界面角存在於許多工程物件之中，且由於材料性質與幾何形狀的不連續，大部分的破裂失效都將發生於此處。鑲嵌於均質材料中之裂紋與接角，或是介於兩種相異材料間之界面裂紋均可算是界面角之特例。應力奇異階次與應力強度因子是在線彈性破裂力學的範疇中被廣泛運用於評估物件潛在的破裂危險程度與破裂模式之兩種非常重要的指標。
異向彈性材料、壓電材料與黏彈性材料時常被使用來當作組成工程物件之原料，其經常運作在溫度會變化的環境之下。此外，若想針對此些工程物件提供真實可靠的模擬分析時，三個空間維度的效應都必須被納入考慮，但此等考慮往往增加了解題時的複雜性與困難度。鑒於三維問題的複雜程度與介於熱彈性問題和上述三種材料間各自不同的本構方程式，此些問題的力學分析時常使用不同的解題方法。然而，藉由某些方法可使得此些問題能夠有所關聯，例如：平面應變、平面應力或軸對稱等假設可使得三維問題退化成二維問題，體積力類比法可使得熱彈性問題的解題流程如純彈性問題般，材料性質的適當擴增使得壓電問題的解題流程如純彈性問題般，拉普拉斯轉換的使用使得黏彈性問題的解題流程如純彈性問題般。
為了在此些相異卻又類似的問題中找出直接的關連，本文提出一通用方法來處理由異向彈性/壓電/黏彈性材料所構成之界面角其考慮或不考慮三維效應與熱效應之破裂分析。此通用方法源自於二維異向彈性力學中著名的史磋公式並被建立於藉由額外溫度場與熱流場之推導而延伸應用於熱彈性問題、藉由某些假設使得二維彈性問題的解仍適用三維彈性問題和藉由適當的對應法則使得壓電問題與黏彈問題的解題流程類似彈性問題。利用本文所提供之方法，由上述三種材料所組成之界面角考慮或不考慮熱效應與三維效應的應力奇異階次解析解與應力強度因子定義式都將維持著一模一樣的數學形式且唯一的不同之處僅在於方程式中的項次組成與維度，此特性對於從事界面角破裂分析相關研究主題之人員提供了非常簡便但適用範圍卻非常廣泛之理論分析工具。

Interface corners are the structural configurations commonly appearing within the engineering objects and failures initiate from these critical regions due to the discontinuities of geometry and material properties. Cracks/corners in homogeneous materials and interface cracks between two dissimilar materials are special cases of interface corners. To evaluate the potential of failure and the mode of fracture of interface corners, the two important parameters, i.e., order of stress singularity and stress intensity factors, are usually employed within the category of linear elastic fracture mechanics.
Anisotropic elastic materials behave differently in different directions. Piezoelectric materials produce an electric field when deformed and undergo deformation when subjected to an electric field. Viscoelastic materials exhibit a time and rate dependence that is completely absent in the elastic materials. These materials are often used as the constituents of engineering objects which may be operated in thermal environments. Besides, the three-dimensional effect should be taken into account if we want to provide a more realistic simulation for a case, but it usually increases the complexity of solution procedure. Due to the complexity of three-dimensional problem and the different constitutive relations among the thermoelastic problem and these three different kinds of materials, their mechanical analyses are usually made by different approaches. Among several different approaches, their connection can be made by the ways such as the degeneration from three-dimensional problem to two-dimensional problem (e.g. plane strain, plane stress, or axis-symmetric assumption), the body force analogy for thermoelastic problem, the expansion of the elastic properties to include the piezoelectric effects, and the use of the Laplace transform to make the viscoelastic stress-strain relations look like linear elastic materials.
In order to build a direct connection between several different but similar problems, in this thesis a unified approach is proposed to deal with the fracture analyses for interface corners in anisotropic elastic/piezoelectric/viscoelastic materials with/without the consideration of thermal and three-dimensional effects. The unified solution technique for these different problem types originates from the Stroh’s complex variable formalism in two-dimensional anisotropic elasticity and is established by extending this formalism to the thermoelastic problem through the extra derivations of temperature and heat flux fields, to the three-dimensional problem through two reasons which make the two-dimensional solutions be still valid, and to piezoelectric problem and viscoelastic problem through proper correspondence principles. By this technique, the analytical solution of singular orders and the definition of stress intensity factors presented in this thesis will preserve the same matrix form expressions for different kinds of cracks/corners composed of different kinds of materials under different kinds of surrounding effects, and the only difference is the contents and dimensions of the formulae and their associated matrices/vectors.

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