延遲氫化龜裂和潛變破裂為用過核子燃料鋯合金護套於乾式貯存期間主要的劣化機制，為確保乾式貯存燃料操作安全性與再取出性，貯存期間燃料護套之完整性必須獲得妥善評估。本文有關延遲氫化龜裂部份，結合破壞力學理論與實驗數據以及有限元素分析程式來探討氫化鋯之方位重排效應並建立分析模式；潛變破裂部份，以20年之貯存期間為評估基準，採用C*積分來建立護套之潛變破裂分析模式，並假設不同初始裂縫長度、氫化鋯方位和乾式貯存期間護套溫度變化的影響，以確認乾式貯存期間最容易造成護套破裂的組合條件。
研究結果發現，護套在乾式貯存環境下，初始裂縫長度與溫度變化是比較關鍵的參數，而乾式貯存之前析出之氫化鋯及其方位與重排對燃料護套完整性，並未呈現重大影響。分析數據顯示，護套內外兩側皆有裂縫的狀況下，穿透護套的時間最短；若貯存溫度保持穩定，護套大部分皆能安全貯存，只有雙裂縫而且裂縫長度是幾種假設數值中最長的，才會發生穿透現象。用過核子燃料於乾式貯存期間，溫度穩定而且逐漸下降，依據目前之分析模式與假設條件，護套將是安全的，不會有裂縫貫穿的情形。
至於核電廠運轉中的燃料爐心行為，本研究預設三種不同裂縫長度，並參考電廠實際升載操作，假設數個不同之運轉功率上升率以進行模擬分析。研究發現，運轉功率上升越快，核燃料護套破損程度增大。而經由應變能密度等高線分佈，我們也可以預判斷裂縫的穩定性與可能成長方向。
本研究所建立之分析模式受限於部份鋯合金護套之材料性質，譬如氫化鋯之楊氏係數與不同氫化鋯含量之潛變特性，分析所得之趨勢尚屬學術性之研究，目前還不適合直接應用於乾式貯存用過核子燃料之完整性評估。未來若相關實驗能提供更多的材料特性，對高然耗燃料的乾式貯存將可提供更可靠的評估。所建立的模式也適用於運轉中核燃料爐心行為分析，結合應變能密度理論，相信對近年來所發現之裂縫由護套外側往內部成長之破損機制將有所貢獻。

The delayed hydride cracking and creep rupture are the failure mechanisms of spent fuel cladding for concerns during dry storage. The regulation requires that the spent fuel be readily retrievable from the storage system, therefore, the cladding integrity during dry storage should be well demonstrated. Concerning the delayed hydride cracking, experimental data and finite element computer code are applied and hydride reorientation is considered in our analysis. For creep rupture, C* is applied in the crack stability evaluation for a 20-year period of storage. Hydride and its reorientation are considered in the analysis, various incipient cracks are assumed on either side of cladding or both sides. Different fuel temperatures are applied in the creep rupture analysis to understand the limiting storage conditions.
The analysis results indicate that the cladding initial crack length and storage temperature dominate the crack stability during dry storage, while the effects of zirconium hydride appears to be minor. Cladding with incipient cracks on both sides seems to be the worst case to form a through crack, and trend of crack propagation is highly related to the storage temperature. As the spent fuel temperature decreases gradually with time in the dry storage facility, the cladding integrity is confirmed.
We intend to apply the analysis methodology to the fuel in core behavior analysis. Calculations for various power ramp rates to simulate the reactor transient operations were performed in the study. The preliminary results show that fuel failure trend depends on the power rate. The strain energy density theory remains superior in the prediction of crack path and stability.
Some assumptions were made in the analysis, for example, the material properties of Zircaloy such as Young’s modulus of zirconium hydride and the creep behavior with various hydride contents. Therefore, the results of spent fuel life prediction for a 20-year storage period may not be appropriate for practical application. However, the analysis methodology will be helpful to long term dry evaluation when further material test data of spent fuel cladding is available in the future. The application of an improved model and strain energy density theory to fuel in-core performance especially the outside-in cracking failure mechanism is expected and will be left for further study.

[1]E. William Brach, Director, “Cladding Considerations for the Transportation and Storage of Spent Fuel,” Interim Staff Guidance – 11, Revision 3, Spent Fuel Project Office, Nuclear Regulatory Commission, November 17, 2003.
[2]H. S. Rosenbaun, J. H. Davies and J. Q. Don, Interaction of Iodine with Zircaloy-2, Geap-51005(1966).
[3]H. S. Rosenbaun, “the interaction of Iodine with Zircaloy-2,”
Electrochem. Tech., Vol.4,pp.153-156(1966).
[4] R. Dutton, et.al., “ Mechanisms of Hydrogen Induced Delayed Cracking in Hydride Forming Materials,” Metallurgical Transactions A (Physical Metallurgy and Materials Science), v A8, pp. 1553-1562, 1977.
[5] C. J. Simpson and C.E. Ells, “Delayed Hydrogen Embrittlement
in Zr-2.5﹪Nb,” J. Nucl. Mat. 52,pp.289-295(1974).
[6] C. E. Coleman and J. F. R. Ambler, “Delayed Hydrogen Crac-
king in Zr-2.5﹪Nb Alloy,” Rev. Coating and Corrosion 3:105
(1979).
[7] N. E. Hoppe, ”Engineering Model for Zircaloy Creep and Growth,” Advanced Nuclear Fuels Corporation, Richland, Washinfton, U.S.A E. Beltrami, Aslle Condizioni di Resistenza dei corpi Elastic, Rendiconto del Reale Istituto Lombardo, Ser. II, Tomo XVIII
(1985)
[8]Mayazumi Masami, Onchi Takeo, Matsuo, Yutaka, “Failure propensities of pressurized zircaloy tube containing iodine and other chemical species,” Journal of Nuclear Science and Technology, Vol. 12, pp. 1288-1298, 1993.
[9]Limback, M. and Andersson, T., “A Model for Analysis of the Effect of Final Annealing on the In- and Out-of-Reactor Creep Behavior of Zircaloy Cladding,” Zirconium in the Nuclear Industry: Eleventh International Symposium, ASTM STP 1295, E. R. Bradley and G. P. Sabol, Eds., American Society for Testing and Materials, pp. 448-468, 1996.
[10]J. D. Eshelby, “Calculation of Energy Release Rate,” Prospects of Fracture Mechanics, pp. 69-84, Sih, Van Elst, Broek, Ed., Noordhoof, 1974.
[11]G. P. Cherepanov, “Crack Propagation in Continuous Media,” USSR, J. Appl. Math. And Mech. Translation 31, pp. 504, 1967.
[12]J. R. Rice, “ A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notchrs and Cracks,” J. Appl. Mech., pp. 379-386, 1968.
[13]J. W. Hutchinson, “ Singular Behavior at th End of a Tensile Crack Tip in a Hardening Material,” J. of the Mechanics and Physics of Solids, Vol. 16, pp. 13-31,1968.
[14]J. R. Rice and G. F. Rosengren, “Plane Strain Deformation near a Crack Tip in a Power-Law Hardening Material,” J. of the Mechanics and Physics of Solids, Vol. 16, pp. 1-12, 1968.
[15]J. D. Landes and J. A. Begley, “A Fracture Mechanics Approach to Creep Crack Growth,” ASTM STP, 590, American Society for Testing and Materials, Philadelphia, pp. 128-148, 1976.
[16]E. Beltrami, Aslle Condizioni di Resistenza dei corpi Elastic, Rendiconto del Reale Istituto Lombardo, Ser. II, Tomo XVIII, 1985.
[17]胡志允, “核燃料棒鋯合金護套裂縫延遲氫化龜裂分析,” 台灣科技大學機械工程系碩士論文, 1998。
[18]A. Tasooji, et.al., “Modeling of zircaloy Stress-Corrosion Crac-king: Texture Effect and Dry Storage Spent Fuel Behavior.” American Society for Testing and Material, pp.595-626(1984).
[19]Sponsored by The Metals Properties Council, “CREEP OF ZIRCONIUM ALLOYS IN NUCLEAR REACTORS,” .
[20]Chao, C. K., Chen, J. Q., Yang, K. C., and Tseng, C. C., 2007, “Analysis of Creep Crack Growth on Spent Fuel Zircaloy Cladding in Interim Storage,” Journal of Theoretical and Applied Fracture Mechanics, 47, pp. 26-34.
[21]Chao, C. K., Yang, K. C., and Tseng, C. C., 2008, “Rupture of Spent Fuel Zircaloy Cladding in Dry Storage Due to Delayed Hydride Cracking,” Nuclear Engineering and Design, 238 (1), pp. 124-129.
[22]C. K. Chao and Che-Chung Tseng, “Pellet crack mechanism at power ramps,” J. Nucl. Mater., Vol. 199, pp. 159-166, 1993.
[23]D. Wappling, a.b., A. R. Massih a.b., P. Stahle, “A Model for Hydride-Induced Embrittlement in Zirconium-Based Alloys,”
J. Nucl. Mater.,249,pp.231-238(1997).
[24]J. B. Bai, et. al., “Hydride Embrittlement in ZIRCALOY-4
Plate:Part 1. Influence of Microstructure on the Hudride Embri-
ttlement in ZIRCALOY-4 at 20 and 350 ,” Metall. Trans.
A25, pp.1185-1197(1994).
[25]K. Wasmer, K. M. Nikbin, G. A. Webster, “Creep crack initiation and growth in thick section steel pipes under internal pressure,” International Journal of Pressure Vessels and Piping, 80, pp. 489-4.
[26]KOICHI YAGI, MASAAKI TABUCHI and KIYOSHI KUBO, “THE INFLUENCE OF FRACTURE MECHANISMS ON THE CREEP CRACK GROWTH BEHAVIOR OF 316 STAINLESS STEEL,” Engineering Fracture Mechanics, Vol. 57, No. 5, pp. 463-473, 1997..
[27]Kwon, K.M. Nikbin, G.A. Webster, K.V. Jata, “Crack growth in the presence of limited creep deformation,” Engineering Fracture Mechanics, Vol. 62, pp. 33-46, 1999.
[28]Kwon, K.M. Nikbin, G.A. Webster, K.V. Jata, “Crack growth in the presence of limited creep deformation,” Engineering Fracture Mechanics, Vol. 62, pp. 33-46, 1999.
[29]B. Cox, “Pellet-Clad Interaction (PCI) Failures of Zirconium Alloy Fuel Cladding - A Review,” J. Nucl. Mater., Vol.172, pp. 249- 292(1990)
[30]C. K. Chao and Che-Chung Tseng, “ Pellet crack mechanism at power ramps,” J. Nucl. Mater.,199,pp.159-166(1993).
[31]曾哲聰, “應變能密度理論於核燃料破損分析之應用,” 國立台灣工業技術學院機械系博士論文, 1992