具次微米組織的合金目前已可由許多製程獲得，但人們對於次微米材料的機械特性的了解仍不足。本研究以AA1050純鋁以等徑轉角擠型(Equal Channel Angular Extrusion, ECAE)的方式製造，再搭配退火處理以獲得不同晶粒之組織，其晶粒範圍從0.35 ~ 45 um. 對於晶粒尺寸、測試溫度及晶界特性分佈有深入的探討。
簡言之，具次微米材料的機械性質是不同於粗晶的。對於拉伸性質，次微米晶鋁於室溫測試時，展現出降服下降接著就加工軟化；而於77K測試時，卻出現陸德氏變形及加工硬化。此外，次微米晶鋁也展現出拉伸壓縮不對稱性，平均上壓縮的降服強度約高於拉伸20%左右。於77K下拉伸測試的強度與延展性皆高於室溫的測試結果。對此現象主要是歸咎於低溫測試時，材料具有較高的加工硬化率。此外，本研究也發現到次微米晶鋁的Hall-Petch斜率遠高於粗晶的外插值，這是因為次微米材料展現不均勻變形所致。而晶界特性也對機械性質有所影響。
當晶粒長至1 ~ 4 um，拉伸試驗出現陸德氏變形及加工硬化。而當晶粒尺寸大於4 mm時，機械性質便恢復正常。

It has been shown that alloys with submicron-grained structure can be produced by severe plastic deformation (SPD). However, our understanding about the characteristics of mechanical behaviors of these materials is still limited. According to the literature, many alloys exhibit quite different mechanical properties as the grain size decreasing to submicrometer range. In this study, commercial purity aluminum (AA1050) of grain size ranging from 0.35 to ~ 45 mm was obtained by the proper combination of equal-channel angular extrusion (ECAE) and annealing treatment. The influences of grain size, testing temperature and boundary character on the mechanical properties were studied in this work.
Generally speaking, the materials of grain sizes below 1mm have quite different mechanical properties than those of coarser grain sizes. In tensile tests, they exhibited yield drop immediately followed by work softening at RT, while they showed Lüders extension followed by work hardening at 77K. In addition, their yield strength at RT was about 20% higher in compression than in tension. The submicron-grained aluminum has much higher strength but lower tensile ductility than large grained aluminum at room temperature, while it exhibits both high strength and good ductility at 77K. This finding suggests that the poor tensile ductility of submicron-grained alloys at room temperature may be improved by reducing the dynamic recovery rate.
The Hall-Petch slope in the submicrometer grain size range showed positive deviation from that extended from coarser grains at both room temperature and 77K. This might be arisen from the phenomenon of inhomogeneous yielding as grain size below 1 mm. In addition, the grain boundary character distribution was found to have influence on the tensile properties of matrials of submicrometer grain sizes.
As the grain size increases to the range between 1 mm and 4 mm, the tensile deformation at RT proceeds by the propagation of Lüders band initially, and followed by strain hardening. For materials of grain sizes greater than 4 mm, a normal strain hardening behavior of coarse-grained aluminum resumes.

CONTENTS

CONTENTS ………………………………………………………………….. i
List of Tables ………………………………………………………………….. iii
List of Figures ………………………………………………………………….. iv
Abstract ………………………………………………………………….. xiii
中文提要 ………………………………………………………………….. xv
Acknowledge ………………………………………………………………….. xvi

Chapter I Introduction ………………………………………………………. 1

Chapter II Literature Review
2.1 The Hall-Petch relation………………………………………………………. 3
2.1.1 Extension of the Hall-Petch relation to ultra-fine grain size……….. 4
2.1.2 Explanations of the deviation of the Hall-Petch relation at submicron grain sizes………………………………………………. 5
2.2 Characteristics of grain boundary……………………………………………. 8
2.3 Mechanical properties of ultrafine-grained materials………………………... 9
2.3.1 Discontinuous yielding phenomenon………………………………. 9
2.3.2 Lüders deformation…………………………………………………. 11
2.3.3 Poor Ductility of ultrafine-grained alloys…………………………... 12
2.3.4 Shear banding behavior…………………………………………….. 14
2.4 Fabrication of ultrafine-grained materials…………………………………… 16
2.5 Annealing of severely deformed metals……………………………………... 18

Chapter III Experimental
3.1 Materials……………………………………………………………………... 20
3.2 Mechanical tests……………………………………………………………... 20
3.2.1 Microhardness measurement……………………………………….. 20
3.2.2 Tensile test………………………………………………………….. 21
3.2.3 Compressive test……………………………………………………. 21
3.2.4 Microscopic observations of deformed specimens…………………. 21
3.3 Microstructure analysis……………………………………………………… 22
3.3.1 Transmission electron microscopy…………………………………. 22
3.3.2 Boundary character analyses……………………………………….. 22
3.3.2 Size and size distribution measurement…………………………… 23


Chapter IV Results
4.1 Annealing behaviors of ECAE aluminum…………………………………… 25
4.1.1 Initial microstructure……………………………………………….. 25
4.1.2 Isochronal annealing………………………………………………... 25
4.1.3 Isothermal annealing………………………………………………... 28
4.1.4 Evolution of texture and boundary misorientation…………………. 29
4.1.5 Summary of annealed structure…………………………………….. 29
4.2 Tensile deformation at room temperature……………………………………. 30
4.2.1 General characteristics……………………………………………… 30
4.2.2 Relationship between tensile properties and grain size……… … 33
4.2.3 Microstructure observations after tensile deformation at RT………. 35
4.2.4 Summary…………………………………………………………… 36
4.3 Tensile deformation at 77K………………………………………………….. 37
4.3.1 General characteristics……………………………………………… 37
4.3.2 Relationship between tensile properties and grain size……..……… 39
4.3.3 Microstructure observations after tensile deformation at 77K……... 40
4.3.4 Summary…………………………………………………………… 40
4.4 Compressive deformation at room temperature……………………………... 41
4.5 The influence of boundary character distribution on mechanical properties... 42

Chapter V Discussions
5.1 Yielding……………………………………………………………………… 45
5.2 Grain size dependence of yield stress and flow stress………………………. 45
5.3 Work hardening behavior of ultrafine-grained aluminum…………………… 49
5.4 Tension-Compression asymmetry…………………………………………… 50
5.5 General characteristics of ultrafine-grained alloys…………………………... 52

Chapter VI Conclusions ………..……………………………………………. 53

References ……………………………………………………………………. 55

Appendix A …….………………………………………………………………. 64
Appendix B …………………………………………………………………….. 65




List of Tables
Table 2-1 Dependences of the fraction of special boundaries, parameter ky, and the Lüders strain on the grain size obtained after recrystallization annealing for 1 hr (Wyrzykowski et al. 1986)…………………………………….66

Table 3-1 Chemical composition of AA1050 aluminum………………………....66

Table 4-1 Microstructure characteristics of all measured grains in specimens processed by various annealing treatments (X and Y plane)…………..67

Table 4-2 Tensile properties obtained at room temperature for different grain sizes…………………………………………………………………….68

Table 4-3 Tensile properties obtained at 77 K for different grain sizes…………..68

Table 5-1 Hall-Petch parameters obtained at RT and 77K.……………………….69

Table 5-2 Summary of tensile and compressive properties.……………………...69

Table 5-3 Characteristics of the tensile behavior of submicron-grained alloys…..69




List of Figures
Figure 2-1 Variation in Vickers microhardness with d-1/2 for nanocrystalline Cu and Pd produced by insert gas method, showing negative slope of Hall-Petch relation (Chokshi et al. 1989)…………………………………...……..70

Figure 2-2 Variation in Vickers microhardness with d-1/2 for Al-3%Mg produced by torsion straining, showing possible division into distinct regions (Furukawa et al. 1996).…………………………….…………………..70

Figure 2-3 Yield stress dependence on both grain and cell size for pure Ni (Thompson 1975).……………………………………………………...71

Figure 2-4 Tensile flow stress plotted against d-1/2 (Lloyd 1980).………...…….…71

Figure 2-5 Sequence of stages in polycrystalline deformation, starting with (a, b) localized plastic flow in the grain regions (microyielding), forming a grain-boundary work hardening layer (c, d) that effectively reinforces the microstructure, and leading to (e, f) macroyielding in which the bulk of the grains undergo plastic deformation (Meyers and Ashworth 1982).……………………….………………………………………….72

Figure 2-6 Polycrystalline aggregate viewed as composite material composed of bulk and grain-boundary material, with flow stresses stB and stGB respectively (Meyers and Ashworth 1982).………………….………...72

Figure 2-7 Combined Hall-Petch response and Coble creep. The critical d* where transition occurs is denoted by dashed line (Masumura et al. 1998).…………………………………………………………………..73

Figure 2-8 Change in frequency of the grain boundary character as a function of individual grain size (Matsumoto et al. 1995).………………….……..74

Figure 2-9 The effect of the temperature on the changes of ky. The symbols G and S were mean the general boundary and the special boundary (Wyrzykowkski et al. 1986).…………………………………………...74

Figure 2-10 (a) Schematic stress-strain curve of a typical metal or alloy; (b) schematic stress-strain curve showing a yield point (Hull 1975)……...75
Figure 2-11 Stress-strain curves of the commercial purity aluminum specimens with various grain sizes, which were ARB-processed by 6 cycles at 473K and annealed for 30 min at various temperatures. The annealing temperatures and the resulted grain sizes indicated in the figure (Tsuji et al. 2000).…………………………………………………………………..75

Figure 2-12 Shear produced by the passage of parallel dislocations (Meyers et al.1984).………………………………………………………………..76

Figure 2-13 Effect of initial density of mobile dislocations on the yield point (Hull 1975).…………………………………………………………………..76

Figure 2-14 A typical microstructure of a Lüders band front is shown in (a), taken from a specimen of circular cross section. The stress axis is vertical, the upper portion is undeformed, and the lower portion has been deformed. An enlarge view is given in (b) (Ananthan et al. 1987)…………………………………………………………………...77

Figure 2-15 The influence of grain size on the true uniform elongation of two low-carbon steels (Morrison 1966).……………………………………78

Figure 2-16 The relationship between the K/S and n are according to the equation [2-11]. Materials with a K/S value which lies above the curve exhibits normal work hardening behavior, but it is plastically unstable during Lüders deformation if the K/S value is below the curve (Morrison et al. 1970)……………………………………….…………………………..78

Figure 2-17 Load-elongation curves of a low-carbon steel at four grain sizes (Morrison et al. 1970).…………………………………………….…...79

Figure 2-18 Torsion flow stress and work hardening rate against strain (Lloyd 1980).…………………………………………………………….…….79

Figure 2-19 Optical micrograph of nanostructured Fe-10 pct Cu alloy shows the development of the shear bands under compression test. The compression axis was vertical (Carsley et al. 1998).……….………….80

Figure 2-20 Optical micrograph of nanostructured Fe shows the development of the shear bands under compression test at plastic strain of 3.7%. The compression axis was vertical (Wei et al. 2002).………………………80

Figure 2-21 Schematic illustration of the principle of the equal channel angular extrusion (ECAE), showing the X, Y, and Z planes (Nakashima et al. 2000).…………………………………………………………………..81

Figure 2-22 Schematic illustration of different routes used for ECAE (Iwahashi et al. 1998c).…………………………………………………………………82

Figure 3-1 The geometry of the tensile specimens.………………………………..83

Figure 3-2 The geometry of the compression specimen.…………………………..83

Figure 3-3 (a) Three non-parallel Kikuchi bands from the reflecting planes intercept at points A, B, C. The distance from O to the points A, B, C correspond to the angles between the beam direction and three zone axes. (b) Three reflecting planes in the specimen with traces AB, AC, and BC around the direct beam, O……………………………………………………...84

Figure 3-4 A schematic representation of EBSD specimen placement in an SEM showing the sample inclined at 70o to the beam. The Kikuchi patterns are observed on a phosphor screen which is viewed by a low-light camera.…………………………………………………………………85

Figure 4-1 Microstructure of aluminum deformed to e~8 at RT by ECAE route Bc, (a) X-plane and (b) Y-plane.…………………………………………...86

Figure 4-2 Cumulative distribution of boundary misorientation of specimens processed by ECAE route Bc and different annealing treatment. The distribution of random grain assembly given by Mackenzie (1958) is included for comparison.………………………………………………87

Figure 4-3 Typical microstructure of X-plane of specimens annealed at a range of 373K ~ 773K, (a) 373K (TEM), (b) 473K (TEM), (c) 523K (TEM), (d) 573K (SEM), and (e) 773K (SEM)…………………………………….88

Figure 4-4 The variation of mean grain size, <d>, and aspect ratio, R, is shown as function of the annealing temperature. The annealing time was one hour at each temperature…………………………………………………….91

Figure 4-5 Variation in Vickers microhardness with annealing temperature for route Bc.……………………………………………………………………...91

Figure 4-6 The distribution of grain size on X-plane for selected annealing conditions, (a) 473K-1h (TEM), (b) 548K-1h (TEM), (c) 573K-1h (SEM), and (d) 673K-1h (SEM).………………………………….…...92

Figure 4-7 The kinetics of grain growth is illustrated by plotting log(<d2> - <do2>) versus 1/T. It also shows a discontinuous transition from low-temperature behavior (regime I) to high-temperature behavior (regime II) at ~548 K…………………………………………………..94

Figure 4-8 Typical microstructures of X plane of specimens annealed at 523K for various times, (a) 1h (TEM), (b) 4h (TEM), (c) 8h (TEM), (d) 24h (TEM), and (e) 96h (SEM)…………………………………………….95

Figure 4-9 Typical microstructures of Y- plane of specimens annealed at 523K for various times, (a) 1h (TEM), (b) 4h (TEM), (c) 24h (TEM), and (d) 48h (TEM).…………………………………………………………………98

Figure 4-10 The distribution of grain size on X-plane for selected annealing conditions, (a) 1h (TEM), (b) 4h (TEM), (c) 48h (TEM), and (d) 96h (SEM).………..……………………………………………………....100

Figure 4-11 The mean grain size <d> is plotted against annealing time at 523 K. It shows a grain growth exponent consistent with normal grain growth. The <d> value of the as-ECAE specimen is taken as <do>…………………………………………………………..……….102

Figure 4-12 (111) Pole figures of (a) as-ECAE, (b) 523K-48h and, (c) 573K-12h specimens. The interval of the contour in the pole figure is 1 x random.……………………………………………………………….103

Figure 4-13 Four different characteristic types of tensile s-e curves……………...104

Figure 4-14 The tensile s-e curves for grain sizes smaller than 0.4 mm show Type I characteristics at RT…………………………………………………..105

Figure 4-15 Optical micrograph of the surface of a specimen (d=0.35 mm) after tensile testing to failure at RT. It shows the typical tensile failure appearance of specimens exhibiting the Type I s-e behavior.…….….106

Figure 4-16 The tensile s-e curves for grain sizes between 0.4 to 1 mm show Type II characteristics at RT.………………………………………………….107

Figure 4-17 Optical micrograph of the surface of a specimen (d=0.78 mm) tensile deformed at RT to, (a) e = 0.015, and (b) e = 0.035 (strain rate = 7.1×10-6 s-1). An enlarger view is given in (c) to show the evolution of fine shear bands in the necked region in (a) and (b)………………….108

Figure 4-18 Optical micrograph of the surface of a specimen (a) d=0.59 mm, (b) d=0.78 mm after tensile testing to failure at RT………………………110

Figure 4-19 SEM observations of the surface of the necked region in a specimen (d=0.59 mm) after tensile test at RT…………………….…………….111

Figure 4-20 The change of relative height across the shear band on the surface of the specimen of d= 0.59 mm after tensile tested at RT.…………………...112

Figure 4-21 The tensile s-e curves for grain sizes between 1 to 4 mm show Type III characteristics at RT.…………………………………………….……113

Figure 4-22 Optical micrograph of the surface of a specimen (d=2.5 mm) after tensile testing to failure at RT.………………………………………..………114

Figure 4-23 SEM observations of the surface of a specimen (d=2.5 mm) after tensile testing to failure at RT. ……………………………....…………...…..114
Figure 4-24 The optical micrograph of the cross section of a specimen (d = 1.72 mm) after tensile testing at RT.…………………………………….……….115

Figure 4-25 The change of relative height across the microscopic shear band on the surface of the specimen of d= 3.6 mm after tensile tested at RT……...116
Figure 4-26 The tensile s-e curves for grain sizes larger than 4 mm show Type IV characteristics at RT…………………………………………………..117

Figure 4-27 Optical micrograph of the surface of a specimen (d=45 mm) after tensile testing to failure at RT.………………………………………………..118

Figure 4-28 The 0.2% offset yield stress and proportional limit plotted against d-1/2.…………………………………………………………..……….119

Figure 4-29 The Vickers microhardness plotted against d-1/2. It results in Ho = 18 Hv and kH = 23 Hvmm1/2 for grain sizes greater than 1 mm………………120

Figure 4-30 Grain size dependence of ductility at RT.…………………………….120

Figure 4-31 Typical fracture surfaces after tensile testing at RT. (a) d=0.35 mm, (b) d=0.59 mm, (c) d=1.72 mm, and (d) d=45 mm.………………………..121

Figure 4-32 L&uuml;ders strain plotted against the inverse grain size at RT.……………121

Figure 4-33 TEM micrographs showing the microstructures in specimen of grain size (1.72 mm) deformed by tensile test at RT (eu~15%), (a) dislocation cell structures formation, (b) dislocations tangled in grain interior.………………………………………………………………..122

Figure 4-34 TEM micrographs showing the microstructures in specimen of grain size (0.78 mm) deformed by tensile test at RT (eu~0.6%), (a) dislocation-free grains, and (b) the deformed structures.……………………………...123

Figure 4-35 TEM micrographs showing the dislocations concentrated nearly boundaries in specimen of grain size (0.78 mm) deformed by tensile test at RT (eu~0.6%), (a) boundaries without misorientation measurement, and (b) boundaries with misorientation measurement.…………………………………………………………124

Figure 4-36 TEM micrograph showing the microstructures in specimen of grain size (0.78 mm) deformed by tensile test at RT (eu~0.6%). It shows the grain boundaries exhibited “spotty” contrast.………………………………125

Figure 4-37 The tensile s-e curves for grain size of 0.35 mm show Type II characteristics at 77K.………………………………………………...126

Figure 4-38 Optical micrograph of the surface of a specimen (d=0.35 mm) after tensile testing to failure at 77K.………………………………………126

Figure 4-39 The tensile s-e curves for grain sizes between 0.4 to 1 mm show Type III characteristics at 77K.………………………………………………...127

Figure 4-40 Optical micrograph of the surface of a specimen (d=0.59 mm) tensile deformed at 77K to, (a) e = 0.07, showing the L&uuml;ders band, which propagates partly through the specimen gauge length, actually consists of uniformly distributed microscopic shear bands, and (b) e = 0.5.…………………………………………………….……………...128

Figure 4-41 The change of relative height across the microscopic shear band on the surface of the specimen of d= 0.78 mm after tensile tested at 77K……………………………………………………………………129

Figure 4-42 The tensile s-e curves for grain sizes larger than 1 mm show Type IV characteristics at 77K.………………………………………………...130

Figure 4-43 Optical micrograph of the surface of a specimen (d=45 mm) after tensile testing to failure at 77K.……………………………………………...130

Figure 4-44 The 0.2% offset yield stress and proportional limit plotted against d-1/2 (77K).…………………………………………………………………131

Figure 4-45 Grain size dependence of tensile ductility at 77K……………………132

Figure 4-46 Typical fracture surfaces after tensile testing at 77K. (a) d=0.35 mm, (b) d=0.59 mm, and (c) d=45 mm.…………………………….…………..132

Figure 4-47 L&uuml;ders strain plotted against the inverse grain size at 77K…………..133

Figure 4-48 TEM micrographs of a specimen (d=0.47 mm) after tensile testing to failure at 77K (eu~24%), (a) dislocations tangled in grain interior, and (b) an enlarge micrograph.…………………………………………....134
Figure 4-49 The micrograph of a specimen (d= 0.47 mm) shows the cell structures formed in grain interior.………………………………………………135

Figure 4-50 Compressive s-e curves obtained at RT. It shows the typical compressive s-e curves as grain size < 1 mm, which exhibit nearly constant flow stress after very small plastic strain…………………...136

Figure 4-51 Compressive deformation behavior of submicron-grained aluminum. (a) Shear bands with 45o ~ 55o respect to compressive axis (CA). Traces of shear bands incline to CA are straight. Traces of shear bands nearly perpendicular to CA are wavy along the trace. (b) Shear offset at edge of specimen.……………………….…………………………………….137

Figure 4-52 The SEI image of compressive tested specimen, showing the shear bands (a) and shear offsets (b) on the specimen surface.………….….139

Figure 4-53 TEM micrographs showing the microstructures in specimen of grain size (0.59 mm) deformed by compressive test at RT (e~3%), (a) deformed region, which exhibits banded structure, and an enlarger view is given in (b), and (c) undeformed region.………………………………………140

Figure 4-54 Cumulative distribution of boundary misorientation of specimens processed by ECAE route Bc and C.…………………………………142

Figure 4-55 Typical microstructures of X plane of specimens annealed at 523K for various times, (a) As-ECAE (route C, TEM), (b) 523K-1h (TEM), and (c) 523K-4hr (TEM).…………………………………………………143
Figure 4-56 The distribution of grain size on X-plane for selected annealing conditions, (a) as-ECAE (TEM), (b) 523K-1h (TEM), (c) 573K-4h (TEM)………………………………………………………………...145

Figure 5-57 The tensile s-e curves for grain sizes between 0.7 to 1 mm show Type II characteristics at RT. The dashed-lines are the results of route C and solid-lines are the results of route Bc.………………………………...147

Figure 4-58 Optical micrograph of the surface of a specimen (d=0.85 mm) after tensile testing to failure at RT.………………………………………..147
Figure 5-1 Tensile behavior at 77K represented by s (e) = si + Cen, where the dashed-lines are the fitting results and solid-lines are the experimental results……………………………………………….………………...148

Figure 5-2 Yield stress plotted against d-1/2. The solid symbol is the experimental data and the open symbol is the fitting data………………..…………148

Figure 5-3 Tensile flow stress plotted against d-1/2, (a) RT, and (b) 77K. See text for detail discussion. The solid symbol is the experimental data and the open symbol is the fitting data…………………………………...…………149
Figure 5-4 Compressive s-e curves obtained at RT. It shows slightly strain softening after very small plastic strain as grain size < 1 mm………...150
Figure 5-5 Yield stress plotted against d-1/2. The solid symbol is the compressive yield stress and the open symbol is the tensile yield stress……….….150

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