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

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 gamma is defined, and the correlations of the stress intensity factors of interface planar crack with two parameters epsilon and gamma 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 hyper-singular 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 K-1, K-2 and K-3 at the same time. The numerical results show that K-1 is very weakly related to epsilon and gamma, K-2 strongly to epsilon and weakly to gamma, and K-3 shows a significant correlation with both parameters epsilon and gamma. K-3 is much smaller than K-1 and K-2 and can be ignored in fracture analysis of problems with remote mode-1 loading. (C) 2020 Elsevier Ltd. All rights reserved.