本文探討在三維界面裂紋問題中，雙層非等向性材料界面裂紋受熱負載作用情況下，裂紋前緣之破壞力學參數之分佈；並利用有限元素法配合虛擬裂紋閉合法計算非等向性雙材料界面裂紋之三維破壞力學參數，包括應變能釋放率、應力強度因子及相位角。其中，應變能釋放率可藉由裂紋尖端元素節點上的力量和位移計算出的裂紋閉合積分式疊加求得。另外，以史蹉公式為基礎理論，從所得之界面裂紋尖端的漸近應力場及漸近位移場與裂紋閉合積分式之理論關係，可求得以裂紋閉合積分式計算應力強度因子及相位角之代數式。由於界面裂紋尖端的奇異彈性應力場具有震盪的行為，因此應力強度因子之值亦會隨著所使用之長度單位而有震盪的行為，此震盪之特性會造成直接使用虛擬裂紋閉合法求解界面裂紋之應力強度因子的困難。對此問題，可藉由特定之材料特徵長度來無因次化震盪的應力強度因子，使其單位回歸至(應力)×(長度)1/2。此外，對於較特殊之界面裂紋問題，包含裂紋尖端發生大範圍接觸及裂紋面受到內壓力之情況，本研究亦提出專用的公式來計算其破壞力學參數。針對於本文所提出之破壞力學參數求解方法，首先透過與界面裂紋問題的理論解析解來比對驗證；而後，本文討論應用虛擬裂紋閉合法來分析半導體電子元件中之雙材料界面裂紋受熱負載情況下，界面裂紋脫層成長之問題。

The problem of a three-dimensional interface crack between two anisotropic materials under thermomechanical load is investigated by using finite element method with the virtual crack closure technique. The fracture mechanics parameters, including the strain energy release rate, the stress intensity factors and phase angles along the interface crack front are obtained by using a numerical approach. In this approach, the crack closure integrals and the strain energy release rate are calculated from the nodal load and displacement solutions of the singular quarter-point crack-tip finite elements. Algebraic equations relating the crack closure integrals and the stress intensity factors are derived from the asymptotic displacement and stress fields around the interface crack tip, and is applied to determine the stress intensity factors and the corresponding phase angles. A complication in applying the VCCT directly to calculate the stress intensity factors for a bimaterial interface crack is that the results would depend on the size of the virtual crack extension. This is due to the oscillating behavior of the elastic singular stress field around the interface crack tip. The issue may be overcome by normalizing the stress intensity factors to a material characteristic length such that the stress intensity factors have a unit of (stress)×(length)1/2. In addition, variations of the equations for determining the fracture mechanics parameters are given for cases including large-scale contacting between interface crack faces and crack under inner pressure. Validation of the proposed approach is performed by comparing the numerically determined stress intensity factors for interface cracks to analytical solutions. The numerical approach is then applied to study the problems of microelectronic component containing interface corner crack fatigue growth under temperature cycling condition.

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