Characterization and Modeling of Lightweight Alloys in the Warm Forming Regime
DISSERTATION
Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University
By
Scott Sutton
Graduate Program in Materials Science and Engineering
The Ohio State University
2018
Dissertation Committee:
Professor Alan Luo, Advisor
Professor Rudolph Buchheit
Professor Stephen Niezgoda
Copyrighted by
Scott Christopher Sutton
2018
Abstract
Lightweighting is used throughout the transportation industry and is an increasingly popular method to increase fuel economy in both automotive and aerospace applications. Magnesium has the lowest density of any structural metal and is an attractive option for substitution into aluminum or steel structures. Aluminum-lithium alloys are also attractive, as they boast lower density, higher modulus, and relatively good strengths compared to conventional aluminum alloys. For different metallurgical reasons, both materials have significantly anisotropic mechanical properties, which limit their formability and service life applications. For both Mg alloys and Al-Li alloys, improved primary processing can address the properties which restrict these materials’ use. This work aims to make processing recommendations for a Mg-RE alloy and an Al-
Li alloy based on relevant deformation traits or microstructural processes in the warm forming regime. Simple mechanical models which can form industrial processing are also presented.
In Mg, rare earth elements in solid solution have significant effects which result in reduced or altered texture, which can mitigate mechanical anisotropy of final components. These so-called rare earth texture effects were studied in Mg alloy ZE20
(Mg-2Zn-0.2Ce-0.3Mn) with the conventional Mg alloy AM30 (Mg-3Al-0.4Mn) as a baseline for comparison. In general, ZE20 had a smaller recrystallized grain size, lower
ii basal texture intensity for recrystallized grains, and somewhat retarded recrystallization kinetics. Processing map-guided investigation of microstructures revealed two regions of processing interest. One region had conventionally favorable traits from the processing map but did not exhibit the rare earth texture effect. Another potentially allowable region had unfavorable flow characteristics but had favorable recrystallization texture and exhibited the rare earth texture component, both of which could be exploited with post- process annealing.
Alloy development is constantly progressing for Al-Li alloys, which suffer strong anisotropy due to the textures that form during processing. Little information is available for the newly-developed AA2070, and its properties were evaluated using simulated forming under warm forming conditions. AA2070 exhibited significant softening or steady-state stress for all elevated temperature tests; this was attributed to dynamic recrystallization at high temperatures and exceptional activity of dynamic recovery at lower temperatures. The initially strong Goss texture and minor β-fiber texture of the billet were not strongly affected by mechanical testing at high temperatures but were reduced in intensity following mechanical testing at lower temperatures. General processing recommendations for AA2070 were made based on pseudo processing maps and experimental microstructures and textures.
In order to more fully inform industrial processing, flow stress during mechanical testing was modeled using two empirical constitutive flow stress models: the hyperbolic sine Arrhenius model and a novel formulation of the extended Ludwik hardening model.
The modified Ludwik model was found to have superior performance for ZE20 and
iii
AA2070 with few added model constants. Further modifications and potential improvements on the extended Ludwik model were described. Viscoplastic self- consistent (VPSC) crystal plasticity simulation was applied to ZE20. VPSC-predicted flow curves and textures were found to only be accurate for some temperatures and strain rates. Despite inaccuracy for some conditions, VPSC was used to provide physically- based validation for the extended Ludwik model which was consistent with theory.
iv
Dedicated to my fiancée, Megan, for her unwavering support.
v
Acknowledgments
I must first acknowledge my advisor, Prof. Alan Luo for his overarching guidance. With his considerable industry experience, he was able to successfully target several grants, rapidly growing a tight-knit research group and fully funding my graduate career as well as several of my coworkers’. He also pushed me into new areas of research, helping me grow as a scientist and an independent scholar. My achievements are in no small part thanks to him.
I acknowledge the constant support and dedication of my fiancée, Megan, to whom this work is dedicated. Always by my side, she followed me to Columbus from
Michigan State (Go Green), while still making great progress in her own career. For her immeasurable support, both in this and as we plan the next chapter of our lives, I thank her.
I would like to thank Prof. Stephen Niezgoda and Prof. Rudy Buchheit of OSU for their guidance toward completion of my degree, especially under an unexpectedly shortened timeframe. I would also like to thank Prof. Niezgoda’s grad students,
Thaddeus Low and Denielle Ricciardi, for teaching me the basics of VPSC and helping me run simulations.
I acknowledge the support of all my coworkers. Though most worked on cast materials, they were unafraid of helping me solve problems for wrought Mg and Al. vi
Among them I thank especially Andrew Klarner, Colin Ridgeway, and Yan Lu for immense help with casting die design and casting simulation, recognized though unfortunately precluded from this work. Thanks to Janet Meier, Emre Cinkilic, and Zhi
Liang for our frequent coffee breaks filled with academically stimulating conversation.
I acknowledge the MSE Department’s support staff, for always quickly and efficiently solving problems that grad students alone are unable. Especially I would like to thank Ross Baldwin and Pete Gosser for teaching me necessary machining skills and always being willing to help in a pinch.
Lastly, I would like to thank my family. My parents have always supported me, no matter the path in life I chose. My sister, who earned her PhD the year I started grad school, was always ready to grouse with me about the academic struggle and was still able to provide advice whenever I needed it.
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Vita
2008...... Troy High School
2013...... B.S. Materials Science and Engineering,
Michigan State University
2016...... M.S. Materials Science and Engineering,
The Ohio State University
2016 to present ...... Graduate Research Associate, Department of
Materials Science and Engineering, The Ohio
State University
Publications
[1] S. C. Sutton and A. A. Luo, “Constitutive Behavior and Processing Maps of a New Wrought
Magnesium Alloy ZE20 (Mg-2Zn-0.2Ce). Provisionally accepted.
[2] X. Shi, A. A. Luo, S. C. Sutton, L. Zeng, S. Wang, X. Zeng, D. Li, and W. Ding,
“Twinning behavior and lattice rotation in a Mg-Gd-Y-Zr alloy under ballistic impact,” J.
Alloys Compd., vol. 650, pp. 622–632, Nov. 2015.
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[3] S. Sutton and A. A. Luo, “Hot Compression Behavior of Magnesium Alloys ZE20
AND AM30,” in Magnesium Technology 2015, Hoboken, NJ, USA: John Wiley & Sons,
Inc., 2015, pp. 25–28.
[4] T. R. Bieler, S. C. Sutton, B. E. Dunalp, Z. A. Keith, P Eisenlohr, M. A. Crimp, and B. L. Boyce, “Grain boundary responses to heterogeneous deformation in tantalum polycrystals,” Jom, vol. 66, no. 1, pp. 121–128, Jan. 2014.
Fields of Study
Major Field: Materials Science and Engineering
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Table of Contents
Abstract ...... ii
Acknowledgments...... vi
Vita ...... viii
List of Tables ...... xiii
List of Figures ...... xiv
Chapter 1: Introduction and Material Properties for Forming ...... 1
1.1 Introduction ...... 1
1.2 Literature Review of Magnesium Forming Properties ...... 3
1.2.1 Single Crystal Properties ...... 3
1.2.2 Texture Formation and Textured Mg Polycrystals ...... 5
1.2.3 Mitigation of Texture Effects ...... 9
1.2.4 The “Rare Earth Texture Effect” ...... 14
1.3 Literature Review of Aluminum Forming Properties ...... 17
1.3.1 Deformation Modes in Aluminum ...... 17
1.3.2 Precipitation Hardening in Aluminum Alloys ...... 18
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1.3.3 Texture Formation and Forming Considerations...... 22
Chapter 2: Thermomechanical Processing and Characterization of Mg ...... 26
2.1 Materials ...... 26
2.1.1 AM30 ...... 26
2.1.2 ZE20 ...... 27
2.2 Mechanical Behavior of Mg Alloys ...... 28
2.2.1 Thermomechanical Testing ...... 28
2.2.2 Processing Maps ...... 36
2.3 Microscopy and Characterization...... 42
2.3.1 Microscopy Procedures ...... 42
2.3.2 Exemplar Microstructures and General Deformation Behavior of AM30 and
ZE20 ...... 44
2.3.3 Process Map-Guided Investigation of ZE20 and Processing Recommendations
...... 54
2.4 Conclusions ...... 67
Chapter 3: Thermomechanical Processing and Characterization of Al ...... 69
3.1 Materials – AA2070 ...... 69
3.2 Thermomechanical Testing and Pseudo-Process Maps ...... 71
3.3 Texture and Microstructure Characterization ...... 81
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3.4 Conclusions ...... 98
Chapter 4: Constitutive Modelling of Mechanical Properties ...... 100
4.1 Sellars-Tegart Flow Stress Relation ...... 101
4.2 Modified Hardening Law Based on Extended Ludwik Equation ...... 110
4.3 Viscoplastic Self-Consistent Crystal Plasticity Simulation of ZE20 ...... 121
4.4 Conclusions ...... 135
Chapter 5: Conclusions and Future Work ...... 137
5.1 Summary ...... 137
5.2 Recommendations for Future Work ...... 141
References ...... 143
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List of Tables
Table 1. Optical emission spectroscopy measured composition of ZE20 ...... 28
Table 2. Composition of AA2070...... 71
Table 3. Sellars-Tegart model coefficients for AM30...... 104
Table 4. Hyperbolic sine Arrhenius model constants for ZE20...... 106
Table 5. Modified Ludwik model constants for ZE20...... 114
Table 6. Modified Ludwik model constants for AA2070...... 115
Table 7. Voce hardening parameters for ZE20 as functions of temperature...... 125
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List of Figures
Figure 1. Schematic representation of thermomechanical testing scheme illustrating thermal and mechanical portions of test...... 30
Figure 2. Stress-strain curves of AM30 at (a) 10-2 s-1, (b) 10-1 s-1, (c) 5.0 s-1, and (d) 100 s-
1...... 32
Figure 3. Stress-strain curves obtained for ZE20 at (a) 10-3 s-1, (b) 10-2 s-1, (c) 10-1 s-1, and (d) 100 s-1...... 34
Figure 4. Processing maps for ZE20 at strains of (a) -0.15, (b) -0.35, (c) -0.65, and (d) -
0.90. Identified domains and instability regions are marked in blue and red respectively.
...... 41
Figure 5. Microstructure and texture of as-cast ZE20. Billet axis is vertical, and billet tangential direction is horizontal. (a) secondary electron image, (b) IPF map, (c) (0001) pole figure, (d) IPF map key, and (e) PF intensity scale...... 45
Figure 6. Microstructure and texture of as-received AM30. Billet axis is vertical, and billet tangential direction is horizontal. (a) backscattered electron image, (b) IPF map, (c) basal PF, (d) prismatic PF, and (e) PF intensity scale...... 46
Figure 7. Secondary electron image of AM30 tested at 350°C and 10-1 s-1. Compression direction is vertical...... 48
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Figure 8. Recrystallization phenomena in AM30. (a) IPF map of AM30 compressed at
200°C and 5.0 s-1, with DTN events circled. (b) GOS map of AM30 compressed at
350°C and 10-1 s-1, and (c) GOS key. Compression direction is vertical...... 49
Figure 9. Microstructure of ZE20 after thermomechanical testing at 400°C and 10-1 s-1.
Compression direction is vertical...... 51
Figure 10. EBSD of ZE20 in regimes where PSN and DTN would be favored. (a) IPF and IQ map of a specimen compressed at 425°C and 10-2 s-1, and (b) IPF map of a specimen compressed at 200°C and 10-1 s-1. Compression direction is vertical...... 52
Figure 11. Texture trends with temperature in ZE20 and AM30. Texture data shown for tests at 5.0 s-1...... 54
Figure 12. EBSD of a specimen compressed to a strain of -1.0 in at peak efficiency in
Domain I. (a) IPF map, (b) IPF map of recrystallized grains only, (c) IPF of deformed grains, (d) IPF of recrystallized grains, and (e) IPF scale. Compression direction is vertical...... 55
Figure 13. EBSD of a specimen compressed to a strain of -0.35 at the efficiency minimum in Domain II. (a) IPF map, (b) IPF map of recrystallized grains only, (c) IPF of deformed grains, (d) IPF of recrystallized grains, and (e) IPF scale. Compression direction is vertical...... 57
Figure 14. EBSD maps showing flow localization within a specimen compressed to a strain of -1.0 at 300°C and 10-1 s-1 (Instability Region I). (a) IPF map, (b) IPF map of recrystallized grains within shear bands, (c) IPF of matrix, (d) IPF of recrystallized grains, and (e) IPF scale. Compression direction is vertical...... 58
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Figure 15. EBSD of shear bands within a specimen compressed to a strain of -1.0 at
300°C and 10-1 s-1 (Instability Region I). (a) IPF map, (b) IPF map of recrystallized grains within shear bands, (c) IPF of matrix, (d) IPF of recrystallized grains, and (e) IPF scale. Compression direction is vertical...... 59
Figure 16. EBSD of a specimen compressed in Instability Region II. (a) IPF map, and
(b) IPF map overlaid with image quality map, with low CI points and subgrain boundaries shown...... 62
Figure 17. Processing region recommendations for ZE20, valid for up to a strain of -1.0.
...... 64
Figure 18. H-forging geometry, with reference directions shown...... 70
Figure 19. Stress-strain curves of AA2070 compressed to a strain of -1.0 at (a) 10-3 s-1,
(b) 10-2 s-1, and (c) 10-1 s-1...... 74
Figure 20. Flow stress curves for AA2070 tested in plane strain compression at (a) 10-3 s-
1, (b) 10-2 s-1, and (c) 10-1 s-1...... 76
Figure 21. Hot tension results for AA2070 at (a) 350°C and (b) 450°C...... 78
Figure 22. Fracture surface of AA2070 specimen tested in tension at 250°C and 10-3 s-1.
L-direction is vertical, T-direction is horizontal, and S-direction is out of plane...... 79
Figure 23. Pseudo-processing maps of AA2070 in compression, plotted at strains of -0.5 and -0.9...... 80
Figure 24. Secondary electron images of initial AA2070 microstructures after solution heat treatment and eight-hour thermal soak at (a) 150°C, (b) 250°C, (c) 350°C, and (d)
450°C...... 82
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Figure 25. EBSD of solution heat treated and soaked AA2070. (a) IPF map, (b) GOS map, (c) PF of deformed material, (d) PF of recrystallized material, and (e) IPF key, (f)
GOS key, and (g) PF scale. L-direction is vertical, T-direction is horizontal, and S- direction is out of plane. IPF key is constant for all AA2070 IPFs, with colors plotted for the S-direction. PF scale is constant for all AA2070 PFs...... 84
Figure 26. EBSD of AA2070 specimen compressed at 450°C and 10-2 s-1. (a) IPF map,
(b) GOS map, (c) PF of deformed material, (d) PF of recrystallized material, (e) PF scale, and (f) GOS scale. L-direction is vertical, T-direction is horizontal, and S-direction is out of plane...... 86
Figure 27. EBSD of AA2070 specimen compressed at 250°C and 10-2 s-1. (a) IPF map,
(b) GOS map, (c) bulk PF, (d) PF scale, and (e) GOS scale. L-direction is vertical, T- direction is horizontal, and S-direction is out of plane...... 88
Figure 28. Microstructure and texture of AA2070 tested in tension at 450°C and 10-2 s-1.
(a) IPF map, (b) GOS map, (c) PF of deformed grains, (d) PF of recrystallized grains, and
(e) PF scale. L-direction is vertical, T-direction is horizontal, and S-direction is out of plane...... 90
Figure 29. Microstructure and texture of AA2070 tested in tension at 250°C and 10-3 s-1.
(a) IPF map, (b) GOS map, (c) bulk PF, (d) PF scale, and (e) GOS scale. L-direction is vertical, T-direction is horizontal, and S-direction is out of plane...... 91
Figure 30. Microstructure and texture of AA2070 tested in plane strain compression at
450°C and 10-3 s-1 to a final strain of -1.0...... 92
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Figure 31. Area fraction of texture components for PSC specimens compressed to a true strain of -0.5. Components of (a, b) deformed grains and (c, d) recrystallized grains, plotted as a function of (a, c) temperature and (b, d) strain rate. Area fractions are relative to the fraction of the stated portion of the microstructure...... 93
Figure 32. Selected Arrhenius model results for AM30 at (a) 425°C and (b) 10-2 s-1. .. 104
Figure 33. Sellars-Tegart model results for ZE20 at (a) 10-3 s-1, (b) 10-2 s-1, (c) 10-1 s-1, and 100 s-1...... 106
Figure 34. Arrhenius model results for AA2070. Model predictions and experimental results at (a) 10-3 s-1, (b) 10-2 s-1, and (c) 10-1 s-1. (d) overall model performance...... 108
Figure 35. Modified Ludwik model results plotted along with experimental data for
ZE20 at (a) 10-3 s-1, (b) 10-2 s-1, (c) 10-1 s-1, and (d) 100 s-1...... 114
Figure 36. Ludwik model results for AA2070. Model predictions and experimental results for (a) 10-3 s-1, (b) 10-2 s-1, and (c) 10-1 s-1...... 116
Figure 37. Performance of the (a,c) Sellars-Tegart model and (b,d) the modified Ludwik model for (a-b) ZE20 and (c-d) AA2070...... 118
Figure 38. Experimental data and VPSC simulation with Voce hardening coefficients fit to strains up to -0.15. (a) 250°C, (b) 350°C, and (c) 450°C...... 125
Figure 39. VPSC results for ZE20 after adding in recrystallization behavior. (a) 10-3 s-1,
(b) 10-2 s-1, (c) 10-1 s-1, and 100 s-1...... 127
Figure 40. VPSC-predicted textures for ZE20 across different temperatures and strain rates for the deformed and recrystallized material...... 129
xviii
Figure 41. Relative activity of deformation modes in ZE20 under different conditions:
(a) 250°C and no recrystallization, (b) 450°C and no recrystallization, (c) 250°C and 10-3 s-1, (d) 250°C and 100 s-1, (e) 450°C and 10-3 s-1, (f) 450°C and 100 s-1 ...... 131
Figure 42. Comparison of hardening constants between VPSC Voce hardening and the modified Ludwik hardening model...... 133
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Chapter 1: Introduction and Material Properties for Forming
1.1 Introduction
Over the past few decades, there has been an increasing push to improve fuel economy across all segments of the transportation industries. Among other engineering developments, one of the most simple and straightforward strategies is lightweighting: by reducing the weight of a vehicle, one reduces the amount of energy or fuel needed for transportation. The most direct and effective approach to accomplish this is by replacing existing structures and materials with components that have lower density or higher specific strength. Following this, there has been increasing interest and research in lightweight materials.
Magnesium has the lowest density of any structural metal (1.73 g/cm3 for pure
Mg), making Mg and Mg alloys a first choice material for lightweighting. As such, magnesium has received attention from the automotive, aviation, and aerospace industries, with the main driver of Mg research being the automotive industry. Several
Mg components are in use in current vehicles, mainly in part-reducing die castings in the vehicle interior, such as the instrument panel [1]. More recently, wrought Mg components have also received attention, because they offer improved properties which would permit the use of Mg in a wider variety of applications. Unfortunately, there are several barriers to the widespread implementation of wrought Mg in the automotive
1
industry. The most significant barrier is magnesium’s low formability at room temperature; but coatings, joining capabilities, corrosion properties, and dynamic strain rate mechanical properties (for crashworthiness) are also significant concerns. Most of these can be mediated by adapting appropriate processing, but additional processing steps carry additional costs which make Mg alloys less cost-competitive with other metals.
Aluminum is another attractive option for lightweighting because it is low cost and has a fairly low density (2.70 g/cm3). Relative to conventional aluminum alloys, aluminum-lithium alloys have even lower density and higher stiffness, with the potential for higher strength [2]. This combination of properties makes Al-Li alloys an excellent candidate for lightweighting, where it serves applications in aviation and aerospace.
However, first and second generation Al-Li alloys had several undesirable characteristics: in-plane and through-thickness anisotropy (for rolled forms), low short-transverse fracture toughness, susceptibility to stress corrosion cracking, and poor thermal stability
[3]. Third generation Al-Li alloys make improvements over previous generation alloys, but research into improved forming and service properties continues.
For both Mg alloys and Al-Li alloys, improved primary processing can address the properties which restrict these materials’ use. Process parameters have heavy influence on microstructure and texture, which in turn dictate the mechanical properties of the final wrought material (or the secondary forming capabilities of the material).
Relevant physical metallurgy concepts necessary to inform the processing of these materials are detailed below.
2
1.2 Literature Review of Magnesium Forming Properties
1.2.1 Single Crystal Properties
In order to understand the strategies taken to improve forming, it is necessary to understand magnesium’s basic deformation behavior. Magnesium has hexagonal close packed (HCP) crystal symmetry with a c/a ratio of 1.624 [4]. Like other HCP metals with a c/a ratio less than the ideal value of 1.633, its preferred deformation mode is
(0001)<101̅0> slip, or basal slip. Other common slip modes available to Mg include
{101̅0}<112̅0> slip, {101̅1}<112̅0> slip, and {101̅1}<112̅3> slip [5], [6]. The common nomenclature for these slip systems is shorthand for the type of plane and Burger’s vector; they are referred to as prismatic slip, pyramidal slip, and pyramidal
Apart from slip, there are two commonly recognized twin systems in Mg. These are {101̅2}<101̅1> twinning and {101̅1}<101̅2> twinning. Due to the polar nature of twinning, these have significant impacts on plasticity in Mg. Because twinning is polar, activation of twinning only occurs under certain favorable stress states. Activation of
{101̅2}<101̅1> twinning is favored in tension along
“tension twinning” or “extension twinning” [7], [8]. Tension twinning results in a
3
volume of twinned material that is rotated 86.3° about <112̅0> relative to the parent material [9]. With its characteristic shear of 0.13, it can extend the crystal by γ/2 (or
0.065) in
“compression twinning” or “contraction twinning” because it can be activated during compression along
Unfortunately, this rotation produces a favorable orientation for subsequent tension twinning, which in turn produces a somewhat favorable orientation for basal slip [10].
Despite its theoretical capability for compressive strain accommodation along
Despite the existence of several independent deformation modes, Mg often has low ductility because basal slip and tension twinning are the only easily activated deformation modes. Temperature, alloying, and measurement type and method (single crystal, polycrystal, experiment, or simulation) all have significant effects on critical resolved shear stress (CRSS), and the values present in the literature have wide ranges.
For room temperature deformation, it is generally accepted that CRSS basal < CRSS tension twin < CRSS prismatic ≤ CRSS pyramidal ≤ CRSS pyramidal
[14]–[16]. Plasticity simulations generally use higher values for CRSS of basal slip, usually between 10 and 25 MPa [14], [17]. Tensile twinning is generally said to have
4
CRSS between 15 and 35 MPa [14], [17], [18]; prismatic slip is said to have a CRSS between 35 and 60 MPa [19], [20]; and pyramidal
CRSS of over 100 MPa [14], [21]. Pyramidal slip is not often reported and is usually excluded from simulation work because it does not provide an independent slip system past what is provided by the combination of basal and prismatic slip. It is usually recognized to have a CRSS slightly higher than prismatic slip but still lower than pyramidal
1.2.2 Texture Formation and Textured Mg Polycrystals
There are two common textures for Mg: basal texture and prismatic fiber texture.
Basal texture, where basal planes are aligned perpendicular to a prior compression axis is common for rolled plate, sheet and extrusions [22], [23]. Prismatic fiber texture, where
{101̅0} planes (prismatic planes) are aligned to a prior tensile axis, is more common for drawn wires, but it can also be seen toward the center of extrusions [24], [25]. In cases where extrusions exhibit prismatic fiber texture, it is simply an additional orientation preference for prismatic planes to be perpendicular to the extrusion direction, caused by a biaxial or triaxial stress state from the extrusion die. The formation of these textures is a result of the limited number of deformation modes available to Mg, and understanding the role of CRSS of these deformation modes is critical to understanding texture formation trends with temperature. Texture formation can be easily understood for a uniaxial stress state in the context of the Schmid law [26], which states that plastic
5
deformation occurs if the resolved shear stress due to an applied stress is greater than the
CRSS of a given deformation mode:
휎 = 휏푅푆푆 ∙ 푚 = 휏푅푆푆 cos 휑 cos 휆 ≥ 휏퐶푅푆푆 ∙ 푚 (1)
In the Schmid law, σ is the applied stress, τRSS is the resolved shear stress of the given deformation mode, φ is the angle between the applied stress and the slip plane normal (or habit plane normal for twinning), and λ is the angle between the Burger’s vector and the applied stress.
In a polycrystal under applied strain, individual grains exhibit approximately the single crystal response to stress and strain, depending on their orientation and local constraints. Consider first room temperature compression. At low stresses, basal slip is easily activated in favorably oriented grains due to its very low CRSS, and it may even occur while grains in “hard” orientations are still deforming elastically [17]. Basal slip tends to rotate grains such that basal planes are perpendicular to the compression direction [27]. Individual grains should not experience a large rotation solely due to basal slip, as twinning at room temperature has a CRSS only slightly higher than basal slip and will activate at low strains due to rapid work hardening of basal slip. When activated, twinning reorients the basal plane normal of the grain by 86.3° about <112̅0> toward the compressive axis and thus is a major contributor to texture formation at relatively low strains. Twinning is usually exhausted by 10% monotonic strain, as the strain it relieves for the polycrystal is still limited by its characteristic shear [7].
Generally, unless the local stress state or changes, tension twinning will not reactivate
6
within a grain. As tension twinning is exhausted, the material should be in a basal or nearly basal orientation. From the Schmid law, for further strain accommodation, the polycrystal must necessarily allow shear with some component along the
Both of these deformation modes have very high CRSS relative to basal slip and twinning and require high applied stress in order to be activated. At room temperature, this usually leads to fracture rather than sustained deformation by
Consider now tension at room temperature. As with compression, basal slip is easily activated at low stresses in favorably oriented grains. Unlike compression though, basal slip tends to rotate grains such that basal planes are parallel with the tension direction [27]. Again, tension twinning has a similarly low CRSS and activates at stresses only slightly higher than required for basal slip. When activated in tension, twinning reorients the basal plane normal of the grain by 86.3° about <112̅0> away from the tensile axis; extension twinning therefore also plays a major role in texture formation in tension. As twinning is exhausted, the material should have a texture such that basal
7
planes are parallel to the tensile axis, with no further orientation preference. According to the Schmid law, prismatic slip, pyramidal slip, and pyramidal
This sequence only generally describes the order of activation of deformation modes based on their CRSS and their contribution to texture formation. During straining of a polycrystal, multiple deformation modes will be simultaneously active, even within an individual grain, based on the resolved shear stress of each mode. Factors such as elevated temperatures, different alloy chemistry, and complicated stress states all change the intensity and character of the textures that form.
The tendency of Mg to rapidly form sharp textures, largely through tension twinning, leads wrought Mg to have mechanical anisotropy similar to Mg single crystals.
This is an issue both in primary production and secondary forming operations of wrought
Mg. For Mg sheet and plate, a basal texture is rapidly reached during rolling, and further rolling reduction becomes difficult because it would be along grains’
Preexisting texture and rapid texture formation also lead to limited formability in sheet forming operations, notoriously including deep drawing [29]. Texture also causes pronounced tension-compression asymmetry in Mg. Strongly textured wrought Mg will display drastically different yielding and flow stress behavior in tension and in
8
compression due to activation of twinning as a low stress deformation mode for only one of either tension or compression [30]. Tension-compression asymmetry can be a serious concern for secondary forming operations, such sheet bending, where springback is a consideration [31]. Tension-compression asymmetry is also a design concern for structures, as structures experiencing an unknown load will need a factor of safety appropriate for the lower yield stress (tensile or compressive).
1.2.3 Mitigation of Texture Effects
There are two basic strategies to mitigate or avoid texture effects in Mg: texture control and grain refinement. Grain refinement methods aim to produce a very fine grain size and take advantage of alternate deformation characteristics at such small grain sizes.
Texture control methods aim to reduce the intensity of basal texture or to induce alternate texture components instead.
Many of the simplest methods of texture control take advantage of alternate processing (mainly loading directions and strain paths) in order to reduce basal texture or induce non-basal texture. Examples of these include differential speed rolling, cross rolling, and orthogonal prerolling. Cross rolling involves alternating RD and TD between passes and results in a decreased basal texture intensity in Mg sheet [32]. Differential speed rolling uses rollers operating at different speeds in order to create a sense of shear in the material as it is being rolled, effectively creating basal texture that is inclined toward the rolling direction [33]. Orthogonal prerolling involves rolling reduction in TD
9
in order to induce texture prior to conventional rolling (in the ND) in order to induce twinning transformation, resulting in lower texture intensity in the final sheet [34].
Despite their efficacy, all of these processes have somewhat limited applicability.
Differential speed rolling requires special equipment, cross rolling is non-industrial because it does not allow for spooling of rolled sheet, and orthogonal prerolling can only be used with plate, not thin sheet. Moreover, each of these is dedicated to sheet operations and cannot be applied to forging or extrusion. Ultimately, methods of texture control which use alternate processing are useful but not as desirable as universally applicable methods.
A broader category of texture control methods can be categorized as effectively altering the CRSS of magnesium’s different deformation modes in order to change its deformation behavior and texture formation tendencies. This includes the traditional approach at increasing formability in Mg: forming at elevated temperature. The CRSS of prismatic slip, pyramidal slip, and Pyramidal
Basal, prismatic, and pyramidal slip can all operate simultaneously, satisfying the von
Mises criterion of five independent slip systems for an arbitrary shape change. As a side effect, this change in relative CRSS also changes the character of the texture produced by deformation. The combination of basal and pyramidal slip operating in tandem causes
10
Mg deformed in compression at high temperatures to have texture character inclined 10° to 25° toward <112̅0> from the basal pole. Heating Mg for ductility is an easily achievable route, but it is not the most industrially preferable. Additional heating for each forming process is expensive and reduces magnesium’s ability to be cost- competitive with other structural metals [16]. Reducing the temperature necessary for ductility in Mg during forming is a very active area of research [1].
Alloying additions in solution have a similar effect as temperature. Solute atoms impose a misfit strain on the crystal lattice. Misfit strains have a twofold effect: they change the material’s stacking fault energy (SFE) and contribute to a change in magnesium’s c/a ratio [35]. Together, these have a significant effect on the mechanical properties of Mg. They change the CRSS of individual deformation modes and change the material’s ability to cross-slip. Unlike high temperatures, alloying additions do not lower CRSS; they raise it for all deformation modes. Favorable additions harden basal slip and twinning relative to prismatic and pyramidal slip. The two most common conventional alloying elements for Mg, Al and Zn, both harden basal slip and twinning relative to other slip modes [20], [36]. Other alloying additions, such as Sn, Ca, and many rare earth elements, also have beneficial effects on CRSS and texture [13], [37],
[38]. Sufficient alloying additions that harden deformation modes such that there is a
1:1:1:1 CRSS ratio for basal slip, tension twinning, prismatic slip, and pyramidal
11
operations. Because alloying additions only harden slip modes, this does not necessarily improve ductility, despite reducing or eliminating tension-compression asymmetry.
Aside from these texture control methods, grain refinement strategies aim to obviate the need for texture control. Slip and twinning have different dependency on grain size [39]. This may be because of a critical strain needed to nucleate twinning that cannot be reached in very fine grains. Below a certain threshold (1µm - 5µm), twinning is suppressed in Mg. In such fine-grained structures, the result is a reduction in tension- compression asymmetry, even at room temperature. At elevated temperatures, such fine grained Mg can exhibit superplasticity, as grain boundary sliding will allow an additional mode of strain accommodation not dependent on grain orientations [40], [41]. This effectively obviates the need for texture control if such fine structures can be reliably produced.
Like with texture control methods, many popular methods of grain refinement involve special processing routes. Specifically for grain refinement, these methods all involve severe plastic deformation (SPD) processing. Some notable examples include equal channel angular pressing (ECAP), high pressure torsion (HPT), and accumulative roll bonding (ARB). Unfortunately, none of these methods are relevant for industrial processing. HPT has the greatest potential for grain refinement and is capable of easily producing submicron grain sizes [42], [43]; but it is a research technique only, limited to small disc-shaped specimens [44]. ARB involves rolling sheet, cutting it, stacking it, and rerolling it in order to achieve higher reductions than possible with conventional rolling.
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ARB is necessarily a batch process, and it is industrially limited because the sheet surfaces require special preparation prior to rerolling [44]. ECAP involves forcing material through an angled die, introducing only shear deformation without changing the material’s cross section. ECAP is limited to solid cross section extrusions (or coiled sheet in the case of conshearing) and presents a bottleneck for industrial production [34],
[44]. Without considering SPD methods, most attempts to produce a refined grain structure in a commercial wrought form use conventional extrusion. Extrusion is capable of imparting high strains which favor recrystallization. Careful determination of extrusion temperature and ram speed can then be used to maximize the fraction of recrystallization in the microstructure while minimizing the grain size. Conventional extrusion does not produce the nano-scale grain sizes achievable by HPT or ARB, but it can be sufficient to impart the beneficial ductility and strength achievable with fine grain sizes.
Aside from processing considerations, grain refinement is relatively easily achieved by introducing precipitates into the material. Precipitate content helps achieve both of the necessary functions for grain refinement: nucleating new grains and slowing the growth of fine grains. Precipitates can act as sites for nucleation of recrystallization during deformation in a phenomenon known as particle-stimulated nucleation (PSN).
After new grains are nucleated, precipitates can act as effective barriers, pinning grain boundaries and restricting grain growth. Design for grain refinement can be quite complicated, though. Simply having high precipitate content will lead to strong alloys
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with refined grains at the cost of ductility. This is evident in the properties of the conventional high-strength alloy ZK60 [16] and can also be seen in high-content alloys of several alloy design studies. Compounding the difficulty is the fact that precipitation is kinetically controlled. For many compositions, homogenization is required for cast billets prior to processing, which may dissolve the grain-refining precipitate of interest.
To address this, recent works take advantage of dynamic precipitation, effectively introducing grain-refining precipitates during hot work [45], [46].
Much current research that deals with texture formation in the warm forming regime is concerned with enhanced recrystallization properties. In conventional Mg alloys containing Al and Zn, recrystallization does not significantly randomize deformation texture. In newer alloys, such as Sn, Ca, and RE-containing alloys, recrystallization leads to some degree of texture weakening. By carefully choosing processing temperatures and strain rates, recrystallization may also address grain refinement.
1.2.4 The “Rare Earth Texture Effect”
Rare earth elements have shown to be particularly effective in either reducing basal texture or producing an alternate “rare earth texture component.” The RE texture component manifests as a <112̅1> || ED peak for extrusions and as split RD texture with greater inclination toward the RD and with greater TD spread for Mg sheets [47], [48].
Mechanistic study of the phenomena varies, as RE texture effects manifest differently for
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different RE elements under different processing conditions [49]. The complete mechanistic basis for this is not yet known, and several mechanisms have been proposed by which rare earth elements enhance texture in wrought Mg. Prevailing hypotheses focus on recrystallization (especially nucleation) mechanisms and strong defect-solute interactions.
The first works to report on texture enhancement via rare earth elements hypothesized that PSN was responsible for texture modification [50]. This has been a prevailing assumption, due to its firm mechanistic basis: surface strains at RE-containing particles may assist nucleation, and nuclei should not have any preferred orientation.
Many works have made either speculative attribution of RE texture reduction to PSN based on RE particle content or with direct observation of PSN [50]–[53]. Others have argued that precipitate content in RE-free alloys which do not display texture weakening invalidates PSN as a texture weakening mechanism [54]. More recent research has shown that precipitate content is not necessary for texture weakening in some Mg-RE alloys; precipitate-free Mg alloys with Y or Gd in solid solution have shown texture weakening effects [55], [56].
Other works have shown shear band nucleation (SBN) of recrystallization contributes significantly to the RE texture component. Stanford and Barnett showed that shear bands forming during extrusion of a Mg-Gd alloy produced recrystallized grains having the RE texture component, while grains nucleated at grain boundaries were nucleated in basal orientations [57]. Basu and Al-Samman proposed a mechanism for
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this, noting that grains could nucleate in any orientation at shear bands, but grains in non- basal orientations would grow preferentially and consume basal-oriented neighboring grains [58]. The relative lack of shear banding in conventional Mg alloys may explain why this texture component is seen mainly in Mg-RE alloys [58]. Jiang, Jonas, and
Mishra studied dynamic strain aging (DSA), which has been associated with shear band formation, and found that temperature and strain rate regimes of DSA coincided with regimes where the RE texture component was observed [56]. The presence of DSA suggests a possible causal basis for the RE texture component because DSA (or the
Portevin-Le Chatelier effect) is caused by strong interaction of solutes with crystal defects [59].
Similar to shear banding, deformation twin nucleation (DTN) can alter texture.
Grains nucleating at twin boundaries have been observed to have significantly different orientations from either the twin or the matrix [60]. The nucleation rate and orientations of the nuclei depend upon the twin type (tension, compression or double twinning) and twin variant [61]. DTN is enhanced for Mg-RE alloys, but it is thought to contribute to texture modification less than SBN because grain growth is restricted to the prior twin
[58], [61].
Aside from enhancing recrystallization via nucleation mechanisms, rare earths have significant grain refinement properties. It was originally assumed that the mechanism for this was Zener pinning, similar to conventional grain refinement; however significant grain refinement is achievable in precipitate-free Mg-RE alloys [57]. Atom-
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probe tomography work by Stanford et al. revealed that Gd has a tendency to segregate to grain boundaries [62]. The reason for such segregation may be due to satisfaction of misfit strains for RE solutes at the grain boundary; it is hypothesized that the resulting solute drag and Cottrell atmospheres have a significant effect on grain refinement [54],
[63].
1.3 Literature Review of Aluminum Forming Properties
1.3.1 Deformation Modes in Aluminum
Aluminum has face-centered cubic (FCC) crystal symmetry. As with any FCC metal, it favors the {111}<110> slip system, or octahedral slip system. In the warm forming regime, additional slip systems can be activated in Al. In addition to the close- packed planes, several non-octahedral slip systems have long been recognized. Among these are {100}<110>, {110}<110>, {112}<110>, and higher order slip systems [64],
[65]. Having lower atomic density and higher interplanar spacing than the octahedral slip planes, these non-octahedral slip planes have higher CRSS. Due to the high symmetry of
FCC crystals, there is always at least one octahedral slip plane with a nonzero Schmid factor, and non-octahedral slip may not be active at room temperature. At elevated temperatures, the CRSS of these non-octahedral systems drops, and they can be activated more easily.
In addition to slip, Al can also deform by twinning; but twinning is rare and only observed in situations contrived specifically for twin formation, such as shock loading
17
[66] or in dimensionally constrained nanocrystalline materials [67]. This is due to the fact that Al has high stacking fault energy (SFE), even relative to other FCC metals.
Such high SFE makes twin nucleation exceedingly unlikely in bulk polycrystals under forming conditions [68].
1.3.2 Precipitation Hardening in Aluminum Alloys
With such an abundance of deformation modes, Al requires some amount of strengthening for use in structural applications. Aluminum can be solid solution strengthened to a degree, but most elements have a very low solubility in Al. The most effective solid solution strengthener in Al is Mg, and dilute Mg content is a primary strengthening mechanism in the 3xxx and 5xxx series of alloys. Even Mg and Cu have relatively low solubility in Al at low temperatures and can precipitate out of solid solution, even at room temperature [69]. Most wrought Al relies instead on precipitation hardening, and due to the low solubility of other elements, there are several notable strengthening precipitates.
There are several factors to what makes an individual precipitate phase desirable.
Among these are shape, orientation, and shear-resistance. Considering shape, high aspect ratio precipitates increase a precipitate’s area and allow it to block dislocations more effectively [70]. For such high aspect ratio precipitates, orientation is important; precipitates lying parallel to a slip plane will block fewer dislocations than those lying perpendicular to the plane [71]. In the literature, a given precipitate is often only said to
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be shear resistant or shearable, even though both types contribute to precipitate hardening to some extent [72]. Whether a precipitate is shearable takes into consideration the precipitate’s shear modulus, the Burger’s vector of a dislocation in the precipitate, and, to some extent, the precipitate’s interface with the matrix (coherent or incoherent) [72].
Other factors for precipitation hardening, such as size or number density (essentially the same if assuming a constant volume fraction of precipitate content) and precipitate dispersion are largely controlled by the heat treatment applied to the alloy.
Precipitation in wrought Al alloys usually occurs via the same general sequence.
Proceeding from supersaturated solid solution, Guinier-Preston zones (GP zones) form, followed by some number of intermediate phases, followed then by a stable phase (or phases for multicomponent alloys). Technically not a phase, GP zones are solute-rich clusters of atoms [73]. Solute content in GP zones can vary, and exact compositions are not completely known [74]. GP zones do have distinct morphology depending on the alloy chemistry, ranging from spherical to plates to needles, but they typically are disc or plate-shaped and only a few atom layers thick. GP zones are fully coherent with the Al matrix, and contribute some amount of strength to the alloy, though they are shearable
[75]. Importantly, GP zones can act as nucleation sites for intermediate and stable phases during heat treatment. There are several intermediate and stable phase(s) for multicomponent Al-Li alloys which vary with alloy chemistry.
Copper provides precipitation strengthening for the 2xxx, and 7xxx series of Al alloys. The precipitation sequence for binary Al-Cu is: GP zones → θ” → θ’ → θ. The
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θ” phase (Al3Cu) tends to nucleate directly from GP zones. θ” is coherent with the Al matrix and consists of two planes of Cu atoms on {100}, separated by three layers of Al atoms [73]. The θ’ phase transforms directly from the θ” phase. Being shear-resistant, it is a major strengthening phase of Al-Cu alloys [74]. θ’ is tetragonal Al2Cu and grows in semi-coherent thin plates on {100} [73]. The stable θ phase is base-centered tetragonal
Al2Cu and nucleates directly from θ’ [73]. Presence of θ in a microstructure is not preferred; heat treatments that produce θ are usually past peak aging and result in a coarsened microstructure with lower hardness [74].
In Al-Cu-Mg alloys, the intermediate phase is S’, and the stable phase is S. S’ and S are both orthorhombic Al2CuMg, differing only in lattice parameter. Instead of nucleating on GP zones, S’ nucleates from dislocations and grows as laths on {210} planes in <100> directions [76]. It is likely that S transforms from S’, and recent work has shown that there may in fact be two stable S phases with lattice parameters both unique from S’ [73], [77]. S’ is shearable and semi-coherent, while S is incoherent with the matrix and is non-shearable [73], [78].
Both Al-Mg-Li and Al-Cu-Li alloys tend to form the intermediate δ’ phase. δ’ is cubic Al3Li and forms as spherical particles due to its low misfit with the matrix [73].
For Al-Mg-Li alloys, this is only proceeded by the Al2LiMg phase, which forms as coarse rods along <110>. In Al-Cu-Li alloys, δ’ is proceeded by the stable δ phase, which is cubic and incoherent AlLi. Al-Cu-Li alloys may also precipitate the T1 phase. T1 is hexagonal Al2CuLi and forms as semi-coherent plates on {111}. The T1 phase
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contributes greatly to hardening – Weldalite TM, the first alloy of third-generation Al-Li alloys achieved a yield stress of 700MPa through fine distribution of T1 precipitates instead of δ’ [2]. Some sources list T1 as shearable [79], while some list it as non- shearable [78].
Second and third generation Al-Li alloys are multicomponent alloys with several alloying elements; many commercial alloys include Cu, Li, Mg, Mn, Zn, and Zr, with some other additions as well. For these alloys, heat treatment schedules can elicit co- precipitation of some or several of the above phases [78], [80]. Al-Li alloys usually rely on some combination of δ’, S’, T1, and θ’ for strengthening [78]. Third generation Al-Li alloys rely on less δ’ than second generation Al-Li alloys, relying on T1 instead for strengthening because it causes less anisotropy for crack formation [2].
In addition to precipitates, many Al alloys rely on dispersoids which act as grain refiners and retard recrystallization during thermomechanical processing. Dispersoids are formed during homogenization, and casting process control is critical to their distribution, which in turn affects the alloy’s forming properties [81]. For Al-Cu-Mg(-Li) alloys, the primary dispersoid phase is base-centered orthorhombic Al20Cu2Mn3, or T phase, which grows as rod-like structures along <100> [74]. The T phase has also had its stoichiometry reported as Al31Cu3Mn5 [82]. For Zr-containing Al alloys, coherent Al3Zr can also form and acts as a dispersoid [3]. Due to the relatively low mobility of Zr, Al3Zr tends to form spherical particles only tens of nanometers in diameter and forms in relatively high number densities [81]. In addition to grain refinement properties, these
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dispersoids can act as heterogeneous nucleation sites for the T1 phase [83], S’ and S phases [84], and the δ’ phase [85] and therefore have significant impact on the overall properties of the alloy.
1.3.3 Texture Formation and Forming Considerations
Texture formation and recrystallization are primary concerns in the warm forming of Al. Texture formation in Al can lead to an undesirable mechanical anisotropy, for plate products both in-plane and through thickness yield asymmetry are observed [86].
Aluminum has two common texture fibers, α-fiber and β-fiber, each with several characteristic components. Using the Euler-Bunge convention, the α-fiber exists at φ2 =
90° and runs from ϕ = 0° to ϕ = 45°. The β-fiber sweeps in the ϕ = 45° plane from φ2 =
90° to φ1 = 90° and φ2 = 45° [87]. Along these two fibers are several important texture components. These components are recognized for their formation in rolled Al sheet, where their notation is {hkl}||ND,
({110}<112>), S ({123}<634>), copper ({112}<111>), Goss ({110}<001>), cube
({100}<001>), rotated cube ({100}<130>), and other less common components [86],
[88], [89]. Of these, copper, brass, and S are common rolling textures, while Goss, cube, and rotated cube are recrystallization textures. Usually, deformed aluminum forms strong a strong brass texture, with minor S and copper components [3]. Recrystallization during subsequent annealing causes the formation of Goss texture with a minor cube component, or less often with a minor rotated cube component [3], [86]. Forming
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processes and heat treatment schedules vary for different alloys but are generally designed to reduce the intensity of the brass texture component in order to mitigate anisotropy in the final wrought product [3], [80]. Of the recrystallization texture components, cube is the most important for subsequent formability. In forming Al sheets, Goss texture is detrimental while cube is beneficial [88], and a strong cube texture is necessary for beverage can forming [90].
The observed textures in Al alloys both during hot working and post-working heat treatment are significantly influenced by temperature and by precipitate distribution. The main effect of process temperature is on the activation of non-octahedral slip. Bacroix and Jonas thoroughly investigated the effects of non-octahedral slip on texture formation during deformation. In their simulation, individually activating {100}, {110}, and {112} slip resulted in S, copper, and brass texture components respectively [64]. Further, they found that the brass component was suppressed when only octahedral slip was allowed, and allowing all systems to activate simultaneously produced textures of mixed brass, copper, and S character [64].
Non-octahedral slip need not be a major deformation mode to have significant effects; short-distance cross-slip onto non-octahedral planes contributes greatly. All of the secondary non-octahedral slip systems mentioned in Section 1.3.1 share the <110>
Burger’s vector with octahedral slip and may be involved in cross slip. Considering that the target microstructures for wrought Al-Li alloys often involves a very high number density of very fine precipitates and dispersoids, cross-slip can significantly lower flow
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stress by increasing particle bypass of non-shearable and shear-resistant precipitates and dispersoids [65], [91]. This is not universal for all precipitates, however. As with hardening, cross slip and precipitate bypass are dependent on precipitate shape; spherical precipitates are bypassed more easily than acicular precipitates lying normal to the slip plane [91].
Cross slip also contributes greatly to dynamic recovery (DRV), which can compete with DRX. In the hot forming regime, DRX is favored, but at lower temperatures where DRX is kinetically restricted, DRV is favored. This change in recovery mechanism necessarily affects the texture produced during hot deformation – a brass deformation texture is produced with DRV, and a cube recrystallization texture is produced with DRX. This is of enough concern that reduction of SFE, which reduces cross-slip, can become relevant for alloying [92]. More toward industrial concerns, increased DRV can reduce the strain hardening rate, which lowers formability [93].
Finally, precipitates and dispersoids have a significant effect on texture. While seemingly counterintuitive, sufficiently fine distribution of dispersoids or precipitates can increase ductility and reduce texture intensity. When finely distributed, non-shearable obstacles necessitate cross-slip in order for the material to accommodate imposed strain.
Successive events break up planar slip which leads to strain localization and failure [3],
[86]. Known as slip dispersal, this has been observed to cause lower overall texture intensities in Al-Li alloys containing sufficiently finely distributed δ precipitates [86].
Slip dispersal has also been reported for Mn-containing dispersoids, leading to increased
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toughness and ductility [94]. In addition to slip dispersal, dispersoid distribution can allow control of texture through DRX or static recrystallization (SRX). Sufficiently small (< 1µm) and finely distributed dispersoids will not contribute much to PSN [88], but still will impede recrystallization. If deformation takes place at low enough temperatures, such that the material accumulates deformation content without recrystallizing, the material can be annealed for SRX after deformation, resulting in a much stronger cube texture [88].
Heat treatment and forming processes in Al-Li alloys are complicated, involving recrystallization annealing between primary and finish rolling as well as post-rolling annealing [80], [86]. Processes necessarily vary depending on target microstructures and properties for a given alloy and service conditions [80].
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Chapter 2: Thermomechanical Processing and Characterization of Mg
The rare earth effect is of critical interest in wrought Mg alloys, as it mitigates the deleterious effects of texture. General mechanisms contributing to the RE texture component are known and are detailed in Section 1.2.4. Though the rare earth component has been reported for ZE20 extrusions [95] and processing has been investigated for similar alloys [29], [56], [96], a thorough investigation into RE effects and the influence of processing on mechanisms contributing to RE effects has not yet been conducted.
In this chapter, the properties of Mg alloy ZE20 are compared to those of a conventional Mg alloy in the warm forming regime in order to investigate the occurrence of RE effects. Mechanical testing is performed at several temperatures and strain rates to examine the conditions under which RE effects occur. Thorough microstructural analysis using EBSD is applied to determine the mechanisms resulting in the RE texture component. Processing recommendations based on experimental findings and conventionally-determined processing maps are presented.
2.1 Materials
2.1.1 AM30
Magnesium alloy AM30 (Mg-3Al-0.4Mn) is a conventional magnesium alloy developed by Luo and Sachdev [97]. The alloy is essentially a zinc-free version of the
26
most widely-available commercial wrought Mg alloy, AZ31 (Mg-3Al-1Zn-0.4Mn); the removal of Zn eliminates a ternary compound which contributes to incipient melting, allowing processing at higher temperatures and higher strain rates [97]. In this work,
AM30 serves as a baseline Mg alloy. It utilizes only conventional alloying elements for
Mg: Al, which has excellent solid solution strengthening capabilities, and Mn, which is added for melt cleanliness in order to improve corrosion resistance and can also act as a grain refiner [53], [97]. In this work, AM30 serves as a baseline conventional alloy against which properties of ZE20 are compared.
A single AM30 billet was received from Ford though the United States
Automotive Materials Partnership (USAMP). The AM30 billet was produced by direct chill casting and was received in the pre-extruded condition. Pre-extrusion involves a
20% reduction in diameter and is performed to improve subsequent workability. In order to reduce influence of billet processing on mechanical testing, all specimens were excised from locations at the same distance along the billet’s radius.
2.1.2 ZE20
Magnesium alloy ZE20 (Mg-2Zn-0.2Ce-0.3Mn) is a recently-developed RE- containing alloy designed to have high formability and moderate strength [95]. ZE20 billets were supplied by Ford through USAMP. Billets were produced by direct-chill casting and were received in the as-cast condition. Compositional analysis of the ZE20 billet is shown in Table 1.
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Table 1. Optical emission spectroscopy measured composition of ZE20
Others Element Ce Mn Zn Th Si (<0.01% Mg each) Composition 0.2686 0.3599 1.966 0.1213 0.01086 0.02863 Balance (wt. %)
2.2 Mechanical Behavior of Mg Alloys
2.2.1 Thermomechanical Testing
Thermomechanical testing was performed with a Gleeble 3800 servo-hydraulic thermomechanical testing system. Force during testing was measured using a load cell with ±1kg resolution and ±1% full scale accuracy for +10,000/-20,000kg full range.
Hydraulic ram displacement during compression and tests was measured using the
Gleeble’s internal LVDT which has± 0.002mm resolution and ±0.25% full scale accuracy over ±62.5mm of travel. The Gleeble system uses direct resistive heating, where current is passed through the specimen in order to heat it. Temperature was monitored and maintained for all tests with a single K-type thermocouple. True stress, true strain, and true strain rate of testing were dynamically calculated by a computer during testing using current values of displacement, force, and specimens’ initial dimensions as inputs and using the traditional assumption of volume conservation for a right cylinder.
Mechanical testing specimens were machined from AM30 and ZE20 billets via electrical discharge machining (EDM). Gleeble compression cylinders were 10mm long 28
by 15mm Ø right cylinders. Any surface imperfections from EDM were manually removed with 400 grit metallographic abrasive paper. Prior to testing, specimens’ exact dimensions were recorded and input into a testing program in order to achieve exact strains and strain rates. Individual 0.01” diameter alumel and chromel thermocouple leads were percussion welded 1mm apart along the midline of the specimen in order to monitor and maintain testing temperature. Specimen/anvil surfaces were well lubricated during testing in order to minimize effects of barreling. Five-mil (0.005”) graphite foil was used as the primary lubricant, and a small amount of Thred Gard conductive graphite-nickel lubricant paste was used to adhere the graphite foil to the anvils prior to testing.
All Gleeble tests followed the same basic three-part program. The first part of the testing program applied a 5°C per second heating rate up to the desired testing temperature. The second portion of the program is a 60 second hold at temperature to ensure that the entire specimen reaches the testing temperature. The final portion of the program is the actual deformation segment, applied at a constant true strain rate up to the desired final strain. This is illustrated schematically in Figure 1. Specimens were water quenched to room temperature as soon as possible after the end of the mechanical test, in order to “set” the specimen microstructure and avoid effects such as postdynamic recrystallization. Specimens were usually quenched within 15 seconds. Specimens could not be quenched earlier, as it would interrupt the testing program and interfere with data collection.
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Figure 1. Schematic representation of thermomechanical testing scheme illustrating thermal and mechanical portions of test.
AM30 and ZE20 were tested in compression at each combination of 200°C,
350°C, 375, 400, and 425°C and 10-2 s-1, 10-1 s-1, 5.0 s-1, and 100 s-1. For all test conditions, AM30 had a relatively smooth surface with low to moderate barreling and ovality and some indication of rollover at the specimens’ corners. Barreling in AM30 had no strong trend with temperature or strain rate, and the average barreling parameter,
B, of specimens was 1.068 with a standard deviation of 0.0156. Flow stress does not necessarily need to be corrected if the barreling parameter B is less than 1.1, as deviations are slight [98]. No specimens had a calculated barreling coefficient of 1.1 or greater.
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AM30 also exhibited slight ovality after testing. Ovality was more severe at higher strain rates, eventually giving way instead to failure by localized shear. The average ratio of maximum diameter to minimum diameter was 1.073 for tested specimens, with only a few high strain rate specimens having ovality ratios greater than 1.1.
Relative to AM30, ZE20 seemed to oxidize more at the same temperatures, having a dark grey surface following deformation at temperatures over 400°C. ZE20 did not appear to deform homogenously, having a ridged surface indicating possible presence of several shear bands. This made quantitative assessment of barreling difficult for
ZE20, where sometimes non-physical values of the barreling coefficient B were obtained.
Qualitatively, the amount of barreling seemed to be lower than that observed in AM30.
No ovality could be measured for ZE20; differences in diameter were less than the
~0.5mm ridges in surface roughness even at high strain rate and low temperature.
Careful observation of ZE20 specimens’ surfaces also revealed the presence of sparse microcracks associated with these ridges for all specimens tested below 300°C and for some specimens tested at 300°C, despite no evidence of this from the flow curves.
Flow curves for AM30 are shown in Figure 2. It is readily apparent that at 10 s-1 there is some combined inaccuracy in temporal resolution of the Gleeble’s load cell,
LVDT, and/or hydraulics. For some flow curves, this causes the appearance of a very low modulus or soft yielding. The overall result is that individual flow curves do not appear to uphold the trend of increasing flow stress with decreasing temperature for all strains, and there is poor confidence in the peak stress for all flow curves. To some
31
extent, this effect is also present with flow curves obtained at 5.0 s-1. Due to the already low confidence in high strain rate data, and in order to facilitate comparison between flow curves, these flow curves were not corrected for adiabatic heating or ovality - the impact of both of which is greatest at high strain rates. For reference, the maximum adiabatic temperature rise was 55°C, 41°C, and 26°C for tests conducted at 200°C, 350°C, and 425°C, respectively. At strain rates up to 100 s-1, the response time of the thermocouple is sufficient that the Gleeble is able to maintain test temperature within 2°C of the desired temperature, and correction for adiabatic heating is not needed.
Figure 2. Stress-strain curves of AM30 at (a) 10-2 s-1, (b) 10-1 s-1, (c) 5.0 s-1, and (d) 100 s-1.
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Despite the uncertainty from testing, several conclusions can be drawn for AM30 based on the flow curves in Figure 2. AM30 exhibits general trends which are seen in nearly all metals: increasing flow stress with increasing strain rate or decreasing temperature. Apart from this, the other most obvious feature is failure prior to reaching full strain for all specimens tested at 200°C and strain rates greater than 10-2 s-1. Failure was typical bulk fracture inclined at 45° to the compression axis, and data in Figure 2 was truncated after the failure point. AM30 tended to exhibit sharp yield points, followed by a “yield plateau,” though this is obfuscated by the acquisition rate higher strain rates.
This behavior is consistent with activation of twinning as the primary deformation mode, as the material’s initial processing gave it a sharp non-basal texture for the compression direction. Exhaustion of twinning at low strains then causes concave-up hardening as non-basal slip systems are activated to accommodate strain. This yield plateau is suppressed at high temperatures and low strain rates (at 375°C and above for 10-2 s-1 and at 425°C for 10-1 s-1), where recrystallization is likely to operate. In such cases, the sharp yield point still corresponds to the initial CRSS, but recrystallization could reorient grains, leading to no concave-up texture hardening as twinning is exhausted. After the peak stress, some amount of softening is observed in all slow curves. This is attributable to DRX and/or DRV. At high strains, steady-state stress is achieved due to continuous operation of DRX.
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Results from ZE20 showed the same effects of data acquisition at high strain rate.
In order to aid mechanical properties investigation, tests were repeated for ZE20 using a refined test matrix at each temperature and strain rate combination of 250°C, 300°C,
350°C, 400°C, and 450°C and 10-3 s-1, 10-2 s-1, 10-1 s-1, and 100 s-1. The results for second round of ZE20 testing are shown in Figure 3.
Figure 3. Stress-strain curves obtained for ZE20 at (a) 10-3 s-1, (b) 10-2 s-1, (c) 10-1 s-1, and (d) 100 s-1.
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Due to the initial as-cast state of ZE20, there are fewer salient features in the flow curves. As with AM30, ZE20 exhibited the expected general trends with temperature and strain rate. There seem to be three regimes of behavior for ZE20, which are best described in terms of Zener-Hollomon parameter, Z (or temperature-compensated strain rate). For ZE20 in low-Z regimes (low strain rate and high temperature), the flow curves nearly resemble those of an ideal plastic: constant flow stress with no hardening or softening. This indicates profuse activation of DRX, or even creep, as the temperature is greater than 0.7 Tm for the stress-strain curves where this behavior is evident. This behavior seems to occur at higher temperatures and lower strain rates than the same behavior in AM30, indicating more kinetically-limited activation of DRX in ZE20. For high-Z conditions (high strain rate and low temperature), hardening occurs until the peak stress, after which there is very little softening. In Al and other materials with higher SFE than Mg, such behavior is associated with DRV. Although the existence of DRV alone as a recovery mechanism is difficult to show, similar flow stress behavior has also been shown and attributed to DRV in Mg alloy ZK60 [99]. All other stress-strain curves in moderate-Z conditions in Figure 3 have similar behavior: yielding, concave-down hardening until a peak stress at about ε = -0.3, and concave-up softening. Such behavior is classically attributable to activation of DRX after the peak stress [99]. Unlike AM30, the flow curves for ZE20 in the moderate-Z regime do not seem to reach steady-state flow stress. These curves still have a downward slope, indicating that there is still some softening occurring at a strain of 1.0 and recrystallization is likely not complete.
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2.2.2 Processing Maps
Processing maps are a useful tool in industry to determine the optimal processing conditions for a given material. Features on processing maps are implicitly related to microstructural phenomena, and processing maps can be used to guide more detailed study of the microstructural processes occurring in ZE20. There are several methods for calculating the basic parts of a processing map, but the most common construction – both in literature [100], [101] and in standard reference publications [102], [103] – is a combination of an efficiency parameter developed by Prasad et al. [104] and an instability criterion developed by Prasad and Kumar [105], [106]. The work of Prasad et al. is premised on a variational principle analysis of rigid viscoplastic material by Oh
[107] and Lee and Kobayashi [108]. Prasad et al. then determine efficiency by modelling the workpiece as a linear dissipator of power using principles of the Dynamic Materials
Model as established by Wellstead [109].
Prasad et al.’s derivation begins with a statement of the power dissipated by the workpiece:
𝜀̇̇ 휎 푃 = 휎̅휀̇̅ = 휎 푑휀̇ + 휀̇ 푑휎 (2) ∫0 ∫0
where P is the total power dissipated by the workpiece, σ̅ is the effective stress, ε ̅ is the effective strain rate, σ is true stress, and ε is true strain rate. This is rewritten as
36
P = G + J (3) where G is the “dissipator content” and J is the “dissipator co-content.” Prasad et al. note that these terms can be conceptualized in thermodynamic quantities: G is the amount of power dissipated by heat or plastic work, and J is the amount of power dissipated by microstructural processes [104]. The term of interest for workability is J, which can be evaluated by assuming power law form of stress (σ=kεm):
σ σ ε̇ m J = ∫ ε̇ dσ = (4) 0 m+1 where m is the strain rate sensitivity of the material. The efficiency of power dissipation,
η, is the ratio of metallurgical power dissipation to the maximum possible metallurgical power dissipation, which occurs at m = 1.
σ ε̇ m J m+1 2m η = = σ ε̇ = (5) Jmax m+1 2
The second portion of the processing map, the instability criterion, comes from work by Ziegler [110]. Ziegler noted that stable flow occurs if
dD D > (6) dε̇ ε̇ where D is the “dissipative function” of the material. Prasad and Kumar noted that if the dissipative function were equal to the metallurgical power dissipation, then metallurgical instability can be found by substituting J for D [105], [106]. The stability criterion, ξ, can be stated by simplifying the resulting inequality:
37
m d ln( ) ξ(ε̇) = m+1 + m > 0 (7) d ln ε̇
These derivations are not universally accepted. They are, however, the basis for standard reference materials [102], [103] and are used more frequently in research publications than other definitions [100], [101]. Material workability is a widely researched concept owing to its direct practical applications, and several definitions of processing maps are available in the literature. The first variation of a process map was developed by Raj [111] on a mechanistic basis; Raj outlined the regions in temperature and strain rate where different mechanisms detrimental to workability were active and showed a safe processing region for Al. Semiatin and Lahoti took a more mathematical approach, proposing a criterion to quantify flow localization, operating under the classical assumption that flow instability occurs upon softening after the peak stress
[112], [113]. Murty has widely criticized Prasad’s work due to the assumption of a power law in Equation 4. providing instead a more general definition [114]–[116].
Poletti et al recently developed an alternate criterion which does not rely on strain rate sensitivity to determine instability, comparing results and outlining discrepancies with
Murty and Prasad’s work [117]. Other notable alternate constructions include work by
Montheillet et al. [118], who work with strain energy density rather than power dissipation, and work by Ghosh [119], who derives quantities based on a thermodynamic definition of D in Equation 6 rather than simple substitution of J for D.
By convention, both η and ξ are related in log(ε ) – T space for a single strain.
Contours are plotted for η, and areas where the stability criterion in Equation 7 is not 38
satisfied are shaded. Processing maps for several strains are often related for a single material, to show how efficiency and instability evolve with imposed strain. It should be noted that processing maps are sensitive to initial material conditions, and a different starting microstructure, perhaps due to different prior thermal or mechanical history, will change the obtained results.
Interpretation of processing maps required some introduction, as the plotted parameters are not necessarily intuitive. Because it is simply derived from bulk tests, efficiency of power dissipation does not carry explicit information about any metallurgical processes. Rather change in the metallurgical processes which dissipate power is implicit, and approximate values of efficiency have been associated with different mechanisms in different materials [120]. The general rule is that processing should occur under conditions of highest η, unless that region has plastic instability [102].
More specifically, DRX is usually said to occur between 30% and 40% efficiency for low
SFE and is said to occur between 50% and 55% for high SFE materials [120].
Superplasticity and/or wedge cracking occur in regions with greater than 60% efficiency
[120]. Ductile fracture occurs in regions of rapidly rising efficiency at low temperatures and high strain rates [120]. Other microstructural dissipative processes, such as DRV and various cracking mechanisms, are recognized but are not assigned general values of efficiency. Most importantly, any microstructural mechanism or domain identified on a processing map should be verified with characterization [102], [103], [120].
39
Processing maps could not be generated for AM30 due to the distribution of strain rates and temperatures for the entire dataset and due to the low confidence in high strain rate data. Processing maps were generated for the refined ZE20 test matrix and are shown in Figure 4. There are two domains and two instability regions identifiable from the processing maps. Domain I is a local maximum of efficiency and is assumed to be a region where DRX is favored. Domain I exists between 400°C and 450°C and between
10-2.5 s-1 and 10-1.5 s-1 and gradually moves to higher temperatures and lower strain rates at progressively higher strains. Domain II is also a local maximum with efficiency, though it could be indicative of DRX or possibly superplasticity. Because the processing map is limited to strain rates above 10-3 s-1, the actual maximum of efficiency is likely hidden at lower strain rates, which limits the information that can be drawn about this domain from mechanical data alone. Instability Region I is a broad region of instability that covers all but the highest temperatures and lowest strain rates at low strains. With increasing strain, Instability Region I gradually moves to lower temperatures and higher strain rates. There is one island of stable processing at low temperature and high strain rate below strains of -0.45, but this is not of industrial interest because it has very low efficiency, and to reach high strains, one must pass through Instability Region I.
Instability Region II is of metallurgical interest because it has negative efficiency. From
Equation 5, this necessarily means that ZE20 has negative strain rate sensitivity in
Instability Region II. This region therefore carries with it the potential for DSA and shear banding to form the RE texture component [56].
40
Figure 4. Processing maps for ZE20 at strains of (a) -0.15, (b) -0.35, (c) -0.65, and (d) -0.90. Identified domains and instability regions are marked in blue and red respectively.
The microstructural processes occurring in each of these domains and instability regions were verified with electron microscopy and EBSD.
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2.3 Microscopy and Characterization
2.3.1 Microscopy Procedures
Specimens were sectioned axially and cold-mounted in epoxy in order to avoid any thermal or mechanical effects that could otherwise be introduced in hot mounting.
Specimens were ground and polished using standard metallographic procedures.
Grinding was accomplished with progressively fine SiC metallographic abrasive paper, down to 1200-grit paper, using water to wash away abraded material. Polishing was accomplished with progressively fine diamond abrasive in an alcohol suspension on a low-nap cloth, down to 1µm grit abrasive. Water was necessary for cleaning specimens, but contact time was minimized in order to avoid oxidation or etching of polished surfaces. Final polish was achieved using colloidal silica and a synthetic neoprene polishing pad. Specimens were quickly cleaned with soapy water, rinsed with water, rinsed with ethanol, and dried using compressed air. Specimens for EBSD were not etched in order to preserve surface planarity and maximize backscattered electron signal.
Specimens for imaging were etched to reveal grain boundaries and twins. Etching consisted of 3-5 seconds of immersion in an acetic-picral etchant (4.2g picric acid, 10ml glacial acetic acid, 70ml ethanol, and 10ml distilled water). Specimens were stored in a desiccator to minimize oxidation and were studied as soon as possible after polishing or etching.
Electron backscatter diffraction data was gathered on an FEI XL-30 microscope equipped with a FEG operating at 20kV and spot size 4. Secondary electron images and
42
backscattered electron images were gathered on either the same microscope operating at
12kV and spot size 5, or were taken on a FEI Apreo microscope with a field emission gun
(FEG) electron source, operating at 5.0 kV and 0.4 nA. Images and EBSD data were gathered along the specimen’s mid-thickness and at half the specimen’s radius. EBSD data was analyzed using TSL OIM Analysis 8 software. A light cleanup was applied to the experimental data. Cleanup consisted of neighbor orientation correlation with a grain tolerance angle of 5° and a minimum confidence index of 0.1, followed by a single iteration of grain dilation using a 5° grain tolerance angle and a minimum grain size of 5 scan points. All data points with confidence index lower than 0.1 were excluded from further analysis.
EBSD scans were partitioned into deformed and recrystallized microstructures based on grain orientation spread (GOS). The GOS of a given grain is the average misorientation of all scan points within that grain, relative to a kernel orientation for that grain. GOS is convenient because it relates the stored deformation content within a grain in a single measurement per grain, and as such it allows for easy partitioning of the microstructure on a grain level. Traditionally for SRX studies, grains with GOS less than
1° are said to be recrystallized, and grains with GOS greater than 5° are said to be deformed. Many grains often have GOS between these values, and treatment of such grains varies with the experiment and experimenter preference. Further, microstructures usually have some distribution of GOS with no clear division, and the division between deformed and recrystallized microstructures is somewhat arbitrary. The same established
43
GOS values are valid for DRX, but the interpretation is slightly different. Hot deformation necessarily involves some deformation of newly recrystallized grains. Any grains – recrystallized and deformed or just deformed – with deformation content over a threshold value are said to be part of the deformed microstructure. For this work, a somewhat conservative value of 2° of GOS was chosen as the division between recrystallized and deformed microstructures.
Inverse pole figure maps and textures were generated for deformed and recrystallized microstructures. Textures were calculated using rank 16 harmonic series expansion, using all points within a given partition. Pole figures (PFs) are shown where relevant, but inverse pole figures (IPFs) are usually sufficient to convey texture in Mg.
2.3.2 Exemplar Microstructures and General Deformation Behavior of AM30 and ZE20
Initial microstructures and textures for ZE20 and AM30 are shown below in
Figure 5 and Figure 6, respectively. For convenience and ease of comparison, the pole figure scale shown in Figure 5 (e) and Figure 6 (e) is the same for all Mg PFs and IPFs.
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Figure 5. Microstructure and texture of as-cast ZE20. Billet axis is vertical, and billet tangential direction is horizontal. (a) secondary electron image, (b) IPF map, (c) (0001) pole figure, (d) IPF map key, and (e) PF intensity scale.
The as-cast ZE20 in Figure 5 has few notable features. Direct-chill casting resulted in a globular dendritic microstructure with large, equiaxed grains having an average diameter of 380µm. A Ce-rich second phase forms in the interdendritic spaces, with some small particles inside the grains. There are several peaks on the pole figure, but none of these have significantly strong preference for any billet directions. It is likely that these peaks exist simply due to sampling a small number of grains, and the material has no initial texture preference. For ease of comparison of subsequent Mg figures, all
IPF maps share the same key (colors plotted for vertical direction – initial billet axis or compression direction), and all PFs and IPFs share the same intensity scale.
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Figure 6. Microstructure and texture of as-received AM30. Billet axis is vertical, and billet tangential direction is horizontal. (a) backscattered electron image, (b) IPF map, (c) basal PF, (d) prismatic PF, and (e) PF intensity scale.
AM30 has several features of its prior processing. From the SEM image alone, not much is evident except for stringers of Al8Mn5 precipitate stringers aligned with the pre-extrusion direction. Analysis of the EBSD data yields more specific information.
Much of the microstructure is recrystallized, including both fine grains and the large, equiaxed grains. Few swaths of elongated, deformed grains remain. Very few recrystallized grains have basal orientations, and all deformed grains have non-basal
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orientations. From the PFs in Figure 7, it is clear that the material has a prismatic fiber texture. There are some basal peaks between the radial and tangential directions of the billet, but these correspond mainly to the large recrystallized grains; there is no real secondary preference for orientation.
Consistent with the flow curves, both alloys exhibited significant recrystallization after mechanical testing at temperatures above 200°C. Both alloys followed the expected general trends for recrystallization during hot deformation. The recrystallized grain size increases with temperature for both alloys but is not significantly affected by strain rate.
The volume fraction of recrystallization increases with both strain rate and temperature.
For AM30, this results in complete recrystallization of the original microstructure at moderate and high temperatures and strain rates. For ZE20, at even the highest temperature and strain rate, approximately 30% of the microstructure remained unrecrystallized. This alone is not sufficient evidence of the RE effect, as AM30 starts with a somewhat refined, partially recrystallized microstructure. More direct evidence is that the recrystallized grain size of ZE20 is smaller than AM30 for all test conditions.
Overall, this indicates that recrystallization is much slower in ZE20. This is likely due to
ZE20’s Ce content, which should exert solute drag on grain boundaries and retard growth of newly recrystallized grains.
Representative microstructures for hot-compressed AM30 are shown in Figure 7.
Many of the features of pre-extrusion of AM30 are annihilated by compression to a strain of -1.0. The stringers of precipitates are still present, which are now bowed slightly due
47
to barreling of the specimen. As previous, the microstructure has a bimodal grain size with many grains on the order of ~20µm and a few large grains tens to hundreds of microns in diameter, but it is impossible to draw conclusions about deformed or recrystallized grains from SEM alone. Most deformed AM30 specimens also had some twinning. Evidence of twinning was seldom observed above 375°C, partly due to nearly complete recrystallization in AM30 at higher temperatures.
Figure 7. Secondary electron image of AM30 tested at 350°C and 10-1 s-1. Compression direction is vertical.
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EBSD reveals more about these large grains. At 200°C, the large grains appear to be retained from the prior microstructure, and have evidence of twinning. In some cases, as highlighted in Figure 8 (a), prior twin boundaries assist DTN recrystallization. Where
DTN was observed, recrystallized grains did not have the RE texture component and did not significantly weaken the texture of the recrystallized material (for comparison, the texture corresponding to Figure 8 (a) is shown in Figure 11). At moderate strain rates and moderate to high temperatures, large grains were still visible in AM30 microstructures, but these grains were fully recrystallized. Figure 8 (b) shows this clearly, as several large grains having GOS less than 1° are present in the microstructure.
At high strain rates or at high temperatures, AM30 tended to recrystallize completely, and this disparity in grain size was not evident.
Figure 8. Recrystallization phenomena in AM30. (a) IPF map of AM30 compressed at 200°C and 5.0 s-1, with DTN events circled. (b) GOS map of AM30 compressed at 350°C and 10-1 s-1, and (c) GOS key. Compression direction is vertical. 49
Several key features are apparent from the tested ZE20 microstructure in Figure 9.
Most notable is clear evidence of localized flow. The overall microstructure is composed of relatively undeformed regions that are separated by regions of intense deformation.
The flow localization was not as intense as shear banding, forming instead shear zones ranging from tens of microns to more than 100 microns in thickness. Microscopy near the edges of compression specimens determined this flow localization to be the cause of the surface roughness for tested specimens. As with the observed surface roughness, the apparent severity of flow localization increased with decreasing temperature and was relatively unaffected by strain rate. Also notable in Figure 9 is the presence of recrystallization occurring preferentially in localized flow zones. This is consistent with classical observation of discontinuous DRX (DDRX) in Mg alloys, where dislocation content accumulates at the grain boundaries, causing grain boundary nucleation and the formation of a necklace-type microstructure [121].
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Figure 9. Microstructure of ZE20 after thermomechanical testing at 400°C and 10-1 s-1. Compression direction is vertical.
Recrystallization occurred nearly exclusively in these localized flow zones in
ZE20. Neither PSN nor DTN were observed in ZE20. Though precipitates are associated with recrystallization in Figure 9, this is only because localized flow occurred more frequently at prior dendrite boundaries, effectively shearing the Ce-rich phase from the interdendritic space and distributing it along the localized flow zone. These precipitates likely affected nucleation, but no recrystallization was observed at the precipitates within the prior grain interiors, possibly because dislocation does not accumulate in the grain interiors [121]. Twinning was also evident in ZE20 specimens
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tested at 200°C, though DTN was not observed. Very little recrystallization was observed in ZE20 specimens tested at 200°C due to poor indexing of the highly deformed material. While it is impossible to show lack of a phenomenon, EBSD scans at temperatures where these mechanisms were favored but were not observed are shown in
Figure 10.
Figure 10. EBSD of ZE20 in regimes where PSN and DTN would be favored. (a) IPF and IQ map of a specimen compressed at 425°C and 10-2 s-1, and (b) IPF map of a specimen compressed at 200°C and 10-1 s-1. Compression direction is vertical.
Aside from microstructure, the texture of both alloys was significantly affected by the test conditions. Generally, with increasing temperature, the texture of both the deformed and recrystallized grains tends to take on an increasingly non-basal character.
Inverse pole figures illustrating this change are shown in Figure 11. For the deformed
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grains of both materials, the basal pole shifts toward <112̅0>. For the recrystallized grains, the peak texture intensity shifts away from the basal pole, but there is less preference for either prismatic I or prismatic II planes (<101̅0> or <112̅0>). In all cases, increasing temperature caused a decrease in texture intensity. Strain rate did not significantly affect the texture of either material. At 200°C, deformed AM30 tends to form slightly sharper textures than ZE20. For all other temperatures (including those not pictured), the deformed grains in both materials had similar texture intensity. Also at
200°C, ZE20 tends to form slightly sharper recrystallization texture than AM30. This may be due to a small sampling of recrystallized grains in ZE20; even at 5.0 s-1, the microstructure was only 13.5% recrystallized. For all other temperatures, ZE20 had moderately lower or significantly lower recrystallization texture intensities.
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Figure 11. Texture trends with temperature in ZE20 and AM30. Texture data shown for tests at 5.0 s-1.
2.3.3 Process Map-Guided Investigation of ZE20 and Processing Recommendations
The domains and instability regions of the processing maps in Figure 4 were investigated using EBSD. Consistent with the analysis of the flow curves and the general deformation behavior of ZE20, Domain I exhibited significant DRX. Figure 12 shows the microstructure of a specimen tested in Domain I. Discontinuous recrystallization is
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evident, as with other specimens. The significant volume fraction of recrystallization is consistent with both the processing map predictions as well as the analysis of the flow curves. Comparing Figure 12 (a) and Figure 12 (b), it seems that many recrystallized grains have subsequently been deformed and are thresholded out of the “recrystallized”
GOS partition. The bulk has a single texture peak of moderate intensity, rotated about
20°C away from a basal orientation toward <112̅0>. The recrystallized material has a single texture peak also rotated 20° away from the basal pole, but it is inclined toward
<101̅0> instead of <112̅0>.
Figure 12. EBSD of a specimen compressed to a strain of -1.0 in at peak efficiency in Domain I. (a) IPF map, (b) IPF map of recrystallized grains only, (c) IPF of deformed grains, (d) IPF of recrystallized grains, and (e) IPF scale. Compression direction is vertical.
The recrystallization behavior in Domain I is similar to that of conventional Mg alloys. The bulk non-basal texture is expected due to increased activation of pyramidal
boundary nucleation produces a recrystallization texture component similar to the bulk texture with slightly lower texture intensity. The greater angular spread of the recrystallization texture is significant and is observed for Mg-RE alloys more frequently than conventional Mg alloys, however this effect is slight.
Domain I would likely be suitable for processing, however it may not produce an optimal material. Usually, smaller grain sizes and higher volume fractions of recrystallized material are desired. The large recrystallized grain size increases the tendency of recrystallized grains to deform and accommodate strain, similar to the bulk material, giving those grains a texture component similar to the bulk. To avoid this, finer grain sizes (and consequently also higher volume fractions of recrystallized material) can be achieved by processing at higher strain rates and lower temperatures to higher final strains. Domain I is still of interest, because it has a relatively wide range of viable temperatures and strain rates. While the specimen shown in Figure 12 was compressed at conditions of peak efficiency, other processing conditions still in Domain I could be chosen.
Microstructures of a specimen compressed at 350°C and 10-3 s-1 in Domain II are shown in Figure 13.
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Figure 13. EBSD of a specimen compressed to a strain of -0.35 at the efficiency minimum in Domain II. (a) IPF map, (b) IPF map of recrystallized grains only, (c) IPF of deformed grains, (d) IPF of recrystallized grains, and (e) IPF scale. Compression direction is vertical.
Domain II lies at the edge of Instability Region I, and the specimen shown in
Figure 13 passed partially through Instability Region I in order to reach Domain II. Flow instability is evident in the specimen, and recrystallization is occurring at the grain boundaries on a localized flow zone which passes from upper left to lower right. Little recrystallization is visible outside this localized flow zone. The parent and recrystallized material both exhibit non-basal texture, but it is not significant. Because the specimen was only compressed to a strain of -0.35, the individual grains of the specimen have not yet fully rotated to the stable basal orientation. It is likely that this is somewhat due to flow localization acting as a strain accommodation mechanism, giving a lower accumulated strain within the original grains. Unfortunately, because of the non-basal bulk texture, the non-basal recrystallized texture is not necessarily relevant. The nuclei are nucleating off of grains with several orientations and seem to share the orientation of 57
their parent grains. Randomly oriented nucleation of new grains is highly desirable in
Mg alloys, but it is unlikely to occur in material with a strong basal texture.
Overall, Domain II likely does not hold industrial relevance. It would require precise process control to avoid having material pass through Instability Region I due to uneven heating of a part. More importantly, Domain II only exists up to a strain of -0.40.
This would be an insufficient strain for most bulk wrought processes, including forging, extrusion, and rolling.
A more varied array of phenomena was visible in Instability Region I. The most prevalent was flow localization, which was observed in all specimens tested in Instability
Region I. A typical microstructure showing profuse flow localization is shown in Figure
14.
Figure 14. EBSD maps showing flow localization within a specimen compressed to a strain of -1.0 at 300°C and 10-1 s-1 (Instability Region I). (a) IPF map, (b) IPF map of recrystallized grains within shear bands, (c) IPF of matrix, (d) IPF of recrystallized grains, and (e) IPF scale. Compression direction is vertical.
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As previously mentioned, bands of recrystallized grains are visible along prior grain boundaries which have sheared heavily due to localized flow. The texture of the deformed material in Figure 14 (c) is strongly basal and is typical of Mg deformed at low to moderate temperatures. The recrystallized grains shown in Figure 14 (b) have slightly lower texture intensity than suggested by the trend in Figure 11, but the recrystallization texture still holds the characteristic basal texture with lower intensity than the bulk. This is typical of grain boundary nucleation in Mg, and as observed, does not lead to the RE texture component. While the low texture intensity of the recrystallized grains does have some merit, the area fraction of recrystallization is only 11.4% - far from the desired fully recrystallized microstructure.
In the same specimen from Instability Region I, another form of plastic instability was observed: shear banding. EBSD of adiabatic shear bands is shown in Figure 15.
Figure 15. EBSD of shear bands within a specimen compressed to a strain of -1.0 at 300°C and 10-1 s-1 (Instability Region I). (a) IPF map, (b) IPF map of recrystallized grains within shear bands, (c) IPF of matrix, (d) IPF of recrystallized grains, and (e) IPF scale. Compression direction is vertical. 59
When they were observed, adiabatic shear bands were far less prevalent. Shear bands were mainly contained in one or a few grains and were not common throughout a given specimen’s microstructure. Shear bands were only observed at lower temperatures and higher strain rates within Instability Region I. Unlike simple localized flow, shear bands were very thin, less than 10μm in thickness, and were aligned approximately 45° to the compression direction. All observed shear bands were fully recrystallized, likely due to the heat and severe deformation generated during their formation. While the texture of the parent material in Figure 15 is not important because it only covers a single grain, the texture of the recrystallized material has a clear RE component due to SBN.
The final plastic instability mechanism observed in Instability Region I was shear cracking. As mentioned previously, surface cracking was also observed in for high strain rate specimens. Microscopy also revealed the presence of sparse microcracking in specimens tested at 250°C and 10-2 s-1 and 10-3 s-1 as well as 300°C and 10-3 s-1. Such acts as an initiation site for potentially catastrophic failure, and any degree of cracking is unacceptable for formability considerations.
Apart from the specific qualia observed, the overall conditions under which plastic instability occurs in Instability Region I are of importance. Apparent flow localization was observed at higher temperatures and lower strain rates than predicted in
Figure 4; take for example the microstructure in Figure 9. At 400°C and 10-1 s-1, ZE20 is only on the edge of Instability Region I. However, plastic instability is clearly not a
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simple binary phenomenon, varying in the forms in which it manifests and the severity to which it occurs. At lower temperatures, as in Figure 14, flow localization is very intense.
At even higher temperatures, flow localization or apparent flow localization is much more diffuse, and its occurrence is subjective. The gradual nature of this boundary for
Instability Region I has design implications.
Instability Region II did not exhibit any of the plastic instability phenomena observed in Instability Region I. As states, Instability Region II has negative efficiency of power dissipation, meaning that it has negative strain rate sensitivity and may undergo
DSA. The existence of DSA was not immediately clear from the flow curves – noise due to the low flow stress obscured any mechanical evidence of the PLC effect. Upon SEM investigation, no shear bands were observed, and the RE texture component was not observed. However, Instability Region II revealed more about the effect of Ce content on
ZE20’s deformation. EBSD of a specimen compressed to a strain of -0.35 in Instability
Region II is shown in Figure 16.
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Figure 16. EBSD of a specimen compressed in Instability Region II. (a) IPF map, and (b) IPF map overlaid with image quality map, with low CI points and subgrain boundaries shown.
It is likely that shear bands did not form in Instability Region II due to the relatively low strain at which it occurs. At a strain of -1.0, the adiabatic shear bands in
Instability Region I were still relatively straight and aligned at 45° to the compression axis. It is likely that those shear bands formed at high strain, as further deformation would have altered these characteristics. Despite the lack of shear banding, there was microstructural evidence of strong solute-defect interaction, which is mechanistically how DSA occurs. Extensive grain boundary bulging was observed in Instability Region
II. Though non indexable via EBSD, precipitates are evident either by the low confidence index points in Figure 16 (a) or the regions of low image quality in Figure 16
(b). Strings of precipitates left over from casting strongly pin the grain boundaries and
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act as nucleation sites for grain boundary nucleation. Subgrain boundaries are also observed to accumulate near clusters of precipitates. This is the mechanism by which
PSN occurs, but this cannot be said to be PSN because prior grain boundaries are also associated with the precipitates, and no new grains are observed to nucleate without a prior grain boundary present. Classically, this evidence is indicative of DSA, but more precise evidence of DSA could be obtained with other methods. Sheared precipitates and changes in subgrain structure are easily observed in TEM. Negative strain rate sensitivity is better determined with strain rate jump tests, rather than the interpolation methods which are employed to determine process maps. Whether or not DSA is active in
Instability Region II, shear banding was not observed, and the RE texture component was not present. Considering the low volume fraction of recrystallization and the low strain at which Instability Region II occurs gives this region little industrial relevance.
The above observations and analyses of domains and instability regions can be combined into a single set of processing recommendations. Combining the processing maps at all strains, and indicating regions of cracking, this is shown visually in Figure 17.
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Figure 17. Processing region recommendations for ZE20, valid for up to a strain of -1.0.
The most viable industrial processing conditions exist at high strain rates and low temperatures, which mean higher production rates and lower heating-related energy costs.
Generally, these preferences coincide with beneficial microstructural characteristics.
Lower processing temperatures result in a finer recrystallized grain size, and higher strain rates result in a greater volume fraction of recrystallized material.
For the “safe” region, the optimal processing region lies along the line between
350°C at 10-2 s-1 and 400°C at 10-1. This is a higher strain rate than Domain II and a 64
higher strain rate and lower temperature than Instability Region II, though neither of those regions had characteristics particularly beneficial for processing. The predicted optimal processing conditions also take place at lower temperatures and slightly higher strain rates than Domain I. Experimentally, the beneficial weak, non-basal texture of
Domain I was also observed at 400°C and 10-2 s-1; and the specimen had a smaller grain size while still maintaining a significant volume fraction of recrystallized material. At
400°C, 10-2 s-1 was the highest tested strain rate at which the specimen did not exhibit significant flow localization. The experimentally-determined optimum processing parameters for ZE20 are therefore between 10-1 s-1 and 10-2 s-1 and at or slightly below
400°C, which coincides with the predicted region of optimum processing.
This analysis is somewhat supported by the work of Luo et al. who studied extrudability of ZE20 relative to AZ31 [95]. Luo et al. found that ZE20 had superior extrudability at 425°C and several extrusion speeds. Their extrusion die geometry was not published, but assuming a typical conical die semiangle of 45°, their extrusion speeds are equivalent to mean strain rates of 10-0.80 s-1 to 10-0.09 s-1. This is higher than the strain rates recommended here, but it is possible that the high imposed strain of extrusion makes it such that the plastic instability which exists up to a strain of -0.65 does not have a significant effect on the properties of the final wrought product. It is also possible that there was significant adiabatic heating during extrusion [56] and that the actual processing conditions were in a higher temperature, higher efficiency region for which plastic instability exists only briefly at low strains.
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Conventional thinking would dictate that the area marked as “potentially allowable” would be undesirable, but this area may have merit as well. Indeed, the main aspects of the microstructures formed after processing in this region are undesirable: heavy localized flow, strong basal texture in the bulk material, and low volume fraction of recrystallization. However, this region was the only region in which shear bands and the RE texture component were observed. Additionally, the recrystallized grain size is finer at lower temperatures, making it more resistant to deformation. As a result, in some cases, recrystallized grains in Instability Region I had lower texture intensity than
Domain I (compare Figure 12 (d) to Figure 14 (d)). Taking advantage of these characteristics, there may be advantageous processing in the “potentially allowable” region.
In the “potentially allowable” region, processing at lower temperature and higher strain rate increases the frequency of shear banding. Provided plastic deformation can still occur without nucleating damage – either due to twinning or cracking, both of which are more prevalent at lower temperatures – either a high number density of nuclei from localized flow zones or a high number density of shear bands could be produced during processing. With post-processing annealing, new grains would grow at the expense of the deformed, basal-oriented matrix. Growing grains nucleated at localized flow zones would result in a refined microstructure with weak basal intensity, and growing grains nucleated at shear bands could potentially provide bulk material with non-basal texture.
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This presents the potential for a high-performance wrought Mg product with the addition of a single additional processing step.
2.4 Conclusions
Mechanical behavior and recrystallization behavior of Mg alloy ZE20 were investigated relative to Mg alloy AM30 in order to study the operation of rare earth effects. From the flow curves alone, the only significant difference between AM30 and
ZE20 was the presence of texture hardening in AM30 due to its prior processing. From microstructural comparison, RE effects were observable which were consistent with the literature: relative to AM30, ZE20 had a smaller recrystallized grain size and relatively retarded recrystallization kinetics. At 350°C and above, ZE20 also exhibited lower basal texture intensities for recrystallized grains.
Processing maps were constructed and were used to guide more detailed investigation in ZE20, as thorough investigation into the processing capabilities of this alloy are somewhat limited in the literature. Two domains and two instability regions were identified. Though Domain II would have interest from classical recommendations and Instability Region II would have interest due to the potential activity of DSA contributing to the RE effect, these regions were ruled out from industrial interest because of the low strain at which they occur and because no relevant microstructural phenomena related to DSA were observed. Final processing recommendations focus on
Domain I and Instability Region I. Domain I had features classically considered
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favorable for processing, including relatively high volume fraction of recrystallization, bulk non-basal texture, weak non-basal recrystallization texture, and low steady state flow stress. These features are not attributable to RE effects. Instability Region I was conventionally undesirable, but had potentially desirable microstructural features, including shear bands which nucleated recrystallized grains having the RE texture component. Instability Region I is marked as “potentially allowable” and is recommended for future processing research.
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Chapter 3: Thermomechanical Processing and Characterization of Al
Just like in Mg, texture and grain structure are critical considerations in Al-Li alloys, having effects on forming behavior as well as effects on the anisotropy in mechanical properties and fracture properties of formed components. The literature is limited on third generation Al-Li alloys, and processing information especially is often proprietary and excluded [80], [122]. In this chapter, simulated forging is used to evaluate the warm forming properties of the newly-developed AA2070, for which the literature lacks much processing information. Mechanical testing is performed at several temperatures and strain rates, and quantitative changes in microstructures and textures are correlated with changes in simulated forging conditions. General processing recommendations are presented based on pseudo processing maps and experimental findings.
3.1 Materials – AA2070
Aluminum alloy 2070 is a newly-developed third generation aluminum-lithium forging alloy. It was developed from AA2060, which relies mainly on the T1 phase for strengthening [2]. A single AA2070 “H-forging” was received from Case Western
Reserve University, purchased from Alcoa. Three H-forgings are pictured in Figure 18.
The directions noted are the longitudinal (L), long transverse (T), and short transverse
(S). The H-forgings have three segments with different thicknesses: 4”, 2”, and 1”. All
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specimens were taken from the 4” section of the H-forging, shown on the left of the centermost forging in Figure 2.
Figure 18. H-forging geometry, with reference directions shown.
As a forging, the material already had significant thermomechanical history.
Briefly, the production of the H-forging is as follows: From the as-cast state, cylindrical billets were A-B upset, heated to the forging temperature for several hours, preformed and forged, and T8 heat treated. A-B upsetting consists of compression along the billet’s axis, followed by compression perpendicular to the billet’s axis. T8 heat treatment consists of solutionization, water quenching, cold work (likely a 2-5% compression), and aging. Exact details (temperatures, thermal soak times, initial billet dimensions, etc.) of
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the H-forging’s thermomechanical history were considered proprietary information and were withheld by Alcoa.
Composition analysis of the as-received material is shown below in Table 2.
Table 2. Composition of AA2070.
Element Cu Li Mg Mn Zn Zr Others Al (<0.04 each) Weight 3.11 0.65 0.18 0.26 0.32 0.12 0.16 Balance fraction (%)
3.2 Thermomechanical Testing and Pseudo-Process Maps
To attempt to replicate microstructural conditions similar to those during forging at Alcoa, excised slabs of the H-forging were solution heat treated at 510°C for 110 minutes (to dissolve precipitates from the T8 heat treatment) and water quenched. Slabs were reheated and held at the testing temperature for 8 hours (to mimic factory conditions of a thermal soak at the forging temperature prior to forging). This should not significantly affect the microstructure or texture of the pre-machined slabs – the H- forging’s prior T8 heat treatment would be sufficient to recrystallize any heavily deformed grains, and the presence of Zr and Mn-based grain refiners should not allow significant grain growth. Slabs were allowed to air cool prior to EDM of specimens.
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Heat treatment conditions were evaluated with Thermo-Calc. At 510°C, the only predicted phases are the dispersoids Al3Zr and Al28Cu4Mn7, which is close in stoichiometry to that of the T phase reported by Shen et al. in [82]. Prediction at lower temperatures for phases that would form during the thermal soak is less useful. Thermo-
Calc does not predict intermediate phases, only equilibrium phases. Additionally, solvi of the intermediate phases (or formation temperature, for fixed composition) differ from those of the stable phases [73], and prediction of stable phases cannot accurately be used as a proxy for prediction of intermediate and stable phases.
Tension, compression, and plane strain compression (PSC) testing at elevated temperatures was performed in the Gleeble 3800. All testing was performed such that the imposed strain was along the S direction. Gleeble compression testing was carried out as described in Section 2.2.1. Plane strain compression testing is very similar, differing mainly in geometry. Plane strain compression specimens were 10mm by 15mm by
20mm rectangular specimens (in the S, L, and T directions respectively) which were compressed in the S direction along the T direction. During PSC testing, as with compression testing, strain was measured using the Gleeble’s internal LVDT. As with compression testing, PSC anvils were lubricated with graphite and a small amount of
Thred Gard lubricant, which helped minimize spreading along the specimen’s breadth.
The tension specimen geometry recommended by Dynamic Systems Inc. (DSI, the company that produces the Gleeble) was 4” x ¼” Ø rods with threaded ends. Tension specimens did not have a reduced diameter. Tension specimens were held securely by
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stainless steel jaws that clamped on the ends of the specimen. During tension testing, strain was measured using a high temperature extensometer with ±0.002mm resolution and ±0.15% full scale accuracy over +5.00/-2.00mm of travel. Tension specimens were pulled to the maximum safe extension allowed by the extensometer, equivalent to a strain of 0.35.
It is important to note that the tension specimens had an approximately 3 ¼” free span, and that direct resistive heating through the specimen combined with cooling at the grips caused tension tests to be non-isothermal. Thermal profiles were measured for exemplar specimens under 100N tensile force. At 250°C, there was a -7°C/cm to -
9°C/cm from the center of the tension specimen outward, and at 450°C, there was a
11°C/cm to 23°C/cm thermal gradient from the center outward. The measured gradients were asymmetric from left to right, which is attributed to a difference in coolant flow through the left and right grips.
Tension, compression, and PSC tests were carried out at four temperatures:
150°C, 250°C, 350°C, and 450°C, and at three strain rates: 10-3 s-1, 10-2 s-1, and 10-1 s-1.
Additional mechanical tests were carried out at 300°C, 400°C, and 425°C in compression to aid the construction of processing maps and constitutive models. Results for compression and PSC are shown in Figure 19 and Figure 19, respectively.
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Figure 19. Stress-strain curves of AA2070 compressed to a strain of -1.0 at (a) 10-3 s-1, (b) 10-2 s-1, and (c) 10-1 s-1.
Post-test compression specimens showed significant evidence of initial anisotropy in the H-forging. Similar to AM30, AA2070 uniaxial compression specimens had slight barreling. Barreling coefficients for AA2070 were on average 1.066 and had a weak dependence on temperature with higher values of B measured at higher temperatures.
Flow stress data was not corrected for barreling, as all measured barreling coefficients were less than 1.1. Compression specimens also exhibited ovality. At lower temperatures, ovality was prominent and was caused by formation of a single, large shear 74
band. When present, these shear bands were inclined toward the L-direction or within
20° of the L-direction. When such shear was not present, the average ratio of maximum to minimum diameter of the tested specimens was 1.06 and did not exceed 1.10. Since the only conditions where ovality was significant constituted failure, data is simply truncated at the strain at which failure initiates.
There are relatively few metallurgical phenomena evident from the flow curves produced from compression testing. AA2070 exhibited a sharp yield point with very little hardening after yielding, most likely due to the initial stable texture of the H- forging. Some “hardening” is evident for flow curves of the material tested at 150°C.
Not true hardening, this is attributed to the formation of a shear band, which acts as a low stress deformation mode, and does not allow the material to display the sharp yielding which is observed for all other temperatures. After yielding, all flow curves have slight linear or nearly linear softening. At high temperatures, this softening decreases in intensity and becomes steady-state flow.
Similar effects were observed for PSC, and results of PSC testing are shown in
Figure 20.
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Figure 20. Flow stress curves for AA2070 tested in plane strain compression at (a) 10-3 s- 1, (b) 10-2 s-1, and (c) 10-1 s-1.
Like with compression, PSC testing at 150°C often led to failure before specimens reached the full strain of the test; this was exacerbated at higher strain rates.
Unlike the compression specimens, failure could occur via formation of a shear band or via shear cracking. As with compression, shear band formation and crack formation was inclined toward the L-direction, though the PSC geometry would not allow effective strain relief for shear in the S-T plane.
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Features of the flow curves for PSC are largely the same as those for compression testing. All specimens exhibited a relatively sharp yield, except for lower temperature specimens which had gradual “hardening” which is attributed to formation of a shear band. PSC specimens had slightly higher yield stresses and flow stresses than uniaxial compression specimens tested under identical conditions. Given that the PSC flow stresses lie very close to the uniaxial compression flow stresses (usually within 5MPa to
10MPa) there is high confidence in the uniaxial compression data without correction for barreling or ovality. Plane strain compression testing elicits slightly different hardening than compression. PSC specimens exhibited slightly concave-up softening and reached steady-state behavior at lower temperatures than compression specimens.
Tension tests were unsuccessful at 150°C and were unsuccessful at 10-2 s-1 and 10-
1 s-1 and 250°C. In both cases, tension specimens fractured outside the gage length at low strains. Due to acquisition lag times, no data could be gathered to measure tensile yield stresses. Because there is no reduced gage for the recommended tension specimen geometry, the grips and the threaded portion of the specimens acted as a significant stress concentrator, which led to premature failure. The thermal gradient experienced by the tension specimen may actually enhance tension testing capabilities at higher temperatures by providing a greater degree of local softening at the specimen’s center. Results for successfully tested tension specimens are shown in Figure 21.
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Figure 21. Hot tension results for AA2070 at (a) 350°C and (b) 450°C.
At 450°C, tension specimens have a sharp yield point followed by softening. The initial softening is dependent on strain rate and is very pronounced for 10-3 s-1 and 10-2 s-
1. This initial yield point (as well as yielding at 350°C) is very close to the observed compressive yield stress. Flow curves for AA2070 in tension at 350°C have significant apparent flow softening. Necking likely contributed to this apparent softening. Necking was pronounced at 350°C but did not necessarily lead to failure at a strain of 0.35.
Similar to the other testing modes, the initial anisotropy of the H-forging was evident for tension specimens. After testing, the specimens had non-circular cross- sections, being elongated in the T-direction. Such elongation was at least slightly present for all specimens and was exaggerated at lower temperatures. Specimens tested at 250°C and 10-3 s-1 fractured prior to tension to a strain of 0.35. Anisotropy of the H-forging was more evident from the fracture surface as shown in Figure 22.
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Figure 22. Fracture surface of AA2070 specimen tested in tension at 250°C and 10-3 s-1. L-direction is vertical, T-direction is horizontal, and S-direction is out of plane.
Tensile fracture surfaces were typical of ductile fracture, having two shear lips inclined 45° to the tensile direction separated by a flat central surface. In Figure 22 (a), a macrograph of the central fracture region is shown, with unresolved shear lips at the top and bottom of the image. At low magnifications, the crack path seemed intergranular, judging by the sharp, faceted appearance of many grains. At higher resolution, as in
Figure 22 (b), dimples typical of ductile fracture are evident. Nearly every dimple was associated with a precipitate, making it apparent that fracture occurred by void coalescence with voids nucleating at what are likely incoherent precipitates or dispersoids.
Regimes of different metallurgical phenomena were investigated with pseudo- processing maps. Due to the different thermal history experienced by each specimen, designed to induce a different microstructure representative of forging conditions, these cannot be said to be true processing maps. Real processing maps would instead use a 79
single starting microstructure; initial microstructure has an effect on mechanical properties and has a strong effect on process maps [120]. These maps should not serve as a guide for forming behavior, as numerical values of efficiency are certainly affected, but they may still allow the reader to infer the activity of metallurgical phenomena at local maxima and minima. Maps were calculated as described in Section 2.2.2.
Figure 23. Pseudo-processing maps of AA2070 in compression, plotted at strains of -0.5 and -0.9.
Indeed, the pseudo-processing maps in Figure 23 have artifacts from heat treatment, as the efficiency contours and instability regions have little dependence on strain rate and strong dependence on temperature. Visually on the maps, this results in much more vertical features. For these pseudo-maps, this can be interpreted as meaning that the combined effect of changes in precipitate content due to thermal history and the effect of test temperature are stronger than the effects of strain rate on the efficiency of
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power dissipation in AA2070. Low efficiency is predicted at all but the highest temperatures, and instability is predicted at low temperatures. The instability region does not cover all the conditions for observed shear bands, though formation of shear bands was inconsistent and less frequent at higher temperatures. The efficiency at high temperatures is lower than that usually required for recrystallization in high-SFE materials such as Al [120], but 450°C is the most favored temperature for DRX according to Figure 23.
3.3 Texture and Microstructure Characterization
Exemplar specimens of untested material as well as compression specimens, tension specimens, and PSC specimens were polished and examined with SEM and
EBSD. EBSD scans were gathered for each test temperature and strain rate for all modes of testing. Compression specimens were sectioned, mounted, and polished as described in Section 2.3.1; exemplar specimens, tension specimens, and PSC specimens were polished unmounted. Compression and tension specimens were sectioned axially in order to accurately track prior billet directions. EBSD scans were captured at mid-thickness of compression specimens, at zero radius. Because some tension specimens experienced necking, tension specimens were not sectioned at the specimen’s midline. Tension specimens were instead sectioned axially such that sections from different specimens had equal cross-sectional area and the same equivalent strain. PSC specimens could not be accurately sectioned perpendicular to the applied strain similar to tension and
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compression specimens. Instead, PSC specimens were sectioned in the S-L plane, and
EBSD scans were gathered at the center of the specimen.
Exemplar microstructures of solution heat treated and soaked AA2070 are shown in Figure 24.
Figure 24. Secondary electron images of initial AA2070 microstructures after solution heat treatment and eight-hour thermal soak at (a) 150°C, (b) 250°C, (c) 350°C, and (d) 450°C.
The 150°C exemplar microstructure shows only what are likely Mn-based dispersoid phases, which were not dissolved by the thermal soak. It is likely that the 82
precipitation kinetics are too slow for formation of an appreciable volume fraction of precipitate content, or perhaps these phases cannot be resolved via SEM. The 250°C microstructure shows high number density formation of precipitates. These precipitates cannot be resolved individually via SEM but their existence is made apparent by a narrow precipitate-free zone (PFZ) along the grain boundaries. Coarser precipitates and dispersoids are visible at the grain boundaries. At 350°C, significant precipitate content lines the grain boundaries, and multiple phases with unique morphologies are visible within the grain interiors. The 450°C specimen shows continued coarsening at higher temperatures. Grain interiors have fewer, coarser precipitates, and grain boundaries have coarse precipitates. Note scale bar for Figure 24 (d) is 50µm rather than the 10µm for
Figure 24 (a – c).
While precipitate content is captured poorly by EBSD, the grain structure and texture of the pre-testing materials more evident in Figure 25.
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Figure 25. EBSD of solution heat treated and soaked AA2070. (a) IPF map, (b) GOS map, (c) PF of deformed material, (d) PF of recrystallized material, and (e) IPF key, (f) GOS key, and (g) PF scale. L-direction is vertical, T-direction is horizontal, and S- direction is out of plane. IPF key is constant for all AA2070 IPFs, with colors plotted for the S-direction. PF scale is constant for all AA2070 PFs.
The microstructure shown in Figure 25 (a) is for an exemplar specimen which was solution heat treated, quenched, and aged at 350°C for 8 hours. The microstructure shows large pancake-shaped grains which are elongated in the L-direction and which have short axes in the S-direction. These large grains and other grains appearing green in the Figure 25 (a) are responsible for the strong Goss texture component in Figure 25 (c) and (d). This is somewhat unusual for Al alloys, as these grains are identified as 84
previously deformed grains by GOS, and the Goss texture component is usually said to be a recrystallization texture component [86]. It is possible that Goss is a stable deformation texture for AA2070, as Al-Li alloys tend to have lower SFE than conventional Al alloys. This would give all slip systems different CRSS and influence cross slip and the stable texture component(s).
The large grains are separated by swaths of smaller grains, which contribute to a minor texture component in Figure 25 (c) and (d) that has characteristics of both copper and brass texture components. From the GOS map in Figure 25 (b), these smaller grains are not necessarily identified as recrystallized; the whole microstructure contains only about 7 area % recrystallization. Instead, these grains may still contain deformation content due to retardation of recrystallization by the Al3Zr phase and the T phase.
Similarly, due to the prior T8 heat treatment of the H-forging and due to the high fraction of dispersoids, the grain structure and texture did not change significantly during solutionization and thermal soaking. The grain structure and texture in Figure 25 is representative of the other thermal soak temperatures as well.
EBSD analysis of specimens after compression is shown in Figure 26 and Figure
27.
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Figure 26. EBSD of AA2070 specimen compressed at 450°C and 10-2 s-1. (a) IPF map, (b) GOS map, (c) PF of deformed material, (d) PF of recrystallized material, (e) PF scale, and (f) GOS scale. L-direction is vertical, T-direction is horizontal, and S-direction is out of plane.
At 450°C, AA2070 had significant recrystallization for all test modes. This is clearly visible from the breakup of the prior grain structure in the IPF map in Figure 26
(a). More quantitative, GOS analysis shows that the microstructure is 50.3% recrystallized. Despite significant recrystallization, the microstructure retains a significant Goss texture, though the texture intensity is significantly reduced compared to
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the exemplar specimen. The minor copper/brass texture component is very weak, only about 3 multiples of random distribution (MRD) in peak intensity. Both texture components are noticeably shifted from the ideal Al texture components. The Goss texture has a small ~5° rotation counter-clockwise and seems to also have an out-of-plane rotation about the L-direction. For the minor texture component, such rotation further obfuscates whether it is copper, brass, or even an S component. Regardless its nature, it is apparent that the minor texture component has a significant out-of-plane rotation, as it is shifted downward relative to the copper, brass, and S ideal texture components.
Unfortunately, such rotation obfuscates texture component identification, even from orientation distribution function plots (ODFs). These shifts in texture components are attributed to local stress states. Nearest neighbor constraints can make grains experience a stress state slightly different from the global stress state and will elicit a texture slightly off from the globally-expected average. This likely affected the observed texture considering that the scan area is small relative to the initial grain size and may be sampling microstructure from only one or two prior grains. Regardless the cause, such rotations make determination of texture components difficult. Features of the brass/copper texture blend together, making attribution to a specific component impossible. Specific texture components are more accurately identified using orientation distribution function plots (ODFs), but the observed rotation and spreading of the texture components makes identification from ODFs even more difficult.
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Similar effects were observed for lower temperature specimens, as in Figure 27 for AA2070 compressed at 250°C.
Figure 27. EBSD of AA2070 specimen compressed at 250°C and 10-2 s-1. (a) IPF map, (b) GOS map, (c) bulk PF, (d) PF scale, and (e) GOS scale. L-direction is vertical, T- direction is horizontal, and S-direction is out of plane.
Notably, at 250°C, a very small area fraction of recrystallization was observed, only 2%. This low fraction of recrystallization is likely caused in part by the test temperature, as 250°C is too low to initiate DRX in high SFE materials such as Al. The high number density of precipitates and dispersoids likely aided retardation of recrystallization. For all studied test temperatures below 450°C, a similarly low area fraction of recrystallization was found, usually below 6%. No clear correlation of recrystallization with strain rate was observed. Though expected, the low fraction of recrystallization is still significant. Nearly negligible amounts of recrystallization dictate
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that all softening observed at moderate and low temperatures in Figure 19, Figure 20, and
Figure 21 must be attributed to significant activity of DRV instead of DRX.
Similar to the specimen in Figure 26, texture components in Figure 27 (c) are rotated from their ideal components. The Goss texture is still apparent and seems to be rotated out of plane about 5-10° about the L-direction. The texture intensity of the bulk in Figure 27 (c) is lower than that for the specimen shown in Figure 26. A general trend of decreasing Goss texture intensity was observed with increasing temperature. No trend of texture intensity was observed with strain rate, and no trend was observed for the minor texture component(s). The reduction of texture intensity with temperature is likely due to the temperature-dependence of the CRSS of non-octahedral slip. Higher CRSS for non-octahedral slip at lower temperature would make the brass texture component – the stable texture component following deformation via octahedral slip – more favored than
Goss. If the brass texture component is favored at 250°C, this may be why there is no decrease in the texture intensity of the minor texture component in Figure 27 (c). The specimen’s thermal history may also play a role in texture reduction. Finer precipitate distribution from the heat treatment at lower temperatures may be more effective at dispersing slip, resulting in decreased Goss texture intensity.
Results for AA20170 in tension were similar to those for compression.
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Figure 28. Microstructure and texture of AA2070 tested in tension at 450°C and 10-2 s-1. (a) IPF map, (b) GOS map, (c) PF of deformed grains, (d) PF of recrystallized grains, and (e) PF scale. L-direction is vertical, T-direction is horizontal, and S-direction is out of plane.
Figure 28 shows the microstructure of a specimen tested in tension at 450°C.
Tension specimens did not exhibit DRX the extent that compression specimens did, as the microstructure is only 19% recrystallized. The 450°C tension specimen had a somewhat higher texture intensity than the 450°C compression specimen. Both of these may be attributed to the fact that the tension fixturing limited the imposed strain to 0.35.
Given this lower strain, the tension specimens exhibited a significant texture rotation.
This is expected; tension specimens should exhibit the <111> fiber texture typical of drawn Al wire [123]. The texture shows a significant ~25° rotation about the T-direction, and one of the peaks from the prior Goss texture is nearing the stable <111> pole.
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Figure 29. Microstructure and texture of AA2070 tested in tension at 250°C and 10-3 s-1. (a) IPF map, (b) GOS map, (c) bulk PF, (d) PF scale, and (e) GOS scale. L-direction is vertical, T-direction is horizontal, and S-direction is out of plane.
Like the compression specimens tested below 450°C, tension specimens tested below 450°C did not exhibit an appreciable area fraction of recrystallization. The GOS map in Figure 29 (b) shows that the microstructure is 11.3 area % recrystallized, but this is likely an over-estimate. Scan quality was somewhat low for lower temperatures, especially in tension. This may cause misidentification of grains, skewed to smaller grain sizes, which are geometrically favored to have a low GOS. As seen in Figure 29 (c), the lower-temperature specimens had a drastic change from the Goss-copper texture of the initial H-forging. Like with compression, this is likely due to the temperature- dependence of CRSS and thermal history of lower temperature specimens. More favored octahedral slip and dispersed slip would very effectively rotate grains and alter the prior texture.
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Unfortunately, the nature of texture intensity as treated above is somewhat imprecise, and the trends with temperature and strain rate are difficult to quantify due to the shift of the texture components. Because PSC specimens were sectioned parallel to the compression axis; and, as shown in Figure 30 (a), a more representative section of the microstructure, comprised of many more grains, could be viewed. Effects of local shear and shifting of the texture components were minimized, and the texture shown in Figure
30 (b) is a combination of nearly ideal Goss and copper components.
Figure 30. Microstructure and texture of AA2070 tested in plane strain compression at 450°C and 10-3 s-1 to a final strain of -1.0.
Due to this more ideal orientation, textures can be more precisely treated.
Microstructures for PSC specimens were partitioned into discrete bins based on ideal 92
texture components for Al. Any point within 10° in Euler-Bunge space was considered to belong to a given texture component, and texture is reported in terms of area fraction of the microstructure belonging to that component. This gives a more precise view of texture than MRD. Texture component fractions of deformed and recrystallized material are shown in Figure 31.
Figure 31. Area fraction of texture components for PSC specimens compressed to a true strain of -0.5. Components of (a, b) deformed grains and (c, d) recrystallized grains, plotted as a function of (a, c) temperature and (b, d) strain rate. Area fractions are relative to the fraction of the stated portion of the microstructure.
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The trends seen here for PSC closely resemble those for compression, but in a more quantitative manner. For plots according to temperature (Figure 31 (a, c)), texture components were averaged across strain rate, and for plots according to strain rate
(Figure 31 (b, d)), texture components were averaged across all temperatures. The Goss component is the strongest texture component present in the deformed material for all temperatures and is the strongest texture component present in the recrystallized material for all temperatures above 150°C. The fraction of Goss texture decreases with decreasing temperature, as does the brass texture component for both deformed and recrystallized material. The minor copper texture component is relatively stable across all temperatures. There is no obvious trend for any texture component with strain rate.
The recrystallized material had a lower fraction of identifiable texture components than the deformed material. The decrease in deformation texture in the recrystallized material is expected. The overall trend is somewhat surprising, as the classic recrystallization textures (cube, rotated cube, and Goss) may be anticipated to increase in intensity. Other less common recrystallization texture components R and P were also investigated but were only found in negligible quantities.
It is somewhat surprising that relatively little of the microstructure is identified as any of the classically observed texture components. At most, for the specimen tested at
450°C and 10-3 s-1, 44% of the EBSD scan points are within 10° of any texture component. Total fractions for all specimens for temperatures lower than 450°C were
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under 30%, which translates to relatively weak texture. The marked decrease of any identifiable texture component at 150°C is likely due to shear banding. Despite only being compressed to a strain of -0.5, shear banding was present at least to some degree for all specimens tested at 150°C. Such shear banding changes the orientation of the material, affecting the texture, but data was still plotted for sake of completion. Overall, the reduction in fraction of Goss texture for temperatures below 450°C indicates that
Goss is not the stable texture component for those temperatures; but a stable texture component is not necessarily observed, as Al does not reach stable texture and microstructure until much higher strains (usually on the order of ε = 4).
Generalized processing recommendations are more difficult to form for AA2070 than for ZE20. There is no equivalent universally desirable microstructure for Al-Li alloys such as a fine-grained microstructure with non-basal texture in Mg. Final forms of wrought Al-Li alloys may be partially recrystallized or unrecrystallized in order to achieve higher strengths, higher fracture toughness, or better fatigue properties [80].
Fully recrystallized Al-Li is more common for sheet and plate, where recrystallization annihilates a highly anisotropic elongated grain structure [80]. Ultimately, the desired microstructure depends on the specific properties required of the final structure. Despite the wealth of design routes and relative lack of information on processing third generation Al-Li alloys, some general recommendations can be made.
Among the microstructures shown in Figure 24, the best microstructure for forging is for the material soaked at 450°C. Over-aged material is acceptable for forging
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and may reduce the texture intensity of the final wrought product [124], though this effect was not studied in the present work. Regardless of slip dispersal, such a microstructure alloys for lower forging stresses. If a post-forging T6 or T8 heat treatment is used
(solutionization followed by aging), then such an over-aged microstructure would be acceptable for all forging processes.
The forging parameters depend on the desired form of the material. If an unrecrystallized material is desired, forging at moderate to high temperatures is recommended. One may forge at high temperatures just below the temperature for initiation of DRX in order to achieve efficient low-stress or high strain rate processing.
Alternately, if mechanical anisotropy due to texture is a concern, one may process at lower temperatures due to the decreasing intensity of Goss texture with decreasing temperature. This would not be a typical processing route for an unrecrystallized wrought product, however. Low temperature processing increases the retained dislocation content within grains, making them susceptible to SRX during heat treatment.
If a fully recrystallized material is desired, which is more typical for Al-Li sheet and plate products [80], two processing routes are available. As mentioned, low temperature processing can be used, after which heat treatment will induce SRX. Due to plastic instability, processing should not occur below 250°C, and moderate to high strain rates should be avoided at 250°C. This presents a somewhat limited processing window, which is not in line with the typical high strain rates seen for rolling. Alternately and more typically, hot rolling can be used with some amount of cold work – usually
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stretching or a 2% to 5% thickness – can be done prior to heat treatment. This allows a much larger processing window and efficient high strain rate, high temperature processing, while still having cold work provide the impetus for recrystallization.
Perhaps more critical than the forming process is the post-process heat treatment.
From the microstructures in Figure 24, the heat treatments used to simulate forging behavior are all insufficient for service properties of wrought Al-Li alloys. The microstructure of the material soaked at 150°C is under-aged and does not contain an appreciable amount of precipitates for strengthening. The microstructure soaked at
450°C is over-aged and contains precipitates too coarse to provide much strengthening; further there are coarse grain boundary precipitates which will lower fracture toughness.
The microstructures of the material soaked at 250°C and 350°C have favorable aspects for the grain interiors but unfavorable grain boundaries, which can lead to poor fracture toughness and stress corrosion cracking (SCC) susceptibility [80]. Notably, in Figure 24
(b), PFZs are present, which can lead to strain localization and failure. In Figure 24 (c), coarse grain boundary precipitates are present which can reduce fracture toughness. The desired microstructure is somewhere between the two – having no obviously heterogeneity at the grain boundary. Such a microstructure could be achieved by heat treatment at an intermediate temperature for a shorter time. Industrial processing would most likely involve a duplex heat treatment consisting of a low temperature anneal to nucleate a fine dispersion of GP zones and precipitates, followed by a higher temperature heat treatment to grow S’, T1, δ’, and θ’ from the nucleated precipitates.
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3.4 Conclusions
The mechanical properties and microstructural and texture evolution of the relatively unstudied AA2070 were examined in the warm forming regime. Mechanical testing was performed in uniaxial compression, plane strain compression, and tension.
Slight flow softening or nearly ideal plastic flow was observed for most temperatures and strain rates for all testing modes. Pseudo processing maps constructed from the mechanical data were able to predict plastic instability fairly accurately and predict general trends for efficiency but they did not accurately predict the operation of recrystallization.
EBSD analysis revealed significant recrystallization for specimens tested at
450°C, but fractions of recrystallization less than or equal to the area fraction of recrystallization in exemplar specimens were present for all other test temperatures. Due to this relative lack of recrystallization at lower temperatures, it was concluded that DRV is responsible for the softening observed for simulated forging conducted at 350°C and below. Significant Goss texture was observed for the initially deformed microstructure.
This is surprising, as Goss is a recrystallization texture, but has been justified with crystal plasticity modelling [122]. Simulated forging at moderate and low temperatures significantly decreased the fraction of the microstructure exhibiting the Goss texture component, but did not significantly increase microstructural fractions exhibiting β-fiber deformation texture components.
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Because only pseudo processing maps could be produced from the simulated forging data, processing recommendations were informed largely by post-test microstructures and by the literature. General processing recommendations were stated for AA2070 in unrecrystallized, partially recrystallized, and fully recrystallized forms. In order to make specific processing recommendations, additional characterization is needed which follows the general recommendations. Processing maps should be developed for over-aged AA2070, and peak aging conditions should be determined for post-forging materials.
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Chapter 4: Constitutive Modelling of Mechanical Properties
Mechanical models are very useful and can influence processing decisions by providing information on flow stress in the warm forming regime. While three- dimensional crystal plasticity or continuum plasticity models are often preferred, even simple constitutive models considering effective stress and effective strain are of industrial value. Currently, the literature does not contain sufficiently complete descriptions of flow stress for ZE20 or AA2070. Gao and Luo applied the Sellars-Tegart model to ZE20 but only model the peak stress [125]. Bingöl and Misiolek applied artificial neural network (ANN) and gene expression protocol (GEP) models to ZE20, but their mechanical testing results are suspect and sparse, not covering the strain rates and temperatures most relevant for processing [126]. Borkowski et al. present an elastic- visco-plastic crystal plasticity model for AA2070, but they do not report critical model constants, including the temperature-dependent stiffness tensor and the single crystal yield surface [122].
This chapter details the derivation of a novel, efficient, hardening-based formulation of the extended Ludwik equation. Model results for ZE20 and AA2070 are evaluated using widely-applied the Sellars-Tegart relation as a baseline. Physically- based viscoplastic self-consistent (VPSC) simulation is also applied to ZE20, and results are evaluated and compared to the modified Ludwik model.
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4.1 Sellars-Tegart Flow Stress Relation
The hyperbolic sine Arrhenius equation proposed by Sellars and McTegart [127] is one of the most widely used empirical descriptions of flow stress. It takes the form
−푄 휀̇ = 퐴 [sinh(훼휎)]푛exp ( ) (8) 푅푇 where σ, ε , T, and Q are flow stress, strain rate, absolute temperature, and activation energy of deformation, respectively; and A, α, and n are material constants; and R is the universal gas constant. At low stresses (for α∙σ < 0.8), Equation 8 simplifies to a power relationship [127]:
−푄 휀̇ = 퐴 휎푛1 ∙ exp ( ) (9) 푅푇 and for high stresses (for α∙σ > 1.2), Equation 8 simplifies to an exponential relationship
[127]:
−푄 휀̇ = 퐴 ∙ exp (훽휎) ∙ exp ( ) (10) 푅푇
Determination of constants in the Sellars-Tegart relationship is simple, involving only plotting methods. From Equation 9 and Equation 10, the constant α in Equation 8, which is valid at all stress levels, can be determined as α = β/n1. By taking the natural logarithm of both Equation 9 and Equation 10, β and n1 can be found as the slopes of σ – ln(ε ) plots and ln(σ) – ln(ε ) plots, respectively. The remaining constants can be determined from
Equation 8. Taking the natural logarithm of both sides of Equation 8 yields
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𝜀̇̇ 푄 ln ( ) = 푛 ∙ 푙푛[푠𝑖푛ℎ(훼휎)] − (11) 퐴 푅푇
From Equation 11, it is clear that n is the inverse of the slope of a ln(ε ) – ln[sinh(ασ)] plot. By differentiating Equation 11 with respect to temperature,
푑{푙푛[푠𝑖푛ℎ(훼휎)]} 푄 = 푅 푛 1 (12) 푑( ⁄푇)
Q can be found as the slope of a d{ln[sinh(ασ)]} – d(1/T) plot. Finally, with all other constants known, ln(A) is determined as the intercept of an ln[sinh(ασ)] – ln(ε ) plot.
Because it contains both a power law and an exponential form of stress, the
Sellars-Tegart equation is able to span different regimes of material behavior from creep stress to hot working flow stress [127]. Further, the Arrhenius term allows determination of activation energy, which can be used to determine the rate-limiting deformation mechanism at steady state (diffusion, recovery, or recrystallization) [128]. For these reasons, the Sellars-Tegart relation is applicable over a wide range of strain rates and temperatures and has become one of the most widely-applied constitutive equations for flow stress.
In the original derivation, as above, strain does not enter the Sellars-Tegart relation. Its original intent was for determination of steady state behavior [128]. Despite this, many authors expand on the Sellars-Tegart relation, applying it in an iterative manner to all experimental strains. Such attempts usually then represent the constants α, n, Q, and A as polynomial functions of strain and achieve satisfactory results for predictive purposes [129]–[132]. In such a form, the constants of the Sellars-Tegart equation are easily reported and relate flow stress as a function of strain, strain rate, and 102
temperature. Unfortunately, the use of polynomial functions leads to very poor predictive results outside the range used to build the model constants. Furthermore, some authors argue that this makes the constants lose physical meaning [133], while others note that the only model constant with true physical meaning is the activation energy of deformation, Q [134], which may have physical meaning as a function of strain.
The Sellars-Tegart relation was applied to AM30, ZE20, and AA2070 in compression. For each of these, model performance was assessed qualitatively, noting whether key features of the flow curves are preserved, and quantitatively with absolute average relative error (AARE) and root mean square error (RMSE). These measures of error have standard definitions:
푖 푖 1 푁 휎푐푎푙푐푢푙푎푡푒푑−휎푒푥푝푒푟푖푚푒푛푡푎푙 푒푟푟퐴퐴푅퐸 = ∑𝑖=1 | 푖 | (13) 푁 휎푒푥푝푒푟푖푚푒푛푡푎푙
1 2 푒푟푟 = √ ∑푁 (휎𝑖 − 휎𝑖 ) (14) 푅푀푆퐸 푁 𝑖=1 푒푥푝푒푟𝑖푚푒푛푡푎푙 푐푎푙푐푢푙푎푡푒푑
Optimization was applied to the polynomial expressions of A, a, and n. A gradient descent method with an initial increment size of 0.001 was used. The AARE of the entire dataset was used as the goal function for minimization. No optimization was applied to Q because it holds physical significance, and changing Q would change the interpretation of the model.
Results for AM30 were poor-fitting and are shown in Figure 32. The values for
A, α, n, and Q all use polynomial functions of strain in the form
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2 푛 푓(휀) = 퐶0 + 휀 ∙ 퐶1 + 휀 ∙ 퐶2 + … + 휀 ∙ 퐶푛 (15) and are detailed in Table 3.
Table 3. Sellars-Tegart model coefficients for AM30. f(ε) C0 C1 C2 C3 C4 C5 C6 C7 α 0.01820 -0.09424 0.4360 -0.7862 0.4435 0.4507 -0.7067 0.2671 n 6.358 17.11 -141.2 369.7 -386.9 141.4 0 0 Q -40.49 1756 -5369 7518 -5114 1396 0 0 A -7.444 305.8 -905.0 1209 -774.7 193.0 0 0
Figure 32. Selected Arrhenius model results for AM30 at (a) 425°C and (b) 10-2 s-1.
The Arrhenius model predicts high strain rate mechanical response fairly well for moderate to high temperatures, as in Figure 32 (a). For those conditions, the Arrhenius model adequately predicts the peak stress, softening and steady-state behavior. The yield stress was poorly predicted, and the initial hardening was somewhat adequately
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predicted. For much of the rest of the test matrix, the Sellars-Tegart model had very poor predictive capacity for yield stress, peak stress, and softening after yield. However, fitting for its original use, the Sellars-Tegart model does predict steady-state flow stress well for most temperatures and strain rates. Moreover, fluctuations in the steady-state flow stress in Figure 32 (b) illustrate the problem of applying polynomial functions to the
Arrhenius equation.
This suggests that the Sellars-Tegart model does not well predict flow stress over regimes where there is a drastic change in deformation mechanism. Classically, the values of Q from the model are related to self-diffusion, creep, hot working, DRX, or
DRV [128], [135]. Even across temperature or strain rate regimes where these mechanisms change, the transition in flow stress is much more gradual than the elimination of texture hardening seen in AM30 at high temperatures. Taking derivatives across strain rates to find the model constants results in an averaging of texture hardening behavior and lack thereof. Higher order polynomial expressions of A, α, n, and Q may improve the model’s fit but will not correct this predictive failure.
The refined test matrix allowed ZE20 to have a much better fit with the hyperbolic sine Arrhenius model. Model constants for ZE20 follow the same form as in
Equation 15, and the model coefficients are listed in Table 4.
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Table 4. Hyperbolic sine Arrhenius model constants for ZE20. f(ε) C0 C1 C2 C3 C4 C5 C6 C7 C8 α 0.1172 -2.086 21.52 -110.2 319.7 -552.2 563.0 -312.8 72.98 n 4.851 23.21 -548.1 3555 -11600 21580 -23210 13440 -3241 Q 229.7 -1254 11790 -57510 160400 -267500 264300 -142700 32450 A 26.17 -13.39 26.34 -37.14 39.81 -18.49 0 0 0
Figure 33. Sellars-Tegart model results for ZE20 at (a) 10-3 s-1, (b) 10-2 s-1, (c) 10-1 s-1, and 100 s-1.
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ZE20 was found to have an initially random texture, and did not exhibit texture hardening as AM30 did. As such, the Sellars-Tegart model fits ZE20 much better. The
Arrhenius model does not consistently over-predict or under-predict any of the flow curves’ features. Similar to with AM30, the Sellars-Tegart model’s best point of predictive accuracy is at high strains when the material is approaching steady-state behavior. The model predicts acceptably at low strains, predicting yield points well for most conditions but predicting fairly poorly for others. Interestingly, one of the Sellars-
Tegart model’s accepted uses is with peak stress; however, this is the model’s lowest point of accuracy for ZE20. At peak stress, the model predicts accurately for only half of the temperatures and strain rates, all others are significantly under-predicted or over- predicted.
Overall the hyperbolic sine Arrhenius model has acceptable performance, achieving an AARE of 3.51% and a RMSE of 2.88 MPa. However, similar to AM30, the hyperbolic sine Arrhenius model predicts identical hardening behavior for all temperatures and strain rates in ZE20. Again, this is due to the model’s construction.
This seems to have negative impact for ZE20 as well. The highest strain rate, lowest temperature stress-strain curve is very poorly predicted. In this regime, macroscopic shear cracking was observed, which may have had a significant effect on the flow stress.
The activation energy for deformation in ZE20 decreases rapidly from 216 kJ/mol at yielding to 177 kJ/mol at a strain of -0.1, then decreases slowly to 158 kJ/mol at a strain of -1.0. These values are significantly higher than the activation energy of self-
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diffusion or hot work in conventional Mg alloys [136], [137] but are on par with that of
Mg-Re alloys [125], [138].
For AA2070, the model constants A, α, n, and Q were allowed to take forms other than polynomial functions. Power functions were found to have better fits and resulted in fewer model constants for A, n, and Q. An exponential function had similarly high accuracy for α. The results of the Arrhenius model are shown in Figure 34.
Figure 34. Arrhenius model results for AA2070. Model predictions and experimental results at (a) 10-3 s-1, (b) 10-2 s-1, and (c) 10-1 s-1. (d) overall model performance.
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The full expression for the model parameters used to achieve these results is as follows:
퐴 = −39.842 휀0.3600 + 88.881 (16)
훼 = 0.001947 exp(−49.88 휀) + 0.005215 exp(0.2665 휀) (17)
푛 = −4.3280 휀0.4643 + 11.121 (18)
Q = −208.52 ε0.3052 + 456.21 (19)
The model fits fairly well, having higher accuracy at higher temperatures. Most flow curves above 300°C are predicted well. The Arrhenius model seems to predict yielding quite poorly for AA2070 at lower temperatures. This, like the issues with ZE20 and AM30, is due to the model’s construction. At high temperatures, AA2070 has little low-strain hardening, and this dominates the model behavior. At low temperatures, no hardening is predicted, resulting in over-prediction of yield followed immediately by softening. For moderate and high temperatures, all points at moderate and high strains are predicted with acceptable accuracy. Overall, the model has adequate performance, having 5.14% AARE and 5.78 MPa RMSE.
Conventional forms of A, α, n, and Q were also implemented. Even with 7th order polynomial functions, the resulting model performance was mediocre, with 6.8% AARE.
However, for high-order polynomial forms the model had greater sensitivity to changes in strain hardening. This was mainly reflected in the yield point, where the present model has only moderate predictive accuracy. 109
Conventional wrought aluminum alloys (2xxx, 6xxx, and 7xxx series) typically have activation energies for hot working on the order of 150 kJ/mol [128], [135], [139].
From Equation 19, the activation energy of hot deformation in AA2070 decreases steadily from 403 kJ/mol at yielding to 265 kJ/mol at a strain of -0.75. Fitting with conventional reporting of a single activation energy for the steady-state region, an activation energy of 265 kJ/mol is high but not unreasonable for a 2xxx series alloy
[135].
4.2 Modified Hardening Law Based on Extended Ludwik Equation
The extended Ludwik equation [140], [141] adds strain rate Ludwik rate hardening to the Hollomon equation via an additional power term. It takes the form
푚 푛 𝜀̇̇ 휎 = 퐾휀푝 ( ) (20) 𝜀̇̇ 0
where K is the strength coefficient, εp is effective plastic strain, n is the strain hardening rate, and m is the strain rate sensitivity. ε0 is an arbitrary strain rate to normalize the power law so that no dimensional terms are exponentiated, chosen to be ε0
= 1 s-1 for simplicity in this work. In the original formulation of the extended Ludwik equation, K, n, and m are taken to be linear polynomial functions of temperature and are independent of strain or strain rate [140]. Based on the Ludwik and Hollomon equations, which both model flow stress fairly accurately in FCC metals, the extended Ludwik equation successfully describes the flow stress of cast aluminum at low strains [132],
[142]. Unfortunately, in its base formulation, it is suited only for moderate strain 110
hardening. With a single-valued strain hardening rate (at a given temperature), it cannot adequately describe the observed flow stresses for ZE20 or AA2070 which exhibit both hardening and softening.
Changes in hardening behavior have been described using the Hollomon equation by allowing the strain hardening exponent to change after some critical strain. Termed the “double-n effect,” this works acceptably to model strain hardening in steels [143].
However, double or even multiple linear hardening rates do not well describe the flow stress of ZE20 and tend to introduce excessively many model constants for critical strains. Expanding on this idea, flow stress can be described with strain hardening rate behaving as a continuous function of strain.
Determination of constants of the extended Ludwik equation is straightforward.
Taking the natural logarithm of Equation 20 results in
ln 휎 = ln 퐾 + 푛 ln 휀 + 푚 ln 휀̇ (21)
Taking the derivative of both sides with respect to strain rate results in the traditional definition of strain rate sensitivity:
푑 ln 휎 푚 = [ ] (22) 푑 ln 𝜀̇̇ 푇
Alternately, the constants K and m can be determined simultaneously via graphical methods. On a ln(σ) – ln(ε ) plot corresponding to a strain of unity, m is the slope and ln(K) is the intercept. Strain hardening rate can be determined similarly by taking the derivative of both sides of Equation 21 with respect to strain:
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푑 ln 휎 푛 = [ ] (23) 푑 ln 𝜀̇ 푇
To instead determine a strain hardening function which varies with strain, one can apply the chain rule when taking the derivative of Equation 21 with respect to strain, resulting in
푑 ln (휎) 푑푛´ 푛´ = ln (휀) + (24) 푑 𝜀̇ 푑𝜀̇ 𝜀̇
At this point, any sufficient form of d(ln(σ))/d(ε) must be chosen. In the present work, an exponential form is found to have good agreement with both ZE20 and AA2070.
Substituting in an exponential function with arbitrary constants results in
푑푛´ 푛´ ln(휀) + = 퐴 exp(퐵휀) + 퐶 (25) 푑𝜀̇ 𝜀̇
Choosing to define A, B, and C such that they are not functions of strain, solving the resulting differential equation results in the form of the strain hardening function
1 퐴 푛´ = [ exp(퐵휀) + 퐶휀 + 퐷] (26) ln (𝜀̇) 퐵 and substituting n’ into Equation 20 results in the overall expression for flow stress:
1 퐴 { [ exp(퐵𝜀̇)+퐶𝜀̇+퐷]} 𝜀̇̇ 푚 휎 = 퐾 (휀 ln (휀) 퐵 ) ( ) (27) 𝜀̇̇ 0
The choice of an exponential function as the substitution function in Equation 24 allows for some attribution of physical significance. In such cases, A is the initial hardening rate, B controls how quickly the hardening rate changes, and C is the final hardening rate. In cases where the material reaches steady-state behavior, C should be zero. Compared to the base version of the extended Ludwik model, this adds a
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significant degree of flexibility. The base version of the extended Ludwik model cannot predict steady-state behavior unless n is zero, in which case the model predicts constant flow stress after yielding (ideal plastic behavior).
In the present work, A, B, C, and D were determined as functions of temperature and strain rate by fitting individual flow curves to Equation 25. K and m were determined as polynomial functions of temperature using Equation 22. With all constants known, a light optimization was applied to A, B, C, and D, similar to the process for the
Sellars-Tegart model. After optimization, n’ values were checked to ensure that they remained accurate to the material’s behavior.
The modified Ludwik equation was applied to the mechanical data for ZE20 and for AA2070 in compression. The present form of the extended Ludwik model could not be successfully applied to AM30. The poor data quality at high strain rates leading to a
“soft yielding” behavior for AM30, discussed in Section 2.2.1, made it such that K and m would take non-physical values, resulting in model failure. Ludwik model results for
ZE20 are shown in Figure 35. The forms of the model constants used to achieve these results take the general form
2 2 3 푓(푇, 휀̇) = 푓1 + 푓2 ln(휀̇) + 푓3푇 + 푓4 ln(휀̇) 푇 + 푓5푇 + 푓6 ln(휀̇) 푇 + 푓7 푇 (28) where T is absolute temperature. Coefficients of these constants for ZE20 are listed in
Table 5.
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Table 5. Modified Ludwik model constants for ZE20. f(T,ε ) f1 f2 f3 f4 f5 f6 f7 A 46.86 0.4147 -0.07495 -0.006939 0.0009218 2.813∙10-5 0 B -38.61 -3.850 0.06502 -0.08063 0.005417 -3.087∙10-5 0 C 0.02421 0.2522 8.003∙10-4 0.006616 -3.399∙10-4 -1.820∙10-6 0 D -1.033 -0.2255 0.002423 -0.01273 2.433∙10-4 -7.639∙10-7 0 m -1.099 0 0.004997 0 -7.744∙10-6 0 4.650∙10-9 K -1074 0 6.702 0 -0.01179 0 6.456∙10-6
Figure 35. Modified Ludwik model results plotted along with experimental data for ZE20 at (a) 10-3 s-1, (b) 10-2 s-1, (c) 10-1 s-1, and (d) 100 s-1.
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The modified Ludwik model predicts several features of the flow curves very well. Yield stress and initial hardening are predicted very well for almost all strain rates and temperatures. The model has exceptional performance at low strain rates, but at higher strain rates, the change in strain of peak stress is captured somewhat poorly.
Because the model tends to predict steady state flow stress well, this manifests as over- prediction of stress prior to the peak stress or under-prediction of stress at and after peak stress. Overall, the model has a good fit with the experimental data, achieving an AARE of 2.24% and a RMSE of 2.03 MPa.
The modified Ludwik model also had good results for AA2070. Results for
AA2070 are shown in Figure 36, and model constants are listed in Table 6.
Table 6. Modified Ludwik model constants for AA2070. f(T,ε̇) f1 f2 f3 f4 f5 f6 f7 A -279.3 -13.72 1.333 0.04500 -0.002050 -3.765 1.020 B 632.4 -15.74 -2.529 0.03020 0.002314 0 0 C -22.91 -0.08026 0.1049 7.065 -1.567 -8.058 7.607 ∙10-4 ∙10-4 ∙10-7 ∙10-8 D -1.302 -0.03401 0.003029 0 0 0 0 m 6.501∙10-4 0 -0.2852 0 0 0 0 K 11290 0 -49.10 0 0.07179 0 -3.516∙10-5
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Figure 36. Ludwik model results for AA2070. Model predictions and experimental results for (a) 10-3 s-1, (b) 10-2 s-1, and (c) 10-1 s-1.
From inspection of Figure 36, the extended Ludwik model performs well for
AA2070 at all temperatures above 250°C. Yield points, softening, and steady-state behavior are predicted well for all these temperatures. At 250°C, the model predicts yielding and initial hardening acceptably for 10-1 s-1 but predicts these relatively poorly for the other strain rates. In all cases at 250°C, the modified Ludwik model fails to accurately predict the peak stress. Flow stress during softening is predicted accurately for
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10-2 s-1 and 10-1 s-1 but very poorly for 10-3 s-1. These low temperature results are far from ideal, but they do highlight a change in hardening behavior that is not easily seen from the flow curves alone. This change in hardening behavior may be due to suppression of shear banding at higher temperatures. Despite somewhat poor accuracy at low temperatures, the modified Ludwik model has good overall performance, achieving an AARE of 2.75% and a RMSE of 4.39 MPa.
The modified Ludwik model’s performance relative to the hyperbolic sine
Arrhenius model can easily be visually assessed by plotting predicted stress against experimental flow stress. Plots for both models and for both materials are shown in
Figure 37.
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Figure 37. Performance of the (a,c) Sellars-Tegart model and (b,d) the modified Ludwik model for (a-b) ZE20 and (c-d) AA2070.
Both models seem to have lower scatter for AA2070 than for ZE20. This is partially due to the nature of the datasets and material properties. ZE20 had a dataset that spanned a smaller range of temperatures, and within that range, the observed flow stresses varied less. In Figure 37 then, the same flow stresses are represented and predicted more often, leading to an apparent scattering of data. ZE20 also exhibited more hardening, while AA2070 exhibited mainly softening. This leads to the hook-shaped features in Figure 37 (a) and (b) as the experimentally measured stress rises, then drops. 118
The hyperbolic sine Arrhenius model tended to over-predict or under-predict whole flow curves, especially for AA2070. This is evident in Figure 37 (c) where single segments exist above or below the ideal R=1 line. This is due to the earlier-mentioned effects of the model’s power law and exponential construction without consideration of strain.
One major benefit of the Ludwik model that is not evident in Figure 37 is that the
Ludwik model can accommodate for missing data in certain flow curves. The Arrhenius model for AA2070 could only predict to strains of -0.75 due to poor data quality gathered at 250°C and 10-1 s-1. Data could not be gathered past this point, as specimens consistently formed shear bands. For the Arrhenius model, model constants are determined based on derivatives of strain rate. When partial data was removed, it changed the number of datasets across which derivatives were taken, resulting in a significant step in the derivative. Ideally, this would be mitigated by a dataset with more strain rates, but specimens tested at higher strain rates would also exhibit shear banding, and strain rates lower than 10-3 s-1 are not useful for forging. In cases such as this, the greater robustness of the Ludwik model is obvious, but caution and common sense should be exercised in model application. As shown in Figure 36 (c), the Ludwik model still predicts past strains which are experimentally unattainable. In such cases where data is excluded from the model, predicted data must be truncated at strains corresponding to actual material failure.
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Numerically, The Ludwik model had lower error for both ZE20 and AA2070.
For ZE20, the Ludwik model has lower accuracy and fewer model constants. The form shown of the Ludwik model for AA2070 has more model constants than the Arrhenius model for AA2070, which is a reflection of the power and exponential forms of A, α, n, and Q for AA2070. Further reduction of model constants for the Ludwik model is possible with only a minimal penalty in accuracy for both ZE20 and AA2070. Examples include m and K for ZE20 in Table 5 and C for AA2070 in Table 6. For these constants, the cubic term in the function of temperature could be eliminated, as the coefficients for the cubic term are on the order of 10-6 to 10-9.
Past simple reduction of constants, the hardening function formulation of the modified Ludwik model presents much greater room for improvement. Equation 24 provides a basis of approach for materials with significantly different behavior. Several other forms of d(ln(σ))/d(ε) were attempted, and many were moderately successful, including polynomial functions, power functions, and rational functions. The present exponential formulation was selected because it had a loose physical significance, easily reported constants, and high accuracy. Incorporation of additional or alternate terms would be appropriate for other materials with more complex hardening behavior. Such attempts were moderately successful for AM30 using a double exponential function, but this expression necessarily had more model constants and lost physical significance of the individual model constants. Without adding a second exponential function, one may multiply C in Equation 25 by (ε – εmax) so that the C term is identically zero (steady state
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behavior) at the full strain of testing. This is a middle ground where A and B maintain some physical basis but are affected by the value of C. Several such modifications or improvements in the hardening function’s form are possible, and this work provides a starting point and proof of concept for new modeling work.
A similar chain rule expansion of strain rate sensitivity could also be implemented in the same fashion. Rate-dependent strain rate sensitivity would likely expand the range of strain rates over which the Ludwik equation is valid, making it more competitive with the Arrhenius model, which is valid across several regimes of material behavior. Rate- dependent strain rate sensitivity may also make it possible to generate processing maps from the extended Ludwik model; in their current forms, neither the modified Ludwik model nor the hyperbolic sine Arrhenius model are suitable for calculation of a processing map.
Alternate forms of the hyperbolic sine Arrhenius model also exist, where some authors expand on the model parameters in order to give activation energy meaning as a function of temperature or strain rate. While useful, these forms sometimes unfortunately make the results difficult to fully report [144].
4.3 Viscoplastic Self-Consistent Crystal Plasticity Simulation of ZE20
Viscoplastic self-consistent (VPSC) crystal plasticity simulation [145] was applied to ZE20 in order to glean more precise understanding of the mechanisms operating during deformation. The following is a brief description of only the equations
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for which constants are determined or related equations. A full, comprehensive description of the polycrystal plasticity formalism can be found in Lebensohn, Tomé, and
Maudlin’s 2004 publication in the Journal of the Mechanics and Physics of Solids [146].
The governing equation of grain-level material behavior in VPSC is the non- linear rate-sensitivity equation:
s s εij(x̅) = ∑s mijγ (x̅) (29) where εij(x) is the deviatoric strain rate, mij is the Schmid tensor associated with the
s deformation system s, and γ (x̅ ) is the shear rate on that deformation system. Eq. (7) can be rewritten as
s n s mklσkl ε̇ij = γ̇0 ∑s mij ( s ) (30) τ0
s where γ 0 is a normalization shear rate, σkl is the deviatoric stress, τ0 is the threshold stress of deformation system s, and n is the inverse of strain rate sensitivity. Individual grain responses are determined by treating them as Eshelby inclusions in the polycrystal, which is treated as an effective homogeneous medium. Twinning is handled in VPSC using a predominant twin reorientation (PTR) scheme. The PTR scheme treats twinning modes as pseudo-slip, allowing them to contribute to shear strain accommodation, then completely reorients individual grains to the twinned orientation once their accumulated twin fraction (based on the accumulated shear) is greater than a threshold value.
s The present work uses Voce hardening to model threshold stress τ0 in Equation
30. The Voce hardening law takes the form
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s s s s s θ0 τ̂ = τ0 + (τ1 + θ1Γ) (1 − exp [−Γ | s |]) (31) τ1 where τ0, τ1, θ0, and θ1 are hardening constants relating to the initial shear stress, final shear stress, initial hardening rate, and final hardening rate of the given deformation system s; and Γ is the accumulated shear within a grain.
All voce hardening constants were restricted to non-negative values. With positive values of θ0 and θ1, this means that Voce hardening model softening due to recovery or recrystallization. The recrystallization scheme of Walde and Riedel [147] was implemented to account for softening due to recrystallization. Walde and Riedel’s model uses a stored energy criterion to determine nucleation of new grains. Stored energy is calculated as
s s 2 En = A ∑s(τn − τ0) (32)
s where En is the stored energy of orientation n, τn is the reference shear stress of that orientation, and A is a material parameter which is set to 1 for this work. If the stored energy within a grain reaches some value (En > Ecrit), nucleation occurs for grain n. The stress and accumulated shear in parent grain n are then modified as:
s s τn = C τ0 (33)
Γnew = D Γold (34) where C and D are model parameters. In the present work, values of C = 1.1 and D =
0.09 are chosen. The most physically realistic values are C = 1 and D = 0, but Walde and
Riedel note that this causes significant stress drops and oscillations in predicted stress
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[147]. After nucleation, growth is simulated by updating the weight of each orientation using a mean field approach:
2 ⁄3 𝑤̇̇푛 = 퐵 (퐸푎푣 − 퐸푛) 𝑤̇푛 (35) where ẇn is the weight of orientation n, B is a material parameter, and Eav is the weighted average of En for all orientations. In the present work, the value of B = 0.11 was chosen.
A synthetic microstructure consisting of 1000 randomly oriented grains with equal weight fractions was used as the input texture. The deformation modes considered in the present work are basal slip, prismatic , pyramidal
For VPSC simulation of Mg, pyramidal is often excluded from simulation because it has higher CRSS than prismatic slip and does not contribute an independent deformation mode not already provided by the combination of basal and prismatic slip. Compression twinning is also often excluded because it has very high CRSS and is seldom activated at elevated temperatures [14]. Latent hardening was not considered for these deformation modes (latent hardening parameters were set to 1, self-hardening). The effective linearization scheme was chosen (neff = 10).
VPSC simulations were performed without accounting for recrystallization in order to determine Voce hardening parameters. τ0 and θ0 were determined by fitting simulated flow curves to the low strain (ε ≤ 0.15) portion of mechanical data in order to reduce the influence of recrystallization of CRSS and initial hardening. Approximate values of τ1 were determined by matching simulated texture components to observed texture components for the bulk material. Values of θ1 were assumed to be equal to 0 for
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slip modes and equal to θ0 for tension twinning. Linear or exponential functions of temperature were then fit to the best-fit Voce parameters. Fitting from high strain rate data is shown in Figure 38, and the resulting expressions for Voce parameters are detailed in Table 7.
Table 7. Voce hardening parameters for ZE20 as functions of temperature.
Deformation τ0 τ1 θ0 θ1 mode Basal -0.01579 T + -0.1309 T + -0.1844 T 0 18.97 106.9 +172.6 Prismatic -0.1015 T + 266.1 exp( 2624 exp( 0 82.26 -0.002241 T) - -0.008091 T) + 32.33 25.32 Pyramidal -0.1743 T + 4824 exp( 3400 exp( 0
Figure 38. Experimental data and VPSC simulation with Voce hardening coefficients fit to strains up to -0.15. (a) 250°C, (b) 350°C, and (c) 450°C.
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From Figure 38, it is obvious that VPSC simulation without recrystallization behavior is inadequate to model ZE20’s flow stress. However, these results are not unexpected. Slip and twinning are the only strain accommodation modes available in the base VPSC simulation. As the material rotates into a basal orientation, rapid hardening occurs until prismatic
With known hardening parameters, an additional round of VPSC simulation was performed accounting for recrystallization. Best fit values for Ecrit were determined for each temperature and strain rate, and a polynomial function was fit to the result. The resulting expression for energy is
2 퐸푐푟𝑖푡 = 532600 − 1278 푇 + 527 log(휀̇) + 0.770 푇 + 12.24 푇 log (휀̇) (36)
In some regions, VPSC simulation with recrystallization could not match softening, resulting in a zero or negative critical energy. Ecrit was capped at a minimum value of
1000 to maintain physically realistic results. Predicted flow curves of VPSC using these values for Ecrit and the Voce parameters in Table 7 are shown in Figure 39.
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Figure 39. VPSC results for ZE20 after adding in recrystallization behavior. (a) 10-3 s-1, (b) 10-2 s-1, (c) 10-1 s-1, and 100 s-1.
VPSC flow curves with recrystallization are much closer to the experimental data, but some features are still very poorly predicted. High strain rate flow curves are predicted somewhat adequately, but they suffer from oscillations in flow stress due to the choice of values for C and D in Equations 33 and 34. Alternate values could correct this, but they would have no physical basis. Apart from the oscillations, VPSC predicts the
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yield stress and initial hardening well. Steady state stress is also predicted, though the accuracy of the prediction is obfuscated by the oscillations in flow stress.
Results become less accurate moving to lower temperatures. In Figure 39 (c), yield stress and initial hardening are predicted well for most temperatures, but flow stress past a strain of -0.5 is inaccurate. The experimental data shows softening, which is not predicted by VPSC. This is an artifact of the critical energy criterion for recrystallization.
As the material hardens, grains’ internal energy increases until a nucleation event occurs.
The stress is reduced due to the addition of new, soft grain(s), and the material again hardens until another nucleation event occurs. The critical energy of recrystallization effectively becomes a steady-state flow stress. Such an effect is also visible for flow curves corresponding to low temperatures in Figure 39 (b).
At the lowest strain rates and highest temperatures, VPSC prediction is completely inaccurate. For these conditions, the yield stress is predicted accurately, but flow stress at even low strains rapidly deviates from the experimental data. This is a consequence of each slip system having a nonzero value of τ1; positive values enforce hardening. However, for these same temperatures, the values of τ1 are appropriate for high strain rates. It would seem to imply from that rate-dependent Voce constants are required, but further analysis shows that VPSC simulation may be unsuited for Mg at high homologous temperatures. These inaccuracies are carried into texture predictions.
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Figure 40. VPSC-predicted textures for ZE20 across different temperatures and strain rates for the deformed and recrystallized material.
Deformed and recrystallized textures were calculated by partitioning VPSC output microstructures according to grain weight. Textures were calculated for selected strain rates and temperatures and are shown in Figure 40. VPSC is able to predict the general trend with temperature for both the recrystallized and deformed material – with increasing temperature, there is decreasing texture intensity and the basal pole becomes inclined toward <112̅0>. Apart from this, the predicted texture trends do not match 129
experiments well. Experimentally, little texture intensity change was observed with changes in strain rate. This is reflected for the deformed material at low and moderate temperatures and moderate to high strain rates. At high temperatures and low strain rates where Ecrit is low, activation of recrystallization is easy enough that the microstructure never fully develops basal texture. For these conditions, nucleation was occurring at up to 80% of the microstructure for each strain step, and growth occurred at the expense of grains which had not necessarily reached basal texture or the stable texture component.
This is easily seen in the simulated deformed microstructure for ZE20 at 450°C and 10-2 s-1; the texture should instead be similar to the deformed texture at the same temperature and 100 s-1. The recrystallized texture from 450°C and 10-2 s-1 is wholly inaccurate and is representative of only a single strain step of newly nucleated randomly oriented grains.
Apart from this, VPSC slightly over-predicts texture intensity for both the deformed and recrystallized material. The texture character for the recrystallized material does not match experiments exactly – much more spread toward the basal pole was observed experimentally.
VPSC also gives useful information about the activity of individual deformation modes; activity plots are shown in Figure 41.
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Figure 41. Relative activity of deformation modes in ZE20 under different conditions: (a) 250°C and no recrystallization, (b) 450°C and no recrystallization, (c) 250°C and 10-3 s-1, (d) 250°C and 100 s-1, (e) 450°C and 10-3 s-1, (f) 450°C and 100 s-1 .
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Some of the inaccuracies for texture and mechanical properties can be explained with information about activity of the individual deformation modes in the simulation.
Figure 41(a) and (b) show the activity of deformation modes in ZE20 at low and high temperatures, without the influence of recrystallization. For these conditions, the material follows the expected trend. At low temperature, twinning and prismatic slip are active at low strains until they cannot accommodate strain effectively, pyramidal
CRSS. These trends do not change for the base VPSC simulations because the Voce parameters are not functions of strain rate. Figure 41 (c) and (e) show the activity of deformation modes with recrystallization behavior accounted for at 250°C. Strain rate does not affect Ecrit much at this temperature, and the predicted relative activity is largely the same. The only significant difference between the simulations with recrystallization and without recrystallization at 250°C is increased pyramidal
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resulting high activity of prismatic slip relative to pyramidal slip explains the predicted prismatic texture component for the same conditions in Figure 40. At 450°C and 100 s-1, the relative activity is closer to expectations. Similar to low temperature behavior, enhanced pyramidal
Despite some obvious inaccuracies, VPSC has fair accuracy at high strain rates and low temperatures. Being physically-based, it is therefore useful for validation of the empirical Ludwik model. There is some similarity in form between the Ludwik hardening model and Voce hardening, and Ludwik constants can be compared to Voce constants. The constants as a function of temperature are shown in Figure 42.
Figure 42. Comparison of hardening constants between VPSC Voce hardening and the modified Ludwik hardening model.
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The most comparable comparison is for CRSS. The terms are not identical across
n models, so τ0 is compared with K∙ε to determine an approximate a “bulk CRSS.” Values of n correspond to a plastic strain of -0.001, and values of K and n at 100 s-1 are used.
The “bulk CRSS” closely follows the CRSS for twinning, which would suggest that twinning behavior has a strong impact on yielding. This is commonly known for Mg alloys, but it is not necessarily evident from Figure 41, in which the activity of twinning is quite low. Another apt comparison is the initial hardening rate. The Ludwik accomplishes this in terms of A, which is the natural log derivative of stress with respect to strain. θ0 is instead a simple derivative of shear stress with respect to strain. These cannot be directly compared, so the initial hardening rate of the bulk is shown along with
A and θ0 in Figure 42 (b). Unsurprisingly, A cannot be directly related to any of the Voce parameters. The bulk hardening rate, however, is very close to the initial hardening rate of pyramidal
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Overall, VPSC is a very powerful tool, but it seems unsuited to accurately represent all the physics occurring in ZE20. The critical energy formulation does not adequately represent recrystallization in ZE20 in the warm forming regime. A more accurate physically-based simulation could be completed with crystal plasticity coupled finite element method (CP-FEM) simulation.
4.4 Conclusions
A derivation of a novel strain hardening function for the extended Ludwik equation was presented. Using the hyperbolic sine Arrhenius equation as a baseline for comparison, the modified Ludwik model was found to have superior accuracy with a similar number of model constants for both ZE20 and AA2070. Neither model could be successfully applied to AM30 due texture hardening effects. General methods for the
Ludwik model derivation are emphasized; further modifications to modified Ludwik model are outlined for increases in predictive accuracy, reduction in the number of model constants, and expansion of the model to handle severe texture hardening (the AM30 case).
Viscoplastic self-consistent modeling using the recrystallization scheme of Walde and Riedel [147] was also applied to the mechanical data from ZE20. The VPSC results were adequate at high strain rates and low temperatures, but failed to accurately predict flow stresses at low strain rates and high temperatures. VPSC-simulated textures had similar predictive accuracy in the same temperature and strain rate regimes. It was found
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that the critical energy formulation of the recrystallization model was an effective steady state stress and caused excessive nucleation of new grains, leading to such inaccuracies.
This was exacerbated by inability of rate-independent Voce parameters to adequately describe flow stress past yielding for high temperatures and low strain rates.
Despite inadequate prediction capabilities for high temperatures and low strain rates, VPSC-determined Voce parameters described yielding and hardening well. Having physical basis, these Voce parameters were compared to values from experiments and the
Ludwik model. Consistent with theory, the initial CRSS for twinning was closely related to the Ludwik model’s yield stress, and the bulk initial hardening rate was similar to the initial hardening rate for pyramidal
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Chapter 5: Conclusions and Future Work
5.1 Summary
Hot working flow stresses were investigated in a conventional Mg alloy, AM30, and a RE-containing Mg alloy, ZE20. Significant effects of initial billet texture were observed for AM30. Mechanisms of recovery and recrystallization were inferred from the flow curves for both alloys. SEM and EBSD investigation were conducted to verify metallurgical processes occurring during hot deformation. Significant influence of initial billet microstructure and texture were confirmed for AM30. Deformation twin nucleation and abnormal grain growth were observed in AM30. AM30 was found to have higher volume fractions of recrystallized material and larger recrystallized grain sizes than
ZE20. The enhanced recrystallization in AM30 was attributed to retarded kinetics due to the rare earth effect in ZE20. ZE20 was found to have lower texture intensities for both deformed and recrystallized portions of the microstructure. This as well was attributed to the rare earth effect – a change in CRSS of non-basal slip in ZE20 due to Ce content in solid solution.
Processing maps were constructed and used to guide EBSD investigation of metallurgical phenomena in ZE20 which informed processing recommendations. Two domains and two instability regions were identified. Domain I was found to have features suitable for processing: bulk non-basal texture, weak non-basal recrystallization texture, and a moderate volume fraction of recrystallized material. Domain II and
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Instability Region II were found to have properties insufficient for forming mainly due to the low strain at which they occurred. Localized flow, shear bands, and shear cracking were observed in Instability Region I. Shear bands were found to recrystallize and form the RE texture component. Within Instability Region I, regions where no shear cracking was observed, the combined operation of flow localization and shear banding were identified as regions of potential processing interest, having the potential to form bulk non-basal wrought products upon annealing.
Forging behavior of a third generation Al-Li alloy AA2070 was investigated.
Specimens were solutionized and heat treated prior to mechanical testing in order to simulate actual forging microstructures. Flow curves were analyzed in tension, compression, and plane strain compression for AA2070. Yield stresses were found to be nearly identical for all testing modes, and flow properties were similar. Significant effects of initial forging anisotropy were visible in even macroscopically in tested specimens, including shear banding, ovality, and grain structure in fracture surfaces.
Pseudo processing maps were generated in order to determine areas of interest.
Thorough microstructural characterization was performed on hot-deformed and exemplar AA2070 specimens. Microstructural characterization of exemplar specimens showed precipitation behavior of the alloy after different heat treatments. EBSD of untested specimens showed a highly anisotropic starting material; there were large, deformed grains, and the microstructure had significant Goss, copper, and brass texture components. EBSD investigation of compression specimens confirmed processing map
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predictions of recrystallization at 450°C. EBSD of compression specimens also showed reduction in the Goss texture component with decreasing temperature and replacement of the brass component with copper texture at most temperatures. Significant shifts from the ideal texture components were observed. EBSD of tension specimens showed less recrystallization at 450°C. Tension specimens were in the process of forming <111> fiber texture instead of Goss texture; lower temperature specimens had weaker remaining
Goss texture components. Plane strain compression specimens allowed more quantitative determination of texture. Temperature and strain rate trends of all common texture components in Al were reported. Processing recommendations were made on the basis of observed microstructure and texture trends.
Two flow stress models were applied to AM30, ZE20, and AA2070. The hyperbolic sine Arrhenius model was found to have poor results for AM30 but adequate results for ZE20 and AA2070. An unconventional constant structure was shown for
AA2070 which reduced the number of model constants and increased predictive accuracy. Steady-state hot working energies for ZE20 and AA2070 were determined to be 168 kJ/mol and 265 kJ/mol, respectively. Modifications to the extended Ludwik hardening model to implement a novel strain hardening function were demonstrated. The
Ludwik model could not be successfully applied to AM30. The modified Ludwik model was found to have superior accuracy to the hyperbolic sine Arrhenius model for both
ZE20 and AA2070. The Arrhenius and Ludwik models were compared, and further potential modifications to the Ludwik model were outlined.
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Viscoplastic self-consistent crystal plasticity simulation was performed for ZE20.
Temperature-dependent Voce hardening parameters were reported. Recrystallization behavior was added to VPSC using the scheme of Walde and Riedel [147]. Critical energy of recrystallization was determined as a function of temperature and strain rate.
Simulated flow curves and textures were assessed. VPSC was found to predict flow stresses adequately for low temperatures and high strain rates. VPSC could not accurately predict flow curves at high temperatures and low strain rates due to formulation of the Voce hardening parameters. The critical energy criterion was found insufficient to model softening after the peak stress, instead resembling a steady state stress criterion. Simulated textures had similar issues. Texture components were accurately predicted for low temperatures and high strain rates, but texture intensities were over-predicted. High temperature, low strain rate textures had very low intensity and inaccurate texture components. Relative activity of the deformation modes was compared, and the inaccuracy was determined to be caused by excessive nucleation and growth of new grains. Ludwik model constants were compared to VPSC-determined
Voce constants. Similarities were found between the bulk yield stress and the CRSS of twinning and between the bulk initial hardening rate and the initial hardening rate of pyramidal
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5.2 Recommendations for Future Work
Further testing and validation is required for the processing recommendations made for ZE20 in section 2.4. Jump-rate mechanical tests could be used as a simple method to verify the negative strain rate sensitivity seen in Domain II. Jump rate testing is also a much simpler method than EBSD which would allow the determination of the temperature and strain rate limits inside which shear bands form in Instability Region I, if those shear bands are linked to DSA. Additionally, Gleeble testing in compression is geometrically limited to a strain of 1.0. Other modes of testing, such as torsion, could provide high enough strains to fully recrystallize the microstructure and would provide more adequate comparison with industrial processes, such as extrusion, which can reach strains in excess of 10. For lower strains, static recrystallization studies on tested specimens to simulate post-test annealing would improve recommendations on processing in Instability Region I. Alternately, simple extrusion trials or rolling trials could be used to validate these processing recommendations. The results of rolling or extrusion trials could also inform optimum processing with formability data.
Much could be done to improve the VPSC results. Often multiple tests are performed in different directions on initially textured material. This helps with precise identification of hardening parameters. With initially randomly textured materials, such as in the present work, there is some uncertainty in hardening parameters. Additionally, the unique mechanical response of a textured material in different directions would make it possible to define strain rate dependent Voce parameters. For the present work, such a
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construction would be under-defined. Additional physics may also be added to the VPSC model in order to more accurately describe flow localization and localization of recrystallization through nearest-neighbor interactions.
Much further characterization and testing could be done to determine definite metallurgical mechanisms and processing recommendations for AA2070. Transmission electron microscopy (TEM) characterization would help determine the exact phases which precipitate during heat treatment. Additional sets of thermomechanical tests performed with a single thermal history (as recommended, overaged at 450°C) could be used to generate real processing maps (not pseudo-maps) to more accurately inform processing, especially with respect to strain rate. Such mechanical testing, especially if paired with EBSD, would also help to decouple the effects of precipitate content, precipitate distribution, and temperature on flow stress and texture development.
Because much of the observed softening is attributed to DRV, TEM investigation would allow study of dislocation networks and confirm the operation of this mechanism.
The flexible form of the proposed hardening function for the Ludwik model gives it room for improvement. Some modifications are already presented in Section 4.2. As seen with AM30, it cannot predict drastic hardening, followed by softening, followed by steady-state behavior. Further development of the extended Ludwik model is recommended. Incorporation of terms which can accommodate drastic changes in strain hardening while still maintaining conventional meaning of the strain hardening exponent and the semi-physical basis is of key interest.
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