Numerical solutions of hypersingular integral equations for stress intensity factors of planar embedded interface cracks and their correlations with bimaterial parameters

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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 ε 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 ε and γ, K2 strongly to ε and weakly to γ, and K3 shows a significant correlation with both parameters ε and γ. K3 is much smaller than K1 and K2 and can be ignored in fracture analysis of problems with remote mode-1 loading.