摘要

論文題目(中文)：界面接角之應力強度因子
論文題目(英文)：Stress Intensity Factors for Interface Corners

研 究 生：郭泰良
指導教授：胡潛濱

在線彈性破壞力學(LEFM)的範疇下，均質裂紋其尖端之應力奇異階次為一定值-1/2，但此應力奇異階次卻與材料性質無關。針對介於兩相異材料間之界面裂紋而言，由於靠近裂紋尖端之應力場有奇異性的震盪行為，故其應力奇異階次時常以一對共軛複數 與一實數-1/2同時發生，而此震盪指數 之量值則取決於相鄰材料各自之材料性質。然而對於一般的界面接角而言，其應力奇異階次不僅僅只受材料性質影響，亦隨著界面接角的角度大小而變化。有鑑於均質裂紋、界面裂紋與界面接角之應力奇異階次皆不相同，故在過往的文獻中均各別定義相關聯的應力強度因子以致於個別之定義在方程式型態上不甚一致，且由於均質裂紋與界面裂紋皆可視為界面接角之特例，故此篇論文提出通用的應力強度因子定義式以便使得上述三者有直接的關聯性。藉由師門早期所提出之複合異向楔形板的解析解，對於廣義的界面接角其鄰近接角尖端之位移場與應力場可依應力奇異階次的重根與否、複變數與否而將被分為五種類型來探討。為了提供廣義混合模式之應力強度因子更穩定與更有效率的計算方法，此篇論文採用了以reciprocal theorem of Betti and Rayleigh為基礎之路徑獨立積分-H積分，而此篇論文亦提供了計算H積分所需之輔助解。為了闡述此篇論文之研究成果，文末列舉了幾種不同類型之範例，如裂紋於均質等向性材料或均質異向性材料、中央凹口或邊緣凹口於均質等向性材料，和介於兩種相異材料間之界面裂紋或界面接角。

Stress Intensity Factors for Interface Corners

Student：Tai-Liang Kuo
Advisor：Chyanbin Hwu
ABSTRACT

Based upon linear fracture mechanics, it is well known that the singular order of stresses near the crack tip in homogeneous materials is a constant value -1/2, which is nothing to do with the material properties. For the interface cracks between two dissimilar materials, their singular orders become and -1/2 due to the singular oscillatory behavior of near tip stresses. The oscillation index is a constant related to the mechanical properties of both materials. While for the general interface corners, their singular orders depend on the corner angle as well as the mechanical properties of the materials. Owing to the difference of the singular orders of homogeneous cracks, interface cracks and interface corners, their associated stress intensity factors are usually defined separately and even not compatibly. Since homogenous cracks and interface cracks are just special cases of interface corners, in order to build a direct connection among them a unified definition for their stress intensity factors is proposed in this paper. Based upon the analytical solutions obtained previously for the multibonded anisotropic wedges, the near tip solutions for the general interface corners have been divided into five different categories depending on whether the singular order is distinct or repeated, real or complex. To provide a stable and efficient computing approach for the general mixed-mode stress intensity factors, the path-independent H-integral based on reciprocal theorem of Betti and Rayleigh is established in this paper. The complementary solutions needed for calculation of H-integral are also provided in this paper. To illustrate our results, several different kinds of examples are shown such as cracks in homogenous isotropic or anisotropic materials, central or edge notches in isotropic materials, interface cracks and interface corners between two dissimilar materials.

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