本文主旨在於利用數值解析的方式對含缺口複合材料進行疲勞破壞分析，藉由數值分析的輔助對含缺口複合材料積層板之疲勞破壞有更進一步的瞭解。缺口形式分為中央鑽孔4mmψ以及雙邊裂縫，利用套裝軟體ANSYS進行有限元素分析。
在鑽孔破壞分析過程中以Tsai-Wu法則判斷複材之破壞，並採階段性增量負載，考慮階段破壞之後續影響，進而求得鑽孔積層板之極限強度。在疲勞損傷方面則採用Miner’s Rule預測疲勞損傷區域之擴展並和實驗之結果比對。而在雙邊裂縫部分，則假設為混和模式，以應力分析配合外插法求得不同裂縫長度之應力強度因子，並將數值帶入假設之幾何修正因子函數求出各項係數，獲得一幾何修正函數。
由分析結果得知，採階段性增量分析對於極限強度之預測有相當不錯的效果，其最終破壞區域也與實驗相符。疲勞損傷之預測則以損傷發生初期較為正確，之後的損傷分佈與實際情形相差較大。而應力強度因子與幾何修正因子均與裂縫長度開根號成正比，符合破壞力學 觀念。惟類似均向疊因受±45度之影響，故其誤差較大。

The purpose of thesis is aimed to analyze fracture and fatigue behaviors of notched composite laminates by numerical method. Types of notch are both central notch 4mmψand double-edged crack. We employed finite element method analysis with ANSYS to perform the numerical analysis.
We adopted Tsai-Wu failure criterion to approach failure of central notch laminates by a step increment method and considered the effect of failure area gradually expanded, thus we obtained the ultimate stress of a laminate. In the work of fatigue testing and evaluation, we used Miner’s rule to predict the extension of fatigue damage zone, and compared it with experimental results. In the analysis of a double-edged crack laminate, it is first assumed mix mode failure. Then, we calculated the stress intensity factors of various crack length by extrapolation, and developed a function of configuration correction factor.
Finally, this study can be concluded as follows. The accuracy of ultimate stress prediction with step-by-step increment analysis is satisfactorily well. The outcome failure area of a laminate is closely corresponding with the observation of experiment. In predicting the fatigue damage zone, the predicted initial damage zone is close to experimental observation, but it is inconsistent with the actual damage extension due to crack propagation. Stress intensity factors and configuration correction factors are directly in proportion to the square root of crack length. It is corresponding with fracture mechanics. However there are some errors in quasi-isotropic laminates due to the existing of ±45°plies.

目錄 ……………………………………………………………….. I
表目錄 ……………………………………………………………..Ⅲ
圖目錄 ……………………………………………………………..Ⅳ
摘要 ………………………………………………………………..Ⅶ
英文摘要 …………………………………………………………..Ⅷ
第一章 緒論 ………………………………………………….1
1-1研究動機 ……………………………………………...1
1-2複合材料概述 ………………………………………….1
1-3研究方向 ..…………………………………………….3
1-4文獻回顧 …..………………………………………….4
1-5組織與章節 .……………………………………………6
第二章 理論基礎與數值分析...…..……………………………9
2-1前言 .……………………………………………………9
2-2 破壞規範..………………………………………………9
2-3 累積損傷理論……….…………………………………11
2-4 應力強度因子...………………………………………..13
2-5 ANSYS軟體簡介………………………………………17
2-6 有限元素模型建立……………………………………..18
第三章 結果與分析..…………………………………………....28
3-1前言……………………………………………………....28
3-2中央鑽孔複材積層板之極限強分析..…………………29
3-3 中央鑽孔複材積層板之疲勞損傷分析...………………31
3-4 雙邊裂縫複合材料積層板應力強度因子之分析….....32
第四章 討論…………………..………………………………..56
4-1 鑽孔複材積層板之極限強度討論……………………...56
4-2 鑽孔複材積層板之疲勞損傷討論……………………...57
4-3 雙邊裂縫複材積層板應力強因子之討論….…………..59
第五章 結論與未來展望………………………………………60
5-1 結論……………………………………………………...60
5-2 未來展望………………………………………………...61
參考文獻………………………………………………………………62
附錄A …………………………………………………………………66
附錄B………………………………………………………………….69


表目錄
表2-1 含缺口複材積層板模型資料………………….…………….21
表2-2 AS-4/PEEK APC-2單向疊層複合材料之基本機械性質…..21
表3-1 中央鑽孔十字疊應力集中係數及極限強度………………..35
表3-2 中央鑽孔類似均向疊應力集中係數及極限強度…………..35
表3-3 等向性材料應力強度因子數值與理論比較………………..36
表3-4 數值解析複材積層板之幾何修正因子……………………..36
表3-5 幾何修正因子之方程式……………………………………..37
表A-1 雙邊裂縫十字疊複材積層板之靜拉伸破斷實驗數據…….66
表A-2 雙邊裂縫類似均向疊複材積層板之靜拉伸破斷實驗數據.67
表A-3 雙邊裂縫複材積層板a=2.5mm承受80% 之疲勞振次..67

圖目錄
圖1-1 製作試片之溫度、壓力與時間分佈圖………………………7
圖1-2 十字疊[0/90]4s之疊序…………………………………………8
圖1-3 類似均向疊[0/+45/90/-45]2s之疊序…………………………..8
圖2-1 S-N曲線與Miner’s Rule ...…………………………………..13
圖2-2 裂縫破壞的三種模式………………………………………..16
圖2-3 第Ⅰ型含裂縫之無限大平板受力示意圖…………………..16
圖2-4 第Ⅱ型含裂縫之無限大平板受力示意圖…………………..17
圖2-5 3-D Solid 46 層元素示意圖…………………………………22
圖2-6 中央鑽孔積層板對稱幾何尺寸示意圖..................................22
圖2-7 雙邊裂縫積層板對稱幾何尺寸示意圖……………………..23
圖2-8 中央鑽孔積層板對稱有限元素模型………………………..23
圖2-9 雙邊裂縫積層板對稱有限元素模型………………………..24
圖2-10 中央鑽孔積層板模型鑽孔處元素細部放大圖……………24
圖2-11 雙邊裂縫積層板模型裂縫處元素細部放大圖……………25
圖2-12 疊層板方向角符號示意圖…………………………………25
圖2-13 1/4對稱之中央鑽孔複材積層板之邊界條件示意圖……..26
圖2-14 1/4對稱之雙邊裂縫複材積層板之邊界條件示意圖……..26
圖2-15 程式分析之流程圖…………………………………………27
圖3-1 鑽孔十字疊鑽孔處截面應力分佈圖………………………..38
圖3-2 鑽孔十字疊0度層之X方向應力分佈…………………….38
圖3-3 鑽孔十字疊90度層之X方向應力分佈…………………….39
圖3-4 鑽孔十字疊0度層之Tsai-Wu法則值………………………39
圖3-5 鑽孔十字疊90度層之Tsai-Wu法則值…………………….40
圖3-6 鑽孔十字疊0度層最後破壞區域…………………………...40
圖3-7 鑽孔十字疊90度層最後破壞區域…………………………41
圖3-8 鑽孔類似均向疊鑽孔處截面應力分佈圖…………………..41
圖3-9 鑽孔類似均向疊0度層之X方向應力分佈……………….42
圖3-10 鑽孔類似均向疊45度層之X方向應力分佈…………….42
圖3-11 鑽孔類似均向疊90度層之X方向應力分佈…………….43
圖3-12 鑽孔類似均向疊-45度層之X方向應力分佈……………43
圖3-13 鑽孔類似均向疊0度層之Tsai-Wu法則值………………44
圖3-14 鑽孔類似均向疊45度層之Tsai-Wu法則值……………..44
圖3-15 鑽孔類似均向疊90度層之Tsai-Wu法則值……………..45
圖3-16 鑽孔類似均向疊-45度層之Tsai-Wu法則值……………..45
圖3-17 鑽孔類似均向疊0度層最後破壞區域……………………46
圖3-18 鑽孔類似均向疊45度層最後破壞區域…………………..46
圖3-19 鑽孔類似均向疊90度層最後破壞區域…………………..47
圖3-20 鑽孔類似均向疊-45度層最後破壞區域…………………..47
圖3-21 Chang模式之十字疊初始破壞區域……………………….48
圖3-22 Chang模式之十字疊最後破壞區域……………………….48
圖3-23 Chang模式之類似均向疊初始破壞區域………………….49
圖3-24 Chang模式之類似均向疊最後破壞區域………………….49
圖3-25 數值模擬各振次下鑽孔十字疊之損傷區域………………50
圖3-26 數值模擬各振次下鑽孔類似均向疊之損傷區域…………51
圖3-27 超音波掃瞄各振次下鑽孔十字疊之損傷區域……………52
圖3-28 超音波掃瞄各振次下鑽孔類似均向疊之損傷區域………52
圖3-29 應力強度因子外插法之示意圖…………………………....53
圖3-30 雙邊裂縫十字疊裂縫長度與應力強度因子之曲線圖……53
圖3-31 雙邊裂縫類似均向疊裂縫長度與應力強度因子之曲線圖54
圖3-32 雙邊裂縫十字疊幾何修正因子方程式之曲線圖…………54
圖3-33 雙邊裂縫類似均向疊幾何修正因子方程式之曲線圖……..55
圖A-1 雙邊裂縫十字疊裂縫長度與極限強度曲線圖…………….68
圖A-2 雙邊裂縫類似均向疊裂縫長度與極限強度曲線圖……….68
圖B-1 數值模擬各振次下雙邊裂縫十字疊之損傷區域………….69
圖B-2 數值模擬各振次下雙邊裂縫類似均相疊之損傷區域…….70

1.Jen, M.-H. R. and C.-H. Lee, “Strength and Life in Thermoplastic Composite Laminates under Static and Fatigue Loading, Part 1: Experimental, “ Int.J. of Fatigue, Vol. 20, No. 9, 1998, pp. 605~625.

2.Jen, M.-H. R. and C.-H. Lee, “Strength and Life in Thermoplastic Composite Laminates under Static and Fatigue Loading, Part 2: Formulation, “ Int.J. of Fatigue, Vol. 20, No. 9, 1998, pp. 617~629.

3.Schutz, O. and Gerharz, J.J., “Fatigue Strength of a Fiber-Reinforced Materials.” Composite, Vol.8, 1977, P.245.

4.Ma, C. C. M.; Lin, S. H. ; Tau, N. H. ; Wu, S. H. and Wu, J. F. “ Fatigue Behavior of Quasi-Isotropic Carbon Fiber/PEEK Laminates Under Tension-Tension Loading ” Polymer Composites, Vol. 16, No. 3, June (1995), pp. 215-223.

5.Song, Dong-Yeul and Nobuo Otani “Fatigue Life Prediction of Cross-Ply Composite Laminates ” Materials Science and Engineering A238 (1997), pp. 329-335.

6.Paepegem, W. Van J. and Degrieck, P. De Baets “Finite Element Approach for Modelling Fatigue Damage in Fiber-Reinforced Composite Materials ”.

7.Jen, M.-H. R. and C.-H. Lee, “Fatigue Response and Modeling of Variable stress Amplitude and Frequency in AS-4/PEEK Composite Laminates, Part1: Experiments,” J. of Composite Materials., Vol.34, No.11, 2000, pp.906~929.

8.Jen, M.-H. R. and C.-H. Lee, “Fatigue Response and Modeling of Variable stress Amplitude and Frequency in AS-4/PEEK Composite Laminates, Part2: Analysis and Formulation,” J. of Comp. Mats., Vol.34, No.11, 2000, pp.930~953

9.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.

10.Bartley-Cho, Jonathan; Gyu Lim, Seung; Hahn, H. Thomas; Shyprykevich, Peter, “Damage Accumulation in Quasi-Isotropic Graphite/Epoxy Laminates Under Constant-Amplitude Fatigue and Block Loading ” Composites Science and Technology Vol. 58 (1998), pp. 1535-1547.

11.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

12.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.

13.Ferreira, J. A. M. ; Costa, J. D. M. and Richardson, M. O.W. “ Effect of Notch and Teat Condition on the Fatigue of the Glass-Fiber-Reinforced Polypropylene Composite” Composites Science and Technology Vol.57 (1997), pp.1243-1248

14.Beaumont, P.W.R.; Cowley, K.D “Damage Accumulation at Notches and the Fracture Stress of Carbon-Fiber/Polymer Composites: Combined Effects of Stress and Temperature ” Composites Science and Technology Vol. 57 (1997), pp. 1211-1219.

15.Pradhan S.C. and Tay T.E., "Three-dimensional finite element modelling of delamination grownth in notched composite laminates under compressionloading", Engineering Fracture Mechanics, Vol. 60, 1998, pp.157~172.

16.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.

17.Hafiani, F. and Dwyer, J.F., “Edge Function Analysis of Anisotropic Materials with Holes and Cracks”, Computers and Structures 72,1999,pp.779~791.

18.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).

19.王楚明，2001，〝含缺口複合材料之損傷行為研究〞，國立台灣大學機械工程學研究所博士論文。

20.Delale, F. and Erdogan, F., “ The Problem of Internal and Edge Cracks in Orthotropic Strip. ” Journal of Applied Mechanics, Vol. 44, Series E, NO.2, pp. 237-242, 1977

21.Mar, J. W. (1976). “ Fracture and Fatigue in Bi-Materials,” in Mechanics of Composite Review, Air Force Materials Laboratory and Air Force Office of Scientific Research Technical Report, pp.117-122

22.吳明勳，1995，〝非尖銳前緣之裂縫在異向性材料中的應力集中問題〞國立清華大學動力機械學系碩士論文。

23.張朝萬，1996，〝 纖維複合材料之位移觀點破壞判準 〞，國立台灣大學機械工程學研究所碩士論文。

24.王琮瑋，1999，〝 疊層複合材料中疲勞裂縫成長之電腦模擬 〞，國立清華大學動力機械研究所碩士論文。

25.Gibson, R. F., Principles of Composite Material Mechanics, McGRAW-Hill, 1994.

26.Broke, D., Elementary Engineering fracture Mechanics, Martinus Nijhoff, 1982.

27.李傳華，1988，"石墨纖維/環氧樹脂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。

28.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。

29.李進發，2001， " 數值解析碳纖維/聚二醚酮複合材料積層板殘留強度 "，國立中山大學機械所碩士論文。

30.蔡豐懋，1995，" 穿透式雙邊傾斜裂縫之實驗與數值分析 ",國立中山大學機械所碩士論文。

31.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。

32.Tada, H.; Paris, P. and Irwin, G., The Stress Analysis of Cracks Handbook, Del Research Corporation, 1985.

33.吳長和，2001，" 碳纖維/聚二醚酮複材積層板疲勞作用殘留性質之實驗分析 "，國立中山大學機械所碩士論文。