臺灣博碩士論文加值系統

1960年代以來,異向性架構的材料已經廣泛應用於許多工業,如航空、航天和軍事的工程運用。近年來所發展之高性能複材，常視不同之需要，以多種相異物性之材料- 如異向/異向或異向/等向之方式結合而成，其中最常見的例子便是疊層複材以及電子封裝中之覆晶組件。這些高性能之複材常常暴露在高温-低溫之循環操作環境下，其最常遇見之問題便是不同材料之界面處產生脫層現象。此原因乃是由於不同材料之熱膨脹係數不同之故。
本論文之目的在於以邊界元素法分析，研究此等多重異向複材在劇烈溫差下其相接層面之熱應力。藉此，得以更進一步分析並了解：如果界面產生脫層現象時裂紋之強度因子與相接材料物性之關聯性。以往邊界元素法在分析異向性材料之熱應力問題時一直受挫，問題之癥結在於熱效應本身在邊界積分式中為一體積分。為此，域內就必須做全域分割，如此便破壞了邊界元素法祗需在邊界分割之特性。此項問題直到最近才由Shiah和Tan【10】經由連續模式處理問題成功的將體積分轉換成邊界積分才得以解決。此外，將更進一步研究在微米甚至奈米區間時多種異向複材受熱時其熱應力問題。

Since the 1960’s, materials with anisotropic properties have been extensively used in numerous commercial, aerospace, and military engineering applications to achieve their ultimate performance. For various purposes, composites are often constructed by combining two or more anisotropic materials such as a combination of anisotropic/anisotropic or anisotropic/isotropic materials. The common examples in industries include layered composites and the assembly of flip chips in electronic packaging. The multiply adjoined composites are often subjected to cycles of ultimate heating and cooling. Under such operation environment, the most serious problem that the composites may encounter is the delamination between interfaces. This is mainly due to the mismatch of thermal expansion coefficients of the adjoined anisotropic materials.
The goal of this project is to analyze the interfacial thermal stresses between dissimilar anisotropic materials that are subjected to severe temperature change. Through this investigation, we may further study the relationship between the stress intensity factors (SIFs) of a crack initialing de-bonding and the constituent materials’ properties. In the past, the boundary element method (BEM) was not successful in analyzing thermoelastic stresses in anisotropic materials. This is because, in the boundary integral equation, the thermal effect reveals itself as an extra volume integral that requires domain discretisation and therefore destroys BEM’s notion as a boundary solution technique. This problem was not resolved until recently when the authors (Shiah, Y. C. and Tan, C. L., 1999) successfully transformed the extra volume integral into a series of boundary ones. In addition, analysis anisotropic materials of two-dimensional thin structures(from mirco- to nano-scales) using boundary element method.

誌謝................................................................i
中文摘要 ...........................................................ii
英文摘要............................................................iii
目錄................................................................iv
圖目錄..............................................................vii
表目錄..............................................................xi
第一章 導論........................................................1
1.1 前言............................................................1
1.2 研究動機........................................................2
1.3 文獻回顧........................................................4
1.4 研究流程與方法..................................................7
第二章 研究理論回顧................................................12
2.1 含異向材料之疊層結構並含層間裂紋之熱傳問題......................12
2.1.1 不同異相材料接合處但無裂紋之界面..............................15
2.1.2 不同異相材料接合處為裂紋之界面................................16
2.2 異向材料之疊層結構熱應力與對應之裂紋強度因子問題................17
2.3 超薄疊層結構之近乎奇異積分問題..................................19
2.3.1 超薄等向結構之近乎奇異積分問題................................20
2.3.2 超薄異向性結構之近乎奇異積分問題..............................23
第三章 分部積分轉換................................................27
3.1 基礎函數 分部積分轉換...........................................27
3.1.1 二階非線性元素之積分轉換推導..................................28
3.1.2 二階線性元素之積分轉換推導....................................39
3.2 基礎函數 分部積分轉換...........................................49
3.2.1 二階非線性元素之積分轉換推導..................................49
3.2.2 二階線性元素之積分轉換推導....................................56
3.3 基礎函數 分部積分轉換...........................................65
3.3.1 二階非線性元素之積分轉換推導..................................66
3.3.2 二階線性元素之積分轉換推導....................................74
3.4 基礎函數 分部積分轉換...........................................82
3.4.1 二階非線性元素之積分轉換推導..................................84
3.4.2 二階線性元素之積分轉換推導....................................98
第四章 驗證分部積分轉換適用與正確性................................110
4.1 非零Jacobian 座標轉換之證明.....................................110
4.2 被積函數之近乎奇異性探討........................................114
4.3 數值驗證........................................................115
4.3.1 二階非線性元素數值驗證........................................116
4.3.2 二階線性元素數值驗證..........................................118
4.3.3 二階非線性元素與線性元素數值比對..............................119
第五章 數值範例....................................................147
5.1 範例1...........................................................148
5.2 範例2...........................................................150
5.3 範例3...........................................................152
5.4 範例4...........................................................153
第六章 結論與展望..................................................179
參考文獻............................................................182
附錄A...............................................................186

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