dispersoids and b) constituent particles in 0.5Mn alloy, and c) combination the two different distributions from a) and b), i.e., not a single distribution). .................................................................................................................................. 65 Figure 5-8 Example of stitched BSE images showing constituent particles in 0.5Mn alloy the three perpendicular surfaces aligned with a) ND-ED plane (along ED), b) ND-TD plane (along TD) and c) ED-TD plane (along ED) for particle size and orientation distribution analysis...................... 66 Figure 5-9 Normalized size distribution and orientation distribution of the constituent particles in 0.5Mn alloy the three perpendicular surfaces aligned with (a, d, g, j) ND-ED plane, (b, e, h, k) ND-TD plane and (c, f, i, l) ED-TD plane. .......................................................................................... 67 Figure 5-10 Backscatter electron images showing the Fe-based particles in 0Mn and 0.5Mn alloy in (a, c) as-cast state, (b, e) after homogenization, (c, f) after extrusion (reproduced from current study and with permission from [102]). ........................................................................................ 70 Figure 5-11 Engineering stress vs. engineering strain plots for the a) 0Mn and b) 0.5Mn extrusions in T4 and T6 tempers. ................................................................................................................... 72 xvi  Figure 5-12 True stress vs. true strain plots for the a) 0Mn and b) 0.5Mn extrusions in T4 and T6 tempers (dashed lines for each test represent the behavior between the necking and final fracture points). .......................................................................................................................................... 72 Figure 5-13 Examples of macroscopic images of the fractured tensile samples for a) 0Mn (T4), b) 0Mn (T6), c) 0.5Mn (T4) and d) 0.5Mn (T6). .............................................................................. 75 Figure 5-14 SEM fractography of tensile samples for the 0Mn alloy in T4 temper in (a, b) ED, (c, d) 45\u00b0 and (e, f) TD direction (Identified particles are pointed by yellow arrows, respectively. Dashed line shows a step in the fracture surface). ........................................................................ 76 Figure 5-15 SEM fractography of tensile samples for the 0Mn alloy in T6 temper in (a,b) ED, (c,d) 45\u00b0 and (e,f) TD direction (Identified particles and cracks are pointed by yellow and green arrows, respectively). ................................................................................................................................. 77 Figure 5-16 SEM fractography of tensile samples for the 0Mn alloy in T4 and T6 tempers in (a, b) ED, (c, d) 45\u00b0 and (e, f) TD direction in x6000 magnification. .................................................... 78 Figure 5-17 SEM fractography of tensile samples for the 0.5Mn alloy in T4 temper in (a, b) ED, (c, d) 45\u00b0 and (e, f) TD direction (Dashed lines show a step in the fracture surface)................... 79 Figure 5-18 SEM fractography of tensile samples for the 0.5Mn alloy in T6 temper in (a, b) ED, (c, d) 45\u00b0 and (e, f) TD direction. ................................................................................................. 80 Figure 5-19 SEM fractography of tensile samples for the 0.5Mn alloy in T4 and T6 tempers in (a, b) ED, (c, d) 45\u00b0 and (e, f) TD direction in x6000 magnification. ............................................... 81 Figure 5-20 111 and 100 pole figures for the texture from the centre region of 0Mn and 0.5Mn alloys obtained from (a, c) calculated ODF and (b, d) EBSD orientations. ................................. 83 xvii  Figure 5-21 For the 0Mn and 0.5Mn alloys at (a, c) T4 and (b, d) T6 temper: plots of the flow curves along the ED. ..................................................................................................................... 84 Figure 5-22 For the 0Mn and 0.5Mn alloys at (a, c) T4 and (b, d) T6 temper: plots of the flow curves along the 45\u00b0 to the ED and TD. ....................................................................................... 86 Figure 5-23 R-value evolutions with the plastic true strain along the ED, at 45\u00b0 to the ED, and the TD, for the 0Mn and 0.5Mn alloy at (a,c) T4 and (b,d) T6 temper. ............................................. 87 Figure 5-24 Force-bend angle curves from VDA bend tests in the ED, 45\u00b0 to ED, and TD deformation direction for T4 and T6 conditions of a) 0Mn and b) 0.5Mn. .................................. 92 Figure 5-25 Top-view SEM images and through-thickness optical micrographs of the fracture surface of the 0Mn alloy in the T4 temper is in the (a,b,c) ED, (d,e,f) 45\u00b0 to ED and (g,h,i) TD deformation direction .................................................................................................................... 94 Figure 5-26 Top-view SEM images and through-thickness optical micrographs of the fracture surface of the 0Mn alloy in the T6 temper is in the (a,b,c) ED, (d,e,f) 45\u00b0 to ED and (g,h,i) TD deformation direction .................................................................................................................... 95 Figure 5-27 Top-view SEM images and through-thickness optical micrographs of the fracture surface of the 0.5Mn alloy in the T4 temper is in the (a,b,c) ED, (d,e,f) 45\u00b0 to ED and (g,h,i) TD deformation direction .................................................................................................................... 96 Figure 5-28 Top-view SEM images and through-thickness optical micrographs of the fracture surface of the 0.5Mn alloy in the T6 temper is in the (a,b,c) ED, (d,e,f) 45\u00b0 to ED and (g,h,i) TD deformation direction .................................................................................................................... 97 Figure 5-29 Through-thickness SEM images of the fracture surface of the 0Mn alloy in the T4 temper bent to 180\u00b0 in ED deformation direction at different magnifications. ............................ 99 xviii  Figure 5-30 Through-thickness SEM images of the fracture surface of the 0.5Mn alloy in the T4 temper bent to 180\u00b0 in ED deformation direction at different magnifications. ............................ 99 Figure 5-31 Schematic figure showing particle alignment and anticipated crack paths in a) TD, and b) ED bend test configurations. .................................................................................................. 101 Figure 5-32 Comparison of bending angles and fracture strain in test direction ED, 45\u00b0 to ED, and TD deformation direction for T4 and T6 conditions for a)0Mn and b)0.5Mn alloy .................. 103 Figure 5-33 Final bending angles plotted vs fracture strain for a) 0Mn and b) 0.5Mn alloy ..... 103 Figure A-1 a) Engineering width strain vs Engineering length strain curve example used for calculating Poisson\u2019s ratio (\ud835\udf10), and b) Engineering stress vs Engineering length strain curve example used for calculating Young\u2019s modulus (E). .................................................................. 116 Figure A-2 a) Plastic true width strain vs plastic true thickness strain curve example and b) R-value vs plastic true length strain curve example showing R-value changes with applied strain. ....... 116        xix  List of Symbols A               Surface Area  a0             Sample thickness before bending test \u0393                Shear strain \ud835\udc4f                 Burgers Vector davg            Average diagonal length of indentation D               Roll Diameter in bend test e                Engineering Strain \ud835\udc38              Young\u2019s modulus f               Applied load\/ Force  f               Volume fraction \ud835\udc53(x)          Probability density function \ud835\udc3a               Shear Modulus \ud835\udc581                  Factor controlling dislocation accumulation (Kocks-Mecking model)  \ud835\udc582           Factor controlling dislocation recovery and annihilation (Kocks-Mecking model) L               Velocity gradient  L                Roll Distance in bend test M               Taylor Factor \ud835\udc5a                Lognormal Average xx  m                Strain rate sensitivity value n                Strain rate sensitivity exponent neff                 Homogenization parameter P               Zener Drag Pressure r                Punch radius in bend test r\u0304              Average anisotropy parameter  \ud835\udc45            Radius \ud835\udc45             Rotation matrix  R2          Coefficient of determination  \ud835\udc60             Lognormal Standard Deviation  S             Engineering Stress S            Punch displacement in bend test T                    Temperature t            Time \u03b1                    Proportionality constant \ud835\udefc\ud835\udc39\ud835\udc5a\ud835\udc4e\ud835\udc65\u221260\ud835\udc41    Final Bending angle \ud835\udefe\ud835\udc3a\ud835\udc35                Grain boundary energy \u03b5 t                  True strain  \u03b5 f                  Fracture strain xxi  \ud835\udf030\ud835\udc60                 Initial work hardening rate  \ud835\udf031\ud835\udc60                 Asymptotic work hardening rate  \u03bb                    Angle between the loading direction and the slip plane normal \ud835\udf07                   Normal Average \ud835\udf0c                   Dislocation Density \ud835\udf0e                   Normal Standard Deviation \ud835\udf0e\ud835\udc5a                 Hydrostatic Stress \ud835\udf0e\ud835\udc52\ud835\udc5e                Equivalent Stress \u03c3t                   True stress \ud835\udf0f                     Resolved Shear Stress  \ud835\udf0f\ud835\udc60                   Critical Resolved Shear Stress (CRSS)  \ud835\udf0f0\ud835\udc60                   Initial CRSS  \ud835\udf0f1\ud835\udc60                   Saturation Stress \ud835\udf10                      Poisson ratio \u03a6                     Second component of orientation vector in Bunge notation  \ud835\udf111                    First component of orientation vector in Bunge notation  \ud835\udf112                   Third component of orientation vector in Bunge notation \u03d5                   Angle between the loading direction and the slip direction xxii  List of Abbreviations  BCC           Body Centered Cubic CI  Confidence Index CRSS          Critical Resolved Shear Stress  DC              Direct Chill EBSD Electron Back-Scatter Diffraction  ED  Extrusion Direction FC              Full Constraints FCC  Face Centered Cubic FEM  Finite Element Method FFT               Fast Fourier Transform HAGB         High Angle Grain Boundary (HR)TEM   (High-Resolution) Transmission Electron Microscopy IPF  Inverse Pole Figure KWN         Kampmann Wagner numerical LAGB         Low Angle Grain Boundary xxiii  ODF  Orientation Distribution Function PCG           Peripheral Coarse Grain PSN            Particle Simulated Nucleation  SC              Simple Cubic  SEM  Scanning Electron Microscopy TD  Transverse Direction VPSC Visco-Plastic Self Consistent  wt%  Weight Percent1  1 Introduction Aluminum alloys from the 6xxx (Al-Mg-Si-Mn-Fe) series are widely applied as structural materials in the automobile industry, e.g., crash tubes, side rails and other body components. To produce the complex shapes needed for these products, extrusion processes at high temperatures are attractive due to the ability to produce high quality components at a competitive cost. The recent increase in the use of aluminum extrusions is driving the need for improved understanding of how these materials behave in situations where multi-axial plastic deformation occurs, e.g., in the forming of complex components and during crash scenarios. This requires characterization of the anisotropic plastic and fracture response of extrusion alloys with different processing histories. Figure 1.1 shows an example of anisotropic fracture response from a variety of 6xxx alloys for bend tests, where the bend axis was a) perpendicular to the extrusion direction (ED), and b) parallel to ED in seven 6xxx aluminum alloys. It can be seen that the bend performance is poorer for the ED tests; in other words, the bend angles (presented in the vertical axis) are lower for bending parallel to ED. One of the objectives of this study will be  to  delineate  possible  reasons  for  this   Figure 1-1 Photograph showing anisotropic fracture response for bend tests where the bend axis was a) perpendicular to the extrusion direction (ED) and b) parallel to the ED, in seven 6xxx aluminum alloys (reprinted with permission from Rio Tinto Aluminum).  2  lower performance in the second case. The studies on the folding and collapse of crash tubes reported by Kyrialkides et al. and Bardi et al. [1] suggest that the anisotropic mechanical behavior of the material can significantly affect the onset of plastic instabilities. For the prediction of cracking during folding of crash tubes, Beland et al. reported that the consideration of material anisotropic mechanical response was important in the finite element (FE) method simulations in order to obtain good agreement with the experiments [1]. For aluminum alloys, a number of sources for anisotropy have been proposed, including i) plastic anisotropy (dependent on crystallographic texture), ii) morphological anisotropy (related to the shape and size of the second phase particles from which the voids nucleate) and topological anisotropy (associated with the spatial distribution of second phase particles [2][3]. Thus, it is necessary to understand the relation between the texture, microstructure and the anisotropic plastic and fracture behavior. The microstructure of 6xxx series alloys contains particles at different length scales, i.e. (i) constituent particles with sizes of 0.5 - 5 \u03bcm, formed at the end of solidification, (ii) dispersoids with sizes of 20 - 150 nm, precipitated during homogenization (in presence of Mn element), and (iii) Mg-Si metastable precipitates with sizes of 1 - 5 nm, which form during artificial aging [1][4]. In the current study, two 6xxx alloys with different Mn content have been chosen, with the aim to study (i) crystallographic texture source of anisotropy in recrystallized and unrecrystallized microstructures, and (ii) particle-induced source of anisotropy in microstructures having single and binary particle size distributions. It is also important to note that industrial extrusion processes inherently involve complex strain paths. In the current study, one of the simplest examples, i.e., extrusion of materials into strips was chosen, where the strain path is nearly plane strain deformation. 3  While there have been broad investigations on plastic anisotropy in tension, there has been few studies on out-of-plane bending and compression, which is the dominant deformation in vehicle crash events. The current study aims to investigate the sources of anisotropy for the two extruded Al-Mg-Si alloys both plastic anisotropy in tension, as well as on out-of-plane bending mode using a standard bend test. In summary, the industrial interest is to tailor the material for crash tubes and other structural components in order to obtain an improved plastic response, based on microstructure and texture. The methodology involves a combination of experiments, industrial extrusion trials and polycrystal plasticity simulations. This work is part of a collaborative project between Rio Tinto Aluminum and The University of British Columbia. This thesis is organized as follows: Chapter 2 will provide a review of the current knowledge available in the literature. In Chapter 3, the scope and objective of this work will be defined. Chapter 4 will introduce the methodology used for the experimental and simulation work. In Chapter 5, the textures and microstructures of the two alloys, anisotropic mechanical and fracture behavior from mechanical tests will be discussed and the visco-plastic self-consistent (VPSC) model used to simulate the deformation texture formed in the deformation conditions will be presented. In addition, the anisotropic R-values examined in the as-extruded strips and simulated from the VPSC model will be compared. In Chapter 6, a summary will be presented with an outlook into future work.    4  2 Literature review  This section provides an overview of anisotropy in 6xxx series aluminum alloys. The structure of this review is as follows: First, background information on 6xxx series aluminum alloys in terms of chemical composition, extrusion route and age hardening treatment is provided; Then, plane strain deformation of 6xxx alloys are discussed regarding crystallographic texture and microstructure obtained. In addition, current knowledge on main sources of anisotropic behavior observations is presented; Then, mechanical behavior of these alloys is discussed considering effect of anisotropy; and current models on crystal plasticity of polycrystalline materials will be reviewed to simulate mechanical behavior. Finally, fracture behavior of these alloys is discussed considering effect of stress triaxiality and anisotropy. 2.1 Review of Al-Mg-Si (6xxx) Aluminum Alloys The 6xxx series or Al-Mg-Si alloys are one of the most important groups of aluminum alloys designed for use in construction, shipbuilding, automotive and aviation industries; this is due to their light weight, satisfactory strength, ease of fabrication process and corrosion resistance [5], [6][7][8]. This has drawn attention to consideration of material behavior in situations where multi-axial plastic deformation occurs, i.e. during forming of complex parts and crash scenarios. It is generally accepted that mechanical and fracture properties are determined by microstructure, which is affected by changes in alloy composition alterations (i.e. alloying elements) and the thermomechanical processing parameters [3].  2.1.1 Extrusion route and age hardening of Al-Mg-Si (6xxx) aluminum alloys Al-Mg-Si (6xxx) aluminum alloy extrusion billets are produced by the direct chill (DC) casting method, and contain a range of intermetallic phases and micro-segregation due to the non-5  equilibrium nature of solidification. Therefore, the DC-casted alloys are not directly extruded, but rather go through a sequence of processes as follows: homogenization, reheating, extrusion and age hardening [6][9]. An example of the thermal history of an AA6082 alloy is shown in Figure 2.1. Homogenization treatment is conducted in order to eliminate the micro-segregation and improve extrudability [10]. In 6xxx series alloys, a short homogenization time at high temperatures (e.g. 10 min at 550\u00b0C [4]) is enough to remove Mg and Si segregation, but long times are needed to homogenize Mn and Cr segregation as they have low diffusivity in aluminum [4][10]. Improvement in extrudability will be partially due to modification of intermetallic phase type and morphology during homogenisation.  After homogenisation, the billets are then reheated to desired extrusion temperature, and extruded to produce the desired profile. Extrusion primarily leads to a change in the aspect ratios  Figure 2-1 Schematic temperature path of the aluminium heating process for AA6082 alloy during the production of extrusion profiles (adapted with permission from [9]). 6  of the grains; the grain elongation parallel to the extrusion direction has been shown to increase with higher extrusion strains, if recrystallization is suppressed [8]. Finally, the extrudates will be cooled with a controlled rate to room temperature.  The aging treatment is applied after cooling which provides the potential for formation of different metastable phases in Al matrix that impede dislocation motion and increase the yield strength [7][11]. Such treatment is referred to as artificial age hardening, and it is the primary strengthening mechanism in 6xxx alloys, mostly due to precipitation of metastable \u03b2'' precipitates during  the aging process [12]. The precipitation phenomena occur in various stages of phase transition, generally accepted as [7] [8][11][13]: supersaturated solid solution \u2192 atomicclusters\/co-clusters\u2192 GP zones \u2192 \u03b2'' \u2192\u03b2'\u2192\u03b2 The chemical composition for the \u03b2'' phase (Mg5Al2Si4 or Mg4Al3Si4) has an Mg\/Si ratio within the range of 0.83-1.25 [14][15][16] and the precipitates form along the <100> direction of the matrix precipitate [7][17][18]. Further aging results in formation of \u03b2' phase (dominant phase in overaged condition) [13] and the final product of decomposition, equilibrium \u03b2 phase (Mg2Si) [7][18]. Table 2.1 presents crystallographic data of the most frequently identified strengthening phases in Al-Mg-Si alloys from transmission electron microscopy (TEM) and high-resolution electron microscopy (HRTEM) analysis.  2.1.2 Chemical composition of Al-Mg-Si (6xxx) aluminum alloys Al-Mg-Si alloys contain magnesium (Mg) and silicon (Si) as their major alloying elements, but can contain transition metals such as iron (Fe), manganese (Mn) and chromium (Cr) [6]. During solidification and\/or heat treatments, these elements combine to form various phases, classified into three categories  i.e.: (i) constituent particles (with sizes of 0.5-5 \u03bcm), (ii) dispersoid particles 7  (with sizes of 20-150 nm) and (iii) Mg-Si metastable precipitates (with sizes of 1-5 nm) [5]. The range of Mg and Si content for these alloys is very broad as shown in Figure 2.2 [11]. The dashed line in Figure 2.2 indicating Mg\/Si ratio of 1:1 is considered an optimal value [14][15], since it is close to the ratio of the main strengthening phase, \u03b2''(Mg5Al2Si4 or Mg4Al3Si4) [5][15]; however, Mg\/Si ratio may decrease to lower values (e.g. 0.5:1) in the presence of excess Si [12]. Excess Si leads to higher strength by promoting precipitation of fine and uniformly distributed  \u03b2'' particles [12], but reduces the peak strength stability in over-aged conditions [2][5][12]. Mechanical properties of 6xxx aluminum alloys are highly influenced by final phases in the microstructure, controlled by composition and thermal-mechanical history of the material [19]; which can be altered by change in homogenization and consequent age hardening parameters. The strength of 6xxx series alloys can increase with an increase in the Mg and Si content [5]. Table 2-1 Crystallographic data of the phases in Al-Mg-Si alloys.  Name Crystal structure Shape Space group Cell dimensions (nm)  Ref. Symbol Constitution A b C \u0392 \u0393  Cluster Mg\/Si:1-2 Unclear Spherical - - - - - - [13][20] GP zone\/ Initial \u03b2''\/pre- \u03b2'' MgxAl5-xSi6 or Mg2+xAl7-x-ySi2+y Monoclinic Spherical \/Needle C2\/m 1.48 0.405 0.648 105.3\u00b0 - [13][20] \u03b2'' Mg5Si6 or Mg4Al3Si4 or Mg5Al2Si4 Base-centered Monoclinic Needle C2\/m 1.516 0.405 0.674 105.3\u00b0 - [15][13][21] \u03b2' Mg1.8Si Hexagonal Needle P63 0.715 - 0.405 - 120\u00b0 [7] [20] \u0392 Mg2Si Cubic Plate Fm\u00af3m 0.635 0.6354 0.635 - - [13][20]  8   Figure 2-2 Approximate compositions (at. %) ranges of commercial 6xxx series alloys, with guidelines for different Mg\/Si-ratios (adapted with permission from [11]). Fe-containing intermetallic phases, which form at the end of solidification, are considered detrimental to mechanical properties such as reducing ductility or bendability [6][22], by appearing as heterogenous nucleation sites for voids [2]. On the other hand, Mn and Cr lead to formation of dispersoids during homogenization  which  affect  the  properties  of  these  alloys  by  supressing  recrystallization  [23]  and  grain  growth  during  the  thermomechanical  processing through the Zener pinning effect [23][24]. A number of studies have reported that addition of Mn in AA6082 alloys results in the precipitation of \u03b1-Al(Mn,Fe)Si dispersoids during the homogenization [25][26]. Wang et al. [24] showed that in the absence of Mn and Cr elements, more than 95% of the second phase particles in the studied Al-Mg-Si alloy after homogenization, are plate shaped \u03b2-Al5FeSi particles and no dispersoids are observed. However, an increase of 0.5wt% Mn and 0.15wt% Cr in the alloy composition, leads to formation of \u03b1-Al(Fe,Mn)Si constituent particles after solidification, in addition to formation of dispersoids during homogenization. Crystallographic data of the common identified phases after homogenization  are  presented  in  Table  2.2 .  The  stoichiometry  of  the   9  Table 2-2 Crystallographic data of the phases after homogenization in Al-Mg-Si alloys.  Name Crystal structure Shape Cell dimensions (nm) Ref. Symbol Constitution A B C \u03b2 \u0393 \u03b1 Particle \u03b1-Al(Mn,Fe)Si Simple cubic Body-centered cubic Sphere 1.265 1.256 - - - - [4][27]  \u03b2-AlFeSi \u03b2-Al5FeSi Monoclinic Plate  1.518 0.981 1.282 91\u00b0 - [27] \ud835\udf39-AlFeSi \ud835\udf39 -Al3FeSi2 \u03b4-Al4FeSi2  Pseudo-tetragonal Plate  0.606 0.606 0.952 - - [27]  \u03b1-Al(Mn,Fe)Si particles has been observed to be variable, with a composition of Al100(Mn,Fe)24Si14 or Al96(MnFe)24Si18, where Mn and Fe can substitute for each other in the microstructure [4]. The change in Fe\/Mn ratio has been associated with the transition of the crystal structure from simple cubic (SC) to body-centered cubic (BCC) [4]. Studies show that after homogenization treatment of Mn containing AA6xxx alloys,  a transition from plate like \u03b2-AlFeSi phase to a spheroidized \u03b1-Al(FeMn)Si phase can be occur [9]. Furthermore, a number of precipitation models following the Kampmann Wagner numerical (KWN) approach have been introduced to predict microstructure evolution as well as (constituent\/dispersoid) particle composition during the homogenization using the chemical composition of the alloy [10][28]. 2.2 Deformation of Al-Mg-Si (6xxx) aluminum alloys  The following section will give a brief review of work hardening during deformation, as well as textures and microstructures obtained after deformation. The main focus will be on plane strain 10  deformation, since a near plane stain deformation mode (due to having some lateral strain) is examined in the current study. 2.2.1 Phenomenology of work hardening With a face-centered crystal structure and high stacking fault energy (160-200 mJ\/m2), aluminum alloys deform plastically through dislocation motion on slip planes of {111} with Burgers vector of a\/2<011> (where a is the lattice parameter) [29][30]. This provides enough slip systems (i.e., 12 slip systems) to be able to accommodate the deformation based on the Taylor\u2019s criterion (i.e. minimum of 5 slip systems) [31]. During plastic deformation, the dislocation density changes through different mechanisms and dislocation interactions; production and accumulation mechanisms such as Frank-read sources, increase the dislocation density; while climb and cross slip of dislocation lead to dislocation annihilation and therefore, reduction in dislocation density. At the initial stage of deformation (i.e., stage II), productive mechanisms dominate; this stage is then followed by a stage referred to as dynamic recovery (i.e., stage III), in which annihilation mechanisms increase. The overall dislocation density changes during deformation can be considered as a competition between dislocation accumulation and annihilation, i.e. [31][32]: \ud835\udc51\ud835\udf0c = \ud835\udc51\ud835\udf0c+ \u2212 \ud835\udc51\ud835\udf0c\u2212  (2.1) where \ud835\udc51\ud835\udf0c is the change in dislocation density, \ud835\udc51\ud835\udf0c+ is the increase of dislocation density and \ud835\udc51\ud835\udf0c\u2212 is the decrease of dislocation density. Kocks and Mecking proposed that the evolution of dislocation density can be assessed as [32]: \ud835\udc51\ud835\udf0c\ud835\udc51\u0393= (\ud835\udc581\ud835\udf0c12 \u2212 \ud835\udc582\ud835\udf0c)  (2.2) \ud835\udc51\ud835\udf0c\ud835\udc51\u0393 is the evolution of dislocation density with respect to the applied shear strain, \u0393, where \ud835\udc581 and \ud835\udc582 are the coefficients relevant to dislocation accumulation and annihilation, respectively. It should be 11  noted that dislocation accumulation is not affected by deformation temperature or strain rate, however, the annihilation of dislocation is significantly dependent upon deformation temperature, strain rate and alloy composition [31]. The critical resolved shear stress (CRSS) can be calculated using the Taylor equation [33]: \ud835\udf0f\ud835\udc60 = \ud835\udefc\ud835\udc3a\ud835\udc4f\ud835\udf0c\ud835\udc51\ud835\udc56\ud835\udc6012   (2.3) where \ud835\udf0f\ud835\udc60 is the CRSS, \ud835\udc3a is the shear modulus, \ud835\udc4f is the magnitude of Burgers vector, and \ud835\udefc is a constant. Integration of Equation 2.2 and substitution into the Equation 2.3 gives: \ud835\udf0f\ud835\udc60 = \ud835\udf0f1\ud835\udc60 [1 \u2212 exp (\u2212\ud835\udf030\ud835\udc60\ud835\udf0f1\ud835\udc60 \ud835\udee4)]  (2.4) where \ud835\udf0f1\ud835\udc60(saturation stress) =\ud835\udc581\ud835\udefc\ud835\udc3a\ud835\udc4f\ud835\udc582 and \ud835\udf030\ud835\udc60(initial hardening rate) =\ud835\udc581\ud835\udefc\ud835\udc3a\ud835\udc4f2 .  Equation 2.4 is often modified to include an initial yield stress (\ud835\udf0f0\ud835\udc60), and to empirically account for a small but non-zero hardening rate, i.e. \ud835\udf031\ud835\udc60, at large strains (also known as stage IV) [1], i.e.: \ud835\udf0f\ud835\udc60 = \ud835\udf0f0\ud835\udc60 + (\ud835\udf0f1\ud835\udc60 + \ud835\udf031\ud835\udc60\ud835\udee4) [1 \u2212 exp (\u2212\ud835\udee4 |\ud835\udf030\ud835\udc60\ud835\udf0f1\ud835\udc60 |)]  (2.5) where \ud835\udf0f0\ud835\udc60, \ud835\udf030\ud835\udc60, \ud835\udf031\ud835\udc60, \ud835\udf0f1\ud835\udc60 are the initial CRSS, the initial hardening rate, the asymptotic hardening rate (stage IV) and the saturation stress, respectively for a certain slip system. In polycrystalline materials, the Taylor factor (\ud835\udc40) can be used to convert single crystal stress-strain curves to those of a random polycrystal and depends on the crystallographic texture of the material (e.g., it is 3.06 for a random oriented set of grains in a face-centered cubic material). The true stress \ud835\udf0e and true plastic strain \ud835\udf00 in polycrystal material are calculated as follows [30]: 12  \ud835\udf0e = \ud835\udc40\ud835\udf0f\ud835\udc60   (2.6) \ud835\udf00 =\ud835\udee4\ud835\udc40   (2.7)  2.2.2 Textures and microstructures (after Plane Strain Deformation) Microstructural changes during deformation include grain shape changes; resulting in an increase of the surface area of grain boundaries. In addition, depending on deformation temperature, strain rate and alloy composition, the dislocation arrangement inside the grain might change from a random distribution of tangled set of individual dislocations to arranged sets of dislocations forming subgrain walls (i.e., low angle grain boundaries) inside the grains [31].  Another significant change during deformation is the change of crystallographic texture, which defines the distribution of preferred crystallographic orientations of grains in a polycrystalline material; crystallographic texture is dependent upon the strain path (e.g. axisymmetric extension, plane strain deformation and simple shear deformation). The current study, however, is mainly focused on nearly plane strain deformation. Plane strain deformation, e.g. rolling, strip extrusion (near plane extrusion), is a common strain path for industrial application of aluminum alloys.  Reports show that Copper ({112}<111> orientation), Brass ({011}<211> orientation) and S ({123}<634> orientation) textural components belong to the deformation texture, while Cube, CubeRD  and Goss are the typical recrystallization texture components [1][34]. The Miller indices and Euler angles of common texture orientations are summarized in Table 2.3 and represented in pole figures {001}, {011}, and {111} in Figure 2.3. The orientations Brass, Copper and S, typically referred to as \u03b2-fiber arise from the preferred dislocation slip systems in the material and represent  13  Table 2-3 Miller indices and Euler angles of  common ideal orientations in deformed and recrystallized microstructure [31][35] Designation Miller indices {hkl}<uvw> Euler angles components \ud835\udf111 \u03a6 \ud835\udf112 Copper {112}<111> 90\u00b0   30\u00b0 45\u00b0 Rolling\/ Extrusion S {123}<634> 59\u00b0  34\u00b0 65\u00b0 Rolling\/ Extrusion Brass {011}<211> 35\u00b0  45\u00b0 0\u00b0\/90\u00b0 Rolling\/ Extrusion Rg {124}<211> 53\u00b0  36\u00b0 60\u00b0 Rolling\/ Extrusion Cube {001}<100> 0\u00b0   0\u00b0 0\u00b0\/90\u00b0 Recrystallization CubeRD {013}<100> 0\u00b0   22\u00b0 0\u00b0\/90\u00b0 Recrystallization CubeND {001}<310> 22\u00b0  0\u00b0 0\u00b0\/90\u00b0 Recrystallization Goss {011}<100> 0\u00b0   45\u00b0 0\u00b0\/90\u00b0 Recrystallization P {011}<122> 65\u00b0   45\u00b0 0\u00b0\/90\u00b0 Recrystallization Q {013}<231> 45\u00b0   15\u00b0 10\u00b0 Recrystallization   Figure 2-3 Ideal texture components for FCC metals, represented in pole figures {001}, {011}, and {111} (adapted with permission from [35]).  rotations of the crystallites during plane strain deformation ending in this stable alignment [36]. The texture can be represented by a series of slices through the orientation density function (ODF) (presented in Euler space) as shown in Figure 2.4a [37]. One example of near plane strain 14  deformation texture is shown in Figure 2.4a [38], which was formed in the center region of extruded AA6082 aluminum alloy (containing 0.5 wt% Mn), after extrusion at 500\u00b0C with an extrusion ratio of 80 [38]. A typical deformation texture is observed in the figure, with a strong \u03b2-fiber running from the Bs orientation over the S orientation to the Cu orientation. The intensities of the Brass, Cube, S and Cu texture components were 26, 25,17 and 8 %, respectively [38]. Zhang et al. [39] reported that for an extruded AA6063 alloy profile homogenized at 580 \u00b0C for 135 min, a fibrous structure, i.e. a non-recrystallized deformation structure was obtained with elongated grains aligned with the extrusion direction. Compared to the initial as-cast material with a random texture, the overall texture of extrudate was strong with the intensities of 22% for Cu-component, 28% for S, 18% for Brass; while the Cube texture intensity was only 3.4%. Figure 2.5a shows an  inverse  pole  figure  map  of  the profile. The texture shown by (001) and (111)   Figure 2-4 (a) orientation distribution function (ODF) figure showing the hot extruded texture of AA6082 (reprinted with permission from [38]) and (b) schematic representation of texture fiber (reprinted with permission from [35]). 15   Figure 2-5 (a) IPF grain maps for 350\u00baC extruded AA6063 profile, overall scan; (b) Texture, in the form of (001) and (111) pole figures for the centre region, and (c) for the near surface region (A2:TD direction, A1:ED direction) [reprinted with permission from [39]]. pole figures for the centre region, and the near surface region are presented in Figure 2.5b and 2.5c, both showing dominant ideal deformation components of Copper, Brass and S. A more careful quantitative analysis of the substructure in Figure 2.5b and 2.5c shows that with the average sub-grain size decreasing towards the surface, the typical plane strain deformation texture in the centre is distorted (\u2018rotated\u2019) around the TD direction. 2.2.3 Recrystallization texture and microstructure (after Plane Strain Deformation) Approximately 99% of the work used for deformation is converted to heat and only about 1% of it will be stored in the material. However, this stored energy is enough to provide the driving force for all the microstructural changes after or during deformation such as recovery, recrystallization and grain growth [31]. For deformation at high temperatures, the stored energy is derived from the accumulation of dislocations and the increase of grain boundary area per unit volume [31]. During recrystallization, grain boundary migration in accumulated misorientations 16  regions results in reduction of dislocation density within the interior of grain regions and transformation of subgrains to grains by the transfer of low angle grain boundaries (LAGBs) to high angle grain boundaries (HAGBs) [31]. Thus, new, strain-free grains form which can subsequently grow to consume the deformed microstructure.  During recrystallization of deformed microstructure, equiaxed grains can form and deformation texture could be transitioned to mostly Cube component ({001}<100> orientation), Goss component  ({011}<100> orientation) and CubeRD (or CubeED in case of extrusion) component ({013}<100> orientation) [34][40][19]. One example of recrystallized texture in A6061 and A6005C alloys, homogenized at 585\u00b0C and extruded at 480\u00b0C, is presented in Figure 2.6. The bulk structure of both the alloys mainly showed Cube and Goss orientations, where (100) was aligned along the ED. The pole figures (PFs) support the observation that the Cube orientation was particularly dominant in the bulk of both alloys [41]. 2.2.3.1 Effect of second phase particles It has been shown that presence of either large second phase particles (constituent particles i.e., with a few microns in diameter) or small second phase particles (dispersoids, with sizes of 20-150 nm) can affect deformation by hindering formation of preferred orientations as well as subgrain formation, provided that a high density of particles is observed in the microstructure [31]. Large second phase particles were found to influence recrystallization, by promoting recrystallization through simulating nuclei (particle simulated nucleation, PSN); while for small second phase dispersoids, inhibition of recrystallization was reported to be through inhibition of grain boundary mobility, referred to as Zener drag effect [10][36][42]. A simple estimation of drag pressure can be obtained as follows: 17   Figure 2-6 (a,d) IPF maps of the profile cross-sections in the extrusion direction (ED), (b,e) IPFs, and (c,f) {001} PFs of (a,b,c) A6061 and (d,e,f) A6005C (reprinted with permission from [41]).  \ud835\udc43\ud835\udc4d\ud835\udc52\ud835\udc5b\ud835\udc52\ud835\udc5f =32\ud835\udefe\ud835\udc3a\ud835\udc35\ud835\udc53\ud835\udc45\ud835\udc43 (2.8) where \ud835\udefe\ud835\udc3a\ud835\udc35 is the grain boundary energy; \ud835\udc45\ud835\udc43 and f are the radius and the volume fraction of the second phase particles, respectively. In the case of concurrent Zener and PSN effects, the Zener pinning may suppress the growth of PSN nuclei [36].  As an example, Sun et al. [43] studied the effect of Mn content (i.e. 0.04, 0.23, 0.46 and 0.64 wt%)  on microstructure evolution and recrystallization behavior of hot rolled AA6061 twin-roll cast plate. They showed that Mn element can significantly change the recrystallization behavior and grain refinement of the alloy. 2.2.4 Sources of plastic anisotropy in 6xxx alloys Like most metallic materials, 6xxx aluminum alloys have a polycrystalline grain structure which is characterized by the size, shape, arrangement and crystallographic orientation of the grains [44]. There are three main sources of plastic anisotropy [3][34]: First, related to the crystallographic texture and preferred orientation of the grains along a defined direction (i.e. 18  extrusion direction); the distribution of the crystal orientations, and its crystallographic texture (which will develop during the extrusion and annealing operations), may give rise to an anisotropy of important materials properties [44], such as strength, work hardening behavior and failure strain in standard tensile tests for different directions [2][29][45].  Second, morphological anisotropy (related to the shape and size of the voids and the particles from which the voids nucleate and grains) [34]; as mentioned previously, deformation can lead to grain shape changes. Grain shape is likely to affect plastic anisotropy of polycrystals in two regards: (i) geometrical constraints associated to the grain arrangement may lead to a \u2018\u2018partial relaxation\u2019\u2019 of certain components of the stress tensor, and (ii) grain shape may cause individual slip systems to strengthen differently, depending on the alignment of the slip plane and shear direction with respect to the grain principal diameters [46][47]. Third, topological anisotropy which comes from the spatial distribution of constituent particles and dislocation structure [34]; spatial distribution of constituent particles and dislocation structure can be highly anisotropic based on the deformation temperature as well as the amount of strain applied during the deformation process [48]. In age-hardenable aluminum alloys, the topography of second-phase particles is considered an alternative source of plastic anisotropy [44]. It has been shown that, plate-shaped precipitates on {111}Al and {110}Al planes, formed during aging, tend to accentuate or retain texture induced anisotropy, whereas precipitates on {100}Al  plane (e.g. \u03b8\u2032 platelets in Cu-containing aluminum alloys) tend to diminish texture induce plastic anisotropy [44][49]; such effect has been explained based on the orientation dependence of a long-range stress, the so-called back-stress, generated by the precipitates [44]. However, Engler showed that the topography of needle-shaped \u03b2\u2032\u2032-particles had negligible effect on the in-plane anisotropic behavior of  alloy AA6016 alloy, in comparison to the effect of crystallographic texture [44]. 19  In most studies on anisotropy in deformed aluminum alloys, the anisotropic mechanical response is dominated by crystallographic texture. An example for tensile properties for extruded profiles of AA6063 (with a recrystallized grain structure)  and AA6110 (with a non-recrystallized grain structure) alloys in five different in-plane directions (i.e. 0, 22.5, 45, 67.5 and 90\u00b0 to ED), is shown in Figure 2.7, where true stress is plotted versus logarithmic strain [50] (Note: the logarithmic strain was calculated from continuous diameter measurements at the minimum cross section in two perpendicular directions by means of a contact-less laser gauge, provided until fracture); Figure 2.7a shows that for the AA6063 tensile samples, with a recrystallized grain structure, the initial work hardening rate varies markedly between the distinct tensile directions; the rate increases from 155.6 MPa for 0\u00b0 direction to \u2248243.1 MPa for the 45\u00b0 direction specimens, and decreases for higher angular specimens, reaching 200.2 MPa for the 90\u00b0 direction. In contrast, for the AA6110 alloy samples (Figure 2.7b) with a non-recrystallized grain structure (i.e., a typical fibrous texture), the hardening rates were similar (\u2248177.4 MPa) in the different tensile directions. Frodal et al.  proposed that these differences in the work-hardening behavior can be attributed to texture evolution and the fact that the texture may evolve differently in different directions depending on the initial texture of the alloy [50]. Figure 2.7 also shows that the point of failure varies with tensile direction, suggesting that the plastic anisotropy introduced might have induced fracture anisotropy, i.e., fracture strength and strain dependency on tensile direction (discussed in Section 2.4.2). However, observation of anisotropy in the yield stress for these two alloys were different from the anisotropic initial work hardening behavior; the unrecrystallized AA6110 alloy showed more anisotropy in yield stress with normalized yield stress (the yield stress along a tensile direction \u03b1the yield stress along the ED ) within range of 0.9-1.0, having the highest value along the  20   Figure 2-7 True stress versus logarithmic strain curves from the experiments on smooth tensile specimens of (a) AA6063 alloy (with recrystallized grain structure) and (b) AA6110 alloy (non-recrystallized grain structure) under different tensile directions (reprinted with permission from [50]). ED; while the recrystallized AA6063 alloy showed similar normalized yield stress of 1.0 for the different directions (with an exception of low value for the 22.5\u00b0 direction). While previous studies show that most anisotropic plastic response can be accounted for crystallographic texture [33][44], in some cases, morphological anisotropy contributes to anisotropic behavior; Mathur [46] investigation on modelling plastic anisotropy of aluminum sheets showed that grain shape significantly affects the anisotropy that develops during large strain deformations, where the grains evolve toward a flat and elongated shape. In addition, following Bate et al. work [51], Tomstad et al. reported that the effect of second phase particles on anisotropic tensile behavior of AA6110 increases by increase in the number and size of particles [52]. One method to charactarize plastic anisotropy is through analysing the plastic strain ratio, which is the ratio of the true plastic strain in the width direction to that in the thickness direction during tension (e.g. a standard tensile test) in different in-plane directions, commonly referred to as the R-value [2][37][44]. Snilsberg et al. [53] measured the R-values for the AA6060 (with recrystallized grain structure) and AA6082 alloy (with fibrous grain structure) in different tensile 21  directions. Both alloys showed almost the same R-value of \u2248 0.6 when the tensile axis was oriented parallel to ED; the fibrous microstructure had the highest R-value when the tensile axis was oriented 45\u00b0 relative to ED (\u2248 1.3), while for the recrystallized AA6060 alloy, the R-value was highest (\u2248 2.6) when the tensile axis was oriented 90\u00b0 relative to ED [53].  In addition to experimental analysis such as above, anisotropic response of material after plastic deformation and R-value measurement have been broadly studied using modelling simulations, as will be discussed in the next section [24][29][34][54]. 2.2.5 Models for simulation of deformation in polycrystals In 1934, Taylor [55] proposed that the plastic strain rate of all the grains within a polycrystal are the same and equal to the externally imposed macroscopic plastic strain rate. However, reports show that Taylor model can not provide a complete theoretical solution to the plastic deformation of the polycrystal. A model which considering both strain rate and stress constraints (neglected in the full-constraints (FC) Taylor model [56]) and combined with the self-consistent approach was developed by Lebensohn et al. [57], i.e. the visco-plastic self-consistent (VPSC) model.  The VPSC model extends the approach to allow for visco-plastic materials and assumes that: (i) each grain is considered as an inclusion and the surrounding grains as a homogeneous matrix; (ii) the inclusion represents a grain which can be characterized by its orientation and the matrix reflects the average homogeneous properties of all the other grains; (iii) the strain rate and stress within the grain are assumed to be homogeneous; (iv) the properties of matrix are homogeneous [57]. Overall, assumption that makes this model to be self-consistent, is that stress is balanced between grains and strain compatibility is also maintained between grains. This model couples the strain rate and stress in each grain (inclusion) and the average strain rate and stress in the surrounding (matrix) by the constitutive relation, considering both crystallographic slip and 22  twinning [56]. The evolution of the critical resolved shear stress (CRSS), \u03c4s, with the accumulated shear strain in a given grain can be described by an extended Voce law (Equation 2.5), with rate sensitivity introduced. The interaction tensor is calculated using the homogenization parameter (neff), the interaction tensor based on the secant approximation (i.e., neff=1, a condition close to the Taylor condition that all grains tend to be deformed with an equal strain rate), and interaction tensor based on the tangent approximation  (i.e., neff= \u221e, a condition tending to uniform stress state or the Sachs condition) [57]. By tuning the homogenization parameter neff  in a range from 1 to \u221e, the VPSC model can be modified from the Taylor condition (neff = 1) to the Sachs condition (neff = \u221e) to obtain an interaction between Taylor and Sachs models [58][59]. Previous work has shown that using neff =10 gives a reasonable balance between the Taylor and Sachs bounds [60]. The inputs for the model are (i) a set of grains of known crystal structure, shape and crystallographic orientations (i.e. the starting texture), (ii) a material constitutive law at the slip system level including work hardening and rate sensitivity, (iii) the deformation strain path as defined by the velocity gradient tensor (note: this may be a constant or varying), and (iv) a homogenization parameter, neff. Besides VPSC, there are other models (e.g.  Crystal Plasticity Finite Element Modelling (CPFEM), GIA, LAMEL\/ALAMEL and Fast Fourier Transform (FFT)) that take different approaches to crystal plasticity [31][61][62], each having certain advantages for different conditions. These models give accurate results with intragranular resolution but, since the number of elements in the problem grows with the number of grains considered, they become extremely computationally expensive for the solution of complex problems at the macroscopic level [61]. For example, recent CPFEM calculations take the finite element method to crystal level, requiring a mesh to represent an aggregate of grains with specific shapes, orientations and 23  neighborhood. Figure 2.8 presents an example of using CPFEM modelling in comparison to experimental tensile testing results, i.e. the normalized yield stress and R-value (strain ratio, defined as \ud835\udc51\ud835\udf00\u22a5(incremental strain in the direction perpendicular to the tensile direction) \ud835\udc51\ud835\udf00\ud835\udc41\ud835\udc37(incremental strain in the thickness direction), for the different tensile directions in the ED\u2013TD plane [50]; tensile tests were conducted on AA6063 alloy (with recrystallized grain structure) and AA6110 alloy (with non-recrystallized grain structure). Frodal et al. concluded that owing to the crystallographic texture being different for the two alloys, there was a clear difference in the variation of both normalized yield stress and R-value with tensile direction.  Figure 2-8 Normalized yield stress versus tensile direction at a plastic work corresponding to 0.01 plastic strain (top) and  Lankford coefficient (R-value) versus tensile direction up to necking (bottom) for the (a) AA6063 alloy and (b) AA6110 alloy (reprinted with permission from [50]).  24  2.3 Fracture behaviour of Al-Mg-Si (6xxx) aluminum alloys Studies on fracture behavior of 6xxx series alloys show that these alloys fail in a ductile, most often transgranular manner [63][64], characterized by the presence of deep dimples [101]. However, in some cases, intergranular fracture is observed, characterized by fracture along grain boundaries [65] and associated with decreased ductility of the alloy [63][66]. The schematic illustration in Figure 2.9 shows the difference between intergranular and transgranular fracture. Transgranular fracture occurs by void coalescence, consisting of (i) nucleation of voids, (ii) growth caused by plasticity and (iii) coalescence of voids, which leads to crack formation and final fracture [66][67]. Void nucleation is often associated with non-deforming particles, controlled by the build-up of internal stresses as a result of incomplete plastic relaxation due to local dislocation storage and hence, local work-hardening around the particles [48][68][69]. Studies show that larger particles generally fracture at lower strains [68]; therefore, the resistance to damage and fracture depends directly on the nature, shape, size, distribution and volume fraction of the second phase particles [67].   Figure 2-9 Intergranular vs transgranular fracture (reprinted with permission from [70]). 25  The applied strain path can also be a factor in ductile fracture. Investigations performed by Westermann [37] showed that localization of strain in the shear bands can be the major failure initiation mechanism in plane-strain bending of the deformed materials, noting that plane strain deformation is favourable for shear band formation compared to uniaxial tension [37]. Thus, ductile fracture in bending occur directly in the shear bands, i.e. at a length scale greater than the mean spacing between voids [37][66]. Material separation across the shear bands will eventually involve void nucleation and coalescence, similar to failure by void coalescence mechanism [66] [71]. Further factors which affect ductility include an increase in the Mg and Si content, which Li et al. [72] showed can decrease the bendability of 6xxx series alloys. This can simply be related to their intrinsically lower tensile ductility of the higher strength alloys, having higher solute content. The influence of dispersoids on fracture behavior for Al-Mg-Si alloys was initially was reported by Dowling and Martin [73]. In case of alloys with Mn containing dispersoids, the dispersoids have shown to change the slip band spacing during deformation by finely distributing slip at the crack tip, as well as promoting grain refinement, which can both reduce the tendency to intergranular fracture [74]; this can change the micro-mechanism of crack nucleation and propagation, thereby, modifying the fracture process [23][75]. Blind and Martin [76] and Poole et al. [45][77] reported more detailed conclusion in their work on deformation behavior of Al-Mg-Si alloys containing different Mn content, in which formation of incoherent Mn-rich particles caused lateral spreading of the slip bands and significantly smaller stress concentrations at the head of the slip bands [73]. Constituent particles are considered to be heterogenous nucleation sites for voids and micro-voids due to particle cracking and\/or decohesion between the particles and the matrix [2] [37] 26  [48][66]. Voids nucleated by particle fracture are initially flat while voids nucleated by decohesion of the particle are initially rounded; which can lead to different void growth rates [66]. Observing large number of particles in the dimples of the fracture surfaces of AA6061, AA6063 and AA6110 alloys, Thomesen et al. [2] suggested that failure in these alloys occurs by void coalescence mechanism around the constituent particles and subsequent decohesion of particles from the matrix. In addition, cracking of an iron-rich intermetallic particles during loading can changes the strain field in the surrounding matrix and creates a region of elevated strain field in the close neighbourhood of voids, facilitating the localization of plasticity during void coalescence stage [3][78][79]. Therefore, reports show that decohesion and cracking of iron-rich constituent particle can influence both the bendability and the tensile ductility of an alloy [80][81]. 2.3.1 Stress triaxiality Stress triaxiality plays an important role in ductile fracture [82]. It is a term used to describe the ratio of the hydrostatic (\ud835\udf0e\ud835\udc5a) to the equivalent stress (\ud835\udf0e\ud835\udc52\ud835\udc5e), \ud835\udf0e\ud835\udc5a\ud835\udf0e\ud835\udc52\ud835\udc5e=13(\ud835\udf0e11+\ud835\udf0e22+\ud835\udf0e33)\u221a(\ud835\udf0e11\u2212\ud835\udf0e22)2+(\ud835\udf0e22\u2212\ud835\udf0e33)2+(\ud835\udf0e33\u2212\ud835\udf0e11)2+6(\ud835\udf0e122 +\ud835\udf0e232 +\ud835\udf0e312 )2. The classic Bridgman analysis of necking in an axisymmetric tensile specimen [83] showed that sample geometry can lead to high stress triaxiality (i.e., completely hydrostatic stress state) at the center of the sample, promoting void growth near the center of the specimen, and formation of a crack with a fibrous, flat fracture surface [84]. Recent studies on fracture analysis of aluminum alloys in tensile testing show that failure strain under tensile loading can depend markedly on the stress triaxiality [2][78][85]. 27  2.3.2 Effect of anisotropy on fracture in 6xxx alloys Three types of sources of anisotropy can impact the fracture behaviour, each with a various degree of contribution [2][3]: 1. Anisotropy of plasticity can have a significant influence on the ductile failure since void nucleation, growth and coalescence, affected by local stress and strain state [3]. 2.  Morphological anisotropy (i.e., the shape of the grains, voids and constituent particles) can be important in during the void nucleation step, e.g. load transfer to second phase particles is dependent on their aspect ratio. 3. Topological anisotropy (i.e., spatial distribution and alignment of the constituent of particles), particularly affects the void coalescence step. During plastic deformation, brittle intermetallic particles may fracture and a stringer-type particle clustering develop may lead to a preferential damage path [3]. In case of ductility assessment in tensile tests, an example of fracture anisotropy observed in Figure 2.10 from Thomesen et al. [2] work, where tensile tests were conducted for three different in-plane directions (i.e. 0, 45 and 90\u00b0 to ED) (Note: the logarithmic strain was calculated from diameter measurements up to failure using a contact-less laser gauge, which created two perpendicular laser beams, aligned with the ND and TD* of the specimen). The results in Figure 2.10a show substantial anisotropy in the fracture behavior for AA6063 alloy with recrystallized microstructure (Cube dominant texture), where the failure strain was highest (1.0-1.1) in the 0\u00b0 (extrusion direction) and 90\u00b0 to the extrusion direction (attributed to the Goss texture component), but lower value of 0.77 was obtained for the 45\u00b0 to the extrusion direction. On the other hand, AA6110 material having an unrecrystallized microstructure, showed less anisotropy (Figure 2.10b), with similar failure strain of \u2248 0.7-0.8 for all the three different directions [2]. 28    Figure 2-10 Representative stress-strain curves from the tension tests on the smooth specimen for (a) AA6063 and (b) AA6110, in the extruded (EX) and the cast and homogenized (CH) conditions. The legend in sub-figure (a) is valid for both sub-figures (reprinted with permission from [2]). Investigations on morphological and topological controlled fracture anisotropy of 6xxx alloys shows instances of anisotropic fracture strain and bendability due to (i) preferential orientation of elongated second phase particles in a specific direction (e.g. deformation direction),  and (ii) clustering of the particles into long bands [37][63][66][85]; It is shown that decohesion, void growth, and coalescence are most likely to occur along particle strings align in the deformation direction, increasing the stress in the regions in between. This makes it easier for the crack to follow a path that goes from string to string [37][86]. In addition, studies show that particle size distribution is another major factor controlling the fracture behavior, in which alloys exhibiting the smaller particles nucleated voids later during deformation, thus, were more ductile [2][3][50]. Thomesen et al. [2] and Tomstad et al. [48] observed the effect of morphological and topological anisotropy induced by constituent particles in tensile fracture behavior of fully recrystallized 6xxx alloys; they concluded that the higher failure strain in the 90\u00b0 tension direction 29  can be due to (i) the shape of the particles, being longer in the ED than in the TD, and (ii) the particle stringers aligned with the ED. Their pair correlation function analysis and SEM imaging indicated that the extruded alloys show topological anisotropy of particles, where the constituent particles have a tendency to cluster along the ED, and form stringer-type particle clusters [48][79]; thus, leading to anisotropic fracture strain. In case of ductility assessment in bend tests, Snilsberg et al. [53] studied anisotropic response in three point bending for AA6060 alloy (with recrystallized grain structure) and AA6082 alloy (with fibrous grain structure), which showed that the presence of particle stringers along ED led to distinctively lower bending angles when the bending axis was parallel with the extrusion direction (ED) than when the bending axis was parallel with the transverse direction (TD) and 45\u00b0 to ED for both alloys [53]. Fracture analysis of Westermann [37] on extruded commercial alloy AA7108 after three-point bend test showed similar results, concluding that decohesion, void growth, and coalescence most likely occur along the direction of strings of particles (i.e., ED), causing a characteristic zigzag crack growth. The optical micrograph and SEM image of the fracture surface is shown in Figure 2.11a and b. However, when the bending axis was perpendicular to the direction of the stringers (i.e., bending axis was parallel to TD), fracture propagation was not affected by them (Figure 2.11c and d) [37]. 30   Figure 2-11 Optical micrographs and SEM images of the fracture surface of the extruded commercial alloy AA7108 after three-point bend test. The bend axis was aligned along the ED in (a) and (b) and along the TD in (c) and (d). The arrows in (b) indicate stringers of particles aligned along the ED (reprinted with permission from [37]).        31  3 Scope and Objectives The recent interest in the replacement of steel by aluminum extrusions for making axial crush tubes or side rails in automotive applications, has motivated a desire to characterize the anisotropy of strength and fracture in high strength extruded AA6xxx alloys.  Multiple studies have tried to identify sources of such anisotropic behavior and claimed the main sources to be: i) crystallographic texture (as caused for instance by the preferred orientation of the grains along a defined direction), ii) morphological anisotropy (related to the shape and size of particles from which the voids nucleate) and topological anisotropy, associated with the spatial distribution of second phase particles. The overall goal of this project is to measure mechanical properties and attempt to relate them to the characterized microstructure, by elucidating the various contributions to anisotropy. Specifically, the current project aims to: \u27a2 Analyze the effect of Mn content on the microstructure and texture, by characterizing the as-extruded microstructures and texture of two AA6082 extruded strips with 0 and 0.5wt% Mn content \u27a2 Analyze effect of Mn content on strength and fracture behavior, by measuring the tensile stress-strain response and bending response of two AA6082 extruded strips with 0 and 0.5wt% Mn content \u27a2 Identify sources of anisotropy in the two extruded AA6082 alloys, using tensile and bend tests conducted at different orientations to the extrusion direction \u27a2 Predict tensile behavior of the two extruded AA6082 alloys through VPSC modelling and find a link between the texture and the relevant anisotropic mechanical response 32  4 Methodology 4.1 Introduction In this chapter, the experimental and simulation methods used will be described. First, characteristics of the starting material, such as chemistry, grain structure and crystallographic texture (using electron backscatter diffraction) will be introduced. Following this, the details of the tensile tests, three-point bend tests and hardness tests will be described. Finally, the details of how the visco-plastic self-consistent (VPSC) was implemented to simulate the tensile response of the materials will be discussed. 4.2 Materials Billets of AA6082 were direct chill cast by Rio Tinto Aluminum in Arvida, Quebec with a dimension of 101 mm in diameter and 405 mm in length. The chemical composition of the alloys is listed in Table 4.1. As it can be seen from Table 4.1, the main difference between the two alloys is the Mn content. After casting, a homogenization treatment was conducted by heating the billets at a rate of 250 \u2103\/h to 500 \u2103, after which the heating rate was lowered to 50 \u2103\/h. Upon reaching the soak temperature of 550 \u2103, the billets were held for 2 h followed by water quenching to room temperature. Subsequently, the billets were reheated in an induction furnace to a temperature of 500 \u2103, prior to entering the extrusion container which had a temperature of 480 \u2103. The billets were then extruded with an extrusion ratio of 33:1 and an extrusion press speed of 9 mm\/s to form strips with a cross section of 90 \u00d7 3 mm, i.e. almost plane strain deformation. The strips were quenched in a standing wave water tank located 2.5 m away from the extrusion press. The details of the extrusion trials are summarized in Table 4.2. Illustrations of the geometry of the die is shown in Figure 4.1  33  Table 4-1 Chemical composition of the AA6082 alloys in wt%, measured using optical emission spectroscopy (OES).  Alloy Grain structure Mg Si Cu Mn Fe Al 0 Mn Recrystallized 0.66 0.94 0.002 0.002 0.21 Bal. 0.5Mn Fibrous 0.74 1.04 0.001 0.520 0.19 Bal.  Table 4-2 Summary of the details of the extrusion trials conducted on the AA6082 alloys.  Billet # Alloy Homogenization condition Die geometry Extrusion temperature (set point\/measured at the exit) Extrusion speed Extrusion ratio Extrudate dimensions 5 0Mn 550 \u2103 - 2 h flat die with 3 mm bearing 500 \u2103\/535 \u2103 9 mm\/s 33:1 90 \u00d7 3 mm 11 0.5Mn 550 \u2103 - 2 h flat die with 3 mm bearing 500 \u2103\/549 \u2103 9 mm\/s 33:1 90 \u00d7 3 mm                   Figure 4-1 a) Illustrations of the geometry of the die, b) actual image of the die and c) expanded view of a). 34  (provided by RTA). The variation of the die bearing length along the die exit is shown in Figure 4.1c. Figures 4.2 and 4.3 illustrate optical microscopy images showing through thickness view of sections normal to the extrusion direction from two locations (front and back) of the extruded profiles, i.e., ED-ND plane (provided by RTA); Figure 4.2 reveals the grains in the microstructure after etching the section surfaces in Barker\u2019s etchant, 0.5% HBF4, at  ambient temperature for 120-180 s; using the ImageJ software analysis for these images, it was estimated that the 0.5Mn extruded profile has a peripheral coarse grain (PCG) layer with 130-180 \u03bcm thickness. Figure 4.3 reveals the distribution of the particles throughout the cross section after etching the surfaces in 0.5% HF etchant for 60-120 s at ambient temperature.   Figure 4-2 Optical images taken from ED-ND plane of the AA6082 alloys after Barker\u2019s etching containing a, a\u2019) 0 wt.% Mn and b, b\u2019) 0.5 wt.% Mn (figures a and b represent the front location, while a\u2019 and b\u2019 represent the back location of extrudate). 35   Figure 4-3 Optical images taken from ED-ND plane of the AA6082 alloys after HF etching containing a, a\u2019) 0 wt.% Mn and b, b\u2019) 0.5 wt.% Mn (figures a and b represent the front location, while a\u2019 and b\u2019 represent the back location of extrudate).  Two different heat treatments were examined after the water quench on the extrusion press: (i) natural ageing (T4), where the extrudates were held at room temperature for approximately 200-300 days before testing (\u2248200 days before tensile and hardness tests, and \u2248300 days before bend tests) and (ii) artificial aging (T6), where the extrudates were naturally aged at room temperature for approximately 190 days and then heat treated at a temperature of 180 \u2103 for 6h in an oil bath, followed by water quenching to room temperature. It is worth noting that according to the equation given by Esmaeili for the yield strength estimation of a similar alloy during natural aging [87], there will be only small changes in the yield stress (\u2248 5MPa) for a natural aging period of 200 vs 300 days. The selection of 6 h for the age time at 180 \u00b0C to prepare peak aged samples (T6) was based on Vickers hardness measurements conducted for different aging times in an oil bath at 180 \u00b0C on 36  both alloys (according to method discussed in 4.4.3). Figure 4.4 shows that the hardness increases with an increase in aging time reaching a peak at 6h for both alloys. For the 0Mn alloy, the hardness increases from 82 Hv in T4 to 107 Hv at the peak. On the other hand, 0.5Mn shows a hardness of 91 Hv in T4 and 122 Hv at peak. Further aging beyond 6h, results in a gradual decrease in hardness for both alloys. The error bar reported for hardness in Figure 4.4 is the standard deviation calculated from 5 repeat hardness measurement for each condition. The value of hardness is reported in kgf\/mm2. 4.3 Microstructure Characterization 4.3.1 Electron Backscatter Diffraction (EBSD)  The crystallographic texture of the material was characterized using electron backscatter diffraction. Surface preparation included grinding with silicon carbide papers (400, 800, 1200 and 2400 grit), polishing with 6 and 1 \u03bcm diamond particles suspension on Leco Imperial cloths (6 and 1 \u03bcm), and 0.05 \u03bcm colloidal silica suspension on a Chemomet cloth. The details about the   Figure 4-4 Vickers hardness of studied alloys as a function of aging time at 180\u00b0C in an oil bath   37  grinding and polishing procedure are summarized in Table 4.3. EBSD maps were taken by a Zeiss \uf053igma scanning electron microscope (SEM) equipped with a Nikon high speed camera and EDAX\/TSL OIM Data collection (6th edition) software; using an acceleration voltage of 20 KV and a 60 \uf06dm aperture. A step size of 3\uf06dm was selected for most cases, while for higher resolution cases, a step size of 1\uf06dm was used. The surface of the sample was positioned in working distance of ~ 13 mm and only the aluminum FCC phase was indexed. Data was captured at a speed of 40 fps with an 8\u00d78 bin size. The results were processed with EDAX\/TSL-OIM Analysis (6th edition) software and MATLAB (using MTEX toolbox). Low confidence (lower than 0.1) data were removed from the dataset and a single step cleaning process using grain dilation was used for grain boundary orientation distribution. The cleaning process involved identification of grains using a threshold disorientation angle of 15\u00b0 and small grains with area less than 3 pixels were removed. Table 4-3 Summary of grinding and polishing procedures for sample surface preparation  Type of grinding paper\/polishing cloth Speed (rpm) Time (min) Polishing solution Lubricant SiC-400 grit 200 \u22482 -  water SiC-800 grit 200 \u22482-5 - water SiC-1200 grit 200 \u22482-5 - water SiC-2400 grit 200 \u22485-10 - water Leco Imperial (6 \u03bcm) 100 \u224820 6 \u03bcm diamond suspension Microid Diamond Compound Extender Leco Imperial (1 \u03bcm) 100 \u224820-40 1 \u03bcm diamond suspension Microid Diamond Compound Extender Buehler Chemomet (0.05 \u03bcm) 100 \u224820-30 0.05 \u03bcm colloidal silica -  38  4.3.2 Scanning Electron Microscope (SEM) High magnification images were taken by a Zeiss \uf053igma field emission gun (FEG) SEM. The microscope was used for observing second phase particles distribution (by both secondary and backscatter electron detectors) and fracture surfaces (secondary electron detector). For observation of second phase particles, sample surface preparation, included manual grinding with silicon carbide papers (400, 800, 1200 and 2400 grit) and polishing with 6 and 1 \u03bcm diamond particles suspension (Table 4.3). Images taken from second phase particles were used to investigate the spatial distribution of constituent particles in microstructure, by fitting an ellipse to each particle and measuring particle size and angle between maximum length of particles and the extrusion\/transverse direction using the ImageJ software. At least 200 particles were included for each measurement. Low magnification images were taken with an FEI Quanta 650 tungsten filament SEM. The microscope was used for capturing images of the entire fracture surfaces, using the secondary electron detector. 4.3.3 Optical Microscope (OM) A Nikon EPIPHOT 300 series inverted microscope attached with a digital camera was used to capture optical images (Magnification: 50-1000x). The microscope equipped with a CLEMEX Tango controllers for motorized stages, as well as a crossed polarizer, lambda filter and analyzer as shown in Figure 4.5. Samples preparation, included manual grinding with silicon carbide papers (400, 800, 1200 and 2400 grit) and polishing with 6 and 1 \u03bcm diamond particles suspension (Table 4.3). After surface preparation, samples were electro-etched with Barkers reagent, 0.5% HBF4 for 120-180 s at ambient temperature, using carbon rod as cathode, the specimen as anode and 39  approximately 40V DC power supply [88]. Polarized light and the lambda filter can enhance the color of the interference film deposited during etching. When polarized light enters each grain, it is split into two rays that are perpendicularly polarized.  Each of the two rays travels at different speeds and are differentially absorbed as they travel through the material, thus the grains exhibit different shades of color [89]. Optical images of Barker\u2019s etched samples were captured for observing crack paths in microstructure of samples after the bend tests using polarized light by inserting a polarizer filter and a lambda filter rotated by 180\u00b0 for color enhancement, prior to capturing the images. The multi-layer capture feature in the image analysis software, Clemex Vision PE 6.0, was used to obtain focused stitched images along the fracture area.  Figure 4-5 Setup for the optical microscope for polarized light observations.  40  4.3.4 Characterization of Second Phase Constituent particles The image analysis software ImageJ was used to determine the area fraction and size of constituents from the SEM images captured using backscatter detector (BSE mode). The magnification of x1000 were selected for characterizing the coarse constituent particles and higher magnifications of x5000-x10000 were chosen for the finer dispersoids, where at least 10 fields of continuous BSE images were processed. The digital grey scale images were transformed into a binary black and white image and a threshold was applied to highlight the particles from the background. A sensitivity analysis on the threshold value shows that the area fraction measured based on optical evaluation was strongly dependent on the threshold level [90]. Examples of the results for different threshold values applied to the same image are shown in Figure 4.6b-d. Figure 4.6e shows the area fraction of particles as a function of the threshold level. Given this intrinsic uncertainty in differentiating second phase from the matrix using optical methods, the mole fraction of phases obtained using the CALPHAD database (TTAl6 in Thermo-Calc) were converted to volume fractions using molar volume ratios, and then used to estimate the area fraction of particles. \u03b2-Al5FeSi, \u03b1-Al(Fe,Mn)Si, and Al molar volumes are known [91], i.e. 9.16 \u00d7 10-6 m3\/mol, 8.88 \u00d7 10-6 m3\/mol and 9.93 \u00d7 10-6 m3\/mol, respectively. Therefore, a suitable threshold was chosen so that the fraction obtained from image analysis matched the Thermo-Calc analysis. This threshold was then used to analyse particle sizes. 41   Figure 4-6 Sensitivity of area fraction measurement in 0Mn alloy using different image thresholding parameter grey scale from 0 (black) to 255 (white) on same image.  Using MATLAB fitting tool, lognormal fit to the experimentally measured grain\/particle size and orientation distribution was used; a lognormal distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed, and it can be formulated as [92]: 42  \ud835\udc53(\ud835\udc65) =1\ud835\udc60\ud835\udc65\u221a2\ud835\udf0b\ud835\udc52\u2212 (\ud835\udc59\ud835\udc5b(\ud835\udc65)\u2212\ud835\udc5a)22\ud835\udc602   (4.1) where \ud835\udc65 is the variable, \ud835\udc53 is the probability density function, \ud835\udc5a, and \ud835\udc60 are the average and the standard deviation of the normally distributed logarithm of the variable. \ud835\udc5a and s are related to the normal average, \ud835\udf07, and the normal standard deviation, \ud835\udf0e according to [92]: \ud835\udc5a = \ud835\udc59\ud835\udc5b (\ud835\udf072\u221a\ud835\udf072+\ud835\udf0e2)   (4.2) \ud835\udc602 = \ud835\udc59\ud835\udc5b(1 +\ud835\udf0e2\ud835\udf072)  (4.3) Note that due to the ease of interpretation, the normal average and normal standard deviation are used for all presentations of the distribution fits in this study. 4.4 Mechanical Testing 4.4.1 Tensile Test Tensile experiments were conducted using an Instron servo-hydraulic test machine (Instron 8872) with a 25 kN load cell. A nominal strain rate of 3\u00d710-3 s-1 (a constant crosshead velocity of 0.1 mm\/s) was applied according to standard for ASTM E8M. The samples for the tensile tests were electric-discharge machined from the extruded strips parallel to the extrusion direction (ED), at 45\u00b0 with respect to ED, and perpendicular to ED (transverse direction, TD), as shown in Figure 4.7. The dimensions of the tensile samples are shown in Figure 4.8. 43   Figure 4-7 Photograph showing the different orientations of tensile samples with respect to the extrusion direction (ED).  Figure 4-8 Dimensions for the tensile samples machined from extruded strips (in mm).   The change in length and width of the samples during the test was measured externally using two clip-on extensometers (shown in Figure 4.9); (i) axial extensometer with gauge length of 25 mm and (ii) width extensometer with initial gauge length of 12.5 mm (i.e., width of sample). 44   Figure 4-9 Figure illustrating location of clip-on extensometers for measuring elongation in length and contraction in width of samples during the test.   Having the applied load (F) and the axial change in length (\uf044L), engineering stress, S, and strain, e, were calculated as S=F\/A0 and e=\uf044L \/L0, where A0 is the initial area of the section bearing the load and L0 is the initial length of the gauge. True strain (\u03b5\ud835\udc61\ud835\udc3f) and true stress (\u03c3t) graphs were then plotted up to necking using the following equations: \u03b5\ud835\udc61\ud835\udc3f = ln (1 + e)  (4.4) \uf073t  = S (1 + e)  (4.5) To calculate the fracture stress and strain, the area of fractured surface (Af) was imaged using secondary electron imaging and then calculated using the ImageJ software as shown in Figure 4.10. The true fracture strain (\u03b5\ud835\udc53\ud835\udc3f) were calculated using the following equations: \u03b5\ud835\udc53\ud835\udc3f =  ln(\ud835\udc34\ud835\udc53\ud835\udc340)  (4.6) 45   Figure 4-10 Figure showing fracture area measurement method using the ImageJ software and secondary electron images. where Ff is the load before fracture point, obtained using the stress-strain curve and the applied load data. In order to calculate the true fracture stress (\uf073f), a correction for the stress triaxiality in the neck of the tensile sample was employed based on the finite element method calculations of Puydt shown in reference [93]. This finite element analysis was made to correct for the effect of triaxiality in the neck of uniaxial tensile test samples of an X80 line-pipe steel weld zone (with an initial cross-sectional area of \u2248 3.5 mm \u00d7 16.0 mm) at fracture [94] [93]. This model used the true stress-strain curve up to the point of necking and linearly extrapolated the true stress-strain data from the point of necking to the fracture point. The ratio of the computed true stress to the model true stress (corrected for triaxiality) versus true strain, shown in Figure 4.11, was used in the correction from the measured values of true fracture stress to account for the effect of triaxiality in the neck [93]. Based on the mentioned study, the true fracture stress was corrected (i.e. reduced) by a factor of:    \ud835\udc36\ud835\udc39 =  {1 +  ( \u03b5\ud835\udc53\ud835\udc3f0.9) \u00d7  0.14          for \u03b5\ud835\udc5b\ud835\udc52\ud835\udc50\ud835\udc58 < \u03b5\ud835\udc53\ud835\udc3f < 0.91.14                                   for                 \u03b5\ud835\udc53\ud835\udc3f > 0.9  (4.7) Therefore, the true fracture stress (\uf073f), was calculated according to:  46   Figure 4-11 Ratio of model output to the input based on the measured as-received condition for stress triaxiality correction [93].  \ud835\udf0e\ud835\udc53 =\ud835\udc39\ud835\udc53\ud835\udc34\ud835\udc53\u00d7\ud835\udc36\ud835\udc39 (4.8) Having the axial elongation in length and contraction in width of samples during the test, plastic anisotropy was characterized by the R-value as follows (based on volume conservation principle): \u03b5\ud835\udc59\ud835\udc5d\ud835\udc59 = \ud835\udc59\ud835\udc5b (\ud835\udc59\ud835\udc59\ud835\udc53) \u2212\ud835\udf0e\ud835\udc61\ud835\udc38   (4.9) \u03b5\ud835\udc64\ud835\udc5d\ud835\udc59 = \ud835\udc59\ud835\udc5b (\ud835\udc64\ud835\udc640) \u2212 \ud835\udf10\ud835\udf0e\ud835\udc61\ud835\udc38   (4.10) \u03b5\ud835\udc61\ud835\udc5d\ud835\udc59 = \u2212(\u03b5\ud835\udc64\ud835\udc5d\ud835\udc59 + \u03b5\ud835\udc59\ud835\udc5d\ud835\udc59)   (4.11) \ud835\udc45 =\u03b5\ud835\udc64\ud835\udc5d\ud835\udc59\ud835\udf00\ud835\udc61\ud835\udc5d\ud835\udc59                      (4.12) where \u03b5\ud835\udc64\ud835\udc5d\ud835\udc59 and \u03b5\ud835\udc61\ud835\udc5d\ud835\udc59 are the plastic true strains in the sample width and thickness directions, respectively; w0 and w are the initial and changed sample widths; \ud835\udc38 and \ud835\udf10 are Young\u2019s modulus (68 GPa) and Poisson ratio (0.3) (see Appendix A); \u03c3t and \u03b5\ud835\udc59\ud835\udc5d\ud835\udc59 are the true stress and plastic true strain in the tensile direction.  47  The R-value was characterized at 5%, 10% and 15% axial strain for the T4 samples and at 5-6% and for the T6 samples when necking occurred before 10% strain. Tensile experiments and the above analysis were conducted for the T4 and T6 conditions, with at least 3 tests for each condition, and the yield stress was determined using the 0.2 % offset method, as follows: first, the Young\u2019s modulus after each test is obtained by finding the slope of the linear elastic part of the stress-strain curve (Figure 4.12); then, by constructing a parallel line offset by 0.002 strain to the linear part of the curve (as shown in Figure 4.12), the intersection of the curve with the line is acquired (shown by \u00d7 mark). The stress value at the intersection point is presented as the yield stress. The work hardening rate was measured by taking the derivative of true stress with respect to true strain (d\u03c3\/d\u03b5) after the yield point, as follows: work hardening rate at each point (i) was defined as the slope of the stress strain curve within the range of 5 data points away from the given point, i.e. ((\u03c3i-5- \u03c3i+5)\/(\u03b5i-5- \u03b5i+5)); this calculation was carried out on all points after the yield and resulted in a irregular curve (see Figure 4.13a) which was then smoothed in Excel using a moving average trendline. By setting the period value of 15 for the trendline, i.e., the average of 15 data points used for each point, a smoother curve was obtained (see trendline in Figure 4.13a) . It  is  worth  noting   Figure 4-12 Figure showing yield stress determination using the 0.2 % offset method from the Engineering stress-strain curve. 48  that ~125 data points were collected per 1% strain during each test. Figure 4.13a shows an example of the work hardening rate measurement and true stress plotted as a function of true strain. In order to investigate the accuracy of the work hardening rate calculation, the stress-strain curves were recalculated using the obtained work hardening rate, where the stress value at each point was estimated using the work hardening rate at that point, according to: \ud835\udf0e\ud835\udc56 = \ud835\udf0e\ud835\udc56\u22121 + (\ud835\udc51\ud835\udf0e\/\ud835\udc51\ud835\udf00)\ud835\udc56(\ud835\udf00\ud835\udc56 \u2212 \ud835\udf00\ud835\udc56\u22121)  (4.13) An example of recalculated stress-strain curve is shown in Figure 4.13b.  According to Considere criteria for instability, the onset of necking occurs at the point where the work hardening rate drops below the value of the flow stress; therefore, the value of strain at the intersection of true stress and work hardening rate, i.e. d\u03c3\/d\u03b5=\u03c3 was considered as the necking strain, i.e. uniform elongation prior to necking. To assess the variability in measurements, 12 tests were conducted on AA7030 alloy tensile samples, where the samples were stretched to 10% strain. The results obtained are presented in Appendix A and were used to estimate standard deviation for the tensile results in this study.  Figure 4-13 a) An example of stress and work hardening rate vs true strain curve used for work hardening rate measurement, b) An example showing reproducibility of stress-strain curve recalculated using the non-smoothed work hardening rate. 49  4.4.2 Three-point bend test  Bend test experiments were conducted using a servo-hydraulic test machine (Instron 8874) with a 25 kN load cell. The samples for the bend tests were waterjet machined from the extruded strips parallel to the extrusion direction (ED), at 45\u00b0 with respect to ED, as shown in Figure 4.14. The dimensions of the bend test samples are shown in Figure 4.15.  Bend tests were conducted using a VDA test rig, employing a punch speed of 2 mm\/min and a roll gap of 2 times the specimen thickness, i.e. 6 mm. The general setup of the test is shown in Figure 4.16. Force was logged as a function of punch displacement, and the test was stopped when the force dropped by 60 N from the maximum. The bend angle at this point was measured manually afterwards using a protractor.  Figure 4-14 Figure showing different orientation of the bend samples with respect to the extrusion direction (ED) machined from the extruded strips (dashed line represents the bend axis). 50   Figure 4-15 Dimensions for the bend test samples machined from extruded strips (in mm).  Figure 4-16 Illustration of a) the general setup of VDA 238-100 bend test and b) the definition of the bend angle. In addition, the bending angles including the final bending angle (\u03b1Fmax-60N) were calculated using the punch displacement at maximum and unloading force, according to the formula from the VDA 238-100 standard [95], as follows: \ud835\udc50 =\ud835\udc372+ \ud835\udc4e0 + \ud835\udc5f \uf02c  \ud835\udc5d =\ud835\udc372+\ud835\udc3f2    (4.14) \ud835\udc4a = \u221a\ud835\udc5d2 + (\ud835\udc46 \u2212 \ud835\udc50)2 \u2212 \ud835\udc502   (4.15) sin (\ud835\udefc2) =\ud835\udc5d\u00d7\ud835\udc50+\ud835\udc4a\u00d7(\ud835\udc46\u2212\ud835\udc50)\ud835\udc5d2+(\ud835\udc46\u2212\ud835\udc50)2   (4.16) 51  where r is the punch radius (0.4 mm in the provided setup), S is the punch displacement, D is the roll diameter (30 mm in the provided setup), L is the roll distance, a0 is sample thickness before bending test in mm, as shown in Figure 4.17. For the final bending angle (\u03b1Fmax-60N) calculations, the punch displacements were corrected to account for the unloading springback, using the unloading curve as shown in Figure 4.18. Subtraction of the springback displacement, simplified comparison between the calculated final bending angles with the measured final bend angles using the protractor, which can only measure the plastic deformation. Having the punch displacement throughout the test, the equations above was used to plot force vs bend angle graphs. Bend test experiments and the above analysis were conducted for the T4 and T6 conditions, with at least 3 tests for each condition. After the test, section from samples were cut for fracture propagation analysis using optical microscopy.  Figure 4-17 Schematic figure illustrating measurement variables from the experimental setup for the bend test (reprinted with permission from [95]).  52   Figure 4-18 Example of Force-Displacement curve showing springback estimation using the unloading curve.  4.4.3 Hardness test Hardness testing was conducted on the ED-ND plane of the extrudates (i.e., from sectioning though the thickness of the profiles, normal to the extrusion direction) using a Micro-Vickers hardness indenter, a dwell time of 10 s and a load of 200 g. Prior to the test, the sample surfaces were manually grinded with silicon carbide papers (400, 800, 1200 and 2400 grit) to provide a smooth surface for measurement of the indent size. The diagonal length of the indent made by the 4 sided pyramid-shaped diamond indenter was measured. The hardness value is calculated from the average diagonal length according to: \ud835\udc3b\ud835\udc4e\ud835\udc5f\ud835\udc51\ud835\udc5b\ud835\udc52\ud835\udc60\ud835\udc60 (\ud835\udc3b\ud835\udc63) =1.8544\ud835\udc39\ud835\udc51\ud835\udc4e\ud835\udc63\ud835\udc542    (4.17) where, F is the load applied in kgf and davg is the average diagonal length in mm. An average value of a minimum of five indents was reported as the hardness. A minimum of 2.5 diagonal length was maintained between the indents to avoid incorrect hardness measurements as a result of work 53  hardening caused by a previous indent. A gap of 2.5 diagonal lengths from the edge of the sample was maintained to measure the bulk hardness and avoid any edge effects. The instrument was calibrated prior to each set of measurements, using a calibration test block. 4.5 Visco-plastic self-consistent (VPSC) model To simulate the stress-strain response and in particular, the R-value under uniaxial straining, the visco-plastic self-consistent (VPSC) model was employed (see Section 2.2.5 for more detail). The inputs to this model are i) the initial material texture, ii) the deformation history (velocity gradient tensor \/ stress tensor), and iii) the constitutive law.  For the simulation texture input, 4000 grains were used to describe the initial texture with each grain having an equal weight factor (note: the representative volume element of 4000 grains was chosen in order to keep the standard deviation negligible in both r-value and yield stress predictions [96] and ensure stabilized texture component volume fractions [97]). To generate the 4000 number of orientations, an orientation distribution function (ODF) was fit to the mean orientation of grains, using direct kernel density estimation method [98]. For ODF calculations, cubic crystal symmetry was assumed and no sample symmetry was enforced. Halfwidth (a full width at half maximum) angle selection is crucial for ODF estimation; however, accurate estimation of the halfwidth is achievable with complementary experiments specifically designed for the task. The correct half-width of 6.7\u00b0 (for 0Mn) and 7.4\u00b0 (for 0.5Mn) was determined by means of the optimal kernel function algorithm calcKernel for orientation distribution function (ODF) estimation available in MTEX. Figure 4.19 illustrates a sample convergence study to determine the optimal halfwidth angle from experimental measurements based on the estimated absolute error for 0Mn alloy. 54   Figure 4-19 Estimated error vs halfwidth angle study performed to determine optimal halfwidth angle for ODF calculation (for 0Mn alloy) in MTEX.   The inverse of the strain rate sensitivity, i.e. n (n = 1\/m, where m is the strain rate sensitivity value) was set to 50 to ensure convergence of the code [99] (same assumption as references [24][29]). As mentioned in Section 2.2.5 in VPSC code, the interaction matrix can be modified by a homogenization parameter, neff, to obtain an interaction between Taylor and Sachs models. In this research, we used neff=10 [57] in order to be consistent with prior works [24][29][100]. To simulate the tensile flow curves, a mixed boundary condition was used as described by velocity gradient tensor and stress tensor, shown in Equations 4.18 and 4.19, respectively (\u2018_\u2019 refers to unconstrained components). The extension direction in the tensile tests was controlled by the velocity gradient L33 = 0.003 s-1, and the directions normal to the extension direction were controlled by the stress components, i.e. \u03c311 = 0 and \u03c322 = 0. An equivalent strain increment of 0.002 was used for each simulation steps to the final strain of 0.3. \ud835\udc3f\ud835\udc61\ud835\udc52\ud835\udc5b\ud835\udc60\ud835\udc56\ud835\udc5c\ud835\udc5b\/\ud835\udc60 = (\u2212 0 00 \u2212 00 0 0.003)   (4.18) \ud835\udf0e\ud835\udc61\ud835\udc52\ud835\udc5b\ud835\udc60\ud835\udc56\ud835\udc5c\ud835\udc5b\/\ud835\udc40\ud835\udc43\ud835\udc4e = (0 \u2212 \u22120 \u2212\u2212)   (4.19) 55  The simulation was conducted using initial Voce hardening parameters (\ud835\udf0f0, \ud835\udf0f1, \ud835\udf030, \ud835\udf031=0, see Figure 4.20) obtained by fitting the computed stress-strain curve to that of an experimental tensile test curve in the extrusion direction. The optimal values for the Voce hardening parameters were found using trial and error on the model curve, to achieve the best fit for that the experimental curve in the extrusion direction; finally, a rigid 2D rotation of crystallographic texture around the sample reference direction (ED) was employed using a 3\u00d73 rotation matrix (\ud835\udc45 = \ud835\udc45\ud835\udc41\ud835\udc37\ud835\udc45\ud835\udc47\ud835\udc37\ud835\udc45\ud835\udc38\ud835\udc37) in order to simulate the curves in the other two orientations (i.e., \u03b8= 45 and 90\u00b0 to ED), according to: \ud835\udc45\ud835\udc41\ud835\udc37 = 0, \ud835\udc45\ud835\udc47\ud835\udc37 = 0, \ud835\udc45\ud835\udc38\ud835\udc37 = [1 0 00 cos \u03b8 \u2212sin \u03b80 sin \u03b8 cos \u03b8]   (4.20)   Figure 4-20 Voce hardening parameters (\ud835\udf0f0, \ud835\udf0f1, \ud835\udf030, \ud835\udf031) shown on stress strain curve (adapted with permission from [99]).    56   5 Results and Discussion 5.1 Material characterization In this section, the crystallographic textures and microstructures of the two materials examined in this work, will be presented and discussed. In addition, the number densities and the area or volume fractions of the dispersoids and constituent particles formed in these two alloys will be summarized based on analysis. 5.1.1 Experimental results 5.1.1.1 Texture and Microstructure Figures 5.1a and 5.2a show EBSD IPF maps illustrating the microstructure of the 0Mn and 0.5Mn alloys along the extrusion direction near the centre of the ND-ED planes. Quantitative analysis on grain size (with a log-normal fit to the data) of the two alloys are presented in 5.1b and 5.2b. A fully recrystallized microstructure with equiaxed grains, with a grain aspect ratio of 1-2 is obtained from the EBSD map analysis for the 0Mn alloy (Figure 5.1a). Grains were identified using a threshold disorientation angle of 15\u00b0 (as discussed in Section 4.3.1) and the grain size distribution (Figure 5.1c) was obtained by fitting a log-normal fit to data. The log-normal fit shows an equivalent area grain diameter of ~ 62 \u03bcm for the 0Mn alloy. However, the 0.5Mn alloy has unrecrystallized microstructure with highly elongated grains. Using the line intercept method [101] and fitting a log-normal curve to the data, the average thickness of elongated grains is ~11 \u03bcm (Figure 5.2c) for this alloy.  57  Figures 5.1d and 5.2d show the 111 and 001 pole figures measured by EBSD where more than 3000 different grains were measured in each case. Volume fraction of orientations within 15\u00b0 away from ideal texture components in the two alloys are summarized in Table 5.1 and illustrated in Figures 5.1b and 5.2b. The 0Mn alloy exhibited a typical recrystallization texture after (near) plane strain deformation, composed of approximately 26.4% Cube, 22.7% CubeED, and 10.2% Goss texture components with remaining fraction nearly random. On the other hand, the 0.5Mn material showed a typical plane strain deformation texture with approximately 6% Cu, 22.8% Brass, 27.7% S, and 9.4% Cube components.  Figure 5-1 EBSD analysis of 0Mn alloy. a) EBSD inverse pole figure (IPF) grain structure map from centre of the ED-ND plane, b) spatial distribution of ideal texture components (Note: for each texture component, the color represents those grains within 15\u00b0 of ideal components. White areas represent other orientations), c) grain size distribution histogram and d) 111 and 100 pole figures showing the macroscopic crystallographic texture. 58   Figure 5-2 EBSD analysis of 0.5Mn alloy. a) EBSD inverse pole figure (IPF) grain structure map from centre of the ED-ND plane, b) spatial distribution of ideal texture components (Note: for each texture component, the color represents those grains within 15\u00b0 of ideal components. White areas represent other orientations), c) grain thickness distribution histogram and d) 111 and 100 pole figures showing the macroscopic crystallographic texture. Table 5-1 Approximate volume fraction of orientations within 15\u00b0 away from ideal texture components  Alloy Copper (%) Brass (%) S (%) Cube (%) Goss (%) CubeED(%) 0Mn 0.0 0.1 0.1 24.1 10.2 19.7 0.5Mn 6.0 22.8 27.7 9.4 0.2 2.0  5.1.1.2 Second phase Characterization Figures 5.3 shows Thermo-Calc calculations (TTAl6 database) for the different phases at various temperatures in equilibrium for the two alloys, based on chemical composition in Table 4.1. Table 5.2, shows a summary of mole and volume fractions (converted from mole fractions 59  according to [91], see Section 4.3.4) for the Fe-based phases at 20\u00b0C from equilibrium for both alloys based on Figure 5.3. The results show that for the 0Mn alloy, the \u03b2-Al5FeSi phase is the dominant Fe-based second phase in microstructure at room temperature with a mole fraction of ~0.006, while \u03b1-Al(Fe,Mn)Si phase is the dominant second phase in 0.5Mn alloy with a mole fraction of ~0.02. The equilibrium diagrams show the presence of Mg2Si and pure silicon. Practically, these phases are not observed due to the formation of metastable phases during artificial aging, as discussed in Section 2.1.1.  Figure 5-3 Thermo-Calc modeling result of different phases at various temperatures in equilibrium for a) 0Mn and b) 0.5Mn alloy (Note: dashed vertical line represents the liquid phase).  Table 5-2 Summary of mole and volume fractions for Fe-based phases at 20\u00b0C from equilibrium in Thermo-Calc (TTAl6) for both alloys based on Figure 5.3 Alloy \u03b2-Al5FeSi \u03b1-Al(Fe,Mn)Si Mole Volume Mole Volume 0Mn 0.0068 0.0060 - 0.5Mn - 0.0200 0.0184  60  Figure 5.4 shows SEM images taken from the three perpendicular surfaces aligned with the extrusion, transverse and normal directions of the extrudate using backscatter electron detector; the figures, qualitatively show the spatial distribution of Fe-based second phase particles in the two alloys.  In the case of the 0Mn alloy in Figure 5.4a, the \u03b2-Al5FeSi phase constituent particles are plate shaped after homogenization, and found to align with the extrusion direction after extrusion. This leads to an anisotropic spatial distribution of particles in the microstructure. However, in the case of the 0.5Mn alloy in Figure 5.4b, the \u03b1-Al(Fe,Mn)Si phase particles appear in two different sizes after homogenization: i) spheroidized constituent particles 500-1000 nm in size and ii) dispersoids 20-150 nm in size [5]. Similar to the 0Mn alloy, the constituent particles seem to have been distributed along lines parallel to extrusion direction during extrusion, but less spatial constraint is observed for the dispersoids as they seem to be uniformly distributed in the 0.5Mn microstructure.  Figure 5-4 Backscatter electron images showing the Fe based particles in the a) 0Mn and b) 0.5Mn alloy. 61  With the use of appropriate threshold in the ImageJ analysis software (discussed in Section 4.3.4), particle sizes of the dispersoids and constituent particles were analysed in the two alloys, using series of 10-15 BSE stitched images along ED\/TD from each plane. Examples of the stitched images and results for the two alloys are presented in the following.  0Mn alloy Figure 5.5 and 5.6 show examples of the stitched images and quantitative results on particle length and orientation distribution for \u03b2-Al5FeSi phase constituent particles in the 0Mn alloy in the three perpendicular surfaces aligned with the extrusion, transverse and normal directions. Summary of the analysis is presented in Table 5.3. The measured angles between maximum length of particles and ED\/TD (from fitted ellipses) show an average orientation of 10-12\u00b0 away from ED\/TD in all three crystallographic planes, which confirms the alignment of particles towards extrusion direction during extrusion. Average maximum length of \u03b2-Al5FeSi particles is within 2.5-2.8 \u03bcm range with an aspect ratio of 4.9-6 in the three planes.  62   Figure 5-5 Example of stitched BSE images showing constituent particles in 0Mn alloy the three perpendicular surfaces aligned with a) ND-ED plane (along ED), b) ND-TD plane (along TD) and c) ED-TD plane (along ED) for particle size and orientation distribution analysis. 63   Figure 5-6 Normalized size distribution and orientation distribution of the constituent particles in 0Mn alloy the three perpendicular surfaces aligned with (a, d, g, j) ND-ED plane, (b, e, h, k) ND-TD plane and (c, f, i, l) ED-TD plane.   64  Table 5-3 Summary of results from log-normal fit to constituent particle distributions in Figure 5.6 and 5.9 (data presents average and the standard deviation of the normally distributed logarithm of the variables).     Size Orientation Alloy Plane Number of particles  Average maximum length (\u03bcm) Average minimum length (\u03bcm) Mean aspect ratio Mean angle between maximum length and ED or TD (\u00b0) 0Mn ND-ED 367 2.5\u00b10.9 0.4\u00b10.1 5.9 11\u00b111 ND-TD 351 2.6\u00b11.3 0.4\u00b10.1 6.0 12\u00b112 ED-TD 312 2.8\u00b11.1 0.6\u00b10.1 4.9 10\u00b18 0.5Mn ND-ED 264 1.1\u00b10.6 0.4\u00b10.1 2.5 5\u00b19 ND-TD 241 1.1\u00b10.6 0.4\u00b10.1 2.5 4\u00b17 ED-TD 201 1.2\u00b10.5 0.5\u00b10.1 2.3 7\u00b19  0.5Mn alloy One challenge for the quantitative analysis of the 0.5Mn alloy is to separate the constituent particles from dispersoids; this is due to their similar composition, i.e., \u03b1-Al(Fe,Mn)Si (not separatable using backscattered electron detector) and shape. Therefore, the difference in size distribution was the only feature focused on for the separation. Figure 5.7 was plotted from analysis of few series of stitched SEM images along ED\/TD from different planes of the microstructure (see Section 4.3.4) from three different magnifications (i.e. x5000-x10000); Figure 5.7a was obtained from population size of over 400 constituent particles using x1000 magnification images, while Figure 5.7b was obtained from analysing over 900 dispersoid using x5000-10000 magnification images. The merged graph of Figure 5.7a and 5.7b is plotted in 5.7c which shows that a cut-off value of 200 nm can readily separate the constituent particles from the dispersoids.  65   Figure 5-7 Normalized size distribution of a) dispersoids and b) constituent particles in 0.5Mn alloy, and c) combination the two different distributions from a) and b), i.e., not a single distribution). Figure 5.7 also shows that the dispersoids have an equivalent radius size of ~60 nm, which is close to previous TEM results conducted on the same alloy [102], where an average radius size of 49 nm was obtained. Examples of the stitched images in the three perpendicular surfaces aligned with the extrusion, transverse and normal directions in the 0.5Mn alloy are shown in Figure 5.8. Quantitative results on particle length and orientation distribution for \u03b1-Al(Fe,Mn)Si phase constituent particles in this alloy is shown in Figure 5.9 and summarized in Table 5.2. An average maximum length of 1.1-1.2 \u03bcm, and a mean aspect of 2-2.5 (Tables 5.3), are obtained for the  \u03b1-Al(Fe,Mn)Si constituent particles in the 0.5Mn microstructure. The measured  66   Figure 5-8 Example of stitched BSE images showing constituent particles in 0.5Mn alloy the three perpendicular surfaces aligned with a) ND-ED plane (along ED), b) ND-TD plane (along TD) and c) ED-TD plane (along ED) for particle size and orientation distribution analysis. 67   Figure 5-9 Normalized size distribution and orientation distribution of the constituent particles in 0.5Mn alloy the three perpendicular surfaces aligned with (a, d, g, j) ND-ED plane, (b, e, h, k) ND-TD plane and (c, f, i, l) ED-TD plane. angles between maximum length of particles and ED\/TD (from fitted ellipses) show an average orientation of 4-7\u00b0 away from ED\/TD in all three crystallographic planes. 68  5.1.2 Discussion Based on the texture and microstructure results, there is a clear difference in level of recrystallization between the two microstructures. The 0Mn alloy has a fully recrystallized microstructure with equiaxed grains (Figure 5.1a) and the 0.5Mn alloy has anunrecrystallized microstructure with highly elongated grains (Figure 5.2b). This difference can be explained by the presence of  Mn dispersoids in the 0.5Mn alloy (formed during homogenization) which are known to suppress recrystallization by the Zener drag mechanism [36] [42]. In addition, a comparison of the pole figures measured by EBSD with the EBSD maps for each alloy (Figures 5.1b and 5.2b) shows that the textures were consistent with the EBSD observations on the grain shape for both alloys, i.e. Cube, CubeED, and Goss texture components were observed for the recrystallized alloy, while S, Cu and Brass components were observed for the unrecrystallized alloy. The results for the area fraction of second phase particles calculated using the TTAl6 database show good consistency with the volume fraction obtained in the work of Liu [102] on extruded AA6082 alloys, having 0 and 0.5 wt% Mn and the same homogenization parameter (i.e., at 550 \u00b0C for 2 h) as the current study. Liu obtained a volume fraction of 0.6% for \u03b2-Al5FeSi phase for the 0Mn alloy (same as 0.6% for the 0Mn alloy in Table 5.2) and 1.75% for \u03b1-Al(Fe,Mn)Si phase for the 0.5Mn (similar to 1.84% for the 0.5Mn alloy in Table 5.2). Note: the extrusion process can affect the particle size and distribution in microstructure after homogenization, but not the volume fraction of particles [103]. Comparing Figures 5.4a and 5.4b, the high density of dispersoids found in the 0.5Mn alloy, is consistent with precipitation of \u03b1-Al(Fe,Mn)Si during homogenization at 550 \u00b0C for 2 h [24][102]. This observation is also consistent with the previous TEM study [23] on chemical 69  composition of the dispersoid particles in Mn-containing 6xxx aluminum alloys. The comparison of these two images is also consistent with the Thermo-Calc results where a higher volume fraction of second phase was achieved for 0.5Mn alloy, compared to 0Mn alloy.  The mean aspect ratio was found to be 4.9-6 for \u03b2-Al5FeSi and 2-2.5 for \u03b1-Al(Fe,Mn)Si particles (Table 5.3). This indicates that particles in 0Mn alloy are less spherical than particles in the 0.5Mn alloy. The measured angles between maximum length of particles and ED\/TD (from fitted ellipses) show an average orientation of 4-7\u00b0 away from ED\/TD in the three analysed planes. Figure 5.10 shows a clearer effect of homogenization and extrusion on particle size and alignment from the as-cast state for both alloys, based on a previous study [102]. It is clear from figure that extrusion process results in the breakup of some of the large aspect ratio particles (especially in the 0Mn alloy) and alignment of particles with ED. In addition, a comparison between Figure 5.10e and 5.10f for the uncrecrystallized alloy shows that the extrusion process may have led to coarsening of dispersoids. Using TEM study, the average radius of dispersoids after homogenization were found to be 45 nm, while it was found to be 85 nm using SEM images and ImageJ analysis; however, inaccuracy of SEM images for dispersoid size analysis should also be considered. Regarding the 0.5Mn alloy particles, the merged graph plotted in 5.7c which shows that a cut-off value of 200 nm can be used to separate the constituent particles from the dispersoids. Based on Figure 5.7 and following the work of Lodgaard [104] and Liu [102] on AA6082, 200 nm in equivalent radius was chosen as the cut-off value for separation of constituent particles from dispersoids for all distribution calculations. 70   Figure 5-10 Backscatter electron images showing the Fe-based particles in 0Mn and 0.5Mn alloy in (a, c) as-cast state, (b, e) after homogenization, (c, f) after extrusion (reproduced from current study and with permission from [102]). It can be observed that after extrusion  (Figures 5.6a,b,c and 5.9a,b,c) there are more rows of particles aligned with the extrusion direction in the ND-ED planes (Figure 5.6a for 0Mn and Figure 5.9a for 0.5Mn alloy) compared to particles aligned with the transverse direction (TD) in the ND-TD planes (Figure 5.6b for 0Mn and Figure 5.9b for 0.5Mn alloy). The alignment of the particles remains unaltered by recrystallization phenomena [37] and therefore, this observation is a common feature in both the fibrous and recrystallized alloys. In summary, the constituent particles are smaller and more round in the 0.5Mn alloy. However, it is worth mentioning that the particles are different in chemical composition and crystal structure for the two alloys (i.e., monoclinic \u03b2-Al5FeSi in the 0Mn and Simple Cubic\/Body-centered Cubic \u03b1-Al(Fe,Mn)Si in the 0.5Mn alloy [27]). In addition, more rows of particle arrangements are observed along the ED in ND-ED planes for both alloys which is not detected along the TD in TD-ND planes. 71  5.2 Tensile response of extruded strips This section consists of the results and discussion on anisotropic tensile plastic and fracture behavior, including the visco-plastic self-consistent (VPSC) model used to simulate the tensile stress-strain curves. 5.2.1 Experimental results and simulation Engineering stress-strain curves and true stress-true strain curves to fracture obtained from tensile test on both alloys are shown in Figures 5.10 and 5.11, respectively. The results from tests in all three directions (i.e. ED, 45\u00b0 and TD directions) are presented in the same plot for comparison of anisotropic tensile behavior. Summary of data for the yield stress, ultimate tensile strength (UTS), and the R-value are presented in Table 5.4. For the true stress-strain curves up to fracture point (in Figure 5.12), true stress and strain values at fracture point were measured from the fracture area (as discussed in Section 4.4.1). The dashed lines for each test represent the behavior between the necking and final fracture points (assuming linear behavior) after correction for triaxiality. The results for the true stress and strain at fracture are summarized in Table 5.4. In general, one can observe that 0.5Mn samples show higher yield and UTS than the 0Mn samples for both tempers in all directions. In addition, both alloys exhibited higher stress and lower uniform elongation in the T6 temper compared to T4. 72   Figure 5-11 Engineering stress vs. engineering strain plots for the a) 0Mn and b) 0.5Mn extrusions in T4 and T6 tempers.   Figure 5-12 True stress vs. true strain plots for the a) 0Mn and b) 0.5Mn extrusions in T4 and T6 tempers (dashed lines for each test represent the behavior between the necking and final fracture points).     73  Table 5-4 Summary of mechanical properties from tensile tests. Variations are based on the standard deviation obtained for each variable in Appendix A (*R-value reported at an axial strain of 10% strain for T4 and 6% for T6)  Recrystallized 0Mn alloy For the recrystallized 0Mn alloy (Figure 5.11a), the yield stress, ultimate tensile strength (UTS) and strain to necking are almost independent of the test direction; the yield stress and UTS values are ~145 and ~285 MPa for the T4 temper, and ~305 and ~339 MPa for the T6 temper, respectively. The strains to necking point are 0.2 and 0.08 for the T4 and T6 tempers, in all the three test directions. However, the R-value show a dependence on loading direction with values of ~0.43, ~0.37 and ~1.04 for the ED, 45\u00b0 and TD loading axes, respectively; independent of the temper (T4 vs T6). In true stress-true strain curve for the 0Mn alloy (Figure 5.12a), the true strain to fracture was 0.46-0.53 for the T4 and ~0.1 for the T6 tempers in all three directions. One can also observe that for the T6 temper, there was almost no post necking strain.   74  Unrecrystallised 0.5Mn alloy In the case of the unrecrystallised 0.5Mn alloy, the situation was more complicated (Figure 5.11b). The yield stress for the ED and TD was similar, with ~190 MPa in the T4 temper and ~350 MPa in T6 conditions, but it is lower for the 45\u00b0, with ~170 and ~310 MPa for the T4 and T6 cases, respectively. The UTS is highest for the ED and TD, with 325-335 and ~377 MPa for the T4 and T6 cases, but it is lower for the 45\u00b0 direction, with ~294 and ~339 MPa for the T4 and T6 conditions, respectively. The strain up to necking values, on the other hand, are lower for the ED and TD, with values of ~0.16 and ~0.07 for the T4 and T6 cases, but higher for the 45\u00b0 loading direction with ~0.20 and ~0.09 for the T4 and T6 cases. The R-values of the unrecrystallised 0.5 Mn alloy were the same for both tempers with values of ~0.35, 1.8 and 1.1 for the ED, 45\u00b0 and TD directions.  For the true stress-true strain curves for the 0.5Mn alloy (Figure 5.12b), the true strain at fracture for samples in the T4 condition was measured to be 0.36 for ED, 0.33 for TD, and 0.63 for 45\u00b0 directions (Figure 5.12b). Similar trend can be observed in the T6 state for this alloy, where true strain at fracture was higher in the 45\u00b0 direction (i.e. values of 0.27, 0.40 and 0.18 for the ED, 45\u00b0 and TD directions, respectively).  Examples of macroscopic images of the fractured tensile samples are presented in Figure 5.13, which shows that the angle of fractured plane with the ND-ED or ND-TD plane is affected by the alloy composition and sample orientation, leading to varied fractures from slant to fracture plane that are perpendicular to the tensile axis. SEM images taken from the fractured surfaces are presented in Figures 5.14-5.19, in which both alloys show a ductile fracture with dimples and second phase particles in the fracture surface. In images taken from the fractured surfaces of 0Mn  75   Figure 5-13 Examples of macroscopic images of the fractured tensile samples for a) 0Mn (T4), b) 0Mn (T6), c) 0.5Mn (T4) and d) 0.5Mn (T6).  76   Figure 5-14 SEM fractography of tensile samples for the 0Mn alloy in T4 temper in (a, b) ED, (c, d) 45\u00b0 and (e, f) TD direction (Identified particles are pointed by yellow arrows, respectively. Dashed line shows a step in the fracture surface). 77   Figure 5-15 SEM fractography of tensile samples for the 0Mn alloy in T6 temper in (a,b) ED, (c,d) 45\u00b0 and (e,f) TD direction (Identified particles and cracks are pointed by yellow and green arrows, respectively). 78   Figure 5-16 SEM fractography of tensile samples for the 0Mn alloy in T4 and T6 tempers in (a, b) ED, (c, d) 45\u00b0 and (e, f) TD direction in x6000 magnification.  79   Figure 5-17 SEM fractography of tensile samples for the 0.5Mn alloy in T4 temper in (a, b) ED, (c, d) 45\u00b0 and (e, f) TD direction (Dashed lines show a step in the fracture surface). 80   Figure 5-18 SEM fractography of tensile samples for the 0.5Mn alloy in T6 temper in (a, b) ED, (c, d) 45\u00b0 and (e, f) TD direction. 81   Figure 5-19 SEM fractography of tensile samples for the 0.5Mn alloy in T4 and T6 tempers in (a, b) ED, (c, d) 45\u00b0 and (e, f) TD direction in x6000 magnification.  alloy for T4 temper (Figure 5.14), grain boundaries are not visible, thus trans-granular fracture, characterized by the presence of deep dimples, is dominant [65]. However, in the case of the T6 temper (Figure 5.15), a mixture of inter-granular and trans-granular fracture with a dominant inter-granular fracture (~55-70% of ragged flat surface areas in the SEM images using the ImageJ 82  software) is observed which resulted in lower fracture strain in T6 state compared to T4. Inter-granular fracture is characterized by ragged flat surfaces showing coalescence of voids nucleated at large precipitates at grain boundaries [65]. In addition, dimple sizes are similar (3-6 \u03bcm) and it is possible to observe particles at the bottom of many of them. Constituent particles are considered to be nucleation sites for voids due to particle cracking and decohesion between the non-deforming particles and the matrix [2], which is controlled by the build-up of internal stresses as a result of incomplete plastic relaxation around the particles [68][69].Thus, the large number of particles observed in the dimples of the fracture surfaces can show that failure occurs by nucleation, growth and coalescence of voids around the constituent particles [63][78]. Fracture surfaces in the T6 state (Figure 5.15) also show presence of dimples on the inter-granular areas, in addition to the trans-granular areas. As for the 0.5Mn specimens in Figures 5.17 and 5.18 (T4 and T6 temper), it is observed that the fracture surface is covered with two categories of dimples, i.e. a lower density of coarse dimples (3-5 \u03bcm) and a higher density of small dimples (~0.4 \u03bcm) on the trans-granular fracture areas. In addition, particles are seen at the bottom of some of the coarse dimples (Figure 5.19). 5.2.1.1 Simulations for tensile response Using the visco-plastic self-consistent (VPSC) model, a simulation of stress-strain curves and R-value evolution during tensile test will be presented in this section. Both the effect of the initial texture and grain shape were accounted for in 0.5Mn alloy simulation. Before the extrusion, the grain shape was assumed to be a sphere with a diameter of 80 \u03bcm (i.e. the equivalent diameter of the average size in as-homogenized condition), and after the extrusion, the grain was assumed to be deformed into an ellipsoid; therefore, the ratio between longest and shortest axes of grains 83  was assumed to be 80:1. However, for the 0Mn alloy, having equiaxed grains, only the effect of the initial texture was considered. Figure 5.20 shows a comparison of the pole figures re-calculated from the ODF (used to produce the input texture file) and the pole figures from EBSD orientations; the difference in the intensities between the two pole figures were found to be 8.25e-8 (calculated using the command calcError in MTEX); thus, it is clear that the texture generated from ODF calculations can represents the experimental texture well. Figure 5.21 plots the VPSC simulated vs experiment stress-strain curves for both alloys with the corresponding initial texture from the central region of the extrudate for the ED direction. Table 5.5 shows a summary of the fit parameters used in constitutive law for VPSC simulations of the ED direction tensile curves.  Figure 5-20 111 and 100 pole figures for the texture from the centre region of 0Mn and 0.5Mn alloys obtained from (a, c) calculated ODF and (b, d) EBSD orientations. 84   Figure 5-21 For the 0Mn and 0.5Mn alloys at (a, c) T4 and (b, d) T6 temper: plots of the flow curves along the ED.  Table 5-5 Summary of the slip system level fit parameters used in constitutive law for VPSC simulations of the ED tensile curves (\ud835\udf0f0 and \ud835\udf0f1 are the resolved shear stresses) Condition \ud835\udf0f0 (MPa) \ud835\udf0f1(MPa) \ud835\udf030(MPa) \ud835\udf031(MPa) Neff Strain rate sensitivity 0Mn_T4 57 81 420 0 10 0.02 0Mn_T6 123 25 211 0 10 0.02 0.5Mn_T4 69 90 400 0 10 0.02 0.5Mn_T6 130 25 202 0 10 0.02  85  In addition, output Taylor factors obtained from simulation for both alloys; They were 2.55 (T4) and 2.51 (T6) for 0Mn alloy, and found to be 2.65 (T4) and 2.67 (T6) for 0.5Mn alloy. This is while an average Taylor factor of 3.06 is considered for FCC metals with a random texture. However, for an ideal cubic texture evolution, Taylor factor of 2.45 has been obtained from both experiment [105] and calculation of Schmid factor for entirely cube grain texture, i.e. [\ud835\udc50\ud835\udc5c\ud835\udc60\ud835\udf19. \ud835\udc50\ud835\udc5c\ud835\udc60\ud835\udf06 =1\/\u221a6], where \u03d5 is the angle between the loading direction and the slip direction, and \u03bb is the angle between the loading direction and the slip plane normal. Figure 5.22 plots the VPSC simulated stress-strain curves in the 45\u00b0 to the ED and TD. The experimental results are also plotted for comparison. In terms of the stress-strain curves, the simulated curves show good agreement with the experiment. A comparison between experimental and model R-values, planar anisotropy parameter \u2206r (\u2206r =12[\ud835\udc5f\ud835\udc38\ud835\udc37 + \ud835\udc5f\ud835\udc47\ud835\udc37 \u2212 2\ud835\udc5f45\u00b0]) and average anisotropy parameter r\u0304 (r\u0305 =14[\ud835\udc5f\ud835\udc38\ud835\udc37 + \ud835\udc5f\ud835\udc47\ud835\udc37 + 2\ud835\udc5f45\u00b0]) are presented in Table 5.6.  For the 0Mn alloy, similar to the plots of the experimental flow curves, the simulated stress-strain curves show the same mechanical response in the 45\u00b0 to the ED and TD. For the 0.5Mn alloy, the simulated stress-strain curves show different mechanical response along these two directions, similar to the plots of the experimental curves. For the simulated curves in T4 temper, the curve at 45\u00b0 to the ED shows a lower stress response while the tests parallel to TD have higher stress results. In detail, the yield stress for the sample of 45\u00b0 to the ED is ~7 MPa lower than that of the TD samples. However, with a further increase of plastic true strain to 0.1, the flow stress for the sample of 45\u00b0 to the ED is ~40 MPa lower than that of TD. Therefore, the noticeable difference of mechanical response in 45\u00b0 to the ED compared to the other TD (and ED) is consistent with experimental results in the 0.5Mn alloy. In addition, for the 0.5Mn alloy (Figure 5.22c,d), there seems to be an overprediction of stress-strain response for the TD samples. 86   Figure 5-22 For the 0Mn and 0.5Mn alloys at (a, c) T4 and (b, d) T6 temper: plots of the flow curves along the 45\u00b0 to the ED and TD. Table 5-6 Summary of R-values from experiment and VPSC simulation (\u201c*\u201d value reported at 10% strain for T4 and 6% strain for T6 state)  87  Figure 5.23 plots the experimental and VPSC simulated vs experimental results for R-value evolutions with the plastic true strain in the three tensile directions. Similar to experimental results of the 0Mn alloy, it can be observed that R-value evolution is different in the three deformation directions, despite the similar stress-strain response. At a plastic strain of 0.1 (for T4 samples) and 0.6 (for T6 samples), the simulated R-values are ~0.41, ~0.32 and ~0.8-0.9 for the case of ED, 45\u00b0 to the ED, and TD, respectively. The VPSC simulated R-value values differ from 0.02-0.25 compared to the average experimental values (in Table 5.6),   Figure 5-23 R-value evolutions with the plastic true strain along the ED, at 45\u00b0 to the ED, and the TD, for the 0Mn and 0.5Mn alloy at (a,c) T4 and (b,d) T6 temper. 88  however, follow similar trend as measured in the experiment. As can be seen in Figure 5.23c, for the 0.5Mn alloy in T4 state, the R-values show a significant dependence on the orientation of the tensile axis, in addition to exhibiting a different directional dependence from that of the 0Mn results. At a plastic strain of 0.1, the simulated R-values for the T4 samples are ~0.49, ~1.83 and ~1.18 for the case of ED, 45\u00b0 to the ED, and TD, respectively. Further, the R-values of the T6 samples exhibit a similar directional dependence, with values of ~0.49, ~1.90 and ~1.20 for the case of ED, 45\u00b0 to the ED, and TD at plastic true strain to 0.06.   5.2.2 Discussion One can observe that 0.5Mn samples show a higher yield, flow stress and fracture stress than the 0Mn samples for both tempers in all directions (see Figure 5.11 and 5.12). The higher flow stress can be attributed to the strengthening effect of the dispersoids [25] and the presence of a dislocation substructure in the unrecrystallized alloy. In addition, both alloys exhibited higher stress and lower uniform elongation in the T6 temper compared to T4 for each direction due to the strengthening mechanism of artificial age hardening. 0Mn alloy There is no significant orientation difference in the yield stress, UTS, strain to necking, true fracture stress and fracture strain in the tensile behavior of the 0Mn alloy (see Table 5.4). However, the R-value shows a dependence on loading direction for both tempers; this indicates that the recrystallization texture affects plastic anisotropy, despite the similar stress-strain curve.  89  Comparison of the fracture surfaces of the 0Mn alloy (Figures 5.14-5.16) with the microstructure (Figure 5.5), shows that the size and number density of the \u03b2-Al5FeSi constituent particles may influence the size and density of the dimples, as proposed by Westermann et. al  [78]. In detail, the fracture surfaces show similar dimple sizes (3-6 \u03bcm), consistent with the single size distribution observed for \u03b2-Al5FeSi constituent particle lengths.  0.5Mn alloy The yield stress, UTS, strain to necking, true fracture stress and strain, and R-values show a dependence on test direction for the 0.5Mn alloy. This anisotropic plastic and fracture behavior, is more significant in the 45\u00b0 direction compared to ED and TD in both T4 and T6 states. This suggests that an unrecrystallised microstructure can affect plastic anisotropy more than a recrystallization texture. It is observed from the fracture surfaces (Figures 5.17-5.19) that the 0.5Mn alloy has a combination of small dimples (~0.4 \u03bcm), and a lower density of coarser dimples (~3-5 \u03bcm), which could be consistent with the binary size distribution of particles observed for the alloy (Figure 5.8). Westermann et.al also observed a binary size distribution of the second phase dimples in their fracture surface analysis of dispersoid-containing Al-Mg-Si alloys, having a coarse dimples density which was consistent with the area fraction of primary particles [78]. Based on previous studies [78] and the comparison of the fracture surfaces of the two alloys at high magnification, it is suggested that the size and number density of the constituent and dispersoid particles influences the size and density of the dimples; i.e., the higher density and smaller sizes for dimples (0.4 and 3-5 \u03bcm) in the 0.5Mn alloy fracture surfaces, compared to 0Mn 90  alloy fracture surfaces dimples (3-6 \u03bcm) is consistent with smaller size and higher density of particles in these alloys (see Figure 5.4). In addition, particles are observed at the bottom of most of the coarse dimples (Figures 5.16 and 5.19) and absence of them at the other coarse dimples may be due to remaining in the counter face of the fracture surface. In general, presence of dimples caused by particles in both alloys shows the role of particles in voids nucleation and linkage under tension, resulting in microcrack formation and fracture. 5.2.2.1 Simulation and experimental comparison Regarding the VPSC simulations, the fit parameters used in constitutive law (Table 5.5) were found to be quite similar to the parameters reported in Yu et. al [24] VPSC simulation for two Al\u2013Mg\u2013Si alloys with same homogenization treatment as applied in this study. One important observation in both experiment and model results is the consistency of directional dependence of R-values for both tempers (Table 5.6) which shows that aging process has negligible effect (no effect in this case) on plastic anisotropy. This was consistent with Engler et. al. [44], where it was shown that the precipitation sequence has no effect on anisotropic tensile response of 6xxx alloys. As observed in Table 5.6, the R-values are similar comparing the experiment and model results for each case. The R-value differences that were observed may be due to effect of different peripheral layer texture from the center texture of the extruded alloy; As mentioned, the central texture was used for the simulation, while the experiments were conducted for alloys with full thickness, including the peripheral layer.  To conclude, with planar anisotropy parameter (\u2206r) of ~1.0 for the 0.5Mn and ~0.3 for the 0Mn alloy (Table 5.6), the anisotropy of the plastic response for the 0.5Mn alloy is higher, with a 91  clear difference between the stress-strain response at 45\u00b0 to the ED compared to the response from parallel to the ED or TD directions.  5.3 Bending response of extruded strips This section presents the results and discussion on bending experiments performed on the samples from both alloys in the T4 and T6 conditions. 5.3.1 Experimental results Force-bend angle curves determined from VDA 3-point bend tests on both alloys are shown in Figure 5.24. Results from tests in all three directions (i.e. ED, 45\u00b0 and TD directions) are presented in the same plot for comparison of anisotropic behavior. Summary of the measured and calculated bend angles are presented in Table 5.7. In general, Figure 5.24 and Table 5.7 show that both alloys exhibited lower bend angle in the T6 temper compared to T4. Table 5.7 also shows that the difference between the average results from the calculated final bending angle values (using equation from standard) and the angles measured using the protractor are within 3\u00b0, indicating that the standard equation can provide good estimation of the final bend angles.  92   Figure 5-24 Force-bend angle curves from VDA bend tests in the ED, 45\u00b0 to ED, and TD deformation direction for T4 and T6 conditions of a) 0Mn and b) 0.5Mn. Table 5-7 Summary of VDA test bend angles after springback (# of repeats= 3) Sample Calculated \ud835\udefc\ud835\udc39\ud835\udc5a\ud835\udc4e\ud835\udc65\u221260\ud835\udc41 (\u00b0) Measured \ud835\udefc\ud835\udc39\ud835\udc5a\ud835\udc4e\ud835\udc65\u221260\ud835\udc41(\u00b0) Alloy Heat treatment Deformation direction 0Mn T4 ED 120\u00b13 121\u00b14 45\u02da 100\u00b13 103\u00b14 TD 98\u00b13 100\u00b15 T6 ED 22\u00b13 23\u00b13 45\u02da 17\u00b14 19\u00b14 TD 17\u00b15 19\u00b13 0.5Mn T4 ED 131\u00b13 132\u00b16 45\u02da 106\u00b13 107\u00b15 TD 90\u00b15 87\u00b15 T6 ED 55\u00b13 52\u00b13 45\u02da 44\u00b14 45\u00b13 TD 43\u00b14 43\u00b13  93  For the 0Mn alloy, the final bend angle range is within 100-120\u00b0 for the T4 and 15-20\u00b0 for the T6 temper (see Table 5.7). In contrast, for the unrecrystallized 0.5Mn alloy (Table 5.7), the bend angle range was wide with a range of 90-130\u00b0 for the T4 and 43-55\u00b0 for the T6 temper. In addition, the final bend angle decreased from ED to 45\u00b0 and TD for both tempers. Despite the clearer anisotropic behavior in the 0.5Mn alloy in all three different directions compared to 0Mn alloy, there are two observations similar for both alloys at both temper: (i) higher bend angles are obtained during deformation direction aligned with ED and (ii) load is generally higher during deformation direction aligned with TD. To further investigate the crack propagation nature and the reason for high bendability in ED, images from through-thickness and surface view of the tested specimens where captured, shown in Figures 5.25-5.28. Through-thickness overview of the crack propagation shows that the crack propagates from the tension side of the samples, independent of microstructure and temper.  94   Figure 5-25 Top-view SEM images and through-thickness optical micrographs of the fracture surface of the 0Mn alloy in the T4 temper is in the (a,b,c) ED, (d,e,f) 45\u00b0 to ED and (g,h,i) TD deformation direction 95   Figure 5-26 Top-view SEM images and through-thickness optical micrographs of the fracture surface of the 0Mn alloy in the T6 temper is in the (a,b,c) ED, (d,e,f) 45\u00b0 to ED and (g,h,i) TD deformation direction 96   Figure 5-27 Top-view SEM images and through-thickness optical micrographs of the fracture surface of the 0.5Mn alloy in the T4 temper is in the (a,b,c) ED, (d,e,f) 45\u00b0 to ED and (g,h,i) TD deformation direction 97   Figure 5-28 Top-view SEM images and through-thickness optical micrographs of the fracture surface of the 0.5Mn alloy in the T6 temper is in the (a,b,c) ED, (d,e,f) 45\u00b0 to ED and (g,h,i) TD deformation direction In case of the 0Mn alloy, the crack front is intense and narrow for the T6 temper (Figure 5.26b,e,h), propagating mostly along the grain boundaries. However, a broader crack tip is observed for the T4 temper samples showing a transgranular crack path (Figure 5.25b,e,h). The broader crack opening in through thickness view of the ED samples in the T4 temper (Figure 5.25b) compared to the other two (Figures 5.25e,h) is due to the higher bend angle in this direction (see Figures 5.24). However, in case of the 0.5Mn alloy, the crack fronts are broad with a trans-granular path in both tempers. One feature observed from through-thickness images in ED sample 98  images; i.e., Figure 5.27c in T4 and Figure 5.28c in T6 temper is crack branching or splitting of cracks into multiple paths towards the extrusion direction. For further investigation, the trial tests were conducted on samples in the ED direction of T4 temper from both alloys, in which the samples were bent to 180\u00b0. Failure was not achieved for either of the samples. The though thickness planes of the fracture surfaces were investigated using SEM, shown in Figures 5.29 and 5.30. Strings of particles are clearly seen in higher magnification images (Figure 5.29b,c,d and Figure 5.30b,c), since the ND-ED plane is being observed. Decohesion, void growth, and coalescence along the strings towards the ED is still observed at this high bend angle. It is also worth mentioning the higher resistance to crack propagation through thickness of 0.5Mn alloy after a bend angle of 180\u00b0 compared to the 0Mn alloy, in Figures 5.29a and 5.30a, since the 0.5Mn alloy has not yet reached the failure point at this angle, unlike the 0Mn alloy.  99   Figure 5-29 Through-thickness SEM images of the fracture surface of the 0Mn alloy in the T4 temper bent to 180\u00b0 in ED deformation direction at different magnifications.  Figure 5-30 Through-thickness SEM images of the fracture surface of the 0.5Mn alloy in the T4 temper bent to 180\u00b0 in ED deformation direction at different magnifications. 100  5.3.2 Discussion As observed in Table 5.7, both alloys exhibited lower bend angle in the T6 temper compared to T4, which can be due to the strengthening mechanism of artificial age hardening. In addition, the consistency of results from the calculated final bending angle values (using equation from standard) and the measured angles shows the validity of using the equation for bend angle estimation. Comparing the results for the two alloys in both tempers, all cases show higher bend angles in ED, which is consistent with a recent study reported by Snilsberg et al. [53], where they also obtained higher bend angles in ED compared to TD direction. There are no obvious fracture features for ED sample in fracture images that could explain the higher bendability in this direction. However, one feature observed from through-thickness images in ED sample images for the 0.5Mn alloy; i.e., Figure 5.27c in T4 and Figure 5.28c in T6 temper is crack branching or splitting of cracks into multiple paths towards the extrusion direction. According to Westermann et al. [37], this crack path appears when the crack follows along particle when aligned as stringers towards the extrusion direction. Therefore, this could be due to alignment of \u03b1-Al(Fe,Mn)Si constituent particle stringers along ED in ND-ED plane observed earlier (Figure 5.8a). Decohesion, void growth, and coalescence are most likely to occur along the stringers, increasing the stress in the regions in between [37] [106]. This suggests that when the specimen is bent, the strings of particles form a preferential crack propagation path, i.e., a stringer-to-stringer path. When the specimen is bent in the ED orientation, low number of stringers (rows of particles) are present in the crack plane (ND-TD) plane (see schematic in Figure 5.31) which means less stress concentration exists in the crack plane; In addition, in this configuration a high number of strings are aligned perpendicular to the deformation direction that could interact with the cracks and change the crack 101  path towards the stringer alignment, also reducing stress concentration in the crack plane. This makes it easier for the crack to follow a path along the strings, leaving the characteristic branched crack growth. Crack propagation along the strings in this configuration, will cause less propagation through the thickness, consistent with the higher bend angles obtained for this direction (ED) in Figure (5.24b). However, when specimen is bent in the TD orientation, the strings of particles are aligned parallel with the deformation direction, which leads to presence of high number of stringers in the crack plane (ND-ED) plane (see schematic in Figure 5.31) resulting in a higher energy crack propagation path and a higher propagation rate through the thickness, consistent with the lower bend angles obtained for this orientation in Figure (5.24b). In addition, the higher load in force-bend angle curves during deformation direction aligned with TD may also explain with the lower bend angles in this direction.  Figure 5-31 Schematic figure showing particle alignment and anticipated crack paths in a) TD, and b) ED bend test configurations.  102  In addition, comparing Figures 5.29a and 5.30a, indicates the higher resistance to crack propagation through thickness of 0.5Mn alloy after a bend angle of 180\u00b0 compared to the 0Mn alloy. This could be due to the more random particle distribution in ND-TD plane of 0.5Mn alloy compared to ND-TD plane of 0Mn alloy (Figures 5.5b and 5.8b). In summary, the higher final bend angles in ED were obtained for both alloys with the different microstructures. Therefore, it is proposed that the anisotropic bending behavior is more likely topologically controlled, dependent on particle string paths which is similar in the two alloys because both microstructures consist of particle string alignments along ED (Figures 5.5 and 5.8). 5.3.3 Correlation between tensile and bend test results Figure 5.32 shows the final bend angle results from bend tests and true fracture strain from tensile tests obtained for the three deformation directions. For the recrystallized 0Mn alloy (Figure 5.32a), there is a very weak dependence of both the final bend angle and the true strain to fracture on deformation direction; In detail, for all three directions for T4 temper, the bend angle was within range of 100-120\u00b0 and true strain to fracture was 0.46-0.53. There was even weaker dependence on deformation direction in the T6 temper with the bend angles being within range of 15-20\u00b0 and true strain to fracture was ~0.1. In contrast, there is considerable dependence on test direction for the unrecrystallized 0.5Mn material (Figure 5.32b). For the bend test, final bend angle decreased from ED to 45\u00b0 to TD directions for both the T4 and T6 tempers, while the true strain to fracture from tensile test was larger at 45\u00b0 compared to ED and TD in both tempers. It has previously been reported that the true strain to fracture and the final bend angle can be correlated [19, 20]; In order to examine validity of this, Figure 5.33 was plotted for the current alloy data. Figure 5.33a shows that for the recrystallized alloy, a linear correlation holds for data  103   Figure 5-32 Comparison of bending angles and fracture strain in test direction ED, 45\u00b0 to ED, and TD deformation direction for T4 and T6 conditions for a)0Mn and b)0.5Mn alloy  Figure 5-33 Final bending angles plotted vs fracture strain for a) 0Mn and b) 0.5Mn alloy  in all directions, however, in the case of the unrecrystallized material (Figure 5.33b), this linear correlation only holds for the ED and TD directions, but not the 45\u00b0 direction. 5.3.4 Correlation between mechanical behavior and sources of anisotropy As noted, the anisotropy of the fracture process depends on the microstructure features i.e. grain shape, crystallographic texture and size\/distribution of second phase particles. In case of the recrystallized material (0Mn), EBSD analysis showed considerable deviation from purely Cube 104  texture, indicating presence of texture anisotropy in the microstructure. In addition, Figure 5.4a showed an obvious morphological and topological anisotropy, due to the distribution of the \u03b2-Al5FeSi second phase platelets along the extrusion direction. It appears that these effects combined in a manner to result in relatively little macroscopic anisotropy for both plastic and fracture behavior in tensile and bending responses in the ED, 45\u00b0 to ED, and TD directions, although deviation from isotropic behavior was observed in other aspects of both tests; i.e. noticeably different R-values in the three tensile directions (Table 5.4) and higher bendability along ED during bend test. As such, it appears that bendability can be correlated with the true strain to fracture in a tensile test for this alloy, in form of linear relationship (Figure 5.33). In case of unrecrystallized 0.5Mn material, texture anisotropy stood out in all analysis, i.e. highly elongated grains parallel to the extrusion direction in microstructure (Figure 5.2a) and significant fraction of \u03b2-fiber texture components (S, Brass and Cu). In addition, the binary size distribution of second phase particles (Mn dispersoids and -Al(Fe,Mn)Si constituent particles) and  the distribution of \u03b1-Al(Fe,Mn)Si constituent particles along the extrusion direction, indicate the existence of morphological and topological anisotropy. These anisotropic features resulted in a strongly orientation dependent tensile test response in yield stress and R-value (Table 5.4). As for the bending responses, a more distinct anisotropic behavior is observed in the ED, 45\u00b0 to ED, and TD direction, specially in the T4 temper, compared to 0Mn alloy. Interestingly, the recrystallized material, with a weaker texture, showed similar (although less significant) deformation direction dependence of bend angles in the three point bend tests. The observed anisotropy in bending angle, therefore, cannot be attributed to texture alone. A possible explanation is the alignment of primary particles during extrusion. In the extrusion process, the 105  primary particles are smeared out in the deformation direction and end up as rows of particles (Figure 5.5a and 5.9a). The alignment of the particles remains unaltered by recrystallization and is, therefore, a common phenomenon in both the fibrous and recrystallized materials. This shows that the role of topological anisotropy may be more significant in anisotropic bending behavior compared to the tensile anisotropy. In summary, it appears that Crystallographic induced plastic anisotropy, morphological and topological anisotropy all contribute to orientation dependence of the response in tensile and bend tests. It is worth noting that aging greatly reduces ductility, but does not play a major factor for the anisotropic plastic response.   106  6 Summary and Future Work  6.1 Summary The objective of this project was to identify different sources of microstructural anisotropy in the two extruded AA6082 alloys and examine the relationship between orientation dependence of mechanical properties measured from uniaxial tensile and 3-point VDA bend tests with the microstructure of Al-Mg-Si aluminum extrusions. Two different microstructures (i.e. recrystallized and unrecrystallized) were studied. The following is the highlight of the main findings from this research:  \u2022 Presence of 0.5wt% Mn in alloy composition resulted in changes in the microstructure and texture. In particular, the addition of 0.5wt% Mn led to a transition from a fully recrystallized equiaxed grain structure (0Mn alloy) with \u03b2-Al5FeSi second phase constituent particles aligned in the extrusion direction to an unrecrystallized elongated grain structure (0.5Mn alloy) having \u03b1-Al(Fe,Mn)Si second phase particles of two different length scales, i.e. dispersoids and constituent particles.  \u2022 Crystallographic induced plastic anisotropy, morphological and topological anisotropy of particles were identified in both alloys. \u2022 Both materials showed aspects of anisotropic plastic response demonstrated by the orientation dependence of the R-values and to a lesser degree, the uniaxial stress-strain response. \u2022 Both materials showed similar aspects of orientation dependance in their bending response, i.e., having the highest bendability in the extrusion direction. \u2022 The results for the recrystallized material exhibited a correlation between the true strain to fracture in a tensile test and the maximum bend angle in a 3-point VDA bend test. However, 107  the unrecrystallized material showed a different dependence, particularly for the samples loaded at 45\u00b0 to the extrusion direction. \u2022 Tensile behavior of the two alloys were predicted through VPSC modelling, showing similar anisotropic response to those obtained experimentally. 6.2 Future Work To improve the results of the current research, the following suggestions can be made: \u2022 A detailed analysis on characterization of diffuse necking and localized necking based on the angle of the fracture plane in tensile samples.  \u2022 Investigation of the grain size and shape effect on fracture anisotropy \u2022 Predicting bending response of the alloys using VPSC modeling \u2022 Determination of peak forces in bend tests for investigating correlation between results     108  References  [1] J. 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Mech., vol. 224, 2020.           115   Appendix A In order to estimate the variability in the results from the tensile results in this study, 12 tensile tests were conducted on samples of an AA7030 alloy, where the samples were stretched to 10% plastic strain. The results obtained are shown in Table A.1. Example of Poisson\u2019s ratio (\ud835\udf10) and Young\u2019s modulus (E) calculation methods used based on the tensile testing data are shown in Figures A.1. Poisson's ratio is the negative of the ratio of transverse strain to axial strain in the initial elastic stage of deformation during the test; it is estimated from the slope of engineering width strain. vs engineering length strain curve up to \u2248 0.25% length strain (Figure A.1a). Young\u2019s modulus is obtained by finding the slope of the linear elastic part of the stress-strain curve, shown in Figure 4.10 and A.1b. Table A-1 Summary of AA7030 tensile test results obtained after 10% strain for variability estimation (measured R-values were obtained using a micrometer before and after the stretch) # Test date E (GPa) \ud835\udf10 Yield stress (MPa) R-value at 5% strain (in situ) R-value at 10% strain (in situ) Measured R-value at 10% strain (ex situ) 1 Jan. 13,2022 63.7 0.31 315 0.59 0.54 0.67 2 Jan. 18,2022 68.9 0.33 317 0.60 0.56 0.65 3 Jan. 18,2022 68.2 0.32 319 0.65 0.62 0.69 4 Jan. 20,2022 63.9 0.30 321 0.59 0.55 0.67 5 Jan. 20,2022 67.6 0.29 317 0.62 0.59 0.68 6 Jan. 20,2022 65.0 0.23 319 0.63 0.58 0.66 7 Jan. 31,2022 69.6 0.31 320 0.60 0.59 - 8 March 24,2022 71.2 0.37 326 0.76 0.72 0.72 9 March 24,2022 71.0 0.34 320 0.62 0.59 0.69 10 Aug. 16,2022 66.6 0.30 327 0.60 0.60 - 11 Sept. 26,2022 67.8 0.28 326 0.59 0.57 - 12 Dec. 21,2022 67.2 0.27 325 0.61 0.59 - Average\u00b1standard deviation 67.5\u00b12.5 0.30\u00b10.04 321\u00b14 0.62\u00b10.05 0.59\u00b10.05 0.67\u00b10.09  116   Examples of plastic true width and length strain changes under loading and R-value changes with the applied strain are presented in Figures A.2a and A.2b, respectively.   Figure A-1 a) Engineering width strain vs Engineering length strain curve example used for calculating Poisson\u2019s ratio (\ud835\udf10), and b) Engineering stress vs Engineering length strain curve example used for calculating Young\u2019s modulus (E).  Figure A-2 a) Plastic true width strain vs plastic true thickness strain curve example and b) R-value vs plastic true length strain curve example showing R-value changes with applied strain.  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