Interface crack between a compressible elastomer and a rigid substrate with finite slippage

We study the deformation of a crack between a soft elastomer and a rigid substrate with finite interfacial slippage. It is assumed that slippage occurs when the interfacial shear traction exceeds a threshold. This leads to a slip zone ahead of the crack tip where the shear traction is assumed to be equal to the constant threshold. We perform asymptotic analysis and determine closed-form solutions describing the near-tip crack opening displacement and the corresponding stress distributions. These solutions are consistent with numerical results based on finite element analysis. Our results reveal that slippage can significantly affect the deformation and stress fields near the tip of the interface crack. Specifically, depending on the direction of slippage, the crack opening profile may appear more blunted or sharpened than the parabola arising from for the case of zero interfacial shear traction or free slippage. The detailed crack opening profile is determined by the constant shear traction in the slip zone. More importantly, we find that the normal stress perpendicular to the interface can increase or decrease when slippage occurs, depending on the direction of slippage and the shear traction in the slip zone.