The formability of Magnesium and Magnesium-Rare Earth ...
Transcript of The formability of Magnesium and Magnesium-Rare Earth ...
The formability of Magnesium and
Magnesium-Rare Earth alloys under the
strain path of cold rolling
A dissertation submitted to The University of Manchester for the degree of Master of
Science by Research in the Faculty of Science and Engineering
2018
By
Pablo Garcia Chao
School of Materials
CONTENTS
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CONTENTS
CONTENTS .................................................................................................................................................. 2
LIST OF FIGURES ......................................................................................................................................... 5
LIST OF TABLES ......................................................................................................................................... 12
LIST OF ABBREVIATIONS .......................................................................................................................... 14
LIST OF SYMBOLS ..................................................................................................................................... 15
ABSTRACT ................................................................................................................................................ 17
DECLARATION .......................................................................................................................................... 18
COPYRIGHT STATEMENT .......................................................................................................................... 18
ACKNOWLEDGEMENTS ............................................................................................................................ 19
1 INTRODUCTION ................................................................................................................................ 21
2 LITERATURE REVIEW ........................................................................................................................ 23
Magnesium sheet for automotive applications ............................................................................. 23
2.1.1 Fundamentals of metal rolling ......................................................................................... 23
2.1.2 The thermomechanical route towards magnesium sheet ............................................... 24
2.1.3 Current limitations of magnesium sheet for automotive applications ............................ 25
2.1.4 Commercially available magnesium sheet alloys and further developments .................. 26
The cold formability of magnesium sheet ..................................................................................... 27
The plastic deformation of conventional magnesium sheet ......................................................... 30
2.3.1 Slip modes in magnesium ................................................................................................. 31
2.3.2 Twinning modes in magnesium ........................................................................................ 33
2.3.3 The basal texture of rolled magnesium............................................................................ 34
2.3.4 The role of deformation mechanisms in the plastic behaviour of magnesium sheet ...... 37
2.3.4.1 Behaviour under uniaxial (UAC) and plane-strain compression (PSC) ............... 37
2.3.4.2 Behaviour under uniaxial and biaxial tension .................................................... 40
2.3.4.3 Behaviour at ultimate failure ............................................................................. 42
2.3.5 The effect of texture on the formability of magnesium sheet ......................................... 44
2.3.6 The effect of grain size on the formability of magnesium sheet ...................................... 46
The plastic deformation of magnesium-rare earth (RE) sheet ...................................................... 51
2.4.1 The effect of rare-earth additions on deformation slip in magnesium ............................ 51
2.4.1.1 The effect of rare-earth elements on non-basal slip .......................................... 51
2.4.1.2 The effect of rare-earth elements on basal slip ................................................. 54
2.4.2 The effect of rare-earth additions on deformation twinning in magnesium ................... 56
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2.4.2.1 The effect of rare-earth elements on contraction twinning .............................. 56
2.4.2.2 The effect of rare-earth elements on tension twinning ..................................... 57
2.4.3 The rare-earth texture of rolled magnesium ................................................................... 58
2.4.3.1 Solute drag and rare-earth texture development .............................................. 63
Focus of the project ....................................................................................................................... 65
3 EXPERIMENTAL METHODS ............................................................................................................... 67
Chemical composition of the alloys ............................................................................................... 67
Thermomechanical preparation of the materials .......................................................................... 68
Characterisation techniques .......................................................................................................... 70
3.3.1 Vickers microhardness testing ......................................................................................... 71
3.3.2 Microstructural assessment through optical microscopy ................................................ 72
3.3.3 Bulk texture measurement through X-ray diffraction (XRD) ............................................ 73
3.3.4 Plane-strain compression (PSC) testing............................................................................ 75
Metallographic sample preparation .............................................................................................. 77
4 RESULTS ........................................................................................................................................... 79
Vickers hardness against annealing temperature ......................................................................... 79
Grain size against annealing temperature ..................................................................................... 80
Bulk texture against annealing temperature ................................................................................. 84
4.3.1 Bulk texture behaviour of Mg-0.03Y ................................................................................ 87
4.3.2 Bulk texture behaviour of Mg-0.6Y .................................................................................. 88
Plane-strain compression (PSC) behaviour against annealing temperature ................................. 89
4.4.1 Plane-strain compression behaviour of Mg-0.03Y ........................................................... 90
4.4.2 Plane-strain compression behaviour of Mg-0.6Y ............................................................. 94
5 DISCUSSION ..................................................................................................................................... 99
The effect of yttrium on the annealing behaviour of magnesium ................................................. 99
5.1.1 The effect of yttrium on the statically recrystallised grain diameter ............................... 99
5.1.2 The effect of yttrium on the activation energy for grain growth ................................... 100
5.1.3 Solute drag by Lücke-Detert’s theory ............................................................................. 103
5.1.4 Static recrystallisation (SRX) temperature and solute drag ........................................... 106
The origin of the TD-split textures of Mg-0.6Y ............................................................................ 107
5.2.1 The origin of TD-split orientations in RE-containing magnesium alloys ......................... 108
5.2.2 The scarcity of TD-split observations in binary Mg-RE alloys ......................................... 112
The effect of annealing on the behaviour of magnesium under the strain path of cold rolling.. 113
5.3.1 Stress saturation in the Stage III of Mg-RE alloys ........................................................... 114
5.3.1.1 The origin of microscopic softening ................................................................. 114
5.3.1.2 Requirements for the onset of stress saturation ............................................. 115
5.3.1.3 The amount of macroscopic softening ............................................................. 117
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5.3.2 The effect of annealing on the parameters defining the Stage II of work hardening .... 118
5.3.2.1 The effect of annealing in Stage II in conventional magnesium alloys ............ 118
5.3.2.2 The effect of annealing in Stage II in Mg-RE alloys .......................................... 120
5.3.3 The formability of magnesium under the strain path of cold rolling ............................. 121
5.3.3.1 The formability of conventional magnesium alloys ......................................... 122
5.3.3.2 The formability of Mg-RE alloys ....................................................................... 124
5.3.3.3 The origin of the high cold rollability of Mg-RE alloys ...................................... 125
5.3.4 The proof behaviour of magnesium under the strain path of cold rolling ..................... 126
5.3.4.1 The interplay between grain size and texture.................................................. 127
5.3.4.2 The sensitivity of proof strength and work hardening upon Stage I ................ 131
6 CONCLUSIONS ................................................................................................................................ 133
7 FUTURE WORK ............................................................................................................................... 135
BIBLIOGRAPHY ....................................................................................................................................... 136
Final word count: 51484
LIST OF FIGURES
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LIST OF FIGURES
Figure 1.1. Comparison of the specific stiffness and strengths of magnesium, aluminium and iron, the base
metals of the three main alloying systems considered for future automotive BIWs [15]. ............ 21
Figure 1.2. BIW of the Superlight-CAR, the outcome of an EU-funded project shaving off around 35% of the
weight of a Volkswagen Golf without compromising vehicle performance or increasing overall cost
[18]. ................................................................................................................................................ 22
Figure 2.1. Schematic of a rolling stage where the coordinate system conventionally used to represent sheet
material is indicated: rolling direction (RD), transverse direction (TD) and normal direction (ND).
The stress and strain states to which the material within the bulk are subjected during rolling are
given. .............................................................................................................................................. 23
Figure 2.2. Edge cracking in a pure magnesium single crystal cold-rolled to 3% reduction [26]. Sheet thickness
is parallel to the vertical direction of paper. .................................................................................. 24
Figure 2.3. Typical tensile properties of the main commercial magnesium sheet alloys employed up to date
(compilation from [31] [35] [40] [46] [47]). The dotted line represents the decreasing trend of
ultimate strength with elongation. ................................................................................................ 25
Figure 2.4. FLDs corresponding to AZ31 (conventional magnesium) [35], ZE10 (Mg-RE alloy) [35], 6016-T4
(aluminium) [62] and DP600 (steel) [63] . The dashed line represents the strain path of equi-biaxial
tension, the dotted line that of ideal uniaxial tension, and the dot-dash line that of plane strain.
........................................................................................................................................................ 28
Figure 2.5. Erichsen value (biaxial tension) as a function of ductility (uniaxial tension) for AZ31 (conventional
magnesium) [68] [69] [70] [71], ZE10 (Mg-RE alloy) [68] [72] [73], 6016-T4 (aluminium) [74] [75]
and DP600 (steel) [76] [77]. ........................................................................................................... 29
Figure 2.6. Slip directions and planes of the slip modes glissile in HCP crystal structures [84]. ..................... 31
Figure 2.7. Twinning directions and planes of the main twinning modes commonly observed in magnesium
crystals [84]. ................................................................................................................................... 33
Figure 2.8. 0001 pole figures for pure magnesium sheet (a) hot-rolled and (b) subsequently cold-rolled to
30% reduction. Band contours correspond to 2x, 4x, 6x… MRD. The basal fibre is displayed in both
conditions, with the latter clearly showing a sharper texture [28]. ............................................... 35
Figure 2.9. Contribution of the deformation mechanisms available in magnesium to the reduction imparted
by cold rolling as predicted by texture modelling using a Taylor polycrystal model. An initially
random texture and conventional room-temperature CRSS values –except for contraction
twinning, not considered in the model– are assumed [116]. ........................................................ 36
Figure 2.10. Basal texture intensity after the isochronal annealing of hot-rolled AZ31 sheet at various
temperatures. The pre-annealing texture intensity is also displayed for the sake of comparison
(redrawn from [120]). .................................................................................................................... 36
LIST OF FIGURES
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Figure 2.11. (a) Stress-strain curves and (b) evolution of work hardening with strain for AZ31 tested under
UAC in the c axis extension (Compression TD-RD) and c axis compression (Compression ND) texture
orientations. Pole figures for the initial textures in the two cases are also given, in which the
direction of the load is perpendicular to paper [111]. ................................................................... 38
Figure 2.12. (a) Stress-strain and work hardening curves, and (b) relative contribution of the various
deformation mechanisms corresponding to the PSC of AZ31 tested under 𝑐 axis extension (Ba =
basal slip, ETW = tension twinning, CT/CTW = contraction twinning, Pr = prismatic slip, Py: <c+a>
slip). A cluster-type deformation texture grain interaction (GIA) model considering (i) slip hardening
with a one parameter law and (ii) twin hardening by reduction in the dislocation free path length
has been used [111]. ...................................................................................................................... 38
Figure 2.13. (a) Contribution of the various slip mechanisms to deformation of AZ31 under uniaxial tension as
a function of the ratio between the CRSSs for prismatic and <c+a> slip as predicted by viscoplastic
self-consistent modelling. Ratios higher than 2 were suggested for room temperature [134]. (b)
Profuse prismatic slip observed in AZ31 after uniaxial tension [129]. ........................................... 40
Figure 2.14. Macroscopic critical stress applied (ratio between CRSS and Schmid factor 𝑚, Schmid’s law) for
the main deformation mechanisms in magnesium under (a) uniaxial tension and (b) uniaxial
compression (twinning accounts here for tension twinning). The angle represents 𝑐 axis inclination
with respect to the direction of the stress [129]............................................................................ 41
Figure 2.15. (a) EBSD scan displaying numerous shear bands in AZ31 after PSC testing. Most shear band
boundaries are consistent with double twin misorientations (yellow), and they are frequently
associated with black (non-indexed) regions [114]. (b) Fracture surface of AZ31 after tensile testing,
showing twin-shaped voids parallel to twin bands [108]. .............................................................. 42
Figure 2.16. Shear bands in AZ31 (a) after 7% effective plastic strain under uniaxial tension, and (b) after 4%
effective plastic strain under biaxial tension [80]. ......................................................................... 43
Figure 2.17. Erichsen cup test specimens corresponding to AZ31 having different initial basal texture intensity.
Both have been hot-rolled and annealed, with the final hot rolling pass carried out at 798 K for the
specimen above and 723 K for the specimen below [123]. ........................................................... 45
Figure 2.18. Relationship between twin density and initial grain size in AZ31 tested under uniaxial tension
(favourable to contraction twinning) and UAC in the 𝑐 axis extension orientation (favourable to
tension twinning) [22]. ................................................................................................................... 46
Figure 2.19. TEM micrographs corresponding to Mg-1Zn deformed to 5% strain under uniaxial tension with
initial grain sizes of (a) 84 µm and (b) 23 µm. All 𝑎 dislocations are visible in the two images. Solid
arrows indicate dislocations parallel to basal plane traces, and dashed ones those orthogonal, i.e.
are associated to cross-slip into prismatic planes [127]. ............................................................... 47
Figure 2.20. Stress-strain curves corresponding to AZ31 with different initial grain sizes and tested under (a)
UAC in 𝑐 axis extension orientations, where greater tension twinning the larger the grain size leads
LIST OF FIGURES
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to (i) more marked concave-up character and (ii) higher peak stress in virtue of greater twinning-
induced hardening [132]; and (b) tensile testing, where coarse grain size results in premature
failure, which has been attributed to enhanced contraction twinning [138]. ............................... 48
Figure 2.21. Microstructures of AZ31 specimens after Erichsen cup testing with initial grain size of (a) 6 µm,
(b) 10 µm, (c) 17 µm and (d) 31 µm. Narrow bands correspond to contraction or double twins [65].
........................................................................................................................................................ 49
Figure 2.22. (a) Total dislocation density and densities of dislocations with 𝑎 and 𝑐 + 𝑎 Burgers vectors as a
function of yttrium content for four binary Mg-Y alloys after creep at 550 K; (b) ratio between the
density of non-basal dislocations (irrespective of Burgers vectors) and total dislocation density
under the same conditions [157]. .................................................................................................. 52
Figure 2.23. IPFs representing IGMA densities for a range of hot-rolled binary Mg-Ce alloys. Texture intensity
after hot rolling has been indicated also [160]. ............................................................................. 53
Figure 2.24. Slip trace analysis in Mg-3Y cold-rolled to 3% strain, where traces of slip on the basal, 1st order
pyramidal and 2nd order pyramidal planes have been identified [30]. .......................................... 53
Figure 2.25. Variation of room-temperature yield strength with solute content of yttrium, aluminium and zinc
included in the corresponding single-phase binary alloys [167]. ................................................... 54
Figure 2.26. Variation in the CRSS of basal slip with temperature in several single-phase Mg-X single crystals
(X = wt% yttrium, dysprosium and zinc). The IPF indicates the stress direction in the UAC tests [168].
........................................................................................................................................................ 55
Figure 2.27. KAM maps and pole figures showing GND distribution and texture of (a) pure magnesium and (b)
Mg-3Y cold-rolled at 10% reduction. The occurrence of shear bands traversing many grains and
characterized by high GND density levels is evident from KAM maps. In turn, pole figures display a
relatively strong basal texture for pure magnesium, and much weaker RE texture for Mg-3Y [29].
........................................................................................................................................................ 56
Figure 2.28. EBSD maps corresponding to hot-rolled (a) Mg-0.01 at% Nd and (b) Mg-0.04 at% Nd, where the
misorientations corresponding to tensile twin (red), contraction twin (blue) and double twin
(yellow) boundaries have been highlighted [118]. ......................................................................... 57
Figure 2.29. (a) Influence of yttrium content on the CRSS of basal slip, 𝑐 + 𝑎 slip and tension twinning as
predicted by elastoplastic self-consistent modelling in [131]; (b) schematic showing the effect of
high yttrium content on the CRSSs for 1012 and 1121 twinning suggested in [177]. .................. 58
Figure 2.30. 0001 pole figures for AZ31 (left) and Mg-1.5Gd (right) hot rolled at 400°C and subsequently
annealed at 450°C for 1 h. The distinct pole figure shape and weaker peak intensity for the Mg-RE
alloy are clearly shown [178]. ........................................................................................................ 59
Figure 2.31. 0001 pole figures for Mg-1Zn (a) as-hot rolled at 150°C and (b) annealed at 400°C for 15 min;
and for ZE10 (Mg-1.0Zn-0.3Ce) (c) as-hot rolled at 150°C, (d) annealed at 400°C for 15 min and (e)
LIST OF FIGURES
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annealed at 400°C for 4 h. The RD-split texture typical of binary Mg-RE alloys gives way in ZE10 to
a TD tilted texture upon annealing [57]. ........................................................................................ 59
Figure 2.32. Pole figures corresponding to pure magnesium and Mg-0.2Ce before cold rolling (h.r.=hot-rolled
state), and after cold rolling (c.r.) at 30% overall reduction after applying 1% reduction per pass
[28]. ................................................................................................................................................ 60
Figure 2.33. Peak texture intensity (in MRD) of hot-rolled and then annealed Mg-RE sheet against RE alloying
content for different RE additions. The vertical lines indicate the solid solubility of each RE element
in magnesium at 525°C [124]. ........................................................................................................ 61
Figure 2.34. EBSD maps (left) and corresponding pole figures (right) for different stages in the annealing of
hot-rolled Mg-1Gd: (a) as-deformed, (b) recrystallised, and (c) after considerable grain growth. The
two first conditions correspond to the deformed and recrystallised fractions of the hot-rolled sheet
annealed for one hour at 300°C, and the third to the same sheet annealed for one hour at 450°C.
Colour coding indicates the tilting to the ND: with this scale, grains with off-RE orientations are
shown in green, and grains with RE orientations in blue. Linear intercept grain sizes for both off-RE
and RE grains are included also [185]. ........................................................................................... 62
Figure 2.35. High-angle annular dark-field scanning-transmission micrographs showing a grain boundary in
as-hot rolled (a) Mg-0.01 at% Gd, and (b) Mg-0.06 at% Gd. The gadolinium atoms are displayed in
bright so that an enriched solute layer surrounding the boundary is noticeable only for the higher
RE concentration [174]. .................................................................................................................. 64
Figure 3.1. Equilibrium phase diagram of the Mg-Y system. The dashed lines represent phase boundaries for
which further confirmation is needed [194]. ................................................................................. 67
Figure 3.2. Schematic of the microstructural evolution expected during the thermomechanical processing
carried out in this project. As-cast precipitated particles are not drawn to scale. ........................ 69
Figure 3.3. Characterisation stages carried out in this project, indicating the specific technique and range of
annealing temperature conditions employed. ............................................................................... 71
Figure 3.4. Cross-section of the indenter used for Vickers testing as pushed down onto the sample surface
(left). Top view of the impression thereby imparted (right) [199]. ................................................ 71
Figure 3.5. Schematic of the arrangement typically used in the cross-polarised optical microscopy technique.
The path followed by the light from source to eyepieces is indicated in blue, with light vibration
directions represented at the critical positions [204]. ................................................................... 73
Figure 3.6. Schematic of a standard Eulerian diffractometer showing the three angles involved in bulk texture
measurement. Incident and reflected beam represented by red lines [205]. ............................... 74
Figure 3.7. (a) Exploded view of the channel-die and plunger fixture designed for the PSC tests of this project,
where contact surfaces have been hatched: on the one hand, the sample is compressed between
the bottom surface of the plunger (black arrow) and the top surface of the channel (orange arrow),
LIST OF FIGURES
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and between the front and back channel walls (blue arrows); on the other hand, the sample can
stretch freely along the RD (red arrows). (b) One of the actual PSC tests of this study. ............... 76
Figure 4.1. Vickers hardness against annealing temperature for the two alloys in study. The error bars
represent standard deviations. Comparison with values predicted by the model developed by Gao
et al. [167] is also displayed. .......................................................................................................... 79
Figure 4.2. Evolution of grain diameter with annealing temperature for the two alloys in study. The dashed
lines correspond to exponential laws calculated with the least squares method and demonstrating
good correlation with experimental data. Comparison with results in similar studies by Nadella et
al. [212] and Hadorn et al. [158] is also included. .......................................................................... 80
Figure 4.3. Optical micrographs obtained for Mg-0.03Y hot-rolled and annealed for one hour at (a) 350°C, (b)
400°C, (c) 425°C, (d) 450°C and (e) 500°C. ..................................................................................... 81
Figure 4.4. Optical micrographs for Mg-0.6Y hot-rolled and annealed for one hour at (a) 400°C, (b) 425°C, (c)
450°C, (d) 475°C and (e) 500°C. Red circles show potential incomplete etching products. .......... 82
Figure 4.5. Optical micrographs for (a) Mg-0.03Y and (b) Mg-0.6Y in the as-hot rolled states. ..................... 82
Figure 4.6. Recalculated 0001 pole figures corresponding to Mg-0.03Y (a) in the as-hot rolled condition, and
after annealing at (b) 350°C, (c) 425°C and (d) 500°C for one hour. Intensities are given in MRD.84
Figure 4.7. Recalculated 1010 pole figures corresponding to Mg-0.03Y (a) in the as-hot rolled condition, and
after annealing at (b) 350°C, (c) 425°C and (d) 500°C for one hour. Intensities are given in MRD.85
Figure 4.8. Recalculated 0001 pole figures corresponding to Mg-0.6Y (a) in the as-hot rolled condition, and
after annealing at (b) 400°C, (c) 450°C and (d) 500°C for one hour. Intensities are given in MRD.86
Figure 4.9. Recalculated 1010 pole figures corresponding to Mg-0.6Y (a) in the as-hot rolled condition, and
after annealing at (b) 400°C, (c) 450°C and (d) 500°C for one hour. Intensities are given in MRD.87
Figure 4.10. Mg-0.6Y (450°C) specimen unloaded shortly after peak stress and represented with the (a) TD-
ND, and (b) RD-ND faces parallel to paper. While TD-ND faces exhibit distinct ‘barrelling’, RD-ND
faces are perfectly plane. ............................................................................................................... 89
Figure 4.11. True stress-true total strain curves corresponding to the PSC of Mg-0.03Y annealed at 350, 425
and 500°C for one hour. Curves have been truncated shortly after failure. .................................. 90
Figure 4.12. True stress-true plastic strain curves corresponding to the PSC of Mg-0.03Y annealed at 350, 425
and 500°C for one hour. Curves have been truncated shortly after failure. .................................. 91
Figure 4.13. RD-ND faces of two different fractured Mg-0.03Y (425°C) specimens: (a) just after peak stress,
and (b) after full unloading. Dashed lines represent approximate positions of catastrophic cracks.
........................................................................................................................................................ 91
Figure 4.14. Work hardening evolution throughout the plastic range for the three annealing conditions tested
for Mg-0.03Y. The schematic represents the three stages of work hardening as previously defined
in magnesium literature [106] [111]. ............................................................................................. 93
LIST OF FIGURES
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Figure 4.15. Work hardening against true stress for the three annealing conditions tested for Mg-0.03Y.
Dotted lines accounting for Stage I have been added for visual guidance. ................................... 93
Figure 4.16. True stress-true total strain curves corresponding to the PSC of Mg-0.6Y annealed at 400, 450
and 500°C for one hour. Curves have been truncated shortly after failure. Arrows in the curves
point at the approximate point of failure. ..................................................................................... 94
Figure 4.17. True stress-true plastic strain curves corresponding to the PSC of Mg-0.6Y annealed at 400, 450
and 500°C for one hour. Curves have been truncated shortly after failure. Arrows in the curves
point at the approximate point of failure. ..................................................................................... 95
Figure 4.18. RD-ND faces of fractured Mg-0.6Y (450°C) specimens (a) just after the onset of failure and (b)
after significantly larger reduction. Cracks starting at each of the four corners are clearly shown.
........................................................................................................................................................ 96
Figure 4.19. RD-ND faces of two fractured Mg-0.6Y (400°C) specimens (a) just after the onset of failure and
(b) after further reduction. Cracks have started at one corner only: top-right in (a), and bottom-left
in (b). .............................................................................................................................................. 96
Figure 4.20. Work hardening response for the three annealing conditions tested for Mg-0.6Y. The schematic
represents the three stages of work hardening as previously defined in magnesium literature [106]
[111]. .............................................................................................................................................. 97
Figure 4.21. Work hardening against true stress for the three annealing conditions tested for Mg-0.03Y. .. 97
Figure 5.1. Logarithm of the increment of grain size squared resulting from grain growth plotted against the
negative reciprocal of annealing temperature for the alloys in study. Data for annealing
temperatures between 400 and 500°C are considered, and the dashed lines correspond to linear
regression equations calculated by the least squares method. ................................................... 102
Figure 5.2. Comparison between the apparent activation energies for grain growth here obtained for Mg-
0.03Y and Mg-0.6Y and comparable values provided by Zhang et al. [213], Fang et al. [214] and
Murty et al. [215]. Estimated activation energies for the interdiffusion of yttrium of magnesium
and the grain boundary self-diffusion of magnesium are also given for assessment of grain
boundary mobility regimes by Lücke-Detert’s theory. ................................................................. 103
Figure 5.3. SRX temperature as a function of solute concentration for various alloying elements added to high-
purity magnesium. The dotted line represents the SRX temperature of the pure metal (after
Ichikawa [200] [228]). ................................................................................................................... 106
Figure 5.4. Rationale suggested in this project for the development of RD- and TD-split texture fibres in RE-
containing magnesium alloys during annealing. The following colour coding has been used: grey =
RD-split orientations, blue = TD-split orientations, yellow = randomly distributed orientations. Solid
circles account for orientations actually noticeable in pole figures, and dashed circles for those in
the microstructure, but with low texture intensities against the background. The situation on the
left side represents accelerated kinetics compared to that on the right side, which is proposed to
LIST OF FIGURES
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occur (i) when increasing solute RE content, (ii) in Mg-Zn-RE as compared to binary Mg-RE alloys,
and (iii) when raising annealing temperature. ............................................................................. 111
Figure 5.5. Hall-Petch plots for the two alloys in study and engineering plastic strains of 0.1%, 0.2% and 0.5%.
Error bars represent standard deviations, and dashed lines are best-fit regression lines with the
form of Hall-Petch equations. ...................................................................................................... 128
Figure 5.6. Expanded view of the PSC stress-strain curves of Mg-0.03Y close to the onset of plastic
deformation. Arrows indicate the approximate point of yield for each condition. ..................... 130
LIST OF TABLES
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LIST OF TABLES
Table 2.1. Chemical composition and summary of properties of the main commercial magnesium sheet alloys
used up to date (compiled from [31] and [35]). ............................................................................. 26
Table 2.2. Strain along the three main directions of sheet material for the strain paths most relevant for
understanding sheet formability. Uniaxial tension is considered parallel to the RD and the TD,
respectively. ................................................................................................................................... 28
Table 2.3. Maximum rolling reduction before edge cracking in one pass for magnesium, steel and aluminium
alloys. ............................................................................................................................................. 30
Table 2.4. Elements of the deformation slip modes possible in HCP crystal structures, including the number
of independent systems provided by each (adapted from [82] and [83]). .................................... 31
Table 2.5. Room-temperature CRSSs for the main deformation modes active in magnesium as measured in
pure magnesium single crystals (compilation from various sources). ........................................... 32
Table 2.6. Elements, resultant shear strains and misorientation angles about the 1210 axis for the main
twinning modes in magnesium crystals. Misorientations after double twinning are also given [105].
........................................................................................................................................................ 33
Table 2.7. Formability parameters under uniaxial and biaxial tension as a function of initial basal texture
intensity and grain size in conditions prepared by hot rolling and subsequent annealing. Data by
Chino et al. [79], Kang et al. [64] and Shi et al. [127] have been included. Yield strengths are also
presented for the sake of discussion in Section 5.3.4. ................................................................... 50
Table 2.8. Shear modulus misfit and strain due to size misfit for yttrium, aluminium and zinc, as well as solid
solution hardening rates as calculated from the room-temperature yield strength of the
corresponding single-phase binary alloys. ..................................................................................... 55
Table 3.1. Bulk yttrium concentrations of the two binary Mg-Y alloys considered in this study as determined
by the company AMG Superalloys UK Ltd. with the ICP-AES technique. ....................................... 68
Table 3.2. Expected and actual sheet thickness after each of the hot rolling stages conducted in this study for
each of the two alloys. ................................................................................................................... 70
Table 3.3. 2𝜃 diffraction angles employed to obtain the pole figures in this project. .................................... 75
Table 4.1. Initial grain size, XRD peak basal texture intensity and tilting of the basal poles to the ND for the
annealing conditions tested under PSC. Comparable data from [141] are provided as a benchmark.
........................................................................................................................................................ 89
Table 4.2. Mechanical properties corresponding to the PSC testing of Mg-0.03Y conditions. Average and
typical deviation corresponding to at least three specimens are indicated in each of the cases.
Results in a comparable study are provided for reference. ........................................................... 90
LIST OF TABLES
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Table 4.3. Parameters defining the Stage II of work hardening for the annealing conditions tested for Mg-
0.03Y: plastic strain at which Stage II is onset 𝜀𝑃𝐼𝐼, plastic strain extent 𝛥𝜀𝑃𝐼𝐼, overall increase of
work hardening ∆𝛩𝐼𝐼, and rate of the work hardening increase 𝛩𝐼𝐼′. Graphical definition of
parameters is shown in Figure 4.14. The increase in strain-to-failure with respect to the condition
displaying the lowest strain-to-failure is also indicated. ................................................................ 94
Table 4.4. Mechanical properties corresponding to the PSC testing of Mg-0.6Y conditions. Average and typical
deviation corresponding to at least three specimens are indicated in each of the cases. ............ 95
Table 4.5. Parameters defining the Stage II of work hardening for the annealing conditions tested for Mg-
0.6Y: plastic strain at which Stage II is onset 𝜀𝑃𝐼𝐼, plastic strain extent 𝛥𝜀𝑃𝐼𝐼, overall increase of
work hardening ∆𝛩𝐼𝐼, and rate of the work hardening increase 𝛩𝐼𝐼′. Graphical definition of
parameters is shown in Figure 4.20. .............................................................................................. 98
Table 5.1. Input parameters for McLean’s equation for the interaction between solute yttrium atoms and
magnesium grain boundaries 𝑈(0) (extracted from [195]). ........................................................ 105
Table 5.2. Hall-Petch parameters 𝜎0 and 𝐾𝑃𝑆 at 0.2% engineering strain for Mg-0.6Y in the present study,
and various magnesium alloys in the literature. Confidence intervals at 80% are given for Mg-0.6Y
as done by the authors in [132]. .................................................................................................. 129
Table 5.3. Sensitivity of proof strength to grain size 𝐾𝑃𝑆 for the two alloys in study at various proof strain
levels............................................................................................................................................. 132
LIST OF ABBREVIATIONS
-14-
LIST OF ABBREVIATIONS
AES Atomic emission spectroscopy
BIW Body in white
CRSS Critical resolved shear stress
DIC Differential interference contrast
DRX Dynamic recrystallisation
DRY Dynamic recovery
DSA Dynamic strain ageing
EBSD Electron backscattered diffraction
EDS Energy-dispersive spectroscopy
ECAP Equal channel angular processing
FLD Forming limit diagram
GND Geometrically necessary dislocation
GBN Grain boundary nucleation
HAADF High-angle annular dark-field
HCP Hexagonal close-packed
ICP Inductively coupled plasma
IGMA Intragranular misorientation axis
IPF Inverse pole figure
KAM Kernel average misorientation
MRD Multiples of a random distribution
ND Normal direction
ODF Orientation distribution function
PSC Plane-strain compression
PSN Particle-stimulated nucleation
RD Rolling direction
RE Rare-earth
SBN Shear band nucleation
SRX Static recrystallisation
TD Transverse direction
TEM Transmission electron microscopy
UAC Uniaxial compression
XRD X-ray diffraction
LIST OF SYMBOLS
-15-
LIST OF SYMBOLS
𝐴 Surface area of Vickers impression
𝑑1, 𝑑2 Projected diagonal lengths of Vickers impression
𝐷, 𝐷0 Average grain diameter, Average statically recrystallised grain diameter
𝐸 Elastic stiffness under PSC testing
𝐹 Load applied (PSC testing)
𝐺 Shear modulus
ℎ0 Initial height of PSC sample (measured along the ND)
𝐻𝑉 Vickers number
𝐾 Bulk modulus
𝐾𝑃𝑆 Sensitivity of proof strength to grain size (Hall-Petch equation)
𝑙 Average linear intercept grain length
𝑚 Schmid factor
𝑃 Load applied (Vickers testing)
𝑄𝐵, 𝑄𝐺𝐵 Activation energy for the interdiffusion of solute yttrium in bulk magnesium and across magnesium grain boundaries
𝑄𝐵′ , 𝑄𝐺𝐵
′ Activation energy for the self-diffusion of magnesium in the bulk and across grain boundaries
𝑄𝐺𝐺 Apparent activation energy for grain boundary migration during grain growth
𝑟 Atomic radius
𝑅 Ideal gas constant
𝑆0 Initial surface area of PSC sample (measured in the RD-TD plane)
𝑇, 𝑇𝑆𝑅𝑋 Annealing temperature, Static recrystallisation temperature
𝑈 Interaction potential between solute atoms and magnesium grain boundaries
∆ Specimen displacement (PSC testing)
𝜀, 𝜀𝑃 True total and true plastic strain
(𝛥𝜀𝑃)𝐼𝐼 Plastic strain extent of Stage II
𝜀1, 𝜀2 Major and minor strains in the sheet plane (sheet metal forming)
𝜀3 Strain along the ND (sheet metal forming)
2𝜃 Bragg’s diffraction angle (diffractometer)
Θ Work or strain hardening
∆Θ𝐼𝐼 Increment of work hardening during Stage II
Θ′ Derivative of work hardening with respect to true plastic strain
Θ𝐼𝐼′ Rate of work hardening increase during Stage II
LIST OF SYMBOLS
-16-
𝜎 True stress
𝜎𝑃𝑆 Proof strength under PSC testing
𝜎0 Initial resistance of the lattice to dislocation motion (Hall-Petch equation)
𝜑 Sample rotation angle (diffractometer)
𝜒 Sample tilting angle (diffractometer)
ABSTRACT
-17-
ABSTRACT
Magnesium sheet components hold great potential to reduce the environmental footprint of road
transport. However, the industrial introduction of magnesium sheet is currently limited by its low
formability under the strain path of cold rolling. In this view, the remarkable formability increases
imparted by rare-earth (RE) additions to magnesium have attracted increasing interest over the last
few years. Three changes induced by RE additions have been put forth to explain the improvement:
(i) weaker texture, (ii) enhanced contraction twinning, and (iii) enhanced non-basal slip.
Within this context, this project aims to explore the effect of material preparation on the formability
of conventional and Mg-RE alloys in the strain path of cold rolling. Attention is paid to texture and
grain size, the main factors affecting magnesium formability according to former research. For this
aim, a set of annealing conditions are prepared for two alloys accounting for conventional and RE-
modified behaviour, respectively: Mg-0.03Y and Mg-0.6Y. Samples are characterized and subjected
to plane-strain compression (PSC) tests reproducing the strain path of cold rolling. The hypothesis
that the action of solute drag is related to the RE texture weakening, proposed in recent literature,
is checked in parallel using activation energies and in the light of Lücke-Detert’s theory.
PSC results show that, whereas the strains-to-failure reached by Mg-0.03Y specimens correlate with
greater basal slip and tension twinning enabled by weaker texture, those of Mg-0.6Y are remarkably
higher for conditions developing stress saturation stages at peak stress. Absent for Mg-0.03Y, such
stages have been associated to the RE promotion of contraction twinning, and found to occur for a
minimum initial grain size only. Therefore, a substantially different approach should be employed
to optimize the formability of conventional and Mg-RE alloys. Moreover, strain-to-failure has been
significantly higher for Mg-0.6Y only in conditions with stress saturation, implying that, among all
three mechanisms proposed, it is contraction twinning that essentially explains the formability of
Mg-RE alloys. Hence, these results outline the importance of enhancing contraction twinning for
magnesium alloy developments. Further, this could also apply to biaxial tension, the other relevant
strain path in practice, due to the analogous role therein expected for contraction twinning.
In addition, considerably higher activation energy for grain growth is measured for Mg-0.6Y than
for Mg-0.03Y. The activation energy of Mg-0.03Y is in line with Lücke-Detert’s breakaway regime,
and that of Mg-0.03Y with the drag regime. This confirms that a shift in the boundary migration
regime is effectively associated to the RE texture weakening. Further, notice has been taken of the
unusual development of a TD-tilted fibre by Mg-0.6Y, mainly observed in ternary Mg-Zn-RE alloys
only so far. This finding has been rationalized through a theory unifying texture observations in both
alloying systems. Future work aimed at contrasting this theory is encouraged.
DECLARATION & COPYRIGHT STATEMENT
-18-
DECLARATION
No portion of the work referred to in this thesis has been submitted in support of an application for
another degree or qualification of this or any other university or other institute of learning.
COPYRIGHT STATEMENT
i. The author of this dissertation (including any appendices and/or schedules to this dissertation)
owns any copyright in it (the “Copyright”) and s/he has given The University of Manchester the right
to use such Copyright for any administrative, promotional, educational and/or teaching purposes.
ii. Copies of this dissertation, either in full or in extracts, may be made only in accordance with the
regulations of the John Rylands University Library of Manchester. Details of these regulations may
be obtained from the Librarian. This page must form part of any such copies made.
iii. The ownership of any patents, designs, trademarks and any and all other intellectual property
rights except for the Copyright (the “Intellectual Property Rights”) and any reproductions of
copyright works, for example graphs and tables (“Reproductions”), which may be described in this
dissertation, may not be owned by the author and may be owned by third parties. Such Intellectual
Property Rights and Reproductions cannot and must not be made available for use without the
prior written permission of the owner(s) of the relevant Intellectual Property Rights and/or
Reproductions.
iv. Further information on the conditions under which disclosure, publication and exploitation of
this dissertation, the Copyright and any Intellectual Property Rights and/or Reproductions
described in it may take place is available from the Head of School of the School of Materials.
ACKNOWLEDGEMENTS
-19-
ACKNOWLEDGEMENTS
The author wishes to gratefully acknowledge Dr Alberto Orozco-Caballero for his patience, advice
and inspiration, without which the completion of this project would certainly have been impossible.
Technical support from Mr. Ken Gyves, Mr. Stuart Morse, Dr. John E. Warren and Dr. Ali Gholinia,
is also appreciated.
Besides, the author would like to especially acknowledge “la Caixa” Foundation for its confidence
and financial support to fund these studies.
ACKNOWLEDGEMENTS
-20-
This project was carried out in the year 2014/15, with countless hours and to
greatest endurance of the author
Madrid, 8th of May 2018
“Don’t worry about the summit – just keep walking, and the summit will find you”
Unknown mountaineer – Djebel Toubkal (Morocco), August 2013
1. INTRODUCTION
-21-
1 INTRODUCTION
Globally, road transport accounts for approximately 22% of energy consumption [1] [2] and 11% of
greenhouse gas emissions [3] [4]. In the light of this situation, stringent goals have been put forward
by the main industrialised countries aiming to reduce the environmental footprint of this sector in
the next few decades [5] [6]. The extent of these regulations is such that their fulfilment is expected
to drive the technical evolution of commercial vehicles by at least 2050 [7].
Among the changes regarded as unavoidable by automakers, vehicle weight reduction has been
assessed as the most cost-effective [8] [9]: estimations predict fuel consumption decreases of 5-
10% per 10% weight reduction [10] [11], and savings of about 9 g CO2/km per 100 kg reduction [12].
For this aim, automakers have attached the most critical role to the body-in-weight (BIW) of
vehicles: as well as accounting for 15-45% of total vehicle weight [13], a “spiralling” effect has been
identified associated to the lightweighting of its components, in that underlying systems (e.g.
chassis, engine, battery) can be downsized accordingly [9]. Nowadays, the majority of BIW parts are
sheet components [14].
Figure 1.1. Comparison of the specific stiffness and strengths of magnesium, aluminium and iron, the base metals of the three main alloying systems considered for future automotive BIWs [15].
Under this scenario, the high specific strength of magnesium (Figure 1.1) has attracted increasing
attention from the automotive industry over the last fifteen years [16] [17]. Being the lightest of all
structural metals, magnesium is 78% lighter than steel and 35% than aluminium [15] [16], the
benchmark materials in current vehicle BIWs. Accordingly, weight savings of 50% compared to steel
and 20% compared to aluminium have been estimated for BIW sheet parts if manufactured in
magnesium [15] [17]. Therefore, it comes as no surprise that sheet magnesium components are
recurrently included in the BIWs of concept cars paving the way for future vehicle generations, e.g.
Volkswagen’s Superlight-CAR (Figure 1.2) [18] or Renault’s EOLAB [19].
1. INTRODUCTION
-22-
Figure 1.2. BIW of the Superlight-CAR, the outcome of an EU-funded project shaving off around 35% of the weight of a Volkswagen Golf without compromising vehicle performance or increasing overall cost [18].
Nevertheless, the practical utilisation of magnesium alloys in the automotive industry is currently
restricted to cast components, which find application outside BIWs only, e.g. in steering wheels or
engine blocks [20] [21]. In particular, the introduction of magnesium sheet parts is hindered by the
well-known difficulty of this metal to withstand deformation at room temperature without failure
[20] [22] [23]. For the case of cold rolling, the reduction in thickness that magnesium can sustain
per stage is nearly negligible, decisively restricting the economic competitiveness of cold-rolled
magnesium sheet against comparable aluminium and steel stock [23] [24] [25].
Within this context, renewed attention has been paid in the last decade to the strikingly high cold
rollability shown to result, as early as in 1959 [26], from the addition of rare-earth (RE) elements to
magnesium. Specifically, novel RE-containing, highly cold-rollable magnesium alloys have been
developed having the potential to be employed in BIW applications [27]. Moreover, the modern
experimental techniques have been applied to the case seeking to understand the origin of the
improved cold rollability, leading to a number of concurrent mechanisms proposed to explain the
effect [28] [29] [30]. On the one hand, this project aims to facilitate the practical introduction of
Mg-RE alloys in the automotive industry by providing material preparation guidelines optimizing
their cold rollability. On the other hand, light is shed onto the actual reason for the strikingly high
cold rollability imparted by RE additions to magnesium.
2. LITERATURE REVIEW
-23-
2 LITERATURE REVIEW
Magnesium sheet for automotive applications
Sheet metal is one of the most frequently used semi-finished products in the industry, for whose
production rolling is the conventional process. The fundamentals of metal rolling are reviewed in
this section, together with the specific route customarily used in the case of magnesium. The main
limitations of currently available magnesium sheet alloys, because of which they have never been
included in mass-production BIW parts to date [31], are also discussed briefly. Finally, the alloying
additions most promising for solving such issues are presented.
2.1.1 Fundamentals of metal rolling
In rolling operations, metal thickness is gradually reduced as the material goes through successive
stages, each composed of a pair of rolls separated by a gap smaller than input thickness (Figure
2.1). In each stage, the material in the bulk is subjected to a state of plane-strain characterized by:
(i) compression in the normal direction (ND) as imposed by the roll gap (𝜀3<0), (ii) extension in the
rolling direction (RD) (𝜀1>0), and (iii) no strain in the transverse direction (TD) (𝜀2=0) (Figure 2.1)
[32]. During rolling, failure occurs in the form of edge cracking (Figure 2.2), since the strain state in
the bulk is superimposed at the edges with shear stresses elevating material susceptibility to
damage. Edge shear stresses are highly dependent on edge shape [33].
Figure 2.1. Schematic of a rolling stage where the coordinate system conventionally used to represent sheet material is indicated: rolling direction (RD), transverse direction (TD) and normal direction (ND). The stress and strain states to
which the material within the bulk are subjected during rolling are given.
Normally, the initial rolling passes are conducted above recrystallisation temperature (hot rolling),
and the finishing stages at room temperature (cold rolling). Although greater reductions per pass
RDTD
ND
ε1>0
ε3<0
ROLL
ROLL
SHEET METAL
σ2<0
σ3<0
2. LITERATURE REVIEW
-24-
without failure –and thus fewer passes– are possible with hot rolling [25] [32], room temperature
is preferred for the last stages due to better resultant quality, namely in terms of:
• Improved surface finish.
• Tighter dimensional tolerances.
• More uniform distribution of properties, as the temperature gradient within the material
that is inevitable during hot rolling is avoided [34].
• Cold rolling offers the chance to include work hardening as a strengthening mechanism
additional to alloying hardening, as shown for magnesium in e.g. [25] and [26].
Figure 2.2. Edge cracking in a pure magnesium single crystal cold-rolled to 3% reduction [26]. Sheet thickness is parallel to the vertical direction of paper.
2.1.2 The thermomechanical route towards magnesium sheet
The thermomechanical route conventionally employed in the industrial production of magnesium
sheet is described in detail in [35], and can be summarised into the following steps:
(i) The starting point is cast slabs, produced most often by the direct chill casting method,
which minimises macrosegregation.
(ii) Before rolling, the slabs are subjected to a homogenisation heat treatment to remove
microsegregation and dissolve any precipitates present in the as-cast microstructure.
(iii) The homogenised metal is then hot-rolled at temperatures within 350-500°C [36]. The
temperature is selected so that dynamic recrystallisation (DRX) is activated [37] [38], which
renders the microstructure more ductile.
(iv) Afterwards, full annealing is conducted to impart static recrystallisation (SRX) to all the
microstructure [35], further increasing ductility in view of the subsequent cold rolling.
(v) During cold rolling, expensive annealing treatments are carried out in-between stages to
avoid edge cracking [39] [40]. Despite this, reductions per pass cannot typically exceed 5-
10% [24]. By contrast, values higher than 65% are common for steel and aluminium [34]
[41], which do not even require intermediate annealing (see Table 2.3).
(vi) In the currently available magnesium sheet alloys, full or partial annealing following the
H24 temper are the most usual conditions [42]. The choice depends on the degree of SRX
needed for the strength-toughness/formability balance desired for the final application.
2. LITERATURE REVIEW
-25-
2.1.3 Current limitations of magnesium sheet for automotive applications
In general, magnesium sheet is only scarcely used in the industry, with the aerospace sector being
its main market nowadays [31]. A range of obstacles [15] [20] hinder the effective introduction of
magnesium sheet into more general applications such as the automotive:
• Relatively high corrosion rates.
• Poor creep resistance and limited strength at elevated temperatures.
• Marked compromise between strength and toughness/formability: alloys strong enough to
compete with aluminium and steel exhibit poor toughness and formability, and vice versa
[20]. An overview of the tensile properties of commercial magnesium sheet alloys is given
in Figure 2.3.
• Poor formability at low temperature (below around 250°C). As dealt with in Section 2.3,
this arises from the specifics of the deformation modes available in its hexagonal close-
packed (HCP) crystal structure [22] [31] [43], and negatively affects both the production of
sheet with rolling and the downstream forming of sheet into end components [15] [23] [44]
[45].
Figure 2.3. Typical tensile properties of the main commercial magnesium sheet alloys employed up to date (compilation from [31] [35] [40] [46] [47]). The dotted line represents the decreasing trend of ultimate strength with elongation.
About the latter obstacle, the surface finish provided by either hot rolling or hot sheet forming is
unacceptable for the quality standards of BIW parts [15] [17]. Hence, the ability to perform both at
room temperature is an unavoidable requisite for the practical introduction of magnesium into this
application [23]. Even so, the scarce strain levels that magnesium can sustain per step without
failure (see Section 2.2) mean that the amount of stages required for its forming is much larger than
for e.g. aluminium or steel. This increases machinery and operation costs well above those resulting
0
5
10
15
20
25
100 150 200 250 300 350
Un
ifo
rm e
lon
gati
on
(%
)
Ultimate tensile strength (MPa)
LA141
ZE10
ZM21
AZ31
HM21
ZK31 ZM21
AZ31
HK31
AZ61 O (fully annealed) H24 (part. annealed) T7 (naturally aged) T8 (artificially aged) F (as-hot rolled)
2. LITERATURE REVIEW
-26-
for the latter [15] [17] [22] [31], decisively compromising the competitiveness of cold-formed
magnesium in high-production sectors such as the automotive. For the particular case of cold
rolling, cold-rolled magnesium sheet has been quoted as three to five times more costly than
comparable aluminium stock [24] despite prices of the raw materials being roughly the same [21].
2.1.4 Commercially available magnesium sheet alloys and further developments
Among the few magnesium sheet alloys currently available, AZ31 is by far the most common [48]
[49]. This has been ascribed to relatively good strength-formability balance [31]. The others aim at
countering its main limitations, especially poor creep behaviour above 100°C [50] and low cold
formability [51] (Table 2.1). In this sense, two main alloying additions have been identified to hold
the potential to overcome the latter limitation: lithium and RE elements.
Table 2.1. Chemical composition and summary of properties of the main commercial magnesium sheet alloys used up to date (compiled from [31] and [35]).
ASTM
name
Nominal alloying content (wt%) Summary of properties
Al Zn Mn Zr Ce Th Li
AZ31 3 1 0.3 Medium strength, weldable
AZ61 6.5 1 0.3 High strength, weldable
ZK31 3 0.7 High strength, creep resistance, not weldable
ZM21 2 1 Low strength, good formability, weldable
HK311 0.7 3.2 Creep resistance (up to 320°C), weldable
HM211 0.8 2 Creep resistance (up to 350°C), weldable
LA1412 1 0.2 14 Low strength, good formability, lightweight
ZE103 1.2 0.2 Low strength, high formability
1 No longer used owing to the environmental restrictions imposed in the use of thorium
2 No longer used 3 Recent development
On the one hand, attention has been historically devoted to the Mg-Li system not only due to its
improved cold formability, but also to its condition as the lightest group of magnesium alloys [45]
[52] [53]. For Mg-Li alloys, improved cold formability has been observed both under rolling [45] [52]
and sheet forming [53]. However, the cost of Mg-Li alloys is prohibitive [47] [54], and they lack
sufficient strength [46] [48] [54] even in the presence of ternary additions [20] (see LA141 in Figure
2.3). As a result, industrial use has been limited to scarce applications of the LA141 alloy (see Table
2.1) in the aerospace industry in the 1960s [47].
On the other hand, Mg-RE alloys have attracted the greatest deal of interest in recent years. In the
same way as for Mg-Li alloys, improved formability has been observed under both cold rolling and
downstream sheet forming (see Section 2.2). By contrast, unlike for those, benefits arise even for
2. LITERATURE REVIEW
-27-
low contents [35], meaning that economic competitiveness is not dramatically compromised.
Furthermore, the effect has also been found when RE elements are included as ternary additions
[55] [56] [57]. As for this, the newly developed ZE10 alloy (see Table 2.1), claimed to be the most
cold-formable of magnesium sheet alloys to date [31], represents a prime example. RE additions
are also beneficial for creep resistance and strength [20] [31], both lying among the limitations of
magnesium sheet.
To sum up, the economic competitiveness of cold-rolled magnesium sheet against aluminium and
steel is an unavoidable condition for magnesium to be practically introduced in BIW applications.
However, this is compromised at present by the low cold formability of traditional alloys, as for
which Mg-RE alloys emerge as the most promising alternative. Formability of conventional and Mg-
RE alloys is discussed in Section 2.2. As will be shown in Section 2.3 and 2.4, incomplete knowledge
of the forming response of magnesium alloys in terms of the effect of microstructural variables
constitutes a barrier for transforming the potential of Mg-RE alloys into real, widespread
applications.
The cold formability of magnesium sheet
In this section, the formability of magnesium sheet alloys is contrasted with that of aluminium and
steel. For this aim, AZ31 and ZE10 (Section 2.1.4) have been chosen to represent conventional and
Mg-RE alloys, respectively. For steel and aluminium, the current alloys of choice for automotive
roof panels –the most likely future BIW application for magnesium sheet [7] [18], e.g. Figure 1.2–
are considered whenever possible, i.e. 6016-T4 aluminium [58] and DP600 steel [59]. For the
comparison, forming limit diagrams (FLDs) are employed as a starting point, and special attention
is then paid to the most relevant strain paths.
Forming limit diagrams (FLDs) [60] are widely used in sheet metal forming, and represent sheet
formability as a function of strain path. They are obtained by drawing sheets with different initial
geometries with a punch, and recording the major and minor strains in the sheet plane (𝜀1, 𝜀2) just
prior to failure through grid optical measurement techniques. The strain component along sheet
thickness 𝜀3 is often calculated assuming volume constancy [61] (Equation 2.1). For FLDs, failure is
usually defined as the onset of localised necking. For the specific case of the materials considered
here, FLDs display that, while the formability of AZ31 is significantly below that of aluminium and
steel throughout strain paths, that of ZE10 lies at essentially the same level of aluminium (Figure
2.4).
𝜀1 + 𝜀2 + 𝜀3 = 0 (2.1)
2. LITERATURE REVIEW
-28-
Figure 2.4. FLDs corresponding to AZ31 (conventional magnesium) [35], ZE10 (Mg-RE alloy) [35], 6016-T4 (aluminium) [62] and DP600 (steel) [63] . The dashed line represents the strain path of equi-biaxial tension, the dotted line that of
ideal uniaxial tension, and the dot-dash line that of plane strain.
Within FLDs, three main strain paths are practically relevant: uniaxial tension, biaxial tension and
plane strain. For each, specific tests can give an account of formability in a simpler way than the
grid analysis required for FLDs. Previous measurements for the materials of interest are presented
below, together with the specific relevance of each path and the nature of the strain components
whereby it is defined (see Table 2.2).
Table 2.2. Strain along the three main directions of sheet material for the strain paths most relevant for understanding sheet formability. Uniaxial tension is considered parallel to the RD and the TD, respectively.
Strain Path RD TD ND
Uniaxial Tension (|| RD) 𝜀1 > 0 𝜀2 = −𝜀12
𝜀3 = −𝜀12
Uniaxial Tension (|| TD) 𝜀2 = −𝜀12
𝜀1 > 0 𝜀3 = −𝜀12
Biaxial Tension 𝜀1 > 0 𝜀2 > 0 𝜀3 < 0
Cold Rolling 𝜀2 > 0 𝜀1 = 0 𝜀3 < 0
Owing to the simplicity of the tensile test, uniaxial tension is the strain path most generally used to
assess metal formability including that of sheet. Upon tensile testing, extension is applied in one of
the directions in the sheet plane (RD or TD, 𝜀1>0). Ideally, the compression fulfilling volume
constancy is equally accommodated by sheet thickness and the direction normal to the load in the
sheet plane (𝜀2 = 𝜀3 = – 𝜀1
2) (Table 2.2). Formability under uniaxial tension is customarily provided
by total elongation at failure (ductility), albeit elongation at the onset of diffuse necking (uniform
elongation) is sometimes used. For the materials of interest here, Figure 2.5 demonstrates that no
significant differences exist between steel, aluminium and either conventional or Mg-RE alloys in
0
0.1
0.2
0.3
0.4
0.5
0.6
-0.2 -0.1 0 0.1 0.2
Maj
or
stra
in ε
1
Minor strain ε2
AZ31
ZE10
6016-T4
DP600𝜀1=𝜀2𝜀1=−𝜀2
2
𝜀2= 0
2. LITERATURE REVIEW
-29-
terms of ductility. Moreover, FLD measurements accounting for uniaxial tension (dotted line in
Figure 2.4) suggest only minor differences between all of them. Accordingly, ductility has often
been quoted as unsuitable to represent the low formability of magnesium [31] [35], and the claim
is often made that, for understanding magnesium formability, attention needs to be paid to the
actual paths of interest, e.g. [64] [65] [66] [67].
Figure 2.5. Erichsen value (biaxial tension) as a function of ductility (uniaxial tension) for AZ31 (conventional magnesium) [68] [69] [70] [71], ZE10 (Mg-RE alloy) [68] [72] [73], 6016-T4 (aluminium) [74] [75] and DP600 (steel) [76]
[77].
Biaxial tension is commonly employed to provide an idea of sheet formability upon sheet metal
forming, as it is often the limiting strain state in such operations [61]. In biaxial tension, extension
is imposed in two directions of the sheet plane (𝜀1,𝜀2>0), so that the compression needed to fulfil
volume constancy can only be accommodated by sheet thickness (𝜀3>0) (Table 2.2). The case of
equi-biaxial tension (𝜀1 = 𝜀2) is customarily assessed in practice with cup stretch tests such as the
Erichsen test [78] (Figure 2.17). Formability under biaxial tension (stretch formability) is thereby
given by the maximum cup height that can be drawn without cracking (e.g. Erichsen value [78]). In
this sense, Figure 2.5 indicates that only about half cup height is possible for AZ31 compared to
aluminium or steel. However, ZE10 succeeds in providing similar stretch formability to aluminium.
As explained in Section 2.1.3, the strain path of cold rolling is not less practically relevant for the
production of sheet components. However, it has not been so actively studied because thickness
reductions per pass are limited in traditional, ductile metals only by machine stability and power
considerations [34]. Nevertheless, a few studies have been conducted, and early research found for
conventional magnesium a maximum reduction possible over six times lower than for steel or
aluminium [33] (Table 2.3). More recently, Sandlöbes et al. have reported a maximum reduction
over four times higher for a Mg-RE alloy than for the pure metal [29] (Table 2.3).
0
2
4
6
8
10
12
0.1 0.15 0.2 0.25 0.3
Eric
hse
n v
alu
e
Ductility
AZ31
ZE10
6016-T4
DP600
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Table 2.3. Maximum rolling reduction before edge cracking in one pass for magnesium, steel and aluminium alloys.
Alloy Rolling reduction limit Ref.
Mg-3Zn 12%
[33]
Al-Cu 70%
Mild Steel 80%
Al-5Mg 81%
Duralumin® 83%
Pure Mg 8% [29]
Mg-3Y 40%
In addition, the case of cold rolling can be related to that of plane strain in the FLD (dot-dash line in
Figure 2.4): in the same way as in cold rolling (Table 2.2), extension in the sheet plane (𝜀1>0) is
balanced by thickness compression (𝜀3<0). In this respect, Figure 2.4 suggests again comparable
formability for ZE10 and aluminium, but significantly lower for AZ31. Moreover, it has often been
noted that, whereas stretch formability is higher than plane strain formability for aluminium and
steel, both are at the same level in conventional magnesium alloys [65] [79] [80] [81]. However,
formability of ZE10 is higher under biaxial tension than under plane strain (Figure 2.4).
In summary, ductility has been observed to break down in accounting for magnesium formability.
Therefore, the actual strain paths of interest should be considered in related studies, with biaxial
tension and that of cold rolling being most relevant to sheet component production. In this sense,
while aluminium and steel consistently exhibit higher formability than conventional magnesium
alloys across strain paths, that of RE-containing alloys lies at the same level of aluminium. In what
follows, reasons for the poor formability of conventional alloys as well as its variation across strain
paths are discussed in the light of the current knowledge of the plastic behaviour of magnesium.
Changes therein induced by RE additions are dealt with subsequently in search for the rationale
behind the formability improvements which they impart.
The plastic deformation of conventional magnesium sheet
Renewed interest in magnesium has resulted in an outburst of studies on its plastic behaviour in
the last fifteen years. Accordingly, the formability of conventional magnesium alloys under the
various strain paths is now believed to be determined by the specific balance between the various
deformation modes available in its HCP structure, namely a range of slip and twinning systems.
Such balance gives rise during rolling to a certain texture fibre whose relative strength is, together
with grain size, the main microstructural variable identified to affect relative deformation mode
activity and, thereby, formability.
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2.3.1 Slip modes in magnesium
Dislocation slip modes available in HCP structures are well-established [82] [83], and have been
summarised in Table 2.4. Despite seven modes theoretically available, ⟨𝑐⟩ dislocations are sessile
[43] [82], and only those with ⟨𝑎⟩ or ⟨𝑐 + 𝑎⟩ Burgers vectors can accommodate plastic strain in
practice. The slip planes and directions of the five glissile modes are represented within the HCP
elemental cell in Figure 2.6.
Table 2.4. Elements of the deformation slip modes possible in HCP crystal structures, including the number of independent systems provided by each (adapted from [82] and [83]).
Slip system Burgers
vector
Slip
direction
Slip
plane
Number of
independent systems
Basal < 𝑎 > < 112̅0 > (0001) 2
Prismatic < 𝑎 > < 112̅0 > {101̅0} 2
Pyramidal 1st order I < 𝑎 > < 112̅0 > {101̅1} 4
Pyramidal 1st order II < 𝑐 + 𝑎 > < 112̅3 > {101̅1} 5
Pyramidal 2nd order < 𝑐 + 𝑎 > < 112̅3 > {12̅12} 5
Axial I < 𝑐 > < 0001 > {101̅0} 2
Axial II < 𝑐 > < 0001 > {12̅10} 2
Figure 2.6. Slip directions and planes of the slip modes glissile in HCP crystal structures [84].
Historically, the behaviour of all the slip systems active in magnesium has been characterised by
critical resolved shear stress (CRSS) values. These have been customarily determined by applying
Schmid factors [85] to the yield stress obtained in mechanical tests on purposely oriented single
crystals. A summary of former CRSS observations for pure magnesium at ambient temperature is
given in Table 2.5. The type of test is also indicated: uniaxial testing or plane-strain compression
(PSC). As shown in Table 2.5, higher CRSSs have been consistently reported under PSC, which has
been attributed to the additional constraint to strain in one of the directions (see Section 3.3.4)
[86]. Moreover, unlike for uniaxial tests, no slip modes other than basal have been encountered to
be active at the yield regardless of single crystal orientation [86] [87] [88].
Pyramidal 1st order II
1123
(112̅2)
1123
Basal Prismatic
(011̅1)
Pyramidal 1st order I
Pyramidal 2nd order
(011̅1)
112̅0 = < 𝑎 >
(011̅0)
0001 = < 𝑐 >
112̅0 = < 𝑎 > 112̅0 = < 𝑎 >
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Table 2.5. Room-temperature CRSSs for the main deformation modes active in magnesium as measured in pure magnesium single crystals (compilation from various sources).
Deformation mode CRSS (MPa) – Uniaxial testing CRSS (MPa) – PSC testing
Basal < 𝑎 > slip 0.5-1 [89] [90] [91] 3-5 [86] [88]
Prismatic < 𝑎 > slip 40-50 [90] [92] N/A
Pyramidal < 𝑐 + 𝑎 > slip 40-80 [93] [94] [95] N/A
Tension twinning 2.4 [96] 7 [86]
Contraction twinning 115 [97] 130-150 [86] [87]
As shown in Table 2.5, basal ⟨𝑎⟩ slip is by far the most easily activated slip mode in magnesium, i.e.
the ‘softest’ [86] [88] [89] [98]. By contrast, higher stress levels are required to activate either ⟨𝑎⟩
pyramidal or ⟨𝑎⟩ prismatic slip, which are thus ‘harder’. Both non-basal ⟨𝑎⟩ slip modes have been
proved to arise in magnesium from the same source: the cross-slip of ⟨𝑎⟩ dislocations gliding in
(0001) planes into {101̅0} and {101̅1} planes, respectively [90] [99] [100] [101]. As a result, ⟨𝑎⟩
pyramidal and prismatic slip are usually regarded as a part of the same effect [43]. Only prismatic
slip will thus be mentioned hereinafter when referring to it.
With regard to ⟨𝑐 + 𝑎⟩ slip, Table 2.4 shows that two possibilities exist in HCP crystals depending
on slip plane. Nonetheless, although glide in {101̅1} planes has been experimentally found (e.g.
upon cold rolling in [30]), {12̅12} slip has been more usually reported [30] [86] [93] [94]. In this
sense, more research is needed to elucidate why and under which conditions {101̅1} slip is more
easily activated. Irrespective of slip plane, ⟨𝑐 + 𝑎⟩ is the ‘hardest’ slip mode in magnesium (Table
2.4) [89] [102]. Furthermore, despite some observations in single crystals [93] [94] [95], it seems
more frequent in polycrystalline aggregates [89] [103] [104], reasons for which are discussed in
Section 2.3.6.
Ductile behaviour of polycrystals has often been rationalised in crystal plasticity with Von Mises’
criterion [85], which states that at least five independent deformation systems are required for a
polycrystal to accommodate homogeneous strain. In the case of magnesium, Table 2.4 shows that
basal and prismatic slip can only give four separate systems. The ⟨𝑎⟩ pyramidal modes are linear
combination of basal and prismatic, i.e. of no additional help [82] [83] [103]. Hence, activation of
⟨𝑐 + 𝑎⟩ slip would be required for magnesium to comply with Von Mises’ criterion, so that its ‘hard’
character has thus been often related to its scarce formability [30] [86] [89] [103]. What is more,
⟨𝑐 + 𝑎⟩ slip is the only slip mode able to accommodate strain along the 𝑐 axis of the HCP cell. As
will be discussed below, this is believed to play a key part in the poor formability of magnesium.
2. LITERATURE REVIEW
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To sum up, the difficulty of both ⟨𝑐 + 𝑎⟩ and non-basal ⟨𝑎⟩ slip in operating in magnesium at room
temperature has often been suggested to account for its poor formability. Even so, the operability
of either has been encountered to be significantly affected by factors such as texture or grain size,
all of which are dealt with below.
2.3.2 Twinning modes in magnesium
The scarcity of easily activated slip modes in HCP crystals has been related to the profuse amount
of deformation twinning they tend to exhibit [82] [83]. An extensive review of past observations in
HCP metals is given in [105]. In magnesium, two modes have been mainly found to be active [105]
[106] [107] [108]: {101̅2} tension twinning and {101̅1} contraction twinning (Figure 2.7 and Table
2.6). These names arise from their distinct polarities: {101̅2} twinning is activated by the extension
of the 𝑐 axis of the HCP cell, and {101̅1} twinning by its contraction. {101̅2} twinning is self-
conjugate, while the {101̅1} mode has a conjugate system in the {101̅3̅} plane [105] [108].
Table 2.6. Elements, resultant shear strains and misorientation angles about the ⟨121̅0⟩ axis for the main twinning modes in magnesium crystals. Misorientations after double twinning are also given [105].
Twinning plane Twinning direction Polarity Shear strain Misorientation
{101̅2} < 101̅1 > Tension 0.131 86°
{101̅1} < 101̅2̅ > Contraction 0.138 56°
{101̅3̅} < 303̅2 > Contraction 0.138 64°
{101̅1}-{101̅2} – Double – 38°
{101̅3}-{101̅2} – Double – 22°
Figure 2.7. Twinning directions and planes of the main twinning modes commonly observed in magnesium crystals [84].
As well as having opposed polarities, both twinning modes differ significantly in terms of ease of
twin nucleation. Using an analogy with deformation slip, this has been assessed in magnesium by
CRSS values. As shown in Table 2.5, these are around one order of magnitude lower for tension
twinning than for contraction modes [86] [87] [96] [97]. Therefore, although not challenging the
condition of basal slip as the most easily activated deformation mechanism, tension twinning is
regarded as ‘soft’, and contraction twinning –in the same way as ⟨𝑐 + 𝑎⟩ slip– as ‘hard’ [31] [107].
(011̅2)
01̅11
Tension Twinning
(011̅3)
03̅32 01̅12
(011̅1)
Contraction Twinning
2. LITERATURE REVIEW
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Regarding twin growth, similar conclusions have been drawn. Tension twins are usually thicker and
grow readily to consume all the parent grain [107] [109] [110] [111]; by contrast, contraction twins
remain in the form of thin bands [106] [108] [110] [111]. What is more, tension twins tend to be
thicker the softer the orientation of the parent grain [107] [109] [112], whereas contraction twins
exhibit no significant differences in this sense [110] [113]. The latter has been ascribed to the
limited character of contraction twin growth in all situations [110].
Precisely activated by 𝑐 axis strain, twinning modes are an alternative to ⟨𝑐 + 𝑎⟩ slip for fulfilling
the five independent systems in Von Mises’ criterion as well as for sustaining strain parallel to the
𝑐 axis [22] [82] [83] [106]. In fact, magnesium single crystal research has predominantly observed
twinning to initiate plastic deformation in single crystals oriented with 𝑐 axes parallel to the load,
e.g. [86] [87] [88] [97] (tension twinning for tensile load, contraction twinning for compressive
load). On the other hand, ⟨𝑐 + 𝑎⟩ slip has only been found in a few cases [93] [94] [95]. Even so,
CRSS values measured under 𝑐 axis compression question this view (Table 2.5): when effectively
found, lower CRSSs have been measured for ⟨𝑐 + 𝑎⟩ slip than for contraction twinning, casting
doubt on the accuracy of single crystal studies on the identification of ⟨𝑐 + 𝑎⟩ slip. Anyhow, as
discussed below, competition between twinning and ⟨𝑐 + 𝑎⟩ slip in accommodating 𝑐 axis strain
has far-reaching effects on the plastic behaviour of magnesium.
Finally, Table 2.6 shows that the amount of strain that can be attributed to twinning itself is, for
either mode, only moderate. Particularly, theoretical calculations have proved that a magnesium
single crystal subjected to uniaxial testing will undergo a maximum macroscopic strain of 0.065 if
fully tension-twinned [83] [88]. For contraction twinning, although the resultant unity shear strain
is slightly higher (Table 2.6), the limited character of its growth would be expected to drastically
diminish its contribution to overall strain.
To sum up, difficulty in the activation of non-basal slip renders deformation twinning highly active
in magnesium. Specifically, tension and contraction twinning modes strongly differing in ease of
activation and growth are operative. However, only moderate contribution to plastic strain may be
expected from either at best. Yet, as will be discussed in Section 2.3.4, associated effects are
believed to decisively affect the formability of magnesium.
2.3.3 The basal texture of rolled magnesium
As will be displayed in following subsections, crystallographic texture exerts a powerful effect on
the plastic behaviour and formability of magnesium. In this sense, typical textures of conventional
magnesium sheet are presented below, and discussed in terms of their formation during the
processing of the material by rolling and further annealing.
2. LITERATURE REVIEW
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During deformation processing, texture evolution would be expected to be driven by the most
active deformation mechanisms. As illustrated above, basal slip and tension twinning are the softest
in magnesium, the operation of each leading to the following reorientations:
• On the one hand, crystal rotations by dislocation slip tend to align slip planes normal to the
directions of compression [98]. Under the strain path of rolling (Table 2.2), basal slip would
thus be expected to rotate grains until basal (0001) planes are parallel to the RD-TD plane,
i.e. 𝑐 axes parallel to the ND.
• On the other hand, tension twinning operates so that stretched 𝑐 axes are reoriented by
angles close to 90° (≈86°, Table 2.6). As extension is parallel to the RD upon rolling, 𝑐 axes
would be realigned towards the ND-TD plane. All possible orientations in this plane are
favourable to basal slip except for –again– that of 𝑐 axes parallel to the ND.
Figure 2.8. {0001} pole figures for pure magnesium sheet (a) hot-rolled and (b) subsequently cold-rolled to 30% reduction. Band contours correspond to 2x, 4x, 6x… MRD. The basal fibre is displayed in both conditions, with the latter
clearly showing a sharper texture [28].
Experimental texture measurements in rolled magnesium effectively confirm a prevalent trend for
𝑐 axes to be aligned with the ND. Conventionally, a single texture fibre with this orientation and
usually referred to as basal fibre is typically found in both hot- [29] [55] [114] [115] and cold-rolled
[28] [29] [103] [116] magnesium (Figure 2.8). Basal texture intensity typically increases with
thickness reduction [28] [29] [117], which has been associated to gradual basal slip and tension
twinning [28] [29] [117]. Accordingly, texture modelling upon cold rolling by Styczynski et al. [116]
has suggested that basal slip is the most active deformation mechanism irrespective of thickness
reduction; tension twinning also plays a relevant role, but in early stages only (Figure 2.9). Even so,
removal of tension twinning from polycrystal modelling accounting for the strain path of cold rolling
has been repeatedly found to underestimate basal texture intensity [111] [117], outlining the key
role of this mode in the formation of basal textures.
(a) (b)
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Figure 2.9. Contribution of the deformation mechanisms available in magnesium to the reduction imparted by cold rolling as predicted by texture modelling using a Taylor polycrystal model. An initially random texture and conventional
room-temperature CRSS values –except for contraction twinning, not considered in the model– are assumed [116].
Upon annealing, basal textures have been observed to be mostly preserved [35] [45] [118]. This has
been ascribed to the dominance of grain boundary nucleation (GBN) as SRX mechanism [119],
known to essentially retain deformation textures [35]. Nevertheless, annealing does affect texture
intensity. On the one hand, SRX in magnesium has generally been found to weaken basal textures
[120] [121] [122] [123], which has been related with GBN producing a range of orientations about
the original [35] [124]. On the other hand, subsequent grain growth has been normally displayed
to increase basal texture intensity [57] [118] [120] [125] [126] [127], e.g. Figure 2.10.
Figure 2.10. Basal texture intensity after the isochronal annealing of hot-rolled AZ31 sheet at various temperatures. The pre-annealing texture intensity is also displayed for the sake of comparison (redrawn from [120]).
In conclusion, powerful activation of basal slip and tension twinning upon rolling gives rise to the
formation of relatively strong basal fibres in conventional magnesium sheet, which are essentially
retained during annealing. The intensities of such textures depend on both rolling and annealing
Original condition
Grain Growth
Static Recrystallisation
Annealing temperature (°C)
1000 200 300 400 5005
7
99
11
13
15
(00
02
) P
ole
figu
re in
ten
sity
(M
RD
)
2. LITERATURE REVIEW
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operations, and specifically on the amount of grain growth imparted in the latter. The far-reaching
effect of basal textures on the formability of conventional magnesium is treated in Section 2.3.5.
2.3.4 The role of deformation mechanisms in the plastic behaviour of magnesium sheet
With the aim of conquering its plastic behaviour, the interplay between the various deformation
modes described above has been extensively studied for magnesium sheet subjected to different
mechanical test types. On the one hand, no qualitative differences have been essentially found
under uniaxial compression (UAC) and PSC testing, the latter of which can account for the strain
path of cold rolling. On the other hand, plainly distinct response has been observed under tensile
testing, which imparts uniaxial tension. By contrast, the case of biaxial tension has been hardly
considered, partly due to the difficulty in monitoring work hardening upon cup testing. All these
are discussed below, together with the role of deformation modes in leading to ultimate fracture,
suggested to be similar across strain paths, but holding distinct implications for each.
2.3.4.1 Behaviour under uniaxial (UAC) and plane-strain compression (PSC)
For the cases of UAC and PSC testing, two extreme orientations of the customary basal texture have
been mainly considered: (i) c axis compression, where the compressive load is parallel to the ND
i.e. 𝑐 axes are prevalently subjected to contraction; and (ii) c axis extension, where the ND is tilted
by 90° i.e. the bulk of 𝑐 axes undergo tension (see Figure 2.11). The most detailed studies have
been performed by Knezevic et al. [106] and Proust et al. [128] for UAC, and Mu et al. [111] and
Barnett and Keshavarz [129] for PSC. In terms of twinning, 𝑐 axis compression is favourable to the
contraction mode, and 𝑐 axis extension to the tension mode. PSC carried out in 𝑐 axis compression
corresponds to the strain path of cold rolling (see Section 3.3.4).
As demonstrated by Figure 2.11, stress-strain curve shapes resulting from UAC and PSC testing
differ significantly under both orientations: whereas 𝑐 axis compression leads to classic “concave-
down” curves characterized by decreasing work hardening, 𝑐 axis extension gives rise to a distinct
“concave-up” shape that has been described in terms of three stages [111] [128] (see Figure 2.12
(a)): elasto-plastic transition (Stage I), increasing work hardening (Stage II), and decreasing work
hardening up to fracture (Stage III). In metals, decreasing work hardening is usually associated to
deformation by slip, and increasing work hardening to deformation by twinning [130] [131]. The
role of the various deformation modes under each of these stages is discussed below in the light of
previous studies.
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Figure 2.11. (a) Stress-strain curves and (b) evolution of work hardening with strain for AZ31 tested under UAC in the c axis extension (Compression TD-RD) and c axis compression (Compression ND) texture orientations. Pole figures for the
initial textures in the two cases are also given, in which the direction of the load is perpendicular to paper [111].
Figure 2.12. (a) Stress-strain and work hardening curves, and (b) relative contribution of the various deformation mechanisms corresponding to the PSC of AZ31 tested under 𝑐 axis extension (Ba = basal slip, ETW = tension twinning,
CT/CTW = contraction twinning, Pr = prismatic slip, Py: <c+a> slip). A cluster-type deformation texture grain interaction (GIA) model considering (i) slip hardening with a one parameter law and (ii) twin hardening by reduction in the
dislocation free path length has been used [111].
According to the favourable orientation under 𝑐 axis extension, polycrystal models have repeatedly
suggested that strain accommodation upon Stage II is dominated by tension twinning, albeit basal
slip being also relevant [111] [128] (Figure 2.12 (b)). The occurrence of extensive tension twinning
in Stage II has been effectively confirmed by electron backscatter diffraction (EBSD) [106] [111]
[128] [129]: most grains nucleate tension twins at the onset of the stage, which grow then to
2. LITERATURE REVIEW
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consume whole parent grains until the stage is exhausted [106] [111]. Under 𝑐 axis extension, the
elasto-plastic transition has been related to the operation of basal slip until a critical dislocation
accumulation threshold is reached that activates tension twinning [106] [128]. Tension-twinned
fractions of 80-90% have been measured under 𝑐 axis extension [128] [129], with sharp basal
textures (𝑐 axes parallel to the ND) already formed at the end of Stage II [106] [111] [128]. The
abrupt interruption in the increase of stress giving way to Stage II has been related to the ease of
growth of tension twins once nucleated [86] [87] [88] [106] [107]. Furthermore, work hardening
rates during this stage have been assessed as “strikingly” [132] high (e.g. one order of magnitude
higher than in HCP titanium [106]), the origin of which has attracted intense debate in recent years.
Specifically, the “hard” grain orientations imparted by tension twinning [106] [129], tension twin
boundary hardening [111] [128], and latent hardening by dislocations emitted for twin
accommodation [133] have all been proposed. However, polycrystal models have repeatedly found
the combination of these effects unable to fully account for work hardening in the last part of Stage
II (from e.g. ≈0.07 strain in Figure 2.12 (a)), and then in Stage III [111] [133].
After basal textures are formed, deformation modes able to sustain 𝑐 axis compression become
necessary. Polycrystal models effectively predict that basal slip activity is accompanied by ⟨𝑐 + 𝑎⟩
slip and contraction twinning in Stage III [111] [128] (Figure 2.12 (b)). In particular, EBSD analysis
has shown that contraction twins appear somewhat (≈0.02 strain) earlier than Stage II exhaustion
[111]. The decreasing work hardening in Stage III –indicating slip dominancy– agrees with the low
strain contribution expectable from the small thickness of contraction twins [106] [111] (Section
2.3.2). Yet, modelling by Mu et al. has highlighted their key role in work hardening: implementation
of the dislocation mean free path reduction by contraction twin boundaries has made it possible to
accurately predict work hardening rates in both Stage II and III [111]. As for textures, they have
been found to be weakened slightly across Stage III [106] [111]. Both ⟨𝑐 + 𝑎⟩ slip [68] [103] [115]
and contraction twinning (Section 2.3.4.3) can reorient 𝑐 axes away from basal orientation.
Under 𝑐 axis compression, Knezevic et al. have reported that both work hardening and texture
evolution are similar to those in the Stage III of 𝑐 axis extension [106] (see Figure 2.11 (b)). What is
more, modelling by Proust et al. predicted similar balance between deformation mechanisms in the
two cases [128]. Following the unfavourable orientation of the initial texture, tension-twinned
fractions lower than 10% have been reported for 𝑐 axis compression [128] [129]. Going one step
further, Barnett and Keshavarz analyzed a range of tilting angles between 𝑐 axis compression (tilting
= 0°) and extension (tilting = 90°), finding a monotonic reduction in both tension-twinned fraction
and the extent of Stage II the closer to 𝑐 axis compression [129].
2. LITERATURE REVIEW
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2.3.4.2 Behaviour under uniaxial and biaxial tension
The role of deformation modes in uniaxial tension has also been analysed by a range of authors.
Detailed studies have been carried out by Proust et al. [128], Barnett and Keshavarz [129] and
Agnew and Duygulu [134]. By contrast, biaxial tension has been scarcely studied, although related
studies are also presented below. For both uniaxial and biaxial tension, 𝑐 axis extension has not
been considered due to the intrinsic difficulty in manufacturing tensile and cup specimens parallel
to the ND i.e. to the bulk of 𝑐 axes. On the contrary, conventional tensile and cup testing in the
sheet plane is normal to the ND, thus promoting 𝑐 axes compression.
Following the unfavourable initial orientation for tension twinning, “concave-up” stress-strain
curves have been customarily obtained after tensile testing of magnesium, e.g. [20] [106] [128]
[129] [130] [134]. In fact, tension-twinned fractions [128] and final textures [128] [135] similar to
those resulting from UAC and PSC under 𝑐 axis compression have been reported. Yet, significant
differences have been found in terms of strain accommodation: unlike for UAC or PSC, polycrystal
modelling has consistently ascribed a predominant role to prismatic slip (60-70% of total strain
accommodation [128] [134], e.g. Figure 2.13 (a)); the rest would be essentially sustained by basal
slip [128] [134]. Extensive prismatic slip in tensile testing has been confirmed by slip trace analysis
[129] (Figure 2.13 (b)) and transmission electron microscopy (TEM) dislocation analysis [134], with
over 50% of ⟨𝑎⟩ dislocations identified to be non-basal by Agnew and Duygulu [134]. The distinct
character of work hardening under uniaxial tension has been underlined by the Sachs-based model
developed by Barnett and Keshavarz, which considered basal slip and tension twinning only [129]:
whereas UAC and PSC behaviour were modelled to reasonable accuracy, this was not the case of
tensile testing, which was attributed to the dominant role of prismatic slip [129].
Figure 2.13. (a) Contribution of the various slip mechanisms to deformation of AZ31 under uniaxial tension as a function of the ratio between the CRSSs for prismatic and <c+a> slip as predicted by viscoplastic self-consistent modelling. Ratios
higher than 2 were suggested for room temperature [134]. (b) Profuse prismatic slip observed in AZ31 after uniaxial tension [129].
2. LITERATURE REVIEW
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Such disparate activation of prismatic slip under uniaxial tension and UAC or PSC was rationalized
by Barnett and Keshavarz using Schmid factor reasoning [129]. Considering the CRSS values best
fitting their Sachs model, prismatic slip would effectively be the most easily activated mode in
uniaxial tension for 𝑐 axes inclinations coinciding with the basal texture (Figure 2.14 (a)). On the
other hand, prismatic slip would be prevented from playing a relevant role under UAC or PSC by
the polarity of tension twinning [129] (Figure 2.14 (b)). Noteworthily, the ratio of CRSSs between
prismatic and basal slip predicted by the model was remarkably lower than suggested by single
crystal studies [129]. This is in agreement with other polycrystal models, which have invariable
found ratios within 2-2.5 (Figure 2.14 (a)) [128] [129] [134] against 40-80 for single crystals (Table
2.5). This apparent promotion of prismatic slip in polycrystalline magnesium has been ascribed to
compatibility effects enforcing ⟨𝑎⟩ dislocation cross-slip [129], especially at grain boundaries [134]
[136] [137] (see Section 2.3.6).
Figure 2.14. Macroscopic critical stress applied (ratio between CRSS and Schmid factor 𝑚, Schmid’s law) for the main deformation mechanisms in magnesium under (a) uniaxial tension and (b) uniaxial compression (twinning accounts here
for tension twinning). The angle represents 𝑐 axis inclination with respect to the direction of the stress [129].
Under biaxial tension, TEM analysis by Chino et al. found the vast majority of ⟨𝑎⟩ dislocations to be
basal and not prismatic [65]. In contrast with the uniaxial case, this suggested a marginal role for
prismatic slip in biaxial tension. The apparent disagreement between paths was rationalized by the
authors in terms of the different strain components imposed by each as indicated in Section 2.2
[65]. On the one hand, stress is fixed under uniaxial tension in one direction only. In ductile metals,
the ideal case of the compression required by compatibility being equally accommodated by the
two normal directions is fulfilled (Table 2.2); on the contrary, in basal-textured magnesium, the
hard character of 𝑐 axes strain would promote accommodation by prismatic slip in the sheet plane
rather than by sheet thickness. In fact, sheet thinning [138] and contraction twinning [127] under
2. LITERATURE REVIEW
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uniaxial tension have been reported just before diffuse necking only, when prismatic slip could be
thought to be exhausted. On the other hand, stress is applied under biaxial tension in two directions
of the sheet plane. The compression ensuring compatibility must thus necessarily follow sheet
thickness (Table 2.2), enforcing 𝑐 axes strain since the beginning so that any prior prismatic slip in
the sheet plane is prevented.
2.3.4.3 Behaviour at ultimate failure
Apart from imparting work hardening as suggested above, the activation of contraction twinning
when strong basal textures are present is believed to play a vital role in the ultimate fracture of
magnesium. This has been related to various effects sequentially following contraction twinning:
double twinning, shear banding and void nucleation. All are described below in conjunction with
implications for the formability of magnesium under the various strain paths.
Due to the crystal orientation within contraction twins, tension twinning has been widely found to
readily occur in their interior [114] [139] [140] [141] [142]. Products of this reaction are usually
called double twins. Finite elements simulations have suggested that such second-order tension
twinning results in loss of twin-matrix coherency, which would explain the restricted growth of
contraction twins [106]. In turn, double twins are oriented so that their Schmid factors for basal slip
are close to ideal [26] [140]. Therefore, marked contrast arises between the relatively soft twin
bands and their parent grains, which remain in the intrinsically hard basal orientation. Accordingly,
extensive evidence of subsequent deformation strongly localizing in double twins has been given
[26] [29] [90] [138], with local strains as high as 1000% derived by slip trace analysis in single crystals
[90].
Figure 2.15. (a) EBSD scan displaying numerous shear bands in AZ31 after PSC testing. Most shear band boundaries are consistent with double twin misorientations (yellow), and they are frequently associated with black (non-indexed)
regions [114]. (b) Fracture surface of AZ31 after tensile testing, showing twin-shaped voids parallel to twin bands [108].
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Formation of narrow bands traversing many grains and characterized by intense strain localization
has been comprehensively reported in magnesium alloys after relatively high macroscopic strains,
e.g. Figure 2.15 (a) and Figure 2.27. Historically referred to as shear bands [26], their boundaries
have been recently proved to possess misorientations consistent with double twin boundaries by
both TEM [142] and EBSD [114] (Figure 2.15 (a)). Therefore, their formation has been associated to
double twins, with the following mechanism proposed [29]: as twin growth is hindered, basal
dislocation pile-ups at the intersection between double twins and grain boundaries would raise the
local stress in the neighbouring grain, eventually exceeding the CRSS for contraction twinning in
that grain, which would yield nucleation of a new twin aligned with the former. Shear bands have
been reported after all uniaxial tension [80] [108], UAC [106], PSC [114], cold rolling [26] [28] [29],
and biaxial tension [80].
Further, void nucleation within contraction twins has often been reported (Figure 2.15 (b)), and
ascribed to the formation of basal dislocation pile-ups inside twins [29] [108] [114] [143]. Hence,
failure in magnesium has been associated to contraction twinning and shear banding in a range of
situations including mechanical testing in 𝑐 axis compression [80] [81] [87] [108] [114] [138] [143]
and 𝑐 axis extension [88] [114] orientations, and operations like cold rolling [29] and cup testing
tension [65] [80] [81]. In all these, ductile failure by void formation and coalescence has been shown
to be the typical fracture mechanism.
Figure 2.16. Shear bands in AZ31 (a) after 7% effective plastic strain under uniaxial tension, and (b) after 4% effective plastic strain under biaxial tension [80].
This connection between shear banding and failure has been put forward by Scott et al. to explain
the earlier failure under biaxial tension compared to the uniaxial case in magnesium [80] [81] (see
Section 2.2): shear banding was observed after 4% effective plastic strain in the former, but only
after 7% effective plastic strain in the latter [80] (Figure 2.16). Earlier shear banding under biaxial
tension has also been predicted by Timár and Fonseca employing crystal plasticity finite element
modelling [144]. Quicker strain accumulation in shear bands under biaxial tension was predicted
also [144], which would further contribute to earlier failure. Such observations can be rationalized
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in terms of the distinct character of ND strain in the two paths as noted in last subsection [80] [81]
[144]: ND strain is imposed since the beginning in biaxial tension, so that 𝑐 axes strain and thus
contraction twinning follow straight after strain by the few grains off the basal texture according to
the easily activated modes (basal slip, tension twinning, prismatic slip) is exhausted; in uniaxial
tension, ND strain is delayed by prior prismatic slip in the sheet plane, so that the onset of 𝑐 axes
strain and thus contraction twinning is retarded accordingly.
In conclusion, although basal slip plays a relevant role in the strain accommodation of magnesium
in all conditions, specificities related to other mechanisms are crucial for understanding its plastic
behaviour under the relevant paths. For instance, the distinct role of prismatic slip under uniaxial
tension is a reasonable explanation for the decent ductility of magnesium as compared to stretch
formability [79] or cold rollability (recall Section 2.2). Likewise, strain localization in contraction
twins leading to failure constitutes a practical realisation for the formal idea that hard dislocation
slip parallel to 𝑐 axes lies behind the scarce formability of magnesium. Throughout strain paths,
contraction twinning is activated after exhaustion of easily activated deformation modes.
2.3.5 The effect of texture on the formability of magnesium sheet
As explained in last subsection, contraction twinning has been proposed to trigger ultimate failure
in magnesium. Consequently, initial basal texture intensity would be expected to directly affect the
formability of conventional magnesium alloys in that the amount of grains with 𝑐 axes initially tilted
away from the ND, and thus able to sustain ND strain following the easily activated modes before
contraction twinning is onset, is determined thereby. Yet, past research has proved that such
relationship is not so straightforward and, again, depends on the strain path considered.
On the one hand, former studies have effectively encountered weaker basal textures to improve
stretch formability [64] [65] [79] [123] [145]. For example, Huang et al. reported a twofold texture
weakening to powerfully increase Erichsen value from 3.4 to 8.8 mm [123] (Figure 2.17), i.e. close
to values typical in aluminium and steel (see Figure 2.5). On the other hand, for uniaxial tension,
ductility improvements by texture weakening have sometimes been reported [115] [123], yet not
always [65] [67] [79] [127]. This contrasts with uniform elongations, consistently demonstrated to
improve with weaker texture [64] [67] [127]. Furthermore, in those cases where weaker textures
did increase ductility, the improvement was stronger for uniform elongations [115] [123]. For the
case of Figure 2.17, Huang et al. reported an increase of 0.03 in uniform elongation, but less than
0.02 in ductility [123]. These results suggest that, while promotion of soft deformation modes by
texture weakening can effectively impart more strain before the onset of necking, other factors are
relevant after the onset of plastic instability. The reports that the bulk of contraction twinning
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appears in tensile testing just prior to diffuse necking [127] [138] indicated also that any effect of
easily activated modes is essentially exhausted at that point.
Figure 2.17. Erichsen cup test specimens corresponding to AZ31 having different initial basal texture intensity. Both have been hot-rolled and annealed, with the final hot rolling pass carried out at 798 K for the specimen above and 723 K for
the specimen below [123].
Studies on the formability of magnesium have also paid attention to two tensile parameters often
employed as sheet formability predictors in ductile metals [61]:
• The Lankford coefficient or r-value is the ratio between strain in the sheet plane and in the
ND. For magnesium, it has been consistently encountered to powerfully diminish with
weaker texture [65] [67] [79] [127], e.g. from 1.9 to 1.2 in the case of Figure 2.17. This
further suggests that weaker textures effectively promote ND strain accommodation by
the easily activated deformation modes.
• The strain hardening coefficient or n-value measures the amount of work hardening upon
tensile testing, and is directly related to uniform elongation by Considère criterion [146],
whose applicability to magnesium has been shown in many studies [64] [107] [108] [138].
Hence, in the same way as uniform elongation, the n-value has been repeatedly displayed
to increase with weaker texture in magnesium [64] [65] [67] [79] [127]. The role of more
profuse tension twinning in imparting work hardening (recall Section 2.3.4.3) and thus
increasing the n-value has been recurrently emphasized [107] [108] [147].
To sum up, weaker basal textures have been consistently encountered to be beneficial for stretch
formability and uniform elongation, but mixed results have been obtained in terms of ductility. This
suggests that other factors may also play a role in the formability of conventional magnesium
including grain size, which is discussed in next subsection. Further, despite being as practically
relevant as biaxial tension, the impact of texture intensity on the formability of conventional
magnesium alloys under the strain path of cold rolling is yet to be studied.
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2.3.6 The effect of grain size on the formability of magnesium sheet
In a similar way as texture, initial grain size has been observed to exert a powerful impact on the
formability of magnesium. This has been interpreted in terms of the distinct effects of grain size on
the various deformation modes available, discussed at the start of this subsection in the light of
recent findings. Implications of these for the plastic behaviour of magnesium as explained in Section
2.3.4 are dealt with later, followed by their role in the formability of conventional magnesium alloys
under the most relevant strain paths.
In accordance with general observations in metals [148], a trend for more profuse deformation
twinning in magnesium with larger grain size has been extensively reported for both tension [22]
[109] [132] [149] [150] and contraction twins [22] [65] [127] [138] [149] [150]. For instance, Barnett
et al. found a strong parabolic dependency for the number of twins of both types at fixed uniaxial
strains [150] (Figure 2.18). Likewise, Chino et al. found significantly enhanced contraction twinning
under biaxial tension for relatively coarse grain sizes [65] (Figure 2.21).
Figure 2.18. Relationship between twin density and initial grain size in AZ31 tested under uniaxial tension (favourable to contraction twinning) and UAC in the 𝑐 axis extension orientation (favourable to tension twinning) [22].
On the other hand, non-basal slip in magnesium is claimed to be more active for smaller sizes. In
particular, TEM analysis by Koike et al. in AZ31 [151] and Shi et al. in Mg-1Zn [127] after uniaxial
tension showed significantly more active cross-slip of ⟨a⟩ dislocations into prismatic planes for
relatively fine sizes (Figure 2.19). This effect was rationalized by Koike et al. by grain boundary
compatibility effects [151]: rotations by basal slip would lead to separation of adjacent grains if no
other slip mode was activated at least near the boundary, for which prismatic slip is the “softest”
option; such boundary-induced activation will be perceived as more homogeneous the smaller the
grain size. Nevertheless, Koike et al. noted that the same reasoning would also encompass eventual
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activation of ⟨c + a⟩ slip [151]. This deformation mode was not encountered in neither of these
studies, which may be ascribed to the relatively low strains considered (2% [151] and 5% [127]). In
this sense, recent TEM work by Kang et al. has effectively suggested more active ⟨c + a⟩ slip after
the equal angular channel processing (ECAP) of AZ31 with finer resultant size [152]. What is more,
molecular dynamics simulations by Wu and Curtin [153] have predicted ⟨c + a⟩ dislocations to be
glissile at certain distance from grain boundaries only, which would be equally perceived as overall
⟨c + a⟩ promotion if grain size is refined [153].
Figure 2.19. TEM micrographs corresponding to Mg-1Zn deformed to 5% strain under uniaxial tension with initial grain sizes of (a) 84 µm and (b) 23 µm. All ⟨𝑎⟩ dislocations are visible in the two images. Solid arrows indicate dislocations
parallel to basal plane traces, and dashed ones those orthogonal, i.e. are associated to cross-slip into prismatic planes [127].
Following this opposed effect of grain size on deformation twinning and slip, a gradual shift in the
relative weight of each in the strain accommodation by magnesium has been recurrently claimed,
with twinning becoming less relevant as grain size is refined, and vice versa [127] [132] [151] [154].
The case of tension twinning has been best illustrated by Barnett et al. after the UAC of AZ31 with
different initial grain sizes in the 𝑐 axis extension orientation [132]. The more limited amount of
tension twinning measured led the concave-down shape to become less evident the finer the grain
size, with the smallest even showing fully concave-down curves [132] (Figure 2.20 (a)). Moreover,
despite yield stress effectively raised with smaller size as per a classic Hall-Petch [155] [156]
relationship, peak stresses were much higher the coarser the grain size (Figure 2.20 (a)). This was
ascribed to greater twinning-imparted hardening (Section 2.3.4), and referred to as “reverse” Hall-
Petch effect of magnesium [132]. The role of contraction twinning enhancement by larger grain size
was highlighted in a further paper by the same authors, where localized necking by twinning-
induced void nucleation was found to arise earlier the coarser the size (even before the onset of
diffuse necking for the largest size considered, see Figure 2.20 (b)) [138].
(b)(a)
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Figure 2.20. Stress-strain curves corresponding to AZ31 with different initial grain sizes and tested under (a) UAC in 𝑐 axis extension orientations, where greater tension twinning the larger the grain size leads to (i) more marked concave-up character and (ii) higher peak stress in virtue of greater twinning-induced hardening [132]; and (b) tensile testing,
where coarse grain size results in premature failure, which has been attributed to enhanced contraction twinning [138].
In this line, for similar starting texture, the ductility of conventional magnesium alloys has been
recurrently observed to improve with finer grain size [65] [79] [127] [138] [151]. This has been
ascribed to both contraction twinning inhibition [127] [138] and the promotion of prismatic slip [65]
[127] [151]. A look at uniform elongation may shed light onto the contribution of each effect, as
prismatic slip would be expected to be more relevant before diffuse necking, and contraction
twinning afterwards (Section 2.3.4.3). Despite this, conflicting results have been reported: Shi et al.
encountered no significant effect of grain size on uniform elongation [127], suggesting all the
benefit corresponds to post-uniform strain; by contrast, a considerable increase in the uniform
range by grain size refinement was observed by Koike et al. [151]: uniform elongation higher than
30% against 15-20% usual for coarser grain sizes [151]. This discrepancy may be explained by the
magnitude of the grain sizes respectively considered: between 20 and 200 µm by Shi et al. [127],
and as small as 6 µm by Koike et al. [151]. In fact, the thickness of the compatibility-affected layer
around boundaries was hypothesized to be of approximately 10 µm in [151]. Likewise, interaction
with texture may also play a role. In this respect, Chino et al. compared two initial basal textures
with markedly different intensity at two grain size levels each: the n-value increased with smaller
size for the relatively weak, but remained unchanged for the relatively strong (Table 2.7) [79]. What
is more, r-values for similar texture intensities do not show clear trends in terms of grain size (Table
2.7) [79] [127]. As a result, further work is required to unravel the contribution of each deformation
mechanism to the ductility improvement by grain size refinement in magnesium, as well as the
interplay of other factors.
On the other hand, stretch formability has been repeatedly ascribed the opposite trend with grain
size [64] [65] [79]. For instance, an Erichsen value increase from 2.9 to 4.9 mm was reported by
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Chino et al. after a grain size enlargement from 6 to 20 µm [79]. This was related to the greater
contraction twinning displayed by coarser sizes (Figure 2.21), which would provide further strain
through the additional basal slip enabled within [65]. The conflicting role of grain size in ductility
and stretch formability was explained by Chino et al. in terms of the greater relevance of ND strain
under biaxial tension (recall Section 2.3.4.3) [65]. While this would represent a plausible
explanation if prismatic slip effectively accounts for the ductility enhancement, the reason why
contraction twinning may hinder ductility but enhance stretch formability remains unexplained.
Figure 2.21. Microstructures of AZ31 specimens after Erichsen cup testing with initial grain size of (a) 6 µm, (b) 10 µm, (c) 17 µm and (d) 31 µm. Narrow bands correspond to contraction or double twins [65].
In conclusion, the impact of grain size on the formability of conventional magnesium alloys has
been found to depend largely on strain path. This has been attributed to its conflicting effect on the
operability of the various deformation mechanisms, whose contribution to strain is also path-
dependent: while twinning is favoured by coarse sizes, non-basal slip is promoted by finer grains.
Accordingly, ductility is promoted by grain refinement, but stretch formability by coarser grains.
Nevertheless, and despite its practical relevance, the impact of grain size on the formability of
conventional magnesium under the strain path of cold rolling is yet to be studied.
Finally, results by several authors make it possible to examine the interplay between basal texture
intensity and grain size on the formability of conventional magnesium alloys in microstructures
resulting from conventional material preparation [64] [79] [127]. A summary of such observations
is given in Table 2.7. For ductility, Table 2.7 shows a consistent tendency for grain size being more
relevant than texture [79] [127]: ductility is invariably increased with finer size in all cases despite
markedly different texture intensities. In fact, this trend can also explain the cases where weaker
basal textures did not yield improved ductility as noted in Section 2.3.5 [65] [67] [79] [127]. By
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contrast, texture has been recurrently encountered to be more relevant than grain size for stretch
formability [64] [79]. For instance, conditions A and C by Chino et al. exhibit much lower Erichsen
values despite their grain sizes comparable to those of B and D (Table 2.7). Likewise, the increase
in grain size from conditions C and D by Kang et al. is hardly effective in increasing Erichsen value
unless texture is significantly weakened, which occurs for condition A but not B (Table 2.7). Again,
the discrepancy between paths can be rationalized by the distinct role of ND strain (Section 2.3.4.3):
contraction twinning is only preceded by off-basal ND strain under biaxial tension, but significant
prior prismatic slip exists in uniaxial tension. While the amount of the former is directly dictated by
texture intensity, grain size has a far-reaching effect on the latter as explained above. A different
impact of grain size on contraction twinning under each path may also play a role, but this is yet to
be clarified.
Table 2.7. Formability parameters under uniaxial and biaxial tension as a function of initial basal texture intensity and grain size in conditions prepared by hot rolling and subsequent annealing. Data by Chino et al. [79], Kang et al. [64] and
Shi et al. [127] have been included. Yield strengths are also presented for the sake of discussion in Section 5.3.4.
Basal texture
intensity
(MRD)
Grain
size
(µm)
Ductility
Erichsen
value
(mm)
Yield strength
(MPa)
A [79] 23.6 6.3 28.8 2.9 259
B [79] 14.0 10.9 28.4 4.1 234
C [79] 26.5 14.2 27.0 3.1 228
D [79] 12.7 20.5 23.0 4.9 206
A [64] 4.3 6.7 n/a 4.1 131
B [64] 5.7 6.4 n/a 3.1 158
C [64] 7.7 3.1 n/a 2.9 208
D [64] 7.6 3.8 n/a 3.1 171
A [127] 6.2 18 28.1 n/a n/a
B [127] 8.7 23 27.2 n/a n/a
C [127] 7.6 37 26.9 n/a n/a
D [127] 8.4 49 26.4 n/a n/a
E [127] 9.5 64 25.9 n/a n/a
F [127] 8.3 84 23.2 n/a n/a
G [127] 11.7 97 22.8 n/a n/a
H [127] 13.7 188 20.4 n/a n/a
I [127] 9.4 226 19.8 n/a n/a
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To sum up, basal texture intensity and grain size have been found to be the main microstructural
variables affecting the formability of conventional magnesium alloys. On the one hand, weaker
basal textures enhance formability following greater activation of basal slip and tension twinning.
On the other hand, whether coarser or finer grains are beneficial is strongly dependent on strain
path, which is associated to the opposed impact of grain size on twinning and non-basal slip. In
addition, texture and grain size vary concurrently upon annealing so that their effects cannot be
separated in actual material preparation conditions. The determination of which is more relevant
to formability in these conditions has been an active research topic, for which the outcome is also
dependent on strain path. While the effects of microstructural variables are now clear for uniaxial
and biaxial tension, studies are still missing for the other practically relevant path, i.e. that of cold
rolling.
The plastic deformation of magnesium-rare earth (RE) sheet
Even small additions of RE elements result in remarkable improvements in the amount of strain
that magnesium can sustain at room temperature. The understanding of the so-called RE effect has
been the subject of extensive research in the last decade, with several explanations proposed: on
the one hand, beneficial effects on the activity of the various deformation modes seem to be
induced by solute RE additions; on the other hand, characteristic RE textures different from the
strong basal fibres of conventional magnesium are developed during hot rolling and subsequent
annealing. Such effects are reviewed in this section, emphasizing observations on the strain path of
cold rolling, which –unlike for conventional alloys, as shown above– has been the subject of some
of the paramount studies on the formability of Mg-RE alloys.
2.4.1 The effect of rare-earth additions on deformation slip in magnesium
Although the prevalence of basal slip as prevalent slip mode is still undisputed in RE-containing
magnesium alloys, considerable evidence of non-basal slip promotion by solute RE additions has
been given. Solute RE atoms have also been ascribed a powerful hardening effect on basal slip
which may also be beneficial to formability, and could explain the unique strengthening potential
of RE elements in magnesium.
2.4.1.1 The effect of rare-earth elements on non-basal slip
Promotion of non-basal glide by RE additions was first claimed in the benchmark study on the creep
behaviour of single-phase Mg-Y alloys by Suzuki et al. [157]. In that study, TEM dislocation analyses
revealed an increasing trend in the total amount of non-basal dislocations with higher yttrium
content, with basal dislocation density mainly unchanged (Figure 2.22). Non-basal ⟨𝑎⟩ slip seemed
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favoured at intermediate yttrium contents, and ⟨𝑐 + 𝑎⟩ slip in the most concentrated and dilute of
the alloys.
Figure 2.22. (a) Total dislocation density and densities of dislocations with ⟨𝑎⟩ and ⟨𝑐 + 𝑎⟩ Burgers vectors as a function of yttrium content for four binary Mg-Y alloys after creep at 550 K; (b) ratio between the density of non-basal
dislocations (irrespective of Burgers vectors) and total dislocation density under the same conditions [157].
More recently, slip system activity in the hot rolling of Mg-RE alloys has often been examined in
exploration of the origin of RE textures. For this purpose, hot-rolled sheet has been subjected to
intragranular misorientation axis (IGMA) analyses by Hadorn et al. [158] [159] [160] and Sanjari et
al. [161] [162]. By these means, misorientation axes between pixels in EBSD maps are used as an
indication of dislocations present in those pixels [122]. However, although prismatic dislocations do
possess unambiguous misorientation axes (they lie on the ⟨0001⟩ vertex of inverse pole figures
(IPFs)), those related to basal and ⟨𝑐 + 𝑎⟩ slip are undistinguishable from one another (both lying
along ⟨211̅̅̅̅ 0⟩-⟨11̅00⟩ boundaries); therefore, only the effect of RE elements on prismatic slip can
be captured by these means. In this sense, IGMA analysis has repeatedly suggested a gradual
transition in the dominant slip mode from basal to prismatic with higher solute content for all
yttrium, neodymium and cerium added to pure magnesium [158] [159] [160] [161] (Figure 2.23).
Moreover, enhancement of prismatic slip was also encountered when comparing Mg-3Y and Mg-
3Zn in [162].
Evidence of non-basal slip promotion in the cold forming of Mg-RE sheet has also been provided.
In this respect, TEM dislocation analysis was used to compare the behaviour of pure magnesium
with that of Mg-0.2Ce under uniaxial tension [66] and UAC [163] by Chino et al., and with that of
Mg-3Y after cold rolling by Sandlöbes et al. [29]. While only basal dislocations were found in pure
magnesium in all cases, significant non-basal ⟨𝑎⟩ slip was demonstrated in the uniaxially tested
specimens [66] [163], and ⟨𝑐 + 𝑎⟩ slip in the cold-rolled samples (Figure 2.24) [29]. Particularly,
⟨𝑐 + 𝑎⟩ dislocations were quantified to be over 60% of all those observed at 3% strain in the latter
case [30]. Similarly, texture polycrystal modelling by Agnew et al. [103] has suggested significant
activation of ⟨𝑐 + 𝑎⟩ slip in Mg-1Y under PSC in comparison to the pure metal. As for non-basal ⟨𝑎⟩
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slip, first-principles simulations by Yasi et al. suggest that chemical interaction between solute RE
elements and prismatic screw cores can decrease the cross-slip stresses for those dislocations [164].
In contrast, Sandlöbes et al. have proposed after density functional theory simulations that the
stabilization of stacking faults acting as ⟨𝑐 + 𝑎⟩ dislocation sources explains the more active ⟨𝑐 + 𝑎⟩
slip [165].
Figure 2.23. IPFs representing IGMA densities for a range of hot-rolled binary Mg-Ce alloys. Texture intensity after hot rolling has been indicated also [160].
Figure 2.24. Slip trace analysis in Mg-3Y cold-rolled to 3% strain, where traces of slip on the basal, 1st order pyramidal and 2nd order pyramidal planes have been identified [30].
The more active non-basal glide in Mg-RE alloys has been suggested by several authors to be able
to enhance formability by retarding the localisation of strain in contraction twins and shear bands.
In this sense, the more homogeneous strain distribution that would result was put forth by Chino
et al. to explain the reduced tendency of shear bands to initiate cracks in Mg-0.2Ce as opposed to
pure magnesium in their UAC tests [163]. For the specific case of cold rolling, Sandlöbes et al. have
proposed that the intense activation of ⟨𝑐 + 𝑎⟩ slip as early as at a strain of 3% should delay the
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onset of contraction twinning significantly in the light of competition between both modes in
accommodating 𝑐 axes strain [29].
2.4.1.2 The effect of rare-earth elements on basal slip
As well as providing evidence of enhanced non-basal slip, Suzuki et al. noted that even 0.2 at% Y
resulted in higher creep strength than aluminium contents as high as 3 at% [166]. Since then, the
solute strengthening imparted by RE elements such as yttrium [167] [168], dysprosium [168],
gadolinium, lanthanum, neodymium and cerium [169] has been recurrently reported to greatly
surpass that of classical additions such as zinc [167] [168] [169] or aluminium [167] [169] added in
similar amounts. This has been proved through both microhardness [167] [169] and uniaxial yield
stresses [167] [168], e.g. Figure 2.25.
Figure 2.25. Variation of room-temperature yield strength with solute content of yttrium, aluminium and zinc included in the corresponding single-phase binary alloys [167].
Seeking an explanation for the high strengthening potential of RE additions, Miura et al. subjected
binary magnesium single crystals to UAC tests purposely oriented for basal slip [168]. As shown in
Figure 2.26, considerably higher CRSSs were effectively obtained for yttrium and dysprosium than
for zinc. In view of this, the authors suggested that, with basal slip the most active deformation
mode in magnesium, the hardening of basal slip by RE elements should account for the overall high
strengthening imparted [168]. Yet, classical solid solution strengthening theories have been
repeatedly found to break down for explaining the solute hardening of basal slip by RE additions
[167] [168] [169]: as shown in Table 2.8, no significant difference exists between yttrium and zinc
or aluminium in terms of either shear modulus [167] or atomic size misfit [168] [169].
In the light of this disagreement, alternative explanations have been suggested in recent times,
such as (i) the promotion of ⟨𝑐 + 𝑎⟩ slip by RE elements leading to dislocation forests and thus work
hardening of basal slip [29] [157] [167] [168], and (ii) dynamic strain ageing (DSA) effects, i.e.
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precipitation of solute RE atoms in super-saturated solution to dislocation lines during plastic
straining [167] [168]. However, although testing of single crystal pure magnesium oriented for basal
slip and counting on prior artificial introduction of ⟨𝑐 + 𝑎⟩ dislocations led to similar work hardening
of basal slip [170], no experimental evidence exists for the same effect induced by RE additions.
Similarly, DSA was found for Mg-Y alloys between 150 and 277°C, but not at ambient temperature
[167] [168], at which RE strengthening has been suggested to be higher [167] [168] (see Figure
2.26). Moreover, while higher chemical strengthening potency is predicted by first-principles
simulations by Yasi et al. for yttrium than for aluminium or zinc [171], the magnitude of the increase
cannot justify CRSS values as those reported by Miura et al [171]. Therefore, more work is required
to unravel the source of the powerful RE hardening of basal slip in magnesium.
Figure 2.26. Variation in the CRSS of basal slip with temperature in several single-phase Mg-X single crystals (X = wt% yttrium, dysprosium and zinc). The IPF indicates the stress direction in the UAC tests [168].
Table 2.8. Shear modulus misfit and strain due to size misfit for yttrium, aluminium and zinc, as well as solid solution hardening rates as calculated from the room-temperature yield strength of the corresponding single-phase binary alloys.
Alloying system Mg-Y Mg-Al Mg-Zn
Solid solution hardening (MPa/(at%)1/2) 737 [167] 118 [172] 578 [173]
Solid solution hardening (MPa/(at%)2/3) 1249 [167] 196 [172] 905 [173]
Shear modulus misfit 0.404 [167] 0.419 [167] 0.867 [167]
Anisotropic size misfit (𝒂 axis) 0.445 [168] -0.361 [168] -0.500 [168]
Anisotropic size misfit (𝒄 axis) 0.338 [168] -0.336 [168] -0.504 [168]
Finally, the beneficial effect to which the harder basal slip induced by RE elements can give rise in
terms of formability has been noted in the past. Particularly, the fraction of strain accommodated
by non-basal slip would be expected to be subsequently increased following the reduction of CRSS
ratio against basal slip [158] [174]. Furthermore, higher hardening rates could also help retard the
onset of plastic instability as per the Considère criterion [29].
2. LITERATURE REVIEW
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In summary, the concomitant hardening of basal slip and softening of non-basal slip promoted by
RE additions have been proposed to explain the better formability of RE-containing magnesium
alloys. Particularly, the subsequently enhanced non-basal slip activity has been suggested to be able
to retard both the onset and localization of strain within contraction twins and shear bands.
Nevertheless, effective evidence of such retardation lying behind the effect is yet to be provided,
and other reasons have been proposed to explain the enhanced formability, which are presented
below.
2.4.2 The effect of rare-earth additions on deformation twinning in magnesium
The effect of RE additions on contraction twinning has been suggested to play a key role in the
enhanced formability of Mg-RE alloys. On the other hand, their impact on tension twinning has not
been as comprehensively treated, albeit noteworthy observations have been reported in two
recent papers.
2.4.2.1 The effect of rare-earth elements on contraction twinning
The discovery of the high cold rollability of Mg-Ce alloys by Couling et al. in 1959 (recall Section 2.2)
was accompanied by observation of intense shear banding in the cold-rolled microstructures of
such alloys [26]. The extensive strains sustained by such high shear-banded fractions (see e.g. Mg-
3Y in Figure 2.27) were immediately related to the enhanced formability [26].
Figure 2.27. KAM maps and pole figures showing GND distribution and texture of (a) pure magnesium and (b) Mg-3Y cold-rolled at 10% reduction. The occurrence of shear bands traversing many grains and characterized by high GND
density levels is evident from KAM maps. In turn, pole figures display a relatively strong basal texture for pure magnesium, and much weaker RE texture for Mg-3Y [29].
More recently, Sandlöbes et al. have shown with kernel average misorientation (KAM) mapping
that the shear band density developed by Mg-3Y during cold rolling is significantly higher than that
2. LITERATURE REVIEW
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of pure magnesium [29] (Figure 2.27). KAM maps are obtained from EBSD data, and provide an
indication of the average misorientation of one pixel with respect to the surrounding. This is
assumed to correlate with the density of geometrically necessary dislocations (GNDs), and thus the
level of strain localised inside each pixel [29]. The more profuse shear banding of Mg-3Y was
hypothesized to result from enhanced contraction twinning by yttrium [29]. Nevertheless, KAM
maps suggested also that more strain is carried on average by the shear bands in pure magnesium
than by those in Mg-3Y (Figure 2.27), leading the authors to propose the enhanced ⟨𝑐 + 𝑎⟩ slip in
Mg-3Y as the reason for its enhanced cold rollability [29] (recall Section 2.4.2.1).
In the past few years, enhanced contraction and double twinning in Mg-RE against conventional
alloys has been effectively confirmed under other operations such as hot rolling [118] [161] [175],
and tensile testing [176] and deep drawing [56] carried out at ambient temperature (Figure 2.28).
As in the case of cold rolling, the promotion of contraction twinning has been linked to higher
formability in these cases through the additional deformation by soft deformation modes enabled
within: higher ductility of binary Mg-RE alloys including gadolinium, lanthanum, neodymium or
cerium than pure magnesium in [176], and better deep drawability of ZE10 as opposed to AZ31 in
[56]. The effect would thus be similar to that claimed for grain size coarsening in conventional
magnesium alloys as explained in Section 2.3.6.
Figure 2.28. EBSD maps corresponding to hot-rolled (a) Mg-0.01 at% Nd and (b) Mg-0.04 at% Nd, where the misorientations corresponding to tensile twin (red), contraction twin (blue) and double twin (yellow) boundaries have
been highlighted [118].
2.4.2.2 The effect of rare-earth elements on tension twinning
Unlike that on contraction twinning, the impact of solute RE additions on tension twinning has only
been scarcely analysed in the past. Yet, two recent papers have focused on the impact of low and
high yttrium additions, respectively, on the nucleation of tensile twins.
(a) (b)
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On the one hand, the self-consistent modelling of neutron diffraction data corresponding to the
UAC of Mg-0.5Y and Mg-2.2Y revealed no significant solute hardening of {101̅2} twinning above
0.5 wt% Y (Figure 2.29 (a)) [131]. By contrast, the finding of the {112̅1} tension twinning mode in
Mg-10Y in [177], uncommon in magnesium and not observed in the same study in Mg-5Y, was
proposed to result from comparatively higher solute hardening of {101̅2} twinning (Figure 2.29
(b)). With apparently conflicting results suggested by both studies, more work is thus needed to
clarify whether the onset of tension twinning is effectively hardened by RE solutes, and how such
hardening may be affected by the level of RE additions included.
Figure 2.29. (a) Influence of yttrium content on the CRSS of basal slip, ⟨𝑐 + 𝑎⟩ slip and tension twinning as predicted by elastoplastic self-consistent modelling in [131]; (b) schematic showing the effect of high yttrium content on the CRSSs for
{101̅2} and {112̅1} twinning suggested in [177].
In conclusion, whereas the effect of RE additions on tension twinning does not seem to have been
fully unravelled, contraction twinning is definitely enhanced. The former leaves any impact of RE
elements on formability through tension twinning open. The latter has been linked to the higher
forming limits of Mg-RE alloys, representing a possible explanation additional to the enhancement
of non-basal slip mentioned above, and the weak RE texture dealt with in next subsection.
2.4.3 The rare-earth texture of rolled magnesium
If the right amount of RE elements is added to magnesium, textures strikingly different from the
strong basal fibres typical of this metal are obtained after its thermomechanical processing by hot
rolling and annealing. Particularly, the RE textures of magnesium sheet are characterised by both
distinct crystallographic orientation and weaker peak intensity, the two changes suggested to be
beneficial from the viewpoint of formability. Accordingly, the rationale behind the formation of RE
textures has been the subject of intense research in the past decade. Although some points seem
now clear, certain aspects still require elucidation.
(a) (b)
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Figure 2.30. {0001} pole figures for AZ31 (left) and Mg-1.5Gd (right) hot rolled at 400°C and subsequently annealed at 450°C for 1 h. The distinct pole figure shape and weaker peak intensity for the Mg-RE alloy are clearly shown [178].
Figure 2.31. {0001} pole figures for Mg-1Zn (a) as-hot rolled at 150°C and (b) annealed at 400°C for 15 min; and for ZE10 (Mg-1.0Zn-0.3Ce) (c) as-hot rolled at 150°C, (d) annealed at 400°C for 15 min and (e) annealed at 400°C for 4 h.
The RD-split texture typical of binary Mg-RE alloys gives way in ZE10 to a TD tilted texture upon annealing [57].
RE textures were first observed by Ball and Prangnell in 1994 in a study on the plastic behaviour of
a cast Mg-Y-Ce alloy [179]. In binary Mg-RE sheet, they are characterised –either after hot rolling
or further annealing– by the splitting of the usual basal fibre into two off-basal lobes [66] [118]
[175] [178] [180] tilted to the RD by angles lying within a 10-20° interval [35] [56] [178] [180] (Figure
2.30). Maximum intensities are comparable to conventional alloys in the hot-rolled condition, but
considerably lower after annealing [66] [118] [175] [178] [180] (Figure 2.30 and Figure 2.31).
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Although RD-split fibres have sometimes been reported for conventional magnesium alloys [55]
[57] [118] [123] [134], the texture weakening upon annealing is regarded as a RE effect only [124].
In the case of ternary Mg-Zn-RE alloys, namely ZE10 (recall Section 2.1.4), hot-rolled textures are
characterized by RD splits also, but these are substituted upon annealing by fibres with the basal
poles split from the ND to the TD by roughly 45° [35] [57] [175] (Figure 2.31 (c) and (d)). Remarkable
texture weakening occurs in the annealing of ternary alloys also, and final intensities tend to be
even lower than in their binary equivalents [175].
In line with the detrimental effect of strong basal textures on the formability of magnesium (recall
Section 2.3.5), the weaker RE textures were immediately associated to the long-known enhanced
formability of Mg-RE alloys [179]. In this sense, the higher fraction of grains with 𝑐 axes oriented
away from the ND has often been acknowledged to extend the activity of soft deformation modes
before 𝑐 axis compression and thus contraction twinning are required [28] [29] [35] [66] [103] [124]
[158] [175] [181]. For the specific case of cold rolling, Barnett et al. suggested this effect as a
plausible explanation for the improved cold rollability after finding that the texture of Mg-0.2Ce
was still weaker than that of pure magnesium at the reduction where the latter exhibited failure
[28] (Figure 2.32). In particular, it was argued that the enhanced basal slip and tension twinning
could retard the localisation of strain in the shear bands [28], so that the RE texture would play a
role similar to that put forth for ⟨𝑐 + 𝑎⟩ slip (recall Section 2.4.1.1).
Figure 2.32. Pole figures corresponding to pure magnesium and Mg-0.2Ce before cold rolling (h.r.=hot-rolled state), and after cold rolling (c.r.) at 30% overall reduction after applying 1% reduction per pass [28].
As for the formation of the RE texture, it has been demonstrated for all cerium [118] [160] [182],
neodymium [118] [159], yttrium [118] [158], gadolinium [174] [182] [183] and lanthanum [182] that
2. LITERATURE REVIEW
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a minimum concentration of RE elements is required for its occurrence. Below this critical content,
basal textures with peak intensities similar to conventional alloys are invariably obtained; above,
RE textures with significantly weaker intensities invariably arise (Figure 2.33). Interestingly,
intensities are not substantially modified beyond the threshold content [118] [158] [159] [160]
[182] [183]. As shown in the figure, RE textures can be found below the solid solubility of each RE
element [158] [162] [176] [184], which, in the understanding of the phenomenon, has directed the
attention of researchers preferentially towards the effect of solute RE atoms.
Figure 2.33. Peak texture intensity (in MRD) of hot-rolled and then annealed Mg-RE sheet against RE alloying content for different RE additions. The vertical lines indicate the solid solubility of each RE element in magnesium at 525°C [124].
In this sense, a mostly satisfactory theory explaining the origin of RE textures has developed across
the last decade. Extensive reviews on the topic are given in [35] and [124]. As dealt with below,
changes induced by solute RE additions in the behaviour of magnesium during all deformation,
recrystallisation and grain growth seem to play a role.
As for the change in preferred orientation, it is believed to arise from deformation effects. In fact,
as mentioned above, the RD-split fibre is already present in hot-rolled textures of both Mg-RE and
Mg-Zn-RE alloys (Figure 2.31). Moreover, the orientation of the RD-split fibre has been shown to
coincide with that inside the shear bands typical of rolled magnesium [28] [184]. Therefore, the
considerably greater amount of shear-banded material in Mg-RE alloys (recall Figure 2.27) is now
thought to lie behind the RD-split [118] [161] [184] [185]. By contrast, no reasons have been put
forward [35] [124] for the TD-split texture typical of Mg-Zn-RE alloys. More research is thus required
to clarify whether TD-split orientations appear during deformation or, conversely, upon annealing.
As for the weak intensity, it results from annealing effects: as noted above, intensities in the as-hot
rolled state are not different from those of conventional alloys (Figure 2.31). In this sense, recent
EBSD analysis of Mg-1Gd [175] and Mg-Zn-Gd alloys [185] hot-rolled and then annealed by Basu
2. LITERATURE REVIEW
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and Al-Samman suggests that the weakening is related to an oriented grain growth effect whereby
grains with off-RD-split orientations gradually consume those with RD-split orientations. The
mechanism by Basu and Al-Samman can be formalized into the following steps (Figure 2.34):
Figure 2.34. EBSD maps (left) and corresponding pole figures (right) for different stages in the annealing of hot-rolled Mg-1Gd: (a) as-deformed, (b) recrystallised, and (c) after considerable grain growth. The two first conditions correspond to the deformed and recrystallised fractions of the hot-rolled sheet annealed for one hour at 300°C, and the third to the same sheet annealed for one hour at 450°C. Colour coding indicates the tilting to the ND: with this scale, grains with off-RE orientations are shown in green, and grains with RE orientations in blue. Linear intercept grain sizes for both off-RE
and RE grains are included also [185].
• The first requisite is the prevalence of shear band nucleation (SBN) as a SRX mechanism in
RE-containing alloys, displayed by several authors in the past [57] [175] [184] [185]. SBN
differs from the GBN dominating SRX in conventional magnesium (recall Section 2.3.3).
• SBN produces two sets of recrystallised grains in terms of orientation (Figure 2.34 (b)): (i)
RD-split grains i.e. with orientations equivalent to those in the as-deformed shear band
(a)
(c)
(b)
𝑙 𝑅 =2.7 µm
𝑙 𝑅 = 3.4 µm
𝑙 𝑅 = 31 µm
𝑙 𝑅 = 1µm
2. LITERATURE REVIEW
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(green in the figure); and (ii) off-RD-split grains i.e. with orientations absent (Figure 2.34
(a)) in the as-deformed band (blue in the figure) [175] [185]. Off-RE orientations have been
proposed by Basu and Al-Samman to nucleate in the areas within the bands with higher
strain localisation [175], although the mechanism whereby such orientations are produced
is still unclear.
• Upon SRX, off-RD-split grains grow more quickly than RD-split grains (see difference in size
in Figure 2.34 (b)). This has been ascribed to driving pressure for recrystallisation being
higher for the former, as they would be nucleated in the areas with higher localised strain
i.e. higher dislocation density [175] [185]. Further dislocation substructure analysis of RD-
split and off-RD-split grains could help confirm this hypothesis.
• Upon grain growth, off-RD-split grains keep growing faster than RD split grains (difference
in size is even larger in Figure 2.34 (c)). Ultimately, this yields the texture weakening: the
overall volume of RD-split grains decays, and the intensity of the RE fibre is concurrently
diminished [185]. Again, this has been ascribed to higher driving pressure giving rise to
quicker kinetics: off-RD grains are already larger than RD-split grains upon impingement
(Figure 2.34 (b)), and the driving force for grain growth is a direct function of grain size
[175] [185].
• Finally, Basu and Al-Samman suggested the operation of solute drag as another requisite
for the oriented growth to occur [175]. The concept, reasons and implications of solute
drag in Mg-RE alloys are discussed below.
2.4.3.1 Solute drag and rare-earth texture development
As explained above, quantitative differences in the driving pressure for grain growth between off-
RD-split and RD-split grains have been proposed to lie behind the weak intensity of RE textures in
magnesium, in turn related to the remarkable formability of Mg-RE alloys. Nevertheless, for the
oriented growth to effectively yield texture weakening, the occurrence of another distinct effect of
RE atoms in magnesium is proposed to be required: formation of solute atmospheres at grain
boundaries, and resultant activation of solute drag during grain growth.
Solute atmospheres are solute-enriched areas surrounding grain boundaries to which, in certain
conditions, atoms in solid solution tend to segregate to reduce the elastic strain caused by atomic
size misfit. By these means, advantage is taken of the less dense atomic packing close to grain
boundaries [186]. Grain boundary mobility in thermally activated events such as recrystallisation
and grain growth is considerably reduced by such atmospheres, which has been formalised as a
solute drag pressure opposing the driving pressure for the process [186] [187].
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In this sense, the most widely accepted theory [186] on solute drag was set forth by Lücke and
Detert in [188], and is explained in detail in [187]. The authors proposed the existence of two
regimes whereby thermally activated boundary migration may be controlled depending on the
amount and nature of solutes added [187]:
(i) For dilute contents and/or small atomic sizes, a breakaway regime (driving pressure >
solute drag). Growth rates are relatively high, and determined by the rate of diffusion of
parent atoms across grain boundaries.
(ii) For higher contents and/or larger atomic sizes, a drag regime (solute drag > driving
pressure) with lower migration rates [186] [187]. This regime would be attained above
certain solute concentration, and growth is limited by the diffusion rate of atmosphere
atoms behind the migrating boundaries.
For the particular case of RE elements in magnesium, the existence of solute atmospheres when
added above their critical contents for RE texture formation has been recurrently proved in the past
few years using high-resolution X-ray energy-dispersive spectroscopy (EDS) [158] [189] [190] [191]
and high-angle annular dark-field (HAADF) scanning-transmission electron microscopy, e.g. Figure
2.35 [174] [189] [191]. The relatively large atomic size of RE elements has been claimed to explain
the existence of RE atmospheres [158] [192], not found for smaller aluminium [158] and zinc [190]
added in similar contents.
Figure 2.35. High-angle annular dark-field scanning-transmission micrographs showing a grain boundary in as-hot rolled (a) Mg-0.01 at% Gd, and (b) Mg-0.06 at% Gd. The gadolinium atoms are displayed in bright so that an enriched solute
layer surrounding the boundary is noticeable only for the higher RE concentration [174].
In the light of these results, Basu and Al-Samman [185] have postulated that operation of the drag
regime should be a requisite for their oriented grain growth: in the breakaway regime, all grains
would be able to break away from the pressure exerted by RE atmospheres, so that differences in
driving force would make no impact on growth rates. Despite this, whether the drag regime is
effectively operative in Mg-RE alloys with RE concentrations above that critical for RE texture
development has not been proved. Moreover, Lücke-Detert theory has been successfully applied
2. LITERATURE REVIEW
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to solute atmospheres in metals like lead, copper, aluminium [187] and zinc [193], but remains to
be attempted for magnesium.
To sum up, failure in Mg-RE alloys has also been ascribed to strain localisation in contraction twins
and shear bands. Accordingly, three distinct effects of RE additions on the plastic behaviour of
magnesium have been suggested to retard such strain localisation, and thus explain the improved
formability of Mg-RE alloys: (i) promotion of ⟨𝑐 + 𝑎⟩ slip, (ii) promotion of contraction twinning,
and (iii) the weak RE texture, from which enhancement of basal slip and tension twinning would be
expected. Nevertheless, although the potential of all these mechanisms to retard the strain
localisation within contraction twins is clear, the actual contribution of each to the formability
improvement is essentially unknown. What is more, unlike for conventional magnesium alloys as
noted in previous section, systematic studies on the impact of microstructural variables on the
formability of Mg-RE alloys are yet to be performed.
Focus of the project
The effects of microstructural variables on the formability of conventional magnesium alloys are
well-established for the strain paths of uniaxial and biaxial tension. Nevertheless, they have not
been studied to date for that of cold rolling. Moreover, any systematic studies are still missing for
the promising Mg-RE alloys, for which considerably improved forming limits have generally been
reported in comparison to conventional alloys. Within this context, the present project explores
the effect of previous material preparation on the formability of conventional and Mg-RE alloys
under the strain path of cold rolling. The poor formability of magnesium under this strain path is
one of the issues historically hindering its introduction in applications such as automotive BIWs.
Therefore, this project is expected to contribute to the widespread utilization of magnesium. In
addition, the extended cold rollability of Mg-RE alloys has been associated in the past to (i) the
distinct RE texture, (ii) more active non-basal slip, and (iii) more profuse contraction twinning, all
these effects promoted by RE additions. This project is also expected to shed light onto which of
these mechanisms effectively lies behind the phenomenon.
For this purpose, a set of annealing conditions is here prepared for two magnesium alloys after hot
rolling, one conventional and the other RE-containing. Pure magnesium and a binary Mg-RE alloy
are selected to represent each category so that the specific effect of RE additions can be evaluated.
Afterwards, PSC tests reproducing the strain path of cold rolling are carried out for the formability
of each of the conditions under this path to be assessed. Unlike actual cold rolling, PSC tests can
provide information on the contribution of the various deformation modes through the evolution
of work hardening.
2. LITERATURE REVIEW
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In addition, the annealing conditions produced are also used to provide insight into the boundary
migration regimes operative in each alloy upon grain growth. In this respect, the activation of the
drag regime for Mg-RE alloys has been suggested by recent research to be a requirement for the
distinct, formability-imparting RE textures to be developed. For this aim, grain growth kinetics are
contrasted against the postulates of Lücke-Detert theory on solute drag, formerly applied to other
metals, but never in magnesium to date.
3. EXPERIMENTAL METHODS
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3 EXPERIMENTAL METHODS
Chemical composition of the alloys
As in a number of previous investigations on the formability of Mg-RE alloys including others also
dealing with the strain path of cold rolling [29] [103], yttrium that has been chosen to represent the
effect of solute RE additions in this work. The specific yttrium contents selected are presented and
justified within this section.
Figure 3.1 shows the most widely accepted Mg-Y phase diagram to date [194]. As can be seen, the
magnesium-rich section of the diagram has a eutectic point at 566±1°C with maximum yttrium
solubility of 3.75±0.15 at% [194] [195]. However, data concerning the solid solubility of yttrium in
magnesium are available only for temperatures above 200°C [194] [195]. The reason is that, due to
its low diffusivity [23], yttrium tends to remain almost indefinitely in supersaturated solution in the
magnesium lattice below such temperature [196] [197]. Among other implications, this means that
equilibrium concentrations at higher temperatures can be maintained at room temperature if
cooling rate is sufficiently rapid.
Figure 3.1. Equilibrium phase diagram of the Mg-Y system. The dashed lines represent phase boundaries for which further confirmation is needed [194].
3. EXPERIMENTAL METHODS
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The chemical compositions of the two alloys considered in this project are displayed in Table 3.1.
Bulk yttrium contents have been determined by AMG Superalloys UK Ltd. using atomic emission
spectroscopy (AES) in conjunction with inductively coupled plasma (ICP). To this end, the company
has been supplied with the sufficient amount of purposely prepared machining fines. According to
specifications by the company, this method can provide an accuracy of 5×10-3at% in elemental
concentration measurement.
On the one hand, the higher yttrium content (≈0.15 at%) has been selected so that it is just above
the critical for the development of RE texture (0.05-0.1 at%, Figure 2.33). Industrial interest lies in
as small RE contents as possible to ensure competitiveness. Yet, comparable RE concentrations
have been found to exhibit non-basal slip [158] and contraction twinning [118] enhancement. On
the other hand, the lower yttrium content (≈0.01 at%) can be assumed practically negligible, and is
intended to account for the behaviour of pure magnesium: it is below the critical for texture
weakening, and former studies have reported no effect of RE contents at this level (<0.03 at%) on
either non-basal slip [158] or contraction twinning [118]. Both concentrations are below the solid
solubility of yttrium in magnesium at the minimum temperature of annealing used in this project
(>1 at% at 250°C, Figure 3.1), so that any impact of RE elements would be expected from solute
atoms only.
Table 3.1. Bulk yttrium concentrations of the two binary Mg-Y alloys considered in this study as determined by the company AMG Superalloys UK Ltd. with the ICP-AES technique.
Alloy
designation
Bulk Y content
(at%)
Bulk Y content
(wt%)
Mg-0.03Y 0.0090 0.033
Mg-0.6Y 0.1523 0.555
Thermomechanical preparation of the materials
The thermomechanical processing used to prepare the two alloys presented above is described in
this section. It has been designed to replicate the route conventionally leading to the cold rolling of
magnesium in the industry as discussed in Section 2.1.3.
For this route, the starting point has been two cast billets purposely prepared by Magnesium
Elektron® USA for The University of Manchester and having the compositions presented in Table
3.1. Both have been machined into 20x55x100 mm3 plates by the mechanical workshop of The
University of Manchester, and then subjected to the following three steps (Figure 3.2):
(i) Solution heat treatment at 550°C for 16 hours, with the goals of (i) dissolving the yttrium,
expected to be in the form of second-phase particles in the as-cast microstructure, and (ii)
3. EXPERIMENTAL METHODS
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removing microsegregation, both effects arising from the slow cooling rates typical of
casting operations. The temperature and time of the heat treatment have been chosen
following the literature for similar alloys [158] [167]. Temperature is close to but below the
eutectic point [194] to prevent the fusion of any fraction of eutectic microconstituent
present in the microsegregated as-cast microstructure.
(ii) Hot rolling at 400°C, for imparting a thickness reduction from 20 to 5 mm in seven stages
with uniform reduction of 18% in each (Table 3.2). The operation has been carried out in
a 10 inch-diameter laboratory-scale rolling mill at constant speed of 6 m/s. Pre-heating to
the rolling temperature for 20 minutes in a Carbolite® LHT6/60 furnace and intermediate
re-heating between stages to the same temperature for five minutes have been ensured.
After the operation, minor edge cracking was found in Mg-0.03Y.
(iii) Full isochronal annealing for 1 hour at a variety of temperatures between 250 and 500°C
with the purpose of obtaining a range of recrystallised microstructures to be analysed in
the project. Such annealing time is conventional in studies on the plastic behaviour of Mg-
RE alloys, e.g. [118] [158] [162] [175] [176].
Figure 3.2. Schematic of the microstructural evolution expected during the thermomechanical processing carried out in this project. As-cast precipitated particles are not drawn to scale.
For the solution and annealing heat treatments, a Lenton® LTF-1200 tube furnace has been used,
with the temperature controlled to be within ±5°C of the intended value with fine-gauge K-type
thermocouples attached to the sample surface. Two additional precautions have been taken:
(i) Inert argon atmospheres have been kept inside the furnaces at all times to avoid oxidation.
This precaution is common in magnesium heat treatments, albeit more critical here due to
the strong tendency of yttrium to form oxides at magnesium processing temperatures
[195], which would lead to matrix depletion.
HOT ROLLING
250°C
500°C
TE
MP
ER
AT
UR
E
550°C
400°C
TIME
HOMOGENISATION + SOLUTION HEAT TREATMENT
ANNEALING
Solvus ≈ 200°C
As-cast
3. EXPERIMENTAL METHODS
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(ii) Materials have been water-quenched straight after heat treatment (and after hot rolling
also) to ensure that yttrium remains in metastable solid solution (Figure 3.1), since all
these operations have been carried out above solvus temperature (see Figure 3.2).
Table 3.2. Expected and actual sheet thickness after each of the hot rolling stages conducted in this study for each of the two alloys.
Pass number 1 2 3 4 5 6 7 End
EX
PE
CT
ED
Initial thickness
(mm) 20.00 16.40 13.40 11.00 9.00 7.40 6.10 5.00
Reduction (%) 18.0 18.3 17.9 18.2 17.8 17.6 18.0
Overall reduction
(%) 18.0 32.8 44.9 54.8 62.9 69.6 75.0
AC
TU
AL
– M
g-0
.6Y
Initial thickness
(mm) 20.12 16.51 13.58 11.04 9.01 7.40 6.29 5.05
Reduction (%) 17.9 17.8 18.7 18.4 17.9 15.0 19.7
Overall reduction
(%) 17.9 32.5 45.1 55.2 63.2 68.7 74.9
Thickness
deviation (%) 0.60 0.67 1.34 0.36 0.11 0.00 3.11 1.00
AC
TU
AL
– M
g-0
.03
Y Initial thickness
(mm) 20.08 16.67 13.57 11.05 9.06 7.45 6.25 4.96
Reduction (%) 17.0 18.6 18.6 18.0 17.8 16.1 20.6
Overall reduction
(%) 17.1 32.6 45.1 55.0 63.0 68.9 75.3
Thickness
deviation (%) 0.40 1.65 1.27 0.45 0.67 0.68 2.46 -0.80
Characterisation techniques
To address the project goals, annealing conditions have been characterised using the techniques
shown in Figure 3.3. The first stage has been aimed at determining the SRX temperature 𝑇𝑆𝑅𝑋 of
each alloy through Vickers microhardness testing. 𝑇𝑆𝑅𝑋 is defined in metallurgy as the minimum
temperature required to obtain a fully recrystallised microstructure after a specific time of static
annealing [198]. Afterwards, grain size and texture of fully recrystallised conditions –i.e. annealed
at temperatures greater than 𝑇𝑆𝑅𝑋– have been measured using optical microscopy and X-ray
diffraction (XRD), respectively. Hardness and grain size have been measured in RD-ND planes, and
bulk textures in RD-TD planes.
Finally, the mechanical behaviour under the strain path of cold rolling has been examined for three
selected conditions for each alloy with plane-strain compression (PSC) tests. Although PSC testing
3. EXPERIMENTAL METHODS
-71-
of all fully recrystallised conditions was initially foreseen, corresponding PSC specimens were lost
by The Royal Mail on their way back from the company in charge of the machining. Since the hot
rolling machine of The University of Manchester was unavailable at the time due to building decant,
the project had to be resumed with few remains of the initially hot-rolled plate, for which only
material for three conditions was left. Together with the minimum and maximum temperatures,
intermediate conditions yielding similar grain size for both alloys were chosen.
The basics of all the characterisation techniques, together with details of their application in this
project, are dealt with in following subsections.
Figure 3.3. Characterisation stages carried out in this project, indicating the specific technique and range of annealing temperature conditions employed.
3.3.1 Vickers microhardness testing
Microhardness tests are used in metallurgy as a rapid means of qualitatively assessing material
microstructure and properties, as they give a general idea of the material resistance to plastic flow
in a practically easy way. In such tests, the surface of the sample is loaded with a given force and
for a certain dwell time with an indenter of standard shape, size and material.
Figure 3.4. Cross-section of the indenter used for Vickers testing as pushed down onto the sample surface (left). Top view of the impression thereby imparted (right) [199].
DETERMINATION OF TSRX FOR EACH ALLOY
EXAMINATION OF MECHANICAL BEHAVIOUR
MEASUREMENT OF BULK TEXTURE
MEASUREMENT OF GRAIN SIZE
Plane-Strain Compression (PSC) TSRX-500°C
X-Ray Diffraction (XRD) TSRX-500°C
Optical Microscopy TSRX-500°C
Vickers Microhardness 250-500°C
INITIAL PROPERTIES
BEHAVIOUR UNDER THE STRAIN PATH OF COLD ROLLING
3. EXPERIMENTAL METHODS
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Among the microhardness tests available, it is the Vickers test that has been used here. Vickers
testing makes use of square-based pyramidal indenters made of diamond and with the geometry
shown in Figure 3.4. In this test, sample hardness is assessed through the Vickers Number 𝐻𝑉,
which arises from dividing the force applied 𝑃 by the surface area of the impression 𝐴, and
expressing the result in kg/mm2. For this purpose, the lengths of the diagonals 𝑑1 and 𝑑2 of the 2D
projection of the impression (Figure 3.4) have been measured after every test using optical
microscopy, and then transformed into the corresponding 𝐻𝑉 value with Equation 3.1 [199].
𝐻𝑉 =
𝑃
𝐴≈
1.85 𝑃
(𝐿1 + 𝐿2
2)2
(3.1)
As mentioned above, hardness tests have been performed to estimate the SRX temperature of each
alloy. Past experimental work on magnesium has successfully related the development of a
completely recrystallised microstructure upon annealing with a relatively abrupt drop in hardness
compared to the as-deformed state [125] [200] [201]. This can be related to the substitution of the
work-hardened, deformed microstructure by strain-free, recrystallised grains. To detect the
softening, large impressions comprising significant grain boundary areas have been considered
preferable. The greatest load available in the Struers® Duramin-2 microhardness tester has thus
been used (i.e. 2 kg), together with a standard dwell time of 15 seconds [202]. Other practical issues
include:
(i) At least ten measurements have been conducted on each sample in order to ensure the
robustness of the values presented against local microstructural variations.
(ii) Measurements have been taken as close to the centreline of the RD-ND plane as possible.
(iii) To avoid the effect of work hardening produced by the impressions, distances between
indentation edges have been kept to at least six times the indentation size [202], and those
between indentations and sample edges to at least three times indentation size [202].
3.3.2 Microstructural assessment through optical microscopy
In this project, optical microscopy has been mainly used for grain size measurement. For this aim,
the linear interception method has been employed, with at least 300 grains considered for each
sample. In the same way as for hardness testing, grains have been selected as close as possible to
the centreline of the RD-ND plane. Those with multiple boundary faces (red circles in Figure 4.4),
have not been included as potential products of incomplete etching. Average linear intercept length
𝑙 has been transformed into average volumetric grain diameter 𝐷 with Equation 3.2, which assumes
the material is formed by grains of spherical shape and similar size [203].
3. EXPERIMENTAL METHODS
-73-
𝐷 = 1.5𝑙 (3.2)
Optical micrographs presented have been obtained by means of a Carl Zeiss® Axioscope in the
cross-polarised mode. Cross-polarised light is an optical microscopy technique which dramatically
enhances contrast in anisotropic materials such as HCP metals, e.g. magnesium [204]. This is
achieved by inserting two polariser lenses into a standard optical microscope, one before (polariser)
and the other after (analyser) the sample (Figure 3.5). The polariser forces the light generated by
the source, vibrating in all directions in principle, to vibrate in one direction only; in turn, the
analyser allows only light vibrating in the normal direction to pass through. Anisotropic materials
have two refraction indices, and so two diffracted beams perpendicular to each other and having
certain phase difference are produced in the polariser. These are then resolved to the direction
allowed by the analyser and integrated therein. As a result of the phase difference, constructive
interference will occur for certain wavelengths i.e. colours, and destructive for others, ultimately
altering the initial colour of the light. In polycrystalline materials, the different crystallographic
orientation of each grain will lead to different interference i.e. colouring, strongly facilitating the
grain boundary identification task.
Figure 3.5. Schematic of the arrangement typically used in the cross-polarised optical microscopy technique. The path followed by the light from source to eyepieces is indicated in blue, with light vibration directions represented at the
critical positions [204].
3.3.3 Bulk texture measurement through X-ray diffraction (XRD)
X-ray diffraction (XRD) is the most common method for bulk texture measurement: in addition to
its practical simplicity, it is non-destructive and mainly material-independent [205]. Furthermore,
XRD makes it possible to directly obtain pole figures, which constitute the most usual way of
representing sheet material textures [205]. For this purpose, each position in a certain pole figure
is measured by placing X-ray source and detector at the angle 2𝜃 to the sample fulfilling Bragg’s
condition for the corresponding set of planes (Figure 3.6). Having the angles of rotation 𝜑 and tilting
3. EXPERIMENTAL METHODS
-74-
𝜒 of the diffractometer fixed, the intensity thereby captured is directly a measure of the volume of
material for which that position is the stereographic projection of the set of planes considered. If,
as depicted in Figure 3.6, the sample is gradually reoriented for 𝜑 and 𝜒 angles covering the whole
stereographic space, the full pole figure is populated.
Figure 3.6. Schematic of a standard Eulerian diffractometer showing the three angles involved in bulk texture measurement. Incident and reflected beam represented by red lines [205].
In this study, XRD pole figures have been measured with a Bruker® D8 Discover diffractometer in
conjunction with a 𝐾𝛼 cobalt source and a silicon detector. Due to the large grain size of some of
the conditions, the spot has been dynamically oscillated along the two directions of the sample
surface. Specimens of around 2x2 cm2 have been prepared.
For all the samples, {0002}, {101̅0}, {101̅1} and {101̅2} pole figures have been obtained. The
corresponding 2𝜃 diffraction angles have been determined a priori, with no significant differences
between each alloy (Table 3.3). Pole figures have then been populated following increments of 5°
in both 𝜑 and 𝜒, with 𝜑 varying between 0 and 360° and 𝜓 between 0 and 85°. The range of 𝜒 has
been limited to 85° owing to geometrical restrictions reducing the amount of reflection that can be
captured as 𝜓 becomes close to 90°. The intensity of the background has been subtracted from all
measurements by means of the DIFFRAC method [206], implemented in the XRD analysis package
DIFFRAC.EVA® and assuming for the subtraction maximum concavity of the background curve at all
peak positions.
Experimental pole figures have then been inverted and combined into corresponding orientation
distribution functions (ODFs). A more quantitatively accurate representation of the data can be
thereby extracted [205]. The procedure has been conducted with the MTEX package, whereby the
ODF is discretised as linear combination of up to 10,000,000 De la Vallée-Poussin functions having
the same halfwidth as experimental pole figure resolution. Fast Fourier techniques are applied then
to compute the recalculated pole figures. The algorithm used by MTEX is explained in depth in
SOURCE
SAMPLE
DIFFRACTOMETER
3. EXPERIMENTAL METHODS
-75-
[207]. {0002} and {101̅0} figures are here presented as common practice in magnesium, e.g. [31]
[115] [162] [189].
Table 3.3. 2𝜃 diffraction angles employed to obtain the pole figures in this project.
Set of crystallographic planes
Diffraction angle 𝟐𝜽
{0002} 40.2°
{101̅0} 37.6°
{101̅1} 42.8°
{101̅2} 56.1°
3.3.4 Plane-strain compression (PSC) testing
Plane-strain compression (PSC) tests constitute a variation of uniaxial compression (UAC) tests in
which strain in one of the directions normal to the load is impeded by the walls of a channel-die
device. Load is transmitted from machine crosshead to specimen through a dedicated plunger
(Figure 3.7). The strain path of rolling (see Figure 2.1) can thus be directly reproduced by PSC testing
by placing the specimen TD normal to channel-die walls, and the ND parallel to the load [32]. This
orientation is analogous to the case of 𝑐 axis compression in magnesium extensively analyzed in the
literature (Section 2.3.4.1). PSC experiments have been used to assess magnesium formability in
the past [103] [114].
The plunger-die fixture used in this study has been purposely designed by the author for sample
dimensions of 5x5x5 mm3, and machined in AISI D2 tool steel [208] by the mechanical workshop of
The University of Manchester. Dimensions of 5x5x10 mm3 were initially foreseen, but reduced to
account for lower material availability after specimens were lost by The Royal Mail (see above). The
die has been conceived as consisting of three bolted components (Figure 3.7), so that channel width
can be adjusted to the specific dimensions of each specimen tested, and ‘dead-material’ zones
remaining undeformed during the test can be avoided. Specimens have been prepared by GTG
Engineering Ltd. by means of wire electrical discharge machining to obtain perfectly parallel, strain-
free faces. All the sides of as-received cubes lied within ±0.10 mm of the ideal dimensions.
The tests have been carried out in an Instron® 5569 universal testing machine, with crosshead
displacement rate kept constant to 2.5·10-2 mm/s for a nominal initial strain rate of 5·10-3 s-1 [103].
Contact surfaces were lubricated with the low-temperature Lubriplate® L0034-086 grease [209] to
minimise friction between sample and die walls, thus ensuring homogeneous strain in the RD-TD
plane. Compliance of the plunger-die fixture has been determined with an off-sample preliminary
3. EXPERIMENTAL METHODS
-76-
test. Furthermore, the PSC elastic stiffness 𝐸 has been estimated after each test by minimum
squares, with the average for each alloy then calculated as presented in Section 4.4.
Figure 3.7. (a) Exploded view of the channel-die and plunger fixture designed for the PSC tests of this project, where contact surfaces have been hatched: on the one hand, the sample is compressed between the bottom surface of the
plunger (black arrow) and the top surface of the channel (orange arrow), and between the front and back channel walls (blue arrows); on the other hand, the sample can stretch freely along the RD (red arrows). (b) One of the actual PSC tests
of this study.
The following procedure has been subsequently used to transform load applied 𝐹 and crosshead
displacement upon the tests into true stress 𝜎, true strain 𝜀 and true plastic strain 𝜀𝑃 values given
in the stress-strain curves presented:
(i) The compliance of the fixture has been removed from crosshead displacement to give the
actual displacement of the sample during the test ∆.
(ii) 𝐹 and ∆ have been converted into true stress 𝜎 and true strain 𝜀 values using Equation 3.3
and Equation 3.4 [32], where ℎ0 represents the initial height of the sample, and 𝑆0 its initial
surface area in the RD-TD plane.
BACK WALL
CHANNEL
RDTD
ND
PLUNGER
(a)
FRONT WALL
(b)
PLUNGER
CHANNEL-DIE
CROSSHEAD
3. EXPERIMENTAL METHODS
-77-
(iii) True total strain 𝜀 has been transformed into true plastic strain 𝜀𝑃 with Equation 3.5 [32]
using the average stiffness 𝐸 mentioned above.
𝜀 = −ln (1 −|∆|
ℎ0) (3.3)
𝜎 =𝐹
𝑆0(1 −
|∆|
ℎ0) (3.4)
𝜀𝑃 = 𝜀 −𝜎
𝐸 (3.5)
As well as stress-strain curves, mechanical properties are also given for each condition. All values
presented are the average of at least three tests. Proof strengths and peak stresses are given as
true values and strains-to-failure as plastic engineering reductions. Due to the difficulty in defining
a pure yield strength from the experimental curves, proof stresses at 0.2% engineering plastic
strains are presented here, as in most of prior studies on the plastic behaviour of magnesium, e.g.
[106] [131] [132] [154] [168] [173] [176] [210]. Confidence intervals have been calculated with the
IBM® SPSS® version 21 package [211].
Finally, the evolution of work hardening Θ against 𝜀𝑃 is also presented as calculated with Equation
3.6 [32]. The resultant curves have been smoothed employing a moving averages procedure. The
derivative of work hardening with respect to plastic strain Θ′ has been calculated as per Equation
3.7. Values presented are average for the intervals selected (i.e. Stage II).
Θ =Δσ
Δ𝜀𝑃 (3.6)
Θ′ =ΔΘ
Δ𝜀𝑃 (3.7)
Metallographic sample preparation
Samples have been cut from annealed plates using a Struers® Discotom-6 machine with a cutting
speed of 0.01-0.02 mm/s. A series of conventional water-lubricated grinding steps has then been
conducted. For samples intended for XRD texture measurement, this has been the last stage. For
those aimed at optical microscopy and microhardness, mechanical polishing with 3 µm diamond
paste and water-free colloidal silica with nominal particle size of 0.25 µm has followed.
In samples intended for optical microscopy, electropolishing has been further conducted in order
to remove the deformed layer resulting from mechanical polishing. For this goal, an electrolyte
consisting of 175 mL methanol and 75 mL nitric acid has been prepared, and maintained at
temperatures between –20 and –30°C during operation. Contact between solution and sample has
3. EXPERIMENTAL METHODS
-78-
been kept for approximately 5-6 seconds, and voltage to 12 V. Finally, in order to reveal the
microstructural details, electropolished surfaces have been chemically etched with an Acetic-Picral
solution (5 mL acetic acid, 6 g picric acid, 10 mL water and 100 mL ethanol), followed by 2% Nital (2
mL nitric acid, 98 mL ethanol), the latter of which enhances grain boundary contrast.
4. RESULTS
-79-
4 RESULTS
Vickers hardness against annealing temperature
The evolution of Vickers hardness with annealing temperature is shown for both alloys in Figure
4.1. The hardness of the as-hot rolled conditions has also been included for completion. Standard
deviations of all measurements have been found to lie within 5% of the corresponding average
values.
Figure 4.1. Vickers hardness against annealing temperature for the two alloys in study. The error bars represent standard deviations. Comparison with values predicted by the model developed by Gao et al. [167] is also displayed.
From a qualitative point of view, the evolution of hardness with annealing temperature has been
mainly the same for the two alloys: both have shown a relatively sharp drop at an intermediate
temperature (indicated by the arrows in the figure), with monotonic softening at constant rates at
higher temperatures, and no apparent impact of annealing at lower temperatures. This trend is
largely the same as in former magnesium studies performing similar analyses [125] [200] [201].
Moreover, the magnitude of the drops lies in the range of those previously attributed to SRX in
those studies [125] [200] [201]. Therefore, it seems reasonable to ascribe values of 𝑇𝑆𝑅𝑋 ≈ 350°𝐶
to Mg-0.03Y and 𝑇𝑆𝑅𝑋 ≈ 00°𝐶 to Mg-0.6Y. This is also in line with past research on Mg-RE alloys
[183] [200], which has invariably found solute RE additions to result in 𝑇𝑆𝑅𝑋 increases even for RE
contents lower than in Mg-0.6Y here [200]. Reasons for this behaviour are discussed in Section
5.1.4.
Figure 4.1 shows also that the hardness of Mg-0.6Y has been higher than that of Mg-0.03Y across
the whole temperature range studied. Nevertheless, the difference has been more pronounced for
the deformed conditions, and both the SRX drop (≈10 HV for Mg-0.6Y and ≈5 HV for Mg-0.03Y) and
25
30
35
40
45
50
55
Vic
kers
Har
dn
ess
HV
Annealing Temperature T (°C)
Mg-0.6Y
Mg-0.03Y
Mg-0.6Y (Gao's model)
Mg-0.03Y (Gao's model)
4. RESULTS
-80-
the monotonic softening (≈0.04 HV/°C for Mg-0.03Y and ≈0.08 HV/°C for Mg-0.6Y) have been about
twice as strong for Mg-0.6Y. Accordingly, stronger SRX drop was reported for Mg-0.5Nd as
compared to pure magnesium in [201]. What is more, Figure 4.1 displays also that the hardness of
Mg-0.6Y is in very good correlation with that predicted by the equation developed by Gao et al.
[167] for the Vickers hardness of binary Mg-Y alloys. In this study, the same indentation load and
time as here were used, as well as grain sizes of ≈210 µm [167], i.e. comparable to those after
annealing at 500°C here (next subsection). By contrast, correlation of Mg-0.03Y with Gao’s model
has not been as good, which may be explained by the fact that only yttrium concentrations above
0.5 wt% were used to derive the model [167].
Grain size against annealing temperature
The evolution of grain diameter with temperatures above 𝑇𝑆𝑅𝑋 is shown in Figure 4.2 for the two
alloys. Optical micrographs corresponding to such conditions are given in Figure 4.3 for Mg-0.03Y
and Figure 4.4 for Mg-0.6Y. None has displayed any traces of incomplete SRX, confirming the
validity of the 𝑇𝑆𝑅𝑋 values inferred in last subsection. Micrographs for the as-rolled conditions are
provided in Figure 4.5 for the sake of completion.
Figure 4.2. Evolution of grain diameter with annealing temperature for the two alloys in study. The dashed lines correspond to exponential laws calculated with the least squares method and demonstrating good correlation with experimental data. Comparison with results in similar studies by Nadella et al. [212] and Hadorn et al. [158] is also
included.
D = 5.4508e0.5598T
R² = 0.9816
D = 32.719e0.2897T
R² = 0.96
0
50
100
150
200
250
300
350 375 400 425 450 475 500
Gra
in D
iam
ete
r D
(µ
m)
Annealing Temperature T (°C)
Mg-0.6Y
Mg-0.03Y
Pure Mg (Nadella et al.)
Mg-0.75Y (Hadorn et al.)
4. RESULTS
-81-
Figure 4.3. Optical micrographs obtained for Mg-0.03Y hot-rolled and annealed for one hour at (a) 350°C, (b) 400°C, (c)
425°C, (d) 450°C and (e) 500°C.
5 00 µm
D =53 µm(a)
5 00 µm
D =62 µm(b)
5 00 µm
D =101 µm(c)
5 00 µm
D =144 µm(d)
5 00 µm
D =265 µm(e)
RD
ND
4. RESULTS
-82-
Figure 4.4. Optical micrographs for Mg-0.6Y hot-rolled and annealed for one hour at (a) 400°C, (b) 425°C, (c) 450°C, (d)
475°C and (e) 500°C. Red circles show potential incomplete etching products.
Figure 4.5. Optical micrographs for (a) Mg-0.03Y and (b) Mg-0.6Y in the as-hot rolled states.
5 00 µm
D =27 µm(a)
5 00 µm
D =50 µm(b)
5 00 µm
D =109 µm(c)
5 00 µm
D =159 µm(d)
5 00 µm
D =247 µm(e)
1000 µm
(a)
1000 µm
(b)
RD
ND
RD
ND
RD
ND
4. RESULTS
-83-
In the same way as for hardness, Figure 4.2 reveals the same qualitative trend for the two alloys:
grain diameters have increased with temperature in both cases, with the increases conforming well
to exponential laws. This is in agreement with past studies conducting isochronal annealing in
magnesium alloys [213] [214] [215] and, in general, expectation for the occurrence of grain growth
after SRX completion (see Section 5.1.2).
In addition, Figure 4.2 shows also that the annealing treatments have led to consistently smaller
grain size for Mg-0.6Y than for Mg-0.03Y irrespective of the temperature of annealing. This is also
in accordance with previous studies on isochronal annealing of single-phase Mg-RE alloys, where
more concentrated alloys invariably displayed the finer sizes [118] [158] [159] [183] [189] [213].
Furthermore, as can be seen in Figure 4.2, results are in good quantitative agreement with past
observations for annealing treatments of the same duration in similar alloys: Mg-0.03Y against pure
magnesium by Nadella et al. [158], and Mg-0.6Y against Mg-0.75Y by Hadorn et al. [212]. In fact,
the slightly smaller grain diameter for Mg-0.75Y in [212] (21 against 27 µm) can be explained by the
somewhat higher yttrium content. Nevertheless, the difference between Mg-0.6Y and Mg-0.03Y
has again been more pronounced at the lower annealing temperatures: whereas the grain size of
Mg-0.6Y has been only about half that of Mg-0.03Y at the 𝑇𝑆𝑅𝑋 (Figure 4.3 (b) and Figure 4.4 (a)),
they have been nearly identical at 500°C (Figure 4.3 (d) and Figure 4.4 (d)).
As for the hot-rolled microstructures, the existence of shear bands in the two alloys is evident in
Figure 4.5. They have been measured to form angles of 22-37° to the RD. This agrees with former
work on rolled magnesium, where shear bands formed from double twins have been reported to
lie within approximately 20-35° to the RD [26] [29] [175] [180]. In addition, the shear bands in Mg-
0.03Y exhibit larger width and are more apparent than those in Mg-0.6Y. However, whereas those
in Mg-0.6Y seem to be homogeneously distributed and cover the whole microstructure, those in
Mg-0.03Y account for a limited material fraction (lower than 5%). This is also in accordance with
former studies comparing hot-rolled microstructures of pure magnesium and single-phase Mg-RE
alloys [57] [125] and, in general, the enhancing effect of RE additions on contraction twinning as
explained in Section 2.4.2.
4. RESULTS
-84-
Bulk texture against annealing temperature
Basal pole figures representing the bulk textures of conditions subjected to PSC testing as measured
by XRD are presented in Figure 4.6 for Mg-0.03Y and Figure 4.8 for Mg-0.6Y. Similarly, pole figures
accounting for {101̅0} prismatic planes are displayed for completion in Figure 4.7 and Figure 4.9,
respectively. As in previous sections, as-hot rolled states have been included for reference.
Figure 4.6. Recalculated {0001} pole figures corresponding to Mg-0.03Y (a) in the as-hot rolled condition, and after annealing at (b) 350°C, (c) 425°C and (d) 500°C for one hour. Intensities are given in MRD.
(a) (b)
(c) (d)
4. RESULTS
-85-
Figure 4.7. Recalculated {101̅0} pole figures corresponding to Mg-0.03Y (a) in the as-hot rolled condition, and after annealing at (b) 350°C, (c) 425°C and (d) 500°C for one hour. Intensities are given in MRD.
(a) (b)
(c) (d)
4. RESULTS
-86-
Figure 4.8. Recalculated {0001} pole figures corresponding to Mg-0.6Y (a) in the as-hot rolled condition, and after annealing at (b) 400°C, (c) 450°C and (d) 500°C for one hour. Intensities are given in MRD.
(a) (b)
(c) (d)
4. RESULTS
-87-
Figure 4.9. Recalculated {101̅0} pole figures corresponding to Mg-0.6Y (a) in the as-hot rolled condition, and after annealing at (b) 400°C, (c) 450°C and (d) 500°C for one hour. Intensities are given in MRD.
4.3.1 Bulk texture behaviour of Mg-0.03Y
As shown in Figure 4.6, Mg-0.03Y has invariably displayed basal textures before and after annealing.
Noteworthily, spread from the basal fibre has been somewhat greater towards the RD than to the
TD, with this effect more pronounced after annealing. Greater spread to the RD in basal textures in
magnesium has been usually reported [45] [117] [125] [178] [183] [189]. Figure 4.6 shows also that
annealing has reduced peak basal intensity irrespective of annealing temperature, albeit intensity
monotonically increasing with annealing temperature (namely, a ~75% rise from 400 to 500°C). This
behaviour agrees with past observations on conventional magnesium, for which basal intensity has
been found to initially decrease as per SRX [35] [120] [121] [122] [123], and then to increase as per
grain growth [57] [118] [120] [125] [126] [127], see e.g. Figure 2.10. Furthermore, all peak basal
intensities here measured for Mg-0.03Y lie in the range of those in the literature for conventional
magnesium alloys, comprised within 4.5-14.0 MRD [45] [115] [125] [162] [178] [183] [189].
(c) (d)
(a) (b)
4. RESULTS
-88-
About prismatic poles, no clear pattern can be distinguished for Mg-0.03Y in any of the conditions
considered (Figure 4.7), i.e. prismatic planes are randomly distributed in the RD-TD plane regardless
of annealing. This is in agreement with past observations in magnesium alloys showing basal texture
components [31] [115] [124] [189]. In addition, the trend shown by peak prismatic intensities is in
line with that of basal pole figures, i.e. peak intensities are lower for all annealed conditions, but
increase monotonically with temperature. Finally, all peak prismatic intensities here presented lie
in the range of those formerly presented for conventional magnesium alloys, comprised within 1.6-
4.4 MRD [45] [115] [126] [162] [189].
4.3.2 Bulk texture behaviour of Mg-0.6Y
As for Mg-0.6Y, the as-hot rolled condition exhibits an RD-split texture (Figure 4.8 (a)), which has
been preserved after annealing at 400°C (Figure 4.8 (b)). The tilting of the RD lobes has been of 14-
15° for these two conditions, which lies in the 10-20° range of values formerly reported for RD-split
textures in Mg-RE sheet [35] [55] [56] [178] [180]. By contrast, Figure 4.8 (c) and (d) show that the
RD-split fibre has been substituted after annealing at 450 and 500°C by a component tilted from
the ND to the TD by 30-50°. Interestingly, a non-dominant component tilted towards the TD by ~42°
is also present after annealing at 400°C (Figure 4.8 (b)), although with much less spread both within
the rolling plane and to the ND. This TD-split fibre is unusual following past observations in binary
Mg-RE alloys (recall Section 2.4.3), and reasons for its occurrence here are discussed in Section 5.2.
Overall, peak basal intensity has been reduced by annealing regardless of temperature, although
with the reduction being only slight at 400°C (~5%), and dramatic at either 450 or 500°C (60 and
40%, respectively). Such dramatic reductions are in agreement with the texture weakening typical
of Mg-RE alloys, expected for this alloy following its yttrium content (recall Figure 2.33). All four
basal peak intensities lie within the 2.4-7.4 MRD range measured in the past for Mg-RE sheet [118]
[125] [158] [176] [178] [183] [189]. As for the TD-split component, its intensity has monotonically
increased with annealing temperature, from 2.1 MRD at 400°C to 3.9 MRD at 500°C.
About prismatic pole figures, Figure 4.9 shows preferential alignment with the RD both after hot
rolling and further annealing, and irrespective of annealing temperature. This agrees with former
observations on RD-split fibres in Mg-RE alloys [162] [189], and implies the RD alignment is common
to both RD-split and TD-split components. Peak prismatic intensities have followed the same trend
for the basal pole figures above, with those corresponding to 450 and 500°C significantly lower
(~20%) than for the as-rolled and 400°C conditions. Similarly, spread has been considerably greater
for the two higher temperatures. All peak prismatic intensities measured here for Mg-0.6Y lie in the
range of those previously reported for Mg-RE alloys [162] [189].
4. RESULTS
-89-
Plane-strain compression (PSC) behaviour against annealing temperature
The outcome of the PSC testing of selected annealing conditions is presented across this section,
namely stress-strain curves, work hardening response and morphology of fractured specimens. For
the sake of clarity, initial grain sizes and key texture parameters are summarized in Table 4.1. Data
corresponding to comparable PSC experiments by Nave and Barnett on basal-textured pure
magnesium in the 𝑐 axis compression and extension orientations [141] are included to facilitate the
comparison with those obtained here.
For reference, Figure 4.10 shows the as-deformed geometry of one of the specimens tested. The
‘barrelling’ effect indicating extension under compression [32] is evident in TD-ND faces (Figure
4.10 (b)), but not in RD-ND faces (Figure 4.10 (a)), which remain perfectly plane and parallel to each
other as before testing. This agrees with the constraint of TD strain expected from channel-die
walls, with the RD allowed to stretch (Figure 3.7), confirming that specimens have effectively
undergone a PSC state equivalent to that of cold rolling.
Table 4.1. Initial grain size, XRD peak basal texture intensity and tilting of the basal poles to the ND for the annealing conditions tested under PSC. Comparable data from [141] are provided as a benchmark.
Annealing
Temperature (°C)
Grain size
𝑫(µm)
Peak basal
intensity (MRD)
Tilting of basal peaks
to the ND (°)
Mg-0.03Y
350 53 7.2 0
425 101 8.5 0
500 266 12.0 0
Mg-0.6Y
400 27 5.1 15
450 110 2.6 50
500 248 4.5 50
Pure Mg [141]
(Nave-Barnett)
𝑐 axis contraction 70 14.0 0
𝑐 axis extension 70 14.0 90
Figure 4.10. Mg-0.6Y (450°C) specimen unloaded shortly after peak stress and represented with the (a) TD-ND, and (b)
RD-ND faces parallel to paper. While TD-ND faces exhibit distinct ‘barrelling’, RD-ND faces are perfectly plane.
(a) (b)(a) (b)
ND
ND
RDRD
ND
ND
TDTD
4. RESULTS
-90-
4.4.1 Plane-strain compression behaviour of Mg-0.03Y
Stress-strain curves corresponding to the three conditions tested for Mg-0.03Y are presented in
Figure 4.11 and Figure 4.12, with the resultant mechanical properties summarized in Table 4.2. All
the curves have been corrected for a mean elastic stiffness of 7.72 ± 2.24 GPa calculated over eleven
specimens in total. This value shows good correlation with work by Backofen and Wonsiewicz, who
reported an elastic stiffness for the PSC of pure magnesium of approximately one fifth of its Young’s
modulus [87] (according to the extensive review given in [216] ,Young’s moduli from 39 to 46 GPa
have been measured in the past for pure magnesium).
Table 4.2. Mechanical properties corresponding to the PSC testing of Mg-0.03Y conditions. Average and typical deviation corresponding to at least three specimens are indicated in each of the cases. Results in a comparable study are provided
for reference.
Figure 4.11. True stress-true total strain curves corresponding to the PSC of Mg-0.03Y annealed at 350, 425 and 500°C for one hour. Curves have been truncated shortly after failure.
0
50
100
150
200
250
300
350
0.00 0.05 0.10 0.15
Tru
e St
ress
σ(M
Pa)
True Strain ε
Mg-0.03Y (350°C) Mg-0.03Y (425°C) Mg-0.03Y (500°C)
Annealing
Temperature (°C)
Proof Strength
0.2% (MPa)
Peak Stress
(MPa)
Strain-to-
failure (%)
Mg-0.03Y
350 31.4±2.1 275.4±2.4 7.8±0.3
425 51.8±2.3 285.4±5.4 4.8±0.1
500 112.8±3.2 273.3±2.4 3.0±0.2
Pure Mg [141]
(Nave-Barnett)
𝑐 axis contraction 116 220 2.8
𝑐 axis extension 29 275 8.0
4. RESULTS
-91-
Figure 4.12. True stress-true plastic strain curves corresponding to the PSC of Mg-0.03Y annealed at 350, 425 and 500°C for one hour. Curves have been truncated shortly after failure.
Figure 4.13. RD-ND faces of two different fractured Mg-0.03Y (425°C) specimens: (a) just after peak stress, and (b) after full unloading. Dashed lines represent approximate positions of catastrophic cracks.
As can be seen in Figure 4.11, plastic flow has started for Mg-0.03Y at lower stress the lower the
annealing temperature, with proof strength nearly four times higher for Mg-0.03Y(500°C) than for
Mg-0.03Y(350°C) (Table 4.2). Likewise, flow has shifted from a distinct concave-up shape for Mg-
0.03Y(350°C) to fully concave-down for Mg-0.03Y(500°C). As for Mg-0.03Y(425°C), its behaviour has
been essentially concave-up, although a short stage of increasing work hardening is apparent below
0.03 total strain (Figure 4.11). Nevertheless, peak stresses have been very similar in all conditions,
i.e. within 5% of each other (Table 4.2). In this sense, specimens have been invariably observed to
be cracked shortly after peak stress (Figure 4.13), meaning that strain-to-failure has decreased with
0
50
100
150
200
250
300
350
0.00 0.05 0.10 0.15
Tru
e St
ress
σ(M
Pa)
True Plastic Strain εP
Mg-0.03Y (350°C) Mg-0.03Y (425°C) Mg-0.03Y (500°C)
(a)
1 mm
(b)
1 mm
ND
ND
RDRD
4. RESULTS
-92-
greater annealing temperature: the overall strain sustained by Mg-0.03Y(350°C) has been over two
and a half times higher than that sustained by Mg-0.03Y(500°C), and about 60% higher than by Mg-
0.03Y(425°C) (Table 4.2). As illustrated in Figure 4.13, Mg-0.03Y samples have consistently shown
after failure V-shaped crack patterns starting far from any specimen corners and converging near
the specimen centreline.
If the present results are compared with those available in the literature for pure magnesium, it is
shown that proof strength and strain-to-failure for all Mg-0.03Y conditions lie in the range of those
reported by Nave and Barnett [141] (Table 4.2). Furthermore, all peak stresses found for Mg-0.03Y
are very close in value to those measured by these authors under 𝑐 axis extension [141]. This good
correspondence adds grounds onto the validity of the present results, with the specifics of the
comparison discussed in more depth in Section 5.3.3 and 5.3.4.
Further, work hardening evolution for the three conditions is displayed as a function of plastic strain
in Figure 4.14 and as a function of stress in Figure 4.15. These plots confirm that Stage II as widely
reported for conventional magnesium alloys tested under 𝑐 axis compression [87] [106] [111] [128]
[129] [141] (e.g. Figure 2.11 and Figure 2.12) is present not only for Mg-0.03Y(350°C), but also for
Mg-0.03Y(425°C). By contrast, Stage II is effectively inhibited for Mg-0.03Y(500°C), in accordance
with general findings for conventional magnesium alloys under 𝑐 axis compression [87] [106] [128]
[129] [141], e.g. Figure 2.11. With regard to Stage I, its extent is so short irrespective of the specific
condition as not to be apparent in Figure 4.14. However, Figure 4.15 shows that the straight line
accounting for elastic behaviour effectively becomes curved prior to the onset of Stage II (dotted
lines). Furthermore, the drop in work hardening associated to Stage I is more rapid the lower the
annealing temperature. For Mg-0.03Y(500°C), the short transient of constant hardening at Θ ≈
1 000 MPa, more clearly displayed in Figure 4.15 also, resembles that encountered by Knezevic et
al. under 𝑐 axis compression [106] (Figure 2.11, just after point I).
Quantitative differences between Stage II in Mg-0.03Y(425°C) and Mg-0.03Y(350°C) are presented
in detail in Table 4.3. Although the plastic strain provided by Stage II (𝛥𝜀𝑃)𝐼𝐼 has been over six times
shorter for Mg-0.03Y(425°C), the overall increase of work hardening during Stage II ∆Θ𝐼𝐼 has been
roughly the same for both. Nevertheless, the rate of the increase as defined by the derivative of
work hardening during Stage II with respect to plastic strain Θ𝐼𝐼′ has been remarkably higher for Mg-
0.03Y(425°C). Finally, the plastic strain at which Stage II has started (𝜀𝑃)𝐼𝐼 has been slightly higher
for Mg-0.03Y(350°C), i.e. Stage I has been slightly longer.
4. RESULTS
-93-
Figure 4.14. Work hardening evolution throughout the plastic range for the three annealing conditions tested for Mg-0.03Y. The schematic represents the three stages of work hardening as previously defined in magnesium literature [106]
[111].
Figure 4.15. Work hardening against true stress for the three annealing conditions tested for Mg-0.03Y. Dotted lines accounting for Stage I have been added for visual guidance.
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
0.00 0.02 0.04 0.06 0.08 0.10 0.12
Wo
rk H
ard
enin
g Θ
(MP
a)
True Plastic Strain εP
Mg-0.03Y (350°C) Mg-0.03Y (425°C) Mg-0.03Y (500°C)
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
0 50 100 150 200 250 300 350
Wo
rk H
ard
en
ing Θ
(MP
a)
True Stress σ
Mg-0.03Y (350°C) Mg-0.03Y (425°C) Mg-0.03Y (500°C)
(𝛥𝜀𝑃)𝐼𝐼
II IIII
𝛥𝛩𝐼𝐼𝛩𝐼𝐼′
(𝜀𝑃)𝐼𝐼
4. RESULTS
-94-
Table 4.3. Parameters defining the Stage II of work hardening for the annealing conditions tested for Mg-0.03Y: plastic strain at which Stage II is onset (𝜀𝑃)𝐼𝐼, plastic strain extent (𝛥𝜀𝑃)𝐼𝐼 , overall increase of work hardening ∆𝛩𝐼𝐼, and rate of
the work hardening increase 𝛩𝐼𝐼′ . Graphical definition of parameters is shown in Figure 4.14. The increase in strain-to-
failure with respect to the condition displaying the lowest strain-to-failure is also indicated.
4.4.2 Plane-strain compression behaviour of Mg-0.6Y
Stress-strain curves corresponding to the conditions tested for Mg-0.6Y are given in Figure 4.16 and
Figure 4.17, with the resultant mechanical properties indicated in Table 4.4. The curves have been
corrected for a mean elastic stiffness of 9.13±2.42 GPa resulting from ten specimens tested. This
value is in good agreement with that reported for Mg-0.03Y in last subsection. In turn, this agrees
with Peng et al., who found the Young’s modulus of pure magnesium to be essentially unaffected
by yttrium contents as low as that in Mg-0.6Y [216].
Figure 4.16. True stress-true total strain curves corresponding to the PSC of Mg-0.6Y annealed at 400, 450 and 500°C for one hour. Curves have been truncated shortly after failure. Arrows in the curves point at the approximate point of
failure.
0
50
100
150
200
250
300
350
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Tru
e St
ressσ
(MP
a)
True Strain ε
Mg-0.6Y (400°C) Mg-0.6Y (450°C) Mg-0.6Y (500°C)
Annealing
Temperature (°C) ( )𝑰𝑰 (𝜟 )𝑰𝑰
∆ 𝑰𝑰
(MPa)
𝑰𝑰′
(MPa)
Increase in strain-
to-failure
Mg-0.03Y
350 0.0035 0.032 1680 52.3 0.047
425 0.0026 0.007 1710 316.7 0.018
500 n/a n/a n/a n/a n/a
4. RESULTS
-95-
Figure 4.17. True stress-true plastic strain curves corresponding to the PSC of Mg-0.6Y annealed at 400, 450 and 500°C for one hour. Curves have been truncated shortly after failure. Arrows in the curves point at the approximate point of
failure.
Table 4.4. Mechanical properties corresponding to the PSC testing of Mg-0.6Y conditions. Average and typical deviation corresponding to at least three specimens are indicated in each of the cases.
Annealing
Temperature (°C)
Proof Strength
0.2% (MPa)
Peak Stress
(MPa)
Strain-to-
failure (%)
Mg-0.6Y
400 103.8±1.9 300.9±3.6 9.1±0.5
450 62.9±3.7 231.6±1.2 19.7±0.6
500 56.8±4.7 223.1±2.1 21.1±0.4
Figure 4.16 and Figure 4.17 show that, unlike for Mg-0.03Y, yielding has occurred earlier the greater
the annealing temperature for Mg-0.6Y. Specifically, while the difference between Mg-0.6Y(450°C)
and Mg-0.6Y(500°C) has been slight only, Mg-0.6Y(400°C) has displayed nearly twice as high proof
stress (Table 4.4). The character of the stress-strain curves of all three conditions has been concave-
up, in line with comparable PSC tests conducted by Drouven et al. on hot-rolled and then annealed
Mg-1Nd sheet [217], and Agnew et al. in as-cast Mg-1Y sheet [103]. Even so, two distinct typologies
have arisen in terms of Stage III (Figure 4.16): in a similar way as for Mg-0.03Y above, fracture has
been followed by quick unloading after peak stress for Mg-0.6Y(400°C); on the other hand, strain
has continued without fracture and in a state of saturation of stress for Mg-0.6Y(450°C) and Mg-
0.6Y(500°C). For the two latter, fracture has occurred at a certain point within the stress saturation
stage, typically noticeable by subtle increase of the softening rate (arrows in Figure 4.16 and Figure
4.17) instead of drastic unloading. Correspondence between such inflection point and fracture has
0
50
100
150
200
250
300
350
0.00 0.05 0.10 0.15 0.20 0.25
Tru
e St
ress
σ(M
Pa)
True Plastic Strain εP
Mg-0.6Y (400°C) Mg-0.6Y (450°C) Mg-0.6Y (500°C)
4. RESULTS
-96-
been checked to ≈1% strain accuracy. In this sense, levels of strain sustained by the stress saturation
stages have been significant, and led the strains-to-failure of Mg-0.6Y(450°C) and Mg-0.6Y(500°C)
to be over twice as high as for Mg-0.6Y(400°C) (Table 4.4). Among the former, Mg-0.6Y(500°C) has
exhibited slightly higher values than Mg-0.6Y(450°C). Interestingly, Drouven et al. reported fracture
readily after peak stress [217], i.e. the same behaviour as for Mg-0.6Y(400°C) here, but Agnew et
al. found stress saturation stages similar to those here [103]. Finally, peak stress has diminished
considerably with greater annealing temperature in virtue of the softer activation of the stress
saturation stage (Table 4.4).
Figure 4.18. RD-ND faces of fractured Mg-0.6Y (450°C) specimens (a) just after the onset of failure and (b) after significantly larger reduction. Cracks starting at each of the four corners are clearly shown.
Figure 4.19. RD-ND faces of two fractured Mg-0.6Y (400°C) specimens (a) just after the onset of failure and (b) after further reduction. Cracks have started at one corner only: top-right in (a), and bottom-left in (b).
Regarding fracture patterns, significant differences have also arisen between Mg-0.6Y(400°C) and
the other two conditions. For the two latter, incipient cracks have been typically encountered close
to three or four of the sample corners (Figure 4.18 (a)). In fact, cross-shaped patterns suggesting
two corner-to-corner propagating directions have been found without exception after sufficiently
(a)
1 mm
(b)
1 mm
(a)
1 mm
(b)
1 mm
ND
ND
RDRD
4. RESULTS
-97-
large reductions (Figure 4.18 (b)). By contrast, for Mg-0.6Y(400°C) specimens, incipient cracks have
been observed close to one of the corners only. After full unloading, one single crack traversing the
cross-section in diagonal has been invariably observed (Figure 4.19).
Figure 4.20. Work hardening response for the three annealing conditions tested for Mg-0.6Y. The schematic represents the three stages of work hardening as previously defined in magnesium literature [106] [111].
Figure 4.21. Work hardening against true stress for the three annealing conditions tested for Mg-0.03Y.
Work hardening evolution for the three conditions is presented in Figure 4.20 and Figure 4.21. Plots
are consistent with the concave-up character noted above, exhibiting the three stages typical of
-1000
0
1000
2000
3000
4000
5000
6000
0.00 0.04 0.08 0.12 0.16
Wo
rk H
ard
enin
g Θ
(MP
a)
True Plastic Strain εP
Mg-0.6Y (400°C) Mg-0.6Y (450°C) Mg-0.6Y (500°C)
-1000
0
1000
2000
3000
4000
5000
6000
0 50 100 150 200 250 300 350
Wo
rk H
ard
enin
g Θ (
MP
a)
True Stress σ
Mg-0.6Y (400°C) Mg-0.6Y (450°C) Mg-0.6Y (500°C)
(𝛥𝜀𝑃)𝐼𝐼
II IIII
𝛥𝛩𝐼𝐼𝛩𝐼𝐼′
(𝜀𝑃)𝐼𝐼
4. RESULTS
-98-
magnesium. With regard to Stage I, the drop in work hardening has been significantly quicker the
greater the temperature. As indicated in Table 4.5, while the onset of Stage II has been earlier the
greater the temperature also, its extent has been remarkably reduced; yet, both the magnitude and
rate of the work hardening increase upon Stage II have been enhanced the higher the temperature.
At the onset of Stage III, the reduction in work hardening has been steady for Mg-0.6Y(400°C), but
monotonic up to failure. By contrast, Mg-0.6Y(450°C) and Mg-0.6Y(500°C) have shown a relatively
quick drop at first, after which work hardening has stabilized at essentially constant values as per
the stress saturation stages noted above. Nevertheless, saturation values have been qualitatively
different for both conditions: practically zero i.e. actual stress saturation for Mg-0.6Y(500°C), but
negative (Θ ≈ 300 MPa) i.e. work softening for Mg-0.6Y(450°C).
Table 4.5. Parameters defining the Stage II of work hardening for the annealing conditions tested for Mg-0.6Y: plastic strain at which Stage II is onset (𝜀𝑃)𝐼𝐼, plastic strain extent (𝛥𝜀𝑃)𝐼𝐼 , overall increase of work hardening ∆𝛩𝐼𝐼, and rate of
the work hardening increase 𝛩𝐼𝐼′ . Graphical definition of parameters is shown in Figure 4.20.
Annealing
Temperature (°C) ( )𝑰𝑰 (𝜟 )𝑰𝑰 ∆ 𝑰𝑰 (MPa) 𝑰𝑰
′ (MPa)
Mg-0.6Y
400 0.025 0.027 510 18.9
450 0.018 0.017 820 47.7
500 0.010 0.016 1710 102.2
5. DISCUSSION
-99-
5 DISCUSSION
The effect of yttrium on the annealing behaviour of magnesium
The effect of yttrium on the annealing behaviour of magnesium as shown in Section 4.1 and 4.2 is
analysed below. The main goal is to determine if the yttrium addition in Mg-0.6Y has produced a
shift in the atomistic grain boundary migration regime operating upon grain growth with respect to
Mg-0.03Y. This has been proposed to be a requirement for the texture weakening typical of Mg-RE
alloys upon annealing, effectively exhibited here by Mg-0.6Y, but not by Mg-0.03Y (recall Section
4.3). For this aim, the statically recrystallised grain diameters of both alloys are derived in the first
subsection, and then used to estimate the apparent activation energies for grain growth in the
second. These are assessed by Lücke-Detert’s theory in the third, which provides a means of
qualitatively assessing grain boundary migration regimes. Finally, the origin of the increase in SRX
temperature in Mg-0.6Y as compared to Mg-0.03Y is discussed in the fourth section.
5.1.1 The effect of yttrium on the statically recrystallised grain diameter
In metallurgy, the statically recrystallised grain diameter 𝐷0 of a given alloy is customarily defined
as the grain diameter measured just after the completion of SRX upon annealing [198], i.e. just at
the start of grain growth.
Particularly, 𝐷0 is known to be dependent on the precedent deformation route, but independent
of the temperature of annealing [186]. Therefore, a single 𝐷0 can be assumed in this study for all
the SRXed conditions corresponding to each alloy, as the hot rolling operation has been the same.
In other words, the differences in grain size in Figure 4.2 can be entirely ascribed for each of the
alloys to the event of grain growth from a fixed 𝐷0 value. Hence, for each alloy, it is the smallest of
the diameters measured –that corresponding to its 𝑇𝑆𝑅𝑋– that will be closer to its 𝐷0. For Mg-
0.03Y, the grain size at its 𝑇𝑆𝑅𝑋 (350°C) can be assumed to be a good approximation for 𝐷0 –i.e.
𝐷0 ≈ 53 µ𝑚– since the difference in grain diameter against the immediately greater temperature
(375°C) is nearly negligible (below 5%) [176]. By contrast, for Mg-0.6Y, it can only be ascertained
that 𝐷0 ≤ 27 µ𝑚. In any case, what is clear is that the addition of yttrium has led to considerably
smaller 𝐷0 (at the most, 50% of that shown by Mg-0.03Y). This is in line with previous studies on
isochronal annealing of single-phase Mg-RE alloys, where RE additions led to 𝐷0 values about 60%
[183] and 25% [162] those of pure magnesium after the same processing routes.
Classically, differences in recrystallised grain sizes have been interpreted as a function of the ratio
between the rate of nucleation and rate of growth of recrystallizing grains [198]: relatively faster
nucleation leads to finer size by producing more grains and thus reducing the volume available for
5. DISCUSSION
-100-
each; relatively faster growth gives rise to coarser size by reducing the amount of grains that can
be nucleated before impingement and thus raising the volume available for each. For the present
case, the following can be stated about nucleation and growth rates:
(i) Nucleation rates are enhanced by greater driving pressures for SRX, i.e. greater stored
energies after deformation [198]. Greater stored energies after hot processing compared
to conventional magnesium alloys have been effectively measured for single-phase Mg-RE
alloys [122] including a single-phase Mg-Y alloy after hot rolling [162]. The subsequently
higher nucleation rates would be in line with the smaller 𝐷0 here measured for Mg-0.6Y.
(ii) As explained in Section 2.4.3, growth rates are rationalised in single-phase alloys as the
outcome of the balance between a positive driving pressure counteracted by solute drag
[186]. According to this, greater stored energy should result in faster growth and thus larger
𝐷0; even so, this effect of driving pressure on growth is in general less powerful than that
on nucleation noted in previous paragraph [198]. Regarding solute drag, it will be proved
more powerful for Mg-0.6Y than for Mg-0.03Y in next subsections. This means that RE
additions would contribute to smaller 𝐷0 not only by increasing the rates of nucleation of
SRXed grains, but also by retarding their growth via solute drag.
In summary, the effect of solute RE additions on the SRXed grain size of magnesium has been here
discussed for this first time. Particularly, it has been proved to be powerfully reduced, which may
be associated to both greater stored energy after rolling and greater solute drag. From a practical
viewpoint, this means that smaller minimum grain size can be obtained in annealed magnesium by
including RE additions, which will be advantageous for any downstream applications where small
grain sizes are preferable, e.g. (i) when sheet is to be formed under strain paths for which
formability is enhanced by finer grain size (Section 2.3.6); (ii) when higher strength is a concern by
enhancing grain boundary hardening; and (iii) when the “orange peel” surface defect typical of
formed sheet is undesirable, as it has been observed in magnesium for grain diameters above 30
µm only [218] [219] [220].
5.1.2 The effect of yttrium on the activation energy for grain growth
As described in Section 2.4.3.1, boundary migration during grain growth operates through atomic
diffusion and, hence, is thermally activated [186] [187] [198]. Therefore, grain growth rates are
described with reasonable accuracy by Arrhenius-type laws [186] [187] [198] like Equation 5.1
[198], where 𝐷 is the average grain diameter, 𝑇 is the temperature of the annealing, 𝑅 is the ideal
gas constant, 𝐾 is an alloy-dependent parameter, and 𝑄𝐺𝐺 represents the apparent activation
5. DISCUSSION
-101-
energy for grain boundary migration during grain growth. This can be understood as the energy
barrier to be overcome for grain boundaries to effectively migrate upon grain growth.
The Arrhenius-like behaviour of grain growth rates can explain the exponential trend followed by
grain sizes in Figure 4.2: if all SRXed conditions share the same 𝐷0 at the start of grain growth (see
last subsection), any differences in grain size after a fixed time of annealing will depend solely on
grain growth rates. Such Arrhenius behaviour explains also why grain sizes of both alloys become
increasingly similar with higher temperature: the effect of the smaller 𝐷0 for Mg-0.6Y is greater at
lower temperatures, at which slow boundary migration allows for limited growth only (virtually
none below 400°C as shown by Mg-0.03Y); at greater temperatures, relatively high growth rates
make the impact of 𝐷0 less significant against that of grain growth. In turn, this tendency for grain
sizes to become equal can account for hardness also becoming increasingly similar above 𝑇𝑆𝑅𝑋. As
indentation size did not vary significantly among conditions (𝑑1 ≈ 𝑑2 ≈ 1 0 µm), the amount of
grain boundary strengthening captured diminished with annealing temperature. For the highest
temperature considered, grain size became significantly larger than indentation size for the two
alloys (𝐷 ≈ 200 µm), so that the different hardness for each can be attributed to solid solution
strengthening only [167].
𝑑𝐷
𝑑𝑡= 𝐾𝑒
𝑄𝐺𝐺𝑅𝑇 (5.1)
More specifically, Equation 5.1 can be integrated with respect to the initial time point of grain
growth to give Equation 5.2, referred to as Reed-Hill’s law for grain growth [198]. Moreover, the
𝑄𝐺𝐺 energy for each of the alloys can be estimated from the grain sizes in Figure 4.2 by taking
natural logarithms in Equation 5.2. As can be seen in Equation 5.3, the quotient 𝑄𝐺𝐺/𝑅 can then
be derived as the slope of a ln (∆𝐷2)–(1/𝑇) plot provided that the time 𝑡 elapsed since the onset
of grain growth is the same for all treatments. This assumption has been successfully made in other
studies developing static grain growth models in magnesium alloys [213] [214] [215]. The
approximation of 𝐷0 ≈ 27 µ𝑚 for Mg-0.6Y (see Section 5.1.1) is also followed hereinafter.
𝐷2 −𝐷02 = ∆𝐷2 = 𝐾𝑡𝑛𝑒
𝑄𝐺𝐺𝑅𝑇 (5.2)
ln(∆𝐷2) = ln(𝐾) + 𝑛 · ln (𝑡) −𝑄𝐺𝐺𝑅𝑇
(5.3)
The grain sizes in this study have been plotted following Equation 5.3 in Figure 5.1. Good linear
correlation is shown between ln (∆𝐷2) and (1/𝑇) for both alloys, confirming the validity of the
Arrhenius approach. Furthermore, substitution of the regression coefficients into Equation 5.3 in
5. DISCUSSION
-102-
conjunction with a value 𝑅 = 8.31 𝐽/(𝐾 · 𝑚𝑜𝑙) [198] gives rise to activation energies of 𝑄𝐺𝐺 =
51.6 𝑘𝐽/𝑚𝑜𝑙 for Mg-0.03Y, and 𝑄𝐺𝐺 = 93.0 𝑘𝐽/𝑚𝑜𝑙 for Mg-0.6Y. As displayed in Figure 5.2, the
former is in line with reports for conventional magnesium alloys with solute zinc and aluminium
additions also hot-rolled and annealed [213] [214] including AZ31 [215]. By contrast, the latter is
similar to that measured in [213] for Mg-1.5Zn-2Er.
Figure 5.1. Logarithm of the increment of grain size squared resulting from grain growth plotted against the negative reciprocal of annealing temperature for the alloys in study. Data for annealing temperatures between 400 and 500°C are
considered, and the dashed lines correspond to linear regression equations calculated by the least squares method.
As alloying additions can only exert retarding effects on grain boundary migration (either solute
drag or particle pinning [186]), the slightly higher 𝑄𝐺𝐺 of Mg-0.03Y (essentially pure magnesium)
compared to Mg-1.5Zn and AZ31 in Figure 5.2 (both with significant solute contents) may seem
counterintuitive. However, Farzadfar et al. reported no significant differences between the grain
growth rates of pure magnesium and Mg-2.9Zn during annealing in [162]. This would point to the
effect of conventional solute additions on 𝑄𝐺𝐺 being small only in the best of cases. By contrast,
elements such as iron, copper [200] (Figure 5.3) or nickel [192], all usual impurities in magnesium
castings [31], have been proved to strongly retard boundary migration in magnesium. Therefore,
considering the castings in this project are of industrial quality only, the higher 𝑄𝐺𝐺 value of Mg-
0.03Y may well be ascribed to the effect of impurities overcoming that observed by Zhang et al.
[213] and Murty et al. [215] for zinc and aluminium.
On the other hand, the relatively high activation energy measured by Zhang et al. for Mg-1.5Zn-2Er
was attributed by the authors to strong pinning by intermetallic Mg-Zn-Er particles [213]. In this
sense, the rise in 𝑄𝐺𝐺 from Mg-0.03Y to Mg-0.6Y here (due to solute yttrium atoms) seems to
quantitatively match that observed by these authors from single-phase Mg-1.5Zn to Mg-1.5Zn-2Er
log (ΔD 2) = 11.19(-1/T·10³ ) + 19.01R² = 0.972
log (ΔD 2) = 6.42(-1/T·10³ ) + 12.74R² = 0.993
2.5
3.0
3.5
4.0
4.5
5.0
-1.45 -1.4 -1.35 -1.3 -1.25
log
(ΔD
2)
-1000/T (1/K)
Mg-0.6Y
Mg-0.03Y
5. DISCUSSION
-103-
[213]. This would go against general observations in metals, for which particle pinning has been
usually found to be more restrictive than solute drag [186]. Yet, other examples exist for solute drag
and particle pinning leading to quantitatively similar effects, e.g. Nb atoms and NbC carbides in
steel [221].
Figure 5.2. Comparison between the apparent activation energies for grain growth here obtained for Mg-0.03Y and Mg-0.6Y and comparable values provided by Zhang et al. [213], Fang et al. [214] and Murty et al. [215]. Estimated activation
energies for the interdiffusion of yttrium of magnesium and the grain boundary self-diffusion of magnesium are also given for assessment of grain boundary mobility regimes by Lücke-Detert’s theory.
To sum up, the effect of solute RE additions on the apparent activation energy for grain growth in
magnesium has been here analysed for the first time. The resultant increase has been found to be
as powerful as to quantitatively match that previously attributed to particle pinning in this metal.
From a practical perspective, this suggests high potential for RE elements to improve the thermal
stability of magnesium, which can help achieve fine microstructures more easily, e.g. by reducing
the effect of unforeseen periods at elevated temperature during processing and thus the need for
robust processing lines [31]. In addition, 𝑄𝐺𝐺 values can be used to shed light onto the atomistic
mechanisms controlling grain growth, which is dealt with in the following subsection.
5.1.3 Solute drag by Lücke-Detert’s theory
Lücke-Detert’s theory is the most widely accepted theory [186] on the effect of solute atoms on
grain boundary mobility. As dealt with in Section 2.4.3.1, two operation regimes depending on
solute content level are proposed: (i) breakaway and (ii) drag. Each is controlled by a different
diffusion mechanism, which has been suggested to reflect on the physical meaning of activation
energies for processes such as recrystallization and grain growth [187]. The following reasoning has
been successfully applied in the past to metals such as lead, copper, aluminium [187] or zinc [193],
but not to magnesium:
0
20
40
60
80
100
120
Mg-0.03Y Mg-0.6Y Mg-1.5Zn(Zhang et al.)
Mg-1.5Zn-2Er(Zhang et al.)
AZ31(Murty et al.)
Mg-4.9Zn(Fang et al.)
Act
ivat
ion
En
ergy
fo
r G
rain
G
row
th Q
GG
(kJ/
mo
l)
𝑄𝐺𝐵′ = 0.5𝑄𝐵
′
𝑄𝐵 + 𝑈(0)
5. DISCUSSION
-104-
(i) In the breakaway regime, growth rates are determined by the rate of diffusion of parent
atoms across grain boundaries. Hence, 𝑄𝐺𝐺 should directly correspond in this case to the
activation energy for the grain boundary self-diffusion of magnesium 𝑄𝐺𝐵′ [187].
(ii) In the drag regime, growth rates are defined by the rate of diffusion of solute atoms behind
migrating grain boundaries. Therefore, 𝑄𝐺𝐺 should equal the sum of the activation energy
for the diffusion of yttrium in bulk magnesium 𝑄𝐵 and the interaction energy between
yttrium atoms and magnesium grain boundaries 𝑈(0) [187].
With regard to the breakaway regime, 𝑄𝐺𝐵′ data for the case of polycrystalline magnesium have not
been found in the literature. However, 𝑄𝐺𝐵′ is often approximated in metallurgy to half the
activation energy for self-diffusion in the bulk 𝑄𝐵′ [186] [187]. In this sense, 𝑄𝐵
′ = 13 .0 𝑘𝐽/𝑚𝑜𝑙
was measured for magnesium in the benchmark study conducted in [222], which would lead to an
estimate of 𝑄𝐺𝐵′ = 67.0 𝑘𝐽/𝑚𝑜𝑙. Although this is somewhat higher than the 𝑄𝐺𝐺 derived for Mg-
0.03Y here (about 21%) as well as for other conventional magnesium alloys in the past (see Figure
5.2), the deviation lies in the range of those resulting for other metals like aluminium (+23%) and
copper (-17%) if their self-diffusion 𝑄𝐺𝐵′ values [223] are compared to 𝑄𝐺𝐺 energies obtained from
annealing [224]. Moreover, it must be recalled at this point that alloy purity has a major influence
on experimentally measured boundary migration rates [187]. Consequently, it can be reasonably
concluded that grain growth in conventional magnesium alloys including those with aluminium and
zinc additions or Mg-0.03Y here operates in the breakaway regime. In turn, this implies that either
aluminium and zinc or solute RE contents below the critical for texture weakening do not suffice to
restrict boundary migration rates during grain growth.
As for the drag regime, diffusion couple experiments conducted in single-phase Mg-Y alloys have
yielded a value of 𝑄𝐵 = 99.1 𝑘𝐽/𝑚𝑜𝑙 [197]. In addition, 𝑈(0) can be estimated from the equation
proposed by McLean for the interaction of solute atoms with grain boundaries [225] (Equation 5.4),
where 𝐾𝑌 is the bulk modulus of yttrium, 𝐺𝑀𝑔 is the shear modulus of magnesium, and 𝑟𝑌 and 𝑟𝑀𝑔
their atomic radii. Values for these properties have been compiled in Table 5.1. Although this
equation only considers the effect of the elastic strain relieved when solute atoms segregate to
grain boundaries from the bulk, thus neglecting chemical and electronic interactions, minor
contribution from the two latter is expected for size misfits higher than 10% [226]. Considering the
data in Table 5.1, this would be effectively the case of yttrium in magnesium (size misfit ≈ 12.5%).
Accepting thus McLean’s equation for the present case, substitution of the data in Table 5.1 into
Equation 5.4 would give rise to an estimation of 𝑈(0) = 8.5 𝑘𝐽/𝑚𝑜𝑙, i.e. 𝑄𝐵 + 𝑈(0) =
107.6 𝑘𝐽/𝑚𝑜𝑙.
5. DISCUSSION
-105-
𝑈(0) =2 𝜋𝐾𝑌𝐺𝑀𝑔𝑟𝑀𝑔
3 (𝑟𝑌 − 𝑟𝑀𝑔
𝑟𝑌)2
3𝐾𝑌 + 𝐺𝑀𝑔 (5.4)
Table 5.1. Input parameters for McLean’s equation for the interaction between solute yttrium atoms and magnesium grain boundaries 𝑈(0) (extracted from [195]).
𝑟𝑀𝑔 Atomic radius of Mg (nm) 0.1601
𝑟𝑌 Atomic radius of Y (nm) 0.1801
𝐺𝑀𝑔 Shear modulus of Mg (GPa) 16.5
𝐾𝑌 Bulk modulus of Y (GPa) 44.0
As shown in Figure 5.2, this means that 𝑄𝐵 + 𝑈(0) would be slightly higher than the 𝑄𝐺𝐺 derived
for Mg-0.6Y (roughly 14%). Nevertheless, such deviation can be accounted for by Gordon and
Vandermeer’s correction [227] to Lücke-Detert’s theory, who, similarly to here, derived for copper
atmospheres in aluminium a 𝑄𝐺𝐺 value about 18% lower than their estimated 𝑄𝐵 + 𝑈(0). These
authors noted that the relatively “loose” atomic packing near grain boundaries should lead the
activation energy for the diffusion of atoms in solute atmospheres to be somewhat lower than that
for their diffusion in the bulk 𝑄𝐵 [227]. Yet, the activation energy for diffusion “near” the boundaries
should be closer to 𝑄𝐵 than to that for diffusion “at” grain boundaries 𝑄𝐺𝐵, where the atomic
packing is much “looser” [225]. With 𝑄𝐺𝐵 often assumed to be 50% of 𝑄𝐵 [186] [187] (in the same
way as in the case of self-diffusion as noted above), this would be effectively the case here: 𝑄𝐺𝐺 for
Mg-0.6Y is much closer to 𝑄𝐵 + 𝑈(0) than to 𝑄𝐺𝐵 +𝑈(0), which would take a value of
58.5 𝑘𝐽/𝑚𝑜𝑙 under the assumption above. Therefore, grain growth in Mg-0.6Y can be concluded
to practically operate in Lücke-Detert’s drag regime. This means that the solute yttrium
atmospheres experimentally reported in recent times for yttrium contents similar to that in Mg-
0.6Y [158] [189] effectively restrict grain boundary mobility during grain growth, proposed to be a
requirement for the texture weakening exhibited by these alloys (Section 2.4.3) including Mg-0.6Y.
In conclusion, the postulates of Lücke-Detert’s theory have been compared for the first time with
activation energies for grain growth in magnesium. It has been found that, whereas conventional
magnesium alloys which do not exhibit texture weakening operate in the breakaway regime, Mg-
0.6Y, which does exhibit this effect, operates in the drag regime. This suggests that, as recurrently
proposed by recent research, the restriction of boundary migration by solute RE atmospheres is
effectively connected with the formation of RE textures.
5. DISCUSSION
-106-
5.1.4 Static recrystallisation (SRX) temperature and solute drag
The hardness measurements in Section 4.1 revealed a significant increase in 𝑇𝑆𝑅𝑋 by the addition
of solute yttrium. Similarly, the extensive survey on the impact of alloying additions on the SRX
temperature of magnesium conducted by Ichikawa in the 1950s found the 𝑇𝑆𝑅𝑋 rise potential of RE
elements to be remarkably higher than that of any other common additions in this metal [200]
[228]: as illustrated in Figure 5.3, while all other additions yielded increases of up to 75°C only,
cerium raised 𝑇𝑆𝑅𝑋 by as much as 125-225°C [200]. Although the increment by yttrium here is not
as powerful, this may be attributed to impurities leading to relatively high 𝑇𝑆𝑅𝑋 in the pure metal
already (i.e. Mg-0.03Y). As displayed through the comparison with other conventional magnesium
alloys in previous section, the effect of impurities was not substantial in terms of 𝑄𝐺𝐺. In any case,
despite the remarkable magnitude of the 𝑇𝑆𝑅𝑋 increase as reported by Ichikawa, no explanations
have been offered so far to the author’s knowledge.
Figure 5.3. SRX temperature as a function of solute concentration for various alloying elements added to high-purity magnesium. The dotted line represents the SRX temperature of the pure metal (after Ichikawa [200] [228]).
In this regard, it must be recalled that, similarly to grain growth, recrystallization operates through
grain boundary migration [186]. Therefore, any restrictions to grain boundary mobility would be
expected to be operative not only during grain growth, but upon recrystallization also. In a similar
way as here displayed for grain growth, this would lead to an increase in the activation energy for
recrystallization which would be ultimately perceived as higher temperature needed for the onset
and completion of recrystallisation in a given amount of time, i.e. greater 𝑇𝑆𝑅𝑋. In fact, solutes like
aluminium and zinc for which the breakaway regime is operative during grain growth (see former
subsection) lie in the range of low 𝑇𝑆𝑅𝑋 increases in Figure 5.3. Moreover, reductions in boundary
mobility due to solute drag or particle pinning have been quoted as the reason for considerable
𝑇𝑆𝑅𝑋 increases in other alloying systems, e.g. [229] [230] [231] [232]. Nonetheless, it may also be
200
250
300
350
400
450
500
0.01 0.1 1
SRX
Te
mp
erat
ure
TSR
X(°
C)
Concentration (at.%)
Sn
Ce
Mn
Cu
Cd
Al
Zn
FePure Mg
5. DISCUSSION
-107-
argued that recrystallisation is a ‘nucleation + growth’ process, so that more difficult formation of
nuclei may also contribute to the greater 𝑇𝑆𝑅𝑋. However, as pointed out in Section 5.1.1, former
work on Mg-RE alloys suggests that nucleation rates are precisely enhanced by RE elements in
magnesium, which would leave out the restriction of mobility as the primary reason.
Noteworthily, the case of cerium is special among RE elements in that its solid solubility is low in
magnesium (Figure 2.33). In fact, in their extensive study on texture weakening (Section 2.4.3),
Basu and Al-Samman considered not only gadolinium (Figure 2.34) but also cerium: for the latter,
they suggested that the boundary mobility restrictions associated to texture weakening arise from
fine precipitates and not from RE atmospheres as in gadolinium [175] [185] or yttrium [158] [189].
However, this does not necessarily mean that RE elements forming solute atmospheres exert a less
powerful effect on 𝑇𝑆𝑅𝑋. On the contrary, grain growth rates have been encountered to be higher
for gadolinium [185] and yttrium [118] than cerium added in the same amount, which may also
apply to 𝑇𝑆𝑅𝑋. No differences in terms of driving pressure and thus nucleation would be expected
either, as no essential differences have been reported between cerium and the other RE elements
in terms of their effect on deformation of magnesium (Section 2.4). In any case, more research is
required to fully characterize the response of RE additions to SRX and to understand the underlying
mechanisms. For yttrium (or gadolinium), a Lücke-Detert approach analogous to that employed
here for grain growth could be applied to conditions at different stages of SRX completion to
determine if the drag regime is also operative during SRX in practice.
To conclude, RE elements have been suggested to powerfully increase the SRX temperatures of
magnesium. To account for this behaviour, the same grain boundary mobility restrictions affecting
grain growth and contributing to texture weakening are proposed here. Further research aimed at
elucidating this point is thus encouraged.
The origin of the TD-split textures of Mg-0.6Y
As noted in Section 2.3.3 and Section 2.4.3, the following texture components have been reported
in the literature for rolled magnesium: (i) basal (typical of conventional alloys), (ii) RD-split (typical
of binary Mg-RE alloys both after hot rolling and subsequent annealing as well as of ternary Mg-Zn-
RE alloys after hot rolling), and (iii) TD-split (typical of Mg-Zn-RE after subsequent annealing only).
Therefore, the TD-split texture here developed by binary Mg-0.6Y during annealing (recall Section
4.3.2) is in apparent disagreement with past magnesium research, as TD-split fibres are considered
by the current literature to be “exclusive” [55] to Mg-Zn-RE alloys [55] [124]. In view of this, reasons
for the occurrence of a TD-split texture in Mg-0.6Y are discussed throughout this section.
5. DISCUSSION
-108-
Nevertheless, it should be noted that, although RD-split fibres are effectively the only ones present
in binary Mg-RE alloys in the vast majority of cases, e.g. [29] [56] [118] [158] [160] [161] [162] [178]
[180] [183] [185] [189] [198], a recent study shows a texture with both RD- and TD-split fibres
simultaneously for hot-rolled, then annealed Mg-2.2Y [131]. The tilting angle of each component is
in line with that demonstrated by Mg-0.6Y here, the texture thus being analogous to that of the
Mg-0.6Y(400°C) condition (Figure 4.8 (b)). Unfortunately, only basal pole figures and not prismatic
are presented by the authors for a more detailed comparison [131]. In addition, regular Mg-RE
texture –i.e. with RD split only– is presented in the same study and after similar processing route
for Mg-0.5Y [131]. As this study was focused on the further deformation behaviour of these alloys,
the presence of a TD-split fibre was not even mentioned by the authors [131]. The richer yttrium
content of Mg-2.2Y as compared to Mg-0.5Y will be proposed below to have played a role in the
development of TD-split fibre by the former only.
Similarly, the TD-split fibres typical of Mg-Zn-RE alloys (e.g. Figure 2.31 (c)-(d)) also resemble closely
those shown by Mg-0.6Y. Firstly, they are centred at about the same tilting angle with respect to
the ND (~45° [57] [124]). Secondly, the preferred orientation is the same as here not only for basal
poles, but also for prismatic, preferentially aligned with the RD [57]. Thirdly, TD-split fibres are not
present in as-hot rolled conditions, but emerge after annealing only [35] [57] [124] [175], also the
case of Mg-0.6Y. Moreover, textures with either TD-split components isolated or combined with
RD-split fibres as that of Mg-0.6Y(400°C) have also been presented for Mg-Zn-RE alloys [57] (Figure
2.31 (d))). In line with these similarities, reasons are given in what follows which support that the
effect is the same in Mg-RE and Mg-Zn-RE alloys. For this purpose, the possible origin of TD-split
fibres in magnesium will be discussed beforehand, as tentative explanations have not been found
in the literature even for Mg-Zn-RE alloys. The relative scarcity of TD-split observations in binary
Mg-RE systems will then be considered in the light of this origin.
5.2.1 The origin of TD-split orientations in RE-containing magnesium alloys
The dominant components in the usual rolled textures of other HCP metals, namely titanium and
zirconium, are known to be also tilted from the ND to the TD [233]. For such metals, this orientation
is accepted to result from the rotation induced upon deformation by prismatic slip, the softest slip
mode for them. By contrast, basal slip is the most active mode in magnesium and produces basal
fibres, which dominate conventional textures in magnesium [233]. Nevertheless, it must be recalled
that prismatic slip has been demonstrated to be considerably enhanced by solute RE additions in
magnesium [158] [159] [160] [161]. Since it is precisely in RE-containing magnesium alloys that TD-
split fibres appear, it would seem reasonable to think of this mechanism as responsible in these
alloys also. In fact, deformation under the strain path of cold rolling of sheet initially oriented to the
5. DISCUSSION
-109-
directions of loading at angles such that prismatic slip is the only deformation mechanism possible
has been repeatedly shown to result in TD-split textures in magnesium also [117] [162] [234].
In addition, if previous magnesium research is considered, no evidence of rotations into TD-split
orientations upon either recrystallization or grain growth seems to have been given [124]. Hence,
the origin of the fibre appears effectively more likely in deformation behaviour. For the Mg-Zn-RE
system, this would be supported by the EBSD analysis by Mackenzie and Pekguleryuz [45], which
found TD-split orientations to be already present in the deformed fractions of hot-rolled sheet. And,
among the deformation mechanisms available in magnesium, prismatic slip is the only for which
evidence of rotations into TD-split orientations has been presented to the author’s knowledge [117]
[162] [234]. Basal slip and tension twinning have been associated to fully basal textures, and ⟨𝑐 + 𝑎⟩
glide and double twinning to RD-split orientations [103] [114] [118] [185] (Section 2.3.3).
Therefore, in the same way as for titanium and zirconium, prismatic slip would represent a plausible
explanation for TD-split textures in RE-containing magnesium alloys. Yet, the usual tilting of basal
poles to the ND for titanium and zirconium is much smaller (20-40° [233]) than in past observations
in Mg-Zn-RE alloys or for Mg-0.6Y here (40-60° [35] [57] [175]). Even so, the TD-split fibres produced
by deformation of magnesium with initial orientations allowing for prismatic slip only also possess
tilting angles larger than 40° [117] [234]. The larger angles appear thus inherent to magnesium, and
their origin would represent an interesting issue for further research.
Assuming thus that it is upon deformation that TD-split orientations appear, the texture changes
presented in Section 4.3.2 may be explained by an oriented grain growth effect. This phenomenon
would be in line with that put forth by Basu and Al-Samman [175] [185] to account for the RE texture
weakening (recall Section 2.4.3). The difference with Basu and Al-Samman’s mechanism would be
that these authors assumed that the orientations of off-RD-split grains consuming RD-split grains
upon annealing are random (Figure 2.34), but here we consider that they preferentially align with
TD-split orientations. By these means, TD-split grains would possess growth advantages over RD-
split grains, gradually increasing in size at their expense and until they disappear.
If the latter is assumed, the absence of TD-split fibre for Mg-0.6Y in the as-hot rolled state would
be explained by initially small size (and scarce quantity) of TD- compared to RD-split grains. After
certain degree of grain growth, the increased size of TD-split grains would make their orientations
statistically significant and, hence, apparent in pole figures; at the same time, RD-split grains would
decay in size/quantity, and so would the intensity of the RD-split fibre. This would explain why both
components coexist for Mg-0.6Y(400°C), with weaker texture for the RD-split than in the hot-rolled
state. After further grain growth (e.g. isochronal annealing at greater temperature), RD-split grains
5. DISCUSSION
-110-
would eventually disappear, leading to the extinction of the RD-split fibre, as here the case for Mg-
0.6Y(450°C). At the same time, with TD-split grains even coarser in size, the intensity of the TD-split
fibre would be higher, as also here for Mg-0.6Y(450°C) against Mg-0.6Y(400°C). This would explain
also the greater spread of the TD-split in Mg-0.6Y(450°C), as orientations about the prevalent one
within the TD-split and also present in grains with growth advantages would equally increase their
statistical significance gradually, and eventually emerge from the background also. Finally, if grain
growth continues further from this point (e.g. isochronal annealing at even greater temperature),
TD-split grains would consume the few remaining RD-split grains, further raising the intensity of the
TD-split fibre, as here for Mg-0.6Y(500°C). The smaller spread in this condition compared to Mg-
0.6Y(450°C) could be explained by the final prevalence of the TD-split orientations with the greater
growth advantages, or just by the smaller number of grains sampled for this condition in virtue of
its relatively large grain size (a fixed sample area has been used for all XRD measurements, Section
3.3.3). The irregular aspect of prismatic poles for Mg-0.6Y(500°C) in comparison to Mg-0.6Y(450°C)
suggests a significantly smaller number of grains sampled for the former. The whole sequence of
preferred orientations as proposed here has been represented for clarity in Figure 5.4. The effect
of increased annealing temperature is also presented in the figure: by leading to quicker kinetics,
grain growth is more advanced the higher the temperature if isochronal treatments are considered.
The underlying oriented grain growth as put forth in this paragraph could be checked with an EBSD
analysis of the four conditions as that carried out by Basu and Al-Samman in [185] (see Figure 2.34).
This rationale would also hold for Mg-Zn-RE alloys, for which the sequence here proposed has been
effectively proved as a function of annealing time [57] (Figure 2.31 (c)-(e)). Similar EBSD analysis of
Mg-Zn-RE alloys would thus be also advisable.
Finally, the apparent discrepancy with Basu and Al-Samman in terms of the orientation of off-RD-
split grains is yet to be discussed. In particular, these authors presented EBSD maps for binary Mg-
1Gd where off-RD-split grains surviving after RD-split orientations are fully extinguished exhibit no
preferential alignment –and, in any case, no TD-split orientations at all [185], see Figure 2.34 (c).
This contrasts with present results, which clearly aim at preferential alignment of off-RD-split grains
with TD-split orientations in also binary Mg-0.6Y. A possibility for explaining this discrepancy is the
small number of grains covered by EBSD maps (less than ~50 grains in Figure 2.34 (c)). Another
option would be that the relative occurrence of TD-split orientations in Mg-RE alloys is strongly
dependent on factors like hot rolling conditions (e.g. reduction, number of passes, temperature),
texture in the as-cast condition, etc. Further research is required to elucidate these points. In any
case, it is clear that random off-RD-split grains also possess growth advantages in this case because
texture intensities of TD-split fibres are significantly lower that of the RD-split at the beginning of
5. DISCUSSION
-111-
annealing. Random orientations were concluded to be nucleated upon SRX by Basu and Al-Samman
[175] [185], and as such have been introduced in Figure 5.4.
Figure 5.4. Rationale suggested in this project for the development of RD- and TD-split texture fibres in RE-containing magnesium alloys during annealing. The following colour coding has been used: grey = RD-split orientations, blue = TD-split orientations, yellow = randomly distributed orientations. Solid circles account for orientations actually noticeable in pole figures, and dashed circles for those in the microstructure, but with low texture intensities against the background.
The situation on the left side represents accelerated kinetics compared to that on the right side, which is proposed to occur (i) when increasing solute RE content, (ii) in Mg-Zn-RE as compared to binary Mg-RE alloys, and (iii) when raising
annealing temperature.
ANNEALING TIME
RD D P
t=0
D P
RD D P
D P
RD
D
RD
D
RD
D
RD
D
AS-ROLLED
RD P
RD
DRD P
RD
D
RD P
RD
D
D
RD P
RD
D
5. DISCUSSION
-112-
5.2.2 The scarcity of TD-split observations in binary Mg-RE alloys
Consequently, (i) significant deformation by prismatic slip and (ii) oriented grain growth would be
the two requirements for the development of TD-split fibres in RE-containing magnesium alloys.
Additionally, Basu and Al-Samman proposed solute drag, practically demonstrated in this project in
Section 5.1.3, to be a requisite for the oriented grain growth (Section 2.4.3). If these mechanisms
are assumed, the scarcity of TD-split findings in binary Mg-RE alloys against Mg-Zn-RE alloys may
be explained by the subsequent impact of zinc additions on these effects:
(i) As for prismatic slip, solute zinc atoms are known to considerably enhance this deformation
mode in magnesium by diminishing prismatic-to-basal CRSS ratios [178] [235] [236] [237].
Moreover, suggestions have been made that zinc and RE atoms pairing at dislocations could
lead to an enhancement of prismatic slip more powerful than that due to either element in
isolation [175]. If the corresponding ternary diagrams [238] are considered, most of zinc
(~80%) present in Mg-Zn-RE alloys studied (i.e. ZE10 [35] [57] [175]) would be effectively
expected to be in solid solution at the hot rolling temperatures used by the main studies
dealing with the textures of such alloys [35] [57] [175]. In terms of the theory here put forth
for the occurrence of TD-split textures, more active prismatic slip would raise the amount
of material having such orientations in the as-rolled condition. This could only be expected
to accelerate the emergence of TD-split fibres upon annealing in comparison to binary Mg-
RE alloys, less prone to prismatic slip.
(ii) As for solute drag, it has also been suggested to be increased by the addition of solute zinc
to Mg-RE alloys by (i) zinc atoms pairing with RE atoms in solute atmospheres [175], and (ii)
leading to additional pinning by Zn-containing particles [125] [175]. Most of zinc present in
Mg-Zn-RE alloys would also be expected to be in solute form at the annealing temperatures
used in former studies on these alloys [35] [57] [175]. In terms of the theory presented for
TD-split fibres here, greater solute drag would enhance any differences in growth kinetics
between grains with varying levels of driving force [175]. The prevalence of grains having
growth advantages, in this case TD-split grains, would thus be accelerated by the addition
of zinc in a similar way as the enhanced prismatic slip above.
As a result, the addition of zinc to Mg-RE alloys may be considered to accelerate the emergence of
TD-split components (Figure 5.4). According to this, it may be easier to capture such fibres after
annealing in the conditions conventionally employed by former research in the case of Mg-Zn-RE
alloys. In fact, annealing times have normally been limited in former studies to one hour or less for
temperatures of 350-450°C [29] [35] [56] [57] [118] [158] [160] [161] [162] [175] [178] [180] [183]
[185] [189] [198]. TD-split fibres have been found in Mg-Zn-RE alloys after annealing times as short
5. DISCUSSION
-113-
as 15 min within the same temperature range [57]. Future research encompassing longer annealing
times could thus help clarify whether this is the reason for the scarcity of TD-split observations in
binary Mg-RE alloys.
In addition, other factors could also facilitate the development of TD-split textures during annealing
and its kinetics. Among them, higher RE concentration would be expected to accelerate its onset
(Figure 5.4): similarly to zinc, RE additions have been repeatedly observed to enhance prismatic slip
more the richer the content [158] [159] [160] (e.g. Figure 2.23), with higher solute contents also
increasing solute drag [186] [187]. In fact, this could be the reason why Mg-2.2Y developed a TD-
split in [131] but not Mg-0.5Y after similar processing. Likewise, specific alloying additions could
have different impacts. In this sense, Basu and Al-Samman showed much higher texture weakening
rates for Mg-1Gd than for Mg-1Ce in [185]. Of course, rolling conditions should also play a role as
exemplified by Mackenzie and Pekguleryuz for ZE10 in [57], where lower rolling temperature while
keeping the same annealing was shown to delay the occurrence of TD-split texture. This could be
related with the thermal activation of prismatic slip.
To sum up, an explanation for the unusual development of a TD-tilted texture component by Mg-
0.6Y has been proposed. The occurrence of this texture fibre is proposed to be intrinsic to binary
Mg-RE alloys, and to have a common origin with its usual development in Mg-Zn-RE alloys, for which
no explanation had been proposed either in the past. Such orientations would be generated by the
deformation of certain grains by prismatic slip during rolling. Oriented grain growth would then
increase their texture intensity gradually upon annealing. This explanation would complement Basu
and Al-Samman’s theory for the RE texture weakening, outlining the tendency of grains consuming
RD-split fibres upon annealing to align with TD-split fibres rather than possess random orientations
only.
The effect of annealing on the behaviour of magnesium under the strain path
of cold rolling
The effect of previous annealing on the behaviour of Mg-0.03Y and Mg-0.6Y in the PSC tests as
shown in Section 4.4 is discussed in this section. Particularly, attention is paid to the main features
of the three work hardening stages typical of the compression of magnesium. Observations are
interpreted in terms of the main influencing microstructural variables resulting from annealing i.e.
grain size and texture, with differences between the two alloys associated to the solute yttrium
addition. The onset of stress saturation stages in Stage III for Mg-0.6Y and parameters defining work
hardening in Stage II for both alloys are discussed first, and then used to unravel the mechanisms
controlling the formability under the strain path of cold rolling for the two alloys, which represents
5. DISCUSSION
-114-
the main goal of this project. Work hardening upon Stage I and its relationship with proof strength
upon the strain path of cold rolling for both alloys is discussed at the end for completion.
5.3.1 Stress saturation in the Stage III of Mg-RE alloys
As shown in Section 4.4.2, the plastic range is considerably prolonged for Mg-0.6Y(450°C) and Mg-
0.6Y(500°C) in Stage III in a state characterized by the saturation of stress. By contrast, such effect
is absent for Mg-0.6Y(400°C) and all of Mg-0.03Y conditions (Section 4.4.1). In the same way as for
Mg-0.03Y, stress saturation stages have not been found in former studies reporting PSC of
conventional magnesium [106] [111] [114] [129] [239] including the pure metal [117] [141]. In the
case of Mg-RE alloys, stress saturation was not observed either in the PSC testing of Mg-1Nd by
Drouven et al. [217], but was effectively present in that of Mg-1Y by Agnew et al. [103]. Even so,
the latter study focused on texture development, was carried out in the infancy of modern
magnesium research, and reasons for the phenomenon were not discussed in depth [103]. In view
of this, the origin of stress saturation stages in the PSC of Mg-RE alloys is addressed below together
with conditions for its development. The distinct character of stress saturation for Mg-0.6Y(450°C)
and Mg-0.6Y(500°C) here is dealt with also. Since Stage III in the UAC and PSC of magnesium is
known to arise from the onset of 𝑐 axis compression (Section 2.3.4.1), reasons connected to ⟨c + a⟩
slip and contraction twinning are mainly sought.
5.3.1.1 The origin of microscopic softening
The saturation of flow stress exhibited by Mg-RE alloys and interrupting the work hardening typical
of metals must necessarily rely on some form of microscopic softening. In magnesium, such effect
has often been recognised for contraction twinning through the crystal reorientation associated
[29] [108] [114] [147] (Section 2.3.4.3). By contrast, ⟨c + a⟩ slip at room temperature has been
mainly related to microscopic hardening, associated in turn to forest hardening resulting from
reactions between ⟨c + a⟩ and ⟨a⟩ dislocations [43] [153] [170] [240]. In fact, empowerment of this
effect by the enhanced ⟨c + a⟩ slip inherent to Mg-RE alloys has been claimed to lie behind the
intrinsically high hardness and uniaxial yield strength typical of these alloys [157] [167] [168]
(Section 2.4.1.2).
Nevertheless, extensive cross-slip of ⟨c + a⟩ dislocations after cold rolling to only 3% strain has been
recently reported by Sandlöbes et al. for Mg-3Y [165]. This effect can lead to microscopic softening
through dynamic recovery (DRY) [165]. Likewise, reactions involving ⟨c + a⟩ dislocations and able
to produce DRY have been proposed by Máthis et al., although experimental evidence for pure
magnesium could be found above 200°C only, and not at room temperature [240]. Even so, much
remains to be known about solute RE effects on ⟨c + a⟩ slip in magnesium [153], and a potential
5. DISCUSSION
-115-
activation of either phenomenon at ambient temperature and stresses higher than the uniaxial
yield or those applied upon hardness testing may not be discarded for Mg-RE alloys. This would be
especially true for the cross-slip reported by Sandlöbes et al., which could be thought to be even
more active at the higher strains and stresses applied at which stress saturation could be expected
to be onset (stress saturation is here activated at ≈9% strain): cross-slip in general is a stress-
activated effect [98], and ⟨c + a⟩ slip in magnesium becomes more active as more grains are
reoriented into the basal fibre upon Stage II [103] [106] [111] [128], e.g. Figure 2.12 (although the
latter is yet to be confirmed for Mg-RE alloys). As a result, whereas the ability of contraction
twinning to produce microscopic softening appears clearer, solute RE effects on ⟨c + a⟩ slip
resulting in such behaviour cannot be ruled out.
In addition, stress saturation stages similar to those found here have been commonly reported for
cubic, ductile metals deformed in PSC conditions. For these, they are well-known to result from the
gradual localization of strain within shear bands, e.g. [241] [242] [243] [244]. As discussed in Section
2.3.4.3, shear bands arising from the accumulation of strain in contraction twins have been
recurrently reported in magnesium deformed under PSC [26] [29] [80] [81] [106] [114], e.g. Figure
2.16 and Figure 2.27. Despite the microstructural rationale behind shear band formation in cubic
metals being different (homogeneous slip interacting with planar obstacles [186] [243]), their role
in strain accommodation is analogous to that described for magnesium: they appear when textures
become too strong for deformation to continue being homogeneous [244], and act as soft bands
localizing further strain until a critical value is reached that triggers void nucleation [241] [242]
[243]. In view of this, shear banding would not be expected to appear in stress-strain curves in
magnesium differently from that in cubic metals, at least when shear banding is sufficiently profuse.
Moreover, specimens failed after shear banding in cubic metals exhibit cross-shaped crack patterns
starting close to corners [242] [243] [245] and similar to those displayed by Mg-0.6Y(450°C) and
Mg-0.6Y(500°C) here (Figure 4.18). The concentration of stress intrinsic to corners means that
associated shear bands localise higher strains, and nucleate voids earlier [245] [246], which lead to
cracks then growing by further void nucleation and coalescence. The hypothesis that contraction
twinning lies behind stress saturation is thus contrasted below with the inhibition of the effect for
some Mg-RE conditions reported here and in the literature.
5.3.1.2 Requirements for the onset of stress saturation
To start with, stress saturation has been here inhibited for Mg-0.6Y(400°C), but not for the other
two conditions corresponding to this alloy. On the one hand, the relatively strong RD-split texture
of Mg-0.6Y(400°C) would be expected to be more favourable to 𝑐 axes deformation modes than
the essentially random TD-split fibres of the other conditions: not only is the tilting of the main fibre
5. DISCUSSION
-116-
to the ND significantly smaller (≈15° vs ≈45°), but the stronger intensity reduces also the amount of
grains off the main fibre and thus with possibly larger tilting. Therefore, texture seems unlikely to
account for the inhibition of stress saturation in Mg-0.6Y(400°C) regardless of whether ⟨c + a⟩ slip
or contraction twinning lies behind the effect. In fact, for contraction twinning, crystal plasticity
simulations by Timár and Fonseca predict shear banding suppression by texture weakening: the
difficulty of contraction twinning in operating in grains with 𝑐 axes tilted away from the ND would
arrest the growth of shear bands into neighbouring grains, precluding the formation of noticeable
banding if the density of such grains is sufficiently high [144].
On the other hand, the initial grain size of Mg-0.6Y(400°C) is much smaller. For both deformation
modes of interest, an unambiguous effect has been put forward for size refinement in magnesium
(recall Section 2.3.6): inhibition of contraction twinning [65] [114] [127] [138], but promotion of
⟨c + a⟩ slip [151] [152] [153]. In line with the analogous behaviour of cubic metals noted above, the
suppression of stress saturation in Mg-0.6Y(400°C) points thus at contraction twinning. In this
sense, the difficulty of fine grains in nucleating contraction twins would be expected to avoid the
formation of not only those formed first in isolation, but also of those induced by neighbouring
twins. This could ultimately preclude the occurrence of noticeable shear bands from any twins
actually formed in a similar way as claimed by Timár and Fonseca for off-basal grains. The smaller
number of cracks for Mg-0.6Y(400°C) at failure (Figure 4.19) may thus be understood in terms of
lower twin density, which would decrease the chance that voids are nucleated close to multiple
specimen corners before the growth of cracks arising from those effectively formed gives rise to
catastrophic failure. Microstructural characterization of deformed specimens is currently ongoing
to ascertain differences in twinning and shear banding between conditions and thus elucidate this
point.
Similarly, the fact that stress saturation was present in the study by Agnew et al. [103] but not in
that by Drouven et al. [217] would work in the same direction. On the one hand, textures were
essentially random for both: as-cast [103] and a TD-split texture with maximum intensity similar to
that in Mg-0.6Y(450°C) [217], respectively. Again, this implies that unfavourable texture cannot
account for the inhibition of stress saturation. By contrast, grain size was markedly different:
relatively large for Agnew et al. (≈80 µm [103]), but fine for Drouven et al. (18 µm [217]). Therefore,
small grain size represents again a plausible explanation, further pointing at contraction twinning
lying behind the effect. The disagreement between recurrent observations of stress saturation in
the presence of random textures and inhibition predictions by Timár and Fonseca could be
explained by the lack of consideration of tension twinning in their model [247]. In this sense, tension
twinning has been recurrently found to be required by polycrystal models for the basal texture
5. DISCUSSION
-117-
sharpening upon Stage II to be accurately predicted [111] [116]. Consequently, Timár and Fonseca
may have overestimated the amount of grains with 𝑐 axes oriented away from the ND when the
CRSS for contraction twinning is reached.
However, the absence of stress saturation for conventional magnesium alloys including Mg-0.03Y
here does not provide any further clue on the underlying mechanism, as both ⟨c + a⟩ slip [29] [30]
[66] [157] [163] and contraction twinning [29] [56] [118] [161] [175] [176] are enhanced by RE
additions (recall Section 2.4.1.1 and 2.4.2.1). Nevertheless, it highlights the RE-specific character of
the effect in magnesium. In this sense, significantly scarcer shear banding in conventional alloys as
shown in Figure 2.27 [29] may be insufficient to produce significant additional deformation, and
thus noticeable stress saturation stages. Moreover, crack patterns in Mg-0.03Y (Figure 4.13) may
be explained by greater contraction twinning inhibition than in Mg-0.6Y(400°C): for this alloy, cracks
have not even started in the areas of highest stress concentration i.e. corners, which could be
explained by slight chance of twins to be formed nearby if activation of contraction twinning is
sufficiently scarce. Microstructural characterization of deformed specimens will help ascertain if
yttrium has effectively imparted more profuse contraction twinning compared to Mg-0.03Y even
for the fine grain size of Mg-0.6Y(400°C).
5.3.1.3 The amount of macroscopic softening
Finally, the distinct evolution of stress shown by Mg-0.6Y(500°C) and Mg-0.6Y(450°C) upon stress
saturation remains to be discussed, in that softening is patent for Mg-0.6Y(450°C), but stress is
essentially constant for Mg-0.6Y(500°C) (Figure 4.20). In this respect, stress evolution would be
expected to be determined by the balance between all the sources of microscopic hardening and
softening active [240]. Particularly, contraction twin boundary strengthening is currently accepted
as the most plausible explanation for the relatively high work hardening rates typical of Stage III in
conventional magnesium [106] [111] [147] (see Section 2.3.4.1). In the present case, the larger grain
size of Mg-0.6Y(500°C) compared to Mg-0.6Y(450°C) would be effectively expected to lead to higher
contraction twin density, and thus greater associated strengthening. This would impart further
microscopic hardening, which could balance the work softening practically dominant for Mg-
0.6Y(450°C). Therefore, contraction twin hardening represents a satisfactory explanation for the
evolution of work hardening in Stage III not only for conventional magnesium, but also for Mg-RE
alloys. The microstructural characterization of deformed specimens currently in progress should
help confirm this hypothesis by providing insight into twin density per condition. What is more, if
strain localisation in contraction twins is the prevalent source of microscopic softening as implied
above, this would mean that the effect of greater contraction twinning via larger grain size is more
effective in imparting microscopic hardening than softening. This same is implied by the high work
5. DISCUSSION
-118-
hardening rates attributed to contraction twinning by conventional magnesium studies. Following
this reasoning, stress could even increase during stress saturation for initial grain sizes larger than
for Mg-0.6Y(500°C).
To sum up, the stress saturation stages displayed by Mg-RE alloys under PSC have been proposed
to result from empowered contraction twinning and shear banding by solute RE atoms. Whereas
random texture does not seem effective in suppressing this effect, a minimum grain size appears
needed to avoid the twinning inhibition inherent to grain refinement. This means that solute RE
atoms can render the plastic behaviour of magnesium in plane-strain conditions closer to that of
ductile, cubic metals, which generally display sustained stress saturation stages under such paths.
In this sense, microstructural characterization of deformed specimens in this project is currently in
progress to confirm the connection between contraction twinning and stress saturation, and to
confirm if the greater softening exhibited by Mg-0.6Y(450°C) upon this stage as compared to Mg-
0.6Y(500°C) here can be effectively due to lower contraction twin boundary hardening.
5.3.2 The effect of annealing on the parameters defining the Stage II of work hardening
As explained in Section 2.3.4.1, Stage II in the PSC of conventional magnesium alloys corresponds
to the sequential activation of all tension twinning available [106] [111] [128]. In fact, the plastic
strain imparted by Stage II (𝛥𝜀𝑃)𝐼𝐼 has been directly correlated with the shear strain provided by
tension twinning and thus tension-twinned fraction [106] [111]. Similarly, work hardening in Stage
II has been claimed to be controlled by tension twinning through twin boundary hardening [106]
[111] [128] [133]. Hence, both the overall work hardening increase in Stage II ∆Θ𝐼𝐼 and the rate of
the increase Θ𝐼𝐼′ would also be expected to increase with the amount of twinning. With the effect
of annealing temperature on Stage II yet to be studied for either conventional or Mg-RE alloys, the
specifics of Stage II for the two alloys in study here as described in Section 4.4.1 and 4.4.2 are
discussed below in terms of the tension twinning expectable for each condition. Points of
disagreement with expectations above are identified for each alloy, and dealt with in detail.
5.3.2.1 The effect of annealing in Stage II in conventional magnesium alloys
For the case of Mg-0.03Y, (𝛥𝜀𝑃)𝐼𝐼 is reduced sharply the higher the annealing temperature (Table
4.3), which would point at the amount of tension twinning decreasing also. Moreover, Stage II is
even absent for Mg-0.03Y(500°C). As the amount of tension twinning has been consistently found
to decrease with finer grain size in magnesium [22] [132] [150] (Figure 2.18), this variable seems
unlikely to account for this behaviour. By contrast, texture represents a plausible explanation: the
stronger basal texture the lower the temperature means that more grains have basal planes tilted
with respect to the sheet plane, and thus 𝑐 axes able to undergo extension when compression is
5. DISCUSSION
-119-
applied in the ND. For Mg-0.03Y(500°C), this would mean that texture intensity is so strong as to
fully suppress Stage II, which has been related to marginal tension twinning only [128] [129] [132].
In fact, as noted in Section 2.3.4.1, full inhibition of Stage II has been usually reported by former
PSC studies on conventional magnesium tested in the 𝑐 axis compression orientation, the same
employed here [106] [111] [128] [129] [141], e.g. Figure 2.11. This may be related to such studies
considering basal textures at least as strong as that of Mg-0.03Y(500°C) [106] [111] [128] [129]
[141]. Therefore, the transition in concave-up to concave-down behaviour exhibited by Mg-0.03Y
here can be reasonably ascribed to increasing texture intensity.
Nevertheless, this would mean that, for Mg-0.03Y(350°C) and Mg-0.03Y(425°C), Θ𝐼𝐼′ has been
higher the scarcer the tension twinning; moreover, ∆Θ𝐼𝐼 is roughly the same for both conditions
(Table 4.3). Since these effects could thus not be accounted for by tension twin hardening, other
explanations should be sought. On the one hand, contraction twin boundary hardening has been
proposed a far-reaching effect upon Stage II by recent studies [106] [111] (Section 2.3.4.1). In this
sense, the greater amount of grains with 𝑐 axes parallel to the ND as per sharper texture could be
thought to enhance contraction twinning in Mg-0.03Y(425°C) (recall last subsection). Even so, this
seems unlikely to lie behind the different Θ𝐼𝐼′ , since the increase in work hardening is quicker for
Mg-0.03Y(425°C) throughout the whole Stage II (Figure 4.14), and contraction twinning has been
reported to become active only just before the end of Stage II [111]. Furthermore, it should be
recalled that a strong basal texture sharpening effect has been proved for tension twinning [111]
[116] [128], meaning that, if more profuse tension twinning is effectively assumed the lower the
temperature, differences in texture intensity between all conditions may have been overcome at
the onset of contraction twinning.
On the other hand, initial texture intensity itself may represent a possible explanation for Θ𝐼𝐼′ and
∆Θ𝐼𝐼. Due to sharper texture, tension-twinning grains in Mg-0.03Y(425°C) are surrounded by more
grains unfavourably oriented for the soft deformation modes. For a certain applied stress, fewer
grains would thus be able to accommodate the shear strain produced by tension twinning in this
condition. In other words, work hardening should increase at higher rate Θ𝐼𝐼′ for further tension
twinning to occur. This could also lead to a greater increase in work hardening accumulated when
all tension twinning available has been effectively released even though tension-twinned fraction
is lower, i.e. higher ∆Θ𝐼𝐼. What is more, this mechanism is in accordance with Θ𝐼𝐼′ being higher for
Mg-0.03Y(425°C) across Stage II, as the sharper texture is present from the onset of straining.
Likewise, texture-induced hardening could also explain why all three Mg-0.03Y conditions exhibit
similar peak stress (Table 4.2) instead of peak stress directly correlating with tension twin fraction
5. DISCUSSION
-120-
as in [132] (Figure 2.20), where the various conditions mainly differed in grain size. In particular,
lower twin-induced hardening the greater the temperature here would be compensated for by
higher texture hardening. The combined effect of both would explain the slightly higher maximum
stress for Mg-0.03Y(425°C). On the other hand, the slightly lower peak stress for Mg-0.03Y(500°C)
would highlight that, despite not being the only mechanism to be considered, the role of tension
twin hardening is still highly significant. Interestingly, similar maximum stresses were reported by
Barnett and Keshavarz [129] and Knezevic et al. [106] (Figure 2.11) for conventional magnesium
alloys tested in the 𝑐 axis extension and compression orientations. While 𝑐 axis extension leads to
more profuse tension twinning [106] [128] [129], less texture hardening would be expected for this
orientation, which is favourable to easily activated tension twinning and prismatic slip (Figure 2.14).
Therefore, these results further emphasize the ability of texture and tension twin hardening to
compensate for each other. By contrast, Nave and Barnett measured significantly lower maximum
stress for pure magnesium under 𝑐 axis compression [141] (Table 4.2). This may be interpreted
again in terms of texture intensity and the resultant reduction in tension twin hardening, as the
initial basal texture was stronger than in either the other studies noted above [106] [129] or Mg-
0.03Y(500°C) here. This would further highlight that, beyond certain basal texture intensity, texture
hardening becomes unable to compensate for the reduction in tension twin hardening associated.
5.3.2.2 The effect of annealing in Stage II in Mg-RE alloys
In the case of Mg-0.6Y, it is Mg-0.6Y(400°C) that exhibits the highest (𝛥𝜀𝑃)𝐼𝐼 (Table 4.5). Even so,
this condition possesses both the finest grain size and the most unfavourable texture for tension
twinning: not only is the tilting of the 𝑐 axis to the ND smaller in the RD-split than in the TD-split
fibre, thus reducing the amount of 𝑐 axes extension in the strain path considered, but texture
intensity is also stronger (recall former subsection). As a result, neither factor could in principle
explain the hypothetically more profuse tension twinning. On the other hand, the monotonic rise
of ∆Θ𝐼𝐼 and Θ𝐼𝐼′ with higher annealing temperature (Table 4.5) would correlate with larger grain
size leading to greater tension twinning. Monotonic increase of Θ𝐼𝐼′ with higher tension-twinned
fraction as per coarser size was explicitly noted by Barnett and Keshavarz in their benchmark study
on the effect of grain size on the UAC of AZ31 [132]. By contrast, texture hardening as proposed for
Mg-0.03Y above does not seem likely to account for the trend of ∆Θ𝐼𝐼 and Θ𝐼𝐼′ , in that Mg-
0.6Y(400°C) exhibits the lowest values i.e. less work hardening, but the least favourable texture for
the easily activated deformation modes (see former subsection). Moreover, texture is essentially
random for both Mg-0.6Y(450°C) and Mg-0.6Y(500°C), but ∆Θ𝐼𝐼 and Θ𝐼𝐼′ are distinctly higher for the
latter.
5. DISCUSSION
-121-
Assuming tension-twinned fraction increases with higher annealing temperature, it would remain
to clarify why (𝛥𝜀𝑃)𝐼𝐼 is diminished in turn. In conventional magnesium alloys, Stage II is accepted
to end when tension twins fully consume parent grains [87] [106] [111] [128]. Furthermore, EBSD
misorientation analysis by Mu et al. has shown that the majority of contraction twinning available
is onset in magnesium before tension twinning is exhausted [111]. Therefore, the powerful work
softening expectable from the extensive contraction twinning enabled by Mg-RE alloys [29] [56]
[118] [161] [175] [176] –proposed to lie behind the stress saturation above– may balance tension
twin hardening and thus terminate the macroscopic work hardening increase which defines Stage
II even before tension twinning is exhausted. If, as also proposed above, contraction twinning is
promoted further the greater the temperature for Mg-0.6Y via coarser grain size, the additional
work softening may counteract tension twin hardening at earlier accumulated strain (𝛥𝜀𝑃)𝐼𝐼 even
though tension-twinned fraction –and thus the strain imparted by tension twinning– is higher. In
the study by Barnett and Keshavarz [132], the end of Stage II occurred at higher strain the coarser
the size (see Figure 2.20). This would imply that interruption of Stage II at earlier strain the larger
the grain size is a RE-specific effect to be added to the onset of stress saturation dealt with above
and presumably produced by the enhancement of contraction twinning also. Further combined
characterization by EBSD and polycrystal modelling may help confirm this hypothesis. In addition,
the earlier interruption of tension twin hardening by greater contraction twinning would explain
why peak stress is decreased the greater the annealing temperature for Mg-0.6Y (Table 4.4).
In conclusion, the amount of tension twinning seems to be controlled by grain size in Mg-0.6Y, but
by texture in Mg-0.03Y. As for the latter, higher basal texture intensity has been proposed to result
in a transition in stress-strain curve shape from concave-up to concave-down in magnesium similar
to that proposed by Barnett and Keshavarz for refined grain size [132] (Figure 2.20). Yet, unlike
suggested by the literature so far, twin hardening alone cannot explain the work hardening
behaviour of either alloy in Stage II. For Mg-0.03Y, results suggest that texture hardening plays a
relevant role in conventional magnesium. For Mg-0.6Y, work softening owing to the promotion of
contraction twinning has been proposed to be of importance in Mg-RE alloys.
5.3.3 The formability of magnesium under the strain path of cold rolling
As demonstrated in Section 4.4.1 and 4.4.2, strain-to-failure has followed the opposite trend with
annealing temperature for both alloys in study. Reasons for the behaviour of each are discussed
below in terms of the effect of microstructural variables i.e. grain size and texture on the activity of
the various deformation mechanisms. For Mg-0.03Y, results obtained for the strain path of cold
rolling here are contrasted with past observations on the formability of conventional magnesium
alloys under other strain paths; for Mg-0.6Y, these are employed to derive expectations for the
5. DISCUSSION
-122-
formability of Mg-RE alloys under other paths. Finally, implications for the origin of the enhanced
cold rollability of Mg-RE alloys, extensively debated in the past, are also considered.
5.3.3.1 The formability of conventional magnesium alloys
In the case of Mg-0.03Y, strain-to-failure has increased with lower annealing temperature (Table
4.2). Similarly, the strain sustained by Stage II (𝛥𝜀𝑃)𝐼𝐼 has followed the same trend (Table 4.3). As
explained in Section 5.3.2, (𝛥𝜀𝑃)𝐼𝐼 can be directly associated to the strain provided by tension
twinning, increased the lower the temperature for Mg-0.03Y in virtue of weaker basal texture. All
the same, Table 4.3 demonstrates also that Stage II alone cannot explain the whole strain-to-failure
increase, especially for Mg-0.03Y(425°C). With the occurrence of tension twinning repeatedly found
to be restricted in magnesium to Stage II only [106] [111] (Section 2.3.4.1), this means that other
deformation mechanisms must also play a role.
In this sense, it should be recalled that Barnett and Keshavarz found the PSC behaviour of AZ31 in
the 𝑐 axis compression orientation to be reasonably predicted by the joint consideration of tension
twinning and basal slip [129]. As the Schmid factor for basal slip is equal to zero in the basal texture
orientation, the activity of this mechanism would be expected to be enhanced by weaker basal
texture, and thus lower annealing temperature. Hence, basal slip is likely to have also contributed
to the strain-to-failure increase by Mg-0.03Y. By contrast, all other deformation mechanisms were
concluded neglectable by Barnett and Keshavarz [129], so that their contribution may be assumed
neglectable in the present case also. In fact, prismatic slip has often been suggested to be promoted
by aluminium and zinc in magnesium [134] [235] [236], meaning that an even lower contribution
would be expected from this mechanism for Mg-0.03Y as compared to AZ31. For ⟨c + a⟩ slip, the
effect of aluminium or zinc is yet to be reported to the author’s knowledge. Nevertheless, increased
⟨c + a⟩ slip activity would be expected from stronger basal texture due to the greater amount of 𝑐
axes oriented parallel to the ND, further suggesting that this deformation mechanism does not
collaborate in the strain-to-failure increase either. For contraction twinning, the same argument
may be applied; what is more, no increase in the plastic range as per stress saturation stages like
those exhibited by Mg-0.6Y has arisen for Mg-0.03Y.
Consequently, enhanced tension twinning and basal slip as per weaker texture can be concluded to
govern the strain-to-failure behaviour of Mg-0.03Y. Such rationale holds also for the comparison
with strains-to-failure reported by Nave and Barnett for pure magnesium [141] (Table 4.2). On the
one hand, the strain-to-failure found by these authors in 𝑐 axis compression is lower than any of
those shown here by Mg-0.03Y, which can be ascribed to the basal texture employed by Nave and
Barnett being stronger also (see Table 4.1). On the other hand, the strain-to-failure measured in 𝑐
5. DISCUSSION
-123-
axis extension is higher than all those observed for Mg-0.03Y here. This can be explained by the
dominant texture fibre in this orientation being ideally oriented for tension twinning (recall last
subsection). Hence, significantly greater contribution would be expected from Stage II than in the
unfavourable case of 𝑐 axis compression considered in this project. Further, weaker basal textures
have been claimed to increase the formability of conventional magnesium alloys under a range of
strain paths, e.g. [64] [65] [67] [79] [115] [123] [127] [145] (recall Section 2.3.5), although this is the
first report for the strain path of cold rolling.
In addition, these results mean that any impact of grain size on the strain-to-failure of Mg-0.03Y is
overridden by that of texture. Whereas this agrees with previous observations on the formability
of conventional magnesium in biaxial tension [64] [65] [79], grain size has been consistently found
to be more relevant under uniaxial tension [64] [65] [67] [79] (see Table 2.7). As discussed in Section
2.3.6, the different role of prismatic slip in both paths as noted by Chino et al. [65] [79] and arising
from the distinct activation of ND compression under each can explain the equally distinct texture-
grain size dominancy. In the same way as for biaxial tension, ND compression is required straight
from the onset of deformation in the strain path of cold rolling (albeit not by volume constancy but
directly imposed, Table 2.2). As in biaxial tension also, this would be expected to neglect any initial
prismatic slip in the sheet plane, and to give way to shear banding and subsequent failure straight
after ND strain provided by off-basal grains following the easily activated modes is exhausted. A
neglectable role of prismatic slip under PSC is effectively supported by conclusions by Barnett and
Keshavarz noted above [129]. Moreover, the analogy between biaxial tension and the strain path
of cold rolling in terms of the amount of strain preceding failure is supported by Scott et al.: these
authors encountered that, for AZ31 subjected to FLD cup testing, shear banding was present from
around the same effective plastic strain under biaxial tension and plane strain, but only after
significantly higher strain under uniaxial tension [80] (4% versus 7% [80]). As in biaxial tension, the
powerful impact of grain size on prismatic slip activity, thought to be the dominant effect in uniaxial
tension [79] [151], would thus be avoided in the strain path of cold rolling. On the contrary, the
level of strain sustained before failure would essentially rely on the amount of off-basal grains,
precisely defined by texture intensity.
Overridden here by texture, the effect of grain size on the formability of conventional magnesium
under the strain path of cold rolling remains thus an open question. Following the parallelism with
biaxial tension noted above, an analogous effect could be expected for both paths. In this sense,
stretch formability has been found to be enhanced by coarser size due to more profuse contraction
twinning [64] [65]. To ascertain if this effectively applies to the strain path of cold rolling, Mg-0.03Y
specimens with similar texture intensity but different grain size could be subjected to further PSC
5. DISCUSSION
-124-
testing. These specimens could be prepared using the same approach followed by Huang et al. in
[123], who varied the temperature of hot rolling while imparting the same annealing.
5.3.3.2 The formability of Mg-RE alloys
For Mg-0.6Y, strain-to-failure is considerably higher for the two greater temperatures (Table 4.4).
The increase is due in both cases to the onset of stress saturation in Stage III, absent for the lower
temperature (Figure 4.11). As discussed in Section 5.3.1, the latter can be ascribed to contraction
twinning inhibition by fine grain size. Among the greater temperatures, strain-to-failure is higher
for Mg-0.6Y(500°C). This can also be associated to this deformation mode, as the larger size for this
condition would be expected to yield more profuse contraction twinning [22] [65] [127] [138] [149]
[150] than for Mg-0.6Y(450°C), e.g. Figure 2.18. The greater amount of material thereby favourably
reoriented for the soft deformation modes would be expected to increase the level of macroscopic
strain imparted before the critical strain localization is reached in any twins or shear bands. More
contraction twinning for Mg-0.6Y(500°C) was also proposed in Section 5.3.1.3 to explain the lower
softening upon stress saturation. Even so, the strain-to-failure difference between Mg-0.6Y(450°C)
and Mg-0.6Y(500°C) is small, suggesting any effect of grain coarsening above the threshold needed
to activate stress saturation is only minor. Further insight into the effect of varying grain size above
the threshold may be obtained with intermediate conditions as initially foreseen here (Section 3.3).
Consequently, the present results suggest that the role of grain size in the strain-to-failure of Mg-
0.6Y is more relevant than that of texture. This contrasts with Mg-0.03Y (see above), underlining
the importance of dealing with conventional and Mg-RE alloys separately in formability studies.
Therefore, the question is opened as to how the formability of Mg-RE alloys may be affected by
microstructural variables under other strain paths, encouraging related research in the future. The
analogous role of ND compression may suggest for biaxial tension a similar trend to that found here
for the strain path of cold rolling. For uniaxial tension, the issue is more complex: homogeneous
prismatic slip has been reported for Mg-RE alloys even for coarse microstructures [66] [158] [159]
[160] [161], casting doubt on any impact of grain size on this mechanism in Mg-RE alloys. In fact,
tensile testing by Basu and Al-Samman for Mg-1Gd in various isochronal annealing conditions points
at the opposite: despite stronger texture, ductility was increased with higher temperature [175]. As
in the present study, this could be explained by more contraction twinning enabled by larger grain
size. Nevertheless, although grain coarsening would be effectively expected by increased annealing
temperature, grain sizes before testing were not supplied by the authors [175], and systematic work
is further required to ascertain this point.
5. DISCUSSION
-125-
5.3.3.3 The origin of the high cold rollability of Mg-RE alloys
Additionally, strains-to-failure are higher for Mg-0.6Y than for Mg-0.03Y irrespective of annealing
condition (Table 4.2 and Table 4.4). However, the increase is dramatically empowered by the onset
of stress saturation: the strain-to-failure of Mg-0.6Y(400°C) is only 20% higher than the maximum
value shown by Mg-0.03Y, while those corresponding to Mg-0.6Y(500°C) and Mg-0.6Y(450°C) are
three to seven times higher than the various Mg-0.03Y values. The latter magnitude resembles the
remarkable formability improvements found to be imparted by RE additions in past studies on the
cold rolling of magnesium [26] [28] [29] (Section 2.2), e.g. five times higher than for the pure metal
as reported by Sandlöbes et al. [29] (Table 2.3). Considering that the strain path applied here is the
same as that of cold rolling, the present results suggest that the vast majority of the cold rollability
improvement is associated to stress saturation.
As explained across Section 2.4, the successive studies on the cold rolling of magnesium have put
forth different effects of RE additions in magnesium to explain the higher cold rollability of Mg-RE
alloys: (i) the enhanced shear banding [26], (ii) the enhanced ⟨c + a⟩ slip [29], and (iii) the weaker
RE texture [28]. The foremost role proved for stress saturation here would directly point at shear
banding i.e. contraction twinning (recall Section 2.3.4.3). In this sense, the weaker texture for cold-
rolled Mg-0.2Ce as found by Barnett et al. (Figure 2.32) may be explained by contraction twinning
and ⟨c + a⟩ slip promoted by cerium, as both mechanisms tend to reorient crystals away from the
basal orientation, e.g. [103] [118] [121] [175]. Moreover, although higher strain sustained by the
parent grains via either ⟨c + a⟩ slip or the further basal slip and tension twinning enabled by the RE
texture could retard the critical strain localisation in contraction twins, the bulk of the improvement
has been proved to rely on the activation of stress saturation itself, and not higher strain sustained
thereby. In fact, competition with the other enhanced mechanisms would be expected to hamper
contraction twinning: by the mechanism suggested by Timár and Fonseca [144] (Section 5.3.1.2)
for basal slip and tension twinning, and by representing a direct alternative to accommodate strain
in the same direction i.e. parallel to 𝑐 axes for ⟨c + a⟩ slip.
Further, it would remain to explain why former studies reported all a significant improvement in
cold rollability by RE additions if the effect is here claimed to be microstructure-dependent. In this
sense, it seems plausible that grain sizes in those studies are larger than the hypothesized threshold
for the activation of stress saturation: all lie between 39 and 53 µm [26] [28] [29], with the threshold
suggested by this project between 27 and 110 µm (Table 4.1). Nevertheless, it must be conceded
that all studies including the present have encompassed different RE additions and levels, the effect
of which on the size threshold –and cold rollability itself– represents a field of further study.
5. DISCUSSION
-126-
Finally, it may be argued that, whereas the PSC experiments conducted here represent the strain
path of cold rolling in the bulk, failure in actual cold rolling occurs at the edges, where the strain
state is different [32] [33]. Nevertheless, such strain state is strongly dependent on specific edge
shape [33]. Edge shape is usually not controlled upon rolling [33], so that it would seem impossible
to universally represent rolling regardless of whether a channel-die test or actual rolling is used. On
the contrary, the strain state in the bulk provides a robust alternative directly correlating with the
strain state of the edges, which arises from nothing but the superposition of the bulk state with
shape-dependent shear stresses [33].
In summary, this project is the first systematic study on the effect of microstructural variables on
the formability of magnesium under the strain path of cold rolling. For conventional magnesium,
imparting weaker texture to enhance basal slip and tension twinning has been shown to be the key.
This is in agreement with former findings on stretch formability but against those on ductility, which
has been rationalised in terms of distinct ND strain activation. By contrast, large enough grain size
to enable contraction twinning seems crucial for Mg-RE alloys. In fact, the results presented suggest
that, among all the mechanisms put forward in the past, the enhancement of contraction twinning
by RE additions is the cornerstone to the long-known extensive cold rollability of the Mg-RE system.
From a practical viewpoint, these results mean that the opposite approach should be envisaged for
both alloy groups in terms of the annealing customarily performed in magnesium before each cold
rolling stage: grain growth should be minimised to avoid texture sharpening in conventional alloys,
but imparted up to at least a grain size threshold for Mg-RE alloys. What is more, this may apply
not only to the strain path of cold rolling, but also to that most relevant for sheet metal forming i.e.
biaxial tension. Therefore, this study highlights the powerful effect that promotion of contraction
twinning via alloying additions can exert on the formability of magnesium. This would be relevant
not only to the Mg-RE system, but also to any new potential magnesium alloy developments.
5.3.4 The proof behaviour of magnesium under the strain path of cold rolling
In the same way as strain-to-failure, proof strength has followed the opposite trend with annealing
temperature for the two alloys: reduction with lower temperature for Mg-0.03Y, but increase for
Mg-0.6Y (Table 4.2 and Table 4.4). Reasons for such conflicting behaviour are sought below in terms
of grain size and texture, with attention paid to the role played by the strain path of cold rolling.
The impact of varying proof strain is also considered, and discussed in the light of work hardening
evolution upon Stage I, on which an opposed effect of annealing temperature on both alloys has
been equally encountered: the drop in work hardening has been quicker the lower the temperature
for Mg-0.03Y, but slower for Mg-0.6Y (Figure 4.15 and Figure 4.21).
5. DISCUSSION
-127-
5.3.4.1 The interplay between grain size and texture
In metals, proof strength is well-known to generally increase with smaller grain size by means of a
grain boundary hardening effect. Most often, a Hall-Petch law [155] [156] of the form of Equation
5.5 [32] is applicable, where 𝜎𝑃𝑆 is proof strength, 𝜎0 represents the initial resistance of the lattice
to dislocation motion, and 𝐾𝑃𝑆 is the sensitivity of proof stress to grain boundary strengthening. In
magnesium, Hall-Petch laws have been extensively proved applicable when grain size is the main
variable into consideration, e.g. [79] [132] [149] [173] [210] [237] [248] [249] [250] [251].
𝜎𝑃𝑆 = 𝜎0 + 𝐾𝑃𝑆 · 𝐷 1/2 (5.5)
Hall-Petch plots at various proof strains are presented for the two alloys in study in Figure 5.5. On
the one hand, Mg-0.03Y is in clear disagreement with Hall-Petch behaviour, as proof stresses are
reduced with smaller grain size. By contrast, although caution should be taken due to the scarce
number of conditions finally available (recall Section 3.3.4), Mg-0.6Y seems to conform well to Hall-
Petch behaviour regardless of proof strain. What is more, 𝜎0 and 𝐾𝑃𝑆 as derived at the usual 0.2%
strain lie for Mg-0.6Y within values formerly reported for magnesium alloys (Table 5.2). This is true
even for 80% confidence intervals [132] (Table 5.2) despite the relatively broad interval range that
results from the small condition number. In fact, 𝜎0 would be expected to depend on solid solution
hardening only for annealed, single-phase alloys such as Mg-0.6Y [173] [210] [251] [252], with the
value measured for this alloy effectively higher than those reported for pure magnesium [248] [249]
[251], and lower than that presented by Somekawa et al. for Mg-1Y [251], i.e. a single-phase alloy
also but with higher solute yttrium content (Table 5.2). In this sense, whereas the friction owing to
channel-die walls may be expected to increase 𝜎0 with respect to uniaxial tests [86] such as those
invariably employed by former Hall-Petch magnesium studies [173] [210] [251] [252] (Table 5.2),
this does not seem to have qualitatively affected the 𝜎0 found for Mg-0.6Y. Therefore, considering
all of the latter, the proof strength behaviour of Mg-0.6Y may be conceivably ascribed to grain size,
but other reasons must be sought for Mg-0.03Y.
5. DISCUSSION
-128-
Figure 5.5. Hall-Petch plots for the two alloys in study and engineering plastic strains of 0.1%, 0.2% and 0.5%. Error bars represent standard deviations, and dashed lines are best-fit regression lines with the form of Hall-Petch equations.
About the effect of texture, former UAC and PSC studies on conventional magnesium may provide
some insight. Particularly, much lower proof stresses have been recurrently reported under 𝑐 axis
extension than under 𝑐 axis compression [106] [111] [128] [129] [141] (see e.g. Figure 2.11 or Table
4.2). To explain this behaviour in UAC, Knezevic et al. proposed that work hardening, initially lower
under 𝑐 axis extension due to the activation of tension twinning (Figure 2.11), would lead to lower
stress at the proof strain despite presumably equal yield stress in both orientations [106]. The idea
of such equal yield stress was supported by the fact that Schmid factors for basal slip, customarily
assumed to occur prior to tension twinning so as to impart a critical dislocation density [106] [128],
were equally zero for the main texture fibre in both orientations [106] (basal planes parallel and
perpendicular to the direction of compression, respectively, Figure 2.11).
R² = 0.9678
R² = 0.9248R² = 0.9063
0
20
40
60
80
100
120
140
0.05 0.10 0.15 0.20
Pro
of
Stre
ngt
h σ
PS
(MP
a)
D-1/2 (µm-1/2)
Mg-0.03Y (strain=0.005)
Mg-0.03Y (strain=0.002)
Mg-0.03Y (strain=0.001)
R² = 0.9760
R² = 0.9857
R² = 0.9586
0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
0.05 0.10 0.15 0.20
Pro
of
Stre
ngt
h σ
PS
(MP
a)
D-1/2 (µm-1/2)
Mg-0.6Y (strain=0.005)
Mg-0.6Y (strain=0.002)
Mg-0.6Y (strain=0.001)
5. DISCUSSION
-129-
Table 5.2. Hall-Petch parameters 𝜎0 and 𝐾𝑃𝑆 at 0.2% engineering strain for Mg-0.6Y in the present study, and various magnesium alloys in the literature. Confidence intervals at 80% are given for Mg-0.6Y as done by the authors in [132].
Alloy Type of test Initial resistance to
dislocation motion 𝝈𝟎
Sensitivity of proof
strength to grain size 𝑲 𝑺
Mg-0.6Y PSC 30 ± 17 378 ± 135
Pure Mg [248] UAC 2 390
Pure Mg [249] UAC 3 540
Pure Mg [251] UAC 8 294
Mg-0.8Zn [173] UAC 9 430
Mg-1Zn [251] UAC 33 273
AZ31 [132] UAC 40 ± 8 304 ± 23
AZ31 [250] Uniaxial tension 32 275
Mg-1Y [251] UAC 63 252
The reasoning by Knezevic et al. can also be applied for Mg-0.03Y here: notwithstanding the small
transient of Stage I, work hardening in the first stages of deformation (below 𝜀𝑃 ≈ 0.01) is lower
with reduced temperature (Figure 4.14), which correlates with the lower proof stress; what is more,
the orientation of the basal fibre and thus the Schmid factors for basal slip have not changed among
conditions here. However, the expanded view of Figure 5.6 shows that deviation from linear, elastic
behaviour distinctly occurs at significantly lower stress the lower the temperature. Hence, unlike
for Knezevic et al., differences in proof stress can be ascribed to distinct yield strength rather than
initial work hardening. As for this, texture hardening in line with that put forward in Section 5.3.2
for Stage II behaviour is a plausible explanation: initial basal slip in most favourably oriented grains
will practically occur only when neighbouring grains can accommodate the resultant shear; the
more unfavourably oriented the latter, the higher the macroscopic stress for their resolved shear
stresses to exceed the CRSS for basal slip. In turn, this would lead the macroscopic stress required
for “soft” grains to deform to be higher also, which would be ultimately perceived as higher yield
stress. Likewise, texture hardening holds also to explain the comparison between Mg-0.03Y and
Nave and Barnett [141] in terms of proof stress (Table 4.2): (i) in 𝑐 axis compression i.e. the same
orientation as here, the sharper texture in [141] would lead to higher proof stress than any of those
shown by Mg-0.03Y here; (ii) in 𝑐 axis extension, the orientation of the main fibre is as unfavourable
to basal slip; even so, it is ideal for tension twinning and prismatic slip (Figure 2.14), the latter of
which could provide a “soft” means of accommodating the initial basal slip needed by tension
twinning (or an alternative way to impart the necessary critical dislocation density [148]). This
would eventually result in a lower proof stress than any of Mg-0.03Y.
5. DISCUSSION
-130-
Figure 5.6. Expanded view of the PSC stress-strain curves of Mg-0.03Y close to the onset of plastic deformation. Arrows indicate the approximate point of yield for each condition.
If texture is thus assumed to control yield strength for Mg-0.03Y, the present results would imply
that, as for formability (see Section 5.3.3.1), texture is more relevant than grain size for the yield
behaviour of conventional magnesium under the strain path of cold rolling. Previous research has
shown that, for conditions with similar grain size, proof stress is also increased by sharper basal
texture under uniaxial tension [67] [123] [253]. Nevertheless, a look into work by Chino et al. [79]
suggests that, in the same way as for ductility, the impact of grain size on the tensile yield is more
powerful than that of texture: as can be seen in Table 2.7, yield stresses measured by these authors
invariably scale with grain size despite texture intensity of condition C, which has intermediate grain
size, being considerably higher. For explaining this discrepancy between PSC and uniaxial tension,
the prominent role of prismatic slip in uniaxial tension, on which grain size exerts a powerful impact,
can be proposed in a similar way as in Section 5.3.3.1 for the discrepancy between both paths in
terms of formability. In fact, both TEM analysis [134] [151] and polycrystal modelling [128] [149]
[210] have suggested that the role of prismatic slip under tensile testing is dominant from the onset
of plastic straining already. Furthermore, studies considering size effects when deformation modes
are isolated have found Hall-Petch slopes for prismatic slip to be much higher than for basal slip or
tension twinning [149] [253] [250]; this would imply that the effect of grain size on prismatic slip is
significantly more powerful than for the deformation modes potentially active at the yield under
the strain path of cold rolling straight from the onset of plastic deformation. In this sense, if the
analogy between biaxial tension and the strain path of cold rolling proposed in Section 5.3.3.1 is
0
20
40
60
80
100
120
0.00 0.01 0.02 0.03 0.04
Tru
e St
ress
σ(M
Pa)
True Strain ε
Mg-0.03Y (350°C) Mg-0.03Y (425°C) Mg-0.03Y (500°C)
5. DISCUSSION
-131-
applied to yield behaviour, texture would be expected to play a dominant role under biaxial tension
also. Yet, data have not been found in the literature to confirm this point.
5.3.4.2 The sensitivity of proof strength and work hardening upon Stage I
In addition, Figure 5.5 shows that Hall-Petch slopes i.e. 𝐾𝑃𝑆 are raised significantly with higher proof
strain for both alloys. For the sake of completion, corresponding 𝐾𝑃𝑆 values are given in Table 5.3.
For Mg-0.6Y, all proof strains considered (up to 0.5%) lie below the strains at which Stage II is onset
(εP)II (the lowest being ≈1% for Mg-0.6Y(500°C), Table 4.5). Therefore, the trend followed by 𝐾𝑃𝑆
can be directly related for this alloy to work hardening upon Stage I. In this sense, Figure 4.21 shows
that the drop in work hardening during this stage is effectively quicker the higher the temperature
for Mg-0.6Y, thus accentuating the trend for higher flow stress already present at the yield (recall
Figure 5.6). In contrast, for Mg-0.03Y, the short extent of Stage I leads the 0.5% proof strain to be
higher than (εP)II, at least for the conditions in which Stage II is present (Table 4.3). Even so, Figure
4.15 demonstrates that, while work hardening is effectively lower across the whole proof strain
range considered the lower the temperature –thus accentuating the trend for lower flow stress
already present at the yield– Stage II does not contribute to this lower value. On the contrary, the
drop in work hardening upon Stage I being quicker the lower the temperature is the only factor
responsible. In fact, the increasing work hardening during Stage II for Mg-0.03Y(400°C) and Mg-
0.03Y(450°C) tends to compensate for their quicker drop upon Stage I against Mg-0.03Y(500°C),
and thus works against the trend exhibited by 𝐾𝑃𝑆.
About the origin of the work hardening Stage I trends, research by Del Valle et al. [254] and Mann
et al. [249] isolating texture [254] and grain size [254] [249] in conventional magnesium alloys can
provide some insight. In fact, stronger basal texture [254] and smaller size [249] [254] were proved
in such studies to significantly retard both the work hardening drop in Stage I. If these conclusions
are assumed for the present study, grain size would be unable to explain the trend of Mg-0.03Y, in
that the work hardening drop is retarded by greater annealing temperature i.e. the coarsest size.
However, the sharper texture as temperature is increased would represent a feasible explanation.
This would suggest that the effect of stronger basal texture in constraining basal slip delays not only
the event of yielding as stress is gradually raised upon testing, but also the subsequent development
of plastic strain across Stage I. By contrast, for Mg-0.6Y, both texture and grain size would represent
a possible explanation. Yet, grain size seems more likely due to the trend clearly extending into the
two greater temperatures, which have essentially random initial texture both. Particularly, Del Valle
et al. related such effect of grain size on work hardening Stage I to the reduction in the mean free
path for basal dislocation slip by grain boundaries [254].
5. DISCUSSION
-132-
Table 5.3. Sensitivity of proof strength to grain size 𝐾𝑃𝑆 for the two alloys in study at various proof strain levels.
Engineering
plastic strain
Sensitivity of proof
strength to grain size 𝑲 𝑺
Mg-0.03Y Mg-0.6Y
0.1% -961 276
0.2% -1071 378
0.5% -1355 440
To sum up, while the proof behaviour of Mg-0.03Y is essentially defined by texture intensity, that
of Mg-0.6Y appears mostly determined by grain size. This applies to work hardening in Stage I also,
and in such a way that differences in proof stress are enhanced the higher the proof strain. On the
one hand, these results imply that, for conventional magnesium, texture intensity is more relevant
than grain size in defining proof strength in the strain path of cold rolling. This disagrees with the
case of uniaxial tension, which has been rationalized by the neglectable role of prismatic slip in the
strain path of cold rolling. On the other hand, these results mean also that such texture dependency
is circumvented by the texture weakening inherent to RE additions in magnesium, thus bringing the
behaviour of this metal closer to the regular Hall-Petch typical of ductile metals.
6. CONCLUSIONS
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6 CONCLUSIONS
A set of annealing conditions have been prepared for two binary magnesium-yttrium alloys varying
in addition levels: (i) Mg-0.03Y, which has shown behaviour consistent with that of conventional
magnesium; and (ii) Mg-0.6Y, which has exhibited typical RE-modified behaviour including texture
weakening. The evolution of each upon annealing and further PSC testing reproducing the strain
path of cold rolling has been examined. The following main conclusions have been drawn:
(i) Lücke-Detert’s theory for grain boundary mobility has been applied to magnesium for the first
time. Results suggest that the breakaway regime is operative for Mg-0.03Y and conventional
alloys including zinc and aluminium in the literature, while the drag regime is active for Mg-
0.6Y. This would confirm that, as widely proposed by recent research, the texture weakening
induced by RE additions in magnesium is effectively related to a shift in the atomistic boundary
migration regime so that migration rates become limited by solute RE atmospheres. In addition,
yttrium has led to significant recrystallized grain size decrease and SRX temperature increase,
for which solute drag also represents a reasonable explanation.
(ii) Mg-0.6Y has developed TD-split textures upon annealing, despite being considered an exclusive
effect of ternary Mg-Zn-RE alloys so far, and for whose origin no explanation had been provided.
In the light of this, a unified rationale has been proposed, based upon the activation of prismatic
slip in certain grains in hot rolling, and subsequent growth advantages upon annealing. Greater
prismatic slip and solute drag due to zinc have been hypothesized to explain easier formation
of TD-split fibres Mg-Zn-RE alloys.
(iii) For Mg-0.03Y, PSC behaviour is determined by basal texture intensity across all work hardening
stages, with no apparent contribution of grain size. Upon Stage I, work hardening is dictated by
texture hardening via the constraining effect of grains in hard orientations i.e. any Hall-Petch
effect is overridden; likewise, proof stress depends on texture intensity and not grain size. In
Stage II, the well-known impact of grain size on tension twin fraction is equally overriden by
texture intensity, which defines the amount of favourably oriented grains. Even so, the amount
of work hardening imparted by Stage II does not correlate with tension twin fraction, and seems
also determined by texure hardening.
(iv) By contrast, the PSC behaviour of Mg-0.6Y can be accounted for by grain size only rather than
texture. On the one hand, work hardening upon Stage I and proof strength are well-explained
by a Hall-Petch effect; likewise, tension twin fraction is determined by grain size, with tension
twin hardening effectively defining the work hardening imparted by Stage II. These differences
with conventional magnesium can be attributed to the texture weakening due to the addition
6. CONCLUSIONS
-134-
of yttrium. On the other hand, stress saturation stages sustaining considerable levels of strain,
absent for Mg-0.03Y, and similar to those present in cubic, ductile metals are onset in Stage III.
The development of such stages has been related to the RE promotion of contraction twinning,
and a minimum grain size has been shown to be required for their activation.
(v) For conventional magnesium, formability under the strain path of cold rolling is determined by
texture intensity i.e. improved by weaker texture by enhancing basal slip and tension twinning.
This disagrees with uniaxial tension, for which grain size is more relevant, and has been ascribed
to the neglectable role of prismatic slip under PSC. In contrast, formability under the strain path
of cold rolling is dictated by grain size for Mg-RE alloys. By these means, the amount of strain
sustained upon stress saturation is enhanced, which has been related to enhanced contraction
twinning. In this sense, the dominant role of stress saturation in the formability improvement
provided by Mg-0.6Y against Mg-0.03Y points at the RE promotion of contraction twinning lying
behind the long-discussed, improved cold rollability of Mg-RE alloys against the other reasons
formerly proposed, i.e. the RE promotion of non-basal slip, and the RE texture weakening.
7. FUTURE WORK
-135-
7 FUTURE WORK
Following this project, further work can be envisaged aimed at extending or confirming the main
conclusions drawn:
• To apply Lücke-Detert theory to recrystallization in order to ascertain whether the solute
drag regime also applies to this process. For this purpose, conditions at different stages of
SRX completion may be generated, and recrystallised fractions then adjusted following an
Arrhenius law.
• Seeking to shed light onto the rationale for TD-split textures, to determine whether such
grain orientations are already present after hot rolling. In that case, to elucidate (i) which
deformation mechanism lies behind their formation, and (ii) the origin of grain growth
advantages. For this goal, TEM dislocation analysis in the hot-rolled condition and EBSD
characterization after hot rolling and at different annealing stages could be used.
• To fully characterize deformation mechanism activity for the conditions presented here. A
combined approach of EBSD, XRD texture measurement and polycrystal modelling would
seem adequate. The observation of differences in shear banding (or contraction twinning)
appears particularly interesting.
• To determine the effect of grain size on the formability of conventional magnesium alloys
under the strain path of cold rolling. For this purpose, producing conditions with varying
hot rolling temperatures and the same annealing treatment may be used [123].
• To characterize the effect of microstructural variables on deformation mechanism activity
(non-basal slip, twinning) and formability of Mg-RE alloys in uniaxial and biaxial tension.
The same conditions here considered could be used.
• In order to optimize RE alloy development, to determine the effect of varying RE content
on the formability of Mg-RE alloys under the various strain paths.
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