臺灣博碩士論文加值系統

晶體材料於塑性變形後所產生之異向性（anisotropic）效應，該異向性效應對於材料的機械性質及在熱處理所發生的再結晶現象有相當重要的影響。因此，有許多學者針對塑性變形所產生之異向性效應進行實驗及理論研究。以往藉由有限元素法電腦模擬軟體之輔助將變形後材料的形變量及應變量視覺化，以達到預測結果以及節省成本之目的。但傳統的有限元素法並未考慮晶體結構固有的異向性特性，以及晶界（grain boundary）與三晶節點（triple junction）在塑性變形過程中所扮演的角色。

為了建立考慮晶體微組織的晶體塑性變形理論，本研究將針對晶體微組織的影響進行實驗及電腦模擬的探討。模擬以有限元素法為基礎，並將單晶晶體之塑性變形理論納入考量，以期望晶體塑性有限元素法（crystal plastic finite element method，CPFEM）之模擬結果能夠顯示出晶體材料於塑性變形後所產生之異向性效應，使晶體的塑性變形過程更符合其實際之情況；藉著電子背向散射衍射技術（Electron Back Scattering Diffraction，EBSD）分析變形前後晶體取向及OIM（Orientation Image Mapping）可觀察晶體變形前後之轉動；此外，搭配本實驗室自行開發之數位影像相關係數法（Digital Image Correlation Method，DIC）測量系統所顯示之微應變分佈，可顯示出顯微結構（晶界與三晶節點）在塑性變形中對各組成晶粒應變量之影響。

Deformation heterogeneity at the mesoscale plays a central role at understanding the Hall-Petch relationship, strain hardening, and recrystallization. This heterogeneity is not predicted by the classical theory of Taylor model in which the features of crystallographic texture are explained. In past, crystal plasticity finite-element (CPFEM) simulations were used in modeling polycrystalline plasticity by considering both compatibility of strain and stress at interfaces. However, the effects of the microstrcutre features, such as grain boundaries and triple junctions, are not still well established on plastic deformation. Therefore, the purpose of this investigation is to understand the interaction between microstructure and plane strain compression.

In this study, experimental and numerical approaches are investigated on the influence of grain boundary and the triple junction during plane strain compression. In the experimental approaches, electron back scattering diffraction (EBSD) and Digital Image Correlation method (DIC) were used to characterize the orientation image mapping and the strain distribution, respectively. With the help of the orientation and strain mappings, the effects of grain boundary and triple junction during deformation can be compared with the results predicted from CPFEM. The results of the systematic analysis are able to contribute the further development of crystal plasticity including the microstructure influence.

中文摘要 I
英文摘要 III
誌謝 IV
目錄 V
表目錄 VIII
圖目錄 IX

第一章、前言 ...........................................01
第二章、文獻回顧與基礎理論 .............................03
2.1 晶體塑性變形理論 ..................................03
2.2 背向散射電子繞射 ..................................03
2.3 有限元素法 ........................................11
2.3.1 平衡方程式 ......................................11
2.3.2 元素種類 ........................................12
2.3.3 位移矩陣 ........................................12
2.3.4 勁度矩陣 ........................................16
2.4 晶體塑性有限元素法 ................................19
2.4.1 彈性模數 ........................................20
2.4.2 Schmid Law ......................................23
2.4.3 變形梯度與速度梯度 ..............................23
2.4.4 流變法則 ........................................27
2.4.5 加工硬化定律 ....................................28
第三章、實驗材料與實驗方法 .............................36
3.1 晶體製備 ..........................................36
3.2 實驗材料 ..........................................38
3.3 實驗方法 ..........................................38
3.3.1 平面壓縮變形 ....................................38
3.3.2 微應變分析 ......................................39
3.3.3 Orientation Image Mapping .......................39
3.4 以CPFEM模擬塑性變形 ...............................40
3.5 實驗流程 ..........................................41
第四章、結果 ...........................................48
4.1 實驗結果 ..........................................48
4.1.1 微應變分析 ......................................48
4.1.2 EBSD分析 ........................................49
4.2 模擬結果 ..........................................53
4.2.1 單晶塑性變形 ....................................53
4.2.2 雙晶塑性變行 ....................................54
4.2.3 三晶塑性變形 ....................................55
第五章、討論 ...........................................72
5.1 雙晶晶界對塑性變形之影響 ..........................72
5.2 三晶節點對塑性變形之影響 ..........................74
第六章、結論 ...........................................78
參考文獻 ...............................................80

附錄I、金屬之固化 ......................................86
I.1 由液相中的晶體生長 ................................86
I.1 成核與成長 ........................................89
附錄II、數位影像相關係數法 .............................94
II.1 位移量之計算 .....................................94
II.2 應變場之計算 .....................................95

[1] Meyers, M.A.,Mishra, A.,Benson, D.J. : Mechanical properties of nano-crystalline materials, In: Progress in Materials Science, 51 (2006), pp427-556.

[2] 郭瑞昭, 童士��, 施明祥, 陳志慶 : 數位光學測量於固體材料 變形分析之應用, 九十四年電子計算機於土木水利應用研討會.

[3] Bickford, B. W. ：A First Course in the Finite Element Method, Burr Ridge, Richard D. Irwin,1989.

[4] Clough, R. W. ：The Finite Element Method in Plane Stress Analysis, Proceedings of American Society of Civil Engineerings, 2nd Conference on Electrionic Computations, Vol. 23, Pittsburgh,1960,pp.345-378

[5] Hrennikoff, A. ：Solution of Problems in Elasticity by the Framework Method, J.Appl.Mech.,Vol.8,No.4,New York,1941,pp.A169-A175.

[6] Zienkiewicz, O. C. ：The Finite Element Method, 3rd. edu., McGraw-Hill,London,1979.

[7] Kuo, J.C., Zaefferer, S., Zhao, Z., Winning, M., Raabe,D. : Deformation Behavior of Aluminum Bicrystals. In: Advanced Engineering Materials, 5 (2003), P.563~567.

[8] Zaefferer, S., Kuo, J.C., Zhao, Z., Winning, M., Raabe, D. : On the influence of the grain boundary misorientation on the plastic deformation of aluminum bicrystals. In: Acta Materialia, 51 (2003), P.4719~4735.

[9] Kuo, J.C. : Mikrostrukturmechanik von Bikristallen mit Kippkorngrenzen (Microstructure Mechanics of Aluminium-Bicrystals with symmetrical tilt boundaries), RWTH Aachen, PhD Dissertation in German , 2004.

[10] Harren, S.V., Deve, H.E., Asaro, R.J. : Shear band formation in plane strain compression, In: Acta metal, 36 (1988), P.2435.

[11] Becker, R.: Analysis of texture evolution in channel-die compression I : Effects of grain interaction. In: Acta metall. mater., 39 (1991), P.1211~1230.

[12] Kalidindi, D.A., Bronkhorst, C.A., Anand, L. : Crysyallographic texture evolution in bluk deformation processing of f.c.c metal. In: J. Mech. Phys. Solids, 40 (1992), P.536~569.

[13] Tatshl, A., Kolednik, O. : On the experimental characterization of crystal plasticity in polycrystals. In: materials science & engineering A, 356 (2003), P.447~463.

[14]Kocks, U.F. ：Constitutive behavior based on crystal plasticity, in：Constitutive Equations for Creep and Plasticity（Ed. A.K. Miller）, Elsevier Appl. Sci., London,1987,pp.1-88.

[15] Taylor, G.I. : Analysis of plastic strain in cubic crystal., 1938.

[16] Hill, R., Rice, J.R. :Constitutive analysisnof elastic-plastic crystalsnat arbitary strain, In: J. Mech. Phys., 20 (1972), P.401~413.

[17] Schoenfeld,S.E, Asaro, R.J. : Through thickness texture gradients in rolled polycrystalline alloys, In: J. Mech. SCi., 38 (1996), P.661~683.

[18] Peirce, D.,Asaro, R.J.,Needleman, A. : An analysis of nonuniform and localized deformation in ductile single crystals, In: Acta metal, 30(1982), P.1087~1119.

[19] Alam, M. N., Blackman, M., Pashley, D. W. High angle Kikuchi patterns/ Proc. Royal Society of London, 1954.

[20] Venables, J. A., Harland, C. J./ Electron backscattering patterns–a new technique for obtaining crystallographic information in the scanning electron microscope/ Phil. Mag., 27, 1193–1200, 1973.

[21] Dingley, D. J.: On-line determination of crystal orientation and texture determination in an SEM/ Proc. Royal Microsc. Soc. 19, 74–75 (1984).

[22] Krieger-Lassen, N. C.: Automated determination of crystal orientations from electron backscattering patterns, Ph. D. Thesis, Danmarks Tekniske Universitet, Lyngby (1994).

[23] Schwartz, A. J., Kumar, M. and Adams, B. L. (eds.): Electron Backscatter Diffraction in Material Science. Kluwer Acad./Plenum Publ., New York 2000.

[24] Dingley, D. J.: Progressive steps in the development of electron backscatter diffraction and orientation imaging microscopy, Journal of Microscopy, 213, 214–224, 2004.

[25] Humphreys, F.J.: Grain and subgrain characterisation by electron backscatter diffraction, Journal of Material Science, 36, 3833–3854, 2001.

[26] Goehner, R. P., Michael J. R./ Phase Identification in a Scanning Electron Microscope Using Backscattered Electron Kikuchi Patterns/ Journal of Research of the National Institute of Standards and Technology, 101(3), 301-308, 1996.

[27] Quested, P. N., Henderson P. J., McLean M./ Observations of deformation and fracture heterogeneities in a nickel-base superalloy using electron back scattering patterns/ Acta Metallurgica, 36(10), 2743-2752, 1988.

[28] Wilkinson, A. J., Dingley, D. J./ Quantitative deformation studies using electron back scatter patterns/ Acta Metallurgica, 39(12), 3047-3055, 1991.

[29]Cook, R. D., Malkus, D.S., and Plesha, M. E.:Concepts and Applications of Finite Element Analysis, 4th ed., John Wiley and sons, New York, 2002.

[30]Carslaw, H. S. and Jaeger, J.C.:Conduction of heat in solids, Oxford University Press, Oxford, 1959.

[31]Timoshenko, S. P. and Goodier, J. N.:Theory of elasticity, 3rd ed, McGraw-Hill, New York, 1970.

[32]Hinton, E.:Introduction to non-linear finite element analysis, NAFEMS, Glasgow, 1992.

[33]Becker, A. A.: Understanding non-linear finite element analysis, NAFEMS, Glasgow, 2001.

[34]Y.C. Fung, Foundations of Solid Mechanics, Prentice Hall, Englewood Cliffs, NJ, 1965.

[35] Kelly, A., Groves, G.W.:Crystallography and crystal defects, Addison-Wesley, 1970.

[36] Teodosiu, C. , Sidoroff, F. : A theory of finite elatstoviscoplasticity of single crystals. In: J. Eng. Sci., 14 (1976), P.165~176.

[37]Asaro, R. J. and Needleman, A. Acta metal. 33, 923, 1985

[38] 張玉龍, 唐磊 : 人工晶體—生長技術、性能與應用, 化學工業出版社, 北京, 2005.

[39] 薛至廷, “摩擦力對純鋁雙晶受平面壓縮應變的影響區之探討”,國立成功大學材料科學及工程學系, 碩士論文, 2006.

[40]洪智梧, “晶界對晶體塑性變形之影響”,國立成功大學材料科學及工程學系, 學士論文, 2006.

[41] 陳志慶, “奈米鋁材料塑性行為之探討”,國立成功大學材料科學及工程學系, 碩士論文, 2006.

[42] Wan, J.; Yue, Z., Non-uniform Stress Field and Stress Concentration Induced by Grain Boundary and Triple Junction of Tricrystal.Journal of Materials Science and Technology., 19 (2003),P.303~308.

[43] Kobayashi, S.; Tsurekawa, S.; Watanabe, T., Grain boundary hardening and triple junction hardening in polycrystalline molybdenum. Acta Materialia., 53 (2005), P.1051~1057.

[44] Jian-song, W.; Zhu-feng, Y., Stress distribution near grain boundary in anisotropic bicrystals and tricrystals. Applied Mathematics and Mechanics., 25 (2004), P.39~46.

[45]Reza Abbaschian, Robert. E. Reed-Hill,:Physical Metallurgy Principles, 3rd ed, PWS-Kent Pub, Boston, 1992.

[46] Chen, C. R.; Li, S. X.; Wen, J. L.; Jia, W. P., Finite element analysis about effects of stiffness distribution on stresses and elastic strain energy near the triple junction in a tricrystal. Materials Science and Engineering A., 282, (2000), P.170~176.

[47] 楊慧德, ：物理冶金學, 第四版, 鼎茂發行, 2003.

[48]盧彥羽, “以光學量測微應變探討巨觀壓痕之異向性”, 國立成功大學材料科學及工程學系, 碩士論文, 2006.

[49] Chu, T.C., Ranson, W.F., Sutton, M.A. and Peters, W.H., Application of Digital-Image-Correlation Techniques to Experimental Mechanics. Experimental Mechanics 25(1985), p.232-244.

[50] Russell, S.S. and Sutton, M.A., Strain field analysis acquired through correlation of x-ray radiography of a fiber reinforced composite laminate. Experimental Mechanics 29(1989), p.237-240.