Abstract This paper studies the stress intensity factors and their correlations with bimaterial parameters for the interface planar cracks by hypersingular integral equations. A new bimaterial parameter γ is defined, and the correlations of the stress intensity factors of interface planar crack with two parameters e and γ are proved. The relative displacement fundamental function is proposed based on the crack's peripheral equation, thus one kind of element with coupled oscillatory characteristic of mode-1 and mode-2 is established for the interface planar crack. For the interface elliptical cracks with b/a = 0.2, 0.4, 0.6, 0.8, 1.0, the stress intensity factors along the crack front are calculated by solving the hypersingular integral equations. Comparison with the existing exact solutions show that the numerical results have a high accuracy. For the interface planar cracks under tensile load, there exist K1, K2 and K3 at the same time. The numerical results show that K1 is very weakly related to e and γ, K2 strongly to e and weakly to γ, and K3 shows a significant correlation with both parameters e and γ. K3 is much smaller than K1 and K2 and can be ignored in fracture analysis of problems with remote mode-1 loading.

中文翻译：

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平面嵌入界面裂纹应力强度因子超奇异积分方程的数值解及其与双材料参数的相关性

摘要 本文通过超奇异积分方程研究了界面平面裂纹应力强度因子及其与双材料参数的相关性。定义了一个新的双材料参数γ，证明了界面平面裂纹应力强度因子与两个参数e和γ的相关性。基于裂纹的外围方程提出了相对位移基本函数，从而为界面平面裂纹建立了一种具有模态1和模态2耦合振荡特性的单元。对于b/a=0.2、0.4、0.6、0.8、1.0的界面椭圆裂纹，通过求解超奇异积分方程计算裂纹前沿的应力强度因子。与现有精确解的比较表明，数值结果具有较高的精度。对于拉伸载荷作用下的界面平面裂纹，同时存在K1、K2和K3。数值结果表明，K1 与e 和γ 的相关性非常弱，K2 与e 的相关性很强，与γ 的相关性很弱，而K3 与参数e 和γ 都显示出显着的相关性。K3 远小于 K1 和 K2，在远程模式 1 加载问题的断裂分析中可以忽略。