Fundamental solutions of a crack impinging upon an interface slippage in laminated anisotropic bodies

Abstract

Intra-ply or inter-ply slippages are commonly seen at the crack tip impinging upon an interface in laminated anisotropic bodies. An interface slippage could occur in the form of yielding (e.g., a well-bonded ductile layer with plastic yielding) or debonding (e.g., a weak, sliding-free one) along the interface direction. This paper presents a fundamental solution for a crack in one individual brittle part impinging normally upon the interface slippage with the neighboring brittle part of laminated anisotropic materials under tensile loading. A superposition method is employed to explicitly solve the problem which combines the solution of a crack in a perfectly bonded elastic homogeneous medium, the solution of a continuous distribution of dislocations which represent slippage at the interface and an appendix solution which offsets the stress on the crack faces induced by the dislocations. This procedure reduces the problem to a singular integral equation which can be numerically solved by using Chebyshev polynomials. The validity of the present solutions is numerically verified where the traction-free condition on the crack faces and the equilibrium of shear stress along the interface slippage can be really satisfied. Numerical implementations are performed to analyze the influence of interface slippage on cracking and stress redistribution in laminated anisotropic bodies. It is found that interface yielding or interface debonding redistributes the stress ahead of the crack tip in the neighboring uncracked part. The presence of interface yielding or debonding lowers the high stress concentration in the tensile stresses ahead of the crack tip. It is also concluded that interface debonding appears to be more effective in lowering the stress concentration than interface plastic yielding.