Interfacial Crack Analysis in Three-Dimensional Transversely Isotropic Bi-Materials by Boundary Integral Equation Method
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摘要: 基于两相三维横观各向同性介质的基本解和Somigliana恒等式，对三维横观各向同性介质中的任意形状的平片界面裂纹，以裂纹面上的不连续位移为待求参量建立了超奇异积分-微分方程，界面平行于横观各向同性面．根据发散积分的有限部积分理论，应用积分方程方法研究得到裂纹前沿的位移和应力场的表达式、奇性指数以及应力强度因子的不连续位移表达式．在非震荡情形下，超奇异积分-微分方程退化为超奇异积分方程，与均匀介质的超奇异积分方程形式完全相同．Abstract: The integr al-differential equations for three-dimensional planar interfacial cracks of arbitrary shape in transversely isotropic bimaterials were derived by virtue of the Somigliana identity and the fundamental solutions,in which the displacement discontinuities across the crack faces are the unknowns to be determined.The interface is parallel to both the planes of isotropy.The singular behaviors of displacement and stress near the crack border were analyzed and the stress singularity indexes were obtained by integral equation method.The stress intensity factors were expressed in terms of the displaceme nt discontinuities.In the non-oscillatory case,the hyper-singular bo undary integral-differential equations werere duced to hyper-singular boundary integral equations similar to those of homogeneously isotropic materials.
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