本文試圖將航空結構完整性評估有關之金屬疲勞裂縫延伸問題與可靠度工程相關之議題結合，並用電腦模擬的方式來評估等振幅負載與隨機負載下裂縫延伸之變異情形，以期能將預測的疲勞可靠度應用於結構完整性評估上。研究工作有下列幾大主軸：（一）、進行一批2024-T351鋁合金試片隨機振幅疲勞實驗與另一批可相對照之等振幅疲勞實驗；（二）、以疲勞實驗者常用之方法來整理實驗數據；（三）、依據統計學家之理論，將實驗數據以機率分佈函數嵌合，並比較不同施力組別間之異同；（四）、透過兩套疲勞裂縫延伸法則，比較其間參數的變異性與相關性，提出與原法則稍有不同的修正式，並配合逐週次法與蒙地卡羅模擬法，建立一套疲勞裂縫延伸之電腦模擬流程；（五）、最後將獲得之模擬數據與實驗結果進行比較，驗證藉由結合疲勞裂縫延伸預估式與可靠度分析並考慮參數相關與變異性所建立之本套電腦模擬流程能適切地嵌合實驗數據，可提供予航空結構完整性與安全性之評估應用。

To study the structural integrity of aeronautical structures, the fatigue crack growth behavior of 2024-T351 aluminum alloy is examined from reliability engineering point of view. A computer simulation algorithm is developed to take into account the scatter of the fatigue crack growth curves in addition to their mean growth trend. Both constant amplitude loading and random loading cases are considered. In summary, the present thesis consists of the following work. (1) To perform a considerable amount of fatigue crack growth tests. (2) To analyze the test results according to the famous Paris law and Yang-Manning law. (3) To analyze the test data using probability and statistical theories and compare the differences between two data sets. (4) To compare parameters between different fatigue crack growth laws and discuss the statistical relations between different parameters. It is found that the computer simulation algorithm can describe the fatigue crack growth curves very well. It can then be used as a tool for the integrity and reliability assessment of aeronautical structures made of 2024-T351 aluminum alloy.

第一章 緒 論 1
1.1 前言 1
1.2 研究動機與目的 2
1.3 文獻回顧 3
1.4 研究方法 6
1.5 本文結構 7
第二章 分析模式之建立 8
2.1 疲勞裂縫延伸模式 8
2.1.1 疲勞破壞簡介 8
2.1.2 應力強度因子 9
2.1.3 Paris法則 10
2.1.4 殘餘壽命之評估 11
2.2 Yang & Manning法則 12
2.3 可靠度評估模式 14
2.3.1 可靠度簡介 14
2.3.2 機率分佈函數 16
2.3.3 機率圖紙與卡方測試 18
2.3.4 蒙地卡羅模擬法 22
第三章 實 驗 概 論 27
3.1 實驗目的 27
3.2 材料及其機械性質 28
3.3 試片與夾具的設計 28
3.3.1 試片的設計 28
3.3.2 夾具的設計 28
3.4 試片預裂 29
3.5 裂縫長度的量測 29
3.6 實驗系統 30
3.6.1 疲勞試驗機及控制系統 30
3.6.2 裂縫長度量測系統 31
3.7 隨機振幅荷重的疲勞拉伸試驗 31
3.7.1 隨機訊號產生理論簡介 32
3.7.2 隨機訊號產生 36
3.8 等振幅荷重的疲勞拉伸試驗 37
3.9 訊號量測與擷取 37
3.10 實驗過程 38
第四章 實驗數據分析 49
4.1 實驗數據的繪製與討論 49
4.2 疲勞模式分析 51
4.3 可靠度模式分析 53
第五章 疲勞裂縫延伸之電腦模擬 80
5.1 參數組（m、C）與（b、Q）之探討 82
5.1.1 參數變異性 82
5.1.2 參數相關性 85
5.2 電腦模擬 90
5.2.1 模擬流程與分析流程 91
5.2.2 電腦模擬之討論 93
第六章 結論與未來展望 116
參考文獻 120

1. S. Suresh, Fatigue Crack Growth, Class Notes, MIT, 2000.
2. 蕭飛賓(召集人)，航空、太空工程技術研究發展規劃書，國科會工程處航空太空學門，民國八十八年十二月。(亦見於國科會連結成大航太所網頁。)
3. K. Ono,“Nondestructive Testing of Aging Aircraft,”Proceedings of Fourth Far East Conference on Nondestructive Testing, pp. 3-18, Cheju-Do, Korea, October, 1997.
4. C. C. Scher, etc., Session on Aging Aircraft, Proceedings of the Seventh International Fatigue Congress, Vol. IV, pp. 2499-2582, 1999.
5. P. C. Paris, and F. Erdogan, “A Critical Analysis of Propagation Laws,” Journal of Basic Engineering, Vol. 85, pp. 528-534, 1960.
6. W. Elber, “Fatigue Crack Closure Under Cyclic Tension,” Engineering Fracture Mechanics, Vol. 2, pp. 37-45, 1970.
7. W. Elber, “The Significance of Fatigue Crack Growth,” ASTM STP 486, American Society for Testing and Material, Philadelphia, pp. 230-241, 1971.
8. T. L. Anderson, Fracture Mechanics Fundamentals and Applications, CRC Press, 1991.
9. J. C. Newman Jr., “A Crack-Closure Model for Predicting Fatigue Crack Growth Under Aircraft Loading, Methods and Models for Predicting Fatigue Crack Growth Under Random Loading,” ASTM STP 748, pp. 53-84, 1981.
10. J. C. Newman Jr., “Prediction of Fatigue Crack Growth Under Variable-Amplitude and Spectrum Loading Using a Closure Model Design of Fatigue and Fracture Resistant Structures,” ASTM STP 761, pp. 255-277, 1982.
11. J. C. Newman Jr., “A Crack Opening Stress Equation For Fatigue Crack Growth,” International Journal of Fracture, Vol. 24, R131-R135, 1984.
12. G. S. Wang and A. F. Blom, “A Strip Model for Fatigue Crack Growth Predictions Under General Load Conditions,” Engineering Fracture Mechanics, Vol. 40, pp. 507-533, 1991.
13. A. Ray and R. Patankar, “Fatigue Crack Growth Under Variable-Amplitude Loading: Part I - Model Formulation in State- Space Setting,” Applied Mathematical Modelling, Vol. 25, pp. 979-994, 2001.
14. T. Lagoda, E. Macha and R. Pawliczek, “The Influence of the Mean Stress on Fatigue Life of 10HZAP Steel Under Random Loading,” International Journal of Fatigue, Vol. 23, pp. 283-291, 2001.
15. L. Tucker and S. Bussa, The SAE Cumulative Fatigue Damage Test Program, in Fatigue Under Complex Loading: Analysis and Experiments (edited by R. M. Wetzel), pp. 1-53, 1977.
16. J. B. De Jonge, D. Schutz, H. Lovak and J. Schijve, A Standardized Load Sequence for Flight Simulation Tests on Transport Aircraft Wing Structures, NLR TR 7309 U, 1973.
17. G. M. Van Dijk and J. B. De Jonge, Introduction to a Fighter Aircraft Loading Standard for Fatigue Evaluation, “FALSTAFF,” Part 1, NLR MP 75017 U, 1975.
18. A. A. Ten Have, HELIX and FELIX: Loading Standards for Use in Fatigue Evaluation of Helicopter Rotor Components, NLR MP 82041 U, 1982.
19. A. A. Ten Have, “European Approaches in Standard spectrum Development, Development of Fatigue Loading Spectra,” ASTM STP 1006, pp. 17-35, 1989.
20. J. Dominguez and J. Zapatero, “Effect of the Loading Spectrum and History Length on Fatigue Life Distribution Under Random Loading,” Engineering Fracture Mechanics, Vol. 42, pp. 925-933, 1992.
21. R. C. Linsley and B. M. Hillberry, “Random Fatigue of 2024-T3 Aluminum under Two Spectra with Identical Peak-Probability Density Functions,” Probabilistic Aspects of Fatigue, ASTM STP 511, pp. 156-167, 1972.
22. H. O. Fuchs and R. I. Stephens, Metal Fatigue in Engineering, John Wiley & Sons, New York, 1980.
23. J. A. Collins, Failure of Materials in Mechanical Design, John Wiley & Sons, New York, 1981.
24. N. E. Dowling, Mechanical Behavior of Materials - Engineering Methods for Deformation, Fracture and Fatigue, Prentice-Hall, Englewood Cliffs, New Jersey, 1993.
25. D. A. Virkler, B. M. Hillberry and P. K. Goel, “The statistic Nature of Fatigue Crack Propagation,” ASME Journal of Engineering Materials and Technology, Vol. 101, pp. 148-153, 1979.
26. J. N. Yang and S. D. Manning, “A Simple Second Order Approximation for Stochastic Crack Growth Analysis,” Engineering Fracture Mechanics, Vol. 53, pp. 677-686, 1996.
27. D. F. Ostergaard and B. M. Hillberry, “Characterization of the Variability Fatigue Crack Propagation Data,” in Probabilistic Fracture Mechanics and Fatigue Method: Application for Structural Design and Maintenance, ASTM STP798, J. M. Bloom and J. C. Ekvall, ASTM, pp. 97-115, 1983.
28. C. E. Bronn, “Analysis if Structural Failure Probability Under Spectrum Loading Conditions,” in Probabilistic Fracture Mechanics and Fatigue Method: Applications for Structural Design and Maintenance, ASTM STP798, J. M. Bloom and J. C. Ekvall, ASTM, pp. 161-183, 1983.
29. S. R. Varanasi and I. C. Whittaker, “Structural Reliability Prediction Method Considering Crack Growth and Residual Strength,” in Fatigue Crack Growth Under Spectrum Loads, ASTM STP 595, American Society for Testing and Materials, pp. 292-305, 1976.
30. S. A. Meguid, Engineering Fracture Mechanics, Elsevier Applied Science, 1989.
31. D. Broek, Elementary Engineering Fracture Mechanics, Fourth Edition, Martinus Nijhoff, Publishers.
32. M. Klesnil and P. Lukas, Fatigue of Metallic Materials, Elsevier Scientific Publishing, 1980.
33. J. N. Yang, W. H. Hsi and S. D. Manning, Stochastic Crack Propagation with Applications to Durability and Damage Tolerance Analyses, Flight Dynamic Laboratory, Technical Report, AFWAL-TR-85-3062, Wright-Patterson Air Force Base, Ohio, 1985.
34. J. N. Yang, W. H. Hsi and S. D. Manning, “Stochastic Crack Growth Models for Applications to Aircraft Structures,” Probability Fracture Mechanics and Reliability, Chapter 4, pp. 171-211, 1987.
35. M. S. Miller and J. P. Gallagher, “An Analysis of Several Fatigue Crack Growth Rate (FCGR) Description Fatigue Crack Growth Measurement and Data Analyses,” ASTM STP 738, pp. 205-251, 1981.
36. K. C. Kapur and L. R. Lamberson, Reliability in Engineering Design, New York, Wiley, 1977.
37. E. E. Charles, An Introduction to Reliability and Maintainability Engineering, McGraw-Hill, 1997.
38. L. J. Devore, Probability and Statistics for Engineering and the Sciences, Fifth Edition, Duxbury, 2000.
39. S. S. Rao, Reliability-Based Design, McGraw-Hill, 1992.
40. ASTM E647-91, Standard Test Method for Measurement of Fatigue Crack Growth Rates, American Society for Testing and Materials, Phiadelphia, 1991.
41. J. Dominguez, J. Zapatero and J. Pascual, “Effect of Load Histories on Scatter of Fatigue Crack Growth in Aluminum Alloy 2024-T351,” Engineering Fracture Mechanics, Vol. 56, pp. 65-76, 1997.
42. J. Dominguez, J. Zapatero and B. Moreno, “A Statistical Model for Fatigue Crack Growth under Random Loads Including Retardation Effects,” Engineering Fracture Mechanics, Vol. 62, pp. 351-369, 1999.
43. S. Ustilovsky and R. Arone, “Random Fatigue Crack Growth in Aluminum Alloys,” International Journal of Fatigue, Vol. 21, pp. 275-282, 1999.
44. S. Y. Lee and J. H. Song, “Crack Closure and Growth Behavior of Physically Short Fatigue Cracks Under Random Loading,” Engineering Fracture Mechanics, Vol. 66, pp. 321-346, 2000.
45. M. Shinozuka, “Digital Simulation of Random Processes and its Applications,” Journal of Sound and Vibration, Vol. 25(1), pp. 111-125, 1972.
46. M. Leonard, Fundamentals of Vibrations, McGraw-Hill, p. 685-718, 2001.
47. G. I. Schueller and M. Shinozuka, Stochastic Methods in Structural Dynamics, Martinus Nijhoff, 1987.
48. 蕭子健等，LabView 進階篇，高立圖書，民國八十七年。
49. 劉宏毅，金屬受隨機負載作用下之疲勞分析模式與探討，國立台灣大學機械工程學研究所博士論文，民國八十七年。
50. J. Y. Mann, “ Scatter in Fatigue Life-A Materials Testing and Design Problem,” Materials, Experimentation and Design in Fatigue. (Edited by E. Sherratt and J. B. Sturgeon), West Bury House, pp. 390-423, 1981.
51. Y. K. Lin and J. N. Yang, “A Stochastic Theory of Fatigue Crack Propagation,” AIAA Journal, Vol. 23, pp. 117-124, 1985.
52. G. S. Wang, “A Probabilistic Damage Accumulation Solution Based on Crack Closure Model,” International Journal of Fatigue, Vol. 21, pp. 531-547, 1999.
53. T. Svensson, “Prediction Uncertainties at Variable Amplitude Fatigue,” International Journal of Fatigue, Vol. 19, pp. S295-S302, 1997.
54. P. C. Paris, “Fracture Mechanics and Fatigue: a Historical Perspective,” Fatigue and Fracture of Engineering Materials and Structures, Vol. 21, pp. 535-540, 1998.
55. I. Hiroshi, I. Tetsuo and P. Y. Huang, “Experimental Estimation of the Probability Distribution of Fatigue Crack Growth Lives,” Probabilistic Engineering Mechanics, Vol. 8, pp. 25-34, 1993.
56. F. Bergner and G. Zouhar, “A New Approach to the Correlation Between the Coefficient and the Exponent in the Power Law Equation of Fatigue Crack Growth,” International Journal of Fatigue, Vol. 22, pp. 229-239, 2000.
57. L. N. McCartney and P. E. Irving, “A Correlation for Fatigue Crack Growth Rate,” Scripta Metallurgica, Vol. 36(4), pp. 181-183, 1977.
58. J. P. Hickerson and R. W. Hertzberg, “The Role of Mechanical Properties in Low-Stress Fatigue Crack Propagation,” Metallurgical Transactions A, Vol. 3A, pp. 179-189, 1972.
59. H. Kitagawa, Journal Japanese Society Mechanical Engineers, Vol. 75, pp. 1068-1080, 1972.
60. M. B. Cortie, “The Irrepressible Relationship Between the Paris Law Parameters,” Engineering Fracture Mechanics, Vol. 40(3), pp. 681-682, 1991.
61. C. R. Krenn and J. W. Morris Jr., “The Compatibility of Crack Closure and Dependent Models of Fatigue Crack Growth,” International Journal of Fatigue, Vol. 21, S147-S155, 1999.
62. 陳志忠，鋁合金裂縫成長行為之可靠度研究，國立台灣大學機械工程學研究所碩士論文，民國九十年。
63. 楊銘堯，符合實驗結果之金屬疲勞裂縫延伸電腦模擬，國立台灣大學機械工程學研究所碩士論文，民國九十年。