本文探討二維平面應變情況下，雙層異向性材料結合面上內含一閉合滑動型界面裂紋之問題。假設裂紋體在無限遠處承受壓力與剪力作用，使得裂紋面在垂面(即 )方向上保持閉合，而在水平方向(即 與 )上則允許自由滑動，以Stroh公式為基礎，應用差排基本解，將此問題模擬推演得滿足界面邊界條件之一組耦合未知差排密度函數之奇異積分方程式。由差排密度函數之解析情形，可推得彈性體之位移場與應力場。文中首先假設裂紋面之摩擦阻力係數為常數，並針對均質異向性材料、雙層單斜晶系材料、雙層正交異向性材料及雙層等向性材料等幾種特殊材料，進行了奇異積分方程式之解析探討。其次，考慮摩擦阻力係數非為常數的問題，此部份則以Gauss-Jacobi數值積分法分析之。文中以雙層正交異向性材料為例，且考慮裂紋面的摩擦阻力係數函數為二次拋物線分佈，數值計算結果顯示，材料常數Λ及裂紋面之摩擦阻力係數分佈函數 ，對於裂紋面上之剪應力 與正向應力 的分佈情形，有顯著的影響。

另外，本文也探討了閉合滑動型界面裂紋尖端之應力奇異性，應用特徵函數展開法，推得決定應力奇異性階數之特徵方程，此特徵方程中與材料常數有關的矩陣 與 ，決定了特徵方程的特徵根為實數或複數。應力奇異性的型態，隨材料組成的不同而有所變化，考慮彈性體為均質異向性材料時，因 ，因此，不論裂紋面的摩擦阻力存在與否，其應力奇異性為平方根；若材料具有 的性質，但其矩陣元素中 且裂紋面無摩擦阻力時，則裂紋尖端仍為平方根應力奇異性；若彈性體為雙層單斜晶系材料且兩材料晶體結構均對稱於 平面時，則反平面問題為平方根應力奇異性，而內平面問題的應力奇異性階數則為實數根，此實數根的大小，與材料常數 及裂紋面的摩擦阻力係數f有關；若為雙層正交異向性材料時，則其裂紋尖端應力奇異性與廣義的Dundurs 常數 有關；若退化為均質等向性材料時，則應力奇異性為平方根，且與裂紋面的摩擦阻力係數無關。

The problem of a frictionally sliding interface crack embedded in a bimaterial, subjected to combined shear and compression at infinity, is investigated. Under remote normal compression and shear load the crack face is treated as completely closed in the direction of the normal load while in other directions the crack faces are allowed to slide. The frictional resistance over the sliding zone is assumed to be uniform. A set of singular integral equations is formulated which is valid for general anisotropic bimaterials. The nature of singularities for frictionally sliding bimaterials is investigated. It is found that for general anisotropic bimaterials the problem may be treated as a homogeneous anisotropy as long as and hence the stress developed on the frictional surface would be uniform for such bimaterials. If is not identically zero but with and with the surface being frictionless then the stresses over the crack faces are square root singular. For monoclinic bimaterials, the orders of stress singularities are found to depend on the material constant and frictional coefficient f and are either of order or depending on the direction of the frictional force. The stresses on the interface for monoclinic bimaterials with the symmetry plane at are also given explicitly. For the sliding interface crack with non-uniform frictional coefficients embedded in an orthotropic bimaterial is also investigated. The stress fields distributed on the interface are solved numerically and demonstrated by graphs in the final section of this paper.

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