Edge dislocation in a thin film with Steigmann–Ogden-type surface effects
摘要
We revisit the plane strain deformation of an elastic thin film containing a line edge dislocation parallel to the surface of the film, in the case of appreciable surface energy existing on the surface of the film. The surface energy effects on the dislocation behavior are described by introducing a non-classical stress boundary condition of the Steigmann–Ogden type in which (residual) surface tension, surface stretching moduli and surface bending stiffness are all incorporated. We develop, in the context of the complex variable formalism of elasticity, a series-based solution for the corresponding boundary value problem, which is validated by comparisons with the existing solution in the literature for the reduced case of vanishing surface bending stiffness. Numerical examples are presented mainly to elucidate for a metallic thin film of few-nanometer thickness the role of surface bending stiffness in altering the image force imposed on the dislocation and the separate contribution of surface tension to the image force in the presence or absence of surface bending stiffness. It is shown that the presence of surface bending stiffness reinforces the surface of the film and reduces the attractive force from the surface to the dislocation with corresponding force reduction depending strongly on the direction of the Burgers vector of the dislocation relative to the surface. Moreover, it is demonstrated that in terms of an edge dislocation on the mid-plane of the film, large surface bending stiffness plays a dominant role in stabilizing its equilibrium if the Burgers vector is perpendicular or at a large angle to the surface of the film, while large surface tension acts as a crucial factor in destabilizing its equilibrium if the Burgers vector is parallel or at a small angle to the surface of the film.