本論文旨在利用數值解析方法預測複材積層板承受疲勞作用後殘留勁度及殘留強度，並配合實驗工作，進行互相比較與驗證。因為複材性質複雜，具有非均質性及異向性，在疲勞作用時，其數據較傳統金屬材料更為散亂，故有關疲勞之複材機械性能，目前尚無統一之理論模式，大多採用半經驗-半理論之公式，配合一些特定之材料性質參數來模擬。本論文期望往後能盡量節省實驗工作所需之人力、財力及時間，而同樣能預測出精確之結果。
在數值解析方面，利用ANSYS套裝軟體建立鑽孔及平板十字疊[0/90]4s、類似均向疊[0/+45/90/-45]2s之三維有限元素切割模型，以軟體內建之Tsai-Wu法則判斷複材之破壞，分別求得平板及鑽孔平板之極限強度，並配合Miner’s Rule求得疲勞損傷，假設疲勞振次損傷等於勁度損傷及強度損傷，以求得複材殘留勁度及殘留強度，並與現有實驗結果比較之。
由分析結果得知，複材積層平板極限強度數值解十字疊誤差3.84%，類似均向疊誤差約8.38%。中央鑽孔積層板極限強度數值解十字疊誤差0.4%，類似均向疊之誤差則高達22.4%。在疲勞振幅作用下，平板十字疊及類似均向疊之殘留勁度及殘留強度會隨著疲勞週次之增加而遞減，其遞減速率在起始階段較為緩慢，而在接近破壞之最後階段則頗為快速，以60% 極限強度較能有效預測殘留強度，80% 則較保守。

The purpose of thesis is aimed to predict the residual stiffness and residual strength of a composite laminate by adopting the method of cumulative damage theories numerically. In association with the experimental work the numerical result can be verified in comparison. The fatigue data in composites are well known more scattered than those in conventional metals, because the material properties are complicated due to nonhomogeneity and anisotropy. Until now there exists very few unified theories to model composite fatigue properties. Most of them are semi-empirical expressions fitted by selecting material characteristic values. This work tries to make a precise prediction with hopefully saving time, money and manpower in future experiments.

On the aspect of numerical analysis, we employ finite element method incorporated with the software of ANSYS to generate 3-D finite element model and obtain the ultimate stress of cross-ply [0/90]4s and quasi-isotropic [0/+45/90/-45] laminates by Tsai-Wu failure criterion. It is assumed that the damage due to fatigue cycles is equal to the damage of stiffness and strength, in association with Miner’s Rule and cumulative damage theories we obtain the residual stiffness and strength. The numerical result in comparison with the available empirical data is found acceptably well.
Finally, this study can be concluded as follows. The error of ultimate stress is 3.84 % in cross-ply[0/90]4s , and 8.38 % in quasi-isotropic[0/45/90/-45]2s laminates. The error of ultimate stress in centrally notched cross-ply[0/90]4s is 0.4 %, and 22.4 % in centrally notched quasi-isotropic laminates. As the fatigue cycles increasing, the residual stiffness and residual strength of the laminates are all decreasing. The decreasing rate is very slight at first and intermediate stages, whilst it is much faster near the last stage. It is found that the prediction of residual strength is more accurate in the case of maximum stress of 60% ultimate stress than that of 80% ultimate stress.

目錄 …………………………………………………………I
表目錄…………………………………………………….III
圖目錄 …………………………………………………….V
摘要 ……………………………………………………IX
英文摘要……………………………………………………X
第一章 緒論 …………………………………………1
1-1 研究動機……………………………………1
1-2 複合材料概述 ……………………………2
1-3 文獻回顧 …………………………………4
1-4 組織與章節 ………………………………7
第二章 理論與數值分析……………………………….9
2-1 前言 ……………………………………..9
2-2 破壞規範 …………………………………10
2-3 累積損傷理論 ……………………….…13
2-4 ANSYS軟體介紹……………………….……16
2-5 有限元素模型的建立 ……………….…17
第三章 結果與分析……………………………………27
3-1 前言 …………………………………….27
3-2 模型準確性評估………………………….27
3-3.1 複材積層平板極限強度 …………….29
3-3.2 中央鑽孔複材積層板極限強度……….31
3-4 複材積層平板殘留勁度及強度……….32
第四章 討論……………………………………………70
4-1 前言……………………………………….70
4-2 極限強度之討論………………………….71
4-3 殘留強度之討論………………………….73
第五章 結論與建議……………………………………76
5-1 結論……………………………………….76
5-2 建議……………………………………….77
參考文獻 ……………………………………………….79

1. 趙少汴與王忠保, 抗疲勞設計-方法與數據,機械工業出版社,1997.
2. Hafiani, F. and Dwyer, J.F. , "Edge Function Analysis of Anisotropic Materials with Holes and Cracks",Computers and Structures 72,1999,pp.779~791.
3. Pradhan, S.C. and Tay, T.E. , "Three-Dimensional Finite Element Modelling of Delamination Grownth in Notched Composite Laminates under Compression Loading", Engineering Fracture Mechanics, Vol. 60, 1998, pp.157~172.
4. Nguyen, Ba Nghiep, "Three-Dimensional Modeling of Damage in Laminated Composites Containing a Central Hole", Journal of Composite Materials Lancaster, Vol. 31, 1997, pp. 1672~1693.
5. Afaghi-Khatibi, Akbar and Ye, Lin, "Residual Strength Simulation of Fibre Reinforced Metal Laminates Containing a Circular Hole", Journal of Composite Materials Lancaster, Vol. 31, 1997, pp.1884~1904.
6. Chow, C.L. and Yang, Fan, "Three-Dimensional Inelastic Stress Analysis of Center Notched Composite Laminates with Damage", International Journal of Damage Mechanics, Vol. 6, 1997, pp.23~50.
7. Waas, A. and Junghyun, A. and Khamseh, A. R. , "Compressive Failure of Notched Uniply Composite Laminates", Composites Part B Engineering Vol. 29, 1998, pp.75~80.
8. Simonds, R.A., Bakis, C.E., and Stinchcomb, W. W., 1989, "Effect of Matrix Toughness on Fatigue Response of Graphite Fiber Composite Laminates ", Composite Materials: Fatigue and Fracture, Second Volume, ASTM STP 1012, P. A. Lagace Ed., P.5.
9. Hwang, W., and Han, K.S., 1986, " Fatigue of Composite-Fatigue Modulus Concept and Life Prediction ", Journal of Composite Materials, Vol. 20, pp. 154-165.
10. Kenny, J. M. and Marchetti, M. "Elasto-Plastic Behavior of Thermoplastic Composite Laminates under Cyclic Loading", Composite Structures 32(1995)375-382
11. Muc, Aleksander "Design of Composite Structures under Cyclic Loads", Computers and Structures76(2000)211-218
12. Diao, X., Lin, Y., and Mai, Y. W., 1997, " Fatigue Behavior of CF / PEEK Composites Laminates Made from Commingled Prepreg. Part I: Experimental Studies ", Composite Part – A, pp.739~747
13. Diao, X., Lin, Y., and Mai, Y. W., 1997, " Fatigue Behavior of CF / PEEK Composites Laminates Made from Commingled Prepreg. Part Ⅱ: Statistical Simulations ", Composite Part – A, pp.749~755
14. Chandler, H. D. ,Campbell, I. M. D. and Stone, M. A. "An Assessment of Failure Criteria for Fibre-Reinforced Composite Laminates", Int. J. Fatigue Vol. 17. No. 7. pp. 513-518, 1995.
15. Jen, Ming-Hwa R. and Lee, C. –H., "Strength and Life in Thermoplastic Composite Laminates under Static and Fatigue Loads. Part I: Experimental ",Int. J. Fatigue Vol. 20, No.9, pp.605-615,1998.
16. Jen, Ming-Hwa R. and Lee, C. –H., "Strength and Life in Thermoplastic Composite Laminates under Static and Fatigue Loads. Part II: Formulation",Int. J. Fatigue Vol. 20, No.9, pp.617-629,1998.
17. Tai, N. H. , Ma, C. C. M. and Wu, S. H. "Fatigue Behaviour of Carbon Fibre/Peek Laminate Composites", Compostes 26. pp.551-559,1995.
18. Diao, X., Lin, Y., and Mai, Y. W., "A Statistical Model of Residual Strength and Fatigue Life of Composite Laminates", Composites Science and Technology 54 (1995), pp.329-336.
19. Lee, L. J., Fu, K. E. and Yang, J. N., "Prediction of Fatigue Damage and Life for Composite Laminates under Service Loading Spectra", Composites Science and Technology 56(1996), pp.635-648.
20. Kam, T. Y. , Chu, K. H. and Tsai, S. Y., "Fatigue Reliability Evaluation for Composite Laminates via a Direct Numerical Integration technique",Int. J. Solids Structures Vol. 35. No.13. pp.1411-1423,1998.
21. Chang, F.K. and K.Y. Chang, "A Progressive Damage Model for Laminated Composites Containing Stress Concentration." J. of Composite Materials,21,834-855(1987a).
22. 李傳華，"石墨纖維/聚二醚酮複材積層板疲勞損傷之量測及應用",國立中山大學機械所碩士論文.
23. 李傳華, 1998, " 複合材料積層板疲勞強度與壽命預測及層間應力分析 ", 國立中山大學機械所博士論文.
24. 彭聖森, 1999, " 碳纖維/聚二醚酮複合材料積層板溫度效應對疲勞破壞行為之影響 ", 國立中山大學機械所碩士論文.
25. 張熙超, 1999, " 碳纖維/聚二醚酮複合材料積層板鑽孔及溫度效應之破壞機制與機械性質分析 ", 國立中山大學機械所碩士論文.
26. 曾育鍾, 2000, " 中央鑽孔碳纖維/聚二醚酮複材積層板之高溫疲勞探討 ",國立中山大學機械所碩士論文.
27. Gibson,R.F., Principles of Composite Material Mechanics ,McGRAW-Hill,1994.
28. Mott, R. L.,Machine Elements in Mechanical Design ,Merrill,1992.
29. Tsai, S.W. and Hahn, H.T.,Introduction to Composite Materials ,Technomic Publishing Company,1980.
30. 鄭合志, 2000, "擬均向性Gr/PEEK複材積層板在變動負荷下之疲勞可靠度研究",國立臺灣大學機械所博士論文.