臺灣博碩士論文加值系統

鋯合金是核能電廠燃料護套所使用的管材材料。鋯管會因運轉過程而產生吸氫作用，在到達一定臨界值後，會發生氫脆化效應。逐漸在鋯管外圍析出一層氫化鋯，造成延展性降低，影響核能電廠的結構安全與可靠性。以往進行氫含量檢測大多使用破壞性檢測法，如熱真空提煉法(Hot vacuum extraction)、鈍氣融合法(Inert gas fusion)和金相觀察法。這些方法雖可得到鋯管護套中的氫含量，但同時也會破壞材料本身結構並耗費大量的金錢和時間。
超音波技術能反應鋯管中氫含量多寡於頻散關係變化中。過去研究中，曾探討過均勻氫分布的鋯管頻散關係。然而，在外圍析出氫化鋯的鋯管，其研究則較為複雜。因為鋯管內層為鋯合金，外層為氫化鋯，可看成是雙層複合材料圓管。所以，本研究即在探討雙層管的理論頻散關係模態，以利檢測具有氫析出物的鋯合金護套之氫含量多寡。
理論和實驗分為兩階段探討，分別為單層圓管和雙層圓管之研究。單層圓管的理論利用Gazis推導出頻散曲線的特徵方程式，並以數值解求得相位速度頻散曲線。雙層圓管的理論模型模擬則利用由Armenakas的雙層複合材料圓管之模型，探討軸對稱與非軸對稱導波的頻散特性。同時本研究亦使用非接觸性之雷射超音波技術，量測具有氫析出物的鋯管之頻散關係。研究結果顯示理論和實驗相吻合，並可利用雷射超音波技術正確量測鋯合金護套之頻散關係。

Zircaloy material often been used in fuel cladding of nuclear power station. When the operation time, it will produce “hydrogen absorbed” in Zircaloy tubes. When reaching the threshold limit value, hydrogen embrittlement will be happened. It will precipitate a layer of ZrH2 on the outer surface of Zircaloy tubes. The hydrogen embrittlement reduces the ductility of Zircaloy tubes. It will influence the structure reliable in nuclear power station. In the past, we detected the hydrogen concentration of Zircaloy tubes by destructive method, for example, hot vacuum extraction method, inert gas fusion method and SEM method. However, these techniques require destructive inspection and cost a lot of money and time, too.
Ultrasonic technique can appear the hydrogen concentration of Zircaloy tubes in the dispersion cuves. In the past studies, they ever researched the dispersion relations of uniform distributed hydrogen in Zircaloy tubes. However, It is more complex that precipitating ZrH2 on the outer surface of Zircaloy tubes. It can be seen for two-layered composite material tubes. So, I study the dispersion relations of two-layered tubes in this research, and it is convenient to inspect the hydrogen concentration of Zircaloy tubes.
Theory and experiment are separated to research in two stages that is one-layered tubes and two-layered tubes. The theory of one-layered tubes was derived by Gazis. The results are given of a numerical evaluation of a characteristic equation derived by Gazis. The theory of two-layered tubes was derived by Armenakas. The results are given of a numerical evaluation of a characteristic equation derived by him. At the same time, this study also uses non-destructive laser ultrasonic technique to measure the dispersion relations of Zircaloy tubes with precipitating ZrH2. It appears that Theory and experiment conform well, and can use laser ultrasonic technique to measure the dispersion relations of Zircaloy tubes correctly.

目錄
指導教授推薦書
口試委員審定書
授權書
誌謝
中文摘要 i
英文摘要 ...................................................................................................ii
目錄 iv
圖目錄 vi
表目錄 ix
第一章 緒論 1
1.1 前言 1
1.2 文獻回顧 2
1.3 研究目的 4
第二章 理論基礎 6
2.1 單層圓管的理論模型(1959 Gazis) 6
2.1.1 縱波模態 9
2.1.2 扭力模態 10
2.1.3 撓曲模態 10
2.2 雙層圓管之理論模型(1967 Armenakas) 11
2.2.1縱波模態 16
2.2.2 扭力模態 17
2.2.3 撓曲模態 18
第三章 實驗量測 19
3.1 試片準備 19
3.1.1 單層圓管試片 19
3.1.2 雙層圓管試片 20
3.2 雷射超音波量測系統 20
3.2.1 訊號激發部分 21
3.2.2 訊號接收處理部分 21
第四章 實驗結果與討論 22
4.1 單層圓管實驗與理論比較結果 22
4.1.1 Bronze01試片 22
4.1.2 Red brass01試片 22
4.1.3 Brass01試片 23
4.1.4 Steel01試片 23
4.1.5 Zircaloy01試片 23
4.2 改變單層圓管內半徑對圓管之波傳行為的影響 24
4.3 雙層圓管實驗與理論比較結果 25
4.3.1 電鍍試片 25
4.3.2 濺鍍試片 26
4.3.3 氫脆化鋯管試片 27
4.4 改變雙層圓管的外層厚度對圓管之波傳行為的影響 28
第五章 結論 30
參考文獻 31

圖目錄
圖1-1 核能電廠結構圖 34
圖1-2 由鋯合金護套所組成的燃料棒組 35
圖1-3 鋯管「吸氫現象」 36
圖2-1 自由邊界下內半徑為a外半徑為b之無限長圓柱管及其參考座標 37
圖2-2 自由邊界下內半徑為a外半徑為d之無限長雙層不同材料的圓管及其參考座標 38
圖3-1 單層圓管試片 39
圖3-2 雷射超音波系統示意 40
圖3-3 圓管剖開示意圖 41
圖3-4 雙層圓管試片 42
圖3-5 不同放大倍率之電鍍雙層圓管的光學顯微鏡量測圖 43
圖3-6 Nd-YAG 雷射聚焦後擊中試片激發超音波之示意圖 44
圖3-7 Nd-YAG脈衝雷射 45
圖3-8 都普勒光纖雷射干涉儀 46
圖3-9 單層圓管的雷射超音波系統掃描訊號圖 47
圖4-1 內半徑2.47 mm 厚度0.28 mm的青銅管之實驗與理論的頻散關係比較圖 48
圖4-2 內半徑3.54 mm 厚度0.46 mm的紅銅管之實驗與理論的頻散關係比較圖 49
圖4-3 內半徑2 mm 厚度1 mm的黃銅管之實驗與理論的頻散關係比較圖 50
圖4-4 內半徑10.15 mm 厚度0.92 mm的鋼管之實驗與理論的頻散關係比較圖 51
圖4-5 內半徑4.35 mm 厚度0.65 mm的鋯管之實驗與理論的頻散關係比較圖 52
圖4-6 改變鋼管(厚度1 mm)的內半徑對頻散曲線的影響。當內半徑增加，頻散曲線會非常趨近平板(如圖f )，在非常低頻除外 53
圖4-7 改變鋼管(厚度1 mm)的內半徑1 mm ~ mm對頻散曲線的影響 54
圖4-8 內半徑為1 mm厚度為1 mm的鋼管，平板可代替圓管之頻散曲線的最小頻率為5.89 MHz，並與相同厚度的平板比較 55
圖4-9 內半徑為5 mm厚度為1 mm的鋼管，平板可代替圓管之頻散曲線的最小頻率為1.178 MHz，並與相同厚度的平板比較 56
圖4-10 鋼管外表面電鍍紅銅的雙層圓管，鋼管內半徑為10.15 mm，壁厚為0.92 mm，紅銅厚度為39 μm 57
圖4-11 基材的單層鋼管和鍍紅銅後的雙層圓管之頻散曲線實驗值比較圖 58
圖4-12 基材的單層鋼管和鍍紅銅後的雙層圓管之頻散曲線實驗值與理論值比較圖 59
圖4-13 青銅外表面濺鍍鋁的雙層圓管，青銅圓管內半徑2.47 mm，壁厚為0.28 mm，鋁厚度為6 μm 60
圖4-14 基材的單層青銅管和鍍鋁後的雙層圓管之頻散曲線實驗值比較圖 61
圖4-15 基材的單層青銅管和鍍鋁後的雙層圓管之頻散曲線實驗值與理論值比較圖 62
圖4-16 鋯管內表面析出氫化鋯的雙層圓管，圓管外半徑為5mm，壁厚為0.554 mm，氫化鋯厚度為20 μm 63
圖4-17 鋯管內表面析出氫化鋯的雙層圓管，圓管外半徑為5mm，壁厚為0.539 mm，氫化鋯厚度為30 μm 64
圖4-18 鋯管外表面析出氫化鋯的雙層圓管，圓管外半徑為5mm，壁厚為0.496 mm，氫化鋯厚度為25 μm 65
圖4-19 鋯管外表面析出氫化鋯的雙層圓管，圓管外半徑為5mm，壁厚為0.455 mm，氫化鋯厚度為35 μ 66
圖4-20 不同氫化鋯厚度的比較圖 67
圖4-21 鋯管和析出氫的鋯管之頻散曲線比較圖 68
圖4-22 雙層平板示意圖 69
圖4-23 雙層平板的頻散曲線圖(h1/H=0.1) 70
圖4-24 雙層平板的頻散曲線圖(h1/H=0.8) 71
圖4-25 雙層圓管厚度示意圖 72
圖4-26 以內半徑等於5 mm，厚度為1 mm的鋼管為基材，外層為厚0.01 mm的紅銅，h2/h1=0.01 73
圖4-27 以內半徑等於5 mm，厚度為1 mm的鋼管為基材，外層為厚0.1 mm的紅銅，h2/h1=0.1 74
圖4-28 以內半徑等於5 mm，厚度為1 mm的鋼管為基材，外層為厚1 mm的紅銅，h2/h1=1 75
圖4-29 以內半徑5 mm，厚度1 mm的鋼管為基材，外層厚度為0.01 mm、0.1 mm和1 mm的紅銅之頻散曲線比較圖 76

表目錄
表3-1 單層圓管的材料性質 77
表3-2 單層圓管的幾何外型 78
表3-3 鋁材的材料性質 78
表3-4 鍍膜雙層圓管的幾何外型 79
表3-5 有析氫層鋯管的材料性質 79
表3-6 有析氫層鋯管的幾何參數 80

[1] Bickel, G.A., Green, L.W., and James, M.W.D., 2002, “The determination of hydrogen and deuterium in Zr-2.5Nb material by hot vacuum extraction mass spectrometry,” Journal of nuclear materials, Vol. 306, pp. 21-29.
[2] Hermann, A., Wiese, H., Bühner, R., Steinemann, M. and Bart, G., 2000, “in: Proceedings of the ANS conference on light water reactor fuel performance,” Park city, Utah.
[3] Herrmann, G. and Mirsky, I., 1956, “Three-dimensional and shell-theory analysis of axially symmetric motions of cylinders,” Journal of Applied Mechanics, No. 56, pp. 563-568.
[4] Gazis, C., 1959, “Three-dimentional investigation of the propagation of waves in hollow circular cylinders. I. analytical foundation,” J. Acoust. Soc. Am., Vol. 31, No. 5, pp. 568-573.
[5] Gazis, C., 1959, “Three-dimentional investigation of the propagation of waves in hollow circular cylinders. Ⅱ. numerical results,” J. Acoust. Soc. Am., Vol. 31, No. 5, pp. 573-578.
[6] Jones, J.P., 1964, “Wave propagation in a two-layered medium,” Journal of Applied Mechanics, No. 63, pp. 213-222.
[7] Mindlin, R.D., 1955, “An introduction to the mathematical theory of vibrations of elastic plates,” prepared for U.S. army signal corps engineering laboratories.
[8] Armenakas, A.E., 1965, “Torsional waves in composite rods,” J. Acoust. Soc. Am., pp. 439-446.
[9] Heimann, J.H. and Kolsky, H., 1966, “The propagation of elastic waves in thin cylindrical shells,” J. Mech. Phys. Solids., Vol. 14, pp. 121-130.
[10] Armenakas, A.E., 1967, “Propagation of harmonic waves in composite circular cylindrical shells. I: theoretical investigation,” AIAA Journal, Vol. 5, No. 4, pp. 740-744.
[11] Armenakas, A.E., 1971, “Propagation of harmonic waves in composite circular cylindrical shells. Ⅱ: numerical analysis,” AIAA Journal, Vol. 9, No. 4, pp. 599-605.
[12] Silk, M.G. and Bainton, K.F., 1979, “The propagation in metal tubing of ultrasonic waves equivalent to Lamb waves,” Ultrasonics, pp. 11-19.
[13] Rattanawangcharoen, N., Shah, A.H. and Datta, S.K., 1992, “Wave propagation in laminated composite circular cylinders,” J. Solids Structures, Vol. 29, No. 6, pp. 767-781.
[14] Pavlakovic, B.N., 1998, “Leaky guided ultrasonic waves in NDT,” University of London for the degree of doctor of philosophy, England, London.
[15] 山中 申介，黑田 雅利， 瀨戶山 大吾， 2002,“Mechanical properties of Zirconium hydride and hydrogen solid solution,” 日本原子力學會和文論文誌, Vol. 1, No. 4, pp. 323-327.
[16] Hay, T.R. and Rose, J.L., 2002, “Flexible PVDF comb transducers for excitation of axisymmetric guided waves in pipe,” Sensors and Actuators A 100, pp. 18-23.
[17] 何政諺， 2002， “蘭姆波法於管路檢測之應用研究”， 中山大學碩士論文， 台灣， 高雄市.
[18] Takahiro Hayashi and Koichiro Kawashima, 2003, “Ultrasonic guided wave calculation for pipe diagnostics,” ATEM'03, JSME-MMD.
[19] Siqueira, M.H.S., Gatts, C.E.N., da Silva, R.R. and Rebello, J.M.A., 2004, “The use of ultrasonic guided waves and wavelets analysis in pipe inspection,” Ultrasonics, Vol. 41, pp. 785-797.
[20] Cheong, Y.M., Lee, D.H. and Jung, H.K., 2004, “Ultrasonic guided wave parameters for detection of axial cracks in feeder pipes of PHWR nuclear power plants,” Ultrasonics, Vol. 42, pp. 883-888.
[21] Li, Jian and Rose, J.L., 2001, “Excitation and propagation of non-axisymmetric guided waves in a hollow cylinder,” J. Acoust. Soc. Am., Vol. 109, No. 2, pp. 457-464.
[22] Demma, A., Cawley, P., Lowe, M., Roosenbrand, A.G. and Pavlakovic, B.N., 2004, “The reflection of guided waves from notches in pipes: a guide for interpreting corrosion measurements,” NDT&E International, Vol. 37, pp. 167-180.
[23] Shin, H.J. and Rose, J.L., 1999, “Guided waves by axisymmetric and non-axisymmetric surface loading on hollow cylinders,” Ultrasonics, Vol. 37, pp. 355-363.
[24] Siqueira, M.H.S., Gatts, C.E.N., da Silva, R.R. and Rebello, J.M.A., 2004, “The use of ultrasonic guided waves and wavelets analysis in pipe inspection,” Ultrasonics, Vol. 41, pp. 785-797.
[25] Lowe, M.J.S., Alleyne, D.N., and Cawley, P. , 1998, “Defect detection in pipes using guided waves,” Ultrasonics, Vol. 36, pp. 147-154.
[26] Hideo Nishino, Mikio Takemoto and Noriyoshi Chubachi, “Estimating the diameter/thickness of a pipe using the primary wave velocity of a hollow cylindrical guided wave,” 2004, Applied physics letters, Vol. 85, No. 6, pp. 1077-1079.
[27] Meitzler, A.H., “Mode coupling occurring in the propagation of elastic pulses in wires,” J. Acoust. Soc. Am., Vol. 33, No. 4, pp. 435-445.
[28] Ditri, J.J., “Utilization of guided elastic waves for the characterization of circumferential cracks in hollow cylinders,” 1994, J. Acoust. Soc. Am., Vol. 96, No. 6, pp. 3769-3775.