Analysis of Multiple Interfacial Cracks in Three Dimensional Bimaterials Using Hypersingular Integral-Differential Equation Method
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摘要: 利用有限部积分的概念,导出了三维无限接合体中多个界面裂纹,在任意载荷作用下的超奇异微积分方程组.数值分析中,未知的位移间断采用基本分布函数和多项式乘积的形式来近似,其中基本分布函数是根据界面裂纹应力的振荡奇异性来选取的.作为典型算例,研究了存在两个矩形界面裂纹时,裂纹之间距离、裂纹形状及双材料弹性常数对应力强度因子的影响.计算表明,应力强度因子随裂纹间的距离的增大而减小.Abstract: Using the finite-part integral concepts, a set of hypersingular integraldifferential equations for multiple interfacial cracks in a three-dimensional infinite bimaterial subjected to arbitrary loads was derived. In the numerical analysis, unknown displacement discontinuities were approximated by the products of the fundamental density functions and power series, where the fundamental functions were chosen to express a two-dimensional interface crack exactly. As illustrative examples, the stress intensity factors for two rectangular interface cracks were calculated for various spacing, crack shape and elastic constants. It is shown that the stress intensity factors decrease with the increasing of crack spacing.
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