本研究主要目的在探討異向性雙層材料之裂縫傳播問題，藉以異向性線彈性理論之雙層材料基本解(Pan and Amadei, 1999)搭配單域邊界積分方程式(Chen, 1996)求解在雙層材料中裂縫尖端之應力強度因子，再結合以最大法線應力準則(Sih et al., 1965)及新增裂縫元素技術模擬裂縫傳播路徑。
有別於傳統之邊界元素分析，本研究之數值模式具有下列幾項優勢: (1)單域邊界積分方程式，可省略架構域內元素邊界，亦無需對材料之接合面設置人為邊界，(2)可有效避開裂縫尖端奇異系統及材料接合面之微振盪現象，(3)在處理裂縫傳播時，簡化繁雜的域內數值運算，不僅快、且有效率的繪製出既有裂縫之傳播路徑，(4)以裂縫尖端相對位移之技術，逼近各新增裂縫尖端求取應力強度因子及初始開裂角度。此數值模式藉由歷年學者提出各案例之解析解，及異向性雙層岩石巴西實驗之裂縫破壞路徑進行數值驗證，其結果顯示皆非常吻合。本研究亦分別探討雙層材料之異向性程度、裂縫幾何位置與材料介面之關係，其結果發現裂縫尖端之應力強度因子皆受異向性程度變化及裂縫尖端與材料介面間之距離遠近而有顯著的影響。

This dissertation presented a numerical technique based on the boundary element method (BEM) for the analysis of linear elastic fracture mechanics (LEFM) problems on stress intensity factor, SIFs, and modeling crack propagation path involving anisotropic bi-materials. The most outstanding feature of this analysis is that it is a single domain method, and yet it is very accurate, efficient and versatile, i.e. Material properties in the medium can be anisotropic as well as isotropic. Problem domain can be finite, infinite or semi-infinite. Cracks can be of multiple, branched or internal type with a straight shape. Furthermore, the body force case can also be analyzed.
The present BEM technique is an extension of the work by Chen (1996) and is such that the displacement and traction integral equations are collocated on the outer boundary and on one side of the crack surface, respectively. This single-domain BEM formulation originally applies to a homogeneous material. This thesis combines it with the Green’s functions of bi-materials (Pan and Amadei, 1999). Then the new formulation can be extended to anisotropic bi-materials. The complete Green’s functions for anisotropic bi-materials are also derived and implemented into the boundary integral formulation so that discretization along the interface can be avoided except for the interfacial crack part. A special crack-tip element (Gao et al., 1992) is introduced to capture exactly the crack-tip behavior. In addition, the BEM formulation combined with the maximum tangential stress (MTS) criterion (Sih et al., 1965) that can be used to predict the crack initial angle and to simulate the propagation path of crack tips.
A computer program with the formula translation (FORTRAN 90) code has been developed to effectively calculate the crack initiation angle, propagation path, and stress intensity factors (SIFs) in an anisotropic bi-material. This BEM program has been verified and shown good accuracy compared with the previous researches. Numerical examples are presented for the calculations of stress intensity factors for a straight crack with various locations in both finite and infinite bi-materials. It is found that very accurate results can be obtained by the proposed method even with relatively simple discretization. The results of numerical analysis also show that material anisotropy can greatly affect the stress intensity factor. Besides, a cracked straight through Brazilian disc (CSTBD) of bi-material specimens was made to conduct the Brazilian test under segmental loading. The result shows that the numerical analysis can predict relatively well for the direction of crack initiation and the path of crack propagation.

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