We consider the role of interfacial slippage in the deformation and stress fields near the tip of a plane interface crack occurring between a compressible hyperelastic material and a rigid substrate. Specifically, we draw comparisons between the two limiting cases of ‘no-slip’ (infinitely high friction) and ‘frictionless’ (zero friction) surfaces by performing corresponding asymptotic analyses in the crack-tip region. Our results indicate that for the no-slip case, when the body is subjected to far-field loading, the crack deforms to a wedge-like shape consistent with experimental observations reported in the literature. Moreover, in this case, the wedge angle is shown to be directly related to ratios of various Cauchy stress components on the bonded surface in the near-tip region. Finite-element simulations reveal that the wedge angle also depends on material compressibility and the far-field loading conditions. By contrast, the analysis of the frictionless case reveals that the crack consistently opens into a smooth parabolic shape with a right wedge angle and near-tip stress field dominated by the normal stress at the surface. The results established here can be used as a basis for the understanding of the role of varying degrees of slippage on interfacial cracks.
Surface mechanics of a stretched elastomer layer bonded on a rigid substrate
