本論文內容可分成三部份，第一部份研究三種非等向性材料之楔形和全相結構尖端之應力奇異性。第二部份探討導體、複合材料及壓電材料分別與壓電材料之全相結構問題。第三部份探討含裂縫之壓電材料的破壞行為。
第一部份以Lekhnitskii公式為基礎，探討三種非等向性材料結構之應力奇異性。應力奇異性階數(l-1)與楔形角度、材料性質及邊界條界有關。利用全圓圖形以等高線描述出空間中任意纖維方向所對應之應力奇異性階數。藉由奇異性等高線圖，可直接找出最強與最弱應力奇異性所對應之纖維方向。最後，改變介相材料之楔形角與材料性質，可得到應力奇異性消失的現象，提供結構設計時重要之參考依據。
第二部份將Lekhnitskii複變函數延伸至壓電材料，探討壓電材料之全相結構問題，分析材料常數、纖維方向(極化方向)及楔形角對奇異性的影響。當壓電材料極化方向平行x-y平面或平行z-軸，應力奇異性階數將可分為面內場及面外場。藉由奇異性階數關係圖得知最強及最弱奇異性所對應之纖維方向與楔形角。
第三部份利用能量密度理論，探討含裂縫之單一壓電材料的破壞行為。能量密度因子S可以應力強度因子KI、KII及電位移(電場)強度因子KD(KE)表示。當極化方向垂直裂縫面，實驗觀察出正電場、負電場分別會幫助及抑制裂縫成長，利用本文所推導之能量密度因子S亦可得到此結果。利用能量密度理論預測裂縫成長角度q0及裂縫成長的驅動力Smin。影響裂縫成長角度及裂縫成長的驅動力與外力型態(機械力s∞、靜電力E∞)及壓電材料的極化方向有關。

This thesis contains three topics: (1) Stress singularities in anisotropic three-material wedges and junctions; (2) Stress singularities at the apex of composite piezoelectric junctions; (3) Fracture analysis of piezoelectric materials with crack for arbitrarily polarized orientation by using energy density criterion.
The first topic discusses the singularity order in three-material wedges and junctions by using Lekhnitskii’s complex potential functions. The stress singularity order depends on the material constants, the fiber orientation and wedge angles. The stress singularity order is plotted in a circular region. With these figures, the weakest and strongest singularity orders can be determined. By changing the wedge angle and material constants of interphase material, the conditions of vanishing singularity order can be obtained. Numerical results provide the designer with some useful suggestions.
By extending Lekhnitskii’s formula, the second topic investigates the stress singularities at the apex of a piezoelectric-conductor, -composite, or -piezoelectric junction with generalized plane deformation are investigated. The singularities of decoupled inplane and antiplane electromechanical fields are investigated respectively when piezoelectric materials are polarized in x-y plane or along z-axis. The emphasis has been placed on the roles of wedge angles and polarization of piezoelectric material.
In the last topic, the fracture analysis of an arbitrarily oriented crack in piezoelectric medium has been predicted by using energy density theory. The expression of the energy density factors S is modified to include the stress intensity factors KI and KII, the electric displacement intensity factor KD (or the electrical intensity factor KE) and the polarized orientation h. According to experiment results, it has shown that positive or negative electric field will aid or impede crack propagation, respectively. The energy density factor can also obtain the same result. The concept of energy density has been applied to predict the crack driving force Smin and its extending angle q0. The influencing factors of crack propagating angle and driving force are the remote mechanical load s∞, remote electric field E∞, and the polarized orientation h related to the crack plane.

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