在複合層板的應用方面，疲勞損傷研究是一個重要的課題，其研究可以提早知道材料性質退化的情況，而殘餘勁度遞減的現象提供了一個度量材料損傷情形的一個指標。經由非破壞性檢測的方法量測勁度之改變，可預測及追蹤複合材料受疲勞作用力下的疲勞損傷程度，Yang[20]以勁度遞減模式為基礎，正確的預估出石墨纖維/環氧樹脂 複合層板的疲勞行為。
　　因勁度遞減模式的計算較為繁瑣，為提升計算上的效率，因而選用一種較快速的方式來預估複合疊層板的疲勞行為，並與實驗結果相比對，以驗證簡化法的正確性。本文將未簡化與簡化的兩種方法去作殘餘勁度、破壞勁度及疲勞壽命的預估，並與實驗值相作比較，以驗證簡化法在疲勞行為預估能力。其結果顯示，快速法與實驗數值相吻合，說明了簡化法在疲勞損傷可正確快速的預估出損傷的分佈。

　　The application aspect of the composite laminates, fatigue behavior is an important subject. The study can know the situation that degradation of the material property. And the phenomenon of the stiffness degradation has offered an index of measuring the material damage. Examining the change of the stiffness reduction via the method amount of non-destructive measuring that can predict and track that the composite endure the fatigue damage degree under fatigue cycling .Based on Yang’ stiffness degradation model, the fatigue behavior of Graphite/Epoxy composite laminates can predicted correctly.
　　The calculation of stiffness degradation model is tedious, in order to improve count efficiency, Therefore select a kind of faster way for use to estimate the fatigue behavior of composite laminates. And compared with experimental result right, in order to prove that simplifies method the exactness. This thesis will go with two kinds of methods to do the residual stiffness, failure stiffness and fatigue life to estimate in advance. Comparing with experiment data, prove that estimates ability in fatigue behavior using simplified method and unreduced method. Its result shows, simplified method identical with experiment data, it proves simplified method correct estimating damage distribution.

1.Barnard, P. M., Butler, R. J. and Curtis, P. T., “The Strength-Life Equal Rank Assumption and Its Application to the Life Prediction of Composite Materials,” International Journal of Fatigue, Vol. 10, pp. 171-177, 1988.
2.Chou P. C. and Croman, “Residual Strength in Fatigue Based on the Strength-Life Rank Assumption,” Journal of Composite Materials, Vol. 12,pp. 177-194 1978
3.Fu, K. E. and Lee, L. J., “Life Prediction under Service Loading Spectra “ Chapter 19, Fatigue in Composites, edited by Harris. B. Woodhead Publishing Ltd, Cambridge, England, 2003.
4.Hahn, H. T., and Kim, R. Y., “Proof Testing of Composite Materials,” Journal of Composite Materials, Vol. 9, 1975, pp. 297 – 311.
5.Hahn, H. T., and Kim, R. Y., “Fatigue Behavior of Composite Materials, ”Journal of Composite Materials, Vol. 10, April 1976, pp. 156 – 180.
6.Hahn, H. T., “Fatigue Behavior and Life Prediction of Composite Laminates,” Composite Materials: Testing and Design (Fifth Conference), ASTM STP 674, S. W. Tsai, Ed., American Society for Testing and Materials, 1979, pp. 383 – 417.
7.Hashin, Z., “Cumulative Damage Theory for Composite Materials: Residual Life and Residual Strength Methods”, Composite Science and Technology, Vol. 23, 1985, pp. 1 – 19.
8.H. A. Whitworth., “Modeling stiffness Reduction of Graphite/Epoxy Composite Laminates”, Journal of Composite Materials, Vol. 21. 1987.
9.H. A. Whitworth., “A stiffness degradation model for composite laminates under fatigue loading”, Composite Structure, Vol. 40. No. 2. pp. 95 – 101, 1998.
10.Hwang, W., and Han, K. S., “Cumulative Damage Models and Multi-Stress Fatigue Life Prediction,” Journal of Composite Materials, Vol. 20, March 1986, pp. 125 – 153.
11.Hwang, W., and Han, K. S., “Fatigue of Composites-Fatigue Modulus Concept and Life Prediction,” Journal of Composite Materials, Vol. 20, March 1986, pp. 154 – 165.
12.Hwang, W. and Han, K. S., “Fatigue of Composite-Damage Model and Life Prediction,” Composite Materials: Fatigue and Fracture, Vol. II, ASTM STP 1012, American Society for Testing and Materials, 1989, pp. 87 – 102.
13.Kapur K. C. and Lamberson L. R. ”Reliability in Engineering Design” john Wiley＆Sons ,New York ,1977
14.Lee, L. J., Yang, J. N., and Fu, K. E., “Prediction of Fatigue Damage And Life For Composite Laminates under Loading Spectra,” Composite Science and Technology, Vol. 56, 1996, pp. 635 – 648.
15.Lee, L. J., Yang, J. N., and Sheu, D. Y., “Modulus Reduction and Fatigue Damage of Matrix Dominated Composite Laminates,” Composite Structures, Vol. 21, 1992, pp. 91 – 100.
16.Lee, L. J., Yang, J. N., and Sheu, D.Y., “Prediction of Fatigue Life for Matrix Dominated Composite Laminates, ”Composite Science and Technology, Vol. 44, 1992.
17.Yang, J. N., “Fatigue and Residual Strength Degradation for Graphite/Epoxy Composites under Tension – Compression Cyclic Loading,” Journal of Composite Materials, Vol. 12, January 1978.
18.Yang, J.N., and Du. Shanyi, “An Exploratory Study for Fatigue of Composite under Spectrum Loading,” Journal of Composite Materials, Vol. 17, November 1983, pp. 511 – 526.
19.Yang, J. N., and Jones, D. L., “Statistical Fatigue of Graphite/Epoxy Angle -Ply Laminates in Shear,” Journal of Composite Materials, Vol. 12, Oct. 1978, pp. 371 – 389.
20.Yang, J. N., Jones, D. L., and Yang, S. H., “A Stiffness – Based Statistical Model For Predicting the Fatigue Life of Graphite/Epoxy Laminates, ”Journal of Composite Technology and Research, Vol. 11, No. 4, Winter 1989, pp. 129 – 134.
21.Yang, J. N., and Liu, M. D., “Residual Strength Degradation Model and Theory of Periodic Proof Test For Graphite/Epoxy Laminate, ”Journal of Composite Materials, Vol. 11, April 1977, pp. 176 – 203.
22.Yang, S. H., “Stiffness Degradation of Composite Laminates,” D. Sc. Dissertation, The George Washington University, 1987.
23.鄭合志，複合材料在變動複合下之疲勞可靠度研究，國立台灣大學機械工程學研究所博士論文，2000