本文主要是利用有限元素法分析函數梯度材料之複合材料承受溫差變形時的應力行為，以及含裂縫之應力強度因子行為。內容中主要分為五個部分：(1)濺鍍層為單一材料之問題； (2)濺鍍層為多層梯度材料之問題； (3)濺度層為S型曲線函數梯度材料之問題； (4)濺度層為倒S曲線函數梯度材料之問題； (5)函數梯度材料含裂縫問題。
本研究成果顯示函數梯度材料之運用可有效減少應力在邊緣處集中之現象，不同的函數材料分佈有不同的應力分佈，研究中顯示p=2之S型以及Metal-rich型函數梯度分佈曲線將有較佳之應力分佈，不會有應力異點的現象，亦不會有過大之應力集中產生，可有效減緩濺鍍層的剝落。
在含裂縫問題方面,裂縫尖端位於S型函數梯度材料時之應力強度因子與Dundurs常數有關，當α>0時，應力強度因子受材料性質之影響而呈現S型變化之特徵，但當α<0時,應力強度因子的行為則類似均質材料。

The subject of this thesis mainly discusses the stress behaviors and stress intensity factors of cracks of composite material with functionally gradient material subjected to thermal loading by finite element method. There are five parts included in this thesis: (1)one material coating problem. (2)multi-layered homogeneous coating problem. (3)S-curve functionally gradient material problem. (4) anti-S-curve functionally gradient material problem. (5) the problem of FGM coating with a crack.
This study indicates that the use of functionally gradient material can efficiently reduce stress concentration at the edge of the interface of the composite material. The different functionally gradient materials led to different stress distributions. Results showed that the S-curve of p=2 and metal rich functionally gradient result in better stress distribution in which there is no stress singularity and lower stress concentrations. Consequently, the debonding of the undercoat can be efficiently reduced.
Moreover, in the aspect of crack problem, stress intensity factor of crack tip in S-curve functionally gradient material was concerned with Dundurs'' constants and . When α>0 and , stress intensity factor appears S-curve character by the influence of functionally gradient material disposition. While when α<0 and , the SIF of a crack in the functionally gradient material is similar with that in homogeneous material.

第一章 緒論...........................................................................................1
1.1 研究動機及目的............................................................................1
1.2 文敵回顧........................................................................................2
1.3 研究內容........................................................................................5
第二章 有限元素法.............................................................................6
2.1 前言................................................................................................6
2.2 有限元表法之分析原理與計算程序............................................7
2.2.1鍵入資料.....................................................................................7
2.2.2 建立元表勁度矩陣及受力向量...........................................…8
2.2.3建立完整結構矩陣...................................................................13
2.2.4解方程試...................................................................................14
2.2.5應力之計算...............................................................................14
2.3 MARC有限元素軟體之應用.......................................................16
第三章 理論基礎................................................................................19
3.1 界面之應力異點..........................................................................20
3.2 雙材料含裂縫之應力強度因子..................................................22
3.2.1 裂縫尖端位於薄膜內或位置基材內...................................22
3.2.2 裂縫尖端位於薄膜-基材之交界面......................................23
3.3 函數梯度材料..........................................................................24
3.3.1 多層梯度材料.......................................................................25
3.3.2 S曲線之函數梯度材料........................................................26
第四章 數值分析................................................................................29
4.1 一層濺鍍層之雙材料問題….....................................................29
4.1.1 問題描述…………................................................................29
4.1.2 雙材料界面之應力行為…....................................................30
4.2 濺鍍層為多層梯度材料問題………………………………...32
4.2.1 問題描述…………................................................................32
4.2.2 多層梯度材料之應力行為…………………………………32
4.3 濺鍍層為S型曲線之函數梯度材料........................................35
4.3.1 問題描述....………................................................................35
4.3.2 濺鍍層為S型曲線之函數梯度材料之應力分析…………36
4.4 濺鍍層為倒S型曲線之函數梯度材料..............................….41
4.4.1 問題描述....………................................................................41
4.4.2 濺鍍層為倒S型曲線之函數梯度材料..…...........................42
4.5 函數梯度材料應用於緩衝層………………...........................44
4.5.1 問題描述....………................................................................44
4.5.2 函數梯度材料應用於緩衝層之應力分析…………………45
4.6 函數梯度材料含裂縫問題................................……………...48
4.6.1 問題描述....………................................................................48
4.6.2 函數梯度材料含裂縫之應力強度因子……………………49
第五章 結論與建議............................................................................52
5.1 結論.............................................................................................52
5.2 建議...........................................................................…………..53
參考文獻………………………………………………………………..55

[1] Y.-D. Lee and F. Erdogan , "Residual / thermal stress in FGM and laminated thermal barrier coatings ",International Journal of Fracture, 69, pp.145-165,(1995)
[2] J. Gunnars， A. Alahelisten， "Thermal stresses in diamond coatings and their influence on coatings wear and failure", Surface and Coatings Technology,Vol. 80,pp.303-312 (1996).
[3] J. H. Selverian and D. O''Neil, "Strength and toughness measurement of thin brittle coatings on substrates", Thin Solid films, 235 , pp.120-128 (1993).
[4] O. Jorgensen,A. Horsewell,B. F. Sorensen and P. Leisenser, "The Multilayered Chromium Coatings", Acta metall. Mater. Vol. 43,No. 11, pp. 3991-4000(1995).
[5] Dunders J. , " Effect of Elastic Constant on Stress in a Composite under Plane Deformation", Journal of Composite Material，1:310(1967)
[6] Suga. T. , Elssner. E. and Schmander S. ,"Composite Parameters and Mechanical Compatibility of Material Joints" ,Jourmal of Composite Material , 22 , pp. 917-934.(1988).
[7] 張燕玲，陳罡，"介面噴塗層與基板種類對Ti10/W90濺鍍層之應力分析，國立台灣科技大學營建工程技術研究所碩士論文，1998
[8] 張燕玲，彭慶灃，"薄膜－基材複合材料之龜裂應力分析"國立台灣科技大學營建工程技術研究所碩士論文，(1997).
[9] M. Case and K. Kokini，in Ceramic Coatings. K.Kokini(ed.), The 1993 ASME Winter Annual Meeting，New Orleans，Louisiana， MD-Vol.44，PP. 149-162(1993).
[10]T. YE,Z. SUO and A. G. Evans "Thin film Cracking and The Roles of Substrate and Interface,"Imt,J,Solids Structures vol.29,