本論文主要目的是分析兩個功能梯度壓電條板接合之面外問題，每條板內各含單一任意方向裂縫，裂縫表面假設為不可滲透型(impermeable)與可滲透型(permeable)裂縫。壓電材料之極化方向為六方對稱型，材料梯度假設為指數型函數。利用傅立葉轉換法(Fourier transform)，分別依據幾何形狀與混合邊界條件化成兩組奇異積分方程式，再藉由Gauss-Chebyshev積分公式進行數值求解，並從數值解中探討邊界條件、裂縫長度、裂縫角度及非均質材料參數對於強度因子、能量密度因子和能量釋放率的影響。相關的退化問題也於文中有詳細的討論。
以不可滲透型為例，在外加電負載作用下能量釋放率會出現負值現象，此現象不符合物理意義，預期裂縫在該情形下將不會成長，因此能量釋放率不適合用來求解壓電材料方面的破壞問題，故本文選用能量密度因子量來求解功能梯度壓電材料的裂縫問題。由於壓電梯度材料的材料參數Scr和Gcr 仍屬未知，故現在尚無法去判斷裂縫開始成長之方向，未來需要實驗去做比較。
研究結果顯示，較大的能量密度因子與能量釋放率皆會發生在材料較弱的裂縫尖端上，而應力強度因子則會發生在材料較強的裂縫尖端上，其強度因子隨著裂縫角度變大而減少，因此裂縫角度對強度因子會有所影響，但其中以非均質材料參數影響甚鉅。

This dissertation studies the anti-plane crack problem of two bonded functionally graded piezoelectric material (FGPM) strips. Each strip contains an arbitrarily oriented crack. The crack surface condition is assumed to be electrically impermeable or permeable. The piezoelectric material has 6mm symmetry and the material properties of the strips are assumed in exponential forms varied in the direction normal to the interface. After employing the Fourier transforms, the unknowns are solved from the interface conditions, boundary conditions and the condition on the crack surfaces. The problem can then be reduced to a system of singular integral equations, which are solved numerically by applying the Gauss-Chebyshev integration formula to obtain the stress intensity factors at the crack tips. Numerical calculations are carried out to obtain the energy density factor and the energy release rate. The effects of edge boundary conditions, crack lengths, crack orientation, and the non-homogeneous material parameters on the intensity factors, energy density factors (S), and energy release rates (G) are discussed. In addition, some degenerated problems are also discussed.
In impermeable case, the energy release rate has been shown to be negative as the electric loads are applied. The using of energy release rate criterion for predicting the crack growth is inappropriate because of the energy release rates become negative. The energy density theory becomes a good choice in evaluation the safety of the cracked FGPM. The positive definite characteristic of the energy density factor makes it possible for predicting the fracture behavior of the cracked structure. The influences of the non-homogeneous parameters and crack orientation on the energy density factors at the crack tips are discussed in detail.
The results show that the energy density factor at the crack tip will be increased when the crack tip is located within the softer material. In general, the factors are larger when crack tips are located in stronger material. Also, the factors increase as the crack is oriented in the direction normal to the interface. The conclusions made in this research can be used to evaluate the safety of two bonded strips once the cracks exist inside the structure.

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