本文利用有限元素法配合虛擬裂紋閉合法(virtual crack closure technique, VCCT)計算雙材料界面裂紋的三維破壞力學參數，包括應變能釋放率(strain energy release rate, SERR)，應力強度因子(stress intensity factor, SIF)和相位角(phase angle)。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，從界面裂紋尖端的漸近應力和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，應力強度因子之值亦會隨著使用之長度單位而有震盪的行為。這個震盪的特性，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，可藉由特定的材料特徵長度來無因次化震盪的應力強度因子，使其單位回復至(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和裂紋面受到內壓力的情况，本研究亦提出專用的公式來計算其破壞力學參數。針對於本文所提出的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比對驗證。而後，本文討論應用虛擬裂紋閉合法來分析雙材料平板之邊緣半圓形界面裂紋受到均勻溫度變化負載的問題。另外，電子覆晶封裝體中鑲埋於矽晶及底填膠界面之角落脫層受到熱負載的問題也在本文中探討。

The fracture mechanics parameters, including the strain energy release rate, the stress intensity factors and phase angles are determined for a three-dimensional interface crack by using numerical finite element approach with the virtual crack closure technique (VCCT). In the VCCT, crack closure integrals are obtained from the solutions of finite element nodal forces and displacements around the crack tip. These crack closure integrals are then summed to obtain the strain energy release rate. 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 given material length such that the units for the stress intensity factors are in (stress) (length)1/2. A set of algebraic equations to express the normalized stress intensity factors and the corresponding phase angles in terms of the crack closure integrals is derived based on the asymptotic elastic fields around the crack tip. In addition, variations of the equations for determining the fracture mechanics parameters are given for cases including contacting between interface crack faces and crack subjected to inner pressure. Validation of the proposed approach is performed by comparing the numerically determined stress intensity factors for interface cracks to analytical solutions. The VCCT is then applied to study the problem of a semi-circular surface crack on the interface of semi-infinite bi-material plate subjected to uniform temperature excursion. The problem of an electronic package containing an embedded interface corner crack under thermomechanical load is also presented as an application example.

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