現今生活中由於複合材料的出現，由不同材料製成的許多物件在工程上的破壞行為變得越來越被關心。Ｈ積分已被證實是在線彈性力學的假設下，用來計算混合破壞模式應力強度因子的一個有效工具。為了能夠計算在三維模型下，經歷溫度變化以及機械負載情況下的應力強度因子，本文使用了一經過修正的Ｈ積分。這個修正過後的Ｈ積分較原先在二維問題中的Ｈ積分多了兩個面積分項：其一和某些應力和位移出平面方向的微分相關，另一則和溫度變化相關。其中後者由於其相關之輔助應變場會產生奇異問題，所以在文中有特殊處理。此外，有鑑於之前在計算應力強度因子時，僅考慮奇異性最大的應力奇異階次可能會有漏失某些破壞模式的情況發生，又為了能夠反應出裂縫或尖角尖端在彈性力學假設下的真實應力強度，所以本文在計算應力強度因子時會將三個應力奇異階次同時考慮，這主要也是為了配合一個在最近才被提出的新的應力強度因子的定義式，此定義式有著將應力強度因子單位統一化、方便比較的特性。最後提出幾個數值例子，如裂縫、尖角經歷溫度變化或經歷熱流通過等問題，來演示本文中提出的計算方法。

Due to the appearance of composite materials, the fracture behavior of objects made of a variety of materials is more and more concerned. It's been verified that H-integral is a very efficient tool for the calculation of stress intensity factor. To calculate the stress intensity factor of a three dimensional model, under the thermal and mechanical loading, a modified H-integral is proposed in this paper. The modified integral contains two extra domain integrals: one relates to the derivative of some stress and displacement components along the out-of-plane direction, and the other relates to the temperature field. Since the latter possesses the singular auxiliary strain field which may disturb the value of integration near the corner or crack tip, the domain integral should be modified with special treatment in the thesis. Furthermore, to consider the true intensity of stress near the corner or crack tip under the assumption of linear elasticity, and also the loss of fracture modes that might be neglected when only the most critical singular order of stress is considered, the first three critical singular orders of stress will be taken into consideration at the same time. This is mainly for introducing a new definition of stress intensity factor, which has the advantage of unifying the units of stress intensity factors, and makes stress intensity factors comparable. A few numerical examples are shown, e.g. crack/corner under a mixed loading, or applied with a heat flow, to carry out the validity of the approach proposed.

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