A mode III interface crack with surface strain gradient elasticity

Abstract

We study the contribution of surface strain gradient elasticity to the anti-plane deformations of an elastically isotropic bimaterial containing a mode~III interface crack. The surface strain gradient elasticity is incorporated using an enriched version of the continuum-based surface/interface model of Gurtin and Murdoch. We obtain a complete semi-analytic solution valid everywhere in the solid (including at the crack tips) by reducing the boundary value problem to two coupled hyper-singular integro-differential equations which are solved numerically using Chebyshev polynomials and a collocation method. Our solution demonstrates that the presence of surface strain gradient elasticity on the crack faces leads to bounded stresses at the crack tips.