Contents
Cover
Half Title page
Title page
Copyright page
Preface
I. Microstructural Evolution
High Strain Monotonic Deformation-Structure and Strength
Abstract
Introduction
Microstructural Evolution
Microstructure and Flow Stress
Concluding Remarks
Acknowledgements
References
Influence of Processing Route on Microstructure and Grain Boundary Development During Equal-Channel Angular Pressing of Pure Aluminum
Abstract
Introduction
Experimental Background
Results and Discussion
Conclusions
Acknowledgement
References
Equal Channel Angular Pressing of Steels (BCC), Al Alloys (FCC) and Pure Titanium (HCP)
Abstract
Introduction
Experimental Procedure
Results and Discussion
Summary
Acknowledgement
References
The Effect of Strain Per Pass on the Microstructure Developed in Aluminum Processed by Equal Channel Angular Extrusion
Abstract
Introduction
Experimental
Results and Discussion
Conclusion
Acknowledgements
Reference
Microstructural Evolution of Titanium Under Twist Extrusion
Abstract
Introduction
The Main Idea behind the TE Method
Experimental Investigation
Conclusion
References
Nanostructure Formation and Carbides Dissolution in Rail Steel Deformed by High Pressure Torsion
Abstract
1. Introduction.
2. Experimental procedure.
3. Results.
4. Discussion.
4. Conclusions
Acknowledgements
References:
Grain Refinement and Texture Development in Asymmetrically Rolled Aluminum Alloy Sheets
Abstract
1. Introduction
2. Experimetnal
3. Results and Discussion
4. Conclusion
Acknowledgement
Reference
Ultrafine Grain Formation During Equal Channel Angular Extrusion in an Al-Mg-Sc Alloy
Abstract
1. Introduction
2. Experimental Material and Procedure
3. Results
4. Discussion
5. Conclusions
Acknowledgment
References
Formation of Nanocrystalline Structure in a Ni-20 % Cr Alloy
Abstract
1. Introduction
2. Materials and Experimental Technique
3. Results
4. Discussion
References
Formation of Ultrafine Grains During Intense Plastic Straining in An Al-Li Alloy at 400°C
Abstract
Introduction
Experimental
Experimental Results
Discussion
Summary and Conclusions.
Referens
Mechanisms of Formation of Submicron Grain Structures During Severe Deformation
Abstract
1. Introduction
2. Grain Refinement during Severe Deformation
3. Conclusions
Acknowledgements
References
Grain Refining Mechanism of Ti During Equal Channel Angular Pressing
Abstract
1. Introduction
2. Experimental Procedures
3. Results and discussion
4. Summary
References
Microstructure Evolution in Nanocrystal Formation During Ball Milling
Abstract
Introduction
Experimental Procedures
Results
Discussion
Conclusions
References
Formation of Nanocrystalline Structure in Two-Phase Titanium Alloys by Warm Severe Plastic Deformation
Abstract
Introduction
Results
Summary
Acknowledgdement
References
Evolution of Microstructure and Mechanical Behavior of Titanium During Warm Multiple Deformation
Abstract
Introduction
Experimental Procedure
Results
Discussion
Summary
Acknowledgement
References
Effect of Pressure on the Final Grain Size After High Pressure Torsion
Abstract
Introduction
Experimental Material and Procedure
Experimental Results
Summary
Acknowledgement
References
Heterogeneous Microstructural Evolution and Reactions During Repeated Intense Deformation
Abstract
Introduction
Microstructural Changes of Multilayers during Cold-Rolling
Nanocrystallization by Mechanical Deformation of Amorphous Precursors
Summary
Acknowledgement
References
Hardness and Microstructure Changes in Severely Deformed and Recrystallized Tantalum
Abstract
Introduction
Experimental Procedures
Results and Discussion
Conclusions
Acknowledgements
References
II. Processing of Ultrafine-Grained Materials
Homogeneity in Ultrafine-Grained Aluminum Prepared by Equal-Channel Angular Pressing
Abstract
Introduction
Experimental Material and Procedures
Experimental Results
Discussion
Summary and Conclusions
Acknowledgement
References
Processing of an Aluminum-6061 Metal Matrix Composite by Equal-Channel Angular Pressing
Abstract
Introduction
Experimental material and procedures
Experimental results and discussion
Summary and Conclusions
Acknowledgement
References
Grain Refinement and Phase Transformations in Al and Fe Based Alloys During Severe Plastic Deformation
Abstract
1. Introduction
2. Experimental Procedure
3. Results and Discussions
4. Conclusions
Acknowledgement
References
Phase Transformations in Ultrafine Grained Fe and Fe-Mn Alloys
Abstract
Introduction
Experimental
Results and Discussion
Conclusions
References
Ultrafine-Grained Tungsten Produced by SPD Techniques
Abstract
Introduction
Materials and Experimetnal Procedures
Experimetnal Results
Discussion
Conclusions
Achnowledegement
References
Metastable Nanostructured Alloys Processed by Severe Plastic Deformation
Abstract
Introduction
Experimental Procedures
Results
Discussion
Summary
Acknowledgement
References
Syntheses of Nd2Ti2O7/Al2O3 Nanocomposites by Spark-Plasma-Sintering and High-Energy Ball-Milling
Abstract
1. Introduction
2. Experimental procedures
3. Results and Discussion
4. Conclusions
Acknowledgements:
References
Properties and Microstructure of Alumina-Niobium Nanocomposites Made by Novel Processing Methods
Abstract
Introduction
Experimental Procedures
Results and Discussion
Conclusions
Acknowledgements:
References
Nano-Nano Composites of Silicon Nitride and Silicon Carbide
Abstract
1. Introduction
2. Experimental Procedure
3. Results and Discussion
4. Conclusion
Acknowledgement
References
The Use of SPD for Fabrication of Bulk Nanostructured Materials from Ball-Milled Powders
Abstract
1. Introduction
2. Experimental.
3. Results and discussion.
Conclusion
References
Numerical Analysis of Plastic Deformation in Constrained Groove Pressing
Abstract
1. Introduction
2. Constrained Groove Pressing (CGP)
3. Numerical Analysis of CGP
4. Constrained Grooved Rolling (CGR)
5. Conclusion
Acknowledgement
References
Effect of Vanadium Addition on Dynamic γ→α Transformation During Hot Deformation of Low Carbon Steels
Abstract
Introduction
Experimental Procedure
Measurement of Volume Fraction of Dynamically Transformed Ferrite [6]
Results
Discussion
Conclusions
Reference
Determination of Dynamic Ferrite Transformation During Deformation in Austenite
Abstract
1. Introduction
2. Experimental Procedure
3. Results and Discussion
Conclusions
Reference
Grain Refinement of Medium Carbon Steel Withcontrolled Thermo-Mechanical Deformation
Abstract
Introduction
Experimental
Results and Discussion
Conclusions
Acknowledgments
References
Enhanced Formability of Superplastic AlMgZr Alloys Made by Particulate Routes
Abstract
Introduction
Particulate Manufacture
Particulate Processing
Microstructural Analysis
Solidification Modelling
High Speed Atomisation
Conclusions
Symbols
Acknowledgements
References
On The Development of Microstructure in A Metal Matrix Composite Using Nano–Materials
Abstract
Introduction
Processing and Characterization Procedures
Microstructure and Microstructural Evolution
Conclusions
References
A New Severe Plastic Deformation Methd: Twist Extrusion
Abstract
Introduction
References
III. Structure and Mechanical Properties
Defects, Microstructure and Dislocation Activity in Nanocrystalline Metals
Abstract
Introduction
Microstructural Factors Affecting Mechanical Behavior
Mechanisms of Deformation
Fracture Toughness and Strain to Failure
Conclusions
Acknowledgments
References
Recent Developments of SPD Processing for Fabrication of Bulk Nanostructured Materials
Abstract
1. Introduction
2. Investigations and development of SPD processing
3. Microstructural Features and Enhancement of Properties
Summary and Conclusions.
Acknowledgements
References
Deformation Mechanisms at Different Grain Sizes in a Cryogenically Ball-Milled Al-Mg Alloy
Abstract
Introduction
Experimental procedures
Results and Discussion
Conclusion
Acknowledgments
References
Properties and Nanostructures of Materials Processed by SPD Techniques
Abstract
1. Introduction
2. Mechanical Properties
3. Nanostructures
4. Conclusions
Acknowledgement
References
Tensile and Fatigue Properties of Al-Mg-Sc-Zr Alloy Fine-Grained by Equal-Channel Angular Pressing
Abstract
1. Introduction
2. Experimental Procedure
3. Experimental Results
Summary
Acknowledgements
References
Structure, Properties and Thermal Stability of Utra-Fine Grained Cu-Cr-Zr Alloy
Abstract
1. Introduction
2. Experimental
3. Results
5. Summary
Acknowledgements
References
Corrosion Fatigue of Ultra-Fine Grain Copper Fabricated by Severe Plastic Deformation
Abstract
1. Introduction
2. Experimental Procedure
3. Results and Discussions.
Summary
References
Strength of Submicrocrystalline Severely Deformed Commercial Aluminum Alloys
Abstract
Introduction
Tensile Strength of Submicrocrystalline Aluminum Alloys
Conclusions
References
Machinability Studies of PM Metal Matrix Composites on EDM
Abstract
1. Introduction
2. Experimental Plan
3. Results and Discussion
4. Conclusions
References
Mechanical Properties of Ultrafine Grained Aluminum and Ultra low Carbon Steel Produced by ARB Process
Abstract
Introduction
Experimental Procedures
Results and Discussions
Conclusions
Acknowledgments
References
Mechanical Properties of Nanostructured Plain Low-Carbon Steels Produced by Conventional Cold-Rolling and Annealing of Martensite Starting Microstructure
Abstract
Introduction
Experimental Procedures
Results
Discussions
Conclusions
Acknowledgments
References
Dry Sliding Wear Behavior of Ultrafine Grained Commercial Purity Aluminum and Low Carbon Steel Produced by Severe Plastic Deformation Techniques
Abstract
Introduction
Experimental
Results and Discussions
Conclusions
Acknowledgments
References
Structural Evolution of Ultrafine-Grained Copper and Copper-Based Alloy During Plastic Deformation
Abstract
1. Introduction
2. Materials and experimental technique
3. Results and their discussion
Acknowledgements
References
Microstructure and Properties of 7475 Aluminum Alloy After Equal-Channel Angular Pressing
Abstract
Introduction
Experimental, Material and Procedures
Results
Mechanical properties after ECAP
Discussion
5. SUMMARY AND CONCLUSIONS
Acknowledgement
References
The Microstructures and Compressive Deformation Behaviors of Nanocrystalline Al-5 at.% Ti Compacts Prepared by UHP-HP
Abstracts
1. Introduction
2. Experimental procedure
3. Results and discussion
4. Concluding Remarks
Acknowledgements
References
IV. Superplasticity and Thermal Stability
Grain Refinement of Copper Based Alloys Using ECAP
Abstract
Introduction
Experimental Materials and Procedures
Experimental Results and Discussion
Summary and Conclusions
Acknowledgements
References
Developing Superplasticity at High Strain Rates Through ECAP Processing
Abstract
Introduction
Grain refinement in ECAP
Superplasticity in the Al-Mg-Li-Zr Alloy
Superplasticity in the Al-Mg-Sc alloy
Summary and conclusions
Acknowledgements
References
Grain Refinement and Superplasticity in Magnesium Alloys
Abstract
Introduction
Superplasticity in Magnesium-Based Materials Processed by Powder Metallurgy Route Using Rapidly Solidified Powder
Superplasticity in Magnesium-Based Materials Processed by Severe Plastic Deformation
Conclusions
References
Effect of The Pressing Strain on the Annealing Behavior of Ultrafine Grained Ferrite in a Low Carbon Steel Fabricated by Equal Channel Angular Pressing
Abstract
Introduction
Experimental
Results and Discussion
Summary
Acknowledgment
References
Significance of Microstructural Thermal Stability in An Al-2219 Alloy Processed by Severe Plastic Deformation
Abstract
Introduction
Experimental Material and Procedures
Experimental Results
Discussion
Summary and Conclusions
Acknowledgements
References
Modelling The Microstructural Evolution During Annealing of A Severely Deformed Al-3% Mg Alloy
Abstract
Introduction
Experimental
Experimental Results
Isochronal annealing
Isothermal Annealing
Modelling
Conclusions
Acknowledgement
Reference
Structure and Stability of Ultrafine-Grained Materials. Role of Impurities and Second-Phase Particles.
Abstract
1. Introduction
2. Material and Method of Study
3. Results and Discussion
Acknowledgments
Reference
Annealing Effect on the Strength of Severe-Plastic-Deformed Titanium
Abstract
Introduction
Experimental
Results
Discussion
Conclusions
Acknowledgments.
References
Structure and Mechanical Behavior of the AMg6 Aluminum Alloy After Severe Plastic Deformation and Annealing
Abstract
Introduction
Experimental
Results and Discussion
Conclusions
References
V. Theory and Modeling
Continuum Mechanics Approach in Severe Plastic Deformation
Abstract
Introduction
Structure Evolution
Deformation Mode and History
Simple Shear versus Pure Shear
References
Deformation of Ti-6Al-4V Via Equal Channel Angular Extrusion
Abstract
Introduction
Materials and Procedures
Results and Discussion
Conclusions
Acknowledgements
References
Kinematics of Damage Governed by Severe Plastic Deformation
Abstract
Introduction
Correlation of Plastic Damage to the Density Change
The Kinetic Equation and Physical Model of Damage Accumulation and Recovery
Density Measurement Technique
Investigation of Density Change during Equal Channel Angular Extrusion (ECAE)
Investigation of Density Change during Equal Channel Angular Drawing (ECAD)
Discussion of Results
Conclusion
References
Strength and Ductility of Ultrafine Grained Metallic Materials
Abstract
Introduction
The Constitutive Mode
Tensile Ductility
Conclusion
Acknowledgements
References
Work Hardening Behavior of Aluminum Over a Wide Range of Strain
Abstract
Introduction
Experimental Material and Procedures
Experimental Results
Discussion
Summary and Conclusions
Acknowledgement
References
Analysis of Principal and Equivalent Strains in Equal Channel Angular Deformation
Abstract
Introduction
Analysis of Large Plastic Strains by Matrix Algebra
Analysis of Principal Strains in ECAD
Analysis of the “Equivalent” Strain in ECAD
5. Discussion
Summary
Acknowledgments
References
Polycrystal Constitutive Modeling of ECAP: Texture and Microstructural Evolution
Abstract
Introduction
Model Description
Results: Texture and Material Response
Results: Grain Refinement
Discussion and Future Work
Acknowledgement
Referenece
Grain Size, Size-Distribution and Dislocation Structure From Diffraction Peak Profile Analysis
Abstract
1. Introduction
2. Evaluation of Broadened Diffraction Peak Profiles
3. Experimental
4. Results and discussions
5. Conclusions
Acknowledgements
References
Defect Characterization of Equal Channel Angular Pressed Cu by Selective Annealing Treatment
Abstract
1. Introduction
2. Experimental
3. Results
4. Discussion
5. Summary and Conclusions
Acknowledgements
References
Size and Shape of Nano-Grains in Polycrystals Subjected to SPD
Abstract
Introduction
The Mean Grains Size
Grain Size Uniformity
Grain Size Effect
Characterization of the Grain Boundaries
Grain Shape
An Example of Applications
Final Remarks
References
X-Ray Analysis of SPD Nanostructured Materials
Abstract
Introduction
Experimental and Modeling Procedures
Results and Discussion
The peculiarities of SPD microstructure in SPD Ti and W
Summary
Acknowledgement
References
Addendum
Effects of Hot Working on Austenite/Ferrite Transformation in HSLA Steel
Abstract
1. Introduction
2. Experimental Procedures
3. Results and Discussion
4. Conclusions
Acknowledgements
References
Equal Channel Angular Processing of Magnesium Alloys
Abstract
Introduction
Experimental Procedures
Results and Discussion
Conclusions
Acknowledgements
References
Microstructural Evolution of Cryomilled Nanocrystalline Al-Ti-Cu Alloy
Abstract
Introduction
Experimental Procedures
Results and Discussion
Conclusion
Acknowledgements
Reference
Microstructure and Mechanical Properties of Non-Heat Treatable Aluminum Alloys Produced by Accumulative Roll Bonding Process
Abstract
Introduction
Experimental
Results and Discussion
Conclusions
Reference
Features of Severe Plastic Deformation as Compared to Conventional Deformation Modes
Abstract
1. Introduction
2. Characteristics of Severe Plastic Deformation
3. Comparison between Dynamic and Static Stress-Strain Characteristics under Varying Hydrostatic Pressure
4. Measurements of Defect Densities and Long Range Internal Stresses under Different Hydrostatic Pressure
5. Measurements and Mechanical Relevancy of Coherently Scattering Lattice Size
6. Conclusions
Acknowledgments
References
Author Index
Subject Index
Ultrafine Grained Materials II
A Publication of The Minerals, Metals & Materials Society
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Library of Congress Catalog Number 2001097450
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PREFACE
Two complementary approaches have been developed to synthesize ultrafine-grained (UFG) materials with grain sizes in the range from 10 to 1000 nm. The first is the “bottom-up” approach in which bulk ultrafine-grained materials are assembled from individual atoms or nanoscale building blocks such as nano-particles. Gleiter’s pioneering work on inert gas condensation (IGC) is a typical example of this approach. Various chemical and physical methods have been developed to synthesize nano-powders for small-scale laboratory investigations as well as for large-scale commercial use. Ceramic and metallic nano-powders can now be readily purchased from an increasing number of nano-technology companies. However, consolidation of these nano-particles into bulk nanostructured materials remains a major challenge.
The second approach for producing UFG materials is the “top-down” approach in which coarse-grained materials are refined into UFG materials. The most successful “top-down” approach has been via severe plastic deformation (SPD) techniques among which the most developed are equal channel angular pressing (ECAP) and high-pressure torsion (HPT). Recently, new SPD techniques have been developed such as accumulative roll-bonding (ARB), multipass-coin-forging (MCF), multi-axis deformation, and repetitive corrugation and straightening (RCS). The main advantage of SPD techniques is their capability for producing bulk UFG materials not only free of porosity but also in dimensions suitable for structural applications.
In the last decade, the processing of UFG materials via SPD techniques has received considerable attention from the materials science community. Many research groups have started to work in this exciting field and the annual number of publications has increased exponentially. The Second International Symposium on Ultrafine Grained Materials provides a forum to examine all aspects of the science and technology of UFG materials produced by SPD techniques. This proceedings book includes papers dealing with recent progress in processing and microstructures, microstructural evolution, mechanical and physical properties, superplasticity, computational and analytical modeling, new SPD technologies, etc.
The editors are grateful to all of the authors and presenters for making this symposium and this proceedings book a great success. Their responses to this symposium far surpassed the organizers’ expectations. The symposium incorporates ninety-three presenters from 15 countries so that this symposium is truly an international forum on UFG materials. Almost all of the papers presented at the symposium are included in these proceedings.
As suggested by the title of this symposium, ultrafine-grained materials will be a continuing theme in future TMS meetings. Future symposia will be held at regular TMS Spring meetings at approximately two-year intervals.
Finally, the editors thank the TMS staff, especially Mr. Stephen J. Kendall, for their considerable guidance and assistance during the preparations for this symposium and in the publication of this important proceedings book.
Yuntian T. Zhu
MS G755
Materials Science and Technology Division
Los Alamos National Laboratory
Los Alamos, NM 87545, USA
Email: yzhu@lanl.gov
Terence G. Langdon
Departments of Aerospace & Mechanical Engineering and Materials Science
University of Southern California
Los Angeles, CA 90089, USA
Email: langdon@usc.edu
Rajiv S. Mishra
Department of Metallurgical Engineering
University of Missouri
Rolla, MO 65409, USA
Email: rsmishra@umr.edu
S. Lee Semiatin
Air Force Research Laboratory
Materials & Manufacturing Directorate
WPAFB, OH 45433, USA
Email: Lee.Semiatin@afrl.af.mil
Michael J. Saran
OES, Inc.
3715 Traynham Rd
Cleveland, OH 44122, USA
Email: saran@2oes.net
Terry C. Lowe
Metallicum LLC
1207 Callejon Arias
Santa Fe, NM 87501, USA
Email: tlowe@cybermesa.com
The microstructural evolution with increasing equivalent strain has been compared in samples deformed to large strain by rolling, torsion, accumulative roll bonding and high pressure torsion. In all cases the evolution follows the same pattern of grain subdivision on a finer and finer scale down to boundary spacings in the range 100 – 300 nm. In parallel the misorientation angle increases giving rise to structures with low and high angle boundaries being spatially mixed. Detailed characterization of the microstructural parameters forms the basis of a flow stress analysis based on grain boundary strengthening and dislocation strengthening being linearly additive. This analysis has been validated by examining six experiments, 3 on deformed specimens and 3 on nanocrystalline specimens.
Keywords: rolling, torsion, accumulative roll bonding, high pressure torsion, deformation microstructure, flow stress
Many deformation processes are under development with a common goal to obtain metals and alloys with ultrafine microstructures and consequently high strength. Common to these processes is also the application of high strains which are introduced without significantly changing the sample dimensions during processing. However, ultrafine structures and high strength also characterize metals and alloys deformed by conventional processes. A comparison between “developing” and “established” processes is, therefore, appropriate. Such a comparison must include a qualitative and quantitative description of the structural evolution during processing based on structural parameters [1]. In the present paper such a comparison includes four processes: two representing established processes, rolling and torsion, and two representing developing processes, accumulative roll bonding (ARB) and high pressure torsion (HPT). These processes have been chosen as they represent two different strain paths. For the two rolling processes the strain path is equivalent to plane strain compression, while for torsion the strain path is equivalent to simple shear. The hydrostatic pressure for the HPT may or may not contribute to the plasticity of the process. The comparative analysis will include the microstructural evolution as a function of strain to equivalent strains in the range of 5–10 followed by an analysis of relationships between flow stress and structural parameters. Only deformation at low temperature is considered. The materials analyzed are medium to high stacking fault energy materials and alloys, especially aluminium, nickel and copper.
The microstructure of metals and alloys deformed to large strains has been treated extensively in early papers and reviews [2–4]. Since this work microscopy techniques have advanced significantly, allowing faster and more accurate structural characterization. This development has led to extensive research within the field of deformation microstructures. Within this vast area this paper shall concentrate on establishing a baseline for comparison by analyzing the microstructural evolution during rolling and torsion. In a following subsection this analysis will be extended to microstructures in ARB and HPT deformed samples.
The analysis will in general be based on the concept of grain subdivision which takes place on a macroscopic scale (or grain scale) into deformation bands and on a smaller scale into cell blocks (CBs) and cells [5–7]. The subdivision is affected by two types of dislocation boundaries: nearly planar extended boundaries and short cell boundaries. At small strains the extended boundaries are dense dislocation walls (DDWs) or double wall microbands (MBs) and at large strain the extended boundaries are lamellar boundaries (LBs) [1,6]. The DDWs, MBs and LBs have all been classified as geometrically necessary boundaries (GNBs). This classification is based on their origin and function, with GNBs accommodating the difference in glide induced lattice rotation in the neighbouring regions [8]. In contrast the cell boundaries arise from statistical trapping of dislocations and are referred to as incidental dislocation boundaries (IDBs) [8]. In the comparisons which follow the two types of dislocation boundaries will be characterized by their morphology, the misorientation angle across the boundaries and the spacing between the boundaries.
Typical deformation microstructures at medium and high strains are illustrated in Figs. 1–3. The figures show a comparable structural evolution during deformation by cold rolling [1,9] and by thin-walled tube torsion [10–12]: From a DDW/MB structure forming an angle with the rolling plane (Fig. 1a) and both parallel and inclined to the shear plane (Fig. 3a), respectively to a structure with lamellar boundaries almost parallel to these planes, Fig. 2a and Fig. 3b, respectively. The change in misorientation angle is shown for aluminium in Fig. 1b and Fig. 2b, note the many high angle boundaries in Fig. 2b. These are the original grain boundaries supplemented by a very large number of deformation induced high angle boundaries. These boundaries separate cell blocks with crystallographic orientation similar to those of the macroscopic texture components: copper (C), S, brass (B) and cube (Fig. 2c). In parallel to the observations for rolling (Fig. 2b) high angle boundaries are also induced by torsion to large strains (Fig. 4). Note in this figure as in Fig. 2b, that the large strain microstructures besides the high angle boundaries also contains a large amount of boundaries with low and medium angles. The similarity between rolling and torsion is further documented in Fig. 5 showing a power law relationship between the misorientation angle across the GNBs and the equivalent strain. Finally, similarity between rolling and torsion has also been observed when analyzing the spacing between the GNBs. This is illustrated in Fig. 6 showing the GNB spacing as function of the strain for rolling and torsion [13] and in Fig. 7 which illustrates that different spacing distributions at different strains can be reduced to a single distribution when the distributions are scaled by their average spacing. A similar scaling behaviour has been observed also to be valid in an analysis of IDB misorientation angle distributions determined in rolled specimens [14].
The comparison between the two processes is based on the structural evolution in commercial purity aluminium (99%). However, the conditions for the ARB processing [15,16] are somewhat different from the rolling process. For example, the ARB samples are deformed at 473K by heterogeneous rolling with a large ratio between contact length and sample thickness. During each ARB cycle the material is deformed 50% corresponding to an equivalent strain of εVM = 0.8. The deformation in sample thickness is from 2 mm to 1 mm and these sample dimensions are maintained through all the cycles. The microstructural evolution shows a fast formation of a lamellar structure. For example after a strain of εVM = 1.6, lamellar boundaries dominate the structure, although some regions still show DDW/MBs, inclined to the rolling plane as in Fig. 1. However, after a strain of εVM = 2.3 and higher the lamellar structure is fully developed [15–17]. An example is illustrated in Fig. 8 showing a clear resemblance with the cold-rolled structure shown in Fig. 2a. Also the reduction in the spacing between the lamellar boundaries with increasing strain is similar in ARB deformed and in rolled samples reaching about 0.25 – 0.3 μm at strains on the order of εVM = 6. A significant difference is observed in the evolution of the misorientation angle across the dislocation boundaries which is faster during the ARB processing than during rolling. Also the fraction of high angle boundaries at large strain is higher in ARB samples than in rolled samples [9, 17]. For example after a strain of about 6, two thirds of the boundaries in the ARB samples are high angle boundaries whereas in rolled samples only one third are of high angle. An explanation for this difference may be sought in the different rolling conditions and in the layers of oxide subdividing the ARB samples. This oxide layer is thin but the layers become closer and closer spaced with increasing strain. For example after a strain of 3.2 (4 cycles) the layer spacing is about 60 μm which further decreases to about 15 μm at a strain of 6.4 (8 cycles).
The comparison between the two processes is based on pure nickel (99.99%). Differences in process conditions are the hydrostatic pressure applied in HPT [18]. Another difference is the sample shape where HPT is carried out in disks whereas thin walled tubes have been used in the torsion experiment. The microstructural evolution during HPT deformation is illustrated in Fig. 9 showing typical structures after low strain (εVM = 0.53) in Fig. 9a and after high strain (εVM = 5.2) in Fig. 9b. A comparison of Fig. 9 with Fig. 3 shows a clear resemblance, with the main difference being the indication of deformation twins in the HPT samples [18]. The decrease in spacing between the lamellar boundaries with increasing strain in HPT samples is similar to that in torsion samples (Fig. 5). As to the evolution in misorientation angle with increasing strain there is no indication of a difference between the two processes.
The analysis has shown great resemblance in the microstructural evolution during the four processes. In drawing that conclusion it must, however, be kept in mind that a significant experimental and theoretical basis exist for the analyses of rolling and torsion deformed specimens. In the case of ARB and HPT the experiments are still in the exploratory phase.
Considering in more detail the microstructural evolution it follows the pattern of grain subdivision on a finer and finer scale leading at large strain to a lamellar structure, where the lamellar boundaries in rolling are almost parallel to the rolling plane (Fig. 2b and Fig. 8) and in torsion almost parallel to the shear plane (Fig. 3b and Fig. 9b). The structural refinement is quantified by the change in boundary spacing measured in given directions or as a random spacing. In the present experiment the boundary spacing has been determined perpendicular to the extended boundaries and along these boundaries to give an aspect ratio. These measurements lead to a calculation of the boundary surface area per unit volume, Sv, which is plotted in Fig. 10. Note on this Figure (i) the power law relationship between Sv and εVM, (ii) the significant finer structure in nickel than in aluminium for a given strain and (iii) the absence of an effect of the deformation mode. On Fig. 10 is also plotted a spacing taking as 3/Sv to illustrate, the very large strain required to produce structures below 50 – 100 nm on the conditions and that the power law relationship in Fig. 10 can be linearly extrapolated and that recovery and recrystallization can be suppressed. As regards the misorientation angle the database is restricted. Therefore, the change in misorientation angle as a function of strain has been limited to the angle measured across the lamellar boundaries (GNBs). These angles are given in Fig. 11 showing a power law relationship between angle and strain for cold rolling whereas the ARB samples show saturation of this angle at high strain. This difference may have several causes related to strain path, texture and content of oxide particles. However, the effect of such parameters has not yet been analyzed.
The relationship between the microstructure and the flow stress will be analyzed in general considering the behaviour of polycrystalline metals in which the building blocks are grains in the undeformed state and grains, cell blocks and cells in the deformed state. Strengthening by grain boundaries, cell block boundaries (GNBs) and cell boundaries (IDBs) must, therefore, be considered. A brief summary is given in the following.
The yield stress (τy) of a polycrystalline material is generally expressed by the Hall-Petch equation
[1]
where D is the grain size and τo and Ky are constants. This equation has been derived theoretically based on a number of different assumptions for interactions between dislocations and grain boundaries. For a review see Ref. 19.
Eq. [1] has been extended [20] to cover also the relationship between the flow stress at a given strain (σ(ε)) and the grain size. This extension led to the following relationship:
[2]
where σo(ε) and K are constants at a particular strain. In this formulation σo(ε) corresponds to the flow stress within a grain and K is related to the resistance met at the end of a slip band upon reaching the grain boundary [20]. Eq. [2] gives a good empirical description of the behaviour of many metals and alloys strained from low to medium strains. An example is given in Fig. 12 for polycrystalline copper strained in tension [21]. In Fig. 12 k(ε) is independent of the plastic strain. This is not always the case; an increase or a decrease is k(ε) with increasing strain has also been observed [19].
Note that the formulation in Eq. [2] is based on the assumption that the dislocation strengthening and boundary strengthening are linearly additive. In other formulations the flow stress is related to only one parameter the dislocation density. This density is taken as the sum of statistically stored dislocations and geometrically necessary dislocations, where the density of the latter is taken to be inverse proportional to the grain size [19]
In Eq. [2] σo(ε) reflects the flow stress of the grain interior in a deformed polycrystal. As deformed grains generally are subdivided by cell block boundaries (GNBs) and cell boundaries (IDBs), strength contributions from these two types of boundaries must be taken into account. Furthermore, dislocations lying between the boundaries may also contribute to the flow stress.
The strength contribution of the GNBs is accounted for by assuming that they have a strengthening affect which is equivalent to that of ordinary grain boundaries, thus
[3]
where DGNB is the spacing between the GNBs. However, in deformed polycrystals ordinary grain boundaries are present together with the GNBs and both types of boundaries must be accounted for. This can be done by calculating a summed contribution to the flow stress K Dav−0.5 where Dav is equal to DGNB • D/(DGNB + D). In most cases, however, DGNB is much smaller than D, i.e. Dav DGNB.
The strength contribution from the IDBs is related to their dislocation density ρIDB, which is equal to (SVρA)IDB where Sv is the boundary area per unit volume and ρA is the dislocation density per unit area of boundary. For a mixed tilt and twist wall ρA = (1.5 θ/b)IDB.
Considering the various strength contributions and assuming that such contributions are additive the flow stress can be expressed by the relationship [1].
[4]
assuming that the contribution from the original grain boundaries is negligible. In Eq. [4], σo is the friction stress, M is the Taylor factor, α is a number, b is Burgers vector and G is the shear modulus
In the following six experiments will be analysed based on the strength-structure relationships given above. First will be considered the behaviour of deformed materials, where rather detailed data are available. Then the strength-structural relations will be discussed briefly for nanocrystalline materials. For the deformed material Eq. [4] will be used whereas nanocrystalline materials will be analysed using Eq. [1] on the assumption that the only strength contribution in these materials is that of grain boundaries.
The microstructure of specimens deformed by the ARB process consists of layers of deformed aluminium separated by thin layers of aluminium oxide particles dispersed in aluminium. This material has been tensile tested both as deformed and after recrystallization [28]. In the deformed state, showing practically no elongation, the ultimate tensile strength was found to be 275 MPa, whereas in the recrystallized state the yield stress (0.2% offset) was about 50 MPa [28]. The aluminium is of commercial purity with a somewhat lower yield stress in the recrystallized state. Considering, however, that the grain size of the recrystallized ARB material is about 10 μm, it appears that the strengthening due to the oxide layers is not very pronounced, of the order of 20 MPa. The ARB aluminium can, therefore, be compared with commercial purity aluminium cold-rolled to a high reduction in thickness. The microstructure of such aluminium is similar to that of ARB deformed aluminium, i.e. the strength properties should be comparable. However, for similar strains the ultimate tensile strength of commercially pure aluminium is significantly lower than observed in the ARB deformed samples. To rationalize this difference requires further characterization especially measurement of texture and the distribution and size of second phase particles.
The microstructure of nickel deformed by high pressure torsion has a microstructure almost similar to that of nickel deformed by torsion, and nickel deformed by cold rolling. The flow stress of the latter agrees well with Eq. [4] (see (i) above) and a similar behaviour is suggested for HPT deformed nickel. This suggestion is based on the close similarity observed between cold-rolled and HPT deformed nickel. This similarity is illustrated in Fig. 13, showing the evolution in boundary spacing and in yield stress for the two deformation modes.