本論文內容可分成三部分，第一部分研究IC封裝體結構因迴銲所導致破裂問題，第二、三部分則分別探討兩種複合材料的全相結構與單一壓電材料之楔形結構之應力奇異性。
　　第一部分利用Muskhelishvili所發展的複變函數法，探討IC結構因承受機械與熱負載而發生爆米花破裂現象，分析晶座與樹脂接合尖端處之應力奇異性，並以二者的楊氏係數之比值作為材料選擇的參考。此外，也探討晶座之壓心深度對結構穩定性的影響。經由有限元素分析，以最小平方法得到尖端處之廣義應力強度因子，並引進應變能密度理論，以判定結構的穩定性及裂紋之擴展方向。
　　其次，以Lekhnitskii公式為基礎，針對兩種非等向性材料之全相結構，分析材料常數、纖維方向及楔形角度，對應力奇異性的影響。利用代表所有纖維方向的圓形區域，繪出結構應力奇異性階數之等高線圖，從圖中可直接瞭解應力奇異性階數最強、最弱或消失時的纖維方向，這提供結構設計時很好的參考依據。
　　最後，將Lekhnitskii公式延伸至壓電材料，討論單一圓柱非等向性之楔形結構問題。以壓電陶瓷PZT-4為例，依據極化方向為徑向、周向及軸向，探討楔形角、邊界條件、材料性質的壓電特性對應力奇異性之影響。

　This dissertation presents the general solutions with application of wedge and junction problems bonded by isotropic, anisotropic, or piezoelectric materials. Three topics are addressed separately: (1) The effect of stiffness and thickness ratios on popcorn cracking in IC packages; (2) A general solution on stress singularities in two-anisotropic material junction; and (3) Stress singularities at the vertex of a piezoelectric wedge with cylindrical anisotropy.
　The first topic discusses the popcorn crack problem in IC package under vapor pressure and thermal load during solder reflow process. Based on the elasticity theory, the singular stress field around the apex of the delaminated interface between die-pad and resin is obtained numerically. The stress intensity factors are computed to evaluate the residual strength of the structure. Also, the structural stability is discussed by using the strain energy density theory. Two factors that are concerned include the relative stiffness ratio Edie-pad/Eresin and the relative thickness . The results show that lower stiffness ratio gives stronger stress singularity. In addition, larger will increase stress intensity factors and structural stability. As a conclusion for our case, moderate value of (say =0) is recommended for design.
　The second topic presents the general solution on stress singularities of a junction composed of two dissimilar anisotropic materials. Based on the Lekhnitskii’s approach, the characteristic equation of the generalized plane deformation problem is developed. The concerned influencing parameters on the stress singularity are material constants, fiber orientations, and the bonding angle. The results of the stress singularity order are contour plotted in a circular region. With these figures, the conditions for minimum or even vanishing singularity order can be determined. The accuracy of this approach is guaranteed as the results are compared with several degenerated cases.
　The objective of final topic is to derive the characteristic equations for a piezoelectric wedge with cylindrical anisotropy by using the extended Lekhnitskii formulation. The piezoelectric material (PZT-4) is poled in radial, circular and axial directions, respectively. The results show that the behavior of stress singularity orders is different from that of a wedge or even for a crack with rectilinear anisotropy.

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