Crack-Tip Fields of a Crack Impinging upon the Yielding/Debonding Slippage in Anisotropic Body

Abstract

This paper presents a fundamental solution for a crack impinging normally upon the slippage in anisotropic materials under tensile loading. The 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). A superposition method is employed to explicitly solve the problem which combines the solution of a crack in an elastic homogeneous medium, the solution of a continuous distribution of dislocations which represent slippage, 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. Numerical implementations are performed to analyze the influence of slippage on cracking and stress redistribution near the crack tip in anisotropic bodies. It is found that yielding or debonding slippage redistributes the stress ahead of the crack tip. The presence of yielding or debonding lowers the high stress concentration in the tensile stresses ahead of the crack tip. It is also concluded that debonding appears to be more effective in lowering the stress concentration than yielding.