Interface cracks with surface elasticity in anisotropic bimaterials

We consider the effect of surface elasticity on an interface crack between two dissimilar anisotropic elastic half-planes under generalized plane strain deformation. The surface mechanics is incorporated by using a modified anisotropic version of the continuum-based surface/interface model of Gurtin and Murdoch (1975). A system of first-order Cauchy singular integro-differential equations is derived by considering a distribution of line dislocations and line forces on the interface crack. The correctness of the obtained singular integro-differential equations is carefully verified by comparison with the existing results of Kim et al. (2010, 2011a,b,c), derived via the complex variable method. Our results show that generally the stresses exhibit only the weak logarithmic singularity at the tips of an interfacial crack when surface elasticity in anisotropic bimaterials is considered. Further, the crack-tip stresses in a homogeneous anisotropic solid exhibit both the stronger inverse square root and the weaker logarithmic singularities if the surface tension is ignored. The solution method for solving a system of singular integro-differential equations is also proposed.