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

CONTENTS

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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 4.10. 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


-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.


-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)


-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


-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)


-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


-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


-30-

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.


-33-

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


-34-

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.


-35-

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)


-36-

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

)


-37-

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.


-38-

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


-39-

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].


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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].


-41-

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


-42-

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].


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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


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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


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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


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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


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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


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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.


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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].


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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)


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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


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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


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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


-72-

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].


-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


-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


-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


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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


-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


-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

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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

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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)


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)


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)


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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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)



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

-133-

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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The formability of Magnesium and Magnesium-Rare Earth