工程設計中為使材料有更多元化的應用，常將材料進行加工，而為使結構的強度提升，常使用結合二種以上材料甚至做成三明治結構。但材料經過合成並加工的過程中，常有令人意想不到的損壞發生。目前，最常使用的材料仍以金屬材料為主，而碳纖維複合材料疊層板是目前被大量使用的複合材料，其有足夠的強度且價格合理，相關研究也相當的多；另一種被大量研究的新興材料為奈米碳管，奈米碳管具有優良的機械與化學特性，因此學界紛紛以奈米碳管為補強材，來製作高性能的奈米複合材料。
本文將結合此二種複合材料，使用環氧樹脂將二種材料接合而成雙材料結構與三明治結構，利用末端刻痕彎曲(end notched flexure)測試，得到雙材料結構與三明治結構之能量釋放率(Gc)。文中也使用有限單元分析，並將實驗結果與有限單元分析結果比較。結果顯示含預裂縫雙材料結構，當上層材料有較好的抗彎曲強度而下層材料有較好的抗拉強度時，能量釋放率明顯變小；含預裂縫三明治結構，當表層材料抵抗彎曲強度的能力較小時能量釋放率明顯下降。

1. H. Y. Ling, K. T. Lau and C. K. Lam, “Effects of Embedded Optical Fibre on Mode II Fracture Behaviours of Woven Composite Laminates,” Composites: Part B, Vol. 36, pp. 534-543, 2005.
2. Y. Zhou, F. Perivn, L. Lewis and S. Jeelani, “Fabrication and Characterization of Carbon/Epoxy Composites Mixed with Multi-walled Carbon Nanotubes,” Materials Science and Engineering A, Vol. 475, pp. 157-165, 2008.
3. B. Fiedler, F. H. Gojny, M. H.G. Wichmann, M. C.M. Nolte and K. Schulte, “Fundamental Aspects of Nano-reinforced Composites,” Composites Science and Technology, Vol. 66, pp. 3115-3125, 2006.
4. M. Arai, Y. Noro, K. I. Sugimoto and M. Endo, “Mode I and Mode II Interlaminar Fracture Toughness of CFRP Laminates Toughened by Carbon Nanofiber Interlayer,” Composites Science and Technology, Vol. 68, pp. 516-525, 2008.
5. J. Ning, J. Zhang, Y. Pan and J. Guo, “Fabrication and Mechanical Properties of SiO2 Matrix Composites Reinforced by Carbon Nanotube”, Materials Science and Engineering A, Vol. 357, pp. 392-396, 2003.
6. T. Yokozeki, T. Ogasawara and T. Aoki, “Correction Method for Evaluation of Interfacial Fracture Toughness of DCB, ENF and MMB Specimens with Residual Thermal Stress,” Composites Science and Technology, Vol. 68, pp. 760-767, 2008.
7. L. Kucherov and M. Ryvkin, “Interface Crack in Periodically Layered Bimaterial Composite,” Internation Journal of Fracture, Vol. 117, pp. 175-194, 2002..
8. M.A.L. Silva, M.F.S.F. D. Moura and J.J.L. Morais, “Numerical Analysis of the ENF Test for Mode II Wood Fracture,” Composites: Part A, Vol. 37, pp. 1334-1344, 2006.
9. L. Tong and X. Sun, “Bending Effect of Through-Thickness Reinforcement Rods on Mode II Delamination Toughness of ENF Specimen: Elastic and Rigid-Perfectly Plastic Analyses,” Composites: Part A, Vol. 38, pp. 323-336, 2007.
10. A.B. Pereira, A.B. D. Morais, A.T. Marques and P.T. D. Castro, “Mode II Interlaminar Fracture of Carbon/Epoxy Multidirectional Laminates,” Composites Science and Technology, Vol. 64, pp. 1653-1659, 2004.
11. F. Aymerich, G. Lecca and P. Priolo, “Modelling of Delamination Growth in Composite Laminates by the Virtual Internal Bond Method,” Composites: Part A, Vol. 39, pp. 145-153, 2008.
12. Z. Ouyang and G. Li, “Nonlinear Interface Shear Fracture of End Notched Flexure Specimens,” Internation Journal of Solids and Structures, Vol. 46, pp. 2659-2668, 2009.
13. P. Feraboli and K. T. Kedward, “Four-Point Bend Interlaminar Shear Testing of Uni- and Multi-Directional Carbon/Epoxy Composite Systems,” Composites: Part A, Vol. 34, pp. 1265-1271, 2003.
14. F. Mujika, N. Carbajal, A. Arrese and I. Mondragon, “Determination of Tensil and Compressive Moduli by Flexural Tests,” Polymer Testing, Vol. 25, pp. 766-771, 2006.
15. S. D. Faulkner, Y. W. Kwon, S. Bartlett and E. A. Rasmussen, “Study of Composite Joint Strength with Carbon Nanotube Reinforcement,” J Mater Sci, Vol. 44, pp. 2858–2864, 2009.
16. Y. Tomita, T. Tamaki and K. Morioka, “Effect of Fiber Strength on Notch Bending Fracture of Unidirectional Long Carbon Fiber-Reinforced Epoxy Composite,” Materials Characterization, Vol. 41, pp. 123-135, 1998.
17. I. M. Daniel and J. L. Abot, “Fabrication, Testing and Analysis of Composite Sandwich Beams,” Composites Science and Technology, Vol. 60, pp. 2455-2463, 2000.
18. V. Vadakke and L. A. Carlsson, “Experimental Investigation of Compression Failure of Sandwich Specimens with Face/Core Debond,” Composites Part B: Engineering, Vol. 35, pp. 583-590, 2004.
19. E. E. Gdoutos, I. M. Daniel, K. A. Wang and J. L. Abot, “Nonlinear Behavior of Composite Sandwich Beams in Three-Point Bending,” Experimental Mechanics, Vol. 41, pp. 182-189, 2001.
20. S. C. Lee, S. T. Jeong, J. N. Park, S. J. Kim and G. J. Cho, “A Study on Mechanical Properties of Carbon Fiber Reinforced Plastics by Three-Point Bending Testing and Transverse Static Response,” Journal of Materials Processing Technology, Vol. 201, pp. 761-764, 2008.
21. T. Hobbiebrunken, M. Hojo, T. Adachi, C. D. Jong and B. Fiedler, “Evaluation of Interfacial Strength in CF/Epoxies Using FEM and In-Situ Experiments,” Composites Part A, Vol. 37, pp. 2248-2256, 2006.
22. L. L. Christian, B. F. Sorensen, C. Berggreen and R. C. Ostergaard, “A Modified DCB Sandwich Specimen for Measuring Mixed-Mode Cohesive Laws,” Engineering Fracture Mechanics, Vol. 75, pp. 2514-2530, 2008.
23. G. Yamamoto, M. Omori, Y. Sato, T. Takahashi, K. Tohji and T. Hashida, “Effects of Polycarbosilane Addition on The Mechanical Properties of Single-Walled Carbon Nanotube Solids,” JSME International Journal Series A, Vol. 48, pp. 189-193, 2005.
24. Y. Yan and S. H. Park, “An Extended Finite Element Method for Modeling Near-Interfacial Crack Propagation in A Layered Structure,” International Journal of Solids and Structures, Vol. 45, pp. 4756-4765, 2008.
25. J. Hohe and W. Becker, “Assessment of The Delamination Hazard of The Core Face Sheet Bond in Structural Sandwich Panels,” International Journal of Fracture, Vol. 109, pp. 413-432, 2001.
26. R. C. Ostergaard and B. F. Sorensen, “Interface Crack in Sandwich Specimen,” International Journal of Fracture., Vol. 143, pp. 301-316, 2007.
27. X. Q. Shi, X. R. Zhang, and J. H. L. Pang, “Determination of Interface Fracture Toughness of Adhesive Joint Subjected to Mixed-Mode Loading Using Finite Element Method,” International Journal of Adhesion & Adhesives, Vol. 26, pp. 249-260, 2006.
28. W. S. Burton and A. K. Noor, “Structural Analysis of the Adhesive Bond in A Honeycomb Core Sandwich Panel,” Finite Element in Analysis and Design, Vol. 26, pp. 213-227, 1997..
29. J. B. Bai and A. Allaoui, “Effect of the Length and the Aggregate Size of MWNTs on the Improvement Efficiency of the Mechanical and Electrical Properties of Nanocomposites – Experimental Investigation,” Composites: Part A, Vol. 34, pp. 689-694, 2003.
30. S. V. Lomov, M. Barburski, Tz. Stoilova, I. Verpoest, R. Akkerman, R. Loendersloot and R.H.W. T. Thije, “Carbon Composites Based on Multiaxial Multiply Stitched Preforms. Part 3: Biaxial Tension, Picture Frame and Compression Tests of the Preforms,” Composites:Part A, Vol. 36, pp. 1188-1206, 2005.
31. T. C. Truong, M. Vettori, S. Lomov and I. Verpoest, “Carbon Composites Based on Multi-axial Multi-ply Stitched Preforms. Part 4. Mechanical Properties of Composites and Damage Observation,” Composites:Part A, Vol. 36, pp. 1207–1221, 2005.
32. M. F. Yu, B. S. Files, S. Arepalli and R. S. Ruoff, “Tensile Loading of Ropes of Single Wall Carbon Nanotubes and their Mechanical Properties,” Physical Review Letters, Vol. 84, pp. 5552–5555, 2000.
33. K. T. Lau, S. Q. Shi and H. M. Cheng, “Micro-Mechanical Properties and Morphological Observation on Fracture Surfaces of Carbon Nanotube Composites Pre-Treated at Different Temperatures,” Composites Science and Technology, Vol. 63, pp. 1161-1164, 2003.
34. 劉家豪, 多壁奈米碳管/酚醛樹脂複合材料之機械性質研究, 國立清華大學動力機械工程研究所碩士論文, 2004.
35. 林佳民, 含奈米複合材料三明治結構之彎曲與破裂特性, 國立清華大學動力機械工程研究所碩士論文, 2008.
36. ANSYS Release 11.0, ANSYS, Inc., PA, 2006.
37. I. M. Daniel and O. Ishai, Engineering Mechanics of Composite Materials, Oxford University Press , New York, 2006.
38. F. Mujika, “On the Difference Between Flexural Moduli Obtained by Three-Point and Four-Point Bending Tests,” Polymer Testing, Vol. 25, pp. 214-220, 2006.
39. J. A. Nairn, “On The Calculation of Energy Release Rates for Cracked Laminates with Residual Stress”, International Journal of Fracture, Vol. 139, pp. 267-293, 2006.
40. E. F. Rybicki and M. F. Kanninen, “A Finite Element Calculation of Stress Intensity Factors by A Modified Crack Closure Integral,” Engineering Fracture Mechanics, Vol. 9, pp. 931-938, 1977.
41. 藤井太一、座古勝，劉松柏譯，複合材料的破壞與力學，五南圖書出版股份有限公司，台灣台北，2006。
42. J. W. Dally and W. F. Riley, “Experimental Stress Analysis,”New York, McGraw-Hill Inc., 1991.
43. ASTM D638-82a, “Standard Test Method for Tensile Properties of Plastics,” Annual Book of ASTM Standards, Vol. 8.2, 1982.
44. Y. Murakami, “Stress Intensity Factors Handbook,” Pergamon Books Ltd., 1987.
45. 蔡秝凱, 正交性複合材料中裂縫前端的微觀尺度應力強度因子, 國立清華大學動力機械工程研究所碩士論文, 2005.