本論文主要目的在於探討含單一嵌入式裂縫功能梯度材料條版面內問題的破壞分析。依據彈性力學之基礎理論，利用傅立葉轉換法，將混合邊界值問題推導出一組奇異積分方程式，再藉由Chebyshev多項式技術化為代數聯立方程組以求數值解，由於其中核函數相當複雜並未如預期順利解出其數值解，而為了進一步利用應變能密度理論觀察其破壞行為，本論文將引用Long及Delale研究中所得應力強度因子之結果代入應變能密度因子公式，因此從應變能密度因子曲線圖中所能討論的破壞行為將受到Long及Delale之研究結果所侷限。我們可從S曲線中找到最小應變能密度因子Smin及裂縫開裂角度Θ0，再配合S理論討論其破壞行為，並探討裂縫長度及裂縫旋轉角度對破壞行為的影響。結果顯示無論裂縫旋轉角度為0°或45°，裂縫開裂的驅動力Smin都將隨裂縫長度增長而增加；當裂縫旋轉角度為0°時，必須藉由實驗得到臨界值Scr才能預測裂縫將從哪端開裂；而當裂縫旋轉角度為45°之情況下，由於在裂縫a端(材料較軟處)的Smin值較b端的Smin值高，因此可判斷裂縫將優先從a端開裂。

　　This thesis deals with the fracture behavior of a functionally graded material strip with an embedded crack under inplane loads. A system of Cauchy-type singular integral equations is formulated by employing the Fourier transforms. Although the numerical technique of using the Chebyshev polynomials is a powerful tool to solve the singular equations, we face some difficulty and fail to get numerical results. In order to apply the strain energy density theory on the fracture problems of nomhomogeneous material, all numerical results of strain energy density factor S are calculated directly from the stress intensity factors plotted in the study of Long and Delale. Therefore, the discussion on the fracture behavior of the problem becomes very limited.
　　From the variations of S with the local coordinate system Θ, the minimum strain energy density factor Smin and crack extension angle Θ0 can be obtained to discuss the effects of crack length and crack angle on the fracture behavior. Two cases of crack angle with θ=0° and 45° are adopted in the discussion. As it is expected, the crack driving force for longer crack length will be higher at both crack tips. Since the critical strain energy density factor Scr for nonhomogeneous materials has to be obtained by testing, there are no sufficient evidences to get the conclusion that the crack will extend at which crack tips for the case　θ=0°. However, for θ=45°, the Smin at the crack tip within softer material (i.e. crack tip a) is greater than that at crack tip b and the crack can be predicted to propagate at crack tip a.

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